text stringlengths 11 320k | source stringlengths 26 161 |
|---|---|
Magnetic 3D bioprinting is a process that utilizes biocompatible magnetic nanoparticles to print cells into 3D structures or 3D cell cultures . In this process, cells are tagged with magnetic nanoparticles, thus making them magnetic. [ 1 ] [ 2 ] Once magnetic, these cells can be rapidly printed into specific 3D patterns using external magnetic forces that mimic tissue structure and function. [ 3 ]
Magnetic 3D bioprinting is an alternative to other 3D printing methods such as extrusion , photolithography , and stereolithography . Benefits of the technique include its rapid process (15 minutes – 1 hour), compared to the often days-long processes of others, [ 4 ] [ 5 ] the capacity for endogenous synthesis of extracellular matrix (ECM) without the need for an artificial protein substrate and fine spatial control, and the capacity for 3D cell culture models to be printed from simple spheroids and rings into more complex organotypic models such as the lung, aortic valve, and white fat. [ 6 ] [ 7 ] [ 8 ] [ 9 ]
The cells first need to be incubated in the presence of magnetic nanoparticles to make them susceptible to manipulation through magnetic fields. The system is a nanoparticle assembly consisting of gold, magnetic iron oxide, and poly-L-lysine which assists in adhesion to the cell membrane via electrostatic interactions. [ 10 ] In this system, cells are printed into 3D patterns (rings or dots) using fields generated by permanent magnets. The cells within the printed construct interact with surrounding cells and the ECM to migrate, proliferate, and ultimately shrink the structure, typically within 24 hours.
When used as a toxicity assay, this shrinkage varies with drug concentration and is a label-free metric of cell function that can be captured and measured with brightfield imaging . [ 11 ] The size of the pattern can be captured using an iPod-based system, which is programmed using an app (Experimental Assistant) to image whole plates of up to 96 structures at intervals as short as one second.
Cells can be assembled without using magnetic nanoparticles by employing diamagnetism . Some materials are more strongly attracted, or susceptible, to magnets than others. Materials with greater magnetic susceptibility will experience stronger attraction to a magnet and move towards it. The more weakly attracted material with lower susceptibility is displaced to lower magnetic field regions that lie away from the magnet. By designing magnetic fields through careful arrangement of magnets, it is possible to use the differences in the magnetic susceptibilities of two materials to concentrate only one within a volume.
An example of usage of this technique is when bio-ink was formulated by suspending human breast cancer cells in a cell culture medium that contained the paramagnetic salt, diethylenetriaminepentaacetic acid gadolinium (III) dihydrogen salt hydrate (Gd-DTPA). Like most cells, these breast cancer cells are much more weakly attracted by magnets than Gd-DTPA, which is an FDA-approved MRI contrast agent for use in humans. Therefore, when a magnetic field was applied, the salt hydrate moved towards the magnets, displacing the cells to a predetermined area of minimum magnetic field strength, which seeded the formation of a 3D cell cluster. [ 12 ]
Magnetic 3D bioprinting can be used to screen for cardiovascular toxicity , which accounts for 30% of cardiac drug withdrawals. [ 13 ] Vascular smooth muscle cells are magnetically printed into 3D rings to mimic blood vessels that can contract and dilate. This system could potentially replace experiments using ex vivo tissue, which are costly and yield little data per experiment. Furthermore, magnetic 3D bioprinting can use human cells to approximate a human in vivo response better than with an animal model. This has been demonstrated by the bioassay which combines the benefits of 3D bioprinting in building tissue-like structures for study with the speed of magnetic printing.
This chemistry -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Magnetic_3D_bioprinting |
The Magnetic Prandtl number ( Pr m ) is a dimensionless quantity occurring in magnetohydrodynamics which approximates the ratio of momentum diffusivity ( viscosity ) and magnetic diffusivity . [ 1 ] It is defined as:
where:
At the base of the Sun 's convection zone the Magnetic Prandtl number is approximately 10 −2 , [ 2 ] and in the interiors of planets and in liquid-metal laboratory dynamos is approximately 10 −5 . | https://en.wikipedia.org/wiki/Magnetic_Prandtl_number |
Magnetic Reference Laboratory (MRL) is an American company founded in 1972. They produce and sell calibration tapes [ 1 ] for analog audio magnetic tape reproducers in the open reel format. It was announced on 11 November 2023 that the company would cease business on 1 December 2023. [ 2 ]
On December 7, 2023 MRL announced via their website that the company will in fact remain open, with "new offices, and new leadership, with MRL engineer Jeff McKnight taking on the role of Interim CEO." [ 2 ]
In 1972 (Jay) John G. McKnight was laid off from Ampex , as was (Tony) Antonio Bardakos, who was making the calibration tapes for Ampex at the time. Along with Ed Seaman (also an ex-Ampex employee), McKnight and Bardakos decided to start their own calibration tape business, and thus Magnetic Reference Lab (MRL) was born in 1972. [ 3 ]
MRL makes a wide variety of calibration tapes (a tape that "contains test signals used to calibrate a tape reproducer so that it will conform to the accepted standards" [ 1 ] ) that are sold world-wide. Examples of available test signals include:
MRL's calibration tapes are used by anyone who wants to have their analog audio magnetic tape reproducer properly calibrated, including: | https://en.wikipedia.org/wiki/Magnetic_Reference_Laboratory |
In magnetohydrodynamics , the magnetic Reynolds number ( R m ) is a dimensionless quantity that estimates the relative effects of advection or induction of a magnetic field by the motion of a conducting medium to the magnetic diffusion . It is the magnetic analogue of the Reynolds number in fluid mechanics and is typically defined by:
where
The mechanism by which the motion of a conducting fluid generates a magnetic field is the subject of dynamo theory . When the magnetic Reynolds number is very large, however, diffusion and the dynamo are less of a concern, and in this case
focus instead often rests on the influence of the magnetic field on the flow.
In the theory of magnetohydrodynamics , the magnetic Reynolds number can be derived from the induction equation :
where
The first term on the right hand side accounts for effects from magnetic induction in the plasma and the second term accounts for effects from magnetic diffusion . The relative importance of these two terms can be found by taking their ratio, the magnetic Reynolds number R m {\displaystyle \mathrm {R} _{\mathrm {m} }} . If it is assumed that both terms share the scale length L {\displaystyle L} such that ∇ ∼ 1 / L {\displaystyle \nabla \sim 1/L} and the scale velocity U {\displaystyle U} such that u ∼ U {\displaystyle \mathbf {u} \sim U} , the induction term can be written as
and the diffusion term as
The ratio of the two terms is therefore
For R m ≪ 1 {\displaystyle \mathrm {R} _{\mathrm {m} }\ll 1} , advection is relatively unimportant, and so
the magnetic field will tend to relax towards a purely diffusive state, determined by the boundary conditions rather than the flow.
For R m ≫ 1 {\displaystyle \mathrm {R} _{\mathrm {m} }\gg 1} , diffusion is relatively unimportant on the length scale L . Flux lines of the magnetic field are then advected with the fluid flow, until such time as gradients are concentrated into regions of short enough length scale that diffusion can balance advection.
The Sun has a large R m {\displaystyle \mathrm {R} _{\mathrm {m} }} , of order 10 6 . [ citation needed ] Dissipative affects are generally small, and there is no difficulty in maintaining a magnetic field against diffusion.
For the Earth, R m {\displaystyle \mathrm {R} _{\mathrm {m} }} is estimated to be of order 10 3 . [ 1 ] Dissipation is more significant, but a magnetic field is supported by motion in the liquid iron outer core. There are other bodies in the Solar System that have working dynamos, e.g. Jupiter, Saturn, and Mercury, and others that do not, e.g. Mars, Venus and the Moon.
The human length scale is very small so that typically R m ≪ 1 {\displaystyle \mathrm {R} _{\mathrm {m} }\ll 1} . The generation of magnetic field by the motion of a conducting fluid has been achieved in only a handful of large experiments using mercury or liquid sodium. [ 2 ] [ 3 ] [ 4 ]
In situations where permanent magnetisation is not possible, e.g. above the Curie temperature , to maintain a magnetic field R m {\displaystyle \mathrm {R} _{\mathrm {m} }} must be large enough such that induction outweighs diffusion.
It is not the absolute magnitude of velocity that is important for induction, but rather the relative differences and shearing in the flow, which stretch and fold magnetic field lines. [ 5 ] A more appropriate form for the magnetic Reynolds number in this case is therefore
where S is a measure of strain.
One of the most well known results is due to Backus [ 6 ] which states that the minimum R m {\displaystyle \mathrm {R} _{\mathrm {m} }} for generation of a magnetic field by flow in a sphere is such that
where L = a {\displaystyle L=a} is the radius of the sphere and S = e m a x {\displaystyle S=e_{max}} is the maximum strain rate.
This bound has since been improved by approximately 25% by Proctor. [ 7 ]
Many studies of the generation of magnetic field by a flow consider the computationally-convenient periodic cube. In this case the minimum is found to be [ 8 ]
where S {\displaystyle S} is the root-mean-square strain over a scaled domain with sides of length 2 π {\displaystyle 2\pi } . If shearing over small length scales in the cube is ruled out, then R m = 1.73 {\displaystyle \mathrm {R} _{\mathrm {m} }=1.73} is the minimum, where U {\displaystyle U} is the root-mean-square value.
The magnetic Reynolds number has a similar form to both the Péclet number and the Reynolds number . All three can be regarded as giving the ratio of advective to diffusive effects for a particular physical field and have the form of the product of a velocity and a length divided by a diffusivity. While the magnetic Reynolds number is related to the magnetic field in an magnetohydrodynamic flow, the Reynolds number is related to the fluid velocity itself and the Péclet number is related to heat. The dimensionless groups arise in the non-dimensionalization of the respective governing equations: the induction equation, the Navier–Stokes equations , and the heat equation .
The dimensionless magnetic Reynolds number, R m {\displaystyle R_{m}} , is also used in cases where there is no physical fluid involved.
For R m < 1 {\displaystyle R_{m}<1} the skin effect is negligible and the eddy current braking torque follows the theoretical curve of an induction motor.
For R m > 30 {\displaystyle R_{m}>30} the skin effect dominates and the braking torque decreases much slower with increasing speed than predicted by the induction motor model. [ 9 ] | https://en.wikipedia.org/wiki/Magnetic_Reynolds_number |
In thermodynamics and thermal physics , the theoretical formulation of magnetic systems entails expressing the behavior of the systems using the Laws of Thermodynamics . Common magnetic systems examined through the lens of Thermodynamics are ferromagnets and paramagnets as well as the ferromagnet to paramagnet phase transition . It is also possible to derive thermodynamic quantities in a generalized form for an arbitrary magnetic system using the formulation of magnetic work. [ 1 ]
Simplified thermodynamic models of magnetic systems include the Ising model , the mean field approximation , and the ferromagnet to paramagnet phase transition expressed using the Landau Theory of Phase Transitions . [ 2 ]
In order to incorporate magnetic systems into the first law of thermodynamics , it is necessary to formulate the concept of magnetic work. The magnetic contribution to the quasi-static work done by an arbitrary magnetic system is [ 1 ]
where H {\displaystyle H} is the magnetic field and B {\displaystyle B} is the magnetic flux density . [ 3 ] So the first law of thermodynamics in a reversible process can be expressed as
Accordingly the change during a quasi-static process in the Helmholtz free energy , F {\displaystyle F} , and the Gibbs free energy , G {\displaystyle G} , will be
In a paramagnetic system, that is, a system in which the magnetization vanishes without the influence of an external magnetic field , assuming some simplifying assumptions (such as the sample system being ellipsoidal ), one can derive a few compact thermodynamic relations. [ 4 ] Assuming the external magnetic field is uniform and shares a common axis with the paramagnet, the extensive parameter characterizing the magnetic state is I {\displaystyle I} , the magnetic dipole moment of the system. The fundamental thermodynamic relation describing the system will then be of the form U = U ( S , V , I , N ) {\displaystyle U=U(S,V,I,N)} . In the more general case where the paramagnet does not share an axis with the magnetic field, the extensive parameters characterizing the magnetic state will be I x , I y , I z {\displaystyle I_{x},I_{y},I_{z}} . In this case, the fundamental relation describing the system will be U = U ( S , V , I x , I y , I z , N ) {\displaystyle U=U(S,V,I_{x},I_{y},I_{z},N)} .
The intensive parameter corresponding to the magnetic moment I {\displaystyle I} is the external magnetic field acting on the paramagnet, B e {\displaystyle B_{e}} . The relation between them is:
where S {\displaystyle S} is the Entropy , V {\displaystyle V} is the Volume and N {\displaystyle N} is the number of particles in the system. Note that in this case, U {\displaystyle U} is the energy added to the system by the insertion of the paramagnet. The total energy in the space occupied by the system includes a component arising from the energy of a magnetic field in a vacuum. This component equals U v a c u u m = B e 2 V 2 μ 0 {\displaystyle U_{vacuum}={\frac {B_{e}^{2}V}{2\mu _{0}}}} , where μ 0 {\displaystyle \mu _{0}} is the permeability of free space , and isn't included as a part of U {\displaystyle U} . The choice if to include U v a c u u m {\displaystyle U_{vacuum}} in U {\displaystyle U} is arbitrary but it is important to note the convention chosen, otherwise, it may lead to confusion emanating from differing results.
The Euler relation for a paramagnetic system is then: U = T S − P V + B e I + μ N {\displaystyle U=TS-PV+B_{e}I+\mu N}
and the Gibbs-Duhem relation for such a system is: S d T − V d P + I d B e + N d μ = 0 {\displaystyle SdT-VdP+IdB_{e}+Nd\mu =0}
An experimental problem that distinguishes magnetic systems from other thermodynamical systems is that the magnetic moment can't be constrained. Typically in thermodynamic systems, all extensive quantities describing the system can be constrained to a specified value. Examples are volume and the number of particles, which can both be constrained by enclosing the system in a box. [ 5 ] On the other hand, there is no experimental method that can directly hold the magnetic moment to a specified constant value. Nevertheless, this experimental concern does not affect the thermodynamic theory of magnetic systems.
Ferromagnetic systems are systems in which the magnetization doesn't vanish in the absence of an external magnetic field. Multiple thermodynamic models have been developed in order to model and explain the behavior of ferromagnets, including the Ising model. The Ising model can be solved analytically in one and two dimensions, numerically in higher dimensions, or using the mean-field approximation in any dimensionality. Additionally, the ferromagnet to paramagnet phase transition is a second-order phase transition and so can be modeled using the Landau theory of phase transitions. [ 1 ] [ 6 ] | https://en.wikipedia.org/wiki/Magnetic_Thermodynamic_Systems |
A magnetic alloy is a combination of various metals from the periodic table such as ferrite that exhibits magnetic properties such as ferromagnetism . Typically the alloy contains one of the three main magnetic elements (which appear on the Bethe-Slater curve ): iron (Fe) , nickel (Ni) , or cobalt (Co) . However, alloys such as Heusler alloys exhibit ferromagnetic properties without any of the preceding 3 elements, and alloys of iron and manganese such as stainless steels may be essentially nonmagnetic at room temperature. [ 1 ] Magnetic properties of an alloy are highly dependent not only on the composition but also on heat treatment and mechanical processing.
Magnetic alloys have become common, especially in the form of steel (iron and carbon), alnico (iron, nickel, cobalt, and aluminum ), and permalloy (iron and nickel). So-called " neodymium magnets " are alloys of neodymium, iron and boron forming the crystal structure Nd 2 Fe 14 B. After magnetization , items made out of these alloys will remain magnetized depending on their remanence and coercivity . [ 2 ] [ 3 ]
Samarium–cobalt magnets are made from an alloy of samarium and cobalt , known for their high magnetic strength, excellent temperature stability and resistance to demagnetization. [ 4 ] They are often used in applications requiring powerful and stable magnets, such as in motors , aerospace , military equipment, and high-temperature environments. [ 5 ]
This alloy-related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Magnetic_alloy |
In condensed matter physics , magnetic anisotropy describes how an object's magnetic properties can be different depending on direction . In the simplest case, there is no preferential direction for an object's magnetic moment . It will respond to an applied magnetic field in the same way, regardless of which direction the field is applied. This is known as magnetic isotropy . In contrast, magnetically anisotropic materials will be easier or harder to magnetize depending on which way the object is rotated.
For most magnetically anisotropic materials, there are two easiest directions to magnetize the material, which are a 180° rotation apart. The line parallel to these directions is called the easy axis . In other words, the easy axis is an energetically favorable direction of spontaneous magnetization . Because the two opposite directions along an easy axis are usually equivalently easy to magnetize along, the actual direction of magnetization can just as easily settle into either direction, which is an example of spontaneous symmetry breaking .
Magnetic anisotropy is a prerequisite for hysteresis in ferromagnets : without it, a ferromagnet is superparamagnetic . [ 1 ]
The observed magnetic anisotropy in an object can happen for several different reasons. Rather than having a single cause, the overall magnetic anisotropy of a given object is often explained by a combination of these different factors: [ 2 ]
The magnetic anisotropy of a benzene ring (A), alkene (B), carbonyl (C), alkyne (D), and a more complex molecule (E) are shown in the figure. Each of these unsaturated functional groups (A-D) create a tiny magnetic field and hence some local anisotropic regions (shown as cones) in which the shielding effects and the chemical shifts are unusual. The bisazo compound (E) shows that the designated proton {H} can appear at different chemical shifts depending on the photoisomerization state of the azo groups. [ 4 ] The trans isomer holds proton {H} far from the cone of the benzene ring thus the magnetic anisotropy is not present. While the cis form holds proton {H} in the vicinity of the cone, shields it and decreases its chemical shift. [ 4 ] This phenomenon enables a new set of nuclear Overhauser effect (NOE) interactions (shown in red) that come to existence in addition to the previously existing ones (shown in blue).
Suppose that a ferromagnet is single-domain in the strictest sense: the magnetization is uniform and rotates in unison. If the magnetic moment is μ {\displaystyle {\boldsymbol {\mu }}} and the volume of the particle is V {\displaystyle V} , the magnetization is M = μ / V = M s ( α , β , γ ) {\displaystyle \mathbf {M} ={\boldsymbol {\mu }}/V=M_{s}\left(\alpha ,\beta ,\gamma \right)} , where M s {\displaystyle M_{s}} is the saturation magnetization and α , β , γ {\displaystyle \alpha ,\beta ,\gamma } are direction cosines (components of a unit vector ) so α 2 + β 2 + γ 2 = 1 {\displaystyle \alpha ^{2}+\beta ^{2}+\gamma ^{2}=1} . The energy associated with magnetic anisotropy can depend on the direction cosines in various ways, the most common of which are discussed below.
A magnetic particle with uniaxial anisotropy has one easy axis. If the easy axis is in the z {\displaystyle z} direction, the anisotropy energy can be expressed as one of the forms:
where V {\displaystyle V} is the volume, K {\displaystyle K} the anisotropy constant, and θ {\displaystyle \theta } the angle between the easy axis and the particle's magnetization. When shape anisotropy is explicitly considered, the symbol N {\displaystyle {\mathcal {N}}} is often used to indicate the anisotropy constant, instead of K {\displaystyle K} . In the widely used Stoner–Wohlfarth model , the anisotropy is uniaxial.
A magnetic particle with triaxial anisotropy still has a single easy axis, but it also has a hard axis (direction of maximum energy) and an intermediate axis (direction associated with a saddle point in the energy). The coordinates can be chosen so the energy has the form
If K a > K b > 0 , {\displaystyle K_{a}>K_{b}>0,} the easy axis is the z {\displaystyle z} direction, the intermediate axis is the y {\displaystyle y} direction and the hard axis is the x {\displaystyle x} direction. [ 5 ]
A magnetic particle with cubic anisotropy has three or four easy axes, depending on the anisotropy parameters. The energy has the form
If K > 0 , {\displaystyle K>0,} the easy axes are the x , y , {\displaystyle x,y,} and z {\displaystyle z} axes. If K < 0 , {\displaystyle K<0,} there are four easy axes characterized by x = ± y = ± z {\displaystyle x=\pm y=\pm z} . | https://en.wikipedia.org/wiki/Magnetic_anisotropy |
Magnetic braking is a theory explaining the loss of stellar angular momentum due to material getting captured by the stellar magnetic field and thrown out at great distance from the surface of the star. It plays an important role in the evolution of binary star systems.
The currently accepted theory of the a planetary system 's evolution states that the system originates from a contracting gas cloud. As the cloud contracts, the angular momentum L {\displaystyle L} must be conserved . Any small net rotation of the cloud will cause the spin to increase as the cloud collapses, forcing the material into a rotating disk. At the dense center of this disk a protostar forms, which gains heat from the gravitational energy of the collapse. As the collapse continues, the rotation rate can increase to the point where the accreting protostar can break up due to centrifugal force at the equator.
Thus the rotation rate must be braked during the first 100,000 years of the star's life to avoid this scenario. One possible explanation for the braking is the interaction of the protostar's magnetic field with the stellar wind. In the case of the Solar System , when the planets' angular momenta are compared to the Sun's own, the Sun has less than 1% of its supposed angular momentum. In other words, the Sun has slowed down its spin while the planets have not.
Ionized material captured by the magnetic field lines will rotate with the Sun as if it were a solid body. As material escapes from the Sun due to the solar wind , the highly ionized material will be captured by the field lines and rotate with the same angular velocity as the Sun, even though it is carried far away from the Sun's surface, until it eventually escapes. This effect of carrying mass far from the centre of the Sun and throwing it away slows down the spin of the Sun. [ 1 ] [ 2 ] The same effect is used in slowing the spin of a rotating satellite ; here two wires spool out weights to a distance slowing the satellites spin, then the wires are cut, letting the weights escape into space and permanently robbing the spacecraft of its angular momentum .
As ionized material follows the Sun's magnetic field lines, [ 3 ] due to the effect of the field lines being frozen in the plasma , the charged particles feel a force F {\displaystyle \mathbf {F} } of the magnitude:
where q {\displaystyle q} is the charge, v {\displaystyle \mathbf {v} } is the velocity and B {\displaystyle \mathbf {B} } is the magnetic field vector. This bending action forces the particles to " corkscrew " around the magnetic field lines while held in place by a "magnetic pressure" P B {\displaystyle P_{B}} , or "energy density", while rotating together with the Sun as a solid body:
Since magnetic field strength decreases with the cube of the distance there will be a place where the kinetic gas pressure P g {\displaystyle P_{g}} of the ionized gas is great enough to break away from the field lines:
where n is the number of particles, m is the mass of the individual particle and v is the radial velocity away from the Sun, or the speed of the solar wind.
Due to the high conductivity of the stellar wind, the magnetic field outside the sun declines with radius like the mass density of the wind, i.e. decline as an inverse square law. [ 4 ] The magnetic field is therefore given by
where B s {\displaystyle B_{s}} is the magnetic field on the surface of the Sun and R {\displaystyle R} is its radius. The critical distance where the material will break away from the field lines can then be calculated as the distance where the kinetic pressure and the magnetic pressure are equal, i.e.
If the solar mass loss is omni-directional then the mass loss n m = d M / d t 4 π r 2 v {\displaystyle nm={\frac {dM/dt}{4\pi r^{2}v}}} ; plugging this into the above equation and isolating the critical radius it follows that
Currently it is estimated that:
This leads to a critical radius r c = 15 R ⊙ {\displaystyle r_{c}=15R_{\odot }} . This means that the ionized plasma will rotate together with the Sun as a solid body until it reaches a distance of nearly 15 times the radius of the Sun; from there the material will break off and stop affecting the Sun.
The amount of solar mass needed to be thrown out along the field lines to make the Sun completely stop rotating can then be calculated using the specific angular momentum:
It has been suggested that the Sun lost a comparable amount of material over the course of its lifetime. [ 6 ]
In 2016 scientists at Carnegie Observatories published a research suggesting that stars at a similar stage of life as the Sun were spinning faster than magnetic braking theories predicted. [ 7 ] To calculate this they pinpointed the dark spots on the surface of stars and tracked them as they moved with the stars' spin. While this method has been successful for measuring the spin of younger stars, the "weakened" magnetic braking in older stars proved harder to confirm, as the latter notoriously have fewer star spots. In a study published in Nature Astronomy in 2021, researchers at the University of Birmingham used a different approach, namely asteroseismology , to confirm that older stars do appear to rotate faster than expected. [ 8 ] | https://en.wikipedia.org/wiki/Magnetic_braking_(astronomy) |
A magnetic chip detector is an electronic instrument that attracts ferromagnetic particles (mostly iron chips). It is mainly used in aircraft engine oil and helicopter gearbox chip detection systems. Chip detectors can provide an early warning of an impending engine failure and thus greatly reduce the cost of an engine overhaul .
Chip Detectors consist of small plugs which can be installed in an engine oil filter , oil sump or aircraft drivetrain gear boxes. Over a period of time, engine wear and tear causes small metal chips to break loose from engine parts and circulate in the engine oil.
The detector houses magnets incorporated into an electric circuit. Magnetic lines of force attract ferrous particles. Collection of these particles continues until the insulated air gap between the magnets (two magnet configuration) or between the magnet and housing (one magnet configuration) is bridged, effectively closing the circuit. The result is an electronic signal for remote indication. Thus, a warning light on the instrument panel illuminates, indicating the presence of metal chips. [ 1 ]
Chip detectors may be positioned in the application with a self-closing valve/adapter through either a bayonet or threaded interface. As the chip detector is disengaged from the valve, the valve closes minimizing any fluid loss from the system.
The chip detectors used on aircraft are inspected in every ' A check ' and higher. They may also be specified intervals such as every 30–40 hours for an engine unit and 100 hours for an APU unit. | https://en.wikipedia.org/wiki/Magnetic_chip_detector |
A magnetic circuit is made up of one or more closed loop paths containing a magnetic flux . The flux is usually generated by permanent magnets or electromagnets and confined to the path by magnetic cores consisting of ferromagnetic materials like iron, although there may be air gaps or other materials in the path. Magnetic circuits are employed to efficiently channel magnetic fields in many devices such as electric motors , generators , transformers , relays , lifting electromagnets , SQUIDs , galvanometers , and magnetic recording heads .
The relation between magnetic flux , magnetomotive force , and magnetic reluctance in an unsaturated magnetic circuit can be described by Hopkinson's law , which bears a superficial resemblance to Ohm's law in electrical circuits, resulting in a one-to-one correspondence between properties of a magnetic circuit and an analogous electric circuit. Using this concept the magnetic fields of complex devices such as transformers can be quickly solved using the methods and techniques developed for electrical circuits.
Some examples of magnetic circuits are:
Similar to the way that electromotive force ( EMF ) drives a current of electrical charge in electrical circuits, magnetomotive force (MMF) 'drives' magnetic flux through magnetic circuits. The term 'magnetomotive force', though, is a misnomer since it is not a force nor is anything moving. It is perhaps better to call it simply MMF. In analogy to the definition of EMF , the magnetomotive force F {\displaystyle {\mathcal {F}}} around a closed loop is defined as:
The MMF represents the potential that a hypothetical magnetic charge would gain by completing the loop. The magnetic flux that is driven is not a current of magnetic charge ; it merely has the same relationship to MMF that electric current has to EMF. (See microscopic origins of reluctance below for a further description.)
The unit of magnetomotive force is the ampere-turn (At), represented by a steady, direct electric current of one ampere flowing in a single-turn loop of electrically conducting material in a vacuum . The gilbert (Gb), established by the IEC in 1930, [ 1 ] is the CGS unit of magnetomotive force and is a slightly smaller unit than the ampere-turn. The unit is named after William Gilbert (1544–1603) English physician and natural philosopher.
The magnetomotive force can often be quickly calculated using Ampère's law . For example, the magnetomotive force F {\displaystyle {\mathcal {F}}} of a long coil is:
where N is the number of turns and I is the current in the coil. In practice this equation is used for the MMF of real inductors with N being the winding number of the inducting coil.
An applied MMF 'drives' magnetic flux through the magnetic components of the system. The magnetic flux through a magnetic component is proportional to the number of magnetic field lines that pass through the cross sectional area of that component. This is the net number, i.e. the number passing through in one direction, minus the number passing through in the other direction. The direction of the magnetic field vector B is by definition from the south to the north pole of a magnet inside the magnet; outside the field lines go from north to south.
The flux through an element of area perpendicular to the direction of magnetic field is given by the product of the magnetic field and the area element. More generally, magnetic flux Φ is defined by a scalar product of the magnetic field and the area element vector. Quantitatively, the magnetic flux through a surface S is defined as the integral of the magnetic field over the area of the surface
For a magnetic component the area S used to calculate the magnetic flux Φ is usually chosen to be the cross-sectional area of the component.
The SI unit of magnetic flux is the weber (in derived units: volt-seconds), and the unit of magnetic flux density (or "magnetic induction", B ) is the weber per square meter, or tesla .
The most common way of representing a magnetic circuit is the resistance–reluctance model, which draws an analogy between electrical and magnetic circuits. This model is good for systems that contain only magnetic components, but for modelling a system that contains both electrical and magnetic parts it has serious drawbacks. It does not properly model power and energy flow between the electrical and magnetic domains. This is because electrical resistance will dissipate energy whereas magnetic reluctance stores it and returns it later. An alternative model that correctly models energy flow is the gyrator–capacitor model .
The resistance–reluctance model for magnetic circuits is a lumped-element model that makes electrical resistance analogous to magnetic reluctance .
In electrical circuits, Ohm's law is an empirical relation between the EMF E {\displaystyle {\mathcal {E}}} applied across an element and the current I {\displaystyle I} it generates through that element. It is written as: E = I R . {\displaystyle {\mathcal {E}}=IR.} where R is the electrical resistance of that material. There is a counterpart to Ohm's law used in magnetic circuits. This law is often called Hopkinson's law , after John Hopkinson , but was actually formulated earlier by Henry Augustus Rowland in 1873. [ 3 ] It states that [ 4 ] [ 5 ] F = Φ R . {\displaystyle {\mathcal {F}}=\Phi {\mathcal {R}}.} where F {\displaystyle {\mathcal {F}}} is the magnetomotive force (MMF) across a magnetic element, Φ {\displaystyle \Phi } is the magnetic flux through the magnetic element, and R {\displaystyle {\mathcal {R}}} is the magnetic reluctance of that element. (It will be shown later that this relationship is due to the empirical relationship between the H -field and the magnetic field B , B = μ H , where μ is the permeability of the material). Like Ohm's law, Hopkinson's law can be interpreted either as an empirical equation that works for some materials, or it may serve as a definition of reluctance.
Hopkinson's law is not a correct analogy with Ohm's law in terms of modelling power and energy flow. In particular, there is no power dissipation associated with a magnetic reluctance in the same way as there is a dissipation in an electrical resistance. The magnetic resistance that is a true analogy of electrical resistance in this respect is defined as the ratio of magnetomotive force and the rate of change of magnetic flux. Here rate of change of magnetic flux is standing in for electric current and the Ohm's law analogy becomes, F = d Φ d t R m , {\displaystyle {\mathcal {F}}={\frac {d\Phi }{dt}}R_{\mathrm {m} },} where R m {\displaystyle R_{\mathrm {m} }} is the magnetic resistance. This relationship is part of an electrical-magnetic analogy called the gyrator-capacitor model and is intended to overcome the drawbacks of the reluctance model. The gyrator-capacitor model is, in turn, part of a wider group of compatible analogies used to model systems across multiple energy domains.
Magnetic reluctance , or magnetic resistance , is analogous to resistance in an electrical circuit (although it does not dissipate magnetic energy). In likeness to the way an electric field causes an electric current to follow the path of least resistance , a magnetic field causes magnetic flux to follow the path of least magnetic reluctance. It is a scalar , extensive quantity , akin to electrical resistance.
The total reluctance is equal to the ratio of the MMF in a passive magnetic circuit and the magnetic flux in this circuit. In an AC field, the reluctance is the ratio of the amplitude values for a sinusoidal MMF and magnetic flux. (see phasors )
The definition can be expressed as: R = F Φ , {\displaystyle {\mathcal {R}}={\frac {\mathcal {F}}{\Phi }},} where R {\displaystyle {\mathcal {R}}} is the reluctance in ampere-turns per weber (a unit that is equivalent to turns per henry ).
Magnetic flux always forms a closed loop, as described by Maxwell's equations , but the path of the loop depends on the reluctance of the surrounding materials. It is concentrated around the path of least reluctance. Air and vacuum have high reluctance, while easily magnetized materials such as soft iron have low reluctance. The concentration of flux in low-reluctance materials forms strong temporary poles and causes mechanical forces that tend to move the materials towards regions of higher flux so it is always an attractive force(pull).
The inverse of reluctance is called permeance . P = 1 R . {\displaystyle {\mathcal {P}}={\frac {1}{\mathcal {R}}}.}
Its SI derived unit is the henry (the same as the unit of inductance , although the two concepts are distinct).
The reluctance of a magnetically uniform magnetic circuit element can be calculated as: R = l μ A . {\displaystyle {\mathcal {R}}={\frac {l}{\mu A}}.} where
This is similar to the equation for electrical resistance in materials, with permeability being analogous to conductivity; the reciprocal of the permeability is known as magnetic reluctivity and is analogous to resistivity. Longer, thinner geometries with low permeabilities lead to higher reluctance. Low reluctance, like low resistance in electric circuits, is generally preferred. [ citation needed ]
The following table summarizes the mathematical analogy between electrical circuit theory and magnetic circuit theory. This is mathematical analogy and not a physical one. Objects in the same row have the same mathematical role; the physics of the two theories are very different. For example, current is the flow of electrical charge, while magnetic flux is not the flow of any quantity.
The resistance–reluctance model has limitations. Electric and magnetic circuits are only superficially similar because of the similarity between Hopkinson's law and Ohm's law. Magnetic circuits have significant differences that need to be taken into account in their construction:
Magnetic circuits obey other laws that are similar to electrical circuit laws. For example, the total reluctance R T {\displaystyle {\mathcal {R}}_{\mathrm {T} }} of reluctances R 1 , R 2 , … {\displaystyle {\mathcal {R}}_{1},\ {\mathcal {R}}_{2},\ \ldots } in series is: R T = R 1 + R 2 + ⋯ {\displaystyle {\mathcal {R}}_{\mathrm {T} }={\mathcal {R}}_{1}+{\mathcal {R}}_{2}+\dotsm }
This also follows from Ampère's law and is analogous to Kirchhoff's voltage law for adding resistances in series. Also, the sum of magnetic fluxes Φ 1 , Φ 2 , … {\displaystyle \Phi _{1},\ \Phi _{2},\ \ldots } into any node is always zero: Φ 1 + Φ 2 + ⋯ = 0. {\displaystyle \Phi _{1}+\Phi _{2}+\dotsm =0.}
This follows from Gauss's law and is analogous to Kirchhoff's current law for analyzing electrical circuits.
Together, the three laws above form a complete system for analysing magnetic circuits, in a manner similar to electric circuits. Comparing the two types of circuits shows that:
Magnetic circuits can be solved for the flux in each branch by application of the magnetic equivalent of Kirchhoff's voltage law ( KVL ) for pure source/resistance circuits. Specifically, whereas KVL states that the voltage excitation applied to a loop is equal to the sum of the voltage drops (resistance times current) around the loop, the magnetic analogue states that the magnetomotive force (achieved from ampere-turn excitation) is equal to the sum of MMF drops (product of flux and reluctance) across the rest of the loop. (If there are multiple loops, the current in each branch can be solved through a matrix equation—much as a matrix solution for mesh circuit branch currents is obtained in loop analysis—after which the individual branch currents are obtained by adding and/or subtracting the constituent loop currents as indicated by the adopted sign convention and loop orientations.) Per Ampère's law , the excitation is the product of the current and the number of complete loops made and is measured in ampere-turns. Stated more generally: F = N I = ∮ H ⋅ d l . {\displaystyle F=NI=\oint \mathbf {H} \cdot \mathrm {d} \mathbf {l} .}
By Stokes's theorem, the closed line integral of H ·d l around a contour is equal to the open surface integral of curl H ·d A across the surface bounded by the closed contour. Since, from Maxwell's equations , curl H = J , the closed line integral of H ·d l evaluates to the total current passing through the surface. This is equal to the excitation, NI , which also measures current passing through the surface, thereby verifying that the net current flow through a surface is zero ampere-turns in a closed system that conserves energy.
More complex magnetic systems, where the flux is not confined to a simple loop, must be analysed from first principles by using Maxwell's equations .
Reluctance can also be applied to variable reluctance (magnetic) pickups . | https://en.wikipedia.org/wiki/Magnetic_circuit |
Magnetic circular dichroism ( MCD ) is the differential absorption of left and right circularly polarized (LCP and RCP) light, induced in a sample by a strong magnetic field oriented parallel to the direction of light propagation. MCD measurements can detect transitions which are too weak to be seen in conventional optical absorption spectra, and it can be used to distinguish between overlapping transitions. Paramagnetic systems are common analytes, as their near-degenerate magnetic sublevels provide strong MCD intensity that varies with both field strength and sample temperature. The MCD signal also provides insight into the symmetry of the electronic levels of the studied systems, such as metal ion sites. [ 1 ]
It was first shown by Faraday that optical activity (the Faraday effect ) could be induced in matter by a longitudinal magnetic field (a field in the direction of light propagation). [ 2 ] The development of MCD really began in the 1930s when a quantum mechanical theory of MOR (magnetic optical rotatory dispersion) in regions outside absorption bands was formulated. The expansion of the theory to include MCD and MOR effects in the region of absorptions, which were referred to as "anomalous dispersions" was developed soon thereafter. There was, however, little effort made to refine MCD as a modern spectroscopic technique until the early 1960s. Since that time there have been numerous studies of MCD spectra for a very large variety of samples, including stable molecules in solutions, in isotropic solids , and in the gas phase, as well as unstable molecules entrapped in noble gas matrices . More recently, MCD has found useful application in the study of biologically important systems including metalloenzymes and proteins containing metal centers. [ 3 ] [ 4 ]
In natural optical activity , the difference between the LCP light and the RCP light is caused by the asymmetry of the molecules (i.e. chiral molecules). Because of the handedness of the molecule, the absorption of the LCP light would be different from the RCP light. However, in MCD in the presence of a magnetic field, LCP and RCP no longer interact equivalently with the absorbing medium. Thus, there is not the same direct relation between magnetic optical activity and molecular stereochemistry which would be expected, because it is found in natural optical activity. So, natural CD is much more rare than MCD which does not strictly require the target molecule to be chiral. [ 5 ]
Although there is much overlap in the requirements and use of instruments, ordinary CD instruments are usually optimized for operation in the ultraviolet , approximately 170–300 nm , while MCD instruments are typically required to operate in the visible to near infrared , approximately 300–2000 nm. The physical processes that lead to MCD are substantively different from those of CD . However, like CD, it is dependent on the differential absorption of left and right hand circularly polarized light. MCD will only exist at a given wavelength if the studied sample has an optical absorption at that wavelength. [ 1 ] This is distinctly different from the related phenomenon of optical rotatory dispersion (ORD), which can be observed at wavelengths far from any absorption band.
The MCD signal ΔA is derived via the absorption of the LCP and RCP light as
This signal is often presented as a function of wavelength λ, temperature T or magnetic field H. [ 1 ] MCD spectrometers can simultaneously measure absorbance and ΔA along the same light path. [ 6 ] This eliminates error introduced through multiple measurements or different instruments that previously occurred before this advent.
The MCD spectrometer example shown below begins with a light source that emits a monochromatic wave of light . This wave is passed through a Rochon prism linear polarizer , which separates the incident wave into two beams that are linearly polarized by 90 degrees. The two beams follow different paths- one beam (the extraordinary beam) traveling directly to a photomultiplier (PMT), and the other beam (the ordinary beam) passing through a photoelastic modulator (PEM) oriented at 45 degrees to the direction of the ordinary ray polarization. The PMT for the extraordinary beam detects the light intensity of the input beam. The PEM is adjusted to cause an alternating plus and minus 1/4 wavelength shift of one of the two orthogonal components of the ordinary beam. This modulation converts the linearly polarized light into circularly polarized light at the peaks of the modulation cycle. Linearly polarized light can be decomposed into two circular components with intensity represented as I 0 = 1 2 ( I − + I + ) {\displaystyle I_{0}={\frac {1}{2}}(I_{-}+I_{+})}
The PEM will delay one component of linearly polarized light with a time dependence that advances the other component by 1/4 λ (hence, quarter-wave shift). The departing circularly polarized light oscillates between RCP and LCP in a sinusoidal time-dependence as depicted below:
The light finally travels through a magnet containing the sample, and the transmittance is recorded by another PMT. The schematic is given below:
The intensity of light from the ordinary wave that reaches the PMT is governed by the equation:
I Δ = I 0 2 [ ( 1 − sin ( δ 0 sin ω t ) ) 10 − A − + ( 1 + sin ( δ 0 sin ω t ) ) 10 − A + ] {\displaystyle I_{\Delta }={\frac {I_{0}}{2}}\left[\left(1-\sin \left(\delta _{0}\sin \omega t\right)\right)10^{-A_{-}}+\left(1+\sin \left(\delta _{0}\sin \omega t\right)\right)10^{-A_{+}}\right]}
Here A – and A + are the absorbances of LCP or RCP, respectively; ω is the modulator frequency – usually a high acoustic frequency such as 50 kHz; t is time; and δ 0 is the time-dependent wavelength shift.
This intensity of light passing through the sample is converted into a two-component voltage via a current/voltage amplifier. A DC voltage will emerge corresponding to the intensity of light passed through the sample. If there is a ΔA, then a small AC voltage will be present that corresponds to the modulation frequency, ω. This voltage is detected by the lock in amplifier, which receives its reference frequency, ω, directly from the PEM. From such voltage, ΔA and A can be derived using the following relations:
Δ A = V a c 1.1515 V d c δ 0 sin ω t {\displaystyle \Delta A={\frac {V_{ac}}{1.1515V_{dc}\delta _{0}\sin \omega t}}}
A = − log ( V d c V e x ) {\displaystyle A=-\log({\frac {V_{dc}}{V_{ex}}})}
where V ex is the (DC) voltage measured by the PMT from the extraordinary wave, and V dc is the DC component of the voltage measured by the PMT for the ordinary wave (measurement path not shown in the diagram).
Some superconducting magnets have a small sample chamber, far too small to contain the entire optical system. Instead, the magnet sample chamber has windows on two opposite sides. Light from the source enters one side, interacts with the sample (usually also temperature controlled) in the magnetic field, and exits through the opposite window to the detector. Optical relay systems that allow the source and detector each to be about a meter from the sample are typically employed. This arrangement avoids many of the difficulties that would be encountered if the optical apparatus had to operate in the high magnetic field, and also allows for a much less expensive magnet.
MCD can be used as an optical technique for the detection of electronic structure of both the ground states and excited states. It is also a strong addition to the more commonly used absorption spectroscopy, and there are two reasons that explain this. First, a transition buried under a stronger transition can appear in MCD if the first derivative of the absorption is much larger for the weaker transition or it is of the opposite sign. Second, MCD will be found where no absorption is detected at all if ΔA > (ΔA min ) but A < A min , where (ΔA) min and A min are the minimum of ΔA and A that are detectable. Typically, (ΔA min ) and A min are of the magnitudes around 10 −5 and 10 −3 respectively. So, a transition can only be detected in MCD, not in the absorption spectroscopy, if ΔA/A > 10 −2 . This happens in paramagnetic systems that are at lower temperature or that have sharp lines in the spectroscopy. [ 7 ]
In biology , metalloproteins are the most likely candidates for MCD measurements, as the presence of metals with degenerate energy levels leads to strong MCD signals. In the case of ferric heme proteins, [ 8 ] MCD is capable of determining both oxidation and spin state to a remarkably exquisite degree. In regular proteins, MCD is capable of stoichiometrically measuring the tryptophan content of proteins , assuming there are no other competing absorbers in the spectroscopic system.
In addition, the application of MCD spectroscopy greatly improved the level of understanding in the ferrous non-heme systems because of the direct observation of the d–d transitions, which generally can not be obtained in optical absorption spectroscopy owing to the weak extinction coefficients and are often electron paramagnetic resonance silent due to relatively large ground-state sublevel splittings and fast relaxation times. [ 9 ]
Consider a system of localized, non-interacting absorbing centers. Based on the semi-classical radiation absorption theory within the electric dipole approximation, the electric vector of the circularly polarized waves propagates along the +z direction. In this system, ω = 2 π ν {\displaystyle \omega =2\pi \nu } is the angular frequency , and n ~ {\displaystyle {\tilde {n}}} = n – ik is the complex refractive index . As the light travels, the attenuation of the beam is expressed as [ 7 ]
where I ( z ) {\displaystyle I(z)} is the intensity of light at position z {\displaystyle z} , k {\displaystyle k} is the absorption coefficient of the medium in the z {\displaystyle z} direction, and c {\displaystyle c} is the speed of light. Circular dichroism (CD) is then defined by the difference between left ( − {\displaystyle -} ) and right ( + {\displaystyle +} ) circularly polarized light, Δ k = k − − k + {\displaystyle \Delta k=k_{-}-k_{+}} , following the sign convention of natural optical activity. In the presence of a static, uniform external magnetic field applied parallel to the direction of propagation of light, [ 2 ] the Hamiltonian for the absorbing center takes the form H ( t ) = H 0 + H 1 ( t ) {\displaystyle {\mathcal {H}}(t)={\mathcal {H}}_{0}+{\mathcal {H}}_{1}(t)} for H 0 {\displaystyle {\mathcal {H}}_{0}} describing the system in the external magnetic field and H 1 ( t ) {\displaystyle {\mathcal {H}}_{1}(t)} describing the applied electromagnetic radiation. The absorption coefficient for a transition between two eigenstates of H 0 {\displaystyle {\mathcal {H}}_{0}} , a {\displaystyle a} and j {\displaystyle j} , can be described using the electric dipole transition operator m {\displaystyle m} as
The ( α 2 / n ) {\displaystyle (\alpha ^{2}/n)} term is a frequency-independent correction factor allowing for the effect of the medium on the light wave electric field, composed of the permittivity α {\displaystyle \alpha } and the real refractive index n {\displaystyle n} .
In cases of a discrete spectrum, the observed Δ k {\displaystyle \Delta k} at a particular frequency ω {\displaystyle \omega } can be treated as a sum of contributions from each transition,
where Δ k a → j ( ω ) {\displaystyle \Delta k_{a\to j}(\omega )} is the contribution at ω {\displaystyle \omega } from the a → j {\displaystyle a\to j} transition, [ Δ k a → j ] {\displaystyle [\Delta k_{a\to j}]} is the absorption coefficient for the a → j {\displaystyle a\to j} transition, and f j a ( ω ) {\displaystyle f_{ja}(\omega )} is a bandshape function ( ∫ 0 ∞ f j a ( ω ) d ω = 1 {\displaystyle \textstyle {\int _{0}^{\infty }f_{ja}(\omega )d\omega =1}} ). Because eigenstates a {\displaystyle a} and j {\displaystyle j} depend on the applied external field, the value of Δ k o b s ( ω ) {\displaystyle \Delta k_{\mathrm {obs} }(\omega )} varies with field. It is frequently useful to compare this value to the absorption coefficient in the absence of an applied field, often denoted
When the Zeeman effect is small compared to zero-field state separations, line width, and k T {\displaystyle kT} and when the line shape is independent of the applied external field H {\displaystyle H} , first-order perturbation theory can be applied to separate Δ k {\displaystyle \Delta k} into three contributing Faraday terms, called A 1 {\displaystyle {\mathcal {A}}_{1}} , B 0 {\displaystyle {\mathcal {B}}_{0}} , and C 0 {\displaystyle {\mathcal {C}}_{0}} . The subscript indicates the moment such that A 1 {\displaystyle {\mathcal {A}}_{1}} contributes a derivative-shaped signal and B 0 {\displaystyle {\mathcal {B}}_{0}} and C 0 {\displaystyle {\mathcal {C}}_{0}} contribute regular absorptions. Additionally, a zero-field absorption term D 0 {\displaystyle {\mathcal {D}}_{0}} is defined. The relationships between Δ k {\displaystyle \Delta k} , k 0 {\displaystyle k^{0}} , and these Faraday terms are
for external field strength H {\displaystyle H} , Boltzmann constant k B {\displaystyle k_{B}} , temperature T {\displaystyle T} , and a proportionality constant γ {\displaystyle \gamma } . This expression requires assumptions that j {\displaystyle j} is sufficiently high in energy that N j ≈ 0 {\displaystyle N_{j}\approx 0} , and that the temperature of the sample is high enough that magnetic saturation does not produce nonlinear C {\displaystyle {\mathcal {C}}} term behavior.
Though one must pay attention to proportionality constants, there is a proportionality between Δ k {\displaystyle \Delta k} and molar extinction coefficient ϵ {\displaystyle \epsilon } and absorbance A / C l {\displaystyle A/Cl} for concentration C {\displaystyle C} and path length l {\displaystyle l} .
These Faraday terms are the usual language in which MCD spectra are discussed. Their definitions from perturbation theory are [ 10 ]
where d A {\displaystyle d_{A}} is the degeneracy of ground state A {\displaystyle A} , K {\displaystyle K} labels states other than A {\displaystyle A} or J {\displaystyle J} , α {\displaystyle \alpha } and λ {\displaystyle \lambda } and κ {\displaystyle \kappa } label the levels within states A {\displaystyle A} and J {\displaystyle J} and K {\displaystyle K} (respectively), E X {\displaystyle E_{X}} is the energy of unperturbed state X {\displaystyle X} , L z {\displaystyle L_{z}} is the z {\displaystyle z} angular momentum operator, S z {\displaystyle S_{z}} is the z {\displaystyle z} spin operator, and ℜ {\displaystyle \Re } indicates the real part of the expression.
The equations in the previous subsection reveal that the A 1 {\displaystyle {\mathcal {A}}_{1}} , B 0 {\displaystyle {\mathcal {B}}_{0}} , and C 0 {\displaystyle {\mathcal {C}}_{0}} terms originate through three distinct mechanisms.
The A 1 {\displaystyle {\mathcal {A}}_{1}} term arises from Zeeman splitting of the ground or excited degenerate states. These field-dependent changes in energies of the magnetic sublevels causes small shifts in the bands to higher/lower energy. The slight offsets result in incomplete cancellation of the positive and negative features, giving a net derivative shape in the spectrum. This intensity mechanism is generally independent of sample temperature.
The B 0 {\displaystyle {\mathcal {B}}_{0}} term is due to the field-induced mixing of states. Energetic proximity of a third state | K ⟩ {\displaystyle |K\rangle } to either the ground state | A ⟩ {\displaystyle |A\rangle } or excited state | J ⟩ {\displaystyle |J\rangle } gives appreciable Zeeman coupling in the presence of an applied external field. As the strength of the magnetic field increases, the amount of mixing increases to give growth of an absorption band shape. Like the A 1 {\displaystyle {\mathcal {A}}_{1}} term, the B 0 {\displaystyle {\mathcal {B}}_{0}} term is generally temperature independent. Temperature dependence of B 0 {\displaystyle {\mathcal {B}}_{0}} term intensity can sometimes be observed when | K ⟩ {\displaystyle |K\rangle } is particularly low-lying in energy.
The C 0 {\displaystyle {\mathcal {C}}_{0}} term requires the degeneracy of the ground state, often encountered for paramagnetic samples. This happens due to a change in the Boltzmann population of the magnetic sublevels, which is dependent on the degree of field-induced splitting of the sublevel energies and on the sample temperature. [ 11 ] Decrease of the temperature and increase of the magnetic field increases the C 0 {\displaystyle {\mathcal {C}}_{0}} term intensity until it reaches the maximum (saturation limit). Experimentally, the C 0 {\displaystyle {\mathcal {C}}_{0}} term spectrum can be obtained from MCD raw data by subtraction of MCD spectra measured in the same applied magnetic field at different temperatures, while A 1 {\displaystyle {\mathcal {A}}_{1}} and B 0 {\displaystyle {\mathcal {B}}_{0}} terms can be distinguished via their different band shapes. [ 9 ]
The relative contributions of A, B and C terms to the MCD spectrum are proportional to the inverse line width, energy splitting, and temperature:
where Δ Γ {\displaystyle \Delta \Gamma } is line width and Δ E {\displaystyle \Delta E} is the zero-field state separation. For typical values of Δ Γ {\displaystyle \Delta \Gamma } = 1000 cm −1 , Δ E {\displaystyle \Delta E} = 10,000 cm −1 and k T {\displaystyle kT} = 6 cm −1 (at 10 K), the three terms make relative contributions 1:0.1:150. So, at low temperature the C 0 {\displaystyle {\mathcal {C}}_{0}} term dominates over A 1 {\displaystyle {\mathcal {A}}_{1}} and B 0 {\displaystyle {\mathcal {B}}_{0}} for paramagnetic samples. [ 12 ]
In the visible and near-ultraviolet regions, the hexacyanoferrate(III) ion ( Fe ( C N ) 6 3− ) exhibits three strong absorptions at 24500, 32700, and 40500 cm −1 , which have been ascribed to ligand to metal charge transfer (LMCT) transitions. They all have lower energy than the lowest-energy intense band for the Fe(II) complex Fe(CN) 6 2− found at 46000 cm −1 . [ 13 ] The red shift with increasing oxidation state of the metal is characteristic of LMCT bands. Additionally, only A terms, which are temperature independent, should be involved in MCD structure for closed-shell species.
These features can be explained as follows. The ground state of the anion is 2 T 2g , which derives from the electronic configuration (t 2g ) 5 . So, there would be an unpaired electron in the d orbital of Fe 3+ From that, the three bands can be assigned to the transitions 2 t 2g → 2 t 1u 1 , 2 t 2g → 2 t 1u 2 , 2 t 2g → 2 t 2u . Two of the excited states are of the same symmetry, and, based on the group theory, they could mix with each other so that there are no pure σ and π characters in the two t 1u states, but for t 2u , there would be no intermixing. The A terms are also possible from the degenerate excited states, but the studies of temperature dependence showed that the A terms are not as dependent as the C term. [ 14 ]
An MCD study of Fe(CN) 6 3− embedded in a thin polyvinyl alcohol (PVA) film revealed a temperature dependence of the C term. The room-temperature C 0 /D 0 values for the three bands in the Fe(CN) 6 3− spectrum are 1.2, −0.6, and 0.6, respectively, and their signs (positive, negative, and positive) establish the energy ordering as 2 t 2g → 2 t 1u 2 < 2 t 2g → 2 t 2u < 2 t 2g → 2 t 1u 1
To have an A- and B-term in the MCD spectrum, a molecule must contain degenerate excited states (A-term) and excited states close enough in energy to allow mixing (B-term). One case exemplifying these conditions is a square planar, d 8 complex such as [(n-C 4 H 9 ) 4 N] 2 Pt(CN) 4 . In addition to containing A- and B-terms, this example demonstrates the effects of spin-orbit coupling in metal to ligand charge transfer (MLCT) transitions. As shown in figure 1 , the molecular orbital diagram of [(n-C 4 H 9 ) 4 N] 2 Pt(CN) 4 reveals MLCT into the antibonding π* orbitals of cyanide. The ground state is diamagnetic (thereby eliminating any C-terms) and the LUMO is the a 2u . The dipole-allowed MLCT transitions are a 1g -a 2u and e g -a 2u . Another transition, b 2u -a 2u , is a weak (orbitally forbidden singlet) but can still be observed in MCD. [ 15 ]
Because A- and B-terms arise from the properties of states, all singlet and triplet excited states are given in figure 2 .
Mixing of all these singlet and triplet states will occur and is attributed to the spin orbit coupling of platinum 5d orbitals (ζ ~ 3500 cm −1 ), as shown in figure 3. The black lines on the figure indicate the mixing of 1 A 2u with 3 E u to give two A 2u states. The red lines show the 1 E u , 3 E u , 3 A 2u , and 3 B 1u states mixing to give four E u states. The blue lines indicate remnant orbitals after spin-orbit coupling that are not a result of mixing. | https://en.wikipedia.org/wiki/Magnetic_circular_dichroism |
A magnetic core is a piece of magnetic material with a high magnetic permeability used to confine and guide magnetic fields in electrical, electromechanical and magnetic devices such as electromagnets , transformers , electric motors , generators , inductors , loudspeakers , magnetic recording heads , and magnetic assemblies. It is made of ferromagnetic metal such as iron, or ferrimagnetic compounds such as ferrites . The high permeability, relative to the surrounding air, causes the magnetic field lines to be concentrated in the core material. The magnetic field is often created by a current-carrying coil of wire around the core.
The use of a magnetic core can increase the strength of magnetic field in an electromagnetic coil by a factor of several hundred times what it would be without the core. However, magnetic cores have side effects which must be taken into account. In alternating current (AC) devices they cause energy losses, called core losses , due to hysteresis and eddy currents in applications such as transformers and inductors. "Soft" magnetic materials with low coercivity and hysteresis, such as silicon steel , or ferrite , are usually used in cores.
An electric current through a wire wound into a coil creates a magnetic field through the center of the coil, due to Ampere's circuital law . Coils are widely used in electronic components such as electromagnets , inductors , transformers , electric motors and generators . A coil without a magnetic core is called an "air core" coil. Adding a piece of ferromagnetic or ferrimagnetic material in the center of the coil can increase the magnetic field by hundreds or thousands of times; this is called a magnetic core. The field of the wire penetrates the core material, magnetizing it, so that the strong magnetic field of the core adds to the field created by the wire. The amount that the magnetic field is increased by the core depends on the magnetic permeability of the core material. Because side effects such as eddy currents and hysteresis can cause frequency-dependent energy losses, different core materials are used for coils used at different frequencies .
In some cases the losses are undesirable and with very strong fields saturation can be a problem, and an 'air core' is used. A former may still be used; a piece of material, such as plastic or a composite, that may not have any significant magnetic permeability but which simply holds the coils of wires in place.
"Soft" ( annealed ) iron is used in magnetic assemblies, direct current (DC) electromagnets and in some electric motors; and it can create a concentrated field that is as much as 50,000 times more intense than an air core. [ 1 ]
Iron is desirable to make magnetic cores, as it can withstand high levels of magnetic field without saturating (up to 2.16 teslas at ambient temperature. [ 2 ] [ 3 ] ) Annealed iron is used because, unlike "hard" iron, it has low coercivity and so does not remain magnetised when the field is removed, which is often important in applications where the magnetic field is required to be repeatedly switched.
Due to the electrical conductivity of the metal, when a solid one-piece metal core is used in alternating current (AC) applications such as transformers and inductors, the changing magnetic field induces large eddy currents circulating within it, closed loops of electric current in planes perpendicular to the field. The current flowing through the resistance of the metal heats it by Joule heating , causing significant power losses. Therefore, solid iron cores are not used in transformers or inductors, they are replaced by laminated or powdered iron cores, or nonconductive cores like ferrite .
In order to reduce the eddy current losses mentioned above, most low frequency power transformers and inductors use laminated cores, made of stacks of thin sheets of silicon steel :
Laminated magnetic cores are made of stacks of thin iron sheets coated with an insulating layer, lying as much as possible parallel with the lines of flux. The layers of insulation serve as a barrier to eddy currents, so eddy currents can only flow in narrow loops within the thickness of each single lamination. Since the current in an eddy current loop is proportional to the area of the loop, this prevents most of the current from flowing, reducing eddy currents to a very small level. Since power dissipated is proportional to the square of the current, breaking a large core into narrow laminations reduces the power losses drastically. From this, it can be seen that the thinner the laminations, the lower the eddy current losses.
A small addition of silicon to iron (around 3%) results in a dramatic increase of the resistivity of the metal, up to four times higher. [ citation needed ] The higher resistivity reduces the eddy currents, so silicon steel is used in transformer cores. Further increase in silicon concentration impairs the steel's mechanical properties, causing difficulties for rolling due to brittleness.
Among the two types of silicon steel , grain-oriented (GO) and grain non-oriented (GNO), GO is most desirable for magnetic cores. It is anisotropic , offering better magnetic properties than GNO in one direction. As the magnetic field in inductor and transformer cores is always along the same direction, it is an advantage to use grain oriented steel in the preferred orientation. Rotating machines, where the direction of the magnetic field can change, gain no benefit from grain-oriented steel.
A family of specialized alloys exists for magnetic core applications. Examples are mu-metal , permalloy , and supermalloy . They can be manufactured as stampings or as long ribbons for tape wound cores. Some alloys, e.g. Sendust , are manufactured as powder and sintered to shape.
Many materials require careful heat treatment to reach their magnetic properties, and lose them when subjected to mechanical or thermal abuse. For example, the permeability of mu-metal increases about 40 times after annealing in hydrogen atmosphere in a magnetic field; subsequent sharper bends disrupt its grain alignment, leading to localized loss of permeability; this can be regained by repeating the annealing step.
Amorphous metal is a variety of alloys (e.g. Metglas ) that are non-crystalline or glassy. These are being used to create high-efficiency transformers. The materials can be highly responsive to magnetic fields for low hysteresis losses, and they can also have lower conductivity to reduce eddy current losses. Power utilities are currently making widespread use of these transformers for new installations. [ 4 ] High mechanical strength and corrosion resistance are also common properties of metallic glasses which are positive for this application. [ 5 ]
Powder cores consist of metal grains mixed with a suitable organic or inorganic binder, and pressed to desired density. Higher density is achieved with higher pressure and lower amount of binder. Higher density cores have higher permeability, but lower resistance and therefore higher losses due to eddy currents. Finer particles allow operation at higher frequencies, as the eddy currents are mostly restricted to within the individual grains. Coating of the particles with an insulating layer, or their separation with a thin layer of a binder, lowers the eddy current losses. Presence of larger particles can degrade high-frequency performance. Permeability is influenced by the spacing between the grains, which form distributed air gap; the less gap, the higher permeability and the less-soft saturation. Due to large difference of densities, even a small amount of binder, weight-wise, can significantly increase the volume and therefore intergrain spacing.
Lower permeability materials are better suited for higher frequencies, due to balancing of core and winding losses.
The surface of the particles is often oxidized and coated with a phosphate layer, to provide them with mutual electrical insulation.
Powdered iron is the cheapest material. It has higher core loss than the more advanced alloys, but this can be compensated for by making the core bigger; it is advantageous where cost is more important than mass and size. Saturation flux of about 1 to 1.5 tesla. Relatively high hysteresis and eddy current loss, operation limited to lower frequencies (approx. below 100 kHz). Used in energy storage inductors, DC output chokes, differential mode chokes, triac regulator chokes, chokes for power factor correction, resonant inductors, and pulse and flyback transformers. [ 6 ]
The binder used is usually epoxy or other organic resin, susceptible to thermal aging. At higher temperatures, typically above 125 °C, the binder degrades and the core magnetic properties may change. With more heat-resistant binders the cores can be used up to 200 °C. [ 7 ]
Iron powder cores are most commonly available as toroids. Sometimes as E, EI, and rods or blocks, used primarily in high-power and high-current parts.
Carbonyl iron is significantly more expensive than hydrogen-reduced iron.
Powdered cores made of carbonyl iron , a highly pure iron, have high stability of parameters across a wide range of temperatures and magnetic flux levels, with excellent Q factors between 50 kHz and 200 MHz. Carbonyl iron powders are basically constituted of micrometer-size spheres of iron coated in a thin layer of electrical insulation . This is equivalent to a microscopic laminated magnetic circuit (see silicon steel, above), hence reducing the eddy currents , particularly at very high frequencies. Carbonyl iron has lower losses than hydrogen-reduced iron, but also lower permeability.
A popular application of carbonyl iron-based magnetic cores is in high-frequency and broadband inductors and transformers , especially higher power ones.
Carbonyl iron cores are often called "RF cores".
The as-prepared particles, "E-type"and have onion-like skin, with concentric shells separated with a gap. They contain significant amount of carbon. They behave as much smaller than what their outer size would suggest. The "C-type" particles can be prepared by heating the E-type ones in hydrogen atmosphere at 400 °C for prolonged time, resulting in carbon-free powders. [ 8 ]
Powdered cores made of hydrogen reduced iron have higher permeability but lower Q than carbonyl iron. They are used mostly for electromagnetic interference filters and low-frequency chokes, mainly in switched-mode power supplies .
Hydrogen-reduced iron cores are often called "power cores".
An alloy of about 2% molybdenum , 81% nickel , and 17% iron. Very low core loss, low hysteresis and therefore low signal distortion. Very good temperature stability. High cost. Maximum saturation flux of about 0.8 tesla. Used in high-Q filters, resonant circuits, loading coils, transformers, chokes, etc. [ 6 ]
The material was first introduced in 1940, used in loading coils to compensate capacitance in long telephone lines. It is usable up to about 200 kHz to 1 MHz, depending on vendor. [ 7 ] It is still used in above-ground telephone lines, due to its temperature stability. Underground lines, where temperature is more stable, tend to use ferrite cores due to their lower cost. [ 8 ]
An alloy of about 50–50% of nickel and iron. High energy storage, saturation flux density of about 1.5 tesla. Residual flux density near zero. Used in applications with high DC current bias (line noise filters, or inductors in switching regulators) or where low residual flux density is needed (e.g. pulse and flyback transformers, the high saturation is suitable for unipolar drive), especially where space is constrained. The material is usable up to about 200 kHz. [ 6 ]
An alloy of 6% aluminium, 9% silicon, and 85% iron. Core losses higher than MPP. Very low magnetostriction , makes low audio noise. Loses inductance with increasing temperature, unlike the other materials; can be exploited by combining with other materials as a composite core, for temperature compensation. Saturation flux of about 1 tesla. Good temperature stability. Used in switching power supplies, pulse and flyback transformers, in-line noise filters, swing chokes, and in filters in phase-fired controllers (e.g. dimmers) where low acoustic noise is important. [ 6 ]
Absence of nickel results in easier processing of the material and its lower cost than both high-flux and MPP.
The material was invented in Japan in 1936. It is usable up to about 500 kHz to 1 MHz, depending on vendor. [ 7 ]
A nanocrystalline alloy of a standard iron-boron-silicon alloy, with addition of smaller amounts of copper and niobium . The grain size of the powder reaches down to 10–100 nanometers. The material has very good performance at lower frequencies. It is used in chokes for inverters and in high power applications. It is available under names like e.g. Nanoperm, Vitroperm, Hitperm and Finemet. [ 7 ]
Ferrite ceramics are used for high-frequency applications. The ferrite materials can be engineered with a wide range of parameters. As ceramics, they are essentially insulators, which prevents eddy currents, although losses such as hysteresis losses can still occur.
A coil not containing a magnetic core is called an air core . This includes coils wound on a plastic or ceramic form in addition to those made of stiff wire that are self-supporting and have air inside them. Air core coils generally have a much lower inductance than similarly sized ferromagnetic core coils, but are used in radio frequency circuits to prevent energy losses called core losses that occur in magnetic cores. The absence of normal core losses permits a higher Q factor , so air core coils are used in high frequency resonant circuits , such as up to a few megahertz. However, losses such as proximity effect and dielectric losses are still present. Air cores are also used when field strengths above around 2 Tesla are required as they are not subject to saturation.
Most commonly made of ferrite or powdered iron, and used in radios especially for tuning an inductor . The coil is wound around the rod, or a coil form with the rod inside. Moving the rod in or out of the coil changes the flux through the coil, and can be used to adjust the inductance . Often the rod is threaded to allow adjustment with a screwdriver. In radio circuits, a blob of wax or resin is used once the inductor has been tuned to prevent the core from moving.
The presence of the high permeability core increases the inductance , but the magnetic field lines must still pass through the air from one end of the rod to the other. The air path ensures that the inductor remains linear . In this type of inductor radiation occurs at the end of the rod and electromagnetic interference may be a problem in some circumstances.
Like a cylindrical rod but is square, rarely used on its own.
This type of core is most likely to be found in car ignition coils.
U and C -shaped cores are used with I or another C or U core to make a square closed core, the simplest closed core shape. Windings may be put on one or both legs of the core.
E-shaped core are more symmetric solutions to form a closed magnetic system. Most of the time, the electric circuit is wound around the center leg, whose section area is twice that of each individual outer leg. In 3-phase transformer cores, the legs are of equal size, and all three legs are wound.
Sheets of suitable iron stamped out in shapes like the ( sans-serif ) letters "E" and "I", are stacked with the "I" against the open end of the "E" to form a 3-legged structure. Coils can be wound around any leg, but usually the center leg is used. This type of core is frequently used for power transformers, autotransformers, and inductors.
Again used for iron cores. Similar to using an "E" and "I" together, a pair of "E" cores will accommodate a larger coil former and can produce a larger inductor or transformer . If an air gap is required, the centre leg of the "E" is shortened so that the air gap sits in the middle of the coil to minimize fringing and reduce electromagnetic interference .
A planar core consists of two flat pieces of magnetic material, one above and one below the coil. It is typically used with a flat coil that is part of a printed circuit board . This design is excellent for mass production and allows a high power , small volume transformer to be constructed for low cost. It is not as ideal as either a pot core or toroidal core [ citation needed ] but costs less to produce.
Usually ferrite or similar. This is used for inductors and transformers . The shape of a pot core is round with an internal hollow that almost completely encloses the coil. Usually a pot core is made in two halves which fit together around a coil former ( bobbin ). This design of core has a shielding effect, preventing radiation and reducing electromagnetic interference .
This design is based on a toroid (the same shape as a doughnut ). The coil is wound through the hole in the torus and around the outside. An ideal coil is distributed evenly all around the circumference of the torus. The symmetry of this geometry creates a magnetic field of circular loops inside the core, and the lack of sharp bends will constrain virtually all of the field to the core material. This not only makes a highly efficient transformer , but also reduces the electromagnetic interference radiated by the coil.
It is popular for applications where the desirable features are: high specific power per mass and volume , low mains hum , and minimal electromagnetic interference . One such application is the power supply for a hi-fi audio amplifier . The main drawback that limits their use for general purpose applications is the inherent difficulty of winding wire through the center of a torus.
Unlike a split core (a core made of two elements, like a pair of E cores), specialized machinery is required for automated winding of a toroidal core. Toroids have less audible noise, such as mains hum, because the magnetic forces do not exert bending moment on the core. The core is only in compression or tension, and the circular shape is more stable mechanically.
The ring is essentially identical in shape and performance to the toroid, except that inductors commonly pass only through the center of the core, without wrapping around the core multiple times.
The ring core may also be composed of two separate C-shaped hemispheres secured together within a plastic shell, permitting it to be placed on finished cables with large connectors already installed, that would prevent threading the cable through the small inner diameter of a solid ring.
The A L value of a core configuration is frequently specified by manufacturers. The relationship between inductance and A L number in the linear portion of the magnetisation curve is defined to be:
where n is the number of turns, L is the inductance (e.g. in nH) and A L is expressed in inductance per turn squared (e.g. in nH/n 2 ). [ 9 ]
When the core is subjected to a changing magnetic field, as it is in devices that use AC current such as transformers , inductors , and AC motors and alternators , some of the power that would ideally be transferred through the device is lost in the core, dissipated as heat and sometimes noise . Core loss is commonly termed iron loss in contradistinction to copper loss , the loss in the windings. [ 10 ] [ 11 ] Iron losses are often described as being in three categories:
When the magnetic field through the core changes, the magnetization of the core material changes by expansion and contraction of the tiny magnetic domains it is composed of, due to movement of the domain walls . This process causes losses, because the domain walls get "snagged" on defects in the crystal structure and then "snap" past them, dissipating energy as heat. This is called hysteresis loss . It can be seen in the graph of the B field versus the H field for the material, which has the form of a closed loop.
The net energy that flows into the inductor expressed in relationship to the B-H characteristic of the core is shown by the equation [ 12 ]
This equation shows that the amount of energy lost in the material in one cycle of the applied field is proportional to the area inside the hysteresis loop . Since the energy lost in each cycle is constant, hysteresis power losses increase proportionally with frequency . [ 13 ] The final equation for the hysteresis power loss is [ 12 ]
If the core is electrically conductive , the changing magnetic field induces circulating loops of current in it, called eddy currents , due to electromagnetic induction . [ 14 ] The loops flow perpendicular to the magnetic field axis. The energy of the currents is dissipated as heat in the resistance of the core material. The power loss is proportional to the area of the loops and inversely proportional to the resistivity of the core material. Eddy current losses can be reduced by making the core out of thin laminations which have an insulating coating, or alternatively, making the core of a magnetic material with high electrical resistance, like ferrite . [ 15 ] Most magnetic cores intended for power converter application use ferrite cores for this reason.
By definition, this category includes any losses in addition to eddy-current and hysteresis losses. This can also be described as broadening of the hysteresis loop with frequency. Physical mechanisms for anomalous loss include localized eddy-current effects near moving domain walls.
An equation known as Legg's equation models the magnetic material core loss at low flux densities. The equation has three loss components: hysteresis, residual, and eddy current, [ 16 ] [ 17 ] [ 18 ] and it is given by
where
Losses in magnetic materials can be characterized by the Steinmetz coefficients, which however do not take into account temperature variability. Material manufacturers provide data on core losses in tabular and graphical form for practical conditions of use. | https://en.wikipedia.org/wiki/Magnetic_core |
Magnetic declination (also called magnetic variation ) is the angle between magnetic north and true north at a particular location on the Earth's surface. The angle can change over time due to polar wandering .
Magnetic north is the direction that the north end of a magnetized compass needle points, which corresponds to the direction of the Earth's magnetic field lines. True north is the direction along a meridian towards the geographic North Pole .
Somewhat more formally, Bowditch defines variation as "the angle between the magnetic and geographic meridians at any place, expressed in degrees and minutes east or west to indicate the direction of magnetic north from true north. The angle between magnetic and grid meridians is called grid magnetic angle, grid variation, or grivation." [ 1 ]
By convention, declination is positive when magnetic north is east of true north, and negative when it is to the west. Isogonic lines are lines on the Earth's surface along which the declination has the same constant value, and lines along which the declination is zero are called agonic lines . The lowercase Greek letter δ (delta) is frequently used as the symbol for magnetic declination.
The term magnetic deviation is sometimes used loosely to mean the same as magnetic declination, but more correctly it refers to the error in a compass reading induced by nearby metallic objects, such as iron on board a ship or aircraft.
Magnetic declination should not be confused with magnetic inclination , also known as magnetic dip, which is the angle that the Earth's magnetic field lines make with the downward side of the horizontal plane.
Magnetic declination varies both from place to place and with the passage of time. As a traveller cruises the east coast of the United States, for example, the declination varies from 16 degrees west in Maine, to 6 in Florida, to 0 degrees in Louisiana, to 4 degrees east in Texas. The declination at London, UK was one degree west (2014), reducing to zero as of early 2020. [ 2 ] [ 3 ] Reports of measured magnetic declination for distant locations became commonplace in the 17th century, and Edmund Halley made a map of declination for the Atlantic Ocean in 1700. [ 4 ]
In most areas, the spatial variation reflects the irregularities of the flows deep in the Earth; in some areas, deposits of iron ore or magnetite in the Earth's crust may contribute strongly to the declination. Similarly, secular changes to these flows result in slow changes to the field strength and direction at the same point on the Earth.
The magnetic declination in a given area may (most likely will) change slowly over time, possibly as little as 2–2.5 degrees every hundred years or so, depending on where it is measured. For a location close to the pole like Ivujivik , the declination may change by 1 degree every three years. This may be insignificant to most travellers, but can be important if using magnetic bearings from old charts or metes (directions) in old deeds for locating places with any precision.
As an example of how variation changes over time, see the two charts of the same area (western end of Long Island Sound ), below, surveyed 124 years apart. The 1884 chart shows a variation of 8 degrees, 20 minutes West. The 2008 chart shows 13 degrees, 15 minutes West.
The magnetic declination at any particular place can be measured directly by reference to the celestial poles —the points in the heavens around which the stars appear to revolve, which mark the direction of true north and true south. The instrument used to perform this measurement is known as a declinometer .
The approximate position of the north celestial pole is indicated by Polaris (the North Star). In the northern hemisphere , declination can therefore be approximately determined as the difference between the magnetic bearing and a visual bearing on Polaris. Polaris currently traces a circle 0.73° in radius around the north celestial pole, so this technique is accurate to within a degree. At high latitudes a plumb-bob is helpful to sight Polaris against a reference object close to the horizon, from which its bearing can be taken. [ 5 ]
A rough estimate of the local declination (within a few degrees) can be determined from a general isogonic chart of the world or a continent, such as those illustrated above. Isogonic lines are also shown on aeronautical and nautical charts .
Larger-scale local maps may indicate current local declination, often with the aid of a schematic diagram. Unless the area depicted is very small, declination may vary measurably over the extent of the map, so the data may be referred to a specific location on the map. The current rate and direction of change may also be shown, for example in arcminutes per year. The same diagram may show the angle of grid north (the direction of the map's north–south grid lines), which may differ from true north.
On the topographic maps of the U.S. Geological Survey (USGS), for example, a diagram shows the relationship between magnetic north in the area concerned (with an arrow marked "MN") and true north (a vertical line with a five-pointed star at its top), with a label near the angle between the MN arrow and the vertical line, stating the size of the declination and of that angle, in degrees, mils , or both. However, the diagram itself is not an accurate depiction of the stated numerical declination angle, but is intentionally exaggerated by the cartographer for purposes of legibility.
Worldwide empirical model of the deep flows described above are available for describing and predicting features of the Earth's magnetic field, including the magnetic declination for any given location at any time in a given timespan. One such model is World Magnetic Model (WMM) of the US and UK. It is built with all the information available to the map-makers at the start of the five-year period it is prepared for. It reflects a highly predictable rate of change, [ a ] and is usually more accurate than a map—which is likely months or years out of date. [ citation needed ] For historical data, the IGRF and GUFM models may be used. Tools for using such models include:
The WMM, IGRF, and GUFM models only describe the magnetic field as emitted at the core-mantle boundary. In practice, the magnetic field is also distorted by the Earth crust, the distortion being magnetic anomaly . For more precise estimates, a larger crust-aware model such as the Enhanced Magnetic Model may be used. (See cited page for a comparison of declination contours.) [ 9 ]
A magnetic compass points to magnetic north, not geographic (true) north. Compasses of the style commonly used for hiking (i.e., baseplate or protractor compass) utilize a dial or bezel which rotates 360 degrees and is independent of the magnetic needle. To manually establish a declination for true north, the bezel is rotated until the desired number of degrees lie between the bezel's designation N (for North) and the direction (east or west) of magnetic north indicated by the polarized tip of the needle (usually painted red). The entire compass is then rotated until the magnetic needle lies within the outlined orienting arrow or box on the bottom of the capsule, and the course heading (in degrees) is displayed at the base of the direction-of-travel arrow on the baseplate. A compass thus adjusted provides a course bearing in relation to true north instead of magnetic north as long as it remains within an area on the same isogonic line.
In the image at the right, the bezel's N has been aligned with the direction indicated by the magnetic end of the compass needle, adjusted for local declination (10 degrees west of magnetic north). The direction-of-travel arrow on the baseplate thus reflects a true north heading.
After determining local declination, a rotating dial compass may be altered to give true north readings by taping or painting a small delta-point or arrowhead on the compass baseplate west or east of magnetic north pointing to true north on the compass bezel. Other compasses of this design utilize an adjustable declination mechanism integrated with the compass bezel, resulting in true north readings each time the needle is aligned with the orienting arrow.
Compasses that utilize a floating magnetized dial or card are commonly found in marine compasses and in certain models used for land navigation that feature a lensatic or prismatic sighting system. A floating card compass always gives bearings in relation to magnetic north and cannot be adjusted for declination. True north must be computed by adding or subtracting local magnetic declination. The example on the left demonstrates a typical conversion of a magnetic bearing from a floating card compass to a true bearing by adding the magnetic declination. The declination in the example is 14°E (+14°). If, instead, the declination was 14°W (−14°), you would still “add” it to the magnetic bearing to obtain the true bearing: 40°+ (−14°) = 26°.
Conversely, local declination is subtracted from a true bearing to obtain a magnetic bearing. With a local declination of 14°E, a true bearing (i.e. obtained from a map) of 54° is converted to a magnetic bearing (for use in the field) by subtracting declination: 54° – 14° = 40°. If the local declination was 14°W (−14°), it is again subtracted from the true bearing to obtain a magnetic bearing: 54°- (−14°) = 68°.
On aircraft or vessels there are three types of bearing : true, magnetic, and compass bearing. Compass error is divided into two parts, namely magnetic variation and magnetic deviation , the latter originating from magnetic properties of the vessel or aircraft. Variation and deviation are signed quantities. As discussed above, positive (easterly) variation indicates that magnetic north is east of geographic north. Likewise, positive (easterly) deviation indicates that the compass needle is east of magnetic north. [ 10 ]
Compass, magnetic and true bearings are related by:
T = M + V M = C + D {\displaystyle {\begin{aligned}T&=M+V\\M&=C+D\end{aligned}}}
The general equation relating compass and true bearings is
T = C + D + V {\displaystyle T=C+D+V}
Where:
For example, if the compass reads 32°, the local magnetic variation is −5.5° (i.e. West) and the deviation is 0.5° (i.e. East), the true bearing will be:
T = 32 ∘ + ( − 5.5 ∘ ) + 0.5 ∘ = 27 ∘ {\displaystyle T=32^{\circ }+(-5.5^{\circ })+0.5^{\circ }=27^{\circ }}
To calculate true bearing from compass bearing (and known deviation and variation):
To calculate compass bearing from true bearing (and known deviation and variation):
These rules are often combined with the mnemonic "West is best, East is least"; that is to say, add W declinations when going from True bearings to Magnetic bearings, and subtract E ones.
Another simple way to remember which way to apply the correction for continental USA is:
Common abbreviations are:
Magnetic deviation is the angle from a given magnetic bearing to the related bearing mark of the compass. Deviation is positive if a compass bearing mark (e.g., compass north) is right of the related magnetic bearing (e.g., magnetic north) and vice versa. For example, if the boat is aligned to magnetic north and the compass' north mark points 3° more east, deviation is +3°. Deviation varies for every compass in the same location and depends on such factors as the magnetic field of the vessel, wristwatches, etc. The value also varies depending on the orientation of the boat. Magnets and/or iron masses can correct for deviation, so that a particular compass accurately displays magnetic bearings. More commonly, however, a correction card lists errors for the compass, which can then be compensated for arithmetically. Deviation must be added to compass bearing to obtain magnetic bearing.
Air navigation is based on magnetic directions thus it is necessary to periodically revise navigational aids to reflect the drift in magnetic declination over time. This requirement applies to VOR beacons, runway numbering, airway labeling, and aircraft vectoring directions given by air traffic control , all of which are based on magnetic direction.
Runways are designated by a number between 01 and 36, which is generally one tenth of the magnetic azimuth of the runway's heading : a runway numbered 09 points east (90°), runway 18 is south (180°), runway 27 points west (270°) and runway 36 points to the north (360° rather than 0°). [ 11 ] However, due to magnetic declination, changes in runway designators have to occur at times to keep their designation in line with the runway's magnetic heading. An exception is made for runways within the Northern Domestic Airspace of Canada; these are numbered relative to true north because proximity to the magnetic North Pole makes the magnetic declination large and changes in it happen at a high pace.
Radionavigation aids located on the ground, such as VORs , are also checked and updated to keep them aligned with magnetic north to allow pilots to use their magnetic compasses for accurate and reliable in-plane navigation.
For simplicity aviation sectional charts are drawn using true north so the entire chart need not be rotated as magnetic declination changes. Instead individual printed elements on the chart (such as VOR compass roses) are updated with each revision of the chart to reflect changes in magnetic declination. For an example refer to the sectional chart slightly west of Winston-Salem, North Carolina in March 2021, magnetic north is 8 degrees west of true north ( Note the dashed line marked 8°W ). [ 12 ]
When plotting a course, some small aircraft pilots may plot a trip using true north on a sectional chart (map), then convert the true north bearings to magnetic north for in-plane navigation using the magnetic compass. These bearings are then converted on a pre-flight plan by adding or subtracting the local variation displayed on a sectional chart.
GPS systems used for aircraft navigation also display directions in terms of magnetic north even though their intrinsic coordinate system is based on true north. This is accomplished by means of lookup tables inside the GPS which account for magnetic declination. If flying under visual flight rules it is acceptable to fly with an outdated GPS declination database however if flying IFR the database must be updated every 28 days per FAA regulation.
As a fail-safe even the most advanced airliner will still have a magnetic compass in the cockpit. When onboard electronics fail, pilots can still rely on paper charts and the ancient and highly reliable device—the magnetic compass. | https://en.wikipedia.org/wiki/Magnetic_declination |
The magnetic detector or Marconi magnetic detector , sometimes called the "Maggie", was an early radio wave detector used in some of the first radio receivers to receive Morse code messages during the wireless telegraphy era around the turn of the 20th century. [ 1 ] [ 2 ] Developed in 1902 by radio pioneer Guglielmo Marconi [ 1 ] [ 2 ] [ 3 ] from a method invented in 1895 by New Zealand physicist Ernest Rutherford , [ 4 ] it was used in Marconi wireless stations until around 1912, when it was superseded by vacuum tubes . [ 5 ] It was widely used on ships because of its reliability and insensitivity to vibration. A magnetic detector was part of the wireless apparatus in the radio room of the RMS Titanic which was used to summon help during its famous 15 April 1912 sinking. [ 6 ]
The primitive spark gap radio transmitters used during the first three decades of radio (1886-1916) could not transmit audio (sound) and instead transmitted information by wireless telegraphy ; the operator switched the transmitter on and off with a telegraph key , creating pulses of radio waves to spell out text messages in Morse code . So the radio receiving equipment of the time did not have to convert the radio waves into sound like modern receivers, but merely detect the presence or absence of the radio signal. Any device that did this was called a detector . The first widely used detector was the coherer , invented in 1890. The coherer was a very poor detector, insensitive and prone to false triggering due to impulsive noise, which motivated much research to find better radio wave detectors.
Ernest Rutherford had first used the hysteresis of iron to detect Hertzian waves in 1896 [ 4 ] [ 7 ] by the demagnetization of an iron needle when a radio signal passed through a coil around the needle, however the needle had to be remagnetized so this was not suitable for a continuous detector. [ 7 ] Many other wireless researchers such as E. Wilson, C. Tissot, Reginald Fessenden , John Ambrose Fleming , Lee De Forest , J.C. Balsillie, and L. Tieri had subsequently devised detectors based on hysteresis, but none had become widely used due to various drawbacks. [ 7 ] Many earlier versions had a rotating magnet above a stationary iron band with coils on it. [ 8 ] This type was only periodically sensitive, when the magnetic field was changing, which occurred as the magnetic poles passed the iron.
During his transatlantic radio communication experiments in December 1902 Marconi found the coherer to be too unreliable and insensitive for detecting the very weak radio signals from long-distance transmissions. It was this need that drove him to develop his magnetic detector. Marconi devised a more effective configuration with a moving iron band driven by a clockwork motor passing by stationary magnets and coils, resulting in a continuous supply of iron that was changing magnetization, and thus continuous sensitivity (Rutherford claimed he had also invented this configuration). [ 8 ] The Marconi magnetic detector was the "official" detector used by the Marconi Company from 1902 through 1912, when the company began converting to the Fleming valve and Audion -type vacuum tubes. It was used through 1918.
See drawing at right. The Marconi version consisted of an endless iron band ( B ) built up of 70 strands of number 40 gage silk-covered iron wire . In operation, the band passes over two grooved pulleys rotated by a wind-up clockwork motor. [ 1 ] [ 2 ] The iron band passes through the center of a glass tube which is close wound with a single layer along several millimeters with number 36 gage silk-covered copper wire. This coil ( C ) functions as the radio frequency excitation coil. Over this winding is a small bobbin wound with wire of the same gauge to a resistance of about 140 ohms . This coil ( D ) functions as the audio pickup coil. Around these coils two permanent horseshoe magnets are arranged to magnetize the iron band as it passes through the glass tube. [ 1 ]
The device works by hysteresis of the magnetization in the iron wires. [ 1 ] [ 2 ] The permanent magnets are arranged to create two opposite magnetic fields each directed toward (or away from) the center of the coils in opposite directions along the wire. This functions to magnetize the iron band along its axis, first in one direction as it approaches the center of the coils, then reverse its magnetism to the opposite direction as it leaves from the other side of the coil. [ 2 ] Due to the hysteresis ( coercivity ) of the iron, a certain threshold magnetic field (the coercive field , H c ) is required to reverse the magnetization. So the magnetization in the moving wires does not reverse in the center of the device where the field reverses, but some way toward the departing side of the wires, when the field of the second magnet reaches H c . [ 1 ] [ 2 ] Although the wire itself is moving through the coil, in the absence of a radio signal the location where the magnetization "flips" is stationary with respect to the pickup coil, so there is no flux change and no voltage is induced in the pickup coil.
The radio signal from the antenna ( A ) is received by a tuner ( not shown ) and passed through the excitation coil C , the other end of which is connected to ground ( E ). [ 2 ] The rapidly reversing magnetic field from the coil exceeds the coercivity H c and cancels the hysteresis of the iron, causing the magnetization change to suddenly move up the wire to the center, between the magnets, where the field reverses. [ 1 ] [ 2 ] This had an effect similar to thrusting a magnet into the coil, causing the magnetic flux through the pickup coil D to change, inducing a current pulse in the pickup coil. The audio pickup coil is connected to a telephone receiver ( earphone ) ( T ) which converts the current pulse to sound . [ 2 ]
The radio signal from a spark gap transmitter consists of pulses of radio waves ( damped waves ) which repeat at an audio rate, around several hundred per second. Each pulse of radio waves produces a pulse of current in the earphone, [ 1 ] so the signal sounds like a musical tone or buzz in the earphone.
The iron band was turned by a mainspring and clockwork mechanism inside the case. Differing values have been given for the speed of the band, from 1.6 to 7.5 cm per second; the device could probably function over a wide range of band speeds. [ 8 ] The operator had to keep the mainspring wound up, using a crank on the side. Operators would sometimes forget to wind it, so the band would stop turning and the detector stop working, sometimes in the middle of a radio message.
The detector produced electronic noise that was heard in the earphone as a "hissing" or "roaring" sound in the background, somewhat fatiguing to listen to. [ 9 ] This was Barkhausen noise due to the Barkhausen effect in the iron. [ 9 ] As the magnetic field in a given area of the iron wire changed as it moved through the detector, the microscopic domain walls between magnetic domains in the iron moved in a series of jerks, as they got hung up on defects in the iron crystal lattice, then pulled free. Each jerk produced a tiny change in the magnetic field through the coil, and induced a pulse of noise.
Because the output was an audio alternating current and not a direct current , the detector could only be used with earphones and not with the common recording instrument used in coherer radiotelegraphy receivers, the siphon paper tape recorder. [ 10 ]
From a technical standpoint, several subtle prerequisites are necessary for operation. The strength of the magnetic field of the permanent magnets at the iron band must be of the same order of magnitude as the strength of the field generated by the radio frequency excitation coil, allowing the radio frequency signal to exceed the threshold hysteresis (coercivity) of the iron. Also, the impedance of the tuner that supplies the radio signal must be low to match the low impedance of the excitation coil, requiring special tuner design considerations. The impedance of the telephone earphone must roughly match the impedance of the audio pickup coil, which is a few hundred ohms. The iron band moves a few millimeters per second. The magnetic detector was much more sensitive than the coherers commonly in use at the time, [ 1 ] although not as sensitive as the Fleming valve , which began to replace it around 1912. [ 5 ]
In the Handbook Of Technical Instruction For Wireless Telegraphists by: J. C. Hawkhead (Second Edition Revised by H. M. Dowsett) on pp 175 are detailed instructions and specifications for operation and maintenance of Marconi's magnetic detector. | https://en.wikipedia.org/wiki/Magnetic_detector |
Magnetic deviation is the error induced in a compass by local magnetic fields , which must be allowed for, along with magnetic declination , if accurate bearings are to be calculated. (More loosely, "magnetic deviation" is used by some to mean the same as "magnetic declination". This article is about the former meaning.)
Compasses are used to determine the direction of true North . However, the compass reading must be corrected for two effects. The first is magnetic declination or variation—the angular difference between magnetic North (the local direction of the Earth's magnetic field ) and true North. [ 1 ] The second is magnetic deviation —the angular difference between magnetic North and the compass needle due to nearby sources of interference such as magnetically permeable bodies, or other magnetic fields within the field of influence. [ 2 ]
In navigation manuals, magnetic deviation refers specifically to compass error caused by magnetized iron within a ship or aircraft. [ 3 ] This iron has a mixture of permanent magnetization and an induced (temporary) magnetization that is induced by the Earth's magnetic field. Because the latter depends on the orientation of the craft relative to the Earth's field, it can be difficult to analyze and correct for it.
The deviation errors caused by magnetism in the ship's structure are minimised by precisely positioning small magnets and iron compensators close to the compass. To compensate for the induced magnetization, two magnetically soft iron spheres are placed on side arms. However, because the magnetic "signature" of every ship changes slowly with location, and with time, it is necessary to adjust the compensating magnets, periodically, to keep the deviation errors to a practical minimum. [ 4 ] Magnetic compass adjustment and correction is one of the subjects in the examination curriculum for a shipmaster's certificate of competency.
The sources of magnetic deviation vary from compass to compass or vehicle to vehicle. However, they are independent of location, and thus the compass can be calibrated to accommodate them.
Non-magnetic methods of taking bearings, such as with gyrocompass , astronomical observations , satellites (as GPS ) or radio navigation , are not subject to magnetic deviation. Thus, a comparison of bearings taken with such methods with the bearing given by a compass can be used to compute local magnetic deviation.
Sailing ships generally had two kinds of compasses: steering compasses , two of which would be mounted in a binnacle in front of the helm for use in maintaining a course; and a bearing compass that was used for taking the bearings of celestial objects, landmarks and the ship's wake. The latter could be moved around the ship, and it was soon observed that the bearing could vary from one part of the ship to another. The explorer Joao de Castro was the first to report such an inconsistency, in 1538, and attributed it to the ship's gun. Many other objects were found to be sources of deviation in ships, including iron particles in brass compass bowls; iron nails in a wooden compass box or binnacle; and metal parts of clothing. The two steering compasses themselves could interfere with each other if they were set too close together. [ 5 ] The "bearing compass" was eventually sited in a fixed position in a binnacle with, as far as possible, an all round view and acquired the name "standard compass". It would nonetheless have a different deviation from the "steering compass", so the compass heading shown on the "steering compass" would be different from the compass heading shown on the "standard compass".
The source of deviation could not always be identified. To reduce this source of error, which was due to induced magnetization in the ship, the surveyor John Churchman proposed a solution known as swinging the ship in 1794. This involved measuring the magnetic deviation as the ship was oriented in several compass directions. These measurements could then be used to correct compass readings. This procedure became standard practice in the 19th century as iron became an increasing component of ships. [ 5 ]
Once the compass has been corrected using small magnets fitted in the base and with soft iron balls, any residual deviation is recorded as a table or graph: the compass correction card, which is kept on board near the compass. [ 6 ]
Archibald Smith in 1862 published Admiralty Manual for ascertaining and applying the Deviations of the Compass caused by the Iron in a Ship . The key insight is that the deviation can be written as a Fourier series in the magnetic heading with terms up to the second frequency components. [ 1 ] This means that only five numbers are required to be estimated to determine the full deviation card. This method is still used by professional compass correctors who are employed to correct the compass and produce a deviation card. | https://en.wikipedia.org/wiki/Magnetic_deviation |
Magnetic dip , dip angle, or magnetic inclination is the angle made with the horizontal by Earth's magnetic field lines . This angle varies at different points on Earth's surface. Positive values of inclination indicate that the magnetic field of Earth is pointing downward, into Earth, at the point of measurement, and negative values indicate that it is pointing upward. The dip angle is in principle the angle made by the needle of a vertically held compass, though in practice ordinary compass needles may be weighted against dip or may be unable to move freely in the correct plane. The value can be measured more reliably with a special instrument typically known as a dip circle .
Dip angle was discovered by the German engineer Georg Hartmann in 1544. [ 1 ] A method of measuring it with a dip circle was described by Robert Norman in England in 1581. [ 2 ]
Magnetic dip results from the tendency of a magnet to align itself with lines of magnetic field. As Earth's magnetic field lines are not parallel to the surface, the north end of a compass needle will point upward in the Southern Hemisphere (negative dip) or downward in the Northern Hemisphere (positive dip). The range of dip is from -90 degrees (at the South Magnetic Pole ) to +90 degrees (at the North Magnetic Pole ). [ 3 ] Contour lines along which the dip measured at Earth's surface is equal are referred to as isoclinic lines . The locus of the points having zero dip is called the magnetic equator or aclinic line . [ 4 ]
The inclination I {\displaystyle I} is defined locally for the magnetic field due to Earth's core, and has a positive value if the field points below the horizontal (i.e. into Earth). Here we show how to determine the value of I {\displaystyle I} at a given latitude, following the treatment given by Fowler. [ 5 ]
Outside Earth's core we consider Maxwell's equations in a vacuum, ∇ × H c = 0 {\displaystyle \nabla \times {\textbf {H}}_{c}={\textbf {0}}} and ∇ ⋅ B c = 0 {\displaystyle \nabla \cdot {\textbf {B}}_{c}=0} where B c = μ 0 H c {\displaystyle {\textbf {B}}_{c}=\mu _{0}{\textbf {H}}_{c}} and the subscript c {\displaystyle c} denotes the core as the origin of these fields. The first means we can introduce the scalar potential ϕ c {\displaystyle \phi _{c}} such that H c = − ∇ ϕ c {\displaystyle {\textbf {H}}_{c}=-\nabla \phi _{c}} , while the second means the potential satisfies the Laplace equation ∇ 2 ϕ c = 0 {\displaystyle \nabla ^{2}\phi _{c}=0} .
Solving to leading order gives the magnetic dipole potential
ϕ c = m ⋅ r 4 π r 3 {\displaystyle \phi _{c}={\frac {{\textbf {m}}\cdot {\textbf {r}}}{4\pi r^{3}}}}
and hence the field
B c = − μ o ∇ ϕ c = μ o 4 π [ 3 r ^ ( r ^ ⋅ m ) − m r 3 ] {\displaystyle {\textbf {B}}_{c}=-\mu _{o}\nabla \phi _{c}={\frac {\mu _{o}}{4\pi }}{\big [}{\frac {3{\hat {\textbf {r}}}({\hat {\textbf {r}}}\cdot {\textbf {m}})-{\textbf {m}}}{r^{3}}}{\big ]}}
for magnetic moment m {\displaystyle {\textbf {m}}} and position vector r {\displaystyle {\textbf {r}}} on Earth's surface. From here it can be shown that the inclination I {\displaystyle I} as defined above satisfies (from tan I = B r / B θ {\displaystyle \tan I=B_{r}/B_{\theta }} )
tan I = 2 tan λ {\displaystyle \tan I=2\tan \lambda }
where λ {\displaystyle \lambda } is the latitude of the point on Earth's surface.
The phenomenon is especially important in aviation. Magnetic compasses on airplanes are made so that the center of gravity is significantly lower than the pivot point. As a result, the vertical component of the magnetic force is too weak to tilt the compass card significantly out of the horizontal plane, thus minimizing the dip angle shown in the compass. However, this also causes the airplane's compass to give erroneous readings during banked turns (turning error) and airspeed changes (acceleration error). [ 6 ]
Magnetic dip shifts the center of gravity of the compass card, causing temporary inaccurate readings when turning north or south. As the aircraft turns, the force that results from the magnetic dip causes the float assembly to swing in the same direction that the float turns. This compass error is amplified with the proximity to either magnetic pole. [ 6 ]
To compensate for turning errors, pilots in the Northern Hemisphere will have to "undershoot" the turn when turning north, stopping the turn prior to the compass rotating to the correct heading; and "overshoot" the turn when turning south by stopping later than the compass. The effect is the opposite in the Southern Hemisphere. [ 6 ]
The acceleration errors occur because the compass card tilts on its mount when under acceleration. [ 7 ] In the Northern Hemisphere, when accelerating on either an easterly or westerly heading, the error appears as a turn indication toward the north. When decelerating on either of these headings, the compass indicates a turn toward the south. [ 6 ] The effect is the opposite in the Southern Hemisphere.
Compass needles are often weighted during manufacture to compensate for magnetic dip, so that they will balance roughly horizontally. This balancing is latitude-dependent; see Compass balancing (magnetic dip) . | https://en.wikipedia.org/wiki/Magnetic_dip |
In electromagnetism , a magnetic dipole is the limit of either a closed loop of electric current or a pair of poles as the size of the source is reduced to zero while keeping the magnetic moment constant.
It is a magnetic analogue of the electric dipole , but the analogy is not perfect. In particular, a true magnetic monopole , the magnetic analogue of an electric charge , has never been observed in nature. However, magnetic monopole quasiparticles have been observed as emergent properties of certain condensed matter systems. [ 2 ] Moreover, one form of magnetic dipole moment is associated with a fundamental quantum property—the spin of elementary particles .
Because magnetic monopoles do not exist, the magnetic field at a large distance from any static magnetic source looks like the field of a dipole with the same dipole moment. For higher-order sources (e.g. quadrupoles ) with no dipole moment, their field decays towards zero with distance faster than a dipole field does.
In classical physics , the magnetic field of a dipole is calculated as the limit of either a current loop or a pair of charges as the source shrinks to a point while keeping the magnetic moment m constant. For the current loop, this limit is most easily derived from the vector potential : [ 3 ]
where μ 0 is the vacuum permeability constant and 4 π r 2 is the surface of a sphere of radius r .
The magnetic flux density (strength of the B-field) is then [ 3 ]
Alternatively one can obtain the scalar potential first from the magnetic pole limit,
and hence the magnetic field strength (or strength of the H-field) is
The magnetic field strength is symmetric under rotations about the axis of the magnetic moment.
In spherical coordinates, with z ^ = r ^ cos θ − θ ^ sin θ {\displaystyle \mathbf {\hat {z}} =\mathbf {\hat {r}} \cos \theta -{\boldsymbol {\hat {\theta }}}\sin \theta } , and with the magnetic moment aligned with the z-axis, then the field strength can more simply be expressed as
The two models for a dipole (current loop and magnetic poles), give the same predictions for the magnetic field far from the source. However, inside the source region they give different predictions. The magnetic field between poles is in the opposite direction to the magnetic moment (which points from the negative charge to the positive charge), while inside a current loop it is in the same direction (see the figure to the right (above for mobile users)). Clearly, the limits of these fields must also be different as the sources shrink to zero size. This distinction only matters if the dipole limit is used to calculate fields inside a magnetic material.
If a magnetic dipole is formed by making a current loop smaller and smaller, but keeping the product of current and area constant, the limiting field is
where δ ( r ) is the Dirac delta function in three dimensions. Unlike the expressions in the previous section, this limit is correct for the internal field of the dipole.
If a magnetic dipole is formed by taking a "north pole" and a "south pole", bringing them closer and closer together but keeping the product of magnetic pole-charge and distance constant, the limiting field is
These fields are related by B = μ 0 ( H + M ) , where
is the magnetization .
The force F exerted by one dipole moment m 1 on another m 2 separated in space by a vector r can be calculated using: [ 4 ]
or [ 5 ] [ 6 ]
where r is the distance between dipoles. The force acting on m 1 is in the opposite direction.
The torque can be obtained from the formula
The magnetic scalar potential ψ produced by a finite source, but external to it, can be represented by a multipole expansion . Each term in the expansion is associated with a characteristic moment and a potential having a characteristic rate of decrease with distance r from the source. Monopole moments have a 1/ r rate of decrease, dipole moments have a 1/ r 2 rate, quadrupole moments have a 1/ r 3 rate, and so on. The higher the order, the faster the potential drops off. Since the lowest-order term observed in magnetic sources is the dipole term, it dominates at large distances. Therefore, at large distances any magnetic source looks like a dipole of the same magnetic moment . | https://en.wikipedia.org/wiki/Magnetic_dipole |
Magnetic dipole–dipole interaction , also called dipolar coupling , refers to the direct interaction between two magnetic dipoles . Roughly speaking, the magnetic field of a dipole goes as the inverse cube of the distance, and the force of its magnetic field on another dipole goes as the first derivative of the magnetic field. It follows that the dipole-dipole interaction goes as the inverse fourth power of the distance.
Suppose m 1 and m 2 are two magnetic dipole moments that are far enough apart that they can be treated as point dipoles in calculating their interaction energy. The potential energy H of the interaction is then given by:
where μ 0 is the magnetic constant , r̂ is a unit vector parallel to the line joining the centers of the two dipoles, and | r | is the distance between the centers of m 1 and m 2 . Last term with δ {\displaystyle \delta } -function vanishes everywhere but the origin, and is necessary to ensure that ∇ ⋅ B {\displaystyle \nabla \cdot \mathbf {B} } vanishes everywhere. Alternatively, suppose γ 1 and γ 2 are gyromagnetic ratios of two particles with spin quanta S 1 and S 2 . (Each such quantum is some integral multiple of 1 / 2 .) Then:
where r ^ {\displaystyle {\hat {\mathbf {r} }}} is a unit vector in the direction of the line joining the two spins, and | r | is the distance between them.
Finally, the interaction energy can be expressed as the dot product of the moment of either dipole into the field from the other dipole:
where B 2 ( r 1 ) is the field that dipole 2 produces at dipole 1, and B 1 ( r 2 ) is the field that dipole 1 produces at dipole 2. It is not the sum of these terms.
The force F arising from the interaction between m 1 and m 2 is given by:
The Fourier transform of H can be calculated from the fact that
and is given by [ citation needed ]
The direct dipole-dipole coupling is very useful for molecular structural studies, since it depends only on known physical constants and the inverse cube of internuclear distance. Estimation of this coupling provides a direct spectroscopic route to the distance between nuclei and hence the geometrical form of the molecule, or additionally also on intermolecular distances in the solid state leading to NMR crystallography notably in amorphous materials.
For example, in water, NMR spectra of hydrogen atoms of water molecules are narrow lines because dipole coupling is averaged due to chaotic molecular motion. [ 1 ] In solids, where water molecules are fixed in their positions and do not participate in the diffusion mobility, the corresponding NMR spectra have the form of the Pake doublet . In solids with vacant positions, dipole coupling is averaged partially due to water diffusion which proceeds according to the symmetry of the solids and the probability distribution of molecules between the vacancies. [ 2 ]
Although internuclear magnetic dipole couplings contain a great deal of structural information, in isotropic solution, they average to zero as a result of diffusion. However, their effect on nuclear spin relaxation results in measurable nuclear Overhauser effects (NOEs).
The residual dipolar coupling (RDC) occurs if the molecules in solution exhibit a partial alignment leading to an incomplete averaging of spatially anisotropic magnetic interactions i.e. dipolar couplings. RDC measurement provides information on the global folding of the protein-long distance structural information. It also provides information about "slow" dynamics in molecules. | https://en.wikipedia.org/wiki/Magnetic_dipole–dipole_interaction |
The magnetic flux , represented by the symbol Φ , threading some contour or loop is defined as the magnetic field B multiplied by the loop area S , i.e. Φ = B ⋅ S . Both B and S can be arbitrary, meaning that the flux Φ can be as well but increments of flux can be quantized. The wave function can be multivalued as it happens in the Aharonov–Bohm effect or quantized as in superconductors . The unit of quantization is therefore called magnetic flux quantum .
The first to realize the importance of the flux quantum was Dirac in his publication on monopoles [ 1 ]
The phenomenon of flux quantization was predicted first by Fritz London then within the Aharonov–Bohm effect and later discovered experimentally in superconductors (see § Superconducting magnetic flux quantum below).
If one deals with a superconducting ring [ 5 ] (i.e. a closed loop path in a superconductor ) or a hole in a bulk superconductor , the magnetic flux threading such a hole/loop is quantized.
The (superconducting) magnetic flux quantum Φ 0 = h /(2 e ) ≈ 2.067 833 848 ... × 10 −15 Wb [ 3 ] is a combination of fundamental physical constants: the Planck constant h and the electron charge e .
Its value is, therefore, the same for any superconductor.
To understand this definition in the context of the Dirac flux quantum one shall consider that the effective quasiparticles active in a superconductors are Cooper pairs with an effective charge of 2 electrons q = 2 e .
The phenomenon of flux quantization was first discovered in superconductors experimentally by B. S. Deaver and W. M. Fairbank [ 6 ] and, independently, by R. Doll and M. Näbauer, [ 7 ] in 1961. The quantization of magnetic flux is closely related to the Little–Parks effect , [ 8 ] but was predicted earlier by Fritz London in 1948 using a phenomenological model . [ 9 ] [ 10 ]
The inverse of the flux quantum, 1/Φ 0 , is called the Josephson constant , and is denoted K J . It is the constant of proportionality of the Josephson effect , relating the potential difference across a Josephson junction to the frequency of the irradiation. The Josephson effect is very widely used to provide a standard for high-precision measurements of potential difference, which (from 1990 to 2019) were related to a fixed, conventional value of the Josephson constant, denoted K J-90 . With the 2019 revision of the SI , the Josephson constant has an exact value of K J = 483 597 .848 416 98 ... GHz⋅V −1 . [ 11 ]
The following physical equations use SI units. In CGS units, a factor of c would appear.
The superconducting properties in each point of the superconductor are described by the complex quantum mechanical wave function Ψ( r , t ) – the superconducting order parameter. As with any complex function, Ψ can be written as Ψ = Ψ 0 e iθ , where Ψ 0 is the amplitude and θ is the phase. Changing the phase θ by 2 πn will not change Ψ and, correspondingly, will not change any physical properties. However, in the superconductor of non-trivial topology, e.g. superconductor with the hole or superconducting loop/cylinder, the phase θ may continuously change from some value θ 0 to the value θ 0 + 2 πn as one goes around the hole/loop and comes to the same starting point. If this is so, then one has n magnetic flux quanta trapped in the hole/loop, [ 10 ] as shown below:
Per minimal coupling , the current density of Cooper pairs in the superconductor is: J = 1 2 m [ ( Ψ ∗ ( − i ℏ ∇ ) Ψ − Ψ ( − i ℏ ∇ ) Ψ ∗ ) − 2 q A | Ψ | 2 ] . {\displaystyle \mathbf {J} ={\frac {1}{2m}}\left[\left(\Psi ^{*}(-i\hbar \nabla )\Psi -\Psi (-i\hbar \nabla )\Psi ^{*}\right)-2q\mathbf {A} |\Psi |^{2}\right].} where q = 2 e is the charge of the Cooper pair.
The wave function is the Ginzburg–Landau order parameter : Ψ ( r ) = ρ ( r ) e i θ ( r ) . {\displaystyle \Psi (\mathbf {r} )={\sqrt {\rho (\mathbf {r} )}}\,e^{i\theta (\mathbf {r} )}.}
Plugged into the expression of the current, one obtains: J = ℏ m ( ∇ θ − q ℏ A ) ρ . {\displaystyle \mathbf {J} ={\frac {\hbar }{m}}\left(\nabla {\theta }-{\frac {q}{\hbar }}\mathbf {A} \right)\rho .}
Inside the body of the superconductor, the current density J is zero, and therefore ∇ θ = q ℏ A . {\displaystyle \nabla {\theta }={\frac {q}{\hbar }}\mathbf {A} .}
Integrating around the hole/loop using Stokes' theorem and ∇ × A = B gives: Φ B = ∮ A ⋅ d l = ℏ q ∮ ∇ θ ⋅ d l . {\displaystyle \Phi _{B}=\oint \mathbf {A} \cdot d\mathbf {l} ={\frac {\hbar }{q}}\oint \nabla {\theta }\cdot d\mathbf {l} .}
Now, because the order parameter must return to the same value when the integral goes back to the same point, we have: [ 12 ] Φ B = ℏ q 2 π = h 2 e . {\displaystyle \Phi _{B}={\frac {\hbar }{q}}2\pi ={\frac {h}{2e}}.}
Due to the Meissner effect , the magnetic induction B inside the superconductor is zero. More exactly, magnetic field H penetrates into a superconductor over a small distance called London's magnetic field penetration depth (denoted λ L and usually ≈ 100 nm). The screening currents also flow in this λ L -layer near the surface, creating magnetization M inside the superconductor, which perfectly compensates the applied field H , thus resulting in B = 0 inside the superconductor.
The magnetic flux frozen in a loop/hole (plus its λ L -layer) will always be quantized. However, the value of the flux quantum is equal to Φ 0 only when the path/trajectory around the hole described above can be chosen so that it lays in the superconducting region without screening currents, i.e. several λ L away from the surface. There are geometries where this condition cannot be satisfied, e.g. a loop made of very thin ( ≤ λ L ) superconducting wire or the cylinder with the similar wall thickness. In the latter case, the flux has a quantum different from Φ 0 .
The flux quantization is a key idea behind a SQUID , which is one of the most sensitive magnetometers available.
Flux quantization also plays an important role in the physics of type II superconductors . When such a superconductor (now without any holes) is placed in a magnetic field with the strength between the first critical field H c1 and the second critical field H c2 , the field partially penetrates into the superconductor in a form of Abrikosov vortices . The Abrikosov vortex consists of a normal core – a cylinder of the normal (non-superconducting) phase with a diameter on the order of the ξ , the superconducting coherence length . The normal core plays a role of a hole in the superconducting phase. The magnetic field lines pass along this normal core through the whole sample. The screening currents circulate in the λ L -vicinity of the core and screen the rest of the superconductor from the magnetic field in the core. In total, each such Abrikosov vortex carries one quantum of magnetic flux Φ 0 .
Prior to the 2019 revision of the SI , the magnetic flux quantum was measured with great precision by exploiting the Josephson effect . When coupled with the measurement of the von Klitzing constant R K = h / e 2 , this provided the most accurate values of the Planck constant h obtained until 2019. This may be counterintuitive, since h is generally associated with the behaviour of microscopically small systems, whereas the quantization of magnetic flux in a superconductor and the quantum Hall effect are both emergent phenomena associated with thermodynamically large numbers of particles.
As a result of the 2019 revision of the SI , the Planck constant h has a fixed value h = 6.626 070 15 × 10 −34 J⋅Hz −1 , [ 13 ] which, together with the definitions of the second and the metre , provides the official definition of the kilogram . Furthermore, the elementary charge also has a fixed value of e = 1.602 176 634 × 10 −19 C [ 14 ] to define the ampere . Therefore, both the Josephson constant K J = 2 e / h and the von Klitzing constant R K = h / e 2 have fixed values, and the Josephson effect along with the von Klitzing quantum Hall effect becomes the primary mise en pratique [ 15 ] for the definition of the ampere and other electric units in the SI. | https://en.wikipedia.org/wiki/Magnetic_flux_quantum |
In plasma physics , magnetic helicity is a measure of the linkage, twist, and writhe of a magnetic field . [ 1 ] [ 2 ]
Magnetic helicity is a useful concept in the analysis of systems with extremely low resistivity, such as astrophysical systems. When resistivity is low, magnetic helicity is conserved over longer timescales, to a good approximation. Magnetic helicity dynamics are particularly important in analyzing solar flares and coronal mass ejections . [ 3 ] Magnetic helicity is relevant in the dynamics of the solar wind . [ 4 ] Its conservation is significant in dynamo processes, and it also plays a role in fusion research , such as reversed field pinch experiments. [ 5 ] [ 6 ] [ 7 ] [ 8 ] [ 9 ]
When a magnetic field contains magnetic helicity, it tends to form large-scale structures from small-scale ones. [ 10 ] This process can be referred to as an inverse transfer in Fourier space . This property of increasing the scale of structures makes magnetic helicity special in three dimensions, as other three-dimensional flows in ordinary fluid mechanics are the opposite, being turbulent and having the tendency to "destroy" structure, in the sense that large-scale vortices break up into smaller ones, until dissipating through viscous effects into heat. Through a parallel but inverted process, the opposite happens for magnetic vortices, where small helical structures with non-zero magnetic helicity combine and form large-scale magnetic fields. This is visible in the dynamics of the heliospheric current sheet , [ 11 ] a large magnetic structure in the Solar System .
Generally, the helicity H f {\displaystyle H^{\mathbf {f} }} of a smooth vector field f {\displaystyle \mathbf {f} } confined to a volume V {\displaystyle V} is the standard measure of the extent to which the field lines wrap and coil around one another. [ 12 ] [ 2 ] It is defined as the volume integral over V {\displaystyle V} of the scalar product of f {\displaystyle \mathbf {f} } and its curl , ∇ × f {\displaystyle \nabla \times {\mathbf {f} }} :
Magnetic helicity H M {\displaystyle H^{\mathbf {M} }} is the helicity of a magnetic vector potential A {\displaystyle {\mathbf {A} }} where ∇ × A = B {\displaystyle \nabla \times {\mathbf {A} }={\mathbf {B} }} is the associated magnetic field confined to a volume V {\displaystyle V} . Magnetic helicity can then be expressed as [ 5 ]
Since the magnetic vector potential is not gauge invariant , the magnetic helicity is also not gauge invariant in general. As a consequence, the magnetic helicity of a physical system cannot be measured directly. In certain conditions and under certain assumptions, one can however measure the current helicity of a system and from it, when further conditions are fulfilled and under further assumptions, deduce the magnetic helicity. [ 13 ]
Magnetic helicity has units of magnetic flux squared: Wb 2 ( webers squared) in SI units and Mx 2 ( maxwells squared) in Gaussian Units . [ 14 ]
The current helicity, or helicity M J {\displaystyle M^{\mathbf {J} }} of the magnetic field B {\displaystyle \mathbf {B} } confined to a volume V {\displaystyle V} , can be expressed as
where J = ∇ × B {\displaystyle {\mathbf {J} }=\nabla \times {\mathbf {B} }} is the current density . [ 15 ] Unlike magnetic helicity, current helicity is not an ideal invariant (it is not conserved even when the electrical resistivity is zero).
Magnetic helicity is a gauge-dependent quantity, because A {\displaystyle \mathbf {A} } can be redefined by adding a gradient to it ( gauge choosing ). However, for perfectly conducting boundaries or periodic systems without a net magnetic flux, the magnetic helicity contained in the whole domain is gauge invariant, [ 15 ] that is, independent of the gauge choice. A gauge-invariant relative helicity has been defined for volumes with non-zero magnetic flux on their boundary surfaces. [ 11 ]
The name "helicity" is because the trajectory of a fluid particle in a fluid with velocity v {\displaystyle {\boldsymbol {v}}} and vorticity ω = ∇ × v {\displaystyle {\boldsymbol {\omega }}=\nabla \times {\boldsymbol {v}}} forms a helix in regions where the kinetic helicity H K = ∫ v ⋅ ω ≠ 0 {\displaystyle \textstyle H^{K}=\int \mathbf {v} \cdot {\boldsymbol {\omega }}\neq 0} . When H K > 0 {\displaystyle \textstyle H^{K}>0} , the resulting helix is right-handed and when H K < 0 {\displaystyle \textstyle H^{K}<0} it is left-handed. This behavior is very similar to that found concerning magnetic field lines.
Regions where magnetic helicity is not zero can also contain other sorts of magnetic structures, such as helical magnetic field lines. Magnetic helicity is a continuous generalization of the topological concept of linking number to the differential quantities required to describe the magnetic field. [ 11 ] Where linking numbers describe how many times curves are interlinked, magnetic helicity describes how many magnetic field lines are interlinked. [ 5 ]
Magnetic helicity is proportional to the sum of the topological quantities twist and writhe for magnetic field lines. The twist is the rotation of the flux tube around its axis, and writhe is the rotation of the flux tube axis itself. Topological transformations can change twist and writhe numbers, but conserve their sum. As magnetic flux tubes (collections of closed magnetic field line loops) tend to resist crossing each other in magnetohydrodynamic fluids, magnetic helicity is very well-conserved.
As with many quantities in electromagnetism, magnetic helicity is closely related to fluid mechanical helicity , the corresponding quantity for fluid flow lines, and their dynamics are interlinked. [ 10 ] [ 16 ]
In the late 1950s, Lodewijk Woltjer and Walter M. Elsässer discovered independently the ideal invariance of magnetic helicity, [ 17 ] [ 18 ] that is, its conservation when resistivity is zero. Woltjer's proof, valid for a closed system, is repeated in the following:
In ideal magnetohydrodynamics , the time evolution of a magnetic field and magnetic vector potential can be expressed using the induction equation as
respectively, where ∇ Φ {\displaystyle \nabla \Phi } is a scalar potential given by the gauge condition (see § Gauge considerations ). Choosing the gauge so that the scalar potential vanishes, ∇ Φ = 0 {\displaystyle \nabla \Phi =\mathbf {0} } , the time evolution of magnetic helicity in a volume V {\displaystyle V} is given by:
The dot product in the integrand of the first term is zero since B {\displaystyle {\mathbf {B} }} is orthogonal to the cross product v × B {\displaystyle {\mathbf {v} }\times {\mathbf {B} }} , and the second term can be integrated by parts to give
where the second term is a surface integral over the boundary surface ∂ V {\displaystyle \partial V} of the closed system. The dot product in the integrand of the first term is zero because ∇ × A = B {\displaystyle \nabla \times {\mathbf {A} }={\mathbf {B} }} is orthogonal to ∂ A / ∂ t . {\displaystyle \partial {\mathbf {A} }/\partial t.} The second term also vanishes because motions inside the closed system cannot affect the vector potential outside, so that at the boundary surface ∂ A / ∂ t = 0 {\displaystyle \partial {\mathbf {A} }/\partial t=\mathbf {0} } since the magnetic vector potential is a continuous function. Therefore,
and magnetic helicity is ideally conserved. In all situations where magnetic helicity is gauge invariant, magnetic helicity is ideally conserved without the need for the specific gauge choice ∇ Φ = 0 . {\displaystyle \nabla \Phi =\mathbf {0} .}
Magnetic helicity remains conserved in a good approximation even with a small but finite resistivity, in which case magnetic reconnection dissipates energy . [ 11 ] [ 5 ]
Small-scale helical structures tend to form larger and larger magnetic structures. This can be called an inverse transfer in Fourier space, as opposed to the (direct) energy cascade in three-dimensional turbulent hydrodynamical flows. The possibility of such an inverse transfer was first proposed by Uriel Frisch and collaborators [ 10 ] and has been verified through many numerical experiments. [ 19 ] [ 20 ] [ 21 ] [ 22 ] [ 23 ] [ 24 ] As a consequence, the presence of magnetic helicity is a possibility to explain the existence and sustainment of large-scale magnetic structures in the Universe.
An argument for this inverse transfer taken from [ 10 ] is repeated here, which is based on the so-called "realizability condition" on the magnetic helicity Fourier spectrum H ^ k M = A ^ k ∗ ⋅ B ^ k {\displaystyle {\hat {H}}_{\mathbf {k} }^{M}={\hat {\mathbf {A} }}_{\mathbf {k} }^{*}\cdot {\hat {\mathbf {B} }}_{\mathbf {k} }} (where B ^ k {\displaystyle {\hat {\mathbf {B} }}_{\mathbf {k} }} is the Fourier coefficient at the wavevector k {\displaystyle {\mathbf {k} }} of the magnetic field B {\displaystyle {\mathbf {B} }} , and similarly for A ^ {\displaystyle {\hat {\mathbf {A} }}} , the star denoting the complex conjugate ). The "realizability condition" corresponds to an application of Cauchy-Schwarz inequality , which yields: | H ^ k M | ≤ 2 E k M | k | , {\displaystyle \left|{\hat {H}}_{\mathbf {k} }^{M}\right|\leq {\frac {2E_{\mathbf {k} }^{M}}{|{\mathbf {k} }|}},} with E k M = 1 2 B ^ k ∗ ⋅ B ^ k {\textstyle E_{\mathbf {k} }^{M}={\frac {1}{2}}{\hat {\mathbf {B} }}_{\mathbf {k} }^{*}\cdot {\hat {\mathbf {B} }}_{\mathbf {k} }} the magnetic energy spectrum. To obtain this inequality, the fact that | B ^ k | = | k | | A ^ k ⊥ | {\displaystyle |{\hat {\mathbf {B} }}_{\mathbf {k} }|=|{\mathbf {k} }||{\hat {\mathbf {A} }}_{\mathbf {k} }^{\perp }|} (with A ^ k ⊥ {\displaystyle {\hat {\mathbf {A} }}_{\mathbf {k} }^{\perp }} the solenoidal part of the Fourier transformed magnetic vector potential, orthogonal to the wavevector in Fourier space) has been used, since B ^ k = i k × A ^ k {\displaystyle {\hat {\mathbf {B} }}_{\mathbf {k} }=i{\mathbf {k} }\times {\hat {\mathbf {A} }}_{\mathbf {k} }} . The factor 2 is not present in the paper [ 10 ] since the magnetic helicity is defined there alternatively as 1 2 ∫ V A ⋅ B d V {\displaystyle {\frac {1}{2}}\int _{V}{\mathbf {A} }\cdot {\mathbf {B} }\ dV} .
One can then imagine an initial situation with no velocity field and a magnetic field only present at two wavevectors p {\displaystyle \mathbf {p} } and q {\displaystyle \mathbf {q} } . We assume a fully helical magnetic field, which means that it saturates the realizability condition: | H ^ p M | = 2 E p M | p | {\displaystyle \left|{\hat {H}}_{\mathbf {p} }^{M}\right|={\frac {2E_{\mathbf {p} }^{M}}{|{\mathbf {p} }|}}} and | H ^ q M | = 2 E q M | q | {\displaystyle \left|{\hat {H}}_{\mathbf {q} }^{M}\right|={\frac {2E_{\mathbf {q} }^{M}}{|{\mathbf {q} }|}}} . Assuming that all the energy and magnetic helicity transfers are done to another wavevector k {\displaystyle \mathbf {k} } , the conservation of magnetic helicity on the one hand and of the total energy E T = E M + E K {\displaystyle E^{T}=E^{M}+E^{K}} (the sum of magnetic and kinetic energy) on the other hand gives:
H k M = H p M + H q M , {\displaystyle H_{\mathbf {k} }^{M}=H_{\mathbf {p} }^{M}+H_{\mathbf {q} }^{M},}
E k T = E p T + E q T = E p M + E q M . {\displaystyle E_{\mathbf {k} }^{T}=E_{\mathbf {p} }^{T}+E_{\mathbf {q} }^{T}=E_{\mathbf {p} }^{M}+E_{\mathbf {q} }^{M}.}
The second equality for energy comes from the fact that we consider an initial state with no kinetic energy. Then we have the necessarily | k | ≤ max ( | p | , | q | ) {\displaystyle |\mathbf {k} |\leq \max(|\mathbf {p} |,|\mathbf {q} |)} . Indeed, if we would have | k | > max ( | p | , | q | ) {\displaystyle |\mathbf {k} |>\max(|\mathbf {p} |,|\mathbf {q} |)} , then:
H k M = H p M + H q M = 2 E p M | p | + 2 E q M | q | > 2 ( E p M + E q M ) | k | = 2 E k T | k | ≥ 2 E k M | k | , {\displaystyle H_{\mathbf {k} }^{M}=H_{\mathbf {p} }^{M}+H_{\mathbf {q} }^{M}={\frac {2E_{\mathbf {p} }^{M}}{|\mathbf {p} |}}+{\frac {2E_{\mathbf {q} }^{M}}{|\mathbf {q} |}}>{\frac {2\left(E_{\mathbf {p} }^{M}+E_{\mathbf {q} }^{M}\right)}{|\mathbf {k} |}}={\frac {2E_{\mathbf {k} }^{T}}{|\mathbf {k} |}}\geq {\frac {2E_{\mathbf {k} }^{M}}{|\mathbf {k} |}},}
which would break the realizability condition. This means that | k | ≤ max ( | p | , | q | ) {\displaystyle |\mathbf {k} |\leq \max(|\mathbf {p} |,|\mathbf {q} |)} . In particular, for | p | = | q | {\displaystyle |{\mathbf {p} }|=|{\mathbf {q} }|} , the magnetic helicity is transferred to a smaller wavevector, which means to larger scales. | https://en.wikipedia.org/wiki/Magnetic_helicity |
Magnetic hysteresis occurs when an external magnetic field is applied to a ferromagnet such as iron and the atomic dipoles align themselves with it. Even when the field is removed, part of the alignment will be retained: the material has become magnetized . Once magnetized, the magnet will stay magnetized indefinitely. To demagnetize it requires heat or a magnetic field in the opposite direction. This is the effect that provides the element of memory in a hard disk drive .
The relationship between field strength H and magnetization M is not linear in such materials. If a magnet is demagnetized ( H = M = 0 ) and the relationship between H and M is plotted for increasing levels of field strength, M follows the initial magnetization curve . This curve increases rapidly at first and then approaches an asymptote called magnetic saturation . If the magnetic field is now reduced monotonically, M follows a different curve. At zero field strength, the magnetization is offset from the origin by an amount called the remanence . If the H - M relationship is plotted for all strengths of applied magnetic field the result is a hysteresis loop called the main loop . The width of the middle section along the H axis is twice the coercivity of the material. [ 1 ] : Chapter 1
A closer look at a magnetization curve generally reveals a series of small, random jumps in magnetization called Barkhausen jumps . This effect is due to crystallographic defects such as dislocations . [ 1 ] : Chapter 15
Magnetic hysteresis loops are not exclusive to materials with ferromagnetic ordering. Other magnetic orderings, such as spin glass ordering, also exhibit this phenomenon. [ 2 ]
The phenomenon of hysteresis in ferromagnetic materials is the result of two effects: rotation of magnetization and changes in size or number of magnetic domains . In general, the magnetization varies (in direction but not magnitude) across a magnet, but in sufficiently small magnets, it doesn't. In these single-domain magnets, the magnetization responds to a magnetic field by rotating. Single-domain magnets are used wherever a strong, stable magnetization is needed (for example, magnetic recording ).
Larger magnets are divided into regions called domains . Within each domain, the magnetization does not vary; but between domains are relatively thin domain walls in which the direction of magnetization rotates from the direction of one domain to another. If the magnetic field changes, the walls move, changing the relative sizes of the domains. Because the domains are not magnetized in the same direction, the magnetic moment per unit volume is smaller than it would be in a single-domain magnet; but domain walls involve rotation of only a small part of the magnetization, so it is much easier to change the magnetic moment. The magnetization can also change by addition or subtraction of domains (called nucleation and denucleation ).
Magnetic hysteresis can be characterized in various ways. In general, the magnetic material is placed in a varying applied H field, as induced by an electromagnet, and the resulting magnetic flux density ( B field) is measured, generally by the inductive electromotive force introduced on a pickup coil nearby the sample. This produces the characteristic B - H curve; because the hysteresis indicates a memory effect of the magnetic material, the shape of the B - H curve depends on the history of changes in H .
Alternatively, the hysteresis can be plotted as magnetization M in place of B , giving an M - H curve. These two curves are directly related since B = μ 0 ( H + M ) {\displaystyle B=\mu _{0}(H+M)} .
The measurement may be closed-circuit or open-circuit , according to how the magnetic material is placed in a magnetic circuit .
With hard magnetic materials (such as sintered neodymium magnets ), the detailed microscopic process of magnetization reversal depends on whether the magnet is in an open-circuit or closed-circuit configuration, since the magnetic medium around the magnet influences the interactions between domains in a way that cannot be fully captured by a simple demagnetization factor. [ 3 ]
The most known empirical models in hysteresis are Preisach and Jiles-Atherton models . These models allow an accurate modeling of the hysteresis loop and are widely used in the industry.
However, these models lose the connection with thermodynamics and the energy consistency is not ensured. A more recent model, with a more consistent thermodynamic foundation, is the vectorial incremental nonconservative consistent hysteresis (VINCH) model of Lavet et al. (2011). is inspired by the kinematic hardening laws and by the thermodynamics of irreversible processes . [ 4 ] In particular, in addition to provide an accurate modeling, the stored magnetic energy and the dissipated energy are known at all times. The obtained incremental formulation is variationally consistent, i.e., all internal variables follow from the minimization of a thermodynamic potential. That allows easily obtaining a vectorial model while Preisach and Jiles-Atherton are fundamentally scalar models.
The Stoner–Wohlfarth model is a physical model explaining hysteresis in terms of anisotropic response ("easy" / "hard" axes of each crystalline grain).
Micromagnetics simulations attempt to capture and explain in detail the space and time aspects of interacting magnetic domains, often based on the Landau-Lifshitz-Gilbert equation .
Toy models such as the Ising model can help explain qualitative and thermodynamic aspects of hysteresis (such as the Curie point phase transition to paramagnetic behaviour), though they are not used to describe real magnets.
There are a great variety in applications of the theory of hysteresis in magnetic materials. Many of these make use of their ability to retain a memory, for example magnetic tape , hard disks , and credit cards . In these applications, hard magnets (high coercivity) like iron are desirable so the memory is not easily erased.
Soft magnets (low coercivity) are used as cores in transformers and electromagnets . The response of the magnetic moment to a magnetic field boosts the response of the coil wrapped around it. Low coercivity reduces that energy loss associated with hysteresis.
Magnetic hysteresis material (soft nickel-iron rods) has been used in damping the angular motion of satellites in low Earth orbit since the dawn of the space age. [ 5 ] | https://en.wikipedia.org/wiki/Magnetic_hysteresis |
Magnetic immunoassay ( MIA ) is a type of diagnostic immunoassay using magnetic beads as labels in lieu of conventional enzymes ( ELISA ), radioisotopes ( RIA ) or fluorescent moieties ( fluorescent immunoassays ) [ 1 ] to detect a specified analyte . MIA involves the specific binding of an antibody to its antigen, where a magnetic label is conjugated to one element of the pair. The presence of magnetic beads is then detected by a magnetic reader ( magnetometer ) which measures the magnetic field change induced by the beads. The signal measured by the magnetometer is proportional to the analyte (virus, toxin, bacteria, cardiac marker, etc.) concentration in the initial sample.
Magnetic beads are made of nanometric-sized iron oxide particles encapsulated or glued together with polymers. These magnetic beads range from 35 nm up to 4.5 μm. The component magnetic nanoparticles range from 5 to 50 nm and exhibit a unique quality referred to as superparamagnetism in the presence of an externally applied magnetic field. [ 2 ] First discovered by Frenchman Louis Néel , Nobel Physics Prize winner in 1970, this superparamagnetic quality has already been used for medical application in Magnetic Resonance Imaging (MRI) and in biological separations, but not yet for labeling in commercial diagnostic applications.
Magnetic labels exhibit several features very well adapted for such applications: [ citation needed ]
Magnetic Immunoassay (MIA) is able to detect select molecules or pathogens through the use of a magnetically tagged antibody. Functioning in a way similar to that of an ELISA or Western Blot, a two-antibody binding process is used to determine concentrations of analytes. MIA uses antibodies that are coating a magnetic bead. These anti-bodies directly bind to the desired pathogen or molecule and the magnetic signal given off the bound beads is read using a magnetometer. The largest benefit this technology provides for immunostaining is that it can be conducted in a liquid medium, where methods such as ELISA or Western Blotting require a stationary medium for the desired target to bind to before the secondary antibody (such as HRP [Horse Radish Peroxidase]) is able to be applied. Since MIA can be conducted in a liquid medium a more accurate measurement of desired molecules can be performed in the model system. Since no isolation must occur to achieve quantifiable results users can monitor activity within a system. Getting a better idea of the behavior of their target. [ citation needed ]
The manners in which this detection can occur are very numerous. The most basic form of detection is to run a sample through a gravity column that contains a polyethylene matrix with the secondary anti-body. The target compound binds to the antibody contained in the matrix, and any residual substances are washed out using a chosen buffer. The magnetic antibodies are then passed through the same column and after an incubation period, any unbound antibodies are washed out using the same method as before. The reading obtained from the magnetic beads bound to the target which is captured by the antibodies on the membrane is used to quantify the target compound in solution. [ citation needed ]
Also, because it is so similar in methodology to ELISA or Western Blot the experiments for MIA can be adapted to use the same detection if the researcher wants to quantify their data in a similar manner.
A simple instrument can detect the presence and measure the total magnetic signal of a sample, however, the challenge of developing an effective MIA is to separate naturally occurring magnetic background (noise) from the weak magnetically labeled target (signal). Various approaches and devices have been employed to achieve a meaningful signal-to-noise ratio (SNR) for bio-sensing applications: [ citation needed ]
But improving SNR often requires a complex instrument to provide repeated scanning and extrapolation through data processing, or precise alignment of target and sensor of miniature and matching size. Beyond this requirement, MIA that exploits the non-linear magnetic properties of magnetic labels [ citation needed ] can effectively use the intrinsic ability of a magnetic field to pass through plastic, water, nitrocellulose , and other materials, thus allowing for true volumetric measurements in various immunoassay formats. Unlike conventional methods that measure the susceptibility of superparamagnetic materials, a MIA-based on non-linear magnetization eliminates the impact of linear dia- or paramagnetic materials such as sample matrix, consumable plastics and/or nitrocellulose. Although the intrinsic magnetism of these materials is very weak, with typical susceptibility values of –10 −5 (dia) or +10 −3 (para), when one is investigating very small quantities of superparamagnetic materials, such as nanograms per test, the background signal generated by ancillary materials cannot be ignored. In MIA based on non-linear magnetic properties of magnetic labels the beads are exposed to an alternating magnetic field at two frequencies, f1 and f2. In the presence of non-linear materials such as superparamagnetic labels, a signal can be recorded at combinatorial frequencies, for example, at f = f1 ± 2×f2. This signal is exactly proportional to the amount of magnetic material inside the reading coil.
This technology makes magnetic immunoassay possible in a variety of formats such as:
It was also described for in vivo applications [ 4 ] and for multiparametric testing.
MIA is a versatile technique that can be used for a wide variety of practices.
Currently it has been used to detect viruses in plants to catch pathogens that would normally devastate crops such as Grapevine fanleaf virus , [ 5 ] [ full citation needed ] and Potato virus X . Its adaptations now include portable devices that allow the user to gather sensitive data in the field. [ 6 ] [ full citation needed ]
MIA can also be used to monitor therapeutic drugs. A case report of a 53-year-old [ 7 ] [ full citation needed ] kidney transplant patient details how the doctors were able to alter the quantities of the therapeutic drug. | https://en.wikipedia.org/wiki/Magnetic_immunoassay |
In the context of nuclear magnetic resonance (NMR), the term magnetic inequivalence refers to the distinction between magnetically active nuclear spins by their NMR signals, owing to a difference in either chemical shift ( magnetic inequivalence by the chemical shift criterion ) or spin–spin coupling ( J-coupling ) ( magnetic inequivalence by the coupling criterion ). Since chemically inequivalent spins (i.e. nuclei not related by symmetry) are expected to also be magnetically distinct (barring accidental overlap of signals), and since an observed difference in chemical shift makes their inequivalence clear, the term magnetic inequivalence most commonly refers solely to the latter type, i.e. to situations of chemically equivalent spins differing in their coupling relationships.
This situation can arise in a number of ways and can give rise to complexities in the corresponding NMR signals (beyond what a first-order analysis would handle) that range from the unnoticeable to the dramatic.
Two (or more) chemically equivalent (symmetry-related) spins will have the same chemical shift, but those that have a different coupling relationship to the same coupling partner are magnetically inequivalent by the coupling criterion. This occurs in molecules bearing two (or more) chemically distinct groups of symmetry-related nuclei, with just one element of symmetry relating them. [ 1 ] Most commonly, two chemically inequivalent pairs of hydrogen nuclei ( protons ) are involved, although other magnetically active nuclei will also show this phenomenon, and the spin system is often labelled an AA′BB′ system. Additional coupling partners may also be present, but it is the two A/A′ and B/B′ signals (at different chemical shifts) that are said to show magnetic inequivalence between the symmetry-related A and A′ (or B and B′) pairs at the same chemical shift. If the chemical shift difference (ν A −ν B ) is large compared to the largest coupling constant , the spin system may be designated AA′XX′.
Magnetic inequivalence may occur with two symmetry-related H A -C-C-H B fragments (where the different subscripts indicate chemical inequivalence) that may or may not be contiguous. In order to distinguish the resulting coupling relationships, the symmetry-related pair would be labelled H A′ -C-C-H B′ .
H-3 and H-6 in any 1,2-homodisubstituted benzene are related by a mirror plane of symmetry bisecting the 1,2 and 4,5 C-C bonds. They are therefore chemically equivalent (and magnetically equivalent by the chemical shift criterion) but, because they have different spatial and connectivity relations to H-4 (with 3-bond vs. 4-bond couplings of different strengths), they are magnetically inequivalent by the coupling criterion. The same is true with respect to their coupling relationships with H-5. Similarly, H-4 and H-5 are chemically equivalent but magnetically inequivalent owing to their different coupling relationships with H-3 (or H-6).
A classic example showing highly complex splitting is that of 1,2-dichlorobenzene. The two signals are nearly mirror-symmetrical. In 1,2-diaminobenzene ( ortho -phenylenediamine ), the two signals have nearly the same chemical shift, so that the resultant signals form a complex multiplet.
H-2 and H-6 in any 1,4-heterodisubstituted benzene are related by a mirror plane of symmetry passing through C-1 and C-4. They are therefore chemically equivalent (and magnetically equivalent by the chemical shift criterion) but, because they have different spatial and connectivity relations to H-3 (with 3-bond vs. 5-bond coupling constants of different strengths), they are magnetically inequivalent by the coupling criterion. The same is true with respect to their coupling relationships with H-5. Similarly, H-3 and H-5 are chemically equivalent but magnetically inequivalent owing to their different coupling relationships with H-2 (or H-6).
An example is provided by 4-nitroaniline. Although each signal retains the gross doublet shape predicted by first-order analysis, a close-up view of each reveals additional peaks.
Any 4-substituted pyridine , pyridine itself, 1-substituted pyrazinium ion, diazine , 1-substituted or unsubstituted pyrrole and related aromatic heterocyclics ( phospholes , furan , thiophene , etc. ) as well as unsubstituted or 1-substituted cyclopentadienes and 1-substituted cyclopentadienides all have the same symmetry framework as para-disubstituted or ortho-homodisubstituted benzenes, and will present chemically equivalent but magnetically inequivalent pairs of protons. In heterocycles and in five-membered rings in general, however, 3 J values can be significantly smaller than in benzenes and the manifestation of magnetic inequivalence may be subtle.
The rarer seven-membered and higher ring systems may also show the same symmetry property, as can linked and fused aromatic ring systems such as biphenyls , naphthalenes and isoindoles . Similarly, 1-H benzimidazoles have the appropriate symmetry if N 1 -deprotonated or N 3 -protonated, or as a result of rapid tautomerization of the neutral form (for instance, in DMSO- d 6 ) where the signals greatly resemble those of 1,2-dichlorobenzene.
The occurrence of symmetry-related pairs of H A -C-C-H B fragments is not limited to aromatic systems. For instance, magnetic inequivalence is found in 1,4-homodisubstituted butadienes. [ 2 ] It might be expected in a molecule such as a symmetrical 2,3,4,5-tetrasubstituted pyrrolidine , but less rigid and less flat sp 3 frameworks tend to show very weak long-range couplings (through 4 or more bonds) so as to not manifest much sign of magnetic inequivalence. Reich gives several additional examples of magnetic inequivalence in non-aromatic H-C-C-H pairs. [ 3 ]
Magnetic inequivalence may occur with H 2 C-CH 2 fragments that are subdivided into two groups of two in either geminal relationships via a mirror plane along the C-C bond, i.e. H A H A′ C-CH B H B′ , or in vicinal relationships via a mirror plane bisecting the C-C bond, i.e. in H A H B C-CH A′ H B′ , [ 4 ] or via a rotational axis of symmetry (a C 2 -axis), i.e. H A H B C-CH B′ H A′ . The coupling constants then differ because of geometry ( cis vs. trans ) or connectivity (2-bond vs. 3-bond) and the level of complexity will depend on the differences. Conformational dynamics may reduce or even obliterate the difference between cis and trans couplings, if fast compared to the NMR timescale. There may also be additional couplings to other nuclei.
The ethylene fragment in 2-substituted dioxolanes can thus show a high level of complexity if the substituent is large. Symmetrical norbornanes and similarly rigid compounds ( e.g. 7-oxabicyclo[2.2.1]heptane) also show complex signals for the ethylene fragments, made more complicated by additional splitting by the bridgehead protons. Reich gives several additional examples of magnetic inequivalence in acyclic and cyclic systems containing H 2 C-CH 2 fragments. [ 3 ]
Any pair of symmetry-related X-C-C-Y fragments (where X and Y are different magnetically active nuclei) as well as XYC-CXY ( cis or trans ) and X 2 C-CY 2 fragments may show magnetic inequivalence when the heteronuclear coupling constants ( 2 J XY or 3 J XY ) are non-negligible. In principle, the magnetically active nuclei may also be disposed on non- carbon atoms.
A classic example is the 1 H-NMR spectrum of 1,1-difluoroethylene . [ 5 ] The single 1 H-NMR signal is made complex by the 2 J H-H and two different 3 J H-F splittings. The 19 F-NMR spectrum will look identical. The other two difluoroethylene isomers give similarly complex spectra. [ 6 ]
Whereas a four-spin AA′BB′ (or AA′XX′) system may have the requisite symmetry and coupling properties, its signals may show more or less complexity and, as with other coupling phenomena, the appearance of a signal from magnetically inequivalent nuclei will also depend on the instrumental field strength. A large number of such systems show less complexity, with fewer lines than is possible, particularly when the instrumental resolution is low, whence nearby peaks appear to coalesce, when J AB ≈ J A′B′ , when J AB ≈ − J AB′ , when J AA′ ≈ J BB′ or when J BB′ ≈ 0. The apparent complexity is also diminished in AA′XX′ systems when ν A −ν X >> J AX . [ 3 ] This kind of simplication is enhanced as the instrumental magnetic field is increased, since the field-independent differences between coupling constants or between a coupling constant and zero appear proportionately smaller on the δ (ppm) scale, and since the field-dependent quantity (ν A −ν X )/ J AX is magnified.
In molecules of uncertain or otherwise unproven structure, the definitive appearance of complexity in a pair of signals, beyond what can be explained by first-order analysis of HC-CH pairs or H 2 C-CH 2 fragments, can be taken to signify the presence of magnetic inequivalence and, therefore, of an element of symmetry aggregating them. Thus, the appearance of such complexity in the aromatic region of the 1 H-NMR spectrum of the bis -(acetylacetonato)ruthenium complex of o-benzoquinonediimine served to prove its C 2 -symmetrical nature. [ 7 ]
Manual analysis of an AA′BB′ or AA′XX′ system is possible, if a sufficient number of peaks are detected. [ 3 ] [ 8 ] The A/A′ and B/B′ chemical shifts and the several coupling constants between each spin can be accurately obtained by quantum-mechanical simulation [ 9 ] of the spin transition probabilities, given a set of guessed chemical shift and coupling constant values, and subsequent refinement of those values by iterative spectral fitting. Several software packages are available for this purpose, a sampling of which is (in no particular order): | https://en.wikipedia.org/wiki/Magnetic_inequivalence |
Magnetic isotope effects arise when a chemical reaction involves spin-selective processes, such as the radical pair mechanism . The result is that some isotopes react preferentially, depending on their nuclear spin quantum number I. This is in contrast to more familiar mass-dependent isotope effects . [ 1 ] [ 2 ] [ 3 ]
This physical chemistry -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Magnetic_isotope_effect |
A magnetic level gauge is a level gauge based on a float device that can experience floatation in both high and low density fluids. Magnetic level gauges may also be designed to accommodate severe environmental conditions up to 210 bars at 370 °C.
Unlike a sight glass , magnetic level gauges do not need to be transparent and can be made out of metal, which increases the durability and operating temperature range of the device. [ 2 ]
Magnetic float level sensors involve the use of a permanent magnet sealed inside a float whose rise and fall causes the opening or closing of a mechanical switch, either through direct contact or in proximity of a reed switch . With mechanically actuated floats, the float is directly connected to a micro switch .
For both magnetic and mechanical float level sensors, chemical compatibility, temperature , specific gravity (density), buoyancy , and viscosity affect the selection of the stem and the float. For example, larger floats may be used with liquids with specific gravities as low as 0.5 while still maintaining buoyancy. The choice of float material is also influenced by temperature-induced changes in specific gravity and viscosity – changes that directly affect buoyancy.
When selecting a magnetic level gauge it is important to take into account the strength of the magnetic field. The magnetic field is the heart of the magnetic level gauge – the stronger the field, the more reliable the instrument will function. Some manufacturers rely on a single magnet for their magnetic level gauges which causes the strength of the north field to be identical to, and as weak as, the south field. It is apparent that at the location of the indicators, switches and transmitters, the field would not be as intense. Some manufacturers use a single annular ring magnet, others use a series of single bar magnets in a circular array in their float design. In this design the relative field strength of the north and south poles will be equal to one another and less than that of a dual magnet design. Moreover, the field strength as you travel around the circumference will have high and low spots as you pass between the individual bar magnets. | https://en.wikipedia.org/wiki/Magnetic_level_gauge |
In the field of astronomy , the magnetic midnight of the North or South Magnetic Pole occurs when the pole is exactly between the sun and an observer on Earth's surface. At that moment, the pole's aurora reaches its largest extent. [ 1 ]
Because Earth's magnetic poles do not coincide with its geographical poles —the angle between Earth 's rotation axis and magnetic axis is about 11°—magnetic midnight differs from conventional midnight . In most of the United States , magnetic midnight occurs about an hour earlier. [ 2 ]
This astronomy -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Magnetic_midnight |
In astrophysics , a magnetic mirror point is a point where the motion of a charged particle trapped in a magnetic field (such as the (approximately) dipole field of the Earth ) reverses its direction. More precisely, it is the point where the projection of the particle's velocity vector in the direction of the field vector is equal to zero.
Whenever charged particles from the sun hit Earth's magnetosphere, it is observed that the magnetic field of Earth reverses direction.
Since the forces that generate our magnetic field are constantly changing, the field itself is also in continual flux, its strength waxing and waning over time. This causes the location of Earth's magnetic north and south poles to gradually shift, and to even completely flip locations every 300,000 years or so. [ 2 ]
This astrophysics -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Magnetic_mirror_point |
In electromagnetism , the magnetic moment or magnetic dipole moment is the combination of strength and orientation of a magnet or other object or system that exerts a magnetic field . The magnetic dipole moment of an object determines the magnitude of torque the object experiences in a given magnetic field. When the same magnetic field is applied, objects with larger magnetic moments experience larger torques. The strength (and direction) of this torque depends not only on the magnitude of the magnetic moment but also on its orientation relative to the direction of the magnetic field. Its direction points from the south pole to the north pole of the magnet (i.e., inside the magnet).
The magnetic moment also expresses the magnetic force effect of a magnet. The magnetic field of a magnetic dipole is proportional to its magnetic dipole moment. The dipole component of an object's magnetic field is symmetric about the direction of its magnetic dipole moment, and decreases as the inverse cube of the distance from the object.
Examples of objects or systems that produce magnetic moments include: permanent magnets; astronomical objects such as many planets , including the Earth , and some moons , stars , etc.; various molecules ; elementary particles (e.g. electrons ); composites of elementary particles ( protons and neutrons —as of the nucleus of an atom); and loops of electric current such as exerted by electromagnets .
The magnetic moment can be defined as a vector (really pseudovector ) relating the aligning torque on the object from an externally applied magnetic field to the field vector itself. The relationship is given by: [ 1 ] τ = m × B {\displaystyle {\boldsymbol {\tau }}=\mathbf {m} \times \mathbf {B} } where τ is the torque acting on the dipole, B is the external magnetic field, and m is the magnetic moment.
This definition is based on how one could, in principle, measure the magnetic moment of an unknown sample. For a current loop, this definition leads to the magnitude of the magnetic dipole moment equaling the product of the current times the area of the loop. Further, this definition allows the calculation of the expected magnetic moment for any known macroscopic current distribution.
An alternative definition is useful for thermodynamics calculations of the magnetic moment. In this definition, the magnetic dipole moment of a system is the negative gradient of its intrinsic energy, U int , with respect to external magnetic field: m = − x ^ ∂ U int ∂ B x − y ^ ∂ U int ∂ B y − z ^ ∂ U int ∂ B z . {\displaystyle \mathbf {m} =-{\hat {\mathbf {x} }}{\frac {\partial U_{\text{int}}}{\partial B_{x}}}-{\hat {\mathbf {y} }}{\frac {\partial U_{\text{int}}}{\partial B_{y}}}-{\hat {\mathbf {z} }}{\frac {\partial U_{\text{int}}}{\partial B_{z}}}.}
Generically, the intrinsic energy includes the self-field energy of the system plus the energy of the internal workings of the system. For example, for a hydrogen atom in a 2p state in an external field, the self-field energy is negligible, so the internal energy is essentially the eigenenergy of the 2p state, which includes Coulomb potential energy and the kinetic energy of the electron. The interaction-field energy between the internal dipoles and external fields is not part of this internal energy. [ 2 ]
The unit for magnetic moment in International System of Units (SI) base units is A⋅m 2 , where A is ampere (SI base unit of current) and m is meter (SI base unit of distance). This unit has equivalents in other SI derived units including: [ 3 ] [ 4 ]
A ⋅ m 2 = N ⋅ m T = J T , {\displaystyle \mathrm {A{\cdot }m^{2}} ={\frac {\mathrm {N{\cdot }m} }{\mathrm {T} }}={\frac {\mathrm {J} }{\mathrm {T} }},}
where N is newton (SI derived unit of force), T is tesla (SI derived unit of magnetic flux density), and J is joule (SI derived unit of energy ). [ 5 ] : 20–21 Although torque (N·m) and energy (J) are dimensionally equivalent, torques are never expressed in units of energy. [ 5 ] : 23
In the CGS system, there are several different sets of electromagnetism units, of which the main ones are ESU , Gaussian , and EMU . Among these, there are two alternative (non-equivalent) units of magnetic dipole moment: 1 s t a t A ⋅ c m 2 ≡ 3.33564095 × 10 − 14 A ⋅ m 2 (ESU) {\displaystyle 1\;\mathrm {statA{\cdot }{cm}^{2}} \equiv 3.33564095\times 10^{-14}\mathrm {A{\cdot }m^{2}} ~~{\text{ (ESU)}}} 1 e r g G ≡ 10 − 3 A ⋅ m 2 (Gaussian and EMU), {\displaystyle 1\;\mathrm {\frac {erg}{G}} \equiv 10^{-3}\mathrm {A{\cdot }m^{2}} ~~{\text{ (Gaussian and EMU),}}}
where statA is statamperes , cm is centimeters , erg is ergs , and G is gauss . The ratio of these two non-equivalent CGS units (EMU/ESU) is equal to the speed of light in free space, expressed in cm ⋅ s −1 .
All formulae in this article are correct in SI units; they may need to be changed for use in other unit systems. For example, in SI units, a loop of current with current I and area A has magnetic moment IA (see below), but in Gaussian units the magnetic moment is IA / c .
Other units for measuring the magnetic dipole moment include the Bohr magneton and the nuclear magneton .
The magnetic moments of objects are typically measured with devices called magnetometers , though not all magnetometers measure magnetic moment: Some are configured to measure magnetic field instead. If the magnetic field surrounding an object is known well enough, though, then the magnetic moment can be calculated from that magnetic field. [ citation needed ]
The magnetic moment is a quantity that describes the magnetic strength of an entire object. Sometimes, though, it is useful or necessary to know how much of the net magnetic moment of the object is produced by a particular portion of that magnet. Therefore, it is useful to define the magnetization M as: M = m Δ V V Δ V , {\displaystyle \mathbf {M} ={\frac {\mathbf {m} _{\Delta V}}{V_{\Delta V}}},} where m Δ V and V Δ V are the magnetic dipole moment and volume of a sufficiently small portion of the magnet Δ V . This equation is often represented using derivative notation such that M = d m d V , {\displaystyle \mathbf {M} ={\frac {\mathrm {d} \mathbf {m} }{\mathrm {d} V}},} where d m is the elementary magnetic moment and d V is the volume element . The net magnetic moment of the magnet m therefore is m = ∭ M d V , {\displaystyle \mathbf {m} =\iiint \mathbf {M} \,\mathrm {d} V,} where the triple integral denotes integration over the volume of the magnet . For uniform magnetization (where both the magnitude and the direction of M is the same for the entire magnet (such as a straight bar magnet) the last equation simplifies to: m = M V , {\displaystyle \mathbf {m} =\mathbf {M} V,} where V is the volume of the bar magnet.
The magnetization is often not listed as a material parameter for commercially available ferromagnetic materials, though. Instead the parameter that is listed is residual flux density (or remanence), denoted B r . The formula needed in this case to calculate m in (units of A⋅m 2 ) is: m = 1 μ 0 B r V , {\displaystyle \mathbf {m} ={\frac {1}{\mu _{0}}}\mathbf {B} _{\text{r}}V,}
where:
The preferred classical explanation of a magnetic moment has changed over time. Before the 1930s, textbooks explained the moment using hypothetical magnetic point charges. Since then, most have defined it in terms of Ampèrian currents. [ 7 ] In magnetic materials, the cause of the magnetic moment are the spin and orbital angular momentum states of the electrons , and varies depending on whether atoms in one region are aligned with atoms in another. [ citation needed ]
The sources of magnetic moments in materials can be represented by poles in analogy to electrostatics . This is sometimes known as the Gilbert model. [ 8 ] : 258 In this model, a small magnet is modeled by a pair of fictitious magnetic monopoles of equal magnitude but opposite polarity . Each pole is the source of magnetic force which weakens with distance. Since magnetic poles always come in pairs, their forces partially cancel each other because while one pole pulls, the other repels. This cancellation is greatest when the poles are close to each other i.e. when the bar magnet is short. The magnetic force produced by a bar magnet, at a given point in space, therefore depends on two factors: the strength p of its poles ( magnetic pole strength ), and the vector ℓ {\displaystyle \mathrm {\boldsymbol {\ell }} } separating them. The magnetic dipole moment m is related to the fictitious poles as [ 7 ] m = p ℓ . {\displaystyle \mathbf {m} =p\,\mathrm {\boldsymbol {\ell }} \,.}
It points in the direction from South to North pole. The analogy with electric dipoles should not be taken too far because magnetic dipoles are associated with angular momentum (see Relation to angular momentum ). Nevertheless, magnetic poles are very useful for magnetostatic calculations, particularly in applications to ferromagnets . [ 7 ] Practitioners using the magnetic pole approach generally represent the magnetic field by the irrotational field H , in analogy to the electric field E .
After Hans Christian Ørsted discovered that electric currents produce a magnetic field and André-Marie Ampère discovered that electric currents attract and repel each other similar to magnets, it was natural to hypothesize that all magnetic fields are due to electric current loops. In this model developed by Ampère, the elementary magnetic dipole that makes up all magnets is a sufficiently small amperian loop of current I . The dipole moment of this loop is m = I S , {\displaystyle \mathbf {m} =I{\boldsymbol {S}},} where S is the area of the loop. The direction of the magnetic moment is in a direction normal to the area enclosed by the current consistent with the direction of the current using the right hand rule.
The magnetic dipole moment can be calculated for a localized (does not extend to infinity) current distribution assuming that we know all of the currents involved. Conventionally, the derivation starts from a multipole expansion of the vector potential . This leads to the definition of the magnetic dipole moment as: m = 1 2 ∭ V r × j ( r ) d V , {\displaystyle \mathbf {m} ={\tfrac {1}{2}}\iiint _{V}\mathbf {r} \times \mathbf {j} (\mathbf {r} )\,\mathrm {d} V,} where × is the vector cross product , r is the position vector, and j is the electric current density and the integral is a volume integral. [ 9 ] : § 5.6 When the current density in the integral is replaced by a loop of current I in a plane enclosing an area S then the volume integral becomes a line integral and the resulting dipole moment becomes m = I S , {\displaystyle \mathbf {m} =I\mathbf {S} ,} which is how the magnetic dipole moment for an Amperian loop is derived.
Practitioners using the current loop model generally represent the magnetic field by the solenoidal field B , analogous to the electrostatic field D .
A generalization of the above current loop is a coil, or solenoid . Its moment is the vector sum of the moments of individual turns. If the solenoid has N identical turns (single-layer winding) and vector area S , m = N I S . {\displaystyle \mathbf {m} =NI\mathbf {S} .}
When calculating the magnetic moments of materials or molecules on the microscopic level it is often convenient to use a third model for the magnetic moment that exploits the linear relationship between the angular momentum and the magnetic moment of a particle. While this relation is straightforward to develop for macroscopic currents using the amperian loop model (see below ), neither the magnetic pole model nor the amperian loop model truly represents what is occurring at the atomic and molecular levels. At that level quantum mechanics must be used. Fortunately, the linear relationship between the magnetic dipole moment of a particle and its angular momentum still holds, although it is different for each particle. Further, care must be used to distinguish between the intrinsic angular momentum (or spin ) of the particle and the particle's orbital angular momentum. See below for more details.
The torque τ on an object having a magnetic dipole moment m in a uniform magnetic field B is: τ = m × B . {\displaystyle {\boldsymbol {\tau }}=\mathbf {m} \times \mathbf {B} .}
This is valid for the moment due to any localized current distribution provided that the magnetic field is uniform. For non-uniform B the equation is also valid for the torque about the center of the magnetic dipole provided that the magnetic dipole is small enough. [ 8 ] : 257
An electron, nucleus, or atom placed in a uniform magnetic field will precess with a frequency known as the Larmor frequency . See Resonance .
A magnetic moment in an externally produced magnetic field has a potential energy U : U = − m ⋅ B {\displaystyle U=-\mathbf {m} \cdot \mathbf {B} }
In a case when the external magnetic field is non-uniform, there will be a force, proportional to the magnetic field gradient , acting on the magnetic moment itself. There are two expressions for the force acting on a magnetic dipole, depending on whether the model used for the dipole is a current loop or two monopoles (analogous to the electric dipole). [ 10 ] The force obtained in the case of a current loop model is F loop = ∇ ( m ⋅ B ) . {\displaystyle \mathbf {F} _{\text{loop}}=\nabla \left(\mathbf {m} \cdot \mathbf {B} \right).}
Assuming existence of magnetic monopole, the force is modified as follows: F loop = ( m × ∇ ) × B = ∇ ( m ⋅ B ) − ( ∇ ⋅ B ) m {\displaystyle {\begin{aligned}\mathbf {F} _{\text{loop}}&=\left(\mathbf {m} \times \nabla \right)\times \mathbf {B} \\[1ex]&=\nabla \left(\mathbf {m} \cdot \mathbf {B} \right)-\left(\nabla \cdot \mathbf {B} \right)\mathbf {m} \end{aligned}}}
In the case of a pair of monopoles being used (i.e. electric dipole model), the force is F dipole = ( m ⋅ ∇ ) B . {\displaystyle \mathbf {F} _{\text{dipole}}=\left(\mathbf {m} \cdot \nabla \right)\mathbf {B} .} And one can be put in terms of the other via the relation F loop = F dipole + m × ( ∇ × B ) − ( ∇ ⋅ B ) m . {\displaystyle \mathbf {F} _{\text{loop}}=\mathbf {F} _{\text{dipole}}+\mathbf {m} \times \left(\nabla \times \mathbf {B} \right)-\left(\nabla \cdot \mathbf {B} \right)\mathbf {m} .}
In all these expressions m is the dipole and B is the magnetic field at its position. Note that if there are no currents or time-varying electrical fields or magnetic charge, ∇× B = 0 , ∇⋅ B = 0 and the two expressions agree.
One can relate the magnetic moment of a system to the free energy of that system. [ 11 ] In a uniform magnetic field B , the free energy F can be related to the magnetic moment M of the system as d F = − S d T − M ⋅ d B {\displaystyle \mathrm {d} F=-S\,\mathrm {d} T-\mathbf {M} \,\cdot \mathrm {d} \mathbf {B} } where S is the entropy of the system and T is the temperature. Therefore, the magnetic moment can also be defined in terms of the free energy of a system as m = − ∂ F ∂ B | T . {\displaystyle m=\left.-{\frac {\partial F}{\partial B}}\right|_{T}.}
In addition, an applied magnetic field can change the magnetic moment of the object itself; for example by magnetizing it. This phenomenon is known as magnetism . An applied magnetic field can flip the magnetic dipoles that make up the material causing both paramagnetism and ferromagnetism . Additionally, the magnetic field can affect the currents that create the magnetic fields (such as the atomic orbits) which causes diamagnetism .
Any system possessing a net magnetic dipole moment m will produce a dipolar magnetic field (described below) in the space surrounding the system. While the net magnetic field produced by the system can also have higher-order multipole components, those will drop off with distance more rapidly, so that only the dipole component will dominate the magnetic field of the system at distances far away from it.
The magnetic field of a magnetic dipole depends on the strength and direction of a magnet's magnetic moment m {\displaystyle \mathbf {m} } but drops off as the cube of the distance such that: H ( r ) = 1 4 π ( 3 r ( m ⋅ r ) | r | 5 − m | r | 3 ) , {\displaystyle \mathbf {H} (\mathbf {r} )={\frac {1}{4\pi }}\left({\frac {3\mathbf {r} (\mathbf {m} \cdot \mathbf {r} )}{|\mathbf {r} |^{5}}}-{\frac {\mathbf {m} }{|\mathbf {r} |^{3}}}\right),}
where H {\displaystyle \mathbf {H} } is the magnetic field produced by the magnet and r {\displaystyle \mathbf {r} } is a vector from the center of the magnetic dipole to the location where the magnetic field is measured. The inverse cube nature of this equation is more readily seen by expressing the location vector r {\displaystyle \mathbf {r} } as the product of its magnitude times the unit vector in its direction ( r = | r | r ^ {\displaystyle \mathbf {r} =|\mathbf {r} |\mathbf {\hat {r}} } ) so that: H ( r ) = 1 4 π 3 r ^ ( r ^ ⋅ m ) − m | r | 3 . {\displaystyle \mathbf {H} (\mathbf {r} )={\frac {1}{4\pi }}{\frac {3\mathbf {\hat {r}} (\mathbf {\hat {r}} \cdot \mathbf {m} )-\mathbf {m} }{|\mathbf {r} |^{3}}}.}
The equivalent equations for the magnetic B {\displaystyle \mathbf {B} } -field are the same except for a multiplicative factor of μ 0 = 4 π × 10 −7 H / m , where μ 0 is known as the vacuum permeability . For example: B ( r ) = μ 0 4 π 3 r ^ ( r ^ ⋅ m ) − m | r | 3 . {\displaystyle \mathbf {B} (\mathbf {r} )={\frac {\mu _{0}}{4\pi }}{\frac {3\mathbf {\hat {r}} (\mathbf {\hat {r}} \cdot \mathbf {m} )-\mathbf {m} }{|\mathbf {r} |^{3}}}.}
As discussed earlier, the force exerted by a dipole loop with moment m 1 on another with moment m 2 is F = ∇ ( m 2 ⋅ B 1 ) , {\displaystyle \mathbf {F} =\nabla \left(\mathbf {m} _{2}\cdot \mathbf {B} _{1}\right),} where B 1 is the magnetic field due to moment m 1 . The result of calculating the gradient is [ 12 ] [ 13 ] F ( r , m 1 , m 2 ) = 3 μ 0 4 π | r | 4 [ m 2 ( m 1 ⋅ r ^ ) + m 1 ( m 2 ⋅ r ^ ) + r ^ ( m 1 ⋅ m 2 ) − 5 r ^ ( m 1 ⋅ r ^ ) ( m 2 ⋅ r ^ ) ] , {\displaystyle \mathbf {F} (\mathbf {r} ,\mathbf {m} _{1},\mathbf {m} _{2})={\frac {3\mu _{0}}{4\pi |\mathbf {r} |^{4}}}\left[\mathbf {m} _{2}(\mathbf {m} _{1}\cdot {\hat {\mathbf {r} }})+\mathbf {m} _{1}(\mathbf {m} _{2}\cdot {\hat {\mathbf {r} }})+{\hat {\mathbf {r} }}(\mathbf {m} _{1}\cdot \mathbf {m} _{2})-5{\hat {\mathbf {r} }}(\mathbf {m} _{1}\cdot {\hat {\mathbf {r} }})(\mathbf {m} _{2}\cdot {\hat {\mathbf {r} }})\right],} where r̂ is the unit vector pointing from magnet 1 to magnet 2 and r is the distance. An equivalent expression is [ 13 ] F = 3 μ 0 4 π | r | 4 [ ( r ^ × m 1 ) × m 2 + ( r ^ × m 2 ) × m 1 − 2 r ^ ( m 1 ⋅ m 2 ) + 5 r ^ ( r ^ × m 1 ) ⋅ ( r ^ × m 2 ) ] . {\displaystyle \mathbf {F} ={\frac {3\mu _{0}}{4\pi |\mathbf {r} |^{4}}}\left[({\hat {\mathbf {r} }}\times \mathbf {m} _{1})\times \mathbf {m} _{2}+({\hat {\mathbf {r} }}\times \mathbf {m} _{2})\times \mathbf {m} _{1}-2{\hat {\mathbf {r} }}(\mathbf {m} _{1}\cdot \mathbf {m} _{2})+5{\hat {\mathbf {r} }}({\hat {\mathbf {r} }}\times \mathbf {m} _{1})\cdot ({\hat {\mathbf {r} }}\times \mathbf {m} _{2})\right].} The force acting on m 1 is in the opposite direction.
The torque of magnet 1 on magnet 2 is τ = m 2 × B 1 . {\displaystyle {\boldsymbol {\tau }}=\mathbf {m} _{2}\times \mathbf {B} _{1}.}
The magnetic field of any magnet can be modeled by a series of terms for which each term is more complicated (having finer angular detail) than the one before it. The first three terms of that series are called the monopole (represented by an isolated magnetic north or south pole) the dipole (represented by two equal and opposite magnetic poles), and the quadrupole (represented by four poles that together form two equal and opposite dipoles). The magnitude of the magnetic field for each term decreases progressively faster with distance than the previous term, so that at large enough distances the first non-zero term will dominate. [ citation needed ]
For many magnets the first non-zero term is the magnetic dipole moment. (To date, no isolated magnetic monopoles have been experimentally detected.) A magnetic dipole is the limit of either a current loop or a pair of poles as the dimensions of the source are reduced to zero while keeping the moment constant. As long as these limits only apply to fields far from the sources, they are equivalent. However, the two models give different predictions for the internal field (see below).
Traditionally, the equations for the magnetic dipole moment (and higher order terms) are derived from theoretical quantities called magnetic potentials [ 9 ] : § 5.6 which are simpler to deal with mathematically than the magnetic fields. [ citation needed ]
In the magnetic pole model, the relevant magnetic field is the demagnetizing field H {\displaystyle \mathbf {H} } . Since the demagnetizing portion of H {\displaystyle \mathbf {H} } does not include, by definition, the part of H {\displaystyle \mathbf {H} } due to free currents, there exists a magnetic scalar potential such that H ( r ) = − ∇ ψ . {\displaystyle {\mathbf {H} }({\mathbf {r} })=-\nabla \psi .}
In the amperian loop model, the relevant magnetic field is the magnetic induction B {\displaystyle \mathbf {B} } . Since magnetic monopoles do not exist, there exists a magnetic vector potential such that B ( r ) = ∇ × A . {\displaystyle \mathbf {B} (\mathbf {r} )=\nabla \times \mathbf {A} .}
Both of these potentials can be calculated for any arbitrary current distribution (for the amperian loop model) or magnetic charge distribution (for the magnetic charge model) provided that these are limited to a small enough region to give: A ( r , t ) = μ 0 4 π ∫ j ( r ′ ) | r − r ′ | d V ′ , ψ ( r , t ) = 1 4 π ∫ ρ ( r ′ ) | r − r ′ | d V ′ , {\displaystyle {\begin{aligned}\mathbf {A} \left(\mathbf {r} ,t\right)&={\frac {\mu _{0}}{4\pi }}\int {\frac {\mathbf {j} \left(\mathbf {r} '\right)}{\left|\mathbf {r} -\mathbf {r} '\right|}}\,\mathrm {d} V',\\[1ex]\psi \left(\mathbf {r} ,t\right)&={\frac {1}{4\pi }}\int {\frac {\rho \left(\mathbf {r} '\right)}{\left|\mathbf {r} -\mathbf {r} '\right|}}\,\mathrm {d} V',\end{aligned}}} where j {\displaystyle \mathbf {j} } is the current density in the amperian loop model, ρ {\displaystyle \rho } is the magnetic pole strength density in analogy to the electric charge density that leads to the electric potential, and the integrals are the volume (triple) integrals over the coordinates that make up r ′ {\displaystyle \mathbf {r} '} . The denominators of these equation can be expanded using the multipole expansion to give a series of terms that have larger of power of distances in the denominator. The first nonzero term, therefore, will dominate for large distances. The first non-zero term for the vector potential is: A ( r ) = μ 0 4 π m × r | r | 3 , {\displaystyle \mathbf {A} (\mathbf {r} )={\frac {\mu _{0}}{4\pi }}{\frac {\mathbf {m} \times \mathbf {r} }{|\mathbf {r} |^{3}}},} where m {\displaystyle \mathbf {m} } is: m = 1 2 ∭ V r × j d V , {\displaystyle \mathbf {m} ={\frac {1}{2}}\iiint _{V}\mathbf {r} \times \mathbf {j} \,\mathrm {d} V,} where × is the vector cross product , r is the position vector, and j is the electric current density and the integral is a volume integral.
In the magnetic pole perspective, the first non-zero term of the scalar potential is ψ ( r ) = m ⋅ r 4 π | r | 3 . {\displaystyle \psi (\mathbf {r} )={\frac {\mathbf {m} \cdot \mathbf {r} }{4\pi |\mathbf {r} |^{3}}}.}
Here m {\displaystyle \mathbf {m} } may be represented in terms of the magnetic pole strength density but is more usefully expressed in terms of the magnetization field as: m = ∭ M d V . {\displaystyle \mathbf {m} =\iiint \mathbf {M} \,\mathrm {d} V.}
The same symbol m {\displaystyle \mathbf {m} } is used for both equations since they produce equivalent results outside of the magnet.
The magnetic flux density for a magnetic dipole in the amperian loop model, therefore, is B ( r ) = ∇ × A = μ 0 4 π ( 3 r ( m ⋅ r ) | r | 5 − m | r | 3 ) . {\displaystyle \mathbf {B} (\mathbf {r} )=\nabla \times {\mathbf {A} }={\frac {\mu _{0}}{4\pi }}\left({\frac {3\mathbf {r} (\mathbf {m} \cdot \mathbf {r} )}{|\mathbf {r} |^{5}}}-{\frac {\mathbf {m} }{|\mathbf {r} |^{3}}}\right).}
Further, the magnetic field strength H {\displaystyle \mathbf {H} } is H ( r ) = − ∇ ψ = 1 4 π ( 3 r ( m ⋅ r ) | r | 5 − m | r | 3 ) . {\displaystyle {\mathbf {H} }({\mathbf {r} })=-\nabla \psi ={\frac {1}{4\pi }}\left({\frac {3\mathbf {r} (\mathbf {m} \cdot \mathbf {r} )}{|\mathbf {r} |^{5}}}-{\frac {\mathbf {m} }{|\mathbf {r} |^{3}}}\right).}
The two models for a dipole (magnetic poles or current loop) give the same predictions for the magnetic field far from the source. However, inside the source region, they give different predictions. The magnetic field between poles (see the figure for Magnetic pole model ) is in the opposite direction to the magnetic moment (which points from the negative charge to the positive charge), while inside a current loop it is in the same direction (see the figure to the right). The limits of these fields must also be different as the sources shrink to zero size. This distinction only matters if the dipole limit is used to calculate fields inside a magnetic material. [ 7 ]
If a magnetic dipole is formed by taking a "north pole" and a "south pole", bringing them closer and closer together but keeping the product of magnetic pole charge and distance constant, the limiting field is [ 7 ] H ( r ) = 3 4 π ( r ^ ⋅ m ) r ^ − m | r | 3 − 1 3 m δ ( r ) . {\displaystyle \mathbf {H} (\mathbf {r} )={\frac {\ 3\ }{4\pi }}{\frac {\ \left(\mathbf {\hat {r}} \cdot \mathbf {m} \right)\ \mathbf {\hat {r}} -\mathbf {m} \ }{~\left|\mathbf {r} \right|^{3}}}-{\frac {\ 1\ }{3}}\mathbf {m} \ \delta (\mathbf {r} )~.}
The fields H and B are related by B = μ 0 ( H + M ) , {\displaystyle \ \mathbf {B} =\mu _{0}\left(\mathbf {H} +\mathbf {M} \right)\ ,} where M ( r ) = m δ ( r ) is the magnetization .
If a magnetic dipole is formed by making a current loop smaller and smaller, but keeping the product of current and area constant, the limiting field is B ( r ) = μ 0 [ 3 4 π ( r ^ ⋅ m ) r ^ − m | r | 3 + 2 3 m δ ( r ) ] . {\displaystyle \mathbf {B} (\mathbf {r} )=\mu _{0}\left[\ {\frac {3}{4\pi }}{\frac {\ \left(\mathbf {\hat {r}} \cdot \mathbf {m} \right)\mathbf {\hat {r}} -\mathbf {m} \ }{~\left|\mathbf {r} \right|^{3}}}+{\frac {\ 2\ }{3}}\mathbf {m} \ \delta (\mathbf {r} )\ \right]~.} Unlike the expressions in the previous section, this limit is correct for the internal field of the dipole. [ 7 ] [ 9 ] : 184
The magnetic moment has a close connection with angular momentum called the gyromagnetic effect . This effect is expressed on a macroscopic scale in the Einstein–de Haas effect , or "rotation by magnetization", and its inverse, the Barnett effect , or "magnetization by rotation". [ 1 ] Further, a torque applied to a relatively isolated magnetic dipole such as an atomic nucleus can cause it to precess (rotate about the axis of the applied field). This phenomenon is used in nuclear magnetic resonance . [ citation needed ]
Viewing a magnetic dipole as current loop brings out the close connection between magnetic moment and angular momentum. Since the particles creating the current (by rotating around the loop) have charge and mass, both the magnetic moment and the angular momentum increase with the rate of rotation. The ratio of the two is called the gyromagnetic ratio or γ {\displaystyle \gamma } so that: [ 14 ] [ 15 ] m = γ L , {\displaystyle \mathbf {m} =\gamma \,\mathbf {L} ,} where L {\displaystyle \mathbf {L} } is the angular momentum of the particle or particles that are creating the magnetic moment.
In the amperian loop model, which applies for macroscopic currents, the gyromagnetic ratio is one half of the charge-to-mass ratio . This can be shown as follows. The angular momentum of a moving charged particle is defined as: L = r × p = μ r × v , {\displaystyle \mathbf {L} =\mathbf {r} \times \mathbf {p} =\mu \,\mathbf {r} \times \mathbf {v} ,} where μ is the mass of the particle and v is the particle's velocity . The angular momentum of the very large number of charged particles that make up a current therefore is: L = ∭ V r × ( ρ v ) d V , {\displaystyle \mathbf {L} =\iiint _{V}\,\mathbf {r} \times (\rho \mathbf {v} )\,\mathrm {d} V\,,} where ρ is the mass density of the moving particles. By convention the direction of the cross product is given by the right-hand rule . [ 16 ]
This is similar to the magnetic moment created by the very large number of charged particles that make up that current: m = 1 2 ∭ V r × ( ρ Q v ) d V , {\displaystyle \mathbf {m} ={\tfrac {1}{2}}\iiint _{V}\mathbf {r} \times (\rho _{Q}\mathbf {v} )\,\mathrm {d} V\,,} where j = ρ Q v {\displaystyle \mathbf {j} =\rho _{Q}\mathbf {v} } and ρ Q {\displaystyle \rho _{Q}} is the charge density of the moving charged particles.
Comparing the two equations results in: m = e 2 μ L , {\displaystyle \mathbf {m} ={\frac {e}{2\mu }}\,\mathbf {L} \,,} where e {\displaystyle e} is the charge of the particle and μ {\displaystyle \mu } is the mass of the particle.
Even though atomic particles cannot be accurately described as orbiting (and spinning) charge distributions of uniform charge-to-mass ratio, this general trend can be observed in the atomic world so that: m = g e 2 μ L , {\displaystyle \mathbf {m} =g\,{\frac {e}{2\mu }}\,\mathbf {L} ,} where the g -factor depends on the particle and configuration. For example, the g -factor for the magnetic moment due to an electron orbiting a nucleus is one while the g -factor for the magnetic moment of electron due to its intrinsic angular momentum ( spin ) is a little larger than 2. The g -factor of atoms and molecules must account for the orbital and intrinsic moments of its electrons and possibly the intrinsic moment of its nuclei as well.
In the atomic world the angular momentum ( spin ) of a particle is an integer (or half-integer in the case of fermions) multiple of the reduced Planck constant ħ . This is the basis for defining the magnetic moment units of Bohr magneton (assuming charge-to-mass ratio of the electron ) and nuclear magneton (assuming charge-to-mass ratio of the proton ). See electron magnetic moment and Bohr magneton for more details.
Fundamentally, contributions to any system's magnetic moment may come from sources of two kinds: 1) motion of electric charges , such as electric currents ; and 2) the intrinsic magnetism due spin of elementary particles , such as the electron . [ citation needed ]
Contributions due to the sources of the first kind can be calculated from knowing the distribution of all the electric currents (or, alternatively, of all the electric charges and their velocities) inside the system, by using the formulas below.
Contributions due to particle spin sum the magnitude of each elementary particle's intrinsic magnetic moment, a fixed number, often measured experimentally to a great precision. For example, any electron's magnetic moment is measured to be −9.284 764 × 10 −24 J/T . [ 17 ] The direction of the magnetic moment of any elementary particle is entirely determined by the direction of its spin , with the negative value indicating that any electron's magnetic moment is antiparallel to its spin.
The net magnetic moment of any system is a vector sum of contributions from one or both types of sources.
For example, the magnetic moment of an atom of hydrogen-1 (the lightest hydrogen isotope, consisting of a proton and an electron) is a vector sum of the following contributions:
Similarly, the magnetic moment of a bar magnet is the sum of the contributing magnetic moments, which include the intrinsic and orbital magnetic moments of the unpaired electrons of the magnet's material and the nuclear magnetic moments.
For an atom, individual electron spins are added to get a total spin, and individual orbital angular momenta are added to get a total orbital angular momentum. These two then are added using angular momentum coupling to get a total angular momentum. For an atom with no nuclear magnetic moment, the magnitude of the atomic dipole moment, m atom {\displaystyle {\mathfrak {m}}_{\text{atom}}} , is then [ 18 ] m atom = g J μ B j ( j + 1 ) {\displaystyle {\mathfrak {m}}_{\text{atom}}=g_{\text{J}}\,\mu _{\text{B}}\,{\sqrt {j\,(j+1)\,}}} where j is the total angular momentum quantum number , g J is the Landé g -factor , and μ B is the Bohr magneton . The component of this magnetic moment along the direction of the magnetic field is then [ 19 ] m atom , z = − m g J μ B . {\displaystyle {\mathfrak {m}}_{{\text{atom}},z}=-m\,g_{\text{J}}\,\mu _{\text{B}}\,.}
The negative sign occurs because electrons have negative charge.
The integer m (not to be confused with the moment, m {\displaystyle {\mathfrak {m}}} ) is called the magnetic quantum number or the equatorial quantum number, which can take on any of 2 j + 1 values: [ 20 ] − j , − ( j − 1 ) , ⋯ , − 1 , 0 , + 1 , ⋯ , + ( j − 1 ) , + j . {\displaystyle -j,\ -(j-1),\ \cdots ,\ -1,\ 0,\ +1,\ \cdots ,\ +(j-1),\ +j~.}
Due to the angular momentum, the dynamics of a magnetic dipole in a magnetic field differs from that of an electric dipole in an electric field. The field does exert a torque on the magnetic dipole tending to align it with the field. However, torque is proportional to rate of change of angular momentum, so precession occurs: the direction of spin changes. This behavior is described by the Landau–Lifshitz–Gilbert equation : [ 21 ] [ 22 ] 1 γ d m d t = m × H eff − λ γ m m × d m d t {\displaystyle {\frac {1}{\gamma }}{\frac {\mathrm {d} \mathbf {m} }{\mathrm {d} t}}=\mathbf {m} \times \mathbf {H} _{\text{eff}}-{\frac {\lambda }{\gamma m}}\mathbf {m} \times {\frac {\mathrm {d} \mathbf {m} }{\mathrm {d} t}}} where γ is the gyromagnetic ratio , m is the magnetic moment, λ is the damping coefficient and H eff is the effective magnetic field (the external field plus any self-induced field). The first term describes precession of the moment about the effective field, while the second is a damping term related to dissipation of energy caused by interaction with the surroundings.
Electrons and many elementary particles also have intrinsic magnetic moments, an explanation of which requires a quantum mechanical treatment and relates to the intrinsic angular momentum of the particles as discussed in the article Electron magnetic moment . It is these intrinsic magnetic moments that give rise to the macroscopic effects of magnetism , and other phenomena, such as electron paramagnetic resonance . [ citation needed ]
The magnetic moment of the electron is m S = − g S μ B S ℏ , {\displaystyle \mathbf {m} _{\text{S}}=-{\frac {g_{\text{S}}\mu _{\text{B}}\mathbf {S} }{\hbar }},} where μ B is the Bohr magneton , S is electron spin , and the g -factor g S is 2 according to Dirac's theory , but due to quantum electrodynamic effects it is slightly larger in reality: 2.002 319 304 36 . The deviation from 2 is known as the anomalous magnetic dipole moment .
Again it is important to notice that m is a negative constant multiplied by the spin , so the magnetic moment of the electron is antiparallel to the spin. This can be understood with the following classical picture: if we imagine that the spin angular momentum is created by the electron mass spinning around some axis, the electric current that this rotation creates circulates in the opposite direction, because of the negative charge of the electron; such current loops produce a magnetic moment which is antiparallel to the spin. Hence, for a positron (the anti-particle of the electron) the magnetic moment is parallel to its spin.
The nuclear system is a complex physical system consisting of nucleons, i.e., protons and neutrons . The quantum mechanical properties of the nucleons include the spin among others. Since the electromagnetic moments of the nucleus depend on the spin of the individual nucleons, one can look at these properties with measurements of nuclear moments, and more specifically the nuclear magnetic dipole moment.
Most common nuclei exist in their ground state , although nuclei of some isotopes have long-lived excited states . Each energy state of a nucleus of a given isotope is characterized by a well-defined magnetic dipole moment, the magnitude of which is a fixed number, often measured experimentally to a great precision. This number is very sensitive to the individual contributions from nucleons, and a measurement or prediction of its value can reveal important information about the content of the nuclear wave function. There are several theoretical models that predict the value of the magnetic dipole moment and a number of experimental techniques aiming to carry out measurements in nuclei along the nuclear chart.
Any molecule has a well-defined magnitude of magnetic moment, which may depend on the molecule's energy state . Typically, the overall magnetic moment of a molecule is a combination of the following contributions, in the order of their typical strength:
In atomic and nuclear physics, the Greek symbol μ represents the magnitude of the magnetic moment, often measured in Bohr magnetons or nuclear magnetons , associated with the intrinsic spin of the particle and/or with the orbital motion of the particle in a system. Values of the intrinsic magnetic moments of some particles are given in the table below: | https://en.wikipedia.org/wiki/Magnetic_moment |
In particle physics , a magnetic monopole is a hypothetical particle that is an isolated magnet with only one magnetic pole (a north pole without a south pole or vice versa). [ 1 ] [ 2 ] A magnetic monopole would have a net north or south "magnetic charge". Modern interest in the concept stems from particle theories , notably the grand unified and superstring theories, which predict their existence. [ 3 ] [ 4 ] The known elementary particles that have electric charge are electric monopoles.
Magnetism in bar magnets and electromagnets is not caused by magnetic monopoles, and indeed, there is no known experimental or observational evidence that magnetic monopoles exist. A magnetic monopole is not necessarily an elementary particle , and models for magnetic monopole production can include (but are not limited to) spin -0 monopoles or spin-1 massive vector mesons . [ 5 ] The term "magnetic monopole" only refers to the nature of the particle, rather than a designation for a single particle.
Some condensed matter systems contain effective (non-isolated) magnetic monopole quasi-particles , [ 6 ] or contain phenomena that are mathematically analogous to magnetic monopoles. [ 7 ]
Many early scientists attributed the magnetism of lodestones to two different "magnetic fluids" ("effluvia"), a north-pole fluid at one end and a south-pole fluid at the other, which attracted and repelled each other in analogy to positive and negative electric charge . [ 8 ] [ 9 ] However, an improved understanding of electromagnetism in the nineteenth century showed that the magnetism of lodestones was properly explained not by magnetic monopole fluids, but rather by a combination of electric currents , the electron magnetic moment , and the magnetic moments of other particles. Gauss's law for magnetism , one of Maxwell's equations , is the mathematical statement that magnetic monopoles do not exist. Nevertheless, Pierre Curie pointed out in 1894 [ 10 ] that magnetic monopoles could conceivably exist, despite not having been seen so far.
The quantum theory of magnetic charge started with a paper by the physicist Paul Dirac in 1931. [ 11 ] In this paper, Dirac showed that if any magnetic monopoles exist in the universe, then all electric charge in the universe must be quantized (Dirac quantization condition). [ 12 ] The electric charge is , in fact, quantized, which is consistent with (but does not prove) the existence of monopoles. [ 12 ]
Since Dirac's paper, several systematic monopole searches have been performed. Experiments in 1975 [ 13 ] and 1982 [ 14 ] produced candidate events that were initially interpreted as monopoles, but are now regarded as inconclusive. [ 15 ] Therefore, whether monopoles exist remains an open question. Further advances in theoretical particle physics , particularly developments in grand unified theories and quantum gravity , have led to more compelling arguments (detailed below) that monopoles do exist. Joseph Polchinski , a string theorist, described the existence of monopoles as "one of the safest bets that one can make about physics not yet seen". [ 16 ] These theories are not necessarily inconsistent with the experimental evidence. In some theoretical models , magnetic monopoles are unlikely to be observed, because they are too massive to create in particle accelerators (see § Searches for magnetic monopoles below), and also too rare in the Universe to enter a particle detector with much probability. [ 16 ]
Some condensed matter systems propose a structure superficially similar to a magnetic monopole, known as a flux tube . The ends of a flux tube form a magnetic dipole , but since they move independently, they can be treated for many purposes as independent magnetic monopole quasiparticles . Since 2009, numerous news reports from the popular media [ 17 ] [ 18 ] have incorrectly described these systems as the long-awaited discovery of the magnetic monopoles, but the two phenomena are only superficially related to one another. [ 19 ] [ 20 ] These condensed-matter systems remain an area of active research. (See § "Monopoles" in condensed-matter systems below.)
All matter isolated to date, including every atom on the periodic table and every particle in the Standard Model , has zero magnetic monopole charge. Therefore, the ordinary phenomena of magnetism and magnets do not derive from magnetic monopoles.
Instead, magnetism in ordinary matter is due to two sources. First, electric currents create magnetic fields according to Ampère's law . Second, many elementary particles have an intrinsic magnetic moment , the most important of which is the electron magnetic dipole moment , which is related to its quantum-mechanical spin .
Mathematically, the magnetic field of an object is often described in terms of a multipole expansion . This is an expression of the field as the sum of component fields with specific mathematical forms. The first term in the expansion is called the monopole term, the second is called dipole , then quadrupole , then octupole , and so on. Any of these terms can be present in the multipole expansion of an electric field , for example. However, in the multipole expansion of a magnetic field, the "monopole" term is always exactly zero (for ordinary matter). A magnetic monopole, if it exists, would have the defining property of producing a magnetic field whose monopole term is non-zero.
A magnetic dipole is something whose magnetic field is predominantly or exactly described by the magnetic dipole term of the multipole expansion. The term dipole means two poles , corresponding to the fact that a dipole magnet typically contains a north pole on one side and a south pole on the other side. This is analogous to an electric dipole , which has positive charge on one side and negative charge on the other. However, an electric dipole and magnetic dipole are fundamentally quite different. In an electric dipole made of ordinary matter, the positive charge is made of protons and the negative charge is made of electrons , but a magnetic dipole does not have different types of matter creating the north pole and south pole. Instead, the two magnetic poles arise simultaneously from the aggregate effect of all the currents and intrinsic moments throughout the magnet. Because of this, the two poles of a magnetic dipole must always have equal and opposite strength, and the two poles cannot be separated from each other.
Maxwell's equations of electromagnetism relate the electric and magnetic fields to each other and to the distribution of electric charge and current. The standard equations provide for electric charge, but they posit zero magnetic charge and current. Except for this constraint, the equations are symmetric under the interchange of the electric and magnetic fields . Maxwell's equations are symmetric when the charge and electric current density are zero everywhere, as in vacuum.
Maxwell's equations can also be written in a fully symmetric form if one allows for "magnetic charge" analogous to electric charge. [ 21 ] With the inclusion of a variable for the density of magnetic charge, say ρ m , there is also a " magnetic current density" variable in the equations, j m .
If magnetic charge does not exist – or if it exists but is absent in a region of space – then the new terms in Maxwell's equations are all zero, and the extended equations reduce to the conventional equations of electromagnetism such as ∇ ⋅ B = 0 (where ∇⋅ is the divergence operator and B is the magnetic flux density ).
In the International System of Quantities used with the SI , there are two conventions for defining magnetic charge q m , each with different units: weber (Wb) and ampere -meter (A⋅m). The conversion between them is q m [Wb] = μ 0 q m [A⋅m] , since the units are 1 Wb = 1 H⋅A = (1 H⋅m −1 )(1 A⋅m) , where H is the henry – the SI unit of inductance .
Maxwell's equations then take the following forms (using the same notation above): [ notes 1 ]
Maxwell's equations can also be expressed in terms of potentials as follows:
where
Maxwell's equations in the language of tensors makes Lorentz covariance clear. We introduce electromagnetic tensors and preliminary four-vectors in this article as follows:
where:
The generalized equations are: [ 24 ] [ 25 ]
Alternatively, [ 26 ] [ 27 ]
F ~ α β = ∂ α A m β − ∂ β A m α + ε α β μ ν ∂ μ A e ν {\displaystyle {\tilde {F}}^{\alpha \beta }=\partial ^{\alpha }A_{\mathrm {m} }^{\beta }-\partial ^{\beta }A_{\mathrm {m} }^{\alpha }+\varepsilon ^{\alpha \beta \mu \nu }\partial _{\mu }A_{{\mathrm {e} }\nu }}
F ~ α β = μ 0 c ( ∂ α A m β − ∂ β A m α ) + ε α β μ ν ∂ μ A e ν {\displaystyle {\tilde {F}}^{\alpha \beta }=\mu _{0}c(\partial ^{\alpha }A_{\mathrm {m} }^{\beta }-\partial ^{\beta }A_{\mathrm {m} }^{\alpha })+\varepsilon ^{\alpha \beta \mu \nu }\partial _{\mu }A_{{\mathrm {e} }\nu }}
where the ε αβμν is the Levi-Civita symbol .
The generalized Maxwell's equations possess a certain symmetry, called a duality transformation . One can choose any real angle ξ , and simultaneously change the fields and charges everywhere in the universe as follows (in Gaussian units): [ 28 ]
where the primed quantities are the charges and fields before the transformation, and the unprimed quantities are after the transformation. The fields and charges after this transformation still obey the same Maxwell's equations.
Because of the duality transformation, one cannot uniquely decide whether a particle has an electric charge, a magnetic charge, or both, just by observing its behavior and comparing that to Maxwell's equations. For example, it is merely a convention, not a requirement of Maxwell's equations, that electrons have electric charge but not magnetic charge; after a ξ = π /2 transformation, it would be the other way around. The key empirical fact is that all particles ever observed have the same ratio of magnetic charge to electric charge. [ 28 ] Duality transformations can change the ratio to any arbitrary numerical value, but cannot change that all particles have the same ratio. Since this is the case, a duality transformation can be made that sets this ratio at zero, so that all particles have no magnetic charge. This choice underlies the "conventional" definitions of electricity and magnetism. [ 28 ]
One of the defining advances in quantum theory was Paul Dirac 's work on developing a relativistic quantum electromagnetism. Before his formulation, the presence of electric charge was simply inserted into the equations of quantum mechanics (QM), but in 1931 Dirac showed that a discrete charge is implied by QM. [ 29 ] That is to say, we can maintain the form of Maxwell's equations and still have magnetic charges.
Consider a system consisting of a single stationary electric monopole (an electron, say) and a single stationary magnetic monopole, which would not exert any forces on each other. Classically, the electromagnetic field surrounding them has a momentum density given by the Poynting vector , and it also has a total angular momentum , which is proportional to the product q e q m , and is independent of the distance between them.
Quantum mechanics dictates, however, that angular momentum is quantized as a multiple of ħ , so therefore the product q e q m must also be quantized. This means that if even a single magnetic monopole existed in the universe, and the form of Maxwell's equations is valid, all electric charges would then be quantized .
Although it would be possible simply to integrate over all space to find the total angular momentum in the above example, Dirac took a different approach. This led him to new ideas. He considered a point-like magnetic charge whose magnetic field behaves as q m / r 2 and is directed in the radial direction, located at the origin. Because the divergence of B is equal to zero everywhere except for the locus of the magnetic monopole at r = 0 , one can locally define the vector potential such that the curl of the vector potential A equals the magnetic field B .
However, the vector potential cannot be defined globally precisely because the divergence of the magnetic field is proportional to the Dirac delta function at the origin. We must define one set of functions for the vector potential on the "northern hemisphere" (the half-space z > 0 above the particle), and another set of functions for the "southern hemisphere". These two vector potentials are matched at the "equator" (the plane z = 0 through the particle), and they differ by a gauge transformation . The wave function of an electrically charged particle (a "probe charge") that orbits the "equator" generally changes by a phase, much like in the Aharonov–Bohm effect . This phase is proportional to the electric charge q e of the probe, as well as to the magnetic charge q m of the source. Dirac was originally considering an electron whose wave function is described by the Dirac equation .
Because the electron returns to the same point after the full trip around the equator, the phase φ of its wave function e iφ must be unchanged, which implies that the phase φ added to the wave function must be a multiple of 2 π . This is known as the Dirac quantization condition . In various units, this condition can be expressed as:
where ε 0 is the vacuum permittivity , ħ = h /2 π is the reduced Planck constant , c is the speed of light , and Z {\displaystyle \mathbb {Z} } is the set of integers .
The hypothetical existence of a magnetic monopole would imply that the electric charge must be quantized in certain units; also, the existence of the electric charges implies that the magnetic charges of the hypothetical magnetic monopoles, if they exist, must be quantized in units inversely proportional to the elementary electric charge.
At the time it was not clear if such a thing existed, or even had to. After all, another theory could come along that would explain charge quantization without need for the monopole. The concept remained something of a curiosity. However, in the time since the publication of this seminal work, no other widely accepted explanation of charge quantization has appeared. (The concept of local gauge invariance—see Gauge theory —provides a natural explanation of charge quantization, without invoking the need for magnetic monopoles; but only if the U(1) gauge group is compact, in which case we have magnetic monopoles anyway.)
If we maximally extend the definition of the vector potential for the southern hemisphere, it is defined everywhere except for a semi-infinite line stretched from the origin in the direction towards the northern pole. This semi-infinite line is called the Dirac string and its effect on the wave function is analogous to the effect of the solenoid in the Aharonov–Bohm effect . The quantization condition comes from the requirement that the phases around the Dirac string are trivial, which means that the Dirac string must be unphysical. The Dirac string is merely an artifact of the coordinate chart used and should not be taken seriously.
The Dirac monopole is a singular solution of Maxwell's equation (because it requires removing the worldline from spacetime); in more sophisticated theories, it is superseded by a smooth solution such as the 't Hooft–Polyakov monopole .
A gauge theory like electromagnetism is defined by a gauge field, which associates a group element to each path in space time. For infinitesimal paths, the group element is close to the identity, while for longer paths the group element is the successive product of the infinitesimal group elements along the way.
In electrodynamics, the group is U(1) , unit complex numbers under multiplication. For infinitesimal paths, the group element is 1 + iA μ dx μ which implies that for finite paths parametrized by s , the group element is:
The map from paths to group elements is called the Wilson loop or the holonomy , and for a U(1) gauge group it is the phase factor which the wavefunction of a charged particle acquires as it traverses the path. For a loop:
So that the phase a charged particle gets when going in a loop is the magnetic flux through the loop. When a small solenoid has a magnetic flux, there are interference fringes for charged particles which go around the solenoid, or around different sides of the solenoid, which reveal its presence.
But if all particle charges are integer multiples of e , solenoids with a flux of 2 π / e have no interference fringes, because the phase factor for any charged particle is exp(2 π i ) = 1 . Such a solenoid, if thin enough, is quantum-mechanically invisible. If such a solenoid were to carry a flux of 2 π / e , when the flux leaked out from one of its ends it would be indistinguishable from a monopole.
Dirac's monopole solution in fact describes an infinitesimal line solenoid ending at a point, and the location of the solenoid is the singular part of the solution, the Dirac string. Dirac strings link monopoles and antimonopoles of opposite magnetic charge, although in Dirac's version, the string just goes off to infinity. The string is unobservable, so you can put it anywhere, and by using two coordinate patches, the field in each patch can be made nonsingular by sliding the string to where it cannot be seen.
In a U(1) gauge group with quantized charge, the group is a circle of radius 2 π / e . Such a U(1) gauge group is called compact . Any U(1) that comes from a grand unified theory (GUT) is compact – because only compact higher gauge groups make sense. The size of the gauge group is a measure of the inverse coupling constant, so that in the limit of a large-volume gauge group, the interaction of any fixed representation goes to zero.
The case of the U(1) gauge group is a special case because all its irreducible representations are of the same size – the charge is bigger by an integer amount, but the field is still just a complex number – so that in U(1) gauge field theory it is possible to take the decompactified limit with no contradiction. The quantum of charge becomes small, but each charged particle has a huge number of charge quanta so its charge stays finite. In a non-compact U(1) gauge group theory, the charges of particles are generically not integer multiples of a single unit. Since charge quantization is an experimental certainty, it is clear that the U(1) gauge group of electromagnetism is compact.
GUTs lead to compact U(1) gauge groups, so they explain charge quantization in a way that seems logically independent from magnetic monopoles. However, the explanation is essentially the same, because in any GUT that breaks down into a U(1) gauge group at long distances, there are magnetic monopoles.
The argument is topological:
Hence, the Dirac monopole is a topological defect in a compact U(1) gauge theory. When there is no GUT, the defect is a singularity – the core shrinks to a point. But when there is some sort of short-distance regulator on spacetime, the monopoles have a finite mass. Monopoles occur in lattice U(1) , and there the core size is the lattice size. In general, they are expected to occur whenever there is a short-distance regulator.
In the universe, quantum gravity provides the regulator. When gravity is included, the monopole singularity can be a black hole, and for large magnetic charge and mass, the black hole mass is equal to the black hole charge, so that the mass of the magnetic black hole is not infinite. If the black hole can decay completely by Hawking radiation , the lightest charged particles cannot be too heavy. [ 31 ] The lightest monopole should have a mass less than or comparable to its charge in natural units .
So in a consistent holographic theory, of which string theory is the only known example, there are always finite-mass monopoles. For ordinary electromagnetism, the upper mass bound is not very useful because it is about same size as the Planck mass .
In mathematics, a (classical) gauge field is defined as a connection over a principal G-bundle over spacetime. G is the gauge group, and it acts on each fiber of the bundle separately.
A connection on a G -bundle tells you how to glue fibers together at nearby points of M . It starts with a continuous symmetry group G that acts on the fiber F , and then it associates a group element with each infinitesimal path. Group multiplication along any path tells you how to move from one point on the bundle to another, by having the G element associated to a path act on the fiber F .
In mathematics, the definition of bundle is designed to emphasize topology, so the notion of connection is added on as an afterthought. In physics, the connection is the fundamental physical object. One of the fundamental observations in the theory of characteristic classes in algebraic topology is that many homotopical structures of nontrivial principal bundles may be expressed as an integral of some polynomial over any connection over it. Note that a connection over a trivial bundle can never give us a nontrivial principal bundle.
If spacetime is R 4 {\displaystyle \mathbb {R} ^{4}} the space of all possible connections of the G -bundle is connected . But consider what happens when we remove a timelike worldline from spacetime. The resulting spacetime is homotopically equivalent to the topological sphere S 2 .
A principal G -bundle over S 2 is defined by covering S 2 by two charts , each homeomorphic to the open 2-ball such that their intersection is homeomorphic to the strip S 1 × I . 2-balls are homotopically trivial and the strip is homotopically equivalent to the circle S 1 . So a topological classification of the possible connections is reduced to classifying the transition functions. The transition function maps the strip to G , and the different ways of mapping a strip into G are given by the first homotopy group of G .
So in the G -bundle formulation, a gauge theory admits Dirac monopoles provided G is not simply connected , whenever there are paths that go around the group that cannot be deformed to a constant path (a path whose image consists of a single point). U(1), which has quantized charges, is not simply connected and can have Dirac monopoles while R {\displaystyle \mathbb {R} } , its universal covering group , is simply connected, doesn't have quantized charges and does not admit Dirac monopoles. The mathematical definition is equivalent to the physics definition provided that—following Dirac—gauge fields are allowed that are defined only patch-wise, and the gauge field on different patches are glued after a gauge transformation.
The total magnetic flux is none other than the first Chern number of the principal bundle, and depends only upon the choice of the principal bundle, and not the specific connection over it. In other words, it is a topological invariant.
This argument for monopoles is a restatement of the lasso argument for a pure U(1) theory. It generalizes to d + 1 dimensions with d ≥ 2 in several ways. One way is to extend everything into the extra dimensions, so that U(1) monopoles become sheets of dimension d − 3 . Another way is to examine the type of topological singularity at a point with the homotopy group π d −2 (G) .
In more recent years, a new class of theories has also suggested the existence of magnetic monopoles.
During the early 1970s, the successes of quantum field theory and gauge theory in the development of electroweak theory and the mathematics of the strong nuclear force led many theorists to move on to attempt to combine them in a single theory known as a Grand Unified Theory (GUT). Several GUTs were proposed, most of which implied the presence of a real magnetic monopole particle. More accurately, GUTs predicted a range of particles known as dyons , of which the most basic state was a monopole. The charge on magnetic monopoles predicted by GUTs is either 1 or 2 gD , depending on the theory.
The majority of particles appearing in any quantum field theory are unstable, and they decay into other particles in a variety of reactions that must satisfy various conservation laws . Stable particles are stable because there are no lighter particles into which they can decay and still satisfy the conservation laws. For instance, the electron has a lepton number of one and an electric charge of one, and there are no lighter particles that conserve these values. On the other hand, the muon , essentially a heavy electron, can decay into the electron plus two quanta of energy, and hence it is not stable.
The dyons in these GUTs are also stable, but for an entirely different reason. The dyons are expected to exist as a side effect of the "freezing out" of the conditions of the early universe, or a symmetry breaking . In this scenario, the dyons arise due to the configuration of the vacuum in a particular area of the universe, according to the original Dirac theory. They remain stable not because of a conservation condition, but because there is no simpler topological state into which they can decay.
The length scale over which this special vacuum configuration exists is called the correlation length of the system. A correlation length cannot be larger than causality would allow, therefore the correlation length for making magnetic monopoles must be at least as big as the horizon size determined by the metric of the expanding universe . According to that logic, there should be at least one magnetic monopole per horizon volume as it was when the symmetry breaking took place.
Cosmological models of the events following the Big Bang make predictions about what the horizon volume was, which lead to predictions about present-day monopole density. Early models predicted an enormous density of monopoles, in clear contradiction to the experimental evidence. [ 32 ] [ 33 ] This was called the " monopole problem ". Its widely accepted resolution was not a change in the particle-physics prediction of monopoles, but rather in the cosmological models used to infer their present-day density. Specifically, more recent theories of cosmic inflation drastically reduce the predicted number of magnetic monopoles, to a density small enough to make it unsurprising that humans have never seen one. [ 34 ] This resolution of the "monopole problem" was regarded as a success of cosmic inflation theory . (However, of course, it is only a noteworthy success if the particle-physics monopole prediction is correct. [ 35 ] ) For these reasons, monopoles became a major interest in the 1970s and 80s, along with the other "approachable" predictions of GUTs such as proton decay .
Many of the other particles predicted by these GUTs were beyond the abilities of current experiments to detect. For instance, a wide class of particles known as the X and Y bosons are predicted to mediate the coupling of the electroweak and strong forces, but these particles are extremely heavy and well beyond the capabilities of any reasonable particle accelerator to create.
Experimental searches for magnetic monopoles can be placed in one of two categories: those that try to detect preexisting magnetic monopoles and those that try to create and detect new magnetic monopoles.
Passing a magnetic monopole through a coil of wire induces a net current in the coil. This is not the case for a magnetic dipole or higher order magnetic pole, for which the net induced current is zero, and hence the effect can be used as an unambiguous test for the presence of magnetic monopoles. In a wire with finite resistance, the induced current quickly dissipates its energy as heat, but in a superconducting loop the induced current is long-lived. By using a highly sensitive "superconducting quantum interference device" ( SQUID ) one can, in principle, detect even a single magnetic monopole.
According to standard inflationary cosmology, magnetic monopoles produced before inflation would have been diluted to an extremely low density today. Magnetic monopoles may also have been produced thermally after inflation, during the period of reheating. However, the current bounds on the reheating temperature span 18 orders of magnitude and as a consequence the density of magnetic monopoles today is not well constrained by theory.
There have been many searches for preexisting magnetic monopoles. Although there has been one tantalizing event recorded, by Blas Cabrera Navarro on the night of February 14, 1982 (thus, sometimes referred to as the " Valentine's Day Monopole" [ 36 ] ), there has never been reproducible evidence for the existence of magnetic monopoles. [ 14 ] The lack of such events places an upper limit on the number of monopoles of about one monopole per 10 29 nucleons .
Another experiment in 1975 resulted in the announcement of the detection of a moving magnetic monopole in cosmic rays by the team led by P. Buford Price . [ 13 ] Price later retracted his claim, and a possible alternative explanation was offered by Luis Walter Alvarez . [ 37 ] In his paper it was demonstrated that the path of the cosmic ray event that was claimed due to a magnetic monopole could be reproduced by the path followed by a platinum nucleus decaying first to osmium , and then to tantalum .
High-energy particle colliders have been used to try to create magnetic monopoles. Due to the conservation of magnetic charge, magnetic monopoles must be created in pairs, one north and one south. Due to conservation of energy, only magnetic monopoles with masses less than half of the center of mass energy of the colliding particles can be produced. Beyond this, very little is known theoretically about the creation of magnetic monopoles in high-energy particle collisions. This is due to their large magnetic charge, which invalidates all the usual calculational techniques. As a consequence, collider-based searches for magnetic monopoles cannot, as yet, provide lower bounds on the mass of magnetic monopoles. They can however provide upper bounds on the probability (or cross section) of pair production, as a function of energy.
The ATLAS experiment at the Large Hadron Collider currently has the most stringent cross section limits for magnetic monopoles of 1 and 2 Dirac charges, produced through Drell–Yan pair production. A team led by Wendy Taylor searches for these particles based on theories that define them as long lived (they do not quickly decay), as well as being highly ionizing (their interaction with matter is predominantly ionizing). In 2019 the search for magnetic monopoles in the ATLAS detector reported its first results from data collected from the LHC Run 2 collisions at center of mass energy of 13 TeV, which at 34.4 fb −1 is the largest dataset analyzed to date. [ 38 ]
The MoEDAL experiment , installed at the Large Hadron Collider, is currently searching for magnetic monopoles and large supersymmetric particles using nuclear track detectors and aluminum bars around LHCb 's VELO detector. The particles it is looking for damage the plastic sheets that comprise the nuclear track detectors along their path, with various identifying features. Further, the aluminum bars can trap sufficiently slowly moving magnetic monopoles. The bars can then be analyzed by passing them through a SQUID.
Since around 2003, various condensed-matter physics groups have used the term "magnetic monopole" to describe a different and largely unrelated phenomenon. [ 19 ] [ 20 ]
A true magnetic monopole would be a new elementary particle , and would violate Gauss's law for magnetism ∇⋅ B = 0 . A monopole of this kind, which would help to explain the law of charge quantization as formulated by Paul Dirac in 1931, [ 39 ] has never been observed in experiments. [ 40 ] [ 41 ]
The monopoles studied by condensed-matter groups have none of these properties. They are not a new elementary particle, but rather are an emergent phenomenon in systems of everyday particles ( protons , neutrons , electrons , photons ); in other words, they are quasi-particles . They are not sources for the B -field (i.e., they do not violate ∇⋅ B = 0 ); instead, they are sources for other fields, for example the H -field , [ 6 ] the " B * -field" (related to superfluid vorticity), [ 7 ] [ 42 ] or various other quantum fields. [ 43 ] They are not directly relevant to grand unified theories or other aspects of particle physics, and do not help explain charge quantization —except insofar as studies of analogous situations can help confirm that the mathematical analyses involved are sound. [ 44 ]
There are a number of examples in condensed-matter physics where collective behavior leads to emergent phenomena that resemble magnetic monopoles in certain respects, [ 18 ] [ 45 ] [ 46 ] [ 47 ] including most prominently the spin ice materials. [ 6 ] [ 48 ] While these should not be confused with hypothetical elementary monopoles existing in the vacuum, they nonetheless have similar properties and can be probed using similar techniques.
Some researchers use the term magnetricity to describe the manipulation of magnetic monopole quasiparticles in spin ice , [ 49 ] [ 50 ] [ 48 ] [ 51 ] in analogy to the word "electricity".
One example of the work on magnetic monopole quasiparticles is a paper published in the journal Science in September 2009, in which researchers described the observation of quasiparticles resembling magnetic monopoles. A single crystal of the spin ice material dysprosium titanate was cooled to a temperature between 0.6 kelvin and 2.0 kelvin. Using observations of neutron scattering , the magnetic moments were shown to align into interwoven tubelike bundles resembling Dirac strings . At the defect formed by the end of each tube, the magnetic field looks like that of a monopole. Using an applied magnetic field to break the symmetry of the system, the researchers were able to control the density and orientation of these strings. A contribution to the heat capacity of the system from an effective gas of these quasiparticles was also described. [ 17 ] [ 52 ] This research went on to win the 2012 Europhysics Prize for condensed matter physics.
In another example, a paper in the February 11, 2011 issue of Nature Physics describes creation and measurement of long-lived magnetic monopole quasiparticle currents in spin ice. By applying a magnetic-field pulse to crystal of dysprosium titanate at 0.36 K, the authors created a relaxing magnetic current that lasted for several minutes. They measured the current by means of the electromotive force it induced in a solenoid coupled to a sensitive amplifier, and quantitatively described it using a chemical kinetic model of point-like charges obeying the Onsager–Wien mechanism of carrier dissociation and recombination. They thus derived the microscopic parameters of monopole motion in spin ice and identified the distinct roles of free and bound magnetic charges. [ 51 ]
In superfluids , there is a field B * , related to superfluid vorticity, which is mathematically analogous to the magnetic B -field. Because of the similarity, the field B * is called a "synthetic magnetic field". In January 2014, it was reported that monopole quasiparticles [ 53 ] for the B * field were created and studied in a spinor Bose–Einstein condensate. [ 7 ] This constitutes the first example of a quasi-magnetic monopole observed within a system governed by quantum field theory. [ 44 ]
Updates to the theoretical and experimental searches in matter can be found in the reports by G. Giacomelli (2000) and by S. Balestra (2011) in the Bibliography section.
This article incorporates material from N. Hitchin (2001) [1994], "Magnetic Monopole" , Encyclopedia of Mathematics , EMS Press , which is licensed under the Creative Commons Attribution/Share-Alike License and GNU Free Documentation License . | https://en.wikipedia.org/wiki/Magnetic_monopole |
Magnetic pulsations are extremely low frequency disturbances in the Earth's magnetosphere driven by its interactions with the solar wind . [ 1 ] These variations in the planet's magnetic field can oscillate for multiple hours when a solar wind driving force strikes a resonance. [ 2 ] This is a form of Kelvin–Helmholtz instability . [ 1 ] The intensity, frequency, and orientation of these variations is measured by Intermagnet . [ 2 ]
In 1964, the International Association of Geomagnetism and Aeronomy (IAGA) proposed a classification of magnetic pulsations into continuous pulsations (Pc) and irregular pulsations (Pi). [ 1 ] [ 3 ]
This astronomy -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Magnetic_pulsations |
Magnetic reluctance , or magnetic resistance , is a concept used in the analysis of magnetic circuits . It is defined as the ratio of magnetomotive force (mmf) to magnetic flux . It represents the opposition to magnetic flux, and depends on the geometry and composition of an object.
Magnetic reluctance in a magnetic circuit is analogous to electrical resistance in an electrical circuit in that resistance is a measure of the opposition to the electric current . The definition of magnetic reluctance is analogous to Ohm's law in this respect. However, magnetic flux passing through a reluctance does not give rise to dissipation of heat as it does for current through a resistance. Thus, the analogy cannot be used for modelling energy flow in systems where energy crosses between the magnetic and electrical domains. An alternative analogy to the reluctance model which does correctly represent energy flows is the gyrator–capacitor model .
Magnetic reluctance is a scalar extensive quantity . The unit for magnetic reluctance is inverse henry , H −1 .
The term reluctance was coined in May 1888 by Oliver Heaviside . [ 1 ] The notion of "magnetic resistance" was first mentioned by James Joule in 1840. [ 2 ] The idea for a magnetic flux law, similar to Ohm's law for closed electric circuits , is attributed to Henry Augustus Rowland in an 1873 paper. [ 3 ] Rowland is also responsible for coining the term magnetomotive force in 1880, [ 4 ] also coined, apparently independently, a bit later in 1883 by Bosanquet. [ 5 ]
Reluctance is usually represented by a cursive capital R {\displaystyle {\mathcal {R}}} .
In both AC and DC fields, the reluctance is the ratio of the magnetomotive force (MMF) in a magnetic circuit to the magnetic flux in this circuit. In a pulsating DC or AC field, the reluctance also pulsates (see phasors ).
The definition can be expressed as follows: R = F Φ {\displaystyle {\mathcal {R}}={\frac {\mathcal {F}}{\Phi }}} where
It is sometimes known as Hopkinson's law and is analogous to Ohm's Law with resistance replaced by reluctance, voltage by MMF and current by magnetic flux.
Permeance is the inverse of reluctance: P = 1 R {\displaystyle {\mathcal {P}}={\frac {1}{\mathcal {R}}}}
Its SI derived unit is the henry (the same as the unit of inductance , although the two concepts are distinct).
Magnetic flux always forms a closed loop, as described by Maxwell's equations , but the path of the loop depends on the reluctance of the surrounding materials. It is concentrated around the path of least reluctance. Air and vacuum have high reluctance, while easily magnetized materials such as soft iron have low reluctance. The concentration of flux in low-reluctance materials forms strong temporary poles and causes mechanical forces that tend to move the materials towards regions of higher flux so it is always an attractive force (pull).
The reluctance of a uniform magnetic circuit can be calculated as: R = l μ 0 μ r A = l μ A {\displaystyle {\mathcal {R}}={\frac {l}{\mu _{0}\mu _{r}A}}={\frac {l}{\mu A}}}
where
Reluctance can also be applied to: | https://en.wikipedia.org/wiki/Magnetic_reluctance |
Magnetic resonance is a process by which a physical excitation ( resonance ) is set up via magnetism .
This process was used to develop magnetic resonance imaging (MRI) and nuclear magnetic resonance spectroscopy (NMRS) technology.
It is also being used to develop nuclear magnetic resonance quantum computers .
The first observation of electron-spin resonance was in 1944 by Y. K. Zavosky, a Soviet physicist then teaching at Kazan State University (now Kazan Federal University). Nuclear magnetic resonance was first observed in 1946 in the US by a team led by Felix Bloch at the same time as a separate team led by Edward Mills Purcell , the two of whom would later be the 1952 Nobel Laureates in Physics. [ 1 ] [ 2 ] [ 3 ]
A natural way to measure the separation between two energy levels is to find a measurable quantity defined by this separation and measure it. However, the precision of this method is limited by measurement precision and thus may be poor.
Alternatively, we can set up an experiment in which the system's behavior depends on the energy level. If we apply an external field of controlled frequency, we can measure the level separation by noting at which frequency a qualitative change happens: that would mean that at this frequency, the transition between two states has a high probability. An example of such an experiment is a variation of Stern–Gerlach experiment , in which magnetic moment is measured by finding resonance frequency for the transition between two spin states. [ 4 ] [ 5 ]
This article about magnetic resonance imaging is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Magnetic_resonance |
In quantum mechanics , magnetic resonance is a resonant effect that can appear when a magnetic dipole is exposed to a static magnetic field and perturbed with another, oscillating electromagnetic field . Due to the static field, the dipole can assume a number of discrete energy eigenstates , depending on the value of its angular momentum (azimuthal) quantum number . The oscillating field can then make the dipole transit between its energy states with a certain probability and at a certain rate. The overall transition probability will depend on the field's frequency and the rate will depend on its amplitude . When the frequency of that field leads to the maximum possible transition probability between two states, a magnetic resonance has been achieved. In that case, the energy of the photons composing the oscillating field matches the energy difference between said states. If the dipole is tickled with a field oscillating far from resonance, it is unlikely to transition. That is analogous to other resonant effects, such as with the forced harmonic oscillator . The periodic transition between the different states is called Rabi cycle and the rate at which that happens is called Rabi frequency . The Rabi frequency should not be confused with the field's own frequency. Since many atomic nuclei species can behave as a magnetic dipole, this resonance technique is the basis of nuclear magnetic resonance , including nuclear magnetic resonance imaging and nuclear magnetic resonance spectroscopy .
As a magnetic dipole, using a spin 1 2 {\displaystyle {\tfrac {1}{2}}} system such as a proton; according to the quantum mechanical state of the system, denoted by | Ψ ( t ) ⟩ {\displaystyle |\Psi (t)\rangle } , evolved by the action of a unitary operator e − i H ^ t / ℏ {\displaystyle e^{-i{{\hat {H}}t}/\hbar }} ; the result obeys Schrödinger equation :
States with definite energy evolve in time with phase e − i E t / ℏ {\displaystyle e^{-iEt/\hbar }} , ( | Ψ ( t ) ⟩ = | Ψ ( 0 ) ⟩ e − i E t / ℏ {\displaystyle |\Psi (t)\rangle =|\Psi (0)\rangle e^{-iEt/\hbar }} ) where E is the energy of the state, since the probability of finding the system in state | ⟨ x | Ψ ( t ) ⟩ | 2 {\displaystyle |\langle x|\Psi (t)\rangle |^{2}} = | ⟨ x | Ψ ( 0 ) ⟩ | 2 {\displaystyle |\langle x|\Psi (0)\rangle |^{2}} is independent of time. Such states are termed stationary states , so if a system is prepared in a stationary state, (i.e. one of the eigenstates of the Hamiltonian operator ), then P ( t ) = 1, i.e. it remains in that state indefinitely. This is the case only for isolated systems. When a system in a stationary state is perturbed, its state changes, so it is no longer an eigenstate of the system's complete Hamiltonian. This same phenomenon happens in magnetic resonance for a spin 1 2 {\displaystyle {\tfrac {1}{2}}} system in a magnetic field.
The Hamiltonian for a magnetic dipole m {\displaystyle \mathbf {m} } (associated with a spin 1 2 {\displaystyle {\tfrac {1}{2}}} particle) in a magnetic field B 0 = B 0 z ^ {\displaystyle \mathbf {B_{0}} =B_{0}{\hat {z}}} is:
Here ω 0 := γ B 0 {\displaystyle \omega _{0}:=\gamma B_{0}} is the Larmor precession frequency of the dipole for B 0 {\displaystyle \mathbf {B_{0}} } magnetic field and σ z {\displaystyle \sigma _{z}} is z Pauli matrix . So the eigenvalues of H ^ {\displaystyle {\hat {H}}} are − ℏ 2 ω 0 {\displaystyle -{\tfrac {\hbar }{2}}\omega _{0}} and ℏ 2 ω 0 {\displaystyle {\tfrac {\hbar }{2}}\omega _{0}} . If the system is perturbed by a weak magnetic field B 1 {\displaystyle \mathbf {B_{1}} } , rotating counterclockwise in x-y plane (normal to B 0 {\displaystyle \mathbf {B_{0}} } ) with angular frequency ω {\displaystyle \omega } , so that B 1 = i ^ B 1 cos ω t − j ^ B 1 sin ω t {\displaystyle \mathbf {B_{1}} ={\hat {i}}B_{1}\cos {\omega t}-{\hat {j}}B_{1}\sin {\omega t}} , then [ 1 0 ] {\displaystyle {\begin{bmatrix}1\\0\end{bmatrix}}} and [ 0 1 ] {\displaystyle {\begin{bmatrix}0\\1\end{bmatrix}}} are not eigenstates of the Hamiltonian, which is modified into
It is inconvenient to deal with a time-dependent hamiltonian. To make H ^ {\displaystyle {\hat {H}}} time-independent requires a new reference frame rotating with B 1 {\displaystyle \mathbf {B_{1}} } , i.e. rotation operator R ^ ( t ) {\displaystyle {\hat {R}}(t)} on | Ψ ( t ) ⟩ {\displaystyle |\Psi (t)\rangle } , which amounts to basis change in Hilbert space . Using this on Schrödinger's equation, the Hamiltonian becomes:
Writing R ^ ( t ) {\displaystyle {\hat {R}}(t)} in the basis of σ z {\displaystyle \sigma _{z}} as-
Using this form of the Hamiltonian a new basis is found:
This Hamiltonian is exactly similar to that of a two state system with unperturbed energies ℏ 2 Δ ω {\displaystyle {\tfrac {\hbar }{2}}\Delta \omega } and − ℏ 2 Δ ω {\displaystyle -{\tfrac {\hbar }{2}}\Delta \omega } with a perturbation expressed by ℏ 2 ( 0 − ω 1 − ω 1 0 ) {\displaystyle {\tfrac {\hbar }{2}}{\begin{pmatrix}0&-\omega _{1}\\-\omega _{1}&0\end{pmatrix}}} ; According to Rabi oscillation , starting with [ 1 0 ] {\displaystyle {\begin{bmatrix}1\\0\end{bmatrix}}} state, a dipole in parallel to B 0 {\displaystyle \mathbf {B_{0}} } with energy − ℏ 2 ω 0 {\displaystyle -{\tfrac {\hbar }{2}}\omega _{0}} , the probability that it will transit to [ 0 1 ] {\displaystyle {\begin{bmatrix}0\\1\end{bmatrix}}} state (i.e. it will flip) is
P 12 = | ω 1 2 | | Δ ω 2 + ω 1 2 | sin 2 [ ω 1 2 + Δ ω 2 t / 2 ] {\displaystyle P_{12}={\frac {|\omega _{1}^{2}|}{|\Delta \omega ^{2}+\omega _{1}^{2}|}}\sin ^{2}[{\sqrt {\omega _{1}^{2}+\Delta \omega ^{2}}}t/2]}
Now consider ω = ω 0 {\displaystyle \omega =\omega _{0}} , i.e. the B 1 {\displaystyle \mathbf {B_{1}} } field oscillates at the same rate the dipole exposed to the B 0 {\displaystyle \mathbf {B_{0}} } field does. That is a case of resonance . Then at specific points in time, namely t = ( 2 n + 1 ) π ω 1 2 + Δ ω 2 {\displaystyle t={\frac {(2n+1)\pi }{\sqrt {\omega _{1}^{2}+\Delta \omega ^{2}}}}} , the dipole will flip, going to the other energy eigenstate [ 0 1 ] {\displaystyle {\begin{bmatrix}0\\1\end{bmatrix}}} with a 100% probability. When ω ≠ ω 0 {\displaystyle \omega \not =\omega _{0}} , the probability of change of energy state is small. Therefore, the resonance condition can be used, for instance, to measure the magnetic moment of a dipole or the magnetic field at a point in space.
A special case occurs where a system oscillates between two unstable levels that have the same life time τ {\displaystyle \tau } . [ 1 ] If atoms are excited at a constant, say n/time, to the first state, some decay and the rest have a probability P 12 {\displaystyle P_{12}} to transition to the second state, so in the time interval between t and ( t + dt ) the number of atoms that jump to the second state from the first is n ( 1 − e − t / τ ) P 12 d t {\displaystyle n(1-e^{-t/\tau })P_{12}dt} , so at time t the number of atoms in the second state is
The rate of decay from state two depends on the number of atoms that were collected in that state from all previous intervals, so the number of atoms in state 2 is ∫ − ∞ 0 n e − t / τ P 12 d t {\textstyle \int _{-\infty }^{0}ne^{-t/\tau }P_{12}\ dt} ; The rate of decay of atoms from state two is proportional to the number of atoms present in that state, while the constant of proportionality is decay constant λ {\displaystyle \lambda } . Performing the integration rate of decay of atoms from state two is obtained as:
From this expression many interesting points can be exploited, such
The existence of spin angular momentum of electrons was discovered experimentally by the Stern–Gerlach experiment . In that study a beam of neutral atoms with one electron in the valence shell , carrying no orbital momentum (from the viewpoint of quantum mechanics) was passed through an inhomogeneous magnetic field. This process was not approximate due to the small deflection angle, resulting in considerable uncertainty in the measured value of the split beam.
Rabi's method was an improvement over Stern-Gerlach. As shown in the figure, the source emits a beam of neutral atoms, having spin angular momentum ℏ / 2 {\displaystyle \hbar /2} . The beam passes through a series of three aligned magnets. Magnet 1 produces an inhomogeneous magnetic field with a high gradient ∂ B ∂ z {\displaystyle {\frac {\partial B}{\partial z}}} (as in Stern–Gerlach), so the atoms having 'upward' spin (with S z = ℏ / 2 {\displaystyle S_{z}=\hbar /2} ) will deviate downward (path 1), i.e. to the region of less magnetic field B, to minimize energy. Atoms with 'downward' spin with S z = − ℏ / 2 {\displaystyle S_{z}=-\hbar /2} ) will deviate upward similarly (path 2). Beams are passed through slit 1, to reduce any effects of source beyond. Magnet 2 produces only a uniform magnetic field in the vertical direction applying no force on the atomic beam, and magnet 3 is actually inverted magnet 1. In the region between the poles of magnet 3, atoms having 'upward' spin get upward push and atoms having 'downward' spin feel downward push, so their path remains 1 and 2 respectively. These beams pass through a second slit S2, and arrive at detector and get detected.
If a horizontal rotating field B 1 {\displaystyle B_{1}} , angular frequency of rotation ω 1 {\displaystyle \omega _{1}} is applied in the region between poles of magnet 2, produced by oscillating current in circular coils then there is a probability for the atoms passing through there from one spin state to another ( S z = + ℏ / 2 − > − ℏ / 2 {\displaystyle S_{z}=+\hbar /2->-\hbar /2} and vice versa), when ω 1 {\displaystyle \omega _{1}} = ω p {\displaystyle \omega _{p}} , Larmor frequency of precession of magnetic moment in B. [ clarification needed ] The atoms that transition from 'upward' to 'downward' spin will experience a downward force while passing through magnet 3, and will follow path 1'. Similarly, atoms that change from 'downward' to 'upward' spin will follow path 2', and these atoms will not reach the detector, causing a minimum in detector count. If angular frequency ω 1 {\displaystyle \omega _{1}} of B 1 {\displaystyle B_{1}} is varied continuously, then a minimum in detector current will be obtained (when ω 1 {\displaystyle \omega _{1}} = ω p {\displaystyle \omega _{p}} ). From this known value of ω 1 {\displaystyle \omega _{1}} ( = g e B / 2 ℏ {\displaystyle =geB/{2\hbar }} , where g is ' Land é g factor '), 'Landé g-factor' is obtained which will enable one to have correct value of magnetic moment μ ( = g q ℏ / 4 m ) {\displaystyle \mu ~(=gq\hbar /{4m})} . This experiment, performed by Isidor Isaac Rabi is more sensitive and accurate compared than Stern-Gerlach.
Spin angular momentum allows magnetic resonance phenomena to be explained via classical physics. When viewed from the reference frame attached to the rotating field, it seems that the magnetic dipole precesses around a net magnetic field ( Δ ω z ^ − ω 1 X ^ ) / γ {\displaystyle (\Delta \omega {\hat {z}}-\omega _{1}{\hat {X}})/\gamma } , where z ^ {\displaystyle {\hat {z}}} is the unit vector along uniform magnetic field B 0 {\displaystyle B_{0}} and X ^ {\displaystyle {\hat {X}}} is the same in the direction of rotating field B 1 {\displaystyle B_{1}} and δ ω = ω − ω 0 {\displaystyle \delta \omega =\omega -\omega _{0}} .
Classical electrodynamics tells us that torque on a magnetic dipole of moment m {\displaystyle \mathbf {m} } is m × B {\displaystyle \mathbf {m} \times \mathbf {B} } , so its equation of motion is d L d t = m × B {\displaystyle {\frac {d\mathbf {L} }{dt}}=\mathbf {m} \times \mathbf {B} } , (where L {\displaystyle \mathbf {L} } is the angular momentum associated with dipole) so –
For the case under consideration the dipole is under the action of magnetic field B {\displaystyle \mathbf {B} } and B 1 {\displaystyle \mathbf {B} _{1}} , hence
It is easier to solve it by transforming co-ordinate system to OXYZ in which B 1 {\displaystyle \mathbf {B} _{1}} becomes OX axis, in that frame –
here ω = ω z ^ . {\displaystyle {\boldsymbol {\omega }}=\omega {\hat {z}}.} Using ω 0 = γ B {\displaystyle \omega _{0}=\gamma B} and ω 1 = γ B 1 {\displaystyle \omega _{1}=\gamma B_{1}} , one can see that –
so, here effective field becomes : B e f f e c t i v e = Δ ω − ω 1 = Δ ω z ^ − ω 1 X ^ {\displaystyle \mathbf {B} _{\rm {effective}}=\Delta {\boldsymbol {\omega }}-{\boldsymbol {\omega _{1}}}=\Delta \omega {\hat {z}}-\omega _{1}{\hat {X}}}
So when ω = ω 0 {\displaystyle \omega =\omega _{0}} , a high precession amplitude allows the magnetic moment to be completely flipped. Classical and quantum mechanical predictions correspond well, which can be viewed as an example of the Bohr Correspondence principle, which states that quantum mechanical phenomena, when predicted in classical regime, should match the classical result. The origin of this correspondence is that the evolution of the expected value of magnetic moment is identical to that obtained by classical reasoning. The expectation value of the magnetic moment is ⟨ m ⟩ = γ ⟨ S ⟩ {\displaystyle \langle \mathbf {m} \rangle =\gamma \langle \mathbf {S} \rangle } . The time evolution of ⟨ m ⟩ {\displaystyle \langle \mathbf {m} \rangle } is given by
so, [ m i , H ^ ] = [ m i , − m j B j ] = [ γ S i , − γ S j B j ] = − γ 2 [ S i , S j B j ] = − γ 2 i ℏ [ S k B j − S j B k ] , ( i ≠ j , k ) {\displaystyle [m_{i},{\hat {H}}]=[m_{i},-m_{j}B_{j}]=[\gamma \mathbf {S} _{i},-\gamma \mathbf {S} _{j}\mathbf {B} _{j}]=-\gamma ^{2}[\mathbf {S} _{i},\mathbf {S} _{j}\mathbf {B} _{j}]=-\gamma ^{2}i\hbar [{\mathbf {S} _{k}\mathbf {B} _{j}-\mathbf {S} _{j}\mathbf {B} _{k}}],(i\neq j,k)}
So, [ m i , H ^ ] = i ℏ γ [ B j m k − B k m j ] {\displaystyle [m_{i},{\hat {H}}]=i\hbar \gamma [\mathbf {B} _{j}\mathbf {m} _{k}-\mathbf {B} _{k}\mathbf {m} _{j}]} and
d d t ⟨ m ( t ) ⟩ = γ ⟨ m ( t ) ⟩ × ⟨ B ( t ) ⟩ {\displaystyle {\frac {d}{dt}}\langle \mathbf {m} (t)\rangle =\gamma \langle \mathbf {m} (t)\rangle \times \langle \mathbf {B} (t)\rangle }
which looks exactly similar to the equation of motion of magnetic moment m {\displaystyle \mathbf {m} } in classical mechanics –
This analogy in the mathematical equation for the evolution of magnetic moment and its expectation value facilitates to understand the phenomena without a background of quantum mechanics.
In magnetic resonance imaging (MRI) the spin angular momentum of the proton is used. The most available source for protons in the human body is represented by hydrogen atoms in water. A strong magnetic field B {\displaystyle B} applied to water causes the appearance of two different energy levels for spin angular momentum, + γ ℏ B / 2 {\displaystyle +\gamma \hbar B/2} and − γ ℏ B / 2 {\displaystyle -\gamma \hbar B/2} , using E = − μ ⋅ B {\displaystyle E=-\mathbf {\mu } \cdot \mathbf {B} } .
According to the Boltzmann distribution , as the number of systems having energy E {\displaystyle E} out of N 0 {\displaystyle N_{0}} at temperature T {\displaystyle T} is N 0 e − E / k T {\displaystyle N_{0}e^{-E/kT}} (where k {\displaystyle k} is the Boltzmann constant ), the lower energy level, associated with spin ℏ / 2 {\displaystyle \hbar /2} , is more populated than the other. In the presence of a rotating magnetic field more protons flip from S z = + ℏ / 2 {\displaystyle S_{z}=+\hbar /2} to S z = − ℏ / 2 {\displaystyle S_{z}=-\hbar /2} than the other way, causing absorption of microwave or radio-wave radiation (from the rotating field). When the field is withdrawn, protons tend to re-equilibrate along the Boltzmann distribution, so some of them transition from higher energy levels to lower ones, emitting microwave or radio-wave radiation at specific frequencies.
Instead of nuclear spin, spin angular momentum of unpaired electrons is used in EPR ( electron paramagnetic resonance ) in order to detect free radicals, etc.
The phenomenon of magnetic resonance is rooted in the existence of spin angular momentum of a quantum system and its specific orientation with respect to an applied magnetic field. Both cases have no explanation in the classical approach and can be understood only by using quantum mechanics. Some people claim [ who? ] that purely quantum phenomena are those that cannot be explained by the classical approach. For example, phenomena in the microscopic domain that can to some extent be described by classical analogy are not really quantum phenomena. Since the basic elements of magnetic resonance have no classical origin, although analogy can be made with classical Larmor precession , MR should be treated as a quantum phenomenon. | https://en.wikipedia.org/wiki/Magnetic_resonance_(quantum_mechanics) |
Magnetic resonance force microscopy ( MRFM ) is an imaging technique that acquires magnetic resonance images ( MRI ) at nanometer scales, and possibly at atomic scales in the future. MRFM is potentially able to observe protein structures which cannot be seen using X-ray crystallography and protein nuclear magnetic resonance spectroscopy . Detection of the magnetic spin of a single electron has been demonstrated using this technique. The sensitivity of a current MRFM microscope is 10 billion times greater than a medical MRI used in hospitals.
The MRFM concept combines the ideas of magnetic resonance imaging (MRI) and atomic force microscopy (AFM). Conventional MRI employs an inductive coil as an antenna to sense resonant nuclear or electronic spins in a magnetic field gradient. MRFM uses a cantilever tipped with a ferromagnetic (iron cobalt) particle to directly detect a modulated spin gradient force between sample spins and the tip. The magnetic particle is characterized using the technique of cantilever magnetometry . As the ferromagnetic tip moves close to the sample, the atoms' nuclear spins become attracted to it and generate a small force on the cantilever. The spins are then repeatedly flipped, causing the cantilever to gently sway back and forth in a synchronous motion. That displacement is measured with an interferometer (laser beam) to create a series of 2-D images of the sample, which are combined to generate a 3-D image. The interferometer measures resonant frequency of the cantilever. Smaller ferromagnetic particles and softer cantilevers increase the signal-to-noise ratio . Unlike the inductive coil approach, MRFM sensitivity scales favorably as device and sample dimensions are reduced.
Because the signal-to-noise ratio is inversely proportional to the sample size, Brownian motion is the primary source of noise at the scale in which MRFM is useful. Accordingly, MRFM devices are cryogenically cooled. MRFM was specifically devised to determine the structure of proteins in situ .
The basic principles of MRFM imaging and the theoretical possibility of this technology were first described in 1991. [ 1 ] The first MRFM image was obtained in 1993 at the IBM Almaden Research Center with 1-μm vertical resolution and 5-μm lateral resolution using a bulk sample of the paramagnetic substance diphenylpicrylhydrazyl . [ 2 ] The spatial resolution reached nanometer -scale in 2003. [ 3 ] Detection of the magnetic spin of a single electron was achieved in 2004. [ 4 ] In 2009 researchers at IBM and Stanford announced that they had achieved resolution of better than 10 nanometers, imaging tobacco mosaic virus particles on a nanometer-thick layer of adsorbed
hydrocarbons. [ 5 ] | https://en.wikipedia.org/wiki/Magnetic_resonance_force_microscopy |
A magnetic shape-memory alloy (MSMA) is a type of smart material that can undergo significant and reversible changes in shape in response to a magnetic field. This behavior arises due to a combination of magnetic and shape-memory properties within the alloy, allowing it to produce mechanical motion or force under magnetic actuation. MSMAs are commonly made from ferromagnetic materials, particularly nickel-manganese-gallium (Ni-Mn-Ga), and are useful in applications requiring rapid, controllable, and repeatable movement.
MSM alloys are ferromagnetic materials that can produce motion and forces under moderate magnetic fields. Typically, MSMAs are alloys of Nickel, Manganese and Gallium (Ni-Mn-Ga).
A magnetically induced deformation of about 0.2% was presented in 1996 by Dr. Kari Ullakko and co-workers at MIT. [ 1 ] Since then, improvements on the production process and on the subsequent treatment of the alloys have led to deformations of up to 6% for commercially available single crystalline Ni-Mn-Ga MSM elements, [ 2 ] as well as up to 10-12 % and 20% for new alloys in R&D stage. [ 3 ] [ 4 ]
The large magnetically induced strain, as well as the short response times make the MSM technology very attractive for the design of innovative actuators to be used in pneumatics, robotics, medical devices and mechatronics. [ 5 ] MSM alloys change their magnetic properties depending on the deformation. This companion effect, which co-exist with the actuation, can be useful for the design of displacement, speed or force sensors and mechanical energy harvesters . [ 6 ]
The magnetic shape memory effect occurs in the low temperature martensite phase of the alloy, where the elementary cells composing the alloy have tetragonal geometry. If the temperature is increased beyond the martensite– austenite transformation temperature, the alloy goes to the austenite phase where the elementary cells have cubic geometry. With such geometry the magnetic shape memory effect is lost.
The transition from martensite to austenite produces force and deformation. Therefore, MSM alloys can be also activated thermally, like thermal shape memory alloys (see, for instance, Nickel-Titanium ( Ni-Ti ) alloys).
The mechanism responsible for the large strain of MSM alloys is the so-called magnetically induced reorientation (MIR), and is sketched in the figure. [ 7 ] Like other ferromagnetic materials, MSM alloys exhibit a macroscopic magnetization when subjected to an external magnetic field, emerging from the alignment of elementary magnetizations along the field direction. However, differently from standard ferromagnetic materials, the alignment is obtained by the geometric rotation of the elementary cells composing the alloy, and not by rotation of the magnetization vectors within the cells (like in magnetostriction ).
A similar phenomenon occurs when the alloy is subjected to an external force. Macroscopically, the force acts like the magnetic field, favoring the rotation of the elementary cells and achieving elongation or contraction depending on its application within the reference coordinate system. The elongation and contraction processes are shown in the figure where, for example, the elongation is achieved magnetically and the contraction mechanically.
The rotation of the cells is a consequence of the large magnetic anisotropy of MSM alloys, and the high mobility of the internal regions. Simply speaking, an MSM element is composed by internal regions, each having a different orientation of the elementary cells (the regions are shown by the figure in green and blue colors). These regions are called twin-variants. The application of a magnetic field or of an external stress shifts the boundaries of the variants, called twin boundaries , and thus favors one variant or the other. When the element is completely contracted or completely elongated, it is formed by only one variant and it is said to be in a single variant state . The magnetization of the MSM element along a fixed direction differs if the element is in the contraction or in the elongation single variant state. The magnetic anisotropy is the difference between the energy required to magnetize the element in contraction single variant state and in elongation single variant state. The value of the anisotropy is related to the maximum work-output of the MSM alloy, and thus to the available strain and force that can be used for applications. [ 8 ]
The main properties of the MSM effect for commercially available elements are summarized in [ 9 ] (where other aspects of the technology and of the related applications are described):
The fatigue life of MSMAs is of particular interest for actuation applications due to the high frequency cycling, so improving the microstructure of these alloys has been of particular interest. Researchers have improved the fatigue life up to 2x10 9 cycles with a maximum stress of 2MPa, providing promising data to support real application of MSMAs in devices. [ 10 ] Although high fatigue life has been demonstrated, this property has been found to be controlled by the internal twinning stress in the material, which is dependent on the crystal structure and twin boundaries. Additionally, inducing a fully strained (elongated or contracted) MSMA has been found to reduce fatigue life, so this must be taken into consideration when designing functional MSMA systems. In general, reducing defects such as surface roughness that cause stress concentration can increase the fatigue life and fracture resistance of MSMAs. [ 11 ]
Standard alloys are Nickel - Manganese - Gallium (Ni-Mn-Ga) alloys, which are investigated since the first relevant MSM effect has been published in 1996. [ 1 ] Other alloys under investigation are Iron - Palladium (Fe-Pd) alloys, Nickel-Iron-Gallium (Ni-Fe-Ga) alloys, and several derivates of the basic Ni-Mn-Ga alloy which further contain Iron (Fe), Cobalt (Co) or Copper (Cu). The main motivation behind the continuous development and testing of new alloys is to achieve improved thermo-magneto-mechanical properties, such as a lower internal friction, a higher transformation temperature and a higher Curie temperature, which would allow the use of MSM alloys in several applications. In fact, the actual temperature range of standard alloys is up to 50 °C. Recently, an 80 °C alloy has been presented. [ 12 ]
Due to the twin boundary motion mechanism required for the magnetic shape memory effect to occur, the highest performing MSMAs in terms of maximum induced strain have been single crystals. Additive manufacturing has been demonstrated as a technique to produce porous polycrystalline MSMAs. [ 13 ] As opposed to fully dense polycrystalline MSMAs, porous structures allow more freedom of motion, which reduces the internal stress required to activate martensitic twin boundary motion. Additionally, post-process heat treatments such as sintering and annealing have been found to significantly increase the hardness and reduce the elastic moduli of Ni-Mn-Ga alloys.
MSM actuator elements can be used where fast and precise motion is required. They are of interest due to the faster actuation using magnetic field as compared to the heating/cooling cycles required for conventional shape memory alloys, which also promises higher fatigue lifetime. Possible application fields are robotics, manufacturing, medical surgery, valves, dampers, sorting. [ 9 ] MSMAs have been of particular interest in the application of actuators (i.e. microfluidic pumps for lab-on-a-chip devices) since they are capable of large force and stroke outputs in relatively small spatial regions. [ 10 ] Also, due to the high fatigue life and their ability to produce electromotive forces from a magnetic flux, MSMAs are of interest in energy harvesting applications. [ 14 ]
The twinning stress, or internal frictional stress, of an MSMA determines the efficiency of actuation, so the operation design of MSM actuators is based on the mechanical and magnetic properties of a given alloy; for example, the magnetic permeability of an MSMA is a function of strain. [ 10 ] The most common MSM actuator design consists of an MSM element controlled by permanent magnets producing a rotating magnetic field and a spring restoring a mechanical force during the shape memory cycling. Limitations on the magnetic shape memory effect due to crystal defects determine the efficiency of MSMAs in applications. Since the MSM effect is also temperature dependent, these alloys can be tailored to shift the transition temperature by controlling microstructure and composition. | https://en.wikipedia.org/wiki/Magnetic_shape-memory_alloy |
In solid state physics , the magnetic space groups , or Shubnikov groups , are the symmetry groups which classify the symmetries of a crystal both in space, and in a two-valued property such as electron spin . To represent such a property, each lattice point is colored black or white, [ 1 ] and in addition to the usual three-dimensional symmetry operations , there is a so-called "antisymmetry" operation which turns all black lattice points white and all white lattice points black. Thus, the magnetic space groups serve as an extension to the crystallographic space groups which describe spatial symmetry alone.
The application of magnetic space groups to crystal structures is motivated by Curie's Principle . Compatibility with a material's symmetries, as described by the magnetic space group, is a necessary condition for a variety of material properties, including ferromagnetism , ferroelectricity , topological insulation .
A major step was the work of Heinrich Heesch , who first rigorously established the concept of antisymmetry as part of a series of papers in 1929 and 1930. [ 2 ] [ 3 ] [ 4 ] [ 5 ] Applying this antisymmetry operation to the 32 crystallographic point groups gives a total of 122 magnetic point groups. [ 6 ] [ 7 ] However, although Heesch correctly laid out each of the magnetic point groups, his work remained obscure, and the point groups were later re-derived by Tavger and Zaitsev. [ 8 ] The concept was more fully explored by Shubnikov in terms of color symmetry . [ 9 ] When applied to space groups, the number increases from the usual 230 three dimensional space groups to 1651 magnetic space groups, [ 10 ] as found in the 1953 thesis of Alexandr Zamorzaev . [ 11 ] [ 12 ] [ 13 ] While the magnetic space groups were originally found using geometry, it was later shown the same magnetic space groups can be found using generating sets . [ 14 ]
The magnetic space groups can be placed into three categories. First, the 230 colorless groups contain only spatial symmetry, and correspond to the crystallographic space groups. Then there are 230 grey groups, which are invariant under antisymmetry. Finally are the 1191 black-white groups, which contain the more complex symmetries. There are two common conventions for giving names to the magnetic space groups. They are Opechowski-Guccione (named after Wladyslaw Opechowski and Rosalia Guccione) [ 15 ] and Belov-Neronova-Smirnova. [ 10 ] For colorless and grey groups, the conventions use the same names, but they treat the black-white groups differently. A full list of the magnetic space groups (in both conventions) can be found both in the original papers, and in several places online. [ 16 ] [ 17 ] [ 18 ]
The types can be distinguished by their different construction. [ 19 ] Type I magnetic space groups, M I {\displaystyle {\mathcal {M}}_{I}} are identical to the ordinary space groups, G {\displaystyle G} .
Type II magnetic space groups, M I I {\displaystyle {\mathcal {M}}_{II}} , are made up of all the symmetry operations of the crystallographic space group, G {\displaystyle G} , plus the product of those operations with time reversal operation, T {\displaystyle {\mathcal {T}}} . Equivalently, this can be seen as the direct product of an ordinary space group with the point group 1 ′ {\displaystyle 1'} .
Type III magnetic space groups, M I I I {\displaystyle {\mathcal {M}}_{III}} , are constructed using a group H {\displaystyle H} , which is a subgroup of G {\displaystyle G} with index 2.
Type IV magnetic space groups, M I V {\displaystyle {\mathcal {M}}_{IV}} , are constructed with the use of a pure translation , { E | t 0 } {\displaystyle \{E|t_{0}\}} , which is Seitz notation [ 20 ] for null rotation and a translation, t 0 {\displaystyle t_{0}} . Here the t 0 {\displaystyle t_{0}} is a vector (usually given in fractional coordinates ) pointing from a black colored point to a white colored point, or vice versa.
The following table lists all of the 122 possible three-dimensional magnetic point groups. This is given in the short version of Hermann–Mauguin notation in the following table. Here, the addition of an apostrophe to a symmetry operation indicates that the combination of the symmetry element and the antisymmetry operation is a symmetry of the structure. There are 32 Crystallographic point groups , 32 grey groups, and 58 magnetic point groups. [ 21 ]
The magnetic point groups which are compatible with ferromagnetism are colored cyan, the magnetic point groups which are compatible with ferroelectricity are colored red, and the magnetic point groups which are compatible with both ferromagnetism and ferroelectricity are purple. [ 22 ] There are 31 magnetic point groups which are compatible with ferromagnetism . These groups, sometimes called admissible , leave at least one component of the spin invariant under operations of the point group. There are 31 point groups compatible with ferroelectricity ; these are generalizations of the crystallographic polar point groups . There are also 31 point groups compatible with the theoretically proposed ferrotorodicity . Similar symmetry arguments have been extended to other electromagnetic material properties such as magnetoelectricity or piezoelectricity . [ 23 ]
The following diagrams show the stereographic projection of most of the magnetic point groups onto a flat surface. Not shown are the grey point groups, which look identical to the ordinary crystallographic point groups, except they are also invariant under the antisymmetry operation.
The black-white Bravais lattices characterize the translational symmetry of the structure like the typical Bravais lattices , but also contain additional symmetry elements. For black-white Bravais lattices, the number of black and white sites is always equal. [ 24 ] There are 14 traditional Bravais lattices, 14 grey lattices, and 22 black-white Bravais lattices, for a total of 50 two-color lattices in three dimensions. [ 25 ]
The table shows the 36 black-white Bravais lattices, including the 14 traditional Bravais lattices , but excluding the 14 gray lattices which look identical to the traditional lattices. The lattice symbols are those used for the traditional Bravais lattices. The suffix in the symbol indicates the mode of centering by the black (antisymmetry) points in the lattice, where s denotes edge centering.
When the periodicity of the magnetic order coincides with the periodicity of crystallographic order, the magnetic phase is said to be commensurate , and can be well-described by a magnetic space group. However, when this is not the case, the order does not correspond to any magnetic space group. These phases can instead be described by magnetic superspace groups , which describe incommensurate order. [ 29 ] This is the same formalism often used to describe the ordering of some quasicrystals .
The Landau theory of second-order phase transitions has been applied to magnetic phase transitions. The magnetic space group of disordered structure, G 0 {\displaystyle G_{0}} , transitions to the magnetic space group of the ordered phase, G 1 {\displaystyle G_{1}} . G 1 {\displaystyle G_{1}} is a subgroup of G 0 {\displaystyle G_{0}} , and keeps only the symmetries which have not been broken during the phase transition. This can be tracked numerically by evolution of the order parameter , which belongs to a single irreducible representation of G 0 {\displaystyle G_{0}} . [ 30 ]
Important magnetic phase transitions include the paramagnetic to ferromagnetic transition at the Curie temperature and the paramagnetic to antiferromagnetic transition at the Néel temperature . Differences in the magnetic phase transitions explain why Fe 2 O 3 , MnCO 3 , and CoCO 3 are weakly ferromagnetic, whereas the structurally similar Cr 2 O 3 and FeCO 3 are purely antiferromagnetic. [ 31 ] This theory developed into what is now known as antisymmetric exchange .
A related scheme is the classification of Aizu species which consist of a prototypical non-ferroic magnetic point group, the letter "F" for ferroic , and a ferromagnetic or ferroelectric point group which is a subgroup of the prototypical group which can be reached by continuous motion of the atoms in the crystal structure. [ 32 ] [ 33 ]
The main application of these space groups is to magnetic structure, where the black/white lattice points correspond to spin up/spin down configuration of electron spin . More abstractly, the magnetic space groups are often thought of as representing time reversal symmetry . [ 34 ] This is in contrast to time crystals , which instead have time translation symmetry . In the most general form, magnetic space groups can represent symmetries of any two valued lattice point property, such as positive/negative electrical charge or the alignment of electric dipole moments. The magnetic space groups place restrictions on the electronic band structure of materials. Specifically, they place restrictions on the connectivity of the different electron bands, which in turn defines whether material has symmetry-protected topological order . Thus, the magnetic space groups can be used to identify topological materials, such as topological insulators . [ 35 ] [ 36 ] [ 37 ]
Experimentally, the main source of information about magnetic space groups is neutron diffraction experiments. The resulting experimental profile can be matched to theoretical structures by Rietveld refinement [ 38 ] or simulated annealing . [ 39 ]
Adding the two-valued symmetry is also a useful concept for frieze groups which are often used to classify artistic patterns. In that case, the 7 frieze groups with the addition of color reversal become 24 color-reversing frieze groups. [ 40 ] Beyond the simple two-valued property, the idea has been extended further to three colors in three dimensions, [ 41 ] and to even higher dimensions and more colors . [ 42 ] | https://en.wikipedia.org/wiki/Magnetic_space_group |
The term magnetic structure of a material pertains to the ordered arrangement of magnetic spins, typically within an ordered crystallographic lattice . Its study is a branch of solid-state physics .
Most solid materials are non-magnetic, that is, they do not display a magnetic structure. Due to the Pauli exclusion principle , each state is occupied by electrons of opposing spins, so that the charge density is compensated everywhere and the spin degree of freedom is trivial. Still, such materials typically do show a weak magnetic behaviour, e.g. due to diamagnetism or Pauli paramagnetism .
The more interesting case is when the material's electron spontaneously break above-mentioned symmetry. For ferromagnetism in the ground state, there is a common spin quantization axis and a global excess of electrons of a given spin quantum number, there are more electrons pointing in one direction than in the other, giving a macroscopic magnetization (typically, the majority electrons are chosen to point up). In the most simple (collinear) cases of antiferromagnetism , there is still a common quantization axis, but the electronic spins are pointing alternatingly up and down, leading again to cancellation of the macroscopic magnetization. However, specifically in the case of frustration of the interactions, the resulting structures can become much more complicated, with inherently three-dimensional orientations of the local spins. Finally, ferrimagnetism as prototypically displayed by magnetite is in some sense an intermediate case: here the magnetization is globally uncompensated as in ferromagnetism, but the local magnetization points in different directions.
The above discussion pertains to the ground state structure. Of course, finite temperatures lead to excitations of the spin configuration. Here two extreme points of view can be contrasted: in the Stoner picture of magnetism (also called itinerant magnetism), the electronic states are delocalized, and their mean-field interaction leads to the symmetry breaking. In this view, with increasing temperature the local magnetization would thus decrease homogeneously, as single delocalized electrons are moved from the up- to the down-channel. On the other hand, in the local-moment case the electronic states are localized to specific atoms, giving atomic spins, which interact only over a short range and typically are analyzed with the Heisenberg model . Here, finite temperatures lead to a deviation of the atomic spins' orientations from the ideal configuration, thus for a ferromagnet also decreasing the macroscopic magnetization.
For localized magnetism, many magnetic structures can be described by magnetic space groups , which give a precise accounting for all possible symmetry groups of up/down configurations in a three-dimensional crystal. However, this formalism is unable to account for some more complex magnetic structures, such as those found in helimagnetism .
Such ordering can be studied by observing the magnetic susceptibility as a function of temperature and/or the size of the applied magnetic field, but a truly three-dimensional picture of the arrangement of the spins is best obtained by means of neutron diffraction . [ 1 ] [ 2 ] Neutrons are primarily scattered by the nuclei of the atoms in the structure. At a temperature above the ordering point of the magnetic moments, where the material behaves as a paramagnetic one, neutron diffraction will therefore give a picture of the crystallographic structure only. Below the ordering point, e.g. the Néel temperature of an antiferromagnet or the Curie-point of a ferromagnet the neutrons will also experience scattering from the magnetic moments because they themselves possess spin. The intensities of the Bragg reflections will therefore change. In fact in some cases entirely new Bragg-reflections will occur if the unit cell of the ordering is larger than that of the crystallographic structure. This is a form of superstructure formation. Thus the symmetry of the total structure may well differ from the crystallographic substructure. It needs to be described by one of the 1651 magnetic ( Shubnikov ) groups rather than one of the non-magnetic space groups . [ 3 ]
Although ordinary X-ray diffraction is 'blind' to the arrangement of the spins, it has become possible to use a special form of X-ray diffraction to study magnetic structure. If a wavelength is selected that is close to an absorption edge of one of elements contained in the materials the scattering becomes anomalous and this component to the scattering is (somewhat) sensitive to the non-spherical shape of the outer electrons of an atom with an unpaired spin. This means that this type of anomalous X-ray diffraction does contain information of the desired type.
More recently, table-top techniques are being developed which allow magnetic structures to be studied without recourse to neutron or synchrotron sources. [ 4 ]
Only three elements are ferromagnetic at room temperature and pressure: iron , cobalt , and nickel . This is because their Curie temperature , T c , is higher than room temperature ( T c > 298K). Gadolinium has a spontaneous magnetization just below room temperature (293 K) and is sometimes counted as the fourth ferromagnetic element. There has been some suggestion that Gadolinium has helimagnetic ordering, [ 5 ] but others defend the longstanding view that Gadolinium is a conventional ferromagnet. [ 6 ]
The elements Dysprosium and Erbium each have two magnetic transitions. They are paramagnetic at room temperature, but become helimagnetic below their respective Néel temperatures, and then become ferromagnetic below their Curie temperatures. The elements Holmium , Terbium , and Thulium display even more complicated magnetic structures. [ 7 ]
There is also antiferromagnetic ordering, which becomes disordered above the Néel temperature . Chromium is somewhat like a simple antiferromagnet, but also has an incommensurate spin density wave modulation on top of the simple up-down spin alternation. [ 8 ] Manganese (in the α-Mn form) has 29 atoms unit cell , leading to a complex, but commensurate antiferromagnetic arrangement at low temperatures ( magnetic space group P 4 2'm'). [ 9 ] [ 10 ] Unlike most elements, which are magnetic due to electrons, the magnetic ordering of copper and silver is dominated by the much weaker nuclear magnetic moment , (compare Bohr magneton and nuclear magneton ) leading to transition temperatures near absolute zero . [ 11 ] [ 12 ]
Those elements which become superconductors exhibit superdiamagnetism below a critical temperature. | https://en.wikipedia.org/wiki/Magnetic_structure |
In electromagnetism , the magnetic susceptibility (from Latin susceptibilis ' receptive ' ; denoted χ , chi ) is a measure of how much a material will become magnetized in an applied magnetic field . It is the ratio of magnetization M ( magnetic moment per unit volume ) to the applied magnetic field intensity H . This allows a simple classification, into two categories, of most materials' responses to an applied magnetic field: an alignment with the magnetic field, χ > 0 , called paramagnetism , or an alignment against the field, χ < 0 , called diamagnetism .
Magnetic susceptibility indicates whether a material is attracted into or repelled out of a magnetic field. Paramagnetic materials align with the applied field and are attracted to regions of greater magnetic field. Diamagnetic materials are anti-aligned and are pushed away, toward regions of lower magnetic fields. On top of the applied field, the magnetization of the material adds its own magnetic field, causing the field lines to concentrate in paramagnetism, or be excluded in diamagnetism. [ 1 ] Quantitative measures of the magnetic susceptibility also provide insights into the structure of materials, providing insight into bonding and energy levels . Furthermore, it is widely used in geology for paleomagnetic studies and structural geology . [ 2 ]
The magnetizability of materials comes from the atomic-level magnetic properties of the particles of which they are made. Usually, this is dominated by the magnetic moments of electrons . Electrons are present in all materials, but without any external magnetic field, the magnetic moments of the electrons are usually either paired up or random so that the overall magnetism is zero (the exception to this usual case is ferromagnetism ). The fundamental reasons why the magnetic moments of the electrons line up or do not are very complex and cannot be explained by classical physics . However, a useful simplification is to measure the magnetic susceptibility of a material and apply the macroscopic form of Maxwell's equations . This allows classical physics to make useful predictions while avoiding the underlying quantum mechanical details.
Magnetic susceptibility is a dimensionless proportionality constant that indicates the degree of magnetization of a material in response to an applied magnetic field. A related term is magnetizability , the proportion between magnetic moment and magnetic flux density . [ 3 ] A closely related parameter is the permeability , which expresses the total magnetization of material and volume.
The volume magnetic susceptibility , represented by the symbol χ v (often simply χ , sometimes χ m – magnetic, to distinguish from the electric susceptibility ), is defined in the International System of Units – in other systems there may be additional constants – by the following relationship: [ 4 ] [ 5 ] M = linear χ v H , {\displaystyle \mathbf {M} \ {\stackrel {\text{linear}}{=}}\ \chi _{\text{v}}\mathbf {H} ,} were
χ v is therefore a dimensionless quantity .
Using SI units , the magnetic induction B is related to H by the relationship B = μ 0 ( H + M ) = linear μ 0 ( 1 + χ v ) H = μ H , {\displaystyle \mathbf {B} =\mu _{0}(\mathbf {H} +\mathbf {M} )\ {\stackrel {\text{linear}}{=}}\ \mu _{0}(1+\chi _{\text{v}})\mathbf {H} =\mu \mathbf {H} ,} where μ 0 is the vacuum permeability (see table of physical constants ), and (1 + χ v ) is the relative permeability of the material. Thus the volume magnetic susceptibility χ v and the magnetic permeability μ are related by the following formula: μ = def μ 0 ( 1 + χ v ) . {\displaystyle \mu \ {\stackrel {\text{def}}{=}}\ \mu _{0}(1+\chi _{\text{v}}).}
Sometimes [ 6 ] an auxiliary quantity called intensity of magnetization I (also referred to as magnetic polarisation J ) and with unit teslas , is defined as I = d e f μ 0 M . {\displaystyle \mathbf {I} \ {\stackrel {\mathrm {def} }{=}}\ \mu _{0}\mathbf {M} .}
This allows an alternative description of all magnetization phenomena in terms of the quantities I and B , as opposed to the commonly used M and H .
There are two other measures of susceptibility, the molar magnetic susceptibility ( χ m ) with unit m 3 /mol, and the mass magnetic susceptibility ( χ ρ ) with unit m 3 /kg that are defined below, where ρ is the density with unit kg/m 3 and M is molar mass with unit kg/mol: χ ρ = χ v ρ ; χ m = M χ ρ = M ρ χ v . {\displaystyle {\begin{aligned}\chi _{\rho }&={\frac {\chi _{\text{v}}}{\rho }};\\\chi _{\text{m}}&=M\chi _{\rho }={\frac {M}{\rho }}\chi _{\text{v}}.\end{aligned}}}
The definitions above are according to the International System of Quantities (ISQ) upon which the SI is based. However, many tables of magnetic susceptibility give the values of the corresponding quantities of the CGS system (more specifically CGS-EMU , short for electromagnetic units, or Gaussian-CGS ; both are the same in this context). The quantities characterizing the permeability of free space for each system have different defining equations: [ 7 ] B CGS = H CGS + 4 π M CGS = ( 1 + 4 π χ v CGS ) H CGS . {\displaystyle \mathbf {B} ^{\text{CGS}}=\mathbf {H} ^{\text{CGS}}+4\pi \mathbf {M} ^{\text{CGS}}=\left(1+4\pi \chi _{\text{v}}^{\text{CGS}}\right)\mathbf {H} ^{\text{CGS}}.}
The respective CGS susceptibilities are multiplied by 4 π to give the corresponding ISQ quantities (often referred to as SI quantities) with the same units: [ 7 ] χ m SI = 4 π χ m CGS {\displaystyle \chi _{\text{m}}^{\text{SI}}=4\pi \chi _{\text{m}}^{\text{CGS}}} χ ρ SI = 4 π χ ρ CGS {\displaystyle \chi _{\text{ρ}}^{\text{SI}}=4\pi \chi _{\text{ρ}}^{\text{CGS}}} χ v SI = 4 π χ v CGS {\displaystyle \chi _{\text{v}}^{\text{SI}}=4\pi \chi _{\text{v}}^{\text{CGS}}}
For example, the CGS volume magnetic susceptibility of water at 20 °C is 7.19 × 10 −7 , which is 9.04 × 10 −6 using the SI convention, both quantities being dimensionless. Whereas for most electromagnetic quantities, which system of quantities it belongs to can be disambiguated by incompatibility of their units, this is not true for the susceptibility quantities.
In physics it is common to see CGS mass susceptibility with unit cm 3 /g or emu/g⋅Oe −1 , and the CGS molar susceptibility with unit cm 3 /mol or emu/mol⋅Oe −1 .
If χ is positive, a material can be paramagnetic . In this case, the magnetic field in the material is strengthened by the induced magnetization. Alternatively, if χ is negative, the material is diamagnetic . In this case, the magnetic field in the material is weakened by the induced magnetization. Generally, nonmagnetic materials are said to be para- or diamagnetic because they do not possess permanent magnetization without external magnetic field. Ferromagnetic , ferrimagnetic , or antiferromagnetic materials possess permanent magnetization even without external magnetic field and do not have a well defined zero-field susceptibility.
Volume magnetic susceptibility is measured by the force change felt upon a substance when a magnetic field gradient is applied. [ 8 ] Early measurements are made using the Gouy balance where a sample is hung between the poles of an electromagnet. The change in weight when the electromagnet is turned on is proportional to the susceptibility. Today, high-end measurement systems use a superconductive magnet. An alternative is to measure the force change on a strong compact magnet upon insertion of the sample. This system, widely used today, is called the Evans balance . [ 9 ] For liquid samples, the susceptibility can be measured from the dependence of the NMR frequency of the sample on its shape or orientation. [ 10 ] [ 11 ] [ 12 ] [ 13 ] [ 14 ]
Another method using NMR techniques measures the magnetic field distortion around a sample immersed in water inside an MR scanner. This method is highly accurate for diamagnetic materials with susceptibilities similar to water. [ 15 ]
The magnetic susceptibility of most crystals is not a scalar quantity. Magnetic response M is dependent upon the orientation of the sample and can occur in directions other than that of the applied field H . In these cases, volume susceptibility is defined as a tensor : M i = H j χ i j {\displaystyle M_{i}=H_{j}\chi _{ij}} where i and j refer to the directions (e.g., of the x and y Cartesian coordinates ) of the applied field and magnetization, respectively. The tensor is thus degree 2 (second order), dimension (3,3) describing the component of magnetization in the i th direction from the external field applied in the j th direction.
In ferromagnetic crystals, the relationship between M and H is not linear. To accommodate this, a more general definition of differential susceptibility is used: χ i j d = ∂ M i ∂ H j {\displaystyle \chi _{ij}^{d}={\frac {\partial M_{i}}{\partial H_{j}}}} where χ d ij is a tensor derived from partial derivatives of components of M with respect to components of H . When the coercivity of the material parallel to an applied field is the smaller of the two, the differential susceptibility is a function of the applied field and self interactions, such as the magnetic anisotropy . When the material is not saturated , the effect will be nonlinear and dependent upon the domain wall configuration of the material.
Several experimental techniques allow for the measurement of the electronic properties of a material. An important effect in metals under strong magnetic fields, is the oscillation of the differential susceptibility as function of 1 / H . This behaviour is known as the De Haas–Van Alphen effect and relates the period of the susceptibility with the Fermi surface of the material.
An analogue non-linear relation between magnetization and magnetic field happens for antiferromagnetic materials . [ 16 ]
When the magnetic susceptibility is measured in response to an AC magnetic field (i.e. a magnetic field that varies sinusoidally ), this is called AC susceptibility . AC susceptibility (and the closely related "AC permeability") are complex number quantities, and various phenomena, such as resonance, can be seen in AC susceptibility that cannot occur in constant-field ( DC ) susceptibility. In particular, when an AC field is applied perpendicular to the detection direction (called the "transverse susceptibility" regardless of the frequency), the effect has a peak at the ferromagnetic resonance frequency of the material with a given static applied field. Currently, this effect is called the microwave permeability or network ferromagnetic resonance in the literature. These results are sensitive to the domain wall configuration of the material and eddy currents .
In terms of ferromagnetic resonance, the effect of an AC-field applied along the direction of the magnetization is called parallel pumping .
The CRC Handbook of Chemistry and Physics has one of the few published magnetic susceptibility tables. The data are listed as CGS quantities. The molar susceptibility of several elements and compounds are listed in the CRC.
In Earth science , magnetism is a useful parameter to describe and analyze rocks. Additionally, the anisotropy of magnetic susceptibility (AMS) within a sample determines parameters as directions of paleocurrents , maturity of paleosol , flow direction of magma injection, tectonic strain, etc. [ 2 ] It is a non-destructive tool which quantifies the average alignment and orientation of magnetic particles within a sample. [ 25 ] | https://en.wikipedia.org/wiki/Magnetic_susceptibility |
In physics , magnetic topological insulators are three dimensional magnetic materials with a non-trivial topological index protected by a symmetry other than time-reversal . [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] This type of material conducts electricity on its outer surface, but its volume behaves like an insulator. [ 6 ]
In contrast with a non-magnetic topological insulator , a magnetic topological insulator can have naturally gapped surface states as long as the quantizing symmetry is broken at the surface. These gapped surfaces exhibit a topologically protected half-quantized surface anomalous Hall conductivity ( e 2 / 2 h {\displaystyle e^{2}/2h} ) perpendicular to the surface. The sign of the half-quantized surface anomalous Hall conductivity depends on the specific surface termination. [ 7 ]
The Z 2 {\displaystyle \mathbb {Z} _{2}} classification of a 3D crystalline topological insulator can be understood in terms of the axion coupling θ {\displaystyle \theta } . A scalar quantity that is determined from the ground state wavefunction [ 8 ]
where A α {\displaystyle {\mathcal {A}}_{\alpha }} is a shorthand notation for the Berry connection matrix
where | u m k ⟩ {\displaystyle |u_{m\mathbf {k} }\rangle } is the cell-periodic part of the ground state Bloch wavefunction .
The topological nature of the axion coupling is evident if one considers gauge transformations . In this condensed matter setting a gauge transformation is a unitary transformation between states at the same k {\displaystyle \mathbf {k} } point
Now a gauge transformation will cause θ → θ + 2 π n {\displaystyle \theta \rightarrow \theta +2\pi n} , n ∈ N {\displaystyle n\in \mathbb {N} } . Since a gauge choice is arbitrary, this property tells us that θ {\displaystyle \theta } is only well defined in an interval of length 2 π {\displaystyle 2\pi } e.g. θ ∈ [ − π , π ] {\displaystyle \theta \in [-\pi ,\pi ]} .
The final ingredient we need to acquire a Z 2 {\displaystyle \mathbb {Z} _{2}} classification based on the axion coupling comes from observing how crystalline symmetries act on θ {\displaystyle \theta } .
The consequence is that if time-reversal or inversion are symmetries of the crystal we need to have θ = − θ {\displaystyle \theta =-\theta } and that can only be true if θ = 0 {\displaystyle \theta =0} (trivial), π {\displaystyle \pi } (non-trivial) (note that − π {\displaystyle -\pi } and π {\displaystyle \pi } are identified) giving us a Z 2 {\displaystyle \mathbb {Z} _{2}} classification. Furthermore, we can combine inversion or time-reversal with other symmetries that do not affect θ {\displaystyle \theta } to acquire new symmetries that quantize θ {\displaystyle \theta } . For example, mirror symmetry can always be expressed as m = I ∗ C 2 {\displaystyle m=I*C_{2}} giving rise to crystalline topological insulators, [ 9 ] while the first intrinsic magnetic topological insulator MnBi 2 {\displaystyle _{2}} Te 4 {\displaystyle _{4}} [ 10 ] [ 11 ] has the quantizing symmetry S = T ∗ τ 1 / 2 {\displaystyle S=T*\tau _{1/2}} .
So far we have discussed the mathematical properties of the axion coupling. Physically, a non-trivial axion coupling ( θ = π {\displaystyle \theta =\pi } ) will result in a half-quantized surface anomalous Hall conductivity ( σ AHC surf = e 2 / 2 h {\displaystyle \sigma _{\text{AHC}}^{\text{surf}}=e^{2}/2h} ) if the surface states are gapped. To see this, note that in general σ AHC surf {\displaystyle \sigma _{\text{AHC}}^{\text{surf}}} has two contribution. One comes from the axion coupling θ {\displaystyle \theta } , a quantity that is determined from bulk considerations as we have seen, while the other is the Berry phase ϕ {\displaystyle \phi } of the surface states at the Fermi level and therefore depends on the surface. In summary for a given surface termination the perpendicular component of the surface anomalous Hall conductivity to the surface will be
The expression for σ AHC surf {\displaystyle \sigma _{\text{AHC}}^{\text{surf}}} is defined mod e 2 / h {\displaystyle {\text{mod}}\ e^{2}/h} because a surface property ( σ AHC surf {\displaystyle \sigma _{\text{AHC}}^{\text{surf}}} ) can be determined from a bulk property ( θ {\displaystyle \theta } ) up to a quantum. To see this, consider a block of a material with some initial θ {\displaystyle \theta } which we wrap with a 2D quantum anomalous Hall insulator with Chern index C = 1 {\displaystyle C=1} . As long as we do this without closing the surface gap, we are able to increase σ AHC surf {\displaystyle \sigma _{\text{AHC}}^{\text{surf}}} by e 2 / h {\displaystyle e^{2}/h} without altering the bulk, and therefore without altering the axion coupling θ {\displaystyle \theta } .
One of the most dramatic effects occurs when θ = π {\displaystyle \theta =\pi } and time-reversal symmetry is present, i.e. non-magnetic topological insulator. Since σ AHC surf {\displaystyle {\boldsymbol {\sigma }}_{\text{AHC}}^{\text{surf}}} is a pseudovector on the surface of the crystal, it must respect the surface symmetries, and T {\displaystyle T} is one of them, but T σ AHC surf = − σ AHC surf {\displaystyle T{\boldsymbol {\sigma }}_{\text{AHC}}^{\text{surf}}=-{\boldsymbol {\sigma }}_{\text{AHC}}^{\text{surf}}} resulting in σ AHC surf = 0 {\displaystyle {\boldsymbol {\sigma }}_{\text{AHC}}^{\text{surf}}=0} . This forces ϕ = π {\displaystyle \phi =\pi } on every surface resulting in a Dirac cone (or more generally an odd number of Dirac cones) on every surface and therefore making the boundary of the material conducting.
On the other hand, if time-reversal symmetry is absent, other symmetries can quantize θ = π {\displaystyle \theta =\pi } and but not force σ AHC surf {\displaystyle {\boldsymbol {\sigma }}_{\text{AHC}}^{\text{surf}}} to vanish. The most extreme case is the case of inversion symmetry (I). Inversion is never a surface symmetry and therefore a non-zero σ AHC surf {\displaystyle {\boldsymbol {\sigma }}_{\text{AHC}}^{\text{surf}}} is valid. In the case that a surface is gapped, we have ϕ = 0 {\displaystyle \phi =0} which results in a half-quantized surface AHC σ AHC surf = − e 2 2 h {\displaystyle \sigma _{\text{AHC}}^{\text{surf}}=-{\frac {e^{2}}{2h}}} .
A half quantized surface Hall conductivity and a related treatment is also valid to understand topological insulators in magnetic field [ 12 ] giving an effective axion description of the electrodynamics of these materials. [ 13 ] This term leads to several interesting predictions including a quantized magnetoelectric effect. [ 14 ] Evidence for this effect has recently been given in THz spectroscopy experiments performed at the Johns Hopkins University . [ 15 ]
Magnetic topological insulators have proven difficult to create experimentally. In 2023 it was estimated that a magnetic topological insulator might be developed in 15 years' time. [ 16 ]
A compound made from manganese, bismuth, and tellurium (MnBi 2 Te 4 ) has been predicted to be a magnetic topological insulator. In 2024, scientists at the University of Chicago used MnBi2Te4 to develop a form of optical memory which is switched using lasers. This memory storage device could store data more quickly and efficiently, including in quantum computing . [ 17 ] | https://en.wikipedia.org/wiki/Magnetic_topological_insulator |
In experimental physics , a magnetic trap is an apparatus which uses a magnetic field gradient to trap neutral particles with magnetic moments . Although such traps have been employed for many purposes in physics research, they are best known as the last stage in cooling atoms to achieve Bose–Einstein condensation . The magnetic trap (as a way of trapping very cold atoms) was first proposed by David E. Pritchard .
Many atoms have a magnetic moment; their energy shifts in a magnetic field according to the formula
According to the principles of quantum mechanics the magnetic moment of an atom will be quantized ; that is, it will take on one of certain discrete values. If the atom is placed in a strong magnetic field, its magnetic moment will be aligned with the field. If a number of atoms are placed in the same field, they will be distributed over the various allowed values of magnetic quantum number for that atom.
If a magnetic field gradient is superimposed on the uniform field, those atoms whose magnetic moments are aligned with the field will have lower energies in a higher field. Like a ball rolling down a hill, these atoms will tend to occupy locations with higher fields and are known as "high-field-seeking" atoms. Conversely, those atoms with magnetic moments aligned opposite the field will have higher energies in a higher field, tend to occupy locations with lower fields, and are called "low-field-seeking" atoms.
It is impossible to produce a local maximum of the magnetic-field magnitude in free space; however, a local minimum may be produced. This minimum can trap atoms which are low-field-seeking if they do not have enough kinetic energy to escape the minimum. Typically, magnetic traps have relatively shallow field minima and are only able to trap atoms whose kinetic energies correspond to temperatures of a fraction of a kelvin . The field minima required for magnetic trapping can be produced in a variety of ways. These include permanent magnet traps, Ioffe configuration traps, QUIC traps and others.
The minimum magnitude of the magnetic field can be realized with the "atom microchip". [ 1 ] One of the first microchip atomic traps is shown on the right. The Z-shaped conductor (actually the golden Z-shaped strip painted on the Si surface) is placed into the uniform magnetic field (the field's source is not shown in the figure). Only atoms with positive spin-field energy were trapped. To prevent the mixing of spin states, the external magnetic field was inclined in the plane of the chip, providing the adiabatic rotation of the spin at the movement of the atom. In the first approximation, magnitude (but not orientation) of the magnetic field is responsible for effective energy of the trapped atom. The chip shown is 2 cm x 2 cm; this size was chosen for ease in manufacture. In principle, the size of such microchip traps can be drastically reduced. An array of such traps can be manufactured with conventional lithographic methods; such an array is considered a prototype of a q-bit memory cell for the quantum computer . Ways of transferring atoms and/or q-bits between traps are under development; the adiabatic optical (with off-resonant frequencies) and/or the electrical control (with additional electrodes) is assumed.
Bose–Einstein condensation (BEC) requires conditions of very low density and very low temperature in a gas of atoms. Laser cooling in a magneto-optical trap (MOT) is typically used to cool atoms down to the microkelvin range. However, laser cooling is limited by the momentum recoils an atom receives from single photons. Achieving BEC requires cooling the atoms beyond the limits of laser cooling, which means the lasers used in the MOT must be turned off and a new method of trapping devised. Magnetic traps have been used to hold very cold atoms, while evaporative cooling has reduced the temperature of the atoms enough to reach BEC. | https://en.wikipedia.org/wiki/Magnetic_trap_(atoms) |
Magnetic tweezers (MT) are scientific instruments for the manipulation and characterization of biomolecules or polymers . These apparatus exert forces and torques to individual molecules or groups of molecules. It can be used to measure the tensile strength or the force generated by molecules.
Most commonly magnetic tweezers are used to study mechanical properties of biological macromolecules like DNA or proteins in single-molecule experiments . Other applications are the rheology of soft matter , and studies of force-regulated processes in living cells. Forces are typically on the order of pico- to nanonewtons (pN to nN). Due to their simple architecture, magnetic tweezers are a popular biophysical tool.
In experiments, the molecule of interest is attached to a magnetic microparticle. The magnetic tweezer is equipped with magnets that are used to manipulate the magnetic particles whose position is measured with the help of video microscopy.
A magnetic tweezers apparatus consists of magnetic micro-particles, which can be manipulated with the help of an external magnetic field. The position of the magnetic particles is then determined by a microscopic objective with a camera.
Magnetic particles for the operation in magnetic tweezers come with a wide range of properties and have to be chosen according to the intended application. Two basic types of magnetic particles are described in the following paragraphs; however there are also others like magnetic nanoparticles in ferrofluids , which allow experiments inside a cell.
Superparamagnetic beads are commercially available with a number of different characteristics. The most common is the use of spherical particles of a diameter in the micrometer range. They consist of a porous latex matrix in which magnetic nanoparticles have been embedded. Latex is auto-fluorescent and may therefore be advantageous for the imaging of their position. Irregular shaped particles present a larger surface and hence a higher probability to bind to the molecules to be studied. [ 1 ] The coating of the microbeads may also contain ligands able to attach the molecules of interest. For example, the coating may contain streptavidin which couples strongly to biotin , which itself may be bound to the molecules of interest.
When exposed to an external magnetic field, these microbeads become magnetized. The induced magnetic moment m → ( B → ) {\displaystyle {\overrightarrow {m}}({\overrightarrow {B}})} is proportional to a weak external magnetic field B → {\displaystyle {\overrightarrow {B}}} :
m → ( B → ) = V χ B → μ 0 {\displaystyle {\overrightarrow {m}}({\overrightarrow {B}})={\frac {V\chi {\overrightarrow {B}}}{\mu _{0}}}}
where μ 0 {\displaystyle \mu _{0}} is the vacuum permeability . It is also proportional to the volume V {\displaystyle V} of the microspheres , which stems from the fact that the number of magnetic nanoparticles scales with the size of the bead. The magnetic susceptibility χ {\displaystyle \chi } is assumed to be scalar in this first estimation and may be calculated by χ = 3 μ r − 1 μ r + 2 {\displaystyle \chi =3{\frac {\mu _{r}-1}{\mu _{r}+2}}} , where μ r {\displaystyle \mu _{r}} is the relative permeability . In a strong external field, the induced magnetic moment saturates at a material dependent value m → s a t {\displaystyle {\overrightarrow {m}}_{sat}} . The force F → {\displaystyle {\overrightarrow {F}}} experienced by a microbead can be derived from the potential U = − 1 2 m → ( B → ) ⋅ B → {\displaystyle U=-{\frac {1}{2}}{\overrightarrow {m}}({\overrightarrow {B}})\cdot {\overrightarrow {B}}} of this magnetic moment in an outer magnetic field: [ 2 ]
F → = − ∇ → U = { V χ 2 μ 0 ∇ → | B → | 2 in a weak magnetic field 1 2 ∇ → ( m → s a t ⋅ B → ) in a strong magnetic field {\displaystyle {\overrightarrow {F}}=-{\overrightarrow {\nabla }}U={\begin{cases}{\frac {V\chi }{2\mu _{0}}}{\overrightarrow {\nabla }}\left|{\overrightarrow {B}}\right|^{2}&\qquad {\text{in a weak magnetic field}}\\{\frac {1}{2}}{\overrightarrow {\nabla }}\left({\overrightarrow {m}}_{sat}\cdot {\overrightarrow {B}}\right)&\qquad {\text{in a strong magnetic field}}\end{cases}}}
The outer magnetic field can be evaluated numerically with the help of finite element analysis or by simply measuring the magnetic field with the help of a Hall effect sensor . Theoretically it would be possible to calculate the force on the beads with these formulae; however the results are not very reliable due to uncertainties of the involved variables, but they allow estimating the order of magnitude and help to better understand the system. More accurate numerical values can be obtained considering the Brownian motion of the beads.
Due to anisotropies in the stochastic distribution of the nanoparticles within the microbead the magnetic moment is not perfectly aligned with the outer magnetic field i.e. the magnetic susceptibility tensor cannot be reduced to a scalar. For this reason, the beads are also subjected to a torque Γ → {\displaystyle {\overrightarrow {\Gamma }}} which tries to align m → {\displaystyle {\overrightarrow {m}}} and B → {\displaystyle {\overrightarrow {B}}} :
Γ → = m → × B → {\displaystyle {\overrightarrow {\Gamma }}={\overrightarrow {m}}\times {\overrightarrow {B}}}
The torques generated by this method are typically much greater than 10 3 p N n m {\displaystyle 10^{3}\mathrm {pNnm} } , which is more than necessary to twist the molecules of interest. [ 3 ]
The use of ferromagnetic nanowires for the operation of magnetic tweezers enlarges their experimental application range. The length of these wires typically is in the order of tens of nanometers up to tens of micrometers, which is much larger than their diameter. In comparison with superparamagnetic beads, they allow the application of much larger forces and torques. In addition to that, they present a remnant magnetic moment. This allows the operation in weak magnetic field strengths. It is possible to produce nanowires with surface segments that present different chemical properties, which allows controlling the position where the studied molecules can bind to the wire. [ 1 ]
To be able to exert torques on the microbeads at least two magnets are necessary, but many other configurations have been realized, reaching from only one magnet that only pulls the magnetic microbeads to a system of six electromagnets that allows fully controlling the 3-dimensional position and rotation via a digital feedback loop . [ 4 ] The magnetic field strength decreases roughly exponentially with the distance from the axis linking the two magnets on a typical scale of about the width of the gap between the magnets. Since this scale is rather large in comparison to the distances, when the microbead moves in an experiment, the force acting on it may be treated as constant. Therefore, magnetic tweezers are passive force clamps due to the nature of their construction in contrast to optical tweezers, although they may be used as positive clamps, too, when combined with a feedback loop. The field strength may be increased by sharpening the pole face of the magnet which, however, also diminishes the area where the field may be considered as constant. An iron ring connection the outer poles of the magnets may help to reduce stray fields. Magnetic tweezers can be operated with both permanent magnets and electromagnets. The two techniques have their specific advantages. [ 3 ]
Permanent magnets of magnetic tweezers are usually out of rare earth materials, like neodymium and can reach field strengths exceeding 1.3 Tesla. [ 5 ] The force on the beads may be controlled by moving the magnets along the vertical axis. Moving them up decreases the field strength at the position of the bead and vice versa. Torques on the magnetic beads may be exerted by turning the magnets around the vertical axis to change the direction of the field. The size of the magnets is in the order of millimeters as well as their spacing. [ 3 ]
The use of electromagnets in magnetic tweezers has the advantage that the field strength and direction can be changed just by adjusting the amplitude and the phase of the current for the magnets. For this reason, the magnets do not need to be moved which allows a faster control of the system and reduces mechanical noise. In order to increase the maximum field strength, a core of a soft paramagnetic material with high saturation and low remanence may be added to the solenoid. In any case, however, the typical field strengths are much lower compared to those of permanent magnets of comparable size. Additionally, using electromagnets requires high currents that produce heat that may necessitate a cooling system. [ 1 ]
The displacement of the magnetic beads corresponds to the response of the system to the imposed magnetic field and hence needs to be precisely measured: In a typical set-up, the experimental volume is illuminated from the top so that the beads produce diffraction rings in the focal plane of an objective which is placed under the tethering surface. The diffraction pattern is then recorded by a CCD-camera . The image can be analyzed in real time by a computer. The detection of the position in the plane of the tethering surface is not complicated since it corresponds to the center of the diffraction rings. The precision can be up to a few nanometers. For the position along the vertical axis, the diffraction pattern needs to be compared to reference images, which show the diffraction pattern of the considered bead in a number of known distances from the focal plane. These calibration images are obtained by keeping a bead fixed while displacing the objective, i.e. the focal plane, with the help of piezoelectric elements by known distances. With the help of interpolation, the resolution can reach precision of up 10 nm along this axis. [ 6 ] The obtained coordinates may be used as input for a digital feedback loop that controls the magnetic field strength, for example, in order to keep the bead at a certain position.
Non-magnetic beads are usually also added to the sample as a reference to provide a background displacement vector. They have a different diameter as the magnetic beads so that they are optically distinguishable. This is necessary to detect potential drift of the fluid. For example, if the density of magnetic particles is too high, they may drag the surrounding viscous fluid with them. The displacement vector of a magnetic bead can be determined by subtracting its initial position vector and this background displacement vector from its current position.
The determination of the force that is exerted by the magnetic field on the magnetic beads can be calculated considering thermal fluctuations of the bead in the horizontal plane: The problem is rotational symmetric with respect to the vertical axis; hereafter one arbitrarily picked direction in the symmetry plane is called x {\displaystyle x} . The analysis is the same for the direction orthogonal to the x-direction and may be used to increase precision. If the bead leaves its equilibrium position on the x {\displaystyle x} -axis by δ x {\displaystyle \delta x} due to thermal fluctuations, it will be subjected to a restoring force F χ {\displaystyle F_{\chi }} that increases linearly with δ x {\displaystyle \delta x} in the first order approximation. Considering only absolute values of the involved vectors it is geometrically clear that the proportionality constant is the force exerted by the magnets F {\displaystyle F} over the length l {\displaystyle l} of the molecule that keeps the bead anchored to the tethering surface:
F χ = F l δ x {\displaystyle F_{\chi }={\frac {F}{l}}\delta x} .
The equipartition theorem states that the mean energy that is stored in this "spring" is equal to 1 2 k B T {\displaystyle {\frac {1}{2}}k_{B}T} per degree of freedom. Since only one direction is considered here, the potential energy of the system reads: ⟨ E p ⟩ = 1 2 F l ⟨ δ x 2 ⟩ = 1 2 k B T {\displaystyle \langle E_{p}\rangle ={\frac {1}{2}}{\frac {F}{l}}\langle \delta x^{2}\rangle ={\frac {1}{2}}k_{B}T} .
From this, a first estimate for the force acting on the bead can be deduced:
F = l k B T ⟨ δ x 2 ⟩ {\displaystyle F={\frac {lk_{B}T}{\langle \delta x^{2}\rangle }}} .
For a more accurate calibration, however, an analysis in Fourier space is necessary. The power spectrum density P ( ω ) {\displaystyle P(\omega )} of the position of the bead is experimentally available. A theoretical expression for this spectrum is derived in the following, which can then be fitted to the experimental curve in order to obtain the force exerted by the magnets on the bead as a fitting parameter. By definition this spectrum is the squared modulus of the Fourier transform of the position X ( ω ) {\displaystyle X(\omega )} over the spectral bandwidth Δ f {\displaystyle \Delta f} :
P ( ω ) = | X ( ω ) | 2 Δ f {\displaystyle P(\omega )={\frac {\left|X(\omega )\right|^{2}}{\Delta f}}}
X ( ω ) {\displaystyle X(\omega )} can be obtained considering the equation of motion for a bead of mass m {\displaystyle m} :
m ∂ 2 x ( t ) ∂ t 2 = − 6 π R η ∂ x ( t ) ∂ t − F l x ( t ) + f ( t ) {\displaystyle m{\frac {\partial ^{2}x(t)}{\partial t^{2}}}=-6\pi R\eta {\frac {\partial x(t)}{\partial t}}-{\frac {F}{l}}x(t)+f(t)}
The term 6 π R η ∂ x ( t ) ∂ t {\displaystyle 6\pi R\eta {\frac {\partial x(t)}{\partial t}}} corresponds to the Stokes friction force for a spherical particle of radius R {\displaystyle R} in a medium of viscosity η {\displaystyle \eta } and F l x ( t ) {\displaystyle {\frac {F}{l}}x(t)} is the restoring force which is opposed to the stochastic force f ( t ) {\displaystyle f(t)} due to the Brownian motion. Here, one may neglect the inertial term m ∂ 2 x ( t ) ∂ t 2 {\displaystyle m{\frac {\partial ^{2}x(t)}{\partial t^{2}}}} , because the system is in a regime of very low Reynolds number ( R e < 10 − 5 ) {\displaystyle \left(\mathrm {Re} <10^{-5}\right)} . [ 1 ]
The equation of motion can be Fourier transformed inserting the driving force and the position in Fourier space:
f ( t ) = 1 2 π ∫ F ( ω ) e i ω t d t x ( t ) = 1 2 π ∫ X ( ω ) e i ω t d t . {\displaystyle {\begin{aligned}f(t)=&{\frac {1}{2\pi }}\int F(\omega )\mathrm {e} ^{i\omega t}\mathrm {d} t\\x(t)=&{\frac {1}{2\pi }}\int X(\omega )\mathrm {e} ^{i\omega t}\mathrm {d} t.\end{aligned}}}
This leads to:
X ( ω ) = F ( ω ) 6 π i R η ω + F l {\displaystyle X(\omega )={\frac {F(\omega )}{6\pi iR\eta \omega +{\frac {F}{l}}}}} .
The power spectral density of the stochastic force F ( ω ) {\displaystyle F(\omega )} can be derived by using the equipartition theorem and the fact that Brownian collisions are completely uncorrelated: [ 7 ]
| F ( ω ) | 2 Δ f = 4 k B T ⋅ 6 π η R {\displaystyle {\frac {\left|F(\omega )\right|^{2}}{\Delta f}}=4k_{B}T\cdot 6\pi \eta R}
This corresponds to the Fluctuation-dissipation theorem . With that expression, it is possible to give a theoretical expression for the power spectrum:
P ( ω ) = 24 π k B T η R 36 π 2 R 2 η 2 ω 2 + ( F l ) 2 {\displaystyle P(\omega )={\frac {24\pi k_{B}T\eta R}{36\pi ^{2}R^{2}\eta ^{2}\omega ^{2}+\left({\frac {F}{l}}\right)^{2}}}}
The only unknown in this expression, F {\displaystyle F} , can be determined by fitting this expression to the experimental power spectrum. For more accurate results, one may subtract the effect due to finite camera integration time from the experimental spectrum before doing the fit. [ 6 ]
Another force calibration method is to use the viscous drag of the microbeads: Therefore, the microbeads are pulled through the viscous medium while recording their position. Since the Reynolds number for the system is very low, it is possible to apply Stokes law to calculate the friction force which is in equilibrium with the force exerted by the magnets:
F = 6 π η R v {\displaystyle F=6\pi \eta Rv} .
The velocity v {\displaystyle v} can be determined by using the recorded velocity values. The force obtained via this formula can then be related to a given configuration of the magnets, which may serve as a calibration. [ 8 ]
This section gives an example for an experiment carried out by Strick, Allemand, Croquette [ 9 ] with the help of magnetic tweezers. A double-stranded DNA molecule is fixed with multiple binding sites on one end to a glass surface and on the other to a magnetic micro bead, which can be manipulated in a magnetic tweezers apparatus. By turning the magnets, torsional stress can be applied to the DNA molecule. Rotations in the sense of the DNA helix are counted positively and vice versa. While twisting, the magnetic tweezers also allow stretching the DNA molecule. This way, torsion extension curves may be recorded at different stretching forces. For low forces (less than about 0.5 pN), the DNA forms supercoils, so called plectonemes, which decrease the extension of the DNA molecule quite symmetrically for positive and negative twists. Augmenting the pulling force already increases the extension for zero imposed torsion. Positive twists lead again to plectoneme formation that reduces the extension. Negative twist, however, does not change the extension of the DNA molecule a lot. This can be interpreted as the separation of the two strands which corresponds to the denaturation of the molecule. In the high force regime, the extension is nearly independent of the applied torsional stress. The interpretation is the apparition of local regions of highly overwound DNA. An important parameter of this experiment is also the ionic strength of the solution which affects the critical values of the applied pulling force that separate the three force regimes. [ 9 ]
Applying magnetic theory to the study of biology is a biophysical technique that started to appear in Germany in the early 1920s. Possibly the first demonstration was published by Alfred Heilbronn in 1922; his work looked at viscosity of protoplasts . [ 10 ] The following year, Freundlich and Seifriz explored rheology in echinoderm eggs. Both studies included insertion of magnetic particles into cells and resulting movement observations in a magnetic field gradient . [ 11 ]
In 1949 at Cambridge University, Francis Crick and Arthur Hughes demonstrated a novel use of the technique, calling it "The Magnetic Particle Method." The idea, which originally came from Dr. Honor Fell , was that tiny magnetic beads, phagocytoced by whole cells grown in culture, could be manipulated by an external magnetic field The tissue culture was allowed to grow in the presence of the magnetic material, and cells that contained a magnetic particle could be seen with a high power microscope. As the magnetic particle was moved through the cell by a magnetic field, measurements about the physical properties of the cytoplasm were made. [ 12 ] Although some of their methods and measurements were self-admittedly crude, their work demonstrated the usefulness of magnetic field particle manipulation and paved the way for further developments of this technique. The magnetic particle phagocytosis method continued to be used for many years to research cytoplasm rheology and other physical properties in whole cells. [ 13 ] [ 14 ]
An innovation in the 1990s lead to an expansion of the technique's usefulness in a way that was similar to the then-emerging optical tweezers method . Chemically linking an individual DNA molecule between a magnetic bead and a glass slide allowed researchers to manipulate a single DNA molecule with an external magnetic field. Upon application of torsional forces to the molecule, deviations from free-form movement could be measured against theoretical standard force curves or Brownian motion analysis. This provided insight into structural and mechanical properties of DNA , such as elasticity . [ 15 ] [ 16 ]
Magnetic tweezers as an experimental technique has become exceptionally diverse in use and application. More recently, the introduction of even more novel methods have been discovered or proposed. Since 2002, the potential for experiments involving many tethering molecules and parallel magnetic beads has been explored, shedding light on interaction mechanics, especially in the case of DNA-binding proteins . [ 17 ] A technique was published in 2005 that involved coating a magnetic bead with a molecular receptor and the glass slide with its ligand . This allows for a unique look at receptor-ligand dissociation force. [ 18 ] In 2007, a new method for magnetically manipulating whole cells was developed by Kollmannsberger and Fabry. The technique involves attaching beads to the extracellular matrix and manipulating the cell from the outside of the membrane to look at structural elasticity. [ 11 ] This method continues to be used as a means of studying rheology , as well as cellular structural proteins . [ 19 ] A study appeared in a 2013 that used magnetic tweezers to mechanically measure the unwinding and rewinding of a single neuronal SNARE complex by tethering the entire complex between a magnetic bead and the slide, and then using the applied magnetic field force to pull the complex apart. [ 20 ]
Magnetic tweezers can be used to measure mechanical properties such as rheology , the study of matter flow and elasticity, in whole cells. The phagocytosis method previously described is useful for capturing a magnetic bead inside a cell. Measuring the movement of the beads inside the cell in response to manipulation from the external magnetic field yields information on the physical environment inside the cell and internal media rheology: viscosity of the cytoplasm, rigidity of internal structure, and ease of particle flow. [ 12 ] [ 13 ] [ 14 ]
A whole cell may also be magnetically manipulated by attaching a magnetic bead to the extracellular matrix via fibronectin -coated magnetic beads. Fibronectin is a protein that will bind to extracellular membrane proteins . This technique allows for measurements of cell stiffness and provides insights into the functioning of structural proteins. [ 11 ] The schematic shown at right depicts the experimental setup devised by Bonakdar and Schilling, et al. (2015) [ 19 ] for studying the structural protein plectin in mouse cells. Stiffness was measured as proportional to bead position in response to external magnetic manipulation.
Magnetic tweezers as a single-molecule method is decidedly the most common use in recent years. Through the single-molecule method, molecular tweezers provide a close look into the physical and mechanical properties of biological macromolecules . Similar to other single-molecule methods, such as optical tweezers , this method provides a way to isolate and manipulate an individual molecule free from the influences of surrounding molecules. [ 17 ] Here, the magnetic bead is attached to a tethering surface by the molecule of interest. DNA or RNA may be tethered in either single-stranded or double-stranded form, or entire structural motifs can be tethered, such as DNA Holliday junctions , DNA hairpins , or entire nucleosomes and chromatin . By acting upon the magnetic bead with the magnetic field, different types of torsional force can be applied to study intra-DNA interactions, [ 21 ] as well as interactions with topoisomerases or histones in chromosomes . [ 17 ]
Magnetic tweezers go beyond the capabilities of other single-molecule methods, however, in that interactions between and within complexes can also be observed. This has allowed recent advances in understanding more about DNA-binding proteins , receptor-ligand interactions, [ 18 ] and restriction enzyme cleavage. [ 17 ] A more recent application of magnetic tweezers is seen in single-complex studies. With the help of DNA as the tethering agent, an entire molecular complex may be attached between the bead and the tethering surface. In exactly the same way as with pulling a DNA hairpin apart by applying a force to the magnetic bead, an entire complex can be pulled apart and force required for the dissociation can be measured. [ 20 ] This is also similar to the method of pulling apart receptor-ligand interactions with magnetic tweezers to measure dissociation force. [ 18 ]
This section compares the features of magnetic tweezers with those of the most important other single-molecule experimental methods: optical tweezers and atomic force microscopy . The magnetic interaction is highly specific to the used superparamagnetic microbeads. The magnetic field does practically not affect the sample. Optical tweezers have the problem that the laser beam may also interact with other particles of the biological sample due to contrasts in the refractive index . In addition to that, the laser may cause photodamage and sample heating. In the case of atomic force microscopy, it may also be hard to discriminate the interaction of the tip with the studied molecule from other nonspecific interactions.
Thanks to the low trap stiffness, the range of forces accessible with magnetic tweezers is lower in comparison with the two other techniques. The possibility to exert torque with magnetic tweezers is not unique: optically tweezers may also offer this feature when operated with birefringent microbeads in combination with a circularly polarized laser beam.
Another advantage of magnetic tweezers is that it is easy to carry out in parallel many single molecule measurements.
An important drawback of magnetic tweezers is the low temporal and spatial resolution due to the data acquisition via video-microscopy. [ 3 ] However, with the addition of a high-speed camera, the temporal and spatial resolution has been demonstrated to reach the Angstrom-level. [ 22 ] | https://en.wikipedia.org/wiki/Magnetic_tweezers |
Magnetic water treatment (also known as anti-scale magnetic treatment or AMT ) is a disproven method of reducing the effects of hard water by passing it through a magnetic field as a non-chemical alternative to water softening . A 1996 study by Lawrence Livermore National Laboratory found no significant effect of magnetic water treatment on the formation of scale. As magnets affect water to a small degree, and water containing ions is more conductive than purer water, magnetic water treatment is an example of a valid scientific hypothesis that failed experimental testing and is thus disproven. Any products claiming to utilize magnetic water treatment are absolutely fraudulent . [ 1 ]
Vendors of magnetic water treatment devices frequently use photos and testimonials to support their claims, but omit quantitative detail and well-controlled studies. [ 2 ] Advertisements and promotions generally omit system variables, such as corrosion or system mass balance analyticals, as well as measurements of post-treatment water such as concentration of hardness ions or the distribution, structure, and morphology of suspended particles. [ 2 ] [ 3 ] [ 4 ] [ 5 ] [ 6 ] [ 7 ] | https://en.wikipedia.org/wiki/Magnetic_water_treatment |
Magnetically assisted slip casting is a manufacturing technique that uses anisotropic stiff nanoparticle platelets in a ceramic , metal or polymer functional matrix to produce [ 1 ] layered objects that can mimic natural objects such as nacre . Each layer of platelets is oriented in a different direction, giving the resulting object greater strength. The inventors claimed that the process is 10x faster than commercial 3D printing . The magnetisation and orientation of the ceramic platelets has been patented. [ 2 ]
The technique involves pouring a suspension of magnetized ceramic micro-plates. Pores in the plaster mold absorb the liquid from the suspension, solidifying the material from the outside in. The particles are subjected to a strong magnetic field as they solidify that causes them to align in one direction. The field's orientation is changed at regular intervals, moving the plates still in suspension, without disturbing already-solidified plates. By varying the composition of the suspension and the direction of the platelets, a continuous process can produce multiple layers with differing material properties in a single object. The resulting objects can closely imitate their natural models. [ 2 ]
Researchers produced an artificial tooth whose microstructure mimicked that of a real tooth. The outer layers, corresponding to enamel, were hard and structurally complex. The outer layers contained glass nanoparticles and aluminium oxide plates were aligned perpendicular to the surface. After the outer layers hardened, a second suspension was poured. It contained no glass, and the plates were aligned horizontally to the surface of the tooth. These deeper layers were tougher, resembling dentine . The tooth was then cooked at 1,600 degrees to compact and harden the material — a process known as sintering . The last step involved filling remaining pores with a synthetic monomer used in dentistry , which polymerizes after treatment. [ 2 ] Hardness and durability approximated that of both the enamel and dentine of a tooth. [ 3 ] | https://en.wikipedia.org/wiki/Magnetically_assisted_slip_casting |
In electrical engineering , a magnetically-controlled shunt reactor ( MCSR , CSR ) represents electrotechnical equipment purposed for compensation of reactive power and stabilization of voltage level in high voltage (HV) electric networks rated for voltage classes 36 – 750 kV. MCSR is a shunt -type static device with smooth regulation by means of inductive reactance .
In 2002, The first Controlled Shunt Reactor (CSR) was developed by Bharat Heavy Electricals Limited . The first such device was commissioned at Power Grid's 400 kV Itarsi substation in Madhya Pradesh. [ 1 ]
Magnetically-controlled shunt reactors are intended for automatic control over reactive power and stabilization of voltage levels; these ensure the following:
On the assumption of tasks to be solved by MCSRs, as well as with consideration of existing experience of their operation, application field of controlled reactors covers (but not limited) the following areas of the power networks:
Ample opportunities of MCSRs ensure expediency of their application for different voltage classes. Furthermore, expected effect could be shown up both at the level of local area consumer’s grids, and at solving the primary tasks of the national power system as a whole.
In the context of building-up of the market relations in the electric energy sector and increase of investments for development of power networks, MCSRs offer the complete series of considerable benefits for all economic entities:
A magnetically-controlled shunt reactor is a transformer-type device which additionally provides functions of semiconducting key apparatus; this is ensured by means of reactor magnetic system operation in the domain of deep saturation. The basing principle allowed optimal employment of existing designs both in transformer production industry, and in the field of power electronics. Magnetic system of MCSR single phase includes two cores with windings, vertical and horizontal yokes. Control windings with opposite connection and power windings with series (accordant) connection are arranged on CST magnetic system cores. MCSR magnetic system cores are free from nonmagnetic gaps, and owing to this effect in case of the reactor connection to the network it will be in no-load condition. Herewith, the value of reactive power consumed from the grid will not exceed 3% of nominal magnitude. To increase reactor load as for reactive power, its operating range should be offset to non-linear area of hysteresis characteristic; and this is achieved for the account of additional biasing of magnetic system. At connection of regulated dc voltage source to the control windings, increase of the bias flux is ensured.
Due to the fact that ac flow of power winding is superimposed on the bias flux, the net flux is offset to the saturation domain of magnetic system cores. Respectively, saturation of the cores is resulted in occurrence of current in the power winding. In case of energy input to or output from the control circuit, the transient process of increase or decrease of network current and, respectively, of reactive power consumed by reactor is ensured.
Reactor power winding current is regulated according to proportional control mode, when control angle of rectified current source thyristors is changed according to proportional mode depending on mismatching between the prescribed voltage setting and the voltage at the point of reactor connection. In case of necessity to implement the rapid transfer of the reactor from one quasi-steady-state mode to another one, the scheme of overexcitation/underexcitation is realized. In such case, time to gain full power starting from no-load condition is reduced up to 0,3 s. Constructively, it is possible to ensure every speed of the reactor power variation. However, based on practical experience of MCSR application, the optimal balance between the reactor operating speed and capacity of biasing system has been determined: speed of power increase/relief within 0,3 – 1,0 s, capacity of biasing system – 1 – 2% of the reactor rated capacity.
Depending upon desired requirements, MCSR is adjusted in such a way that would be possible to realize either voltage level stabilization, or consumed reactive power value, or consumed current magnitude. Controlled reactors, same as their non-controlled analogues, are subdivided into bus reactors and line reactors. Based on this principle, MCSR design would be completed with additional element which ensures pre-biasing of electromagnetic part and subsequent inertialess energizing of the reactor (with power increase time less than one cycle of power frequency). Similar to all transformer equipment, MCSR is able to withstand long-term overload up to 120 – 130% as well as should-term overload up to 200%. Moreover, considering the additional measures and the control algorithms, MCSR realizes all functions of uncontrolled shunt reactor including ability to operate within the interval of single-phase automatic reclosing. | https://en.wikipedia.org/wiki/Magnetically_controlled_shunt_reactor |
In classical electromagnetism , magnetization is the vector field that expresses the density of permanent or induced magnetic dipole moments in a magnetic material. Accordingly, physicists and engineers usually define magnetization as the quantity of magnetic moment per unit volume. [ 1 ] It is represented by a pseudovector M . Magnetization can be compared to electric polarization , which is the measure of the corresponding response of a material to an electric field in electrostatics .
Magnetization also describes how a material responds to an applied magnetic field as well as the way the material changes the magnetic field, and can be used to calculate the forces that result from those interactions.
The origin of the magnetic moments responsible for magnetization can be either microscopic electric currents resulting from the motion of electrons in atoms , or the spin of the electrons or the nuclei. Net magnetization results from the response of a material to an external magnetic field .
Paramagnetic materials have a weak induced magnetization in a magnetic field, which disappears when the magnetic field is removed. Ferromagnetic and ferrimagnetic materials have strong magnetization in a magnetic field, and can be magnetized to have magnetization in the absence of an external field, becoming a permanent magnet . Magnetization is not necessarily uniform within a material, but may vary between different points.
The magnetization field or M -field can be defined according to the following equation: M = d m d V {\displaystyle \mathbf {M} ={\frac {\mathrm {d} \mathbf {m} }{\mathrm {d} V}}}
Where d m {\displaystyle \mathrm {d} \mathbf {m} } is the elementary magnetic moment and d V {\displaystyle \mathrm {d} V} is the volume element ; in other words, the M -field is the distribution of magnetic moments in the region or manifold concerned. This is better illustrated through the following relation: m = ∭ M d V {\displaystyle \mathbf {m} =\iiint \mathbf {M} \,\mathrm {d} V} where m is an ordinary magnetic moment and the triple integral denotes integration over a volume. This makes the M -field completely analogous to the electric polarization field , or P -field, used to determine the electric dipole moment p generated by a similar region or manifold with such a polarization: P = d p d V , p = ∭ P d V , {\displaystyle \mathbf {P} ={\mathrm {d} \mathbf {p} \over \mathrm {d} V},\quad \mathbf {p} =\iiint \mathbf {P} \,\mathrm {d} V,} where d p {\displaystyle \mathrm {d} \mathbf {p} } is the elementary electric dipole moment.
Those definitions of P and M as a "moments per unit volume" are widely adopted, though in some cases they can lead to ambiguities and paradoxes. [ 1 ]
The M -field is measured in amperes per meter (A/m) in SI units . [ 2 ]
The behavior of magnetic fields ( B , H ), electric fields ( E , D ), charge density ( ρ ), and current density ( J ) is described by Maxwell's equations . The role of the magnetization is described below.
The magnetization defines the auxiliary magnetic field H as
which is convenient for various calculations. The vacuum permeability μ 0 is, approximately, 4π × 10 −7 V · s /( A · m ).
A relation between M and H exists in many materials. In diamagnets and paramagnets , the relation is usually linear:
where χ is called the volume magnetic susceptibility , and μ is called the magnetic permeability of the material. The magnetic potential energy per unit volume (i.e. magnetic energy density ) of the paramagnet (or diamagnet) in the magnetic field is:
the negative gradient of which is the magnetic force on the paramagnet (or diamagnet) per unit volume (i.e. force density).
In diamagnets ( χ < 0 {\displaystyle \chi <0} ) and paramagnets ( χ > 0 {\displaystyle \chi >0} ), usually | χ | ≪ 1 {\displaystyle |\chi |\ll 1} , and therefore M ≈ χ B μ 0 {\displaystyle \mathbf {M} \approx \chi {\frac {\mathbf {B} }{\mu _{0}}}} .
In ferromagnets there is no one-to-one correspondence between M and H because of magnetic hysteresis .
Alternatively to the magnetization, one can define the magnetic polarization , I (often the symbol J is used, not to be confused with current density). [ 3 ]
This is by direct analogy to the electric polarization , D = ε 0 E + P {\displaystyle \mathbf {D} =\varepsilon _{0}\mathbf {E} +\mathbf {P} } .
The magnetic polarization thus differs from the magnetization by a factor of μ 0 :
Whereas magnetization is given with the unit ampere/meter, the magnetic polarization is given with the unit tesla.
The magnetization M makes a contribution to the current density J , known as the magnetization current. [ 4 ]
and for the bound surface current :
so that the total current density that enters Maxwell's equations is given by
where J f is the electric current density of free charges (also called the free current ), the second term is the contribution from the magnetization, and the last term is related to the electric polarization P .
In the absence of free electric currents and time-dependent effects, Maxwell's equations describing the magnetic quantities reduce to
These equations can be solved in analogy with electrostatic problems where
In this sense −∇⋅ M plays the role of a fictitious "magnetic charge density" analogous to the electric charge density ρ ; (see also demagnetizing field ).
The time-dependent behavior of magnetization becomes important when considering nanoscale and nanosecond timescale magnetization. Rather than simply aligning with an applied field, the individual magnetic moments in a material begin to precess around the applied field and come into alignment through relaxation as energy is transferred into the lattice.
Magnetization reversal, also known as switching, refers to the process that leads to a 180° (arc) re-orientation of the magnetization vector with respect to its initial direction, from one stable orientation to the opposite one. Technologically, this is one of the most important processes in magnetism that is linked to the magnetic data storage process such as used in modern hard disk drives . [ 5 ] As it is known today, there are only a few possible ways to reverse the magnetization of a metallic magnet:
Demagnetization is the reduction or elimination of magnetization. [ 7 ] One way to do this is to heat the object above its Curie temperature , where thermal fluctuations have enough energy to overcome exchange interactions , the source of ferromagnetic order, and destroy that order. Another way is to pull it out of an electric coil with alternating current running through it, giving rise to fields that oppose the magnetization. [ 8 ]
One application of demagnetization is to eliminate unwanted magnetic fields. For example, magnetic fields can interfere with electronic devices such as cell phones or computers, and with machining by making cuttings cling to their parent. [ 8 ] | https://en.wikipedia.org/wiki/Magnetization |
In classical electromagnetism , magnetization is the vector field that expresses the density of permanent or induced magnetic dipole moments in a magnetic material. Accordingly, physicists and engineers usually define magnetization as the quantity of magnetic moment per unit volume. [ 1 ] It is represented by a pseudovector M . Magnetization can be compared to electric polarization , which is the measure of the corresponding response of a material to an electric field in electrostatics .
Magnetization also describes how a material responds to an applied magnetic field as well as the way the material changes the magnetic field, and can be used to calculate the forces that result from those interactions.
The origin of the magnetic moments responsible for magnetization can be either microscopic electric currents resulting from the motion of electrons in atoms , or the spin of the electrons or the nuclei. Net magnetization results from the response of a material to an external magnetic field .
Paramagnetic materials have a weak induced magnetization in a magnetic field, which disappears when the magnetic field is removed. Ferromagnetic and ferrimagnetic materials have strong magnetization in a magnetic field, and can be magnetized to have magnetization in the absence of an external field, becoming a permanent magnet . Magnetization is not necessarily uniform within a material, but may vary between different points.
The magnetization field or M -field can be defined according to the following equation: M = d m d V {\displaystyle \mathbf {M} ={\frac {\mathrm {d} \mathbf {m} }{\mathrm {d} V}}}
Where d m {\displaystyle \mathrm {d} \mathbf {m} } is the elementary magnetic moment and d V {\displaystyle \mathrm {d} V} is the volume element ; in other words, the M -field is the distribution of magnetic moments in the region or manifold concerned. This is better illustrated through the following relation: m = ∭ M d V {\displaystyle \mathbf {m} =\iiint \mathbf {M} \,\mathrm {d} V} where m is an ordinary magnetic moment and the triple integral denotes integration over a volume. This makes the M -field completely analogous to the electric polarization field , or P -field, used to determine the electric dipole moment p generated by a similar region or manifold with such a polarization: P = d p d V , p = ∭ P d V , {\displaystyle \mathbf {P} ={\mathrm {d} \mathbf {p} \over \mathrm {d} V},\quad \mathbf {p} =\iiint \mathbf {P} \,\mathrm {d} V,} where d p {\displaystyle \mathrm {d} \mathbf {p} } is the elementary electric dipole moment.
Those definitions of P and M as a "moments per unit volume" are widely adopted, though in some cases they can lead to ambiguities and paradoxes. [ 1 ]
The M -field is measured in amperes per meter (A/m) in SI units . [ 2 ]
The behavior of magnetic fields ( B , H ), electric fields ( E , D ), charge density ( ρ ), and current density ( J ) is described by Maxwell's equations . The role of the magnetization is described below.
The magnetization defines the auxiliary magnetic field H as
which is convenient for various calculations. The vacuum permeability μ 0 is, approximately, 4π × 10 −7 V · s /( A · m ).
A relation between M and H exists in many materials. In diamagnets and paramagnets , the relation is usually linear:
where χ is called the volume magnetic susceptibility , and μ is called the magnetic permeability of the material. The magnetic potential energy per unit volume (i.e. magnetic energy density ) of the paramagnet (or diamagnet) in the magnetic field is:
the negative gradient of which is the magnetic force on the paramagnet (or diamagnet) per unit volume (i.e. force density).
In diamagnets ( χ < 0 {\displaystyle \chi <0} ) and paramagnets ( χ > 0 {\displaystyle \chi >0} ), usually | χ | ≪ 1 {\displaystyle |\chi |\ll 1} , and therefore M ≈ χ B μ 0 {\displaystyle \mathbf {M} \approx \chi {\frac {\mathbf {B} }{\mu _{0}}}} .
In ferromagnets there is no one-to-one correspondence between M and H because of magnetic hysteresis .
Alternatively to the magnetization, one can define the magnetic polarization , I (often the symbol J is used, not to be confused with current density). [ 3 ]
This is by direct analogy to the electric polarization , D = ε 0 E + P {\displaystyle \mathbf {D} =\varepsilon _{0}\mathbf {E} +\mathbf {P} } .
The magnetic polarization thus differs from the magnetization by a factor of μ 0 :
Whereas magnetization is given with the unit ampere/meter, the magnetic polarization is given with the unit tesla.
The magnetization M makes a contribution to the current density J , known as the magnetization current. [ 4 ]
and for the bound surface current :
so that the total current density that enters Maxwell's equations is given by
where J f is the electric current density of free charges (also called the free current ), the second term is the contribution from the magnetization, and the last term is related to the electric polarization P .
In the absence of free electric currents and time-dependent effects, Maxwell's equations describing the magnetic quantities reduce to
These equations can be solved in analogy with electrostatic problems where
In this sense −∇⋅ M plays the role of a fictitious "magnetic charge density" analogous to the electric charge density ρ ; (see also demagnetizing field ).
The time-dependent behavior of magnetization becomes important when considering nanoscale and nanosecond timescale magnetization. Rather than simply aligning with an applied field, the individual magnetic moments in a material begin to precess around the applied field and come into alignment through relaxation as energy is transferred into the lattice.
Magnetization reversal, also known as switching, refers to the process that leads to a 180° (arc) re-orientation of the magnetization vector with respect to its initial direction, from one stable orientation to the opposite one. Technologically, this is one of the most important processes in magnetism that is linked to the magnetic data storage process such as used in modern hard disk drives . [ 5 ] As it is known today, there are only a few possible ways to reverse the magnetization of a metallic magnet:
Demagnetization is the reduction or elimination of magnetization. [ 7 ] One way to do this is to heat the object above its Curie temperature , where thermal fluctuations have enough energy to overcome exchange interactions , the source of ferromagnetic order, and destroy that order. Another way is to pull it out of an electric coil with alternating current running through it, giving rise to fields that oppose the magnetization. [ 8 ]
One application of demagnetization is to eliminate unwanted magnetic fields. For example, magnetic fields can interfere with electronic devices such as cell phones or computers, and with machining by making cuttings cling to their parent. [ 8 ] | https://en.wikipedia.org/wiki/Magnetization_reversal |
Magnetic roasting technology refers to the process of heating materials or ores under specific atmospheric conditions to induce chemical reactions. [ 1 ] This process selectively converts weakly magnetic iron minerals such as hematite (Fe 2 O 3 ), siderite (FeCO 3 ), and limonite (Fe 2 O 3 ·nH 2 O) into strongly magnetic magnetite (Fe 3 O 4 ) or maghemite (γ-Fe 2 O 3 ), while the magnetic properties of gangue minerals remain almost unchanged. [ 2 ]
By artificially increasing the magnetic disparity between iron oxides and gangue minerals through magnetic roasting, the selectivity of iron ore is improved, making it the most effective method for separating refractory iron ores. Additionally, the roasting process can eliminate harmful impurities such as crystalline water, sulfur , and arsenic from the ore, loosening the ore structure and enhancing subsequent grinding efficiency. [ 3 ]
Researchers in mineral processing have been developing magnetic roasting technology for iron ore since the early 20th century. Depending on the type of reactor used, magnetic roasting can be classified into shaft furnace roasting, rotary kiln roasting, fluidized bed roasting, and microwave roasting . [ 4 ]
Shaft furnace magnetization roasting is a metallurgical process , mainly used to treat iron ore, so that in a high temperature environment by reacting with reducing agents (such as coal, coke or gas), the iron oxides (such as hematite, limonite, etc.) to reduce to magnetic iron minerals (mainly magnetite). The process is usually carried out in the vertical furnace, the charge is top-down under the action of gravity, through layer by layer heating and reduction reaction, and finally obtain magnetic iron ore, so as to improve its magnetic separation performance, and facilitate the subsequent beneficiation and smelting process.
The main steps of magnetizing roasting in shaft furnace include: Charge preparation: Mix iron ore with reducing agent in a certain proportion. Heating: The charge is added from the top of the shaft furnace and heated layer by layer as it falls to a roasting temperature (usually between 700 °C and 900 °C). Reduction reaction: The iron oxide in the ore reacts with the reducing agent and is reduced to magnetic iron minerals (such as magnetite). Cooling and discharge: The roasted material is cooled and discharged from the bottom of the shaft furnace. [ 5 ]
Magnetization roasting in rotary kiln is to reduce iron oxides (such as hematite, limonite, etc.) in the ore to magnetic iron minerals (mainly magnetite) by reacting iron ore containing iron ore with reducing agents (such as coal, coke or natural gas) in a rotating high-temperature kiln. This process helps to improve the magnetic separation performance of iron ore and facilitate subsequent beneficiation and smelting operations. [ 6 ] [ 7 ] .
The main steps of magnetization roasting in rotary kiln include: Raw material preparation: Mix the iron ore with the appropriate amount of reducing agent, and add the binder if necessary to improve the roasting effect.
Feed: The mixture is uniformly fed into the kiln head of the rotary kiln through the feed device. Roasting: The rotary kiln is rotated at high temperatures (usually between 700 °C and 900 °C), and the material is continuously rolled and moved forward in the kiln, in full contact with the reducing atmosphere, so that the iron oxide is reduced to magnetic iron minerals (such as magnetite). Cooling and discharge: The calcined material is cooled by a cooling system (such as a cooling kiln or cooling cylinder) and discharged from the end of the rotary kiln. [ 6 ]
Fluidized bed magnetic roasting is the use of suspension roaster to fully mix and contact fine ore with reducing agents (such as pulverized coal, natural gas, etc.) in high temperature environment, so that the iron oxides in the ore (such as hematite, limonite, etc.) are reduced to magnetic iron minerals (mainly magnetite), thereby improving the magnetic separation performance of the ore and facilitating subsequent beneficiation and smelting operations [ 5 ] [ 8 ] [ 9 ] .
The main steps of suspension magnetization roasting include: Raw material preparation: Mix iron ore powder with reducing agent, add auxiliary agent if necessary to improve roasting effect. Roasting: The mixed material is suspended in the baking furnace by air flow, and at high temperatures (usually between 700 °C and 900 °C), the material is fully in contact with the reducing gas, and the reduction reaction is carried out to convert the iron oxide into magnetic iron minerals. Cooling and collection: The roasted material is cooled by a cooling system and collected by equipment such as a cyclone or a cloth bag collector. [ 1 ]
Microwave magnetization roasting uses microwave as an energy source to reduce iron oxides (such as hematite, limonite, etc.) in iron ore to magnetic iron minerals (mainly magnetite). In this process, the ore is rapidly heated, so that the reduction reaction is completed in a short time, so as to improve the magnetic separation performance of the ore, and facilitate subsequent beneficiation and smelting operations. [ 10 ] [ 11 ] [ 12 ]
The main steps of microwave magnetization roasting include: Raw material preparation: Mix iron ore powder with reducing agent (such as toner, pulverized coal, etc.) evenly. Microwave heating: The mixture is placed in a microwave oven and heated by microwave radiation. Microwave energy acts directly on the material to rapidly heat it to the desired roasting temperature (usually between 500 °C and 900 °C). Reduction reaction: At high temperatures, iron oxides and reducing agents undergo a reduction reaction to produce magnetic iron minerals (such as magnetite). Cooling and collection: The roasted material is cooled by a cooling system and collected for treatment [ 13 ]
The commonly used magnetization roasting methods can be divided into reduction roasting, neutral roasting, oxidation roasting, redox roasting and reduction oxidation roasting. [ 14 ]
After heating to a certain temperature, hematite, limonite and iron-manganese ore can be transformed into strong magnetic magnetite by reacting with an appropriate amount of reducing agent. Commonly used reducing agents are C, CO, H2 and so on. The reaction of hematite with reducing agent is as follows: [ 1 ]
Carbonated iron ores such as siderite, magnesite, magnesite and magnesium siderite can be decomposed to produce magnetite after heating to a certain temperature (300-- 400 degrees Celsius) without air or by injecting a small amount of air. The chemical reaction is as follows: [ 15 ]
Pyrite is oxidized in oxygen for a short time to oxidize to pyrite. If the roasting time is very long, the pyrite can continue to react into magnetite. The chemical reaction is as follows. [ 16 ]
Iron ore containing siderite, hematite or limonite, when the ratio of siderite to hematite is less than 1, the siderite is oxidized to hematite to a certain extent in the oxidizing atmosphere, and then it is reduced to magnetite together with the original hematite in the ore in the reducing atmosphere. [ 17 ]
Reduction oxidation roasting The magnetite produced by magnetization roasting of various iron ore can be oxidized into strong magnetic hematite when cooled to below 400 °C in an oxygen-free atmosphere and then in contact with the air. The chemical reaction is as follows: [ 16 ] | https://en.wikipedia.org/wiki/Magnetization_roasting_technology |
Magnetization transfer (MT), in NMR and MRI , refers to the transfer of nuclear spin polarization and/or spin coherence from one population of nuclei to another population of nuclei, and to techniques that make use of these phenomena. [ 1 ] There is some ambiguity regarding the precise definition of magnetization transfer, however the general definition given above encompasses all more specific notions. NMR active nuclei, those with non-zero spin, can be energetically coupled to one another under certain conditions. The mechanisms of nuclear-spin energy-coupling have been extensively characterized and are described in the following articles: Angular momentum coupling , Magnetic dipole–dipole interaction , J-coupling , Residual dipolar coupling , Nuclear Overhauser effect , Spin–spin relaxation , and Spin saturation transfer . Alternatively, some nuclei in a chemical system are labile and exchange between non-equivalent environments. A more specific example of this case is presented in the section Chemical Exchange Magnetization transfer .
In either case, magnetization transfer techniques probe the dynamic relationship between two or more distinguishable nuclei populations, in so far as energy exchange between the populations can be induced and measured in an idealized NMR experiment.
In magnetic resonance imaging or NMR of macromolecular samples, such as protein solutions, at least two types of water molecules, free (bulk) and bound (hydration), are present. Bulk water molecules have many mechanical degrees of freedom, and motion of such molecules thus exhibits statistically averaged behavior. Because of this uniformity, most free water protons have resonance frequencies very near the average Larmor frequency of all such protons. On a properly acquired NMR spectrum this is seen as a narrow Lorentzian line (at 4.8 ppm, 20 C). Bulk water molecules are also relatively far from magnetic field perturbing macromolecules, such that free water protons experience a more homogeneous magnetic field, which results in slower transverse magnetization dephasing and a longer T 2 * . Conversely, hydration water molecules are mechanically constrained by extensive interactions with the local macromolecules and hence magnetic field inhomogeneities are not averaged out, which leads to broader resonance lines. This results in faster dephasing of the magnetization that produces the NMR signal and much shorter T 2 values (<200 μs). Because the T 2 values are so short, the NMR signal from the protons of bound water is not typically observed in MRI.
However, using an off-resonance saturation pulse to irradiate protons in the bound (hydration) population can have a detectable effect on the NMR signal of the mobile (free) proton pool. When a population of spins is saturated, such that the magnitude of the macroscopic magnetization vector approaches zero, there is no remaining spin polarization with which to produce an NMR signal. Longitudinal relaxation refers to the return of longitudinal spin polarization, which occurs at a rate described by T1. While the number of hydration water molecules may be insufficient to produce an observable signal, exchange of water molecules between the hydration and bulk population allows characterization of the hydration population, and measurement of the rate at which molecules are exchanging between bulk and bound sites. Such experiments are often termed saturation transfer or chemical exchange saturation transfer (CEST) , because the signal of the bulk water is observed to decrease when the hydration population is saturated. Considering these techniques from the opposite perspective, that magnetization (i.e. spin polarization) is being transferred from the bulk water to the spin-saturated hydration population, allows one to conceptually unify chemical exchange methods with other techniques that transfer magnetization between nuclei populations. Since the extent of signal decay depends on the exchange rate between free and hydration water, MT can be used to provide an alternative contrast method in addition to T 1 , T 2 , and proton density differences.
MT is believed to be a nonspecific indicator of the structural integrity of the tissue being imaged.
An extension of MT, the magnetization transfer ratio (MTR) has been used in neuroradiology to highlight abnormalities in brain structures. (The MTR is ( M o - M t )/ M o .)
A systematic modulation of the precise frequency offset for the saturation pulse can be plotted against the free-water signal to form a "Z-spectrum". This technique is often referred to as "Z-spectroscopy". | https://en.wikipedia.org/wiki/Magnetization_transfer |
A magneto-optic effect is any one of a number of phenomena in which an electromagnetic wave propagates through a medium that has been altered by the presence of a quasistatic magnetic field . In such a medium, which is also called gyrotropic or gyromagnetic , left- and right-rotating elliptical polarizations can propagate at different speeds, leading to a number of important phenomena. When light is transmitted through a layer of magneto-optic material, the result is called the Faraday effect : the plane of polarization can be rotated, forming a Faraday rotator . The results of reflection from a magneto-optic material are known as the magneto-optic Kerr effect (not to be confused with the nonlinear Kerr effect ).
In general, magneto-optic effects break time reversal symmetry locally (i.e., when only the propagation of light, and not the source of the magnetic field, is considered) as well as Lorentz reciprocity , which is a necessary condition to construct devices such as optical isolators (through which light passes in one direction but not the other).
Two gyrotropic materials with reversed rotation directions of the two principal polarizations, corresponding to complex-conjugate ε tensors for lossless media, are called optical isomers .
In particular, in a magneto-optic material the presence of a magnetic field (either externally applied or because the material itself is ferromagnetic ) can cause a change in the permittivity tensor ε of the material. The ε becomes anisotropic, a 3×3 matrix, with complex off-diagonal components, depending on the frequency ω of incident light. If the absorption losses can be neglected, ε is a Hermitian matrix . The resulting principal axes become complex as well, corresponding to elliptically-polarized light where left- and right-rotating polarizations can travel at different speeds (analogous to birefringence ).
More specifically, for the case where absorption losses can be neglected, the most general form of Hermitian ε is:
or equivalently the relationship between the displacement field D and the electric field E is:
where ε ′ {\displaystyle \varepsilon '} is a real symmetric matrix and g = ( g x , g y , g z ) {\displaystyle \mathbf {g} =(g_{x},g_{y},g_{z})} is a real pseudovector called the gyration vector , whose magnitude is generally small compared to the eigenvalues of ε ′ {\displaystyle \varepsilon '} . The direction of g is called the axis of gyration of the material. To first order, g is proportional to the applied magnetic field :
where χ ( m ) {\displaystyle \chi ^{(m)}\!} is the magneto-optical susceptibility (a scalar in isotropic media, but more generally a tensor ). If this susceptibility itself depends upon the electric field, one can obtain a nonlinear optical effect of magneto-optical parametric generation (somewhat analogous to a Pockels effect whose strength is controlled by the applied magnetic field).
The simplest case to analyze is the one in which g is a principal axis (eigenvector) of ε ′ {\displaystyle \varepsilon '} , and the other two eigenvalues of ε ′ {\displaystyle \varepsilon '} are identical. Then, if we let g lie in the z direction for simplicity, the ε tensor simplifies to the form:
Most commonly, one considers light propagating in the z direction (parallel to g ). In this case the solutions are elliptically polarized electromagnetic waves with phase velocities 1 / μ ( ε 1 ± g z ) {\displaystyle 1/{\sqrt {\mu (\varepsilon _{1}\pm g_{z})}}} (where μ is the magnetic permeability ). This difference in phase velocities leads to the Faraday effect.
For light propagating purely perpendicular to the axis of gyration, the properties are known as the Cotton-Mouton effect and used for a Circulator .
Kerr rotation and Kerr ellipticity are changes in the polarization of incident light which comes in contact with a gyromagnetic material. Kerr rotation is a rotation in the plane of polarization of transmitted light, and Kerr ellipticity is the ratio of the major to minor axis of the ellipse traced out by elliptically polarized light on the plane through which it propagates. Changes in the orientation of polarized incident light can be quantified using these two properties.
According to classical physics, the speed of light varies with the permittivity of a material:
v p = 1 ϵ μ {\displaystyle v_{p}={\frac {1}{\sqrt {\epsilon \mu }}}}
where v p {\displaystyle v_{p}} is the velocity of light through the material, ϵ {\displaystyle \epsilon } is the material permittivity, and μ {\displaystyle \mu } is the material permeability. Because the permittivity is anisotropic, polarized light of different orientations will travel at different speeds.
This can be better understood if we consider a wave of light that is circularly polarized (seen to the right). If this wave interacts with a material at which the horizontal component (green sinusoid) travels at a different speed than the vertical component (blue sinusoid), the two components will fall out of the 90 degree phase difference (required for circular polarization) changing the Kerr ellipticity.
A change in Kerr rotation is most easily recognized in linearly polarized light, which can be separated into two circularly polarized components: Left-handed circular polarized (LHCP) light and right-handed circular polarized (RHCP) light. The anisotropy of the magneto-optic material permittivity causes a difference in the speed of LHCP and RHCP light, which will cause a change in the angle of polarized light. Materials that exhibit this property are known as birefringent .
From this rotation, we can calculate the difference in orthogonal velocity components, find the anisotropic permittivity, find the gyration vector, and calculate the applied magnetic field [ 1 ] H {\displaystyle \mathbf {H} } .
This article incorporates public domain material from Federal Standard 1037C . General Services Administration . Archived from the original on 2022-01-22. | https://en.wikipedia.org/wiki/Magneto-optic_effect |
In atomic, molecular, and optical physics , a magneto-optical trap ( MOT ) is an apparatus which uses laser cooling and a spatially varying magnetic field to create a trap which can produce samples of cold neutral atoms . Temperatures achieved in a MOT can be as low as several microkelvins , depending on the atomic species, which is two or three times below the photon-recoil limit . However, for atoms with an unresolved hyperfine structure , such as 7 Li , the temperature achieved in a MOT will be higher than the Doppler cooling limit.
A MOT is formed from the intersection of the zero of a weak quadrupolar magnetic field and six circularly polarized red-detuned optical molasses beams. Counterpropagating beams have opposite handed polarization. As atoms travel away from the zero field at the center of the trap, the spatially varying Zeeman shift brings an atomic transition into resonance with the laser beams. The polarization of the beam propagating in the opposite direction of this atomic motion is chosen to drive this transition. The absorption of these photons gives rise to a scattering force that pushes the atoms back towards the center of the trap.
In this way, a MOT is able to trap and cool atoms over repeated absorption and spontaneous emission cycles with initial velocities of hundreds of meters per second down to tens of centimeters per second (again, depending upon the atomic species).
Two coils in an anti-Helmholtz configuration are used to generate a weak quadrupolar magnetic field; by convention, the coils are separated along the z {\displaystyle z} -axis. In the proximity of the field zero, located halfway between the two coils along the z {\displaystyle z} -direction, the field gradient is uniform and the field itself varies linearly with displacement from the field zero. For this discussion, consider an atom with ground and excited states with J = 0 {\displaystyle J=0} and J = 1 {\displaystyle J=1} , respectively, where J {\displaystyle J} is the magnitude of the total angular momentum vector. Due to the Zeeman effect , the J ≠ 0 {\displaystyle J\neq 0} states will each be split into 2 J + 1 {\displaystyle 2J+1} sublevels with associated values of m J {\displaystyle m_{J}} , denoted by | J , m J ⟩ {\displaystyle |J,m_{J}\rangle } . This results in spatially-dependent energy shifts of the excited-state sublevels, as the Zeeman shift is linearly proportional to the field strength. As a note, the Maxwell equation ∇ ⋅ B = 0 {\displaystyle \nabla \cdot \mathbf {B} =0} implies that the field gradient is twice as strong along the z {\displaystyle z} -direction than in the x {\displaystyle x} and y {\displaystyle y} -directions, and thus the trapping force along the z {\displaystyle z} -direction is twice as strong.
In combination with the magnetic field, three pairs of counter-propagating circularly-polarized laser beams are sent in along orthogonal axes, such that their intersection lies at the location of the magnetic field zero. The beams are red-detuned from the J = 0 → J = 1 {\displaystyle J=0\rightarrow J=1} transition by an amount δ {\displaystyle \delta } such that δ ≡ ν 0 − ν L > 0 {\displaystyle \delta \equiv \nu _{0}-\nu _{L}>0} , or equivalently, ν L = ν 0 − δ {\displaystyle \nu _{L}=\nu _{0}-\delta } , where ν L {\displaystyle \nu _{L}} is the frequency of the laser beams and ν 0 {\displaystyle \nu _{0}} is the frequency of the transition. The beams must be circularly polarized to ensure that photon absorption can only occur for certain transitions between the ground state | 0 , 0 ⟩ {\displaystyle |0,0\rangle } and the sublevels of the excited state | 1 , m J ⟩ {\displaystyle |1,m_{J}\rangle } , where m J = − 1 , 0 , 1 {\displaystyle m_{J}=-1,0,1} . In other words, the circularly-polarized beams enforce selection rules on the allowed electric dipole transitions between states.
Now consider an atom which is displaced from the field zero in the + z {\displaystyle +z} -direction. The Zeeman effect shifts the energy of the | J = 1 , m J = − 1 ⟩ {\displaystyle |J=1,m_{J}=-1\rangle } state lower in energy, decreasing the energy gap between it and the | J = 0 , m J = 0 ⟩ {\displaystyle |J=0,m_{J}=0\rangle } state; that is, the frequency associated with the transition decreases. Red-detuned σ − {\displaystyle \sigma ^{-}} photons, which only drive Δ m J = − 1 {\displaystyle \Delta m_{J}=-1} transitions, propagating in the − z {\displaystyle -z} -direction thus become closer to resonance as the atom travels further from the center of the trap, increasing the scattering rate and scattering force. When an atom absorbs a σ − {\displaystyle \sigma ^{-}} photon, it is excited to the | J = 1 , m J = − 1 ⟩ {\displaystyle |J=1,m_{J}=-1\rangle } state and gets a "kick" of one photon recoil momentum, ℏ k {\displaystyle \hbar k} , in the direction opposite to its motion, where k = 2 π ν 0 / c {\displaystyle k=2\pi \nu _{0}/c} . The atom, now in an excited state, will then spontaneously emit a photon in a random direction as it returns to the ground state, which will result in another momentum "kick". Because this "kick" from the emitted photon occurs in a random direction, the net effect of many absorption-spontaneous emission events will result in the atom being "pushed" back towards the field-zero of the trap. This trapping process will also occur for an atom moving in the − z {\displaystyle -z} -direction if σ + {\displaystyle \sigma ^{+}} photons are traveling in the + z {\displaystyle +z} -direction, the only difference being that the excitation will be from | J = 0 , m J = 0 ⟩ {\displaystyle |J=0,m_{J}=0\rangle } to | J = 1 , m J = + 1 ⟩ {\displaystyle |J=1,m_{J}=+1\rangle } since the magnetic field is negative for z < 0 {\displaystyle z<0} . Since the magnetic field gradient near the trap center is uniform, the same phenomenon of trapping and cooling occurs along the x {\displaystyle x} and y {\displaystyle y} -directions as well. At the center of the trap, the magnetic field is zero and atoms are "dark" to incident red-detuned photons. That is, at the center of the trap, the Zeeman shift is zero for all states and so the transition frequency ν 0 {\displaystyle \nu _{0}} from J = 0 → J = 1 {\displaystyle J=0\rightarrow J=1} remains unchanged. The detuning of the photons from this frequency means that there will not be an appreciable amount of absorption by atoms in the center of the trap, hence the term "dark". Thus, the coldest, slowest moving atoms accumulate in the center of the MOT where they scatter very few photons.
Mathematically, the radiation pressure force that atoms experience in a MOT is given by: [ 1 ]
F M O T = − α v − α g μ B ℏ k r ∇ ‖ B ‖ , {\displaystyle \mathbf {F} _{\mathrm {MOT} }=-\alpha \mathbf {v} -{\frac {\alpha g\mu _{B}}{\hbar k}}\mathbf {r} \nabla \|\mathbf {B} \|,}
where α = 4 ℏ k 2 I I 0 2 δ / Γ [ 1 + ( 2 δ / Γ ) 2 ] 2 {\displaystyle \alpha =4\hbar k^{2}{\frac {I}{I_{0}}}{\frac {2\delta /\Gamma }{[1+(2\delta /\Gamma )^{2}]^{2}}}} is the damping coefficient, g {\displaystyle g} is the Landé g-factor , μ B {\displaystyle \mu _{B}} is the Bohr magneton, ℏ {\displaystyle \hbar } is the reduced Planck constant, I 0 {\displaystyle I_{0}} is the saturation intensity, δ {\displaystyle \delta } is the laser detuning, Γ {\displaystyle \Gamma } is the linewidth of the atom-cooling transition and k {\displaystyle k} is the norm of its wavevector.
As a thermal atom at room temperature has many thousands of times the momentum of a single photon, the cooling of an atom must involve many absorption-spontaneous emission cycles, with the atom losing up to ħk of momenta each cycle.
Because of this, if an atom is to be laser cooled, it must possess a specific energy level structure known as a closed optical loop, where following an excitation-spontaneous emission event, the atom is always returned to its original state. 85 Rubidium, for example, has a closed optical loop between the 5 S 1 / 2 F = 3 {\displaystyle 5S_{1/2}\ F=3} state and the 5 P 3 / 2 F = 4 {\displaystyle 5P_{3/2}\ F=4} state. Once in the excited state, the atom is forbidden from decaying to any of the 5 P 1 / 2 {\displaystyle 5P_{1/2}} states, which would not conserve parity , and is also forbidden from decaying to the 5 S 1 / 2 F = 2 {\displaystyle 5S_{1/2}\ F=2} state, which would require an angular momentum change of −2, which cannot be supplied by a single photon.
Many atoms that do not contain closed optical loops can still be laser cooled, however, by using repump lasers which re-excite the population back into the optical loop after it has decayed to a state outside of the cooling cycle. The magneto-optical trapping of rubidium 85, for example, involves cycling on the closed 5 S 1 / 2 F = 3 → 5 P 3 / 2 F = 4 {\displaystyle 5S_{1/2}\ F=3\to 5P_{3/2}\ F=4} transition. On excitation, however, the detuning necessary for cooling gives a small, but non-zero overlap with the 5 P 3 / 2 F = 3 {\displaystyle 5P_{3/2}\ F=3} state. If an atom is excited to this state, which occurs roughly every thousand cycles, the atom is then free to decay either the F = 3 {\displaystyle F=3} , light coupled upper hyperfine state, or the F = 2 {\displaystyle F=2} "dark" lower hyperfine state. If it falls back to the dark state, the atom stops cycling between ground and excited state, and the cooling and trapping of this atom stops. A repump laser which is resonant with the 5 S 1 / 2 F = 2 → 5 P 3 / 2 F = 3 {\displaystyle 5S_{1/2}\ F=2\to 5P_{3/2}\ F=3} transition is used to recycle the population back into the optical loop so that cooling can continue.
All magneto-optical traps require at least one trapping laser plus any necessary repumper lasers (see above). These lasers need stability, rather than high power, requiring no more than the saturation intensity , but a linewidth much less than the Doppler width , usually several megahertz. Because of their low cost, compact size and ease of use, laser diodes are used for many of the standard MOT species while the linewidth and stability of these lasers is controlled using servo systems, which stabilises the lasers to an atomic frequency reference by using, for example, saturated absorption spectroscopy and the Pound-Drever-Hall technique to generate a locking signal.
By employing a 2-dimensional diffraction grating it is possible to generate the configuration of laser beams required for a magneto-optical trap from a single laser beam and thus have a very compact magneto-optical trap. [ 2 ]
The MOT cloud is loaded from a background of thermal vapour, or from an atomic beam, usually slowed down to the capture velocity using a Zeeman slower . However, the trapping potential in a magneto-optical trap is small in comparison to thermal energies of atoms and most collisions between trapped atoms and the background gas supply enough energy to the trapped atom to kick it out of the trap. If the background pressure is too high, atoms are kicked out of the trap faster than they can be loaded, and the trap does not form. This means that the MOT cloud only forms in a vacuum chamber with a background pressure of less than 100 micropascals (10 −9 bar)}. [ 3 ]
The minimum temperature and maximum density of a cloud in a magneto-optical trap is limited by the spontaneously emitted photon in cooling each cycle. While the asymmetry in atom excitation gives cooling and trapping forces, the emission of the spontaneously emitted photon is in a random direction, and therefore contributes to a heating of the atom. Of the two ħk kicks the atom receives in each cooling cycle, the first cools, and the second heats: a simple description of laser cooling which enables us to calculate a point at which these two effects reach equilibrium, and therefore define a lower temperature limit, known as the Doppler cooling limit .
The density is also limited by the spontaneously emitted photon. As the density of the cloud increases, the chance that the spontaneously emitted photon will leave the cloud without interacting with any further atoms tends to zero. The absorption, by a neighboring atom, of a spontaneously emitted photon gives a 2ħk momentum kick between the emitting and absorbing atom which can be seen as a repulsive force, similar to coulomb repulsion, which limits the maximum density of the cloud.
As of 2022 the method has been demonstrated to work up to triatomic molecules. [ 4 ] [ 5 ]
Because of the continuous cycle of absorption and spontaneous emission, which causes decoherence , any quantum manipulation experiments must be performed with the MOT beams turned off. As a result of low densities and speeds of atoms achieved by optical cooling, the mean free path in a ball of MOT cooled atoms is very long, and atoms may be treated as ballistic . This is useful for quantum information experiments where it is necessary to have long coherence times (the time an atom spends in a defined quantum state). In this case, it is common to stop the expansion of the cloud while the MOT is off by loading the cooled atoms into a dipole trap .
A magneto-optical trap is usually the first step to achieving Bose–Einstein condensation . Atoms are cooled in a MOT down to a few times the recoil limit, and then evaporatively cooled which lowers the temperature and increases the density to the required phase space density.
A MOT of 133 Cs was used to make some of the best measurements of CP violation . [ citation needed ]
MOTs are used in a number of quantum technologies (i.e. cold atom gravity gradiometers ) and have been deployed on several platforms (i.e. UAVs) and in several environments (i.e. down boreholes [ 6 ] ). | https://en.wikipedia.org/wiki/Magneto-optical_trap |
The Magneto Inductive Remote Activation Munition System (MI-RAMS) is a variant of the Remote Munition System (RAMS) that uses electromagnetic induction to control electronic equipment, including demolition charges , munitions , and active barriers. [ 1 ] The handheld MI-RAMS receiver consists of a box-shaped device with a fixed bulkhead-style receptacle connector on the top with a non-leaking metal shell threaded in the rear section of the connector and sealed with an O-ring . [ 2 ]
With the use of quasi-static AC magnetic fields, MI-RAMS is capable of sending signals through ice, rock, soil, water, and concrete. As a result, MI-RAMS is often used to remotely control ordnance items and communication systems in areas in which radio frequency devices under-perform or fail. [ 3 ] These areas include caves, bunkers, tunnels, dense jungle, ice fields, urban structures, and up to 66 feet underwater. [ 2 ] [ 4 ] The wireless channel created by MI-RAMS does not produce any far field (RF) emissions, which decreases likelihood of detection outside of the operating area. [ 3 ] The MI-RAMS transmitters and receivers have also been designed to work with existing communication technology, allowing other types of handsets to link to the system and communicate with each other as long as one MI-RAMS unit is present. [ 5 ]
MI-RAMS was designed and modified by researchers at the Army Research Laboratory for U.S. Army Combat Engineer Forces and Army and Navy Special Operations Forces (SEALs) to aid in establishing terrain dominance. [ 1 ] [ 6 ] | https://en.wikipedia.org/wiki/Magneto_Inductive_Remote_Activation_Munition_System |
Magnetoactive phase transitional matter (MPTM) are miniature robotic machines that can change their shape by switching between liquid and solid state. [ 1 ]
MPTMs consist of liquid metal embedded with a neodymium magnet . [ 1 ] MPTMs can be programmed to change shape when needed, by using heating and ambient cooling. [ 1 ] Heat is generated from an incorporated heating element, or by use of magnetic pulses, switching the robot into liquid mode. [ 1 ] Ambient temperatures provides cooling to change the robot into a solid state. [ 1 ] The magnetism of the metal holds the machine together while in liquid mode. [ 1 ]
MPTMs were first created by a collaboration of scientists from Sun Yat-sen University , Carnegie Mellon University , Chinese University of Hong Kong , and Zhejiang University . [ 2 ] [ 3 ] Their robot incorporated a heating element, and was able to melt itself to change shape. [ 3 ] The first MPTM incorporated neodymium , iron , and boron microparticles in gallium and had a melting point of 29.8 °C. [ 2 ] [ 4 ]
A January 2023 academic paper demonstrated the potential to use MPTMs for mechanical assembly in hard to reach locations, and in medical procedures. [ 1 ] Medical use cases were delivery of drugs in the human stomach and the removal of foreign objects. [ 1 ] | https://en.wikipedia.org/wiki/Magnetoactive_phase_transitional_matter |
Magnetobiology is the study of biological effects of mainly weak static and low-frequency magnetic fields, which do not cause heating of tissues. Magnetobiological effects have unique features that obviously distinguish them from thermal effects; often they are observed for alternating magnetic fields just in separate frequency and amplitude intervals. Also, they are dependent of simultaneously present static magnetic or electric fields and their polarization.
Magnetobiology is a subset of bioelectromagnetics . Bioelectromagnetism and biomagnetism are the study of the production of electromagnetic and magnetic fields by biological organisms. The sensing of magnetic fields by organisms is known as magnetoreception .
Biological effects of weak low frequency magnetic fields, less than about 0.1 millitesla (or 1 Gauss ) and 100 Hz correspondingly, constitutes a physics problem. The effects look paradoxical, for the energy quantum of these electromagnetic fields is by many orders of value less than the energy scale of an elementary chemical act. On the other hand, the field intensity is not enough to cause any appreciable heating of biological tissues or irritate nerves by the induced electric currents.
An example of a magnetobiological effect is the magnetic navigation by migrant animals by means of magnetoreception .
Many animal orders, such as certain birds, marine turtles, reptiles, amphibians and salmonoid fishes are able to detect small variations of the geomagnetic field and its magnetic inclination to find their seasonal habitats. They are said to use an "inclination compass". Certain crustaceans, spiny lobsters, bony fish, insects and mammals have been found to use a "polarity compass", whereas in snails and cartilageous fish the type of compass is as yet unknown. Little is known about other vertebrates and arthropods. [ 1 ] Their perception can be on the order of tens of nanoteslas. [ citation needed ]
Magnetic intensity as a component of the navigational ‘map’ of pigeons had been discussed since the late nineteenth century. [ 2 ] One of the earliest publications to prove that birds use magnetic information was a 1972 study on the compass of European robins by Wolfgang Wiltschko . [ 3 ] A 2014 double blinded study showed that European robins exposed to low level electromagnetic noise between about 20 kHz and 20 MHz, could not orient themselves with their magnetic compass. When they entered aluminium-screened huts, which attenuated electromagnetic noise in the frequency range from 50 kHz to 5 MHz by approximately two orders of magnitude, their orientation reappeared. [ 4 ]
For human health effects see electromagnetic radiation and health .
Several neurobiological models on the primary process which mediates the magnetic input have been proposed:
In the radical pair mechanism photopigments absorb a photon, which elevates it to the singlet state . They form singlet radical pairs with antiparallel spin , which, by singlet–triplet interconversion, may turn into triplet pairs with parallel spin . Because the magnetic field alters the transition between spin state the amount of triplets depends on how the photopigment is aligned within the magnetic field. Cryptochromes , a class of photopigments known from plants and animals appear to be the receptor molecules. [ 5 ]
The induction model would only apply to marine animals because as a surrounding medium with high conductivity only salt water is feasible. Evidence for this model has been lacking. [ 1 ]
The magnetite model arose with the discovery of chains of single domain magnetite in certain bacteria in the 1970s. Histological evidence in a large number of species belonging to all major phyla. Honey bees have magnetic material in the front part of the abdomen while in vertebrates mostly in the ethmoid region of the head. Experiments prove that the input from magnetite-based receptors in birds and fish is sent over the ophthalmic branch of the trigeminal nerve to the central nervous system . [ 1 ]
Practical significance of magnetobiology is conditioned by the growing level of the background electromagnetic exposure of people. Some electromagnetic fields at chronic exposures may pose a threat to human health. World Health Organization considers enhanced level of electromagnetic exposure at working places as a stress factor. Present electromagnetic safety standards, worked out by many national and international institutions, differ by tens and hundreds of times for certain EMF ranges; this situation reflects the lack of research in the area of magnetobiology and electromagnetobiology. Today [ when? ] , most of the standards take into account biological effects just from heating by electromagnetic fields, and peripheral nerve stimulation from induced currents.
Practitioners of magnet therapy attempt to treat pain or other medical conditions by relatively weak electromagnetic fields. These methods have not yet received clinical evidence in accordance with accepted standards of evidence-based medicine . Most institutions recognize the practice as a pseudoscientific one. | https://en.wikipedia.org/wiki/Magnetobiology |
The magnetocaloric effect ( MCE , from magnet and calorie ) is a scientific phenomenon in which certain materials warm up when a magnetic field is applied. The warming is due to changes in the internal state of the material releasing heat. When the magnetic field is removed, the material returns to its original state, reabsorbing the heat, and returning to original temperature. This can be used to achieve refrigeration, by allowing the material to radiate away its heat while in the magnetized hot state. Removing the magnetism, the material then cools to below its original temperature.
The effect was first observed in 1881 by a German physicist Emil Warburg , followed by French physicist P. Weiss and Swiss physicist A. Piccard in 1917. [ 1 ] The fundamental principle was suggested by P. Debye (1926) and W. Giauque (1927). [ 2 ] The first working magnetic refrigerators were constructed by several groups beginning in 1933. Magnetic refrigeration was the first method developed for cooling below about 0.3 K (the lowest temperature attainable before magnetic refrigeration, by pumping on 3 He vapors).
The magnetocaloric effect can be used to attain extremely low temperatures , as well as the ranges used in common refrigerators . [ 3 ] [ 4 ] [ 5 ] [ 6 ]
The effect was first observed by German physicist Emil Warburg in 1881 [ 7 ] Subsequently by French physicist Pierre Weiss and Swiss physicist Auguste Piccard in 1917. [ 1 ]
Major advances first appeared in the late 1920s when cooling via adiabatic demagnetization was independently proposed by chemistry Nobel Laureates Peter Debye in 1926 and William F. Giauque in 1927.
It was first demonstrated experimentally by Giauque and his colleague D. P. MacDougall in 1933 for cryogenic purposes when they reached 0.25 K. [ 8 ] Between 1933 and 1997, advances in MCE cooling occurred. [ 9 ]
In 1997, the first near room-temperature proof of concept magnetic refrigerator was demonstrated by Karl A. Gschneidner, Jr. by the Iowa State University at Ames Laboratory . This event attracted interest from scientists and companies worldwide who started developing new kinds of room temperature materials and magnetic refrigerator designs. [ 10 ]
A major breakthrough came 2002 when a group at the University of Amsterdam demonstrated the giant magnetocaloric effect in MnFe(P,As) alloys that are based on abundant materials. [ 11 ]
Refrigerators based on the magnetocaloric effect have been demonstrated in laboratories, using magnetic fields starting at 0.6 T up to 10 T. Magnetic fields above 2 T are difficult to produce with permanent magnets and are produced by a superconducting magnet (1 T is about 20.000 times the Earth's magnetic field ).
Recent research has focused on near room temperature. Constructed examples of room temperature magnetic refrigerators include:
In one example, Prof. Karl A. Gschneidner, Jr. unveiled a proof of concept magnetic refrigerator near room temperature on February 20, 1997. He also announced the discovery of the GMCE in Gd 5 Si 2 Ge 2 on June 9, 1997. [ 27 ] Since then, hundreds of peer-reviewed articles have been written describing materials exhibiting magnetocaloric effects.
The MCE is a magneto- thermodynamic phenomenon in which a temperature change of a suitable material is caused by exposing the material to a changing magnetic field. This is also known by low temperature physicists as adiabatic demagnetization . In that part of the refrigeration process, a decrease in the strength of an externally applied magnetic field allows the magnetic domains of a magnetocaloric material to become disoriented from the magnetic field by the agitating action of the thermal energy ( phonons ) present in the material. If the material is isolated so that no energy is allowed to (re)migrate into the material during this time, (i.e., an adiabatic process) the temperature drops as the domains absorb the thermal energy to perform their reorientation. The randomization of the domains occurs in a similar fashion to the randomization at the Curie temperature of a ferromagnetic material, except that magnetic dipoles overcome a decreasing external magnetic field while energy remains constant, instead of magnetic domains being disrupted from internal ferromagnetism as energy is added.
One of the most notable examples of the magnetocaloric effect is in the chemical element gadolinium and some of its alloys . Gadolinium's temperature increases when it enters certain magnetic fields. When it leaves the magnetic field, the temperature drops. The effect is considerably stronger for the gadolinium alloy Gd 5 (Si 2 Ge 2 ) . [ 10 ] Praseodymium alloyed with nickel ( PrNi 5 ) has such a strong magnetocaloric effect that it has allowed scientists to approach to within one millikelvin, one thousandth of a degree of absolute zero . [ 28 ]
The magnetocaloric effect can be quantified with the following equation:
Δ T a d = − ∫ H 0 H 1 ( T C ( T , H ) ) H ( ∂ M ( T , H ) ∂ T ) H d H {\displaystyle \Delta T_{ad}=-\int _{H_{0}}^{H_{1}}\left({\frac {T}{C(T,H)}}\right)_{H}{\left({\frac {\partial M(T,H)}{\partial T}}\right)}_{H}dH}
where Δ T a d {\displaystyle \Delta T_{ad}} is the adiabatic change in temperature of the magnetic system around temperature T, H is the applied external magnetic field, C is the heat capacity of the working magnet (refrigerant) and M is the magnetization of the refrigerant.
From the equation we can see that the magnetocaloric effect can be enhanced by:
The adiabatic change in temperature, Δ T a d {\displaystyle \Delta T_{ad}} , can be seen to be related to the magnet's change in magnetic entropy ( Δ S {\displaystyle \Delta S} ) since [ 29 ]
Δ S ( T ) = ∫ H 0 H 1 ( ∂ M ( T , H ′ ) ∂ T ) d H ′ {\displaystyle \Delta S(T)=\int _{H_{0}}^{H_{1}}\left({\frac {\partial M(T,H')}{\partial T}}\right)dH'}
This implies that the absolute change in the magnet's entropy determines the possible magnitude of the adiabatic temperature change under a thermodynamic cycle of magnetic field variation. T
The cycle is performed as a refrigeration cycle that is analogous to the Carnot refrigeration cycle , but with increases and decreases in magnetic field strength instead of increases and decreases in pressure. It can be described at a starting point whereby the chosen working substance is introduced into a magnetic field , i.e., the magnetic flux density is increased. The working material is the refrigerant, and starts in thermal equilibrium with the refrigerated environment.
Once the refrigerant and refrigerated environment are in thermal equilibrium, the cycle can restart.
The basic operating principle of an adiabatic demagnetization refrigerator (ADR) is the use of a strong magnetic field to control the entropy of a sample of material, often called the "refrigerant". Magnetic field constrains the orientation of magnetic dipoles in the refrigerant. The stronger the magnetic field, the more aligned the dipoles are, corresponding to lower entropy and heat capacity because the material has (effectively) lost some of its internal degrees of freedom . If the refrigerant is kept at a constant temperature through thermal contact with a heat sink (usually liquid helium ) while the magnetic field is switched on, the refrigerant must lose some energy because it is equilibrated with the heat sink. When the magnetic field is subsequently switched off, the heat capacity of the refrigerant rises again because the degrees of freedom associated with orientation of the dipoles are once again liberated, pulling their share of equipartitioned energy from the motion of the molecules , thereby lowering the overall temperature of a system with decreased energy. Since the system is now insulated when the magnetic field is switched off, the process is adiabatic, i.e., the system can no longer exchange energy with its surroundings (the heat sink), and its temperature decreases below its initial value, that of the heat sink.
The operation of a standard ADR proceeds roughly as follows. First, a strong magnetic field is applied to the refrigerant, forcing its various magnetic dipoles to align and putting these degrees of freedom of the refrigerant into a state of lowered entropy. The heat sink then absorbs the heat released by the refrigerant due to its loss of entropy. Thermal contact with the heat sink is then broken so that the system is insulated, and the magnetic field is switched off, increasing the heat capacity of the refrigerant, thus decreasing its temperature below the temperature of the heat sink. In practice, the magnetic field is decreased slowly in order to provide continuous cooling and keep the sample at an approximately constant low temperature. Once the field falls to zero or to some low limiting value determined by the properties of the refrigerant, the cooling power of the ADR vanishes, and heat leaks will cause the refrigerant to warm up.
The MCE is an intrinsic property of a magnetic solid. This thermal response of a solid to the application or removal of magnetic fields is maximized when the solid is near its magnetic ordering temperature. Thus, the materials considered for magnetic refrigeration devices should be magnetic materials with a magnetic phase transition temperature near the temperature region of interest. [ 31 ] For refrigerators that could be used in the home, this temperature is room temperature. The temperature change can be further increased when the order-parameter of the phase transition changes strongly within the temperature range of interest. [ 4 ]
The magnitudes of the magnetic entropy and the adiabatic temperature changes are strongly dependent upon the magnetic ordering process. The magnitude is generally small in antiferromagnets , ferrimagnets and spin glass systems but can be much larger for ferromagnets that undergo a magnetic phase transition. First order phase transitions are characterized by a discontinuity in the magnetization changes with temperature, resulting in a latent heat. [ 31 ] Second order phase transitions do not have this latent heat associated with the phase transition. [ 31 ]
In the late 1990s Pecharksy and Gschneidner reported a magnetic entropy change in Gd 5 (Si 2 Ge 2 ) that was about 50% larger than that reported for Gd metal, which had the largest known magnetic entropy change at the time. [ 27 ] This giant magnetocaloric effect (GMCE) occurred at 270 K, which is lower than that of Gd (294 K). [ 6 ] Since the MCE occurs below room temperature these materials would not be suitable for refrigerators operating at room temperature. [ 32 ] Since then other alloys have also demonstrated the giant magnetocaloric effect. These include Gd 5 (Si x Ge 1− x ) 4 , La(Fe x Si 1− x ) 13 H x and MnFeP 1− x As x alloys. [ 31 ] [ 32 ] Gadolinium and its alloys undergo second-order phase transitions that have no magnetic or thermal hysteresis . [ 33 ] However, the use of rare earth elements makes these materials very expensive.
Ni 2 Mn-X (X = Ga, Co, In, Al, Sb) Heusler alloys are also promising candidates for magnetic cooling applications because they have Curie temperatures near room temperature and, depending on composition, can have martensitic phase transformations near room temperature. [ 5 ] These materials exhibit the magnetic shape memory effect and can also be used as actuators, energy harvesting devices, and sensors. [ 34 ] When the martensitic transformation temperature and the Curie temperature are the same (based on composition) the magnitude of the magnetic entropy change is the largest. [ 4 ] In February 2014, GE announced the development of a functional Ni-Mn-based magnetic refrigerator. [ 35 ] [ 36 ]
The development of this technology is very material-dependent and will likely not replace vapor-compression refrigeration without significantly improved materials that are cheap, abundant, and exhibit much larger magnetocaloric effects over a larger range of temperatures. Such materials need to show significant temperature changes under a field of two tesla or less, so that permanent magnets can be used for the production of the magnetic field. [ 37 ] [ 38 ]
The original proposed refrigerant was a paramagnetic salt , such as cerium magnesium nitrate . The active magnetic dipoles in this case are those of the electron shells of the paramagnetic atoms.
In a paramagnetic salt ADR, the heat sink is usually provided by a pumped 4 He (about 1.2 K) or 3 He (about 0.3 K) cryostat . An easily attainable 1 T magnetic field is generally required for initial magnetization. The minimum temperature attainable is determined by the self-magnetization tendencies of the refrigerant salt, but temperatures from 1 to 100 mK are accessible. Dilution refrigerators had for many years supplanted paramagnetic salt ADRs, but interest in space-based and simple to use lab-ADRs has remained, due to the complexity and unreliability of the dilution refrigerator.
At a low enough temperature, paramagnetic salts become either diamagnetic or ferromagnetic, limiting the lowest temperature that can be reached using this method. [ citation needed ]
One variant of adiabatic demagnetization that continues to find substantial research application is nuclear demagnetization refrigeration (NDR). NDR follows the same principles, but in this case the cooling power arises from the magnetic dipoles of the nuclei of the refrigerant atoms, rather than their electron configurations. Since these dipoles are of much smaller magnitude, they are less prone to self-alignment and have lower intrinsic minimum fields. This allows NDR to cool the nuclear spin system to very low temperatures, often 1 μK or below. Unfortunately, the small magnitudes of nuclear magnetic dipoles also makes them less inclined to align to external fields. Magnetic fields of 3 teslas or greater are often needed for the initial magnetization step of NDR.
In NDR systems, the initial heat sink must sit at very low temperatures (10–100 mK). This precooling is often provided by the mixing chamber of a dilution refrigerator [ 39 ] or a paramagnetic salt.
Research and a demonstration proof of concept device in 2001 succeeded in applying commercial-grade materials and permanent magnets at room temperatures to construct a magnetocaloric refrigerator. [ 40 ]
On August 20, 2007, the Risø National Laboratory (Denmark) at the Technical University of Denmark , claimed to have reached a milestone in their magnetic cooling research when they reported a temperature span of 8.7 K. [ 41 ] They hoped to introduce the first commercial applications of the technology by 2010.
As of 2013 this technology had proven commercially viable only for ultra-low temperature cryogenic applications available for decades. Magnetocaloric refrigeration systems are composed of pumps, motors, secondary fluids, heat exchangers of different types, magnets and magnetic materials. These processes are greatly affected by irreversibilities and should be adequately considered.
At year-end, Cooltech Applications announced that its first commercial refrigeration equipment would enter the market in 2014. Cooltech Applications launched their first commercially available magnetic refrigeration system on 20 June 2016.
At the 2015 Consumer Electronics Show in Las Vegas, a consortium of Haier , Astronautics Corporation of America and BASF presented the first cooling appliance. [ 42 ] BASF claim of their technology a 35% improvement over using compressors. [ 43 ]
In November 2015, at the Medica 2015 fair, Cooltech Applications presented, in collaboration with Kirsch medical GmbH, the world's first magnetocaloric medical cabinet. [ 44 ] One year later, in September 2016, at the 7th International Conference on Magnetic Refrigeration at Room Temperature (Thermag VII)] held in Torino, Italy, Cooltech Applications presented the world's first magnetocaloric frozen heat exchanger. [ 45 ]
In 2017, Cooltech Applications presented a fully functional 500 liters' magnetocaloric cooled cabinet with a 30 kg (66 lb) load and an air temperature inside the cabinet of +2 °C. That proved that magnetic refrigeration is a mature technology, capable of replacing the classic refrigeration solutions.
One year later, in September 2018, at the 8th International Conference on Magnetic Refrigeration at Room Temperature (Thermag VIII]), Cooltech Applications presented a paper on a magnetocaloric prototype designed as a 15 kW proof-of-concept unit. [ 46 ] This has been considered by the community as the largest magnetocaloric prototype ever created. [ 47 ]
At the same conference, Dr. Sergiu Lionte announced that, due to financial issues, Cooltech Applications declared bankruptcy. [ 48 ] Later on, in 2019 Ubiblue company, today named Magnoric, is formed by some of the old Cooltech Application's team members. The entire patent portfolio form Cooltech Applications was taken over by Magnoric since then, while publishing additional patents at the same time.
In 2019, at the 5th Delft Days Conference on Magnetocalorics, Dr. Sergiu Lionte presented Ubiblue's (former Cooltech Application) last prototype. [ 49 ] Later, the magnetocaloric community acknowledged that Ubiblue had the most developed magnetocalorics prototypes. [ 50 ]
Thermal and magnetic hysteresis problems remain to be solved for first-order phase transition materials that exhibit the GMCE. [ 37 ]
Vapor-compression refrigeration units typically achieve performance coefficients of 60% of that of a theoretical ideal Carnot cycle , much higher than current MR technology. Small domestic refrigerators are however much less efficient. [ 51 ]
In 2014 giant anisotropic behavior of the magnetocaloric effect was found in HoMn 2 O 5 at 10 K. The anisotropy of the magnetic entropy change gives rise to a large rotating MCE offering the possibility to build simplified, compact, and efficient magnetic cooling systems by rotating it in a constant magnetic field. [ 52 ]
In 2015 Aprea et al. [ 53 ] presented a new refrigeration concept, GeoThermag, which is a combination of magnetic refrigeration technology with that of low-temperature geothermal energy. To demonstrate the applicability of the GeoThermag technology, they developed a pilot system that consists of a 100-m deep geothermal probe; inside the probe, water flows and is used directly as a regenerating fluid for a magnetic refrigerator operating with gadolinium. The GeoThermag system showed the ability to produce cold water even at 281.8 K in the presence of a heat load of 60 W. In addition, the system has shown the existence of an optimal frequency f AMR, 0.26 Hz, for which it was possible to produce cold water at 287.9 K with a thermal load equal to 190 W with a COP of 2.20. Observing the temperature of the cold water that was obtained in the tests, the GeoThermag system showed a good ability to feed the cooling radiant floors and a reduced capacity for feeding the fan coil systems. | https://en.wikipedia.org/wiki/Magnetocaloric_effect |
Magnetocapacitance is a property of some dielectric , insulating materials, and metal–insulator–metal heterostructures that exhibit a change in the value of their capacitance when an external magnetic field is applied to them. Magnetocapacitance can be an intrinsic property of some dielectric materials, such as multiferroic compounds like BiMnO 3 , [ 1 ] or can be a manifest of properties extrinsic to the dielectric but present in capacitance structures like Pd, Al 2 O 3 , and Al. [ 2 ] | https://en.wikipedia.org/wiki/Magnetocapacitance |
Magnetochromism is the term applied when a chemical compound changes colour under the influence of a magnetic field . In particular the magneto-optical effects exhibited by complex mixed metal compounds are called magnetochromic when they occur in the visible region of the spectrum . Examples include K2V3O8, lithium molybdenum purple bronze Li0.9Mo6O17, and related mixed oxides. Reported magnetochromic compounds are multiferroic manganese tungsten oxide [ 1 ] and multiferroic bismuth ferrite . [ 2 ]
Magnetically–induced color change can also occur in aqueous solutions of colloidal Fe3O4 nanoparticles that are ~10 nm in diameter. Paramagnetic Fe3O4 particles are extracted from a petroleum–based ferrofluid or synthesized in a laboratory and then suspended in water. When exposed to a strengthening magnetic field these particles organize into chains that diffract light and cause the solution to change color from a brown to red, yellow, green and then blue. Manufacturers encapsulate microscopic droplets of this solution in a thin plastic film to create a magnetochromic magnetic field viewing screen. [ 3 ] | https://en.wikipedia.org/wiki/Magnetochromism |
In physics , a ferromagnetic material is said to have magnetocrystalline anisotropy if it takes more energy to magnetize it in certain directions than in others. These directions are usually related to the principal axes of its crystal lattice . It is a special case of magnetic anisotropy . In other words, the excess energy required to magnetize a specimen in a particular direction over that required to magnetize it along the easy direction is called crystalline anisotropy energy.
The spin-orbit interaction is the primary source of magnetocrystalline anisotropy . It is basically the orbital motion of the electrons which couples with crystal electric field giving rise to the first order contribution to magnetocrystalline anisotropy. The second order arises due to the mutual interaction of the magnetic dipoles. This effect is weak compared to the exchange interaction and is difficult to compute from first principles, although some successful computations have been made. [ 1 ]
Magnetocrystalline anisotropy has a great influence on industrial uses of ferromagnetic materials. Materials with high magnetic anisotropy usually have high coercivity , that is, they are hard to demagnetize. These are called "hard" ferromagnetic materials and are used to make permanent magnets . For example, the high anisotropy of rare-earth metals is mainly responsible for the strength of rare-earth magnets . During manufacture of magnets, a powerful magnetic field aligns the microcrystalline grains of the metal such that their "easy" axes of magnetization all point in the same direction, freezing a strong magnetic field into the material.
On the other hand, materials with low magnetic anisotropy usually have low coercivity, their magnetization is easy to change. These are called "soft" ferromagnets and are used to make magnetic cores for transformers and inductors . The small energy required to turn the direction of magnetization minimizes core losses , energy dissipated in the transformer core when the alternating current changes direction.
The magnetocrystalline anisotropy energy is generally represented as an expansion in powers of the direction cosines of the magnetization. The magnetization vector can be written M = M s ( α,β,γ ) , where M s is the saturation magnetization . Because of time reversal symmetry , only even powers of the cosines are allowed. [ 2 ] The nonzero terms in the expansion depend on the crystal system ( e.g. , cubic or hexagonal ). [ 2 ] The order of a term in the expansion is the sum of all the exponents of magnetization components, e.g. , α β is second order.
More than one kind of crystal system has a single axis of high symmetry (threefold, fourfold or sixfold). The anisotropy of such crystals is called uniaxial anisotropy . If the z axis is taken to be the main symmetry axis of the crystal, the lowest order term in the energy is [ 5 ]
The ratio E/V is an energy density (energy per unit volume). This can also be represented in spherical polar coordinates with α = cos ϕ {\displaystyle \phi } sin θ , β = sin ϕ {\displaystyle \phi } sin θ , and γ = cos θ :
The parameter K 1 , often represented as K u , has units of energy density and depends on composition and temperature.
The minima in this energy with respect to θ satisfy
If K 1 > 0 ,
the directions of lowest energy are the ± z directions. The z axis is called the easy axis . If K 1 < 0 , there is an easy plane perpendicular to the symmetry axis (the basal plane of the crystal).
Many models of magnetization represent the anisotropy as uniaxial and ignore higher order terms. However, if K 1 < 0 , the lowest energy term does not determine the direction of the easy axes within the basal plane. For this, higher-order terms are needed, and these depend on the crystal system ( hexagonal , tetragonal or rhombohedral ). [ 2 ]
In a hexagonal system the c axis is an axis of sixfold rotation symmetry. The energy density is, to fourth
order, [ 7 ]
The uniaxial anisotropy is mainly determined by these first two terms. Depending on the values K 1 and K 2 , there are four different kinds of anisotropy (isotropic, easy axis, easy plane and easy cone): [ 7 ]
The basal plane anisotropy is determined by the third term, which is sixth-order. The easy directions are projected onto three axes in the basal plane.
Below are some room-temperature anisotropy constants for hexagonal ferromagnets. Since all the values of K 1 and K 2 are positive, these materials have an easy axis.
Higher order constants, in particular conditions, may lead to first order magnetization processes FOMP .
The energy density for a tetragonal crystal is [ 2 ]
Note that the K 3 term, the one that determines the basal plane anisotropy, is fourth order (same as the K 2 term). The definition of K 3 may vary by a constant multiple between publications.
The energy density for a rhombohedral crystal is [ 2 ]
In a cubic crystal the lowest order terms in the energy are [ 10 ] [ 2 ]
If the second term can be neglected, the easy axes are the ⟨100⟩ axes ( i.e. , the ± x , ± y , and ± z , directions) for K 1 > 0 and the ⟨111⟩ directions for K 1 < 0 (see images on right).
If K 2 is not assumed to be zero, the easy axes depend on both K 1 and K 2 . These are given in the table below, along with hard axes (directions of greatest energy) and intermediate axes ( saddle points ) in the energy). In energy surfaces like those on the right, the easy axes are analogous to valleys, the hard axes to peaks and the intermediate axes to mountain passes.
Below are some room-temperature anisotropy constants for cubic ferromagnets. The compounds involving Fe 2 O 3 are ferrites , an important class of ferromagnets. In general the anisotropy parameters for cubic ferromagnets are higher than those for uniaxial ferromagnets. This is consistent with the fact that the lowest order term in the expression for cubic anisotropy is fourth order, while that for uniaxial anisotropy is second order.
The magnetocrystalline anisotropy parameters have a strong dependence on temperature. They generally decrease rapidly as the temperature approaches the Curie temperature , so the crystal becomes effectively isotropic. [ 11 ] Some materials also have an isotropic point at which K 1 = 0 . Magnetite ( Fe 3 O 4 ), a mineral of great importance to rock magnetism and paleomagnetism , has an isotropic point at 130 kelvin . [ 9 ]
Magnetite also has a phase transition at which the crystal symmetry changes from cubic (above) to monoclinic or possibly triclinic below. The temperature at which this occurs, called the Verwey temperature, is 120 Kelvin. [ 9 ]
The magnetocrystalline anisotropy parameters are generally defined for ferromagnets that are constrained to remain undeformed as the direction of magnetization changes. However, coupling between the magnetization and the lattice does result in deformation, an effect called magnetostriction . To keep the lattice from deforming, a stress must be applied. If the crystal is not under stress, magnetostriction alters the effective magnetocrystalline anisotropy. If a ferromagnet is single domain (uniformly magnetized), the effect is to change the magnetocrystalline anisotropy parameters. [ 16 ]
In practice, the correction is generally not large. In hexagonal crystals, there is no change in K 1 . [ 17 ] In cubic crystals, there is a small change, as in the table below.
[ 1 ]
[ 2 ] | https://en.wikipedia.org/wiki/Magnetocrystalline_anisotropy |
In its most general form, the magnetoelectric effect (ME) denotes any coupling between the magnetic and the electric properties of a material. [ 1 ] [ 2 ] The first example of such an effect was described by Wilhelm Röntgen in 1888, who found that a dielectric material moving through an electric field would become magnetized. [ 3 ] A material where such a coupling is intrinsically present is called a magnetoelectric .
Some promising applications of the ME effect are sensitive detection of magnetic fields, advanced logic devices and tunable microwave filters. [ 4 ]
The first example of a magnetoelectric effect was discussed in 1888 by Wilhelm Röntgen , who showed that a dielectric material moving through an electric field would become magnetized. [ 3 ] The possibility of an intrinsic magnetoelectric effect in a (non-moving) material was conjectured by Pierre Curie [ 5 ] in 1894, while the term "magnetoelectric" was coined by Peter Debye [ 6 ] in 1926.
A mathematical formulation of the linear magnetoelectric effect was included in Lev Landau and Evgeny Lifshitz 's Course of Theoretical Physics . [ 7 ] Only in 1959 did Igor Dzyaloshinskii , [ 8 ] using an elegant symmetry argument, derive the form of a linear magnetoelectric coupling in chromium(III) oxide (Cr 2 O 3 ). The experimental confirmation came just a few months later when the effect was observed for the first time by D. Astrov. [ 9 ] The general excitement which followed the measurement of the linear magnetoelectric effect lead to the organization of the series of Magnetoelectric Interaction Phenomena in Crystals (MEIPIC) conferences. Between the prediction of Dzyaloshinskii and the MEIPIC first edition (1973), more than 80 linear magnetoelectric compounds were found. Recently, technological and theoretical progress, driven in large part by the advent of multiferroic materials, [ 10 ] triggered a renaissance of these studies [ 11 ] and magnetoelectric effect is still heavily investigated. [ 1 ]
Historically, the first and most studied example of this effect is the linear magnetoelectric effect . Mathematically, while the electric susceptibility χ e {\displaystyle \chi ^{e}} and magnetic susceptibility χ v {\displaystyle \chi ^{v}} describe the electric and magnetic polarization responses to an electric, resp. a magnetic field, there is also the possibility of a magnetoelectric susceptibility α i j {\displaystyle \alpha _{ij}} which describes a linear response of the electric polarization to a magnetic field, and vice versa: [ 7 ]
The tensor α {\displaystyle \alpha } must be the same in both equations. Here, P is the electric polarization , M the magnetization , E and H the electric and magnetic fields . In SI units , α {\displaystyle \alpha } has units of second per meter.
The first material where an intrinsic linear magnetoelectric effect was predicted theoretically and confirmed experimentally was Cr 2 O 3 . [ 8 ] [ 9 ] This is a single-phase material. Multiferroics are another example of single-phase materials that can exhibit a general magnetoelectric effect [ 11 ] if their magnetic and electric orders are coupled. Composite materials are another way to realize magnetoelectrics. There, the idea is to combine, say a magnetostrictive and a piezoelectric material. These two materials interact by strain, leading to a coupling between magnetic and electric properties of the compound material.
If the coupling between magnetic and electric properties is analytic, then the magnetoelectric effect can be described by an expansion of the free energy as a power series in the electric and magnetic fields E {\displaystyle E} and H {\displaystyle H} : [ 1 ]
Differentiating the free energy will then give the electric polarization P i = − ∂ F ∂ E i {\displaystyle P_{i}=-{\frac {\partial F}{\partial E_{i}}}} and the magnetization M i = − 1 μ 0 ∂ F ∂ H i {\displaystyle M_{i}=-{\frac {1}{\mu _{0}}}{\frac {\partial F}{\partial H_{i}}}} .
Here, P s {\displaystyle P^{s}} and M s {\displaystyle M^{s}} are the static polarization, resp. magnetization of the material, whereas χ e {\displaystyle \chi ^{e}} and χ v {\displaystyle \chi ^{v}} are the electric, resp. magnetic susceptibilities. The tensor α {\displaystyle \alpha } describes the linear magnetoelectric effect, which corresponds to an electric polarization induced linearly by a magnetic field, and vice versa. The higher terms with coefficients β {\displaystyle \beta } and γ {\displaystyle \gamma } describe quadratic effects. For instance, the tensor γ {\displaystyle \gamma } describes a linear magnetoelectric effect which is, in turn, induced by an electric field. [ 12 ]
The possible terms appearing in the expansion above are constrained by symmetries of the material. Most notably, the tensor α {\displaystyle \alpha } must be antisymmetric under time-reversal symmetry . [ 7 ] Therefore, the linear magnetoelectric effect may only occur if time-reversal symmetry is explicitly broken, for instance by the explicit motion in Röntgens' example, or by an intrinsic magnetic ordering in the material. In contrast, the tensor β {\displaystyle \beta } may be non-vanishing in time-reversal symmetric materials.
There are several ways in which a magnetoelectric effect can arise microscopically in a material.
In crystals, spin–orbit coupling is responsible for single-ion magnetocrystalline anisotropy which determines preferential axes for the orientation of the spins (such as easy axes). An external electric field may change the local symmetry seen by magnetic ions and affect both the strength of the anisotropy and the direction of the easy axes. Thus, single-ion anisotropy can couple an external electric field to spins of magnetically ordered compounds.
The main interaction between spins of transition metal ions in solids is usually provided by superexchange , also called symmetric exchange . This interaction depends on details of the crystal structure such as the bond length between magnetic ions and the angle formed by the bonds between magnetic and ligand ions. In magnetic insulators it usually is the main mechanism for magnetic ordering, and, depending on the orbital occupancies and bond angles, can lead to ferro- or antiferromagnetic interactions. As the strength of symmetric exchange depends on the relative position of the ions, it couples the spin orientations to the lattice structure. Coupling of spins to a collective distortion with a net electric dipole can occur if the magnetic order breaks inversion symmetry. Thus, symmetric exchange can provide a handle to control magnetic properties through an external electric field. [ 13 ]
Because materials exist that couple strain to electrical polarization (piezoelectrics, electrostrictives, and ferroelectrics) and that couple strain to magnetization (magnetostrictive/ magnetoelastic /ferromagnetic materials), it is possible to couple magnetic and electric properties indirectly by creating composites of these materials that are tightly bonded so that strains transfer from one to the other. [ 14 ]
Thin film strategy enables achievement of interfacial multiferroic coupling through a mechanical channel in heterostructures consisting of a magnetoelastic and a piezoelectric component. [ 15 ] This type of heterostructure is composed of an epitaxial magnetoelastic thin film grown on a piezoelectric substrate. For this system, application of a magnetic field will induce a change in the dimension of the magnetoelastic film. This process, called magnetostriction, will alter residual strain conditions in the magnetoelastic film, which can be transferred through the interface to the piezoelectric substrate. Consequently, a polarization is introduced in the substrate through the piezoelectric process.
The overall effect is that the polarization of the ferroelectric substrate is manipulated by an application of a magnetic field, which is the desired magnetoelectric effect (the reverse is also possible). In this case, the interface plays an important role in mediating the responses from one component to another, realizing the magnetoelectric coupling. [ 16 ] For an efficient coupling, a high-quality interface with optimal strain state is desired. In light of this interest, advanced deposition techniques have been applied to synthesize these types of thin film heterostructures. Molecular beam epitaxy has been demonstrated to be capable of depositing structures consisting of piezoelectric and magnetostrictive components. Materials systems studied included cobalt ferrite, magnetite , SrTiO3, BaTiO3, PMNT. [ 17 ] [ 18 ] [ 19 ]
Magnetically driven ferroelectricity is also caused by inhomogeneous [ 20 ] magnetoelectric interaction. This effect appears due to the coupling between inhomogeneous order parameters. It was also called as flexomagnetoelectric effect. [ 21 ] Usually it is describing using the Lifshitz invariant (i.e. single-constant coupling term): [ 22 ]
F F M E = γ 0 P ( M ( ∇ M ) − ( M ∇ ) M ) {\displaystyle F_{FME}=\gamma _{0}{\mathbf {P}}{\biggl (}{\mathbf {M}}(\nabla {\mathbf {M}})-({\mathbf {M}}\nabla ){\mathbf {M}}{\biggr )}} ,
where γ 0 {\displaystyle \gamma _{0}} is a constant of flexomagnetoelectric interaction in a cubic hexoctahedral crystal. This free energy term is valid in the case of variational problem with the unknown M ( r ) {\displaystyle {\mathbf {M}}({\mathbf {r}})} . It was shown that in general case of cubic m 3 ¯ m {\displaystyle m{\bar {3}}m} crystal the four-phenomenological constants approach is correct: [ 23 ]
F F M E = γ 1 P i ∇ i M i 2 + γ 2 ( P ∇ ) M 2 + γ 3 P ( M ∇ ) M + γ 4 ( P M ) ∇ M {\displaystyle F_{FME}=\gamma _{1}P_{i}\nabla _{i}M_{i}^{2}+\gamma _{2}{\Bigl (}{\mathbf {P}}\nabla {\Bigr )}{\mathbf {M}}^{2}+\gamma _{3}{\mathbf {P}}{\Bigl (}{\mathbf {M}}\nabla {\Bigr )}{\mathbf {M}}+\gamma _{4}{\Bigl (}{\mathbf {P}}{\mathbf {M}}{\Bigr )}\nabla {\mathbf {M}}}
The flexomagnetoelectric effect appears in spiral multiferroics [ 24 ] or micromagnetic structures like domain walls [ 25 ] and magnetic vortexes. [ 26 ] [ 27 ] Ferroelectricity developed from micromagnetic structure can appear in any magnetic material even in centrosymmetric one. [ 28 ] Building of symmetry classification of domain walls leads to determination of the type of electric polarization rotation in volume of any magnetic domain wall. Existing symmetry classification [ 29 ] of magnetic domain walls was applied for predictions of electric polarization spatial distribution in their volumes. [ 30 ] [ 31 ] The predictions for almost all symmetry groups conform with phenomenology in which inhomogeneous magnetization couples with homogeneous polarization . The total synergy between symmetry and phenomenology theory appears if energy terms with electrical polarization spatial derivatives are taken into account. [ 32 ] | https://en.wikipedia.org/wiki/Magnetoelectric_effect |
Magnetoelectrochemistry is a branch of electrochemistry dealing with magnetic effects in electrochemistry.
These effects have been supposed to exist since the time of Michael Faraday.
There have also been observations on the existence of Hall effect in electrolytes. Until these observations, magnetoelectrochemistry was an esoteric curiosity, though
this field has had a rapid development in the past years and is now an active area of research. Other scientific fields which contributed to the development of magnetoelectrochemistry are magnetohydrodynamics and convective diffusion theory. [ citation needed ]
There are three types of magnetic effects in electrochemistry:
This electrochemistry -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Magnetoelectrochemistry |
Magnetofection is a transfection method that uses magnetic fields to concentrate particles containing vectors to target cells in the body. [ 1 ] Magnetofection has been adapted to a variety of vectors, including nucleic acids , non-viral transfection systems, and viruses . This method offers advantages such as high transfection efficiency and biocompatibility which are balanced with limitations.
The term magnetofection, currently trademarked by the company OZ Biosciences, combines the words magnetic and transfection. [ 2 ] Magnetofection uses nucleic acids associated with magnetic nanoparticles . These molecular complexes are then concentrated and transported into cells using an applied magnetic field .
The magnetic nanoparticles are typically made from iron oxide , which is fully biodegradable, using methods such as coprecipitation or microemulsion . [ 3 ] [ 4 ]
The nanoparticles are then combined with gene vectors ( DNA , siRNA , ODN , virus , etc.). One method involves linking viral particles to magnetic particles using an avidin - biotin interaction. [ 5 ] Viruses can also bind to the nanoparticles via hydrophobic interaction . [ 6 ]
Another synthesis method involves coating magnetic nanoparticles with cationic lipids or polymers via salt-induced aggregation. For example, nanoparticles may be conjugated with the polyethylenimine (PEI) , a positively charged polymer used commonly as a transfection agent. [ 7 ] The PEI solution must have a high pH during synthesis to encourage high gene expression. [ 8 ] The positively charged nanoparticles can then associate with negatively charged nucleic acids via electrostatic interaction. [ 9 ]
Magnetic particles loaded with vectors are concentrated on the target cells by the influence of an external magnetic field. The cells then take up genetic material naturally via endocytosis and pinocytosis . Consequently, membrane architecture and structure stays intact, in contrast to other physical transfection methods such as electroporation or gene guns that damage the cell membrane. [ 10 ]
The nucleic acids are then released into the cytoplasm by different mechanisms depending upon the formulation used:
Magnetofection works with cells that are not dividing or slowly dividing, meaning that the genetic materials can go to the cell nucleus without cell division . [ 11 ]
Magnetofection has been tested on a broad range of cell lines , hard-to-transfect and primary cells. [ 12 ] Several optimized and efficient magnetic nanoparticle formulations have been specifically developed for several types of applications such as DNA, siRNA, and primary neuron transfection as well as viral applications. [ 13 ]
Magnetofection research is currently in the preclinical stage. This technique has primarily been tested in vivo using plasmid DNA in mouse, rat, and rabbit models for applications in the hippocampus, subcutaneous tumors, lungs, spinal cord, and muscle. [ 14 ]
Some applications include:
Magnetofection attempts to unite the advantages of biochemical (cationic lipids or polymers) and physical ( electroporation , gene gun ) transfection methods. It allows for local delivery with high transfection efficiency, faster incubation time, and biocompatibility. [ 19 ]
Coupling magnetic nanoparticles to gene vectors results in hundreds-fold increase of the uptake of these vectors on a time scale of minutes, thus leading to high transfection efficiency. [ 20 ] Gene vector and magnetic nanoparticle complexes are transfected into cells after 10–15 minutes, which is faster than the 2–4 hours that other transfection methods require. [ 21 ] After 24, 48 or 72 hours, most of the particles are localized in the cytoplasm , in vacuoles (membranes surrounded structure into cells) and occasionally in the cell nucleus . [ 22 ]
Magnetic nanoparticles do not aggregate easily once the magnet is removed, and therefore are unlikely to block capillaries or cause thrombosis . [ 23 ] In addition, iron oxide is biodegradable, and the iron can be reused in hemoglobin or iron metabolism pathways. [ 24 ] [ 25 ]
Magnetic nanoparticle synthesis can sometimes lead to a wide range of differently sized particles. [ 26 ] The size of particles can influence their usefulness. Specifically, nanoparticles that are less than 10 nm or greater than 200 nm in size tend to be cleared from the body more quickly. [ 27 ]
While magnets can be used to localize magnetic nanoparticles to desired cells, this mechanism may be difficult to maintain in practice. The nanoparticles can be concentrated in 2D space such as on a culture plate or at the surface of the body, but it can be more difficult to localize them in the 3D space of the body. Magnetofection does not work well for organs or blood vessels far from the surface of the body, since the magnetic field weakens as distance increases. [ 28 ] [ 29 ] In addition, the user must consider the frequency and timing of applying the magnetic field, as the particles will not necessarily stay in the desired location once the magnet is removed. [ 30 ]
While iron oxide used to make nanoparticles is biodegradable, the toxicity of magnetic nanoparticles is still under investigation. Some research has found no signs of damage to cells, while others claim that small (< 2 nm) nanoparticles can diffuse across cell membranes and disrupt organelles. [ 31 ] [ 32 ]
In addition, very high concentrations of iron oxide can disrupt homeostasis and lead to iron overload , which can damage or alter DNA, affect cellular responses, and kill cells. [ 33 ] Lysosymes can also digest the nanoparticles and release free iron which can react with hydrogen peroxide to form free radicals, leading to cytotoxic, mutagenic, and carcinogenic effects. [ 34 ] | https://en.wikipedia.org/wiki/Magnetofection |
Magnetofossils are the fossil remains of magnetic particles produced by magnetotactic bacteria (magnetobacteria) and preserved in the geologic record. The oldest definitive magnetofossils formed of the mineral magnetite come from the Cretaceous chalk beds of southern England, while magnetofossil reports, not considered to be robust, extend on Earth to the 1.9-billion-year-old Gunflint Chert ; they may include the four-billion-year-old Martian meteorite ALH84001 .
Magnetotactic organisms are prokaryotic , with only one example of giant magnetofossils , likely produced by eukaryotic organisms, having been reported. [ 1 ] Magnetotactic bacteria, the source of the magnetofossils, are magnetite (Fe 3 O 4 ) or greigite (Fe 3 S 4 ) producing bacteria found in both freshwater and marine environments. These magnetite bearing magnetotatic bacteria are found in the oxic -anoxic transition zone where conditions are such that oxygen levels are less than those found in the atmosphere ( microaerophilic ). [ 2 ] Compared to the magnetite producing magnetotactic bacteria and subsequent magnetofossils, little is known about the environments in which greigite magnetofossils are created and the magnetic properties of the preserved greigite particles.
Existence of magnetotactic bacteria was first suggested in the 1960s, when Salvatore Bellini of the University of Pavia discovered bacteria in a bog that appeared to align themselves with the magnetic field lines of the Earth . [ 3 ] Following this discovery researchers began to think of the effect of magnetotactic bacteria on the fossil record and magnetization of sedimentary layers .
Most of the research concentrated on marine environments, [ 4 ] although it has been suggested that these magnetofossils can be found in terrestrial sediments (derived from terrestrial sources). [ 5 ] These magnetofossils can be found throughout the sedimentary record, and therefore are influenced by deposition rate. Episodes of high sedimentation, not correlating with an increase in magnetobacterial and thus magnetofossil production, can decrease magnetofossil concentrations vastly, although this is not always the case. An increase in sedimentation normally coincides with an increase of land erosion, and therefore an increase in iron abundance and nutrient supply.
Within the magnetotactic bacteria, magnetite and greigite crystals are biosynthesized ( biomineralized ) within organelles called magnetosomes . These magnetosomes form chains within the bacterial cell and in doing so, provide the organism with a permanent magnetic dipole. The organism uses it for geomagnetic navigation, to align itself with the Earth's geomagnetic field ( magnetotaxis ) and to reach the optimal position along vertical chemical gradients.
When an organism dies the magnetosomes become trapped in sediments. Under the right conditions, primarily if the redox conditions are correct, the magnetite can then be fossilized and therefore stored in the sedimentary record. [ 5 ] The fossilization of the magnetite (magnetofossils) within sediments contributes largely to the natural remanent magnetization of the sediment layers. The natural remanent magnetization is the permanent magnetism remaining in a rock or sediment after it has formed.
Magnetotactic bacteria use iron to create magnetite in magnetosomes. As a result of this process, increased iron levels correlate with increased production of magnetotactic bacteria. Increases in iron levels have been long associated with hyperthermal [ 6 ] (period of warming, usually between 4-8 degrees Celsius) periods in the Earth's history. These hyperthermal events, such as the Palaeocene-Eocene Thermal Maximum or the Holocene Warm Period (HWP), stimulated increased productivity in planktonic and benthic foraminifera, [ 6 ] which in turn, resulted in higher levels of sedimentation. Furthermore, an increase in temperature (like the one in the HWP) may also be associated with a wet period. These warm and wet conditions were favourable for magnetofossil production due to an increased nutrient supply in a period of post-glacial warming during the HWP. As a result, this period shows an increase in magnetofossil concentration. Using this increase in concentration, researchers can use magnetofossils as an indicator of a period of relatively high (or low) temperatures in Earth's history. Dating of these rocks can provide information about the time period of this climate change and can be correlated to other rock formations or depositional environments in which the Earth's climate at that time may not have been as clear. Sediment aging and dissolution or alteration of magnetite present problems with providing useful measurements as the crystals structural integrity may not be preserved. [ 2 ]
Magnetofossils are not only being studied for their paleoenvironmental or paleoclimatic indicators. As mentioned above, magnetofossils hold a remanent magnetization when they are formed. That is, the magnetite (or greigite) aligns in the direction of the geomagnetic field. The magnetite crystals can be thought of as being a simple magnet with a north and south pole, this north–south orientation aligns with the north–south magnetic poles of the Earth. These fossils are then buried within the rock record. Researchers can examine these rock samples in a remanent magnetometer where the effects of Earth's current magnetic field is removed, to determine the remanent, or initial, magnetization of the rock sample when it was formed. In knowing the orientation of the rock in-situ and the remanent magnetization, researchers can determine the Earth's geomagnetic field at the time the rock was formed. This can be used as an indicator of magnetic field direction, or reversals in the Earth's magnetic field , where the Earth's north and south magnetic poles switch (which happen on average every 450,000 years).
There are many methods for detecting and measuring magnetofossils, although there are some issues with the identification. Current research is suggesting that the trace elements found in the magnetite crystals [ 2 ] formed in magnetotactic bacteria differ from crystals formed by other methods. It has also been suggested that calcium and strontium incorporation can be used to identify magnetite inferred from magnetotactic bacteria. Other methods such as transmission electron microscopy (TEM) [ 7 ] of samples from deep boreholes and ferromagnetic resonance (FMR) [ 8 ] spectroscopy are being used. FMR spectroscopy of chains of cultured magnetotactic bacteria compared to sediment samples are being used to infer magnetofossil preservation over geological time frames. Research suggests that magnetofossils retain their remanent magnetization at deeper burial depths, although this is not entirely confirmed. FMR measurements of saturation isothermal remanent magnetization (SIRM) in some samples, compared with FMR and rainfall measurements taken over the past 70 years, have shown that magnetofossils can retain a record of paleorainfall variations [ 9 ] on a shorter time-scale (hundreds of years), making a very useful recent history paleoclimate indicator. [ 5 ]
The process of magnetite and greigite formation from magnetotactic bacteria and the formation of magnetofossils are well understood, although the more specific relationships, like those between the morphology of these fossils and the effect on the climate, nutrient availability and environmental availability would require more research. This however, does not alter the promise of better insight into the Earth's microbial ecology [ 9 ] and geomagnetic variations over a large time scale presented by magnetofossils. Unlike some other methods used to provide information of the Earth's history, magnetofossils normally have to be seen in large abundances to provide useful information of Earth's ancient history. Although lower concentrations can tell their own story of the more recent paleoclimate, paleoenvironmental and paleoecological history of the Earth. | https://en.wikipedia.org/wiki/Magnetofossil |
Magnetogenetics is a medical research technique whereby magnetic fields are used to affect cell function. [ 1 ]
The development of genetic technologies that can modulate cellular processes has greatly contributed to biological research. A representative example is the development of optogenetics , which is a neuromodulation tool kit that involves light-sensitive proteins such as opsins. This progress provided the grounds for a breakthrough in linking the causal relationship between neuronal activity and behavioral outcome.
The foremost strength of the genetic toolkits used in neuromodulation is that it can provide either spatially or temporally, or both, precise modulation of the brain nervous system. To date, several technologies are adapted with genetics (e.g. optogenetics , chemogenetics , etc.), and each technology has strengths and limits. For example, optogenetics has advantages in that it can provide temporally and spatially precise manipulation of neurons. On the other hand, it involves light stimulation, which cannot penetrate tissues effectively and requires implanted optical devices, limiting its applications for in vivo live animal studies
Techniques that rely on the magnetic control of cellular process are relatively new. This technique may provide an approach that does not require implantation of invasive electrodes or optical devices. This method will allow penetration in to the deeper region of the brain, and may have lower response latency. [ 2 ] In 1980, Young and colleagues have shown that magnetic fields with magnitudes in millitesla range are able to penetrate into the brain without attenuation of the signal or side effects because of the negligible magnetic susceptibility and low conductivity of biological tissue. [ 3 ] Early attempts to manipulate electrical signaling within brain using magnetic fields was performed by Baker et al., who later developed devices for transcranial magnetic stimulation (TMS) in 1985.
To apply magnetogenetics in biological and neuroscientific research, fusing TRPV class receptors with a paramagnetic protein (typically ferritin ) was suggested. These paramagnetic proteins, which typically contain iron or have iron-containing cofactors, are then magnetically stimulated. How this technique can modulate neuronal activity remains unclear but it is thought that the ion channels are activated and opened either by mechanical force exerted by the paramagnetic proteins, or by heating of these via magnetic stimulation. However, availability of such paramagnetic proteins as a transducer for magnetic field to mechanical or temperature stimuli is controversial.
On the other hand, nanoparticles have been suggested as possible candidates that can function as the transducer of magnetic field to the stimulus cue. Based on this concept, next generation of magnetogenetics technique is being developed. In 2010, Arnd Pralle and colleges showed that the first in vivo magneto-thermal stimulation of heat sensitive ion channel TRPV1 that employs magnetic nanoparticles as a transducer in C. elegans . [ 4 ] In 2012, Seung Chan Kim showed gene expression profile change of total human genome approximately 30,000 genes using 0.2T static magnetic fields. [ 5 ] In 2015, Polina Anikeeva 's research group demonstrated that similar concept can enhance the neuronal signals in mammalian brain. [ 6 ] In 2021, Jinwoo Cheon 's research group has successfully developed the magneto-mechanical genetics which uses magnetic stimulation derived mechanical force in mammalian. [ 7 ] In this study, magnetic torque by rotating magnetic field was employed to activate the mechanosensitive cation channel Piezo1 . Results of this study show that remote, in vivo manipulation of behavior of mice can be done using magnetogenetics. Cheon's group further developed a magnetogenetic system enables cell-type-specific modulation of deep brain neural circuits. [ 8 ] This was achieved by combining Piezo1 ion channels and Cre-loxP technology, allowing precise, reversible, and wireless control of neuronal activity in freely moving animals. The study demonstrated significant potential for neuroscience research by demonstrating several applications such as feeding behavior modulation, long-term obesity control, and social interaction studies. This torque-based system developed by Cheon is anticipated to be valuable not only for neuroscience research but also for various deep tissue in vivo applications and therapeutics.
One of the main issues in magnetogenetics is related the physical properties of the ferritin . [ 9 ] The ferritin is composed of 24 subunits of protein complex and a small iron oxide core. The core of the ferritin is in the form of ferric hydroxide which has antiferromagnetic properties. Some researchers have reported that ferritin has remnant magnetization due to their intrinsic defect and impurities. [ 10 ] However, even with optimistic calculations, the magnetic interaction energy for heat or force generation is several orders below than thermal fluctuation energy . Recently, other researchers hypothesized that there are other possible mechanisms for activating the ion channels, but these studies remain inconclusive. | https://en.wikipedia.org/wiki/Magnetogenetics |
A magnetogravity wave is a type of plasma wave . A magnetogravity wave is an acoustic gravity wave which is associated with fluctuations in the background magnetic field . [ 1 ] In this context, gravity wave refers to a classical fluid wave, and is completely unrelated to the relativistic gravitational wave .
Magnetogravity waves are found in the corona of the Sun.
This plasma physics –related article is a stub . You can help Wikipedia by expanding it .
This astrophysics -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Magnetogravity_wave |
A magnetohydrodynamic converter ( MHD converter ) is an electromagnetic machine with no moving parts involving magnetohydrodynamics , the study of the kinetics of electrically conductive fluids ( liquid or ionized gas) in the presence of electromagnetic fields . Such converters act on the fluid using the Lorentz force to operate in two possible ways: either as an electric generator called an MHD generator , extracting energy from a fluid in motion; or as an electric motor called an MHD accelerator or magnetohydrodynamic drive , putting a fluid in motion by injecting energy. MHD converters are indeed reversible, like many electromagnetic devices. [ 1 ]
Michael Faraday first attempted to test a MHD converter in 1832. MHD converters involving plasmas were highly studied in the 1960s and 1970s, with many government funding and dedicated international conferences . One major conceptual application was the use of MHD converters on the hot exhaust gas in a coal fired power plant , where it could extract some of the energy with very high efficiency, and then pass it into a conventional steam turbine . The research almost stopped after it was considered the electrothermal instability would severely limit the efficiency of such converters when intense magnetic fields are used, [ 2 ] although solutions may exist. [ 3 ] [ 4 ] [ 5 ] [ 6 ]
(linear Faraday type with segmented electrodes)
A magnetohydrodynamic generator is an MHD converter that transforms the kinetic energy of an electrically conductive fluid, in motion with respect to a steady magnetic field, into electricity . MHD power generation has been tested extensively in the 1960s with liquid metals and plasmas as working fluids. [ 7 ]
Basically, a plasma is hurtling down within a channel whose walls are fitted with electrodes. Electromagnets create a uniform transverse magnetic field within the cavity of the channel. The Lorentz force then acts upon the trajectory of the incoming electrons and positive ions, separating the opposite charge carriers according to their sign. As negative and positive charges are spatially separated within the chamber, an electric potential difference can be retrieved across the electrodes. While work is extracted from the kinetic energy of the incoming high-velocity plasma, the fluid slows down during the process.
A magnetohydrodynamic accelerator is an MHD converter that imparts motion to an electrically conductive fluid initially at rest, using cross electric current and magnetic field both applied within the fluid. MHD propulsion has been mostly tested with models of ships and submarines in seawater . [ 8 ] [ 9 ] Studies are also ongoing since the early 1960s about aerospace applications of MHD to aircraft propulsion and flow control to enable hypersonic flight : action on the boundary layer to prevent laminar flow from becoming turbulent, shock wave mitigation or cancellation for thermal control and reduction of the wave drag and form drag, inlet flow control and airflow velocity reduction with an MHD generator section ahead of a scramjet or turbojet to extend their regimes at higher Mach numbers, combined to an MHD accelerator in the exhaust nozzle fed by the MHD generator through a bypass system. Research on various designs are also conducted on electromagnetic plasma propulsion for space exploration . [ 10 ] [ 11 ] [ 12 ] [ 13 ]
In an MHD accelerator, the Lorentz force accelerates all charge carriers in the same direction whatever their sign, as well as neutral atoms and molecules of the fluid through collisions. The fluid is ejected toward the rear and as a reaction, the vehicle accelerates forward. | https://en.wikipedia.org/wiki/Magnetohydrodynamic_converter |
A magnetohydrodynamic drive or MHD accelerator is a method for propelling vehicles using only electric and magnetic fields with no moving parts , accelerating an electrically conductive propellant ( liquid or gas ) with magnetohydrodynamics . The fluid is directed to the rear and as a reaction , the vehicle accelerates forward. [ 1 ] [ 2 ]
Studies examining MHD in the field of marine propulsion began in the late 1950s. [ 3 ] [ 4 ] [ 5 ] [ 6 ] [ 7 ]
Few large-scale marine prototypes have been built, limited by the low electrical conductivity of seawater . Increasing current density is limited by Joule heating and water electrolysis in the vicinity of electrodes , and increasing the magnetic field strength is limited by the cost, size and weight (as well as technological limitations) of electromagnets and the power available to feed them. [ 8 ] [ 9 ] In 2023 DARPA launched the PUMP program to build a marine engine using superconducting magnets expected to reach a field strength of 20 Tesla . [ 10 ]
Stronger technical limitations apply to air-breathing MHD propulsion (where ambient air is ionized) that is still limited to theoretical concepts and early experiments. [ 11 ] [ 12 ] [ 13 ]
Plasma propulsion engines using magnetohydrodynamics for space exploration have also been actively studied as such electromagnetic propulsion offers high thrust and high specific impulse at the same time, and the propellant would last much longer than in chemical rockets . [ 14 ]
The working principle involves the acceleration of an electrically conductive fluid (which can be a liquid or an ionized gas called a plasma ) by the Lorentz force , resulting from the cross product of an electric current (motion of charge carriers accelerated by an electric field applied between two electrodes ) with a perpendicular magnetic field . The Lorentz force accelerates all charged particles , positive and negative species (in opposite directions). If either positive or negative species dominate the vehicle is put in motion in the opposite direction from the net charge.
This is the same working principle as an electric motor (more exactly a linear motor ) except that in an MHD drive, the solid moving rotor is replaced by the fluid acting directly as the propellant . As with all electromagnetic devices, an MHD accelerator is reversible: if the ambient working fluid is moving relatively to the magnetic field, charge separation induces an electric potential difference that can be harnessed with electrodes : the device then acts as a power source with no moving parts, transforming the kinetic energy of the incoming fluid into electricity , called an MHD generator .
As the Lorentz force in an MHD converter does not act on a single isolated charged particle nor on electrons in a solid electrical wire , but on a continuous charge distribution in motion, it is a "volumetric" (body) force, a force per unit volume:
where f is the force density (force per unit volume), ρ the charge density (charge per unit volume), E the electric field , J the current density (current per unit area) and B the magnetic field . [ clarification needed ]
MHD thrusters are classified in two categories according to the way the electromagnetic fields operate:
As induction MHD accelerators are electrodeless, they do not exhibit the common issues related to conduction systems (especially Joule heating, bubbles and redox from electrolysis) but need much more intense peak magnetic fields to operate. Since one of the biggest issues with such thrusters is the limited energy available on-board, induction MHD drives have not been developed out of the laboratory.
Both systems can put the working fluid in motion according to two main designs:
Internal flow systems concentrate the MHD interaction in a limited volume, preserving stealth characteristics. External field systems on the contrary have the ability to act on a very large expanse of surrounding water volume with higher efficiency and the ability to decrease drag , increasing the efficiency even further. [ 15 ]
MHD has no moving parts, which means that a good design might be silent, reliable, and efficient. Additionally, the MHD design eliminates many of the wear and friction pieces of the drivetrain with a directly driven propeller by an engine. Problems with current technologies include expense and slow speed compared to a propeller driven by an engine. [ 8 ] [ 9 ] The extra expense is from the large generator that must be driven by an engine. Such a large generator is not required when an engine directly drives a propeller.
The first prototype, a 3-meter (10-feet) long submarine called EMS-1, was designed and tested in 1966 by Stewart Way, a professor of mechanical engineering at the University of California, Santa Barbara . Way, on leave from his job at Westinghouse Electric , assigned his senior year undergraduate students to build the operational unit. This MHD submarine operated on batteries delivering power to electrodes and electromagnets, which produced a magnetic field of 0.015 tesla. The cruise speed was about 0.4 meter per second (15 inches per second) during the test in the bay of Santa Barbara, California , in accordance with theoretical predictions. [ 16 ] [ 17 ] [ 18 ] [ 15 ]
Later, a Japanese prototype, the 3.6-meter long "ST-500", achieved speeds of up to 0.6 m/s in 1979. [ 19 ]
In 1991, the world's first full-size prototype Yamato 1 was completed in Japan after six years of research and development (R&D) by the Ship & Ocean Foundation (later known as the Ocean Policy Research Foundation ). The ship successfully carried a crew of ten plus passengers at speeds of up to 15 km/h (8.1 kn) in Kobe Harbour in June 1992. [ 2 ] [ 20 ]
Small-scale ship models were later built and studied extensively in the laboratory, leading to successful comparisons between the measurements and the theoretical prediction of ship terminal speeds. [ 8 ] [ 9 ]
Military research about underwater MHD propulsion included high-speed torpedoes , remotely operated underwater vehicles (ROV), autonomous underwater vehicles (AUV), up to larger ones such as submarines . [ 21 ]
First studies of the interaction of plasmas with hypersonic flows around vehicles date back to the late 1950s, with the concept of a new kind of thermal protection system for space capsules during high-speed reentry . As low-pressure air is naturally ionized at such very high velocities and altitude, it was thought to use the effect of a magnetic field produced by an electromagnet to replace thermal ablative shields by a "magnetic shield". Hypersonic ionized flow interacts with the magnetic field, inducing eddy currents in the plasma. The current combines with the magnetic field to give Lorentz forces that oppose the flow and detach the bow shock wave further ahead of the vehicle, lowering the heat flux which is due to the brutal recompression of air behind the stagnation point . Such passive flow control studies are still ongoing, but a large-scale demonstrator has yet to be built. [ 22 ] [ 23 ]
Active flow control by MHD force fields on the contrary involves a direct and imperious action of forces to locally accelerate or slow down the airflow , modifying its velocity, direction, pressure, friction, heat flux parameters, in order to preserve materials and engines from stress, allowing hypersonic flight . It is a field of magnetohydrodynamics also called magnetogasdynamics , magnetoaerodynamics or magnetoplasma aerodynamics , as the working fluid is the air (a gas instead of a liquid) ionized to become electrically conductive (a plasma).
Air ionization is achieved at high altitude (electrical conductivity of air increases as atmospheric pressure reduces according to Paschen's law ) using various techniques: high voltage electric arc discharge , RF ( microwaves ) electromagnetic glow discharge , laser , e-beam or betatron , radioactive source ... with or without seeding of low ionization potential alkali substances (like caesium ) into the flow. [ 24 ] [ 25 ]
MHD studies applied to aeronautics try to extend the domain of hypersonic planes to higher Mach regimes:
The Russian project Ayaks (Ajax) is an example of MHD-controlled hypersonic aircraft concept. [ 13 ] A US program also exists to design a hypersonic MHD bypass system, the Hypersonic Vehicle Electric Power System (HVEPS). A working prototype was completed in 2017 under development by General Atomics and the University of Tennessee Space Institute , sponsored by the US Air Force Research Laboratory . [ 36 ] [ 37 ] [ 38 ] These projects aim to develop MHD generators feeding MHD accelerators for a new generation of high-speed vehicles. Such MHD bypass systems are often designed around a scramjet engine, but easier to design turbojets are also considered, [ 39 ] [ 40 ] [ 41 ] as well as subsonic ramjets . [ 42 ]
Such studies covers a field of resistive MHD with magnetic Reynolds number ≪ 1 using nonthermal weakly ionized gases, making the development of demonstrators much more difficult to realize than for MHD in liquids. "Cold plasmas" with magnetic fields are subject to the electrothermal instability occurring at a critical Hall parameter, which makes full-scale developments difficult. [ 43 ]
MHD propulsion has been considered as the main propulsion system for both marine and space ships since there is no need to produce lift to counter the gravity of Earth in water (due to buoyancy ) nor in space (due to weightlessness ), which is ruled out in the case of flight in the atmosphere .
Nonetheless, considering the current problem of the electric power source solved (for example with the availability of a still missing multi-megawatt compact fusion reactor ), one could imagine future aircraft of a new kind silently powered by MHD accelerators, able to ionize and direct enough air downward to lift several tonnes . As external flow systems can control the flow over the whole wetted area, limiting thermal issues at high speeds, ambient air would be ionized and radially accelerated by Lorentz forces around an axisymmetric body (shaped as a cylinder , a cone , a sphere ...), the entire airframe being the engine. Lift and thrust would arise as a consequence of a pressure difference between the upper and lower surfaces, induced by the Coandă effect . [ 44 ] [ 45 ] In order to maximize such pressure difference between the two opposite sides, and since the most efficient MHD converters (with a high Hall effect ) are disk-shaped, such MHD aircraft would be preferably flattened to take the shape of a biconvex lens . Having no wings nor airbreathing jet engines , it would share no similarities with conventional aircraft, but it would behave like a helicopter whose rotor blades would have been replaced by a "purely electromagnetic rotor" with no moving part, sucking the air downward. Such concepts of flying MHD disks have been developed in the peer review literature from the mid 1970s mainly by physicists Leik Myrabo with the Lightcraft , [ 46 ] [ 47 ] [ 48 ] [ 49 ] [ 50 ] and Subrata Roy with the Wingless Electromagnetic Air Vehicle (WEAV). [ 51 ] [ 52 ] [ 53 ]
These futuristic visions have been advertised in the media although they still remain beyond the reach of modern technology. [ 54 ] [ 11 ] [ 55 ]
A number of experimental methods of spacecraft propulsion are based on magnetohydrodynamics. As this kind of MHD propulsion involves compressible fluids in the form of plasmas (ionized gases) it is also referred to as magnetogasdynamics or magnetoplasmadynamics .
In such electromagnetic thrusters , the working fluid is most of the time ionized hydrazine , xenon or lithium . Depending on the propellant used, it can be seeded with alkali such as potassium or caesium to improve its electrical conductivity. All charged species within the plasma, from positive and negative ions to free electrons, as well as neutral atoms by the effect of collisions, are accelerated in the same direction by the Lorentz "body" force, which results from the combination of a magnetic field with an orthogonal electric field (hence the name of "cross-field accelerator"), these fields not being in the direction of the acceleration. This is a fundamental difference with ion thrusters which rely on electrostatics to accelerate only positive ions using the Coulomb force along a high voltage electric field.
First experimental studies involving cross-field plasma accelerators (square channels and rocket nozzles) date back to the late 1950s. Such systems provide greater thrust and higher specific impulse than conventional chemical rockets and even modern ion drives, at the cost of a higher required energy density. [ 56 ] [ 57 ] [ 58 ] [ 59 ] [ 60 ] [ 61 ]
Some devices also studied nowadays besides cross-field accelerators include the magnetoplasmadynamic thruster sometimes referred to as the Lorentz force accelerator (LFA), and the electrodeless pulsed inductive thruster (PIT).
Even today, these systems are not ready to be launched in space as they still lack a suitable compact power source offering enough energy density (such as hypothetical fusion reactors ) to feed the power-greedy electromagnets , especially pulsed inductive ones. The rapid ablation of electrodes under the intense thermal flow is also a concern. For these reasons, studies remain largely theoretical and experiments are still conducted in the laboratory, although over 60 years have passed since the first research in this kind of thrusters.
Oregon, a ship in the Oregon Files series of books by author Clive Cussler , has a magnetohydrodynamic drive. This allows the ship to turn very sharply and brake instantly, instead of gliding for a few miles. In Valhalla Rising , Clive Cussler writes the same drive into the powering of Captain Nemo 's Nautilus .
The film adaptation of The Hunt for Red October popularized the magnetohydrodynamic drive as a "caterpillar drive" for submarines , a nearly undetectable "silent drive" intended to achieve stealth in submarine warfare . In reality, the current traveling through the water would create gases and noise, and the magnetic fields would induce a detectable magnetic signature. In the film, it was suggested that this sound could be confused with geological activity. In the novel from which the film was adapted, the caterpillar that Red October used was actually a pump-jet of the so-called "tunnel drive" type (the tunnels provided acoustic camouflage for the cavitation from the propellers).
In the Ben Bova novel The Precipice , the ship where some of the action took place, Starpower 1, built to prove that exploration and mining of the asteroid belt was feasible and potentially profitable, had a magnetohydrodynamic drive mated to a fusion power plant. | https://en.wikipedia.org/wiki/Magnetohydrodynamic_drive |
A magnetohydrodynamic generator ( MHD generator ) is a magnetohydrodynamic converter that transforms thermal energy and kinetic energy directly into electricity . An MHD generator, like a conventional generator, relies on moving a conductor through a magnetic field to generate electric current. The MHD generator uses hot conductive ionized gas (a plasma ) as the moving conductor. The mechanical dynamo, in contrast, uses the motion of mechanical devices to accomplish this.
MHD generators are different from traditional electric generators in that they operate without moving parts (e.g. no turbines), so there is no limit on the upper temperature at which they can operate. They have the highest known theoretical thermodynamic efficiency of any electrical generation method. MHD has been developed for use in combined cycle power plants to increase the efficiency of electric generation , especially when burning coal or natural gas . The hot exhaust gas from an MHD generator can heat the boilers of a steam power plant , increasing overall efficiency.
Practical MHD generators have been developed for fossil fuels , but these were overtaken by less expensive combined cycles in which the exhaust of a gas turbine or molten carbonate fuel cell heats steam to power a steam turbine .
MHD dynamos are the complement of MHD accelerators , which have been applied to pump liquid metals , seawater , and plasmas.
Natural MHD dynamos are an active area of research in plasma physics and are of great interest to the geophysics and astrophysics communities since the magnetic fields of the Earth and Sun are produced by these natural dynamos.
In a conventional thermal power plant, like a coal-fired power station or nuclear power plant , the energy created by the chemical or nuclear reactions is absorbed in a working fluid , usually water. In a coal plant, for instance, the coal burns in an open chamber which is surrounded by tubes carrying water. The heat from the combustion is absorbed by the water which boils into steam. The steam is then sent into a steam turbine which extracts energy from the steam by turning it into rotational motion. The steam is slowed and cooled as it passes through the turbine. The rotational motion then turns an electrical generator . [ 1 ]
The efficiency of this overall cycle, known as the Rankine cycle , is a function of the temperature difference between the inlet to the boiler and the outlet to the turbine. The maximum temperature at the turbine is a function of the energy source; and the minimum temperature at the inlet is a function of the surrounding environment's ability to absorb waste heat. For many practical reasons, coal plants generally extract about 35% of the heat energy from the coal, the rest is ultimately dumped into the cooling system or escapes through other losses. [ 2 ]
MHD generators can extract more energy from the fuel source than turbine-generator systems. They do this by skipping the step where the heat is transferred to another working fluid. Instead, they use the hot exhaust directly as the working fluid. In the case of a coal plant, the exhaust is directed through a nozzle that increases its velocity, essentially a rocket nozzle , and then directs it through a magnetic system that directly generates electricity. In a conventional generator, rotating magnets move past a material filled with nearly-free electrons, typically copper wire (or vice versa depending on the design). In the MHD system the electrons in the exhaust gas move past a stationary magnet. Ultimately the effect is the same, the working fluid is slowed down and cools as its kinetic energy is transferred to electrons, and is thereby converted to electrical power. [ 3 ]
MHD can only be used with power sources that produce large amounts of fast moving plasma , like the gas from burning coal. This means it is not suitable for systems that work at lower temperatures or do not produce an ionized gas, like a solar power tower or nuclear reactor . In the early days of development of nuclear power , one alternative design was the gaseous fission reactor , which did produce plasma, and this led to some interest in MHD for this role. This style of reactor was never built, however, and interest from the nuclear industry waned. The vast majority of work on MHD for electrical generation has been related to coal fired plants. [ citation needed ]
The Lorentz Force Law describes the effects of a charged particle moving in a constant magnetic field. The simplest form of this law is given by the vector equation. F = Q ( v × B ) {\displaystyle \mathbf {F} =Q\left(\mathbf {v} \times \mathbf {B} \right)}
where
The vector F is perpendicular to both v and B according to the right hand rule .
Typically, for a large power station to approach the operational efficiency of computer models , steps must be taken to increase the electrical conductivity of the conductive substance. Heating a gas to its plasma state, or adding other easily ionizable substances like the salts of alkali metals, can help to accomplish this. In practice, a number of issues must be considered in the implementation of an MHD generator : generator efficiency, economics, and toxic byproducts. These issues are affected by the choice of one of the three MHD generator designs: the Faraday generator, the Hall generator, and the disc generator.
The Faraday generator is named for Michael Faraday's experiments on moving charged particles in the Thames River.
A simple Faraday generator consists of a wedge-shaped pipe or tube of some non- conductive material. When an electrically conductive fluid flows through the tube, in the presence of a significant perpendicular magnetic field, a voltage is induced in the fluid. This can be drawn off as electrical power by placing electrodes on the sides, at 90-degree angles to the magnetic field.
There are limitations on the density and type of field used in this example. The amount of power that can be extracted is proportional to the cross-sectional area of the tube and the speed of the conductive flow. The conductive substance is also cooled and slowed by this process. MHD generators typically reduce the temperature of the conductive substance from plasma temperatures to just over 1000 °C.
The main practical problem of a Faraday generator is that differential voltages and currents in the fluid may short through the electrodes on the sides of the duct. The generator can also experience losses from the Hall effect current, which makes the Faraday duct inefficient. [ citation needed ] Most further refinements of MHD generators have tried to solve this problem. The optimal magnetic field on duct-shaped MHD generators is a sort of saddle shape. To get this field, a large generator requires an extremely powerful magnet. Many research groups have tried to adapt superconducting magnets to this purpose, with varying success.
The typical solution has been to use the Hall effect to create a current that flows with the fluid. (See illustration.) This design has arrays of short, segmented electrodes on the sides of the duct. The first and last electrodes in the duct power the load. Each other electrode is shorted to an electrode on the opposite side of the duct. These shorts of the Faraday current induce a powerful magnetic field within the fluid, but in a chord of a circle at right angles to the Faraday current. This secondary, induced field makes the current flow in a rainbow shape between the first and last electrodes.
Losses are less than in a Faraday generator, and voltages are higher because there is less shorting of the final induced current.
However, this design has problems because the speed of the material flow requires the middle electrodes to be offset to "catch" the Faraday currents. As the load varies, the fluid flow speed varies, misaligning the Faraday current with its intended electrodes, and making the generator's efficiency very sensitive to its load.
The third and, currently, the most efficient design is the Hall effect disc generator. This design currently holds the efficiency and energy density records for MHD generation. A disc generator has fluid flowing between the center of a disc, and a duct wrapped around the edge. (The ducts are not shown.) The magnetic excitation field is made by a pair of circular Helmholtz coils above and below the disk. (The coils are not shown.)
The Faraday currents flow in a perfect dead short around the periphery of the disk.
The Hall effect currents flow between ring electrodes near the center duct and ring electrodes near the periphery duct.
The wide flat gas flow reduced the distance, hence the resistance of the moving fluid. This increases efficiency.
Another significant advantage of this design is that the magnets are more efficient. First, they cause simple parallel field lines. Second, because the fluid is processed in a disk, the magnet can be closer to the fluid, and in this geometry, magnetic field strengths increase as the 7th power of distance. Finally, the generator is compact, so the magnet is smaller and uses a much smaller percentage of the generated power.
The efficiency of the direct energy conversion in MHD power generation increases with the magnetic field strength and the plasma conductivity , which depends directly on the plasma temperature , and more precisely on the electron temperature. As very hot plasmas can only be used in pulsed MHD generators (for example using shock tubes ) due to the fast thermal material erosion, it was envisaged to use nonthermal plasmas as working fluids in steady MHD generators, where only free electrons are heated a lot (10,000–20,000 kelvins ) while the main gas (neutral atoms and ions) remains at a much lower temperature, typically 2500 kelvins. The goal was to preserve the materials of the generator (walls and electrodes) while improving the limited conductivity of such poor conductors to the same level as a plasma in thermodynamic equilibrium ; i.e. completely heated to more than 10,000 kelvins, a temperature that no material could stand. [ 4 ] [ 5 ] [ 6 ] [ 7 ]
Evgeny Velikhov first discovered theoretically in 1962 and experimentally in 1963 that an ionization instability, later called the Velikhov instability or electrothermal instability , quickly arises in any MHD converter using magnetized nonthermal plasmas with hot electrons, when a critical Hall parameter is reached, depending on the degree of ionization and the magnetic field. [ 8 ] [ 9 ] [ 10 ] This instability greatly degrades the performance of nonequilibrium MHD generators. The prospects of this technology, which initially predicted high efficiencies, crippled MHD programs all over the world as no solution to mitigate the instability was found at that time. [ 11 ] [ 12 ] [ 13 ] [ 14 ]
Without implementing solutions to overcome the electrothermal instability, practical MHD generators had to limit the Hall parameter or use moderately-heated thermal plasmas instead of cold plasmas with hot electrons, which severely lowers efficiency.
As of 1994, the 22% efficiency record for closed-cycle disc MHD generators was held by Tokyo Technical Institute. The peak enthalpy extraction in these experiments reached 30.2%. Typical open-cycle Hall & duct coal MHD generators are lower, near 17%. These efficiencies make MHD unattractive, by itself, for utility power generation, since conventional Rankine cycle power plants can reach 40%.
However, the exhaust of an MHD generator burning fossil fuel is almost as hot as a flame. By routing its exhaust gases into a heat exchanger for a turbine Brayton cycle or steam generator Rankine cycle , MHD can convert fossil fuels into electricity with an overall estimated efficiency of up to 60 percent, compared to the 40 percent of a typical coal plant.
A magnetohydrodynamic generator might also be the first stage of a gas core reactor . [ 15 ]
MHD generators have problems in regard to materials, both for the walls and the electrodes. Materials must not melt or corrode at very high temperatures. Exotic ceramics were developed for this purpose, selected to be compatible with the fuel and ionization seed. The exotic materials and the difficult fabrication methods contribute to the high cost of MHD generators.
MHDs also work better with stronger magnetic fields. The most successful magnets have been superconducting , and very close to the channel. A major difficulty was refrigerating these magnets while insulating them from the channel. The problem is worse because the magnets work better when they are closer to the channel. There are also risks of damage to the hot, brittle ceramics from differential thermal cracking: magnets are usually near absolute zero, while the channel is several thousand degrees.
For MHDs, both alumina (Al 2 O 3 ) and magnesium peroxide (MgO 2 ) were reported to work for the insulating walls. Magnesium peroxide degrades near moisture. Alumina is water-resistant and can be fabricated to be quite strong, so in practice, most MHDs have used alumina for the insulating walls.
For the electrodes of clean MHDs (i.e. burning natural gas), one good material was a mix of 80% CeO 2 , 18% ZrO 2 , and 2% Ta 2 O 5 . [ 16 ]
Coal-burning MHDs have highly corrosive environments with slag. The slag both protects and corrodes MHD materials. In particular, migration of oxygen through the slag accelerates the corrosion of metallic anodes. Nonetheless, very good results have been reported with stainless steel electrodes at 900 K. [ 17 ] Another, perhaps superior option is a spinel ceramic, FeAl 2 O 4 - Fe 3 O 4 . The spinel was reported to have electronic conductivity, absence of a resistive reaction layer but with some diffusion of iron into the alumina. The diffusion of iron could be controlled with a thin layer of very dense alumina, and water cooling in both the electrodes and alumina insulators. [ 18 ]
Attaching the high-temperature electrodes to conventional copper bus bars is also challenging. The usual methods establish a chemical passivation layer, and cool the busbar with water. [ 16 ]
MHD generators have not been used for large-scale mass energy conversion because other techniques with comparable efficiency have a lower lifecycle investment cost. Advances in natural gas turbines achieved similar thermal efficiencies at lower costs, by having the turbine exhaust drive a Rankine cycle steam plant. To get more electricity from coal, it is cheaper to simply add more low-temperature steam-generating capacity.
A coal-fueled MHD generator is a type of Brayton power cycle , similar to the power cycle of a combustion turbine. However, unlike the combustion turbine, there are no moving mechanical parts; the electrically conducting plasma provides the moving electrical conductor. The side walls and electrodes merely withstand the pressure within, while the anode and cathode conductors collect the electricity that is generated. All Brayton cycles are heat engines. Ideal Brayton cycles also have an ideal efficiency equal to ideal Carnot cycle efficiency. Thus, the potential for high energy efficiency from an MHD generator. All Brayton cycles have higher potential for efficiency the higher the firing temperature. While a combustion turbine is limited in maximum temperature by the strength of its air/water or steam-cooled rotating airfoils; there are no rotating parts in an open-cycle MHD generator. This upper bound in temperature limits the energy efficiency in combustion turbines. The upper bound on Brayton cycle temperature for an MHD generator is not limited, so inherently an MHD generator has a higher potential capability for energy efficiency.
The temperatures at which linear coal-fueled MHD generators can operate are limited by factors that include: (a) the combustion fuel, oxidizer, and oxidizer preheat temperature which limit the maximum temperature of the cycle; (b) the ability to protect the sidewalls and electrodes from melting; (c) the ability to protect the electrodes from electrochemical attack from the hot slag coating the walls combined with the high current or arcs that impinge on the electrodes as they carry off the direct current from the plasma; and (d) by the capability of the electrical insulators between each electrode. Coal-fired MHD plants with oxygen/air and high oxidant preheats would probably provide potassium-seeded plasmas of about 4200 °F, 10 atmospheres pressure, and begin expansion at Mach 1.2. These plants would recover MHD exhaust heat for oxidant preheat, and for combined cycle steam generation. With aggressive assumptions, one DOE-funded feasibility study of where the technology could go, 1000 MWe Advanced Coal-Fired MHD/Steam Binary Cycle Power Plant Conceptual Design , published in June 1989, showed that a large coal-fired MHD combined cycle plant could attain a HHV energy efficiency approaching 60 percent—well in excess of other coal-fueled technologies, so the potential for low operating costs exists.
However, no testing at those aggressive conditions or size has yet occurred, and there are no large MHD generators now under test. There is simply an inadequate reliability track record to provide confidence in a commercial coal-fuelled MHD design.
U25B MHD testing in Russia using natural gas as fuel used a superconducting magnet, and had an output of 1.4 megawatts. A coal-fired MHD generator series of tests funded by the U.S. Department of Energy (DOE) in 1992 produced MHD power from a larger superconducting magnet at the Component Development and Integration Facility (CDIF) in Butte , Montana . None of these tests were conducted for long-enough durations to verify the commercial durability of the technology. Neither of the test facilities were in large-enough scale for a commercial unit.
Superconducting magnets are used in the larger MHD generators to eliminate one of the large parasitic losses: the power needed to energize the electromagnet. Superconducting magnets, once charged, consume no power and can develop intense magnetic fields 4 teslas and higher. The only parasitic load for the magnets are to maintain refrigeration, and to make up the small losses for the non-supercritical connections.
Because of the high temperatures, the non-conducting walls of the channel must be constructed from an exceedingly heat-resistant substance such as yttrium oxide or zirconium dioxide to retard oxidation. Similarly, the electrodes must be both conductive and heat-resistant at high temperatures. The AVCO coal-fueled MHD generator at the CDIF was tested with water-cooled copper electrodes capped with platinum, tungsten, stainless steel, and electrically conducting ceramics.
MHD reduces the overall production of fossil fuel wastes because it increases plant efficiency. In MHD coal plants, the patented commercial "Econoseed" process developed by the U.S. (see below) recycles potassium ionization seed from the fly ash captured by the stack-gas scrubber. However, this equipment is an additional expense. If molten metal is the armature fluid of an MHD generator, care must be taken with the coolant of the electromagnetics and channel. The alkali metals commonly used as MHD fluids react violently with water. Also, the chemical byproducts of heated, electrified alkali metals and channel ceramics may be poisonous and environmentally persistent.
The first practical MHD power research was funded in 1938 in the U.S. by Westinghouse in its Pittsburgh, Pennsylvania laboratories, headed by Hungarian Bela Karlovitz . The initial patent on MHD is by B. Karlovitz, U.S. Patent No. 2,210,918, "Process for the Conversion of Energy", August 13, 1940. World War II interrupted development.
In 1962, the First International Conference on MHD Power was held in Newcastle upon Tyne, UK by Dr. Brian C. Lindley of the International Research and Development Company Ltd. The group set up a steering committee to set up further conferences and disseminate ideas. In 1964, the group held a second conference in Paris, France, in consultation with the European Nuclear Energy Agency .
Since membership in the ENEA was limited, the group persuaded the International Atomic Energy Agency to sponsor a third conference, in Salzburg, Austria, July 1966. Negotiations at this meeting converted the steering committee into a periodic reporting group, the ILG-MHD (international liaison group, MHD), under the ENEA, and later in 1967, also under the International Atomic Energy Agency. Further research in the 1960s by R. Rosa established the practicality of MHD for fossil-fueled systems.
In the 1960s, AVCO Everett Aeronautical Research began a series of experiments, ending with the Mk. V generator of 1965. This generated 35 MW, but used about 8 MW to drive its magnet. In 1966, the ILG-MHD had its first formal meeting in Paris, France. It began issuing a periodic status report in 1967. This pattern persisted, in this institutional form, up until 1976. Toward the end of the 1960s, interest in MHD declined because nuclear power was becoming more widely available.
In the late 1970s, as interest in nuclear power declined, interest in MHD increased. In 1975, UNESCO became persuaded that MHD might be an efficient way to utilise world coal reserves, and in 1976, sponsored the ILG-MHD. In 1976, it became clear that no nuclear reactor in the next 25 years would use MHD, so the International Atomic Energy Agency and ENEA (both nuclear agencies) withdrew support from the ILG-MHD, leaving UNESCO as the primary sponsor of the ILG-MHD.
Engineers in former Yugoslavian Institute of Thermal and Nuclear Technology (ITEN), Energoinvest Co., Sarajevo, built and patented the first experimental Magneto-Hydrodynamic facility power generator in 1989. [ 19 ] [ 20 ]
In the 1980s, the U.S. Department of Energy began a multiyear program, culminating in a 1992 50 MW demonstration coal combustor at the Component Development and Integration Facility (CDIF) in Butte, Montana . This program also had significant work at the Coal-Fired-In-Flow-Facility (CFIFF) at University of Tennessee Space Institute .
This program combined four parts:
Initial prototypes at the CDIF operated for short durations, with various coals: Montana Rosebud, and a high-sulphur corrosive coal, Illinois No. 6. A great deal of engineering, chemistry, and material science was completed. After the final components were developed, operational testing completed with 4,000 hours of continuous operation, 2,000 on Montana Rosebud, 2,000 on Illinois No. 6. The testing ended in 1993. [ citation needed ]
The Japanese program in the late 1980s concentrated on closed-cycle MHD. The belief was that it would have higher efficiencies, and smaller equipment, especially in the clean, small, economical plant capacities near 100 megawatts (electrical) which are suited to Japanese conditions. Open-cycle coal-powered plants are generally thought to become economic above 200 megawatts.
The first major series of experiments was FUJI-1, a blow-down system powered from a shock tube at the Tokyo Institute of Technology . These experiments extracted up to 30.2% of enthalpy, and achieved power densities near 100 megawatts per cubic meter. This facility was funded by Tokyo Electric Power, other Japanese utilities, and the Department of Education. Some authorities believe this system was a disc generator with a helium and argon carrier gas and potassium ionization seed.
In 1994, there were detailed plans for FUJI-2, a 5 MWe continuous closed-cycle facility, powered by natural gas, to be built using the experience of FUJI-1. The basic MHD design was to be a system with inert gases using a disk generator. The aim was an enthalpy extraction of 30% and an MHD thermal efficiency of 60%. FUJI-2 was to be followed by a retrofit to a 300 MWe natural gas plant.
From the 1980s, Professor Hugo Messerle at The University of Sydney researched coal-fueled MHD. This resulted in a 28 MWe topping facility that was operated outside Sydney. Messerle also wrote a key reference work on MHD, as part of a UNESCO education program. [ 21 ]
The Italian program began in 1989 with a budget of about 20 million $US, and had three main development areas:
A joint U.S.-China national programme ended in 1992 by retrofitting the coal-fired No. 3 plant in Asbach. [ citation needed ] A further eleven-year program was approved in March 1994. This established centres of research in:
The 1994 study proposed a 10 W (electrical, 108 MW thermal) generator with the MHD and bottoming cycle plants connected by steam piping, so either could operate independently.
In 1971, the natural-gas-fired U-25 plant was completed near Moscow, with a designed capacity of 25 megawatts. By 1974 it delivered 6 megawatts of power. [ 22 ] By 1994, Russia had developed and operated the coal-operated facility U-25, at the High-Temperature Institute of the Russian Academy of Science in Moscow. U-25's bottoming plant was operated under contract with the Moscow utility, and fed power into Moscow's grid. There was substantial interest in Russia in developing a coal-powered disc generator. In 1986 the first industrial power plant with MHD generator was built, but in 1989 the project was cancelled before MHD launch and this power plant later joined to Ryazan Power Station as a 7th unit with ordinary construction. | https://en.wikipedia.org/wiki/Magnetohydrodynamic_generator |
Magnetolithography ( ML ) is a photoresist -less and photomaskless lithography method for patterning wafer surfaces. ML is based on applying a magnetic field on the substrate using paramagnetic metal masks named "magnetic masks" placed on either topside or backside of the wafer. [ 1 ] [ 2 ] Magnetic masks are analogous to a photomask in photolithography, in that they define the spatial distribution and shape of the applied magnetic field. [ 2 ] The fabrication of the magnetic masks involves the use of conventional photolithography and photoresist however. [ 2 ] The second component of the process is ferromagnetic nanoparticles (analogous to the photoresist in photolithography, e.g. cobalt nanoparticles) that are assembled over the substrate according to the field induced by the mask which blocks its areas from reach of etchants or depositing materials (e.g. dopants or metallic layers). [ 1 ] [ 2 ]
ML can be used for applying either a positive or negative approach. In the positive approach, the magnetic nanoparticles react chemically or interact via chemical recognition with the substrate. Hence, the magnetic nanoparticles are immobilized at selected locations, where the mask induces a magnetic field, resulting in a patterned substrate. In the negative approach, the magnetic nanoparticles are inert to the substrate. Hence, once they pattern the substrate, they block their binding site on the substrate from reacting with another reacting agent. After the adsorption of the reacting agent, the nanoparticles are removed, resulting in a negatively patterned substrate.
ML is also a backside lithography , which has the advantage of ease in producing multilayer with high accuracy of alignment and with the same efficiency for all layers. | https://en.wikipedia.org/wiki/Magnetolithography |
The magnetomechanical effect is a fundamental feature of ferromagnetism. The fact that the application of external stresses alters the flux density of a magnetized ferromagnet, and thus the shape, and size of its hysteresis loops is easily changeable .
Simply, it is the phenomenon of changing the magnetic properties of ferromagnetic materials by applying external stresses.
Magnetomechanical effects connect magnetic, mechanical and electric phenomena in solid materials.
Magnetostriction is thermodynamically opposite to inverse magnetostriction effect. The same situation occurs for Wiedemann and Matteuci effects.
For magnetic, mechanical and electric phenomena in fluids see Magnetohydrodynamics and Electrohydrodynamics . | https://en.wikipedia.org/wiki/Magnetomechanical_effects |
A magnetometer is a device that measures magnetic field or magnetic dipole moment . Different types of magnetometers measure the direction, strength, or relative change of a magnetic field at a particular location. A compass is one such device, one that measures the direction of an ambient magnetic field, in this case, the Earth's magnetic field . Other magnetometers measure the magnetic dipole moment of a magnetic material such as a ferromagnet , for example by recording the effect of this magnetic dipole on the induced current in a coil.
The invention of the magnetometer is usually credited to Carl Friedrich Gauss in 1832. [ 1 ] [ 2 ] Earlier, more primitive instruments were developed by Christopher Hansteen in 1819, [ 3 ] and by William Scoresby by 1823. [ 4 ]
Magnetometers are widely used for measuring the Earth's magnetic field, in geophysical surveys , to detect magnetic anomalies of various types, and to determine the dipole moment of magnetic materials. In an aircraft's attitude and heading reference system , they are commonly used as a heading reference. Magnetometers are also used by the military as a triggering mechanism in magnetic mines to detect submarines. Consequently, some countries, such as the United States, Canada and Australia, classify the more sensitive magnetometers as military technology, and control their distribution.
Magnetometers can be used as metal detectors : they can detect only magnetic ( ferrous ) metals, but can detect such metals at a much greater distance than conventional metal detectors, which rely on conductivity. Magnetometers are capable of detecting large objects, such as cars, at over 10 metres (33 ft), while a conventional metal detector's range is rarely more than 2 metres (6 ft 7 in).
In recent years, magnetometers have been miniaturized to the extent that they can be incorporated in integrated circuits at very low cost and are finding increasing use as miniaturized compasses ( MEMS magnetic field sensor ).
Magnetic fields are vector quantities characterized by both strength and direction. The strength of a magnetic field is measured in units of tesla in the SI units , and in gauss in the cgs system of units. 10,000 gauss are equal to one tesla. [ 5 ] Measurements of the Earth's magnetic field are often quoted in units of nanotesla (nT), also called a gamma. [ 6 ] The Earth's magnetic field can vary from 20,000 to 80,000 nT depending on location, fluctuations in the Earth's magnetic field are on the order of 100 nT, and magnetic field variations due to magnetic anomalies can be in the picotesla (pT) range. [ 7 ] Gaussmeters and teslameters are magnetometers that measure in units of gauss or tesla, respectively. In some contexts, magnetometer is the term used for an instrument that measures fields of less than 1 millitesla (mT) and gaussmeter is used for those measuring greater than 1 mT. [ 5 ]
There are two basic types of magnetometer measurement. Vector magnetometers measure the vector components of a magnetic field. Total field magnetometers or scalar magnetometers measure the magnitude of the vector magnetic field. [ 8 ] Magnetometers used to study the Earth's magnetic field may express the vector components of the field in terms of declination (the angle between the horizontal component of the field vector and true, or geographic, north) and the inclination (the angle between the field vector and the horizontal surface). [ 9 ]
Absolute magnetometers measure the absolute magnitude or vector magnetic field, using an internal calibration or known physical constants of the magnetic sensor. [ 10 ] Relative magnetometers measure magnitude or vector magnetic field relative to a fixed but uncalibrated baseline. Also called variometers , relative magnetometers are used to measure variations in magnetic field.
Magnetometers may also be classified by their situation or intended use. Stationary magnetometers are installed to a fixed position and measurements are taken while the magnetometer is stationary. [ 8 ] Portable or mobile magnetometers are meant to be used while in motion and may be manually carried or transported in a moving vehicle. Laboratory magnetometers are used to measure the magnetic field of materials placed within them and are typically stationary. Survey magnetometers are used to measure magnetic fields in geomagnetic surveys; they may be fixed base stations, as in the INTERMAGNET network, or mobile magnetometers used to scan a geographic region. An early adoption (in the 1950s) of airborne magnetometry by Inco prompted the discovery of Thompson, Manitoba . [ 11 ]
The performance and capabilities of magnetometers are described through their technical specifications. Major specifications include [ 5 ] [ 7 ]
The compass , consisting of a magnetized needle whose orientation changes in response to the ambient magnetic field, is a simple type of magnetometer, one that measures the direction of the field. The oscillation frequency of a magnetized needle is proportional to the square-root of the strength of the ambient magnetic field; so, for example, the oscillation frequency of the needle of a horizontally situated compass is proportional to the square-root of the horizontal intensity of the ambient field. [ citation needed ]
In 1823 William Scoresby (1789-1857), an English explorer, scientist and clergyman, was deeply involved in magnetic science, particularly in improving ships' compasses. In 1823, he published a paper in the Transactions of the Royal Society of Edinburgh titled "Description of Magnetimenter, being a new instrument for measuring magnetic attractions and finding the dip of the needle; with an accont of experiments made with it."
In 1833, Carl Friedrich Gauss , head of the Geomagnetic Observatory in Göttingen, published a paper on measurement of the Earth's magnetic field. [ 12 ] It described a new instrument that consisted of a permanent bar magnet suspended horizontally from a gold fibre. The difference in the oscillations when the bar was magnetised and when it was demagnetised allowed Gauss to calculate an absolute value for the strength of the Earth's magnetic field. [ 13 ]
The gauss , the CGS unit of magnetic flux density was named in his honour, defined as one maxwell per square centimeter; it equals 1×10 −4 tesla (the SI unit ). [ 14 ]
Francis Ronalds and Charles Brooke independently invented magnetographs in 1846 that continuously recorded the magnet's movements using photography , thus easing the load on observers. [ 15 ] They were quickly utilised by Edward Sabine and others in a global magnetic survey and updated machines were in use well into the 20th century. [ 16 ] [ 17 ]
Laboratory magnetometers measure the magnetization , also known as the magnetic moment of a sample material. Unlike survey magnetometers, laboratory magnetometers require the sample to be placed inside the magnetometer, and often the temperature, magnetic field, and other parameters of the sample can be controlled. A sample's magnetization, is primarily dependent on the ordering of unpaired electrons within its atoms, with smaller contributions from nuclear magnetic moments , Larmor diamagnetism , among others. Ordering of magnetic moments are primarily classified as diamagnetic , paramagnetic , ferromagnetic , or antiferromagnetic (although the zoology of magnetic ordering also includes ferrimagnetic , helimagnetic , toroidal , spin glass , etc.). Measuring the magnetization as a function of temperature and magnetic field can give clues as to the type of magnetic ordering, as well as any phase transitions between different types of magnetic orders that occur at critical temperatures or magnetic fields. This type of magnetometry measurement is very important to understand the magnetic properties of materials in physics, chemistry, geophysics and geology, as well as sometimes biology.
SQUIDs are a type of magnetometer used both as survey and as laboratory magnetometers. SQUID magnetometry is an extremely sensitive absolute magnetometry technique. However SQUIDs are noise sensitive, making them impractical as laboratory magnetometers in high DC magnetic fields, and in pulsed magnets. Commercial SQUID magnetometers are available for sample temperatures between 300 mK and 400 K, and magnetic fields up to 7 tesla.
Inductive pickup coils (also referred as inductive sensor) measure the magnetic dipole moment of a material by detecting the current induced in a coil due to the changing magnetic moment of the sample. The sample's magnetization can be changed by applying a small ac magnetic field (or a rapidly changing dc field), as occurs in capacitor-driven pulsed magnets. These measurements require differentiating between the magnetic field produced by the sample and that from the external applied field. Often a special arrangement of cancellation coils is used. For example, half of the pickup coil is wound in one direction, and the other half in the other direction, and the sample is placed in only one half. The external uniform magnetic field is detected by both halves of the coil, and since they are counter-wound, the external magnetic field produces no net signal.
Vibrating-sample magnetometers (VSMs) detect the dipole moment of a sample by mechanically vibrating the sample inside of an inductive pickup coil or inside of a SQUID coil. Induced current or changing flux in the coil is measured. The vibration is typically created by a motor or a piezoelectric actuator. Typically the VSM technique is about an order of magnitude less sensitive than SQUID magnetometry. VSMs can be combined with SQUIDs to create a system that is more sensitive than either one alone. Heat due to the sample vibration can limit the base temperature of a VSM, typically to 2 kelvin. VSM is also impractical for measuring a fragile sample that is sensitive to rapid acceleration.
Pulsed-field extraction magnetometry is another method making use of pickup coils to measure magnetization. Unlike VSMs where the sample is physically vibrated, in pulsed-field extraction magnetometry, the sample is secured and the external magnetic field is changed rapidly, for example in a capacitor-driven magnet. One of multiple techniques must then be used to cancel out the external field from the field produced by the sample. These include counterwound coils that cancel the external uniform field and background measurements with the sample removed from the coil.
Magnetic torque magnetometry can be even more sensitive than SQUID magnetometry. However, magnetic torque magnetometry doesn't measure magnetism directly as all the previously mentioned methods do. Magnetic torque magnetometry instead measures the torque τ acting on a sample's magnetic moment μ as a result of a uniform magnetic field B, τ = μ × B. A torque is thus a measure of the sample's magnetic or shape anisotropy. In some cases the sample's magnetization can be extracted from the measured torque. In other cases, the magnetic torque measurement is used to detect magnetic phase transitions or quantum oscillations . The most common way to measure magnetic torque is to mount the sample on a cantilever and measure the displacement via capacitance measurement between the cantilever and nearby fixed object, or by measuring the piezoelectricity of the cantilever, or by optical interferometry off the surface of the cantilever.
Faraday force magnetometry uses the fact that a spatial magnetic field gradient produces force that acts on a magnetized object, F = (M⋅∇)B. In Faraday force magnetometry the force on the sample can be measured by a scale (hanging the sample from a sensitive balance), or by detecting the displacement against a spring. Commonly a capacitive load cell or cantilever is used because of its sensitivity, size, and lack of mechanical parts. Faraday force magnetometry is approximately one order of magnitude less sensitive than a SQUID. The biggest drawback to Faraday force magnetometry is that it requires some means of not only producing a magnetic field, but also producing a magnetic field gradient. While this can be accomplished by using a set of special pole faces, a much better result can be achieved by using set of gradient coils. A major advantage to Faraday force magnetometry is that it is small and reasonably tolerant to noise, and thus can be implemented in a wide range of environments, including a dilution refrigerator . Faraday force magnetometry can also be complicated by the presence of torque (see previous technique). This can be circumvented by varying the gradient field independently of the applied DC field so the torque and the Faraday force contribution can be separated, and/or by designing a Faraday force magnetometer that prevents the sample from being rotated.
Optical magnetometry makes use of various optical techniques to measure magnetization. One such technique, Kerr magnetometry makes use of the magneto-optic Kerr effect , or MOKE. In this technique, incident light is directed at the sample's surface. Light interacts with a magnetized surface nonlinearly so the reflected light has an elliptical polarization, which is then measured by a detector. Another method of optical magnetometry is Faraday rotation magnetometry . Faraday rotation magnetometry utilizes nonlinear magneto-optical rotation to measure a sample's magnetization. In this method a Faraday modulating thin film is applied to the sample to be measured and a series of images are taken with a camera that senses the polarization of the reflected light. To reduce noise, multiple pictures are then averaged together. One advantage to this method is that it allows mapping of the magnetic characteristics over the surface of a sample. This can be especially useful when studying such things as the Meissner effect on superconductors. Microfabricated optically pumped magnetometers (μOPMs) can be used to detect the origin of brain seizures more precisely and generate less heat than currently available superconducting quantum interference devices, better known as SQUIDs. [ 18 ] The device works by using polarized light to control the spin of rubidium atoms which can be used to measure and monitor the magnetic field. [ 19 ]
Survey magnetometers can be divided into two basic types:
A vector is a mathematical entity with both magnitude and direction. The Earth's magnetic field at a given point is a vector. A magnetic compass is designed to give a horizontal bearing direction, whereas a vector magnetometer measures both the magnitude and direction of the total magnetic field. Three orthogonal sensors are required to measure the components of the magnetic field in all three dimensions.
They are also rated as "absolute" if the strength of the field can be calibrated from their own known internal constants or "relative" if they need to be calibrated by reference to a known field.
A magnetograph is a magnetometer that continuously records data over time. This data is typically represented in magnetograms. [ 20 ]
Magnetometers can also be classified as "AC" if they measure fields that vary relatively rapidly in time (>100 Hz), and "DC" if they measure fields that vary only slowly (quasi-static) or are static. AC magnetometers find use in electromagnetic systems (such as magnetotellurics ), and DC magnetometers are used for detecting mineralisation and corresponding geological structures. [ citation needed ]
Proton precession magnetometer s, also known as proton magnetometers , PPMs or simply mags, measure the resonance frequency of protons (hydrogen nuclei) in the magnetic field to be measured, due to nuclear magnetic resonance (NMR). Because the precession frequency depends only on atomic constants and the strength of the ambient magnetic field, the accuracy of this type of magnetometer can reach 1 ppm . [ 21 ]
A direct current flowing in a solenoid creates a strong magnetic field around a hydrogen -rich fluid ( kerosene and decane are popular, and even water can be used), causing some of the protons to align themselves with that field. The current is then interrupted, and as protons realign themselves with the ambient magnetic field, they precess at a frequency that is directly proportional to the magnetic field. This produces a weak rotating magnetic field that is picked up by a (sometimes separate) inductor, amplified electronically, and fed to a digital frequency counter whose output is typically scaled and displayed directly as field strength or output as digital data.
For hand/backpack carried units, PPM sample rates are typically limited to less than one sample per second. Measurements are typically taken with the sensor held at fixed locations at approximately 10 metre increments.
Portable instruments are also limited by sensor volume (weight) and power consumption. PPMs work in field gradients up to 3,000 nT/m, which is adequate for most mineral exploration work. For higher gradient tolerance, such as mapping banded iron formations and detecting large ferrous objects, Overhauser magnetometers can handle 10,000 nT/m, and caesium magnetometers can handle 30,000 nT/m.
They are relatively inexpensive (< US$8,000) and were once widely used in mineral exploration. Three manufacturers dominate the market: GEM Systems, Geometrics and Scintrex. Popular models include G-856/857, Smartmag, GSM-18, and GSM-19T.
For mineral exploration, they have been superseded by Overhauser, caesium, and potassium instruments, all of which are fast-cycling, and do not require the operator to pause between readings.
The Overhauser effect magnetometer or Overhauser magnetometer uses the same fundamental effect as the proton precession magnetometer to take measurements. By adding free radicals to the measurement fluid, the nuclear Overhauser effect can be exploited to significantly improve upon the proton precession magnetometer. Rather than aligning the protons using a solenoid, a low power radio-frequency field is used to align (polarise) the electron spin of the free radicals, which then couples to the protons via the Overhauser effect. This has two main advantages: driving the RF field takes a fraction of the energy (allowing lighter-weight batteries for portable units), and faster sampling as the electron-proton coupling can happen even as measurements are being taken. An Overhauser magnetometer produces readings with a 0.01 nT to 0.02 nT standard deviation while sampling once per second.
The optically pumped caesium vapour magnetometer is a highly sensitive (300 fT/Hz 0.5 ) and accurate device used in a wide range of applications. It is one of a number of alkali vapours (including rubidium and potassium ) that are used in this way. [ 22 ]
The device broadly consists of a photon emitter, such as a laser, an absorption chamber containing caesium vapour mixed with a " buffer gas " through which the emitted photons pass, and a photon detector, arranged in that order. The buffer gas is usually helium or nitrogen and they are used to reduce collisions between the caesium vapour atoms.
The basic principle that allows the device to operate is the fact that a caesium atom can exist in any of nine energy levels , which can be informally thought of as the placement of electron atomic orbitals around the atomic nucleus . When a caesium atom within the chamber encounters a photon from the laser, it is excited to a higher energy state, emits a photon and falls to an indeterminate lower energy state. The caesium atom is "sensitive" to the photons from the laser in three of its nine energy states, and therefore, assuming a closed system, all the atoms eventually fall into a state in which all the photons from the laser pass through unhindered and are measured by the photon detector. The caesium vapour has become transparent. This process happens continuously to maintain as many of the electrons as possible in that state.
At this point, the sample (or population) is said to have been optically pumped and ready for measurement to take place. When an external field is applied it disrupts this state and causes atoms to move to different states which makes the vapour less transparent. The photo detector can measure this change and therefore measure the magnitude of the magnetic field.
In the most common type of caesium magnetometer, a very small AC magnetic field is applied to the cell. Since the difference in the energy levels of the electrons is determined by the external magnetic field, there is a frequency at which this small AC field makes the electrons change states. In this new state, the electrons once again can absorb a photon of light. This causes a signal on a photo detector that measures the light passing through the cell. The associated electronics use this fact to create a signal exactly at the frequency that corresponds to the external field.
Another type of caesium magnetometer modulates the light applied to the cell. This is referred to as a Bell-Bloom magnetometer, after the two scientists who first investigated the effect. If the light is turned on and off at the frequency corresponding to the Earth's field, [ clarification needed ] there is a change in the signal seen at the photo detector. Again, the associated electronics use this to create a signal exactly at the frequency that corresponds to the external field. Both methods lead to high performance magnetometers.
Potassium is the only optically pumped magnetometer that operates on a single, narrow electron spin resonance (ESR) line in contrast to other alkali vapour magnetometers that use irregular, composite and wide spectral lines and helium with the inherently wide spectral line. [ 23 ]
Magnetometers based on helium-4 excited to its metastable triplet state thanks to a plasma discharge have been developed in the 1960s and 70s by Texas Instruments , then by its spinoff Polatomic, [ 24 ] and from late 1980s by CEA-Leti . The latter pioneered a configuration which cancels the dead-zones, [ 25 ] which are a recurrent problem of atomic magnetometers. This configuration was demonstrated to show an accuracy of 50 pT in orbit operation. The ESA chose this technology for the Swarm mission , which was launched in 2013. An experimental vector mode, which could compete with fluxgate magnetometers was tested in this mission with overall success. [ 26 ]
The caesium and potassium magnetometers are typically used where a higher performance magnetometer than the proton magnetometer is needed. In archaeology and geophysics, where the sensor sweeps through an area and many accurate magnetic field measurements are often needed, caesium and potassium magnetometers have advantages over the proton magnetometer.
The caesium and potassium magnetometer's faster measurement rate allows the sensor to be moved through the area more quickly for a given number of data points. Caesium and potassium magnetometers are insensitive to rotation of the sensor while the measurement is being made.
The lower noise of caesium and potassium magnetometers allow those measurements to more accurately show the variations in the field with position.
Vector magnetometers measure one or more components of the magnetic field electronically. Using three orthogonal magnetometers, both azimuth and dip (inclination) can be measured. By taking the square root of the sum of the squares of the components the total magnetic field strength (also called total magnetic intensity, TMI) can be calculated by the Pythagorean theorem .
Vector magnetometers are subject to temperature drift and the dimensional instability of the ferrite cores. They also require leveling to obtain component information, unlike total field (scalar) instruments. For these reasons they are no longer used for mineral exploration.
The magnetic field induces a sine wave in a rotating coil . The amplitude of the signal is proportional to the strength of the field, provided it is uniform, and to the sine of the angle between the rotation axis of the coil and the field lines. This type of magnetometer is obsolete.
The most common magnetic sensing devices are solid-state Hall effect sensors. These sensors produce a voltage proportional to the applied magnetic field and also sense polarity. They are used in applications where the magnetic field strength is relatively large, such as in anti-lock braking systems in cars, which sense wheel rotation speed via slots in the wheel disks.
These are made of thin strips of Permalloy , a high magnetic permeability , nickel-iron alloy, whose electrical resistance varies with a change in magnetic field. They have a well-defined axis of sensitivity, can be produced in 3-D versions and can be mass-produced as an integrated circuit. They have a response time of less than 1 microsecond and can be sampled in moving vehicles up to 1,000 times/second. They can be used in compasses that read within 1°, for which the underlying sensor must reliably resolve 0.1°. [ 27 ]
A fluxgate magnetometer consists of a small magnetically susceptible core wrapped by two coils of wire. An alternating electric current is passed through one coil, driving the core through an alternating cycle of magnetic saturation ; i.e., magnetised, unmagnetised, inversely magnetised, unmagnetised, magnetised, and so forth. This constantly changing field induces a voltage in the second coil which is measured by a detector. In a magnetically neutral background, the input and output signals match. However, when the core is exposed to a background field, it is more easily saturated in alignment with that field and less easily saturated in opposition to it. Hence the alternating magnetic field and the induced output voltage, are out of step with the input current. The extent to which this is the case depends on the strength of the background magnetic field. Often, the signal in the output coil is integrated, yielding an output analog voltage proportional to the magnetic field.
The fluxgate magnetometer was invented by H. Aschenbrenner and G. Goubau in 1936. [ 22 ] [ 28 ] : 4 A team at Gulf Research Laboratories led by Victor Vacquier developed airborne fluxgate magnetometers to detect submarines during World War II and after the war confirmed the theory of plate tectonics by using them to measure shifts in the magnetic patterns on the sea floor. [ 29 ]
A wide variety of sensors are currently available and used to measure magnetic fields. Fluxgate compasses and gradiometers measure the direction and magnitude of magnetic fields. Fluxgates are affordable, rugged and compact with miniaturization recently advancing to the point of complete sensor solutions in the form of IC chips, including examples from both academia [ 30 ] and industry. [ 31 ] This, plus their typically low power consumption makes them ideal for a variety of sensing applications. Gradiometers are commonly used for archaeological prospecting, and unexploded ordnance (UXO) detection such as the German military's popular Foerster . [ 32 ] Utility location specialists also use gradiometers for locating underground utilities such as pipeline valves, septic tanks, and manhole covers. [ 33 ]
The typical fluxgate magnetometer consists of a "sense" (secondary) coil surrounding an inner "drive" (primary) coil that is closely wound around a highly permeable core material, such as mu-metal or permalloy . An alternating current is applied to the drive winding, which drives the core in a continuous repeating cycle of saturation and unsaturation. To an external field, the core is alternately weakly permeable and highly permeable. The core is often a toroidally wrapped ring or a pair of linear elements whose drive windings are each wound in opposing directions. Such closed flux paths minimise coupling between the drive and sense windings. In the presence of an external magnetic field, with the core in a highly permeable state, such a field is locally attracted or gated (hence the name fluxgate) through the sense winding. When the core is weakly permeable, the external field is less attracted. This continuous gating of the external field in and out of the sense winding induces a signal in the sense winding, whose principal frequency is twice that of the drive frequency, and whose strength and phase orientation vary directly with the external-field magnitude and polarity.
There are additional factors that affect the size of the resultant signal. These factors include the number of turns in the sense winding, magnetic permeability of the core, sensor geometry, and the gated flux rate of change with respect to time.
Phase synchronous detection is used to extract these harmonic signals from the sense winding and convert them into a DC voltage proportional to the external magnetic field. Active current feedback may also be employed, such that the sense winding is driven to counteract the external field. In such cases, the feedback current varies linearly with the external magnetic field and is used as the basis for measurement. This helps to counter inherent non-linearity between the applied external field strength and the flux gated through the sense winding.
SQUIDs , or superconducting quantum interference devices, measure extremely small changes in magnetic fields. They are very sensitive vector magnetometers, with noise levels as low as 3 fT Hz −½ in commercial instruments and 0.4 fT Hz −½ in experimental devices. Many liquid-helium-cooled commercial SQUIDs achieve a flat noise spectrum from near DC (less than 1 Hz) to tens of kilohertz, making such devices ideal for time-domain biomagnetic signal measurements. SERF atomic magnetometers demonstrated in laboratories so far reach competitive noise floor but in relatively small frequency ranges.
SQUID magnetometers require cooling with liquid helium ( 4.2 K ) or liquid nitrogen ( 77 K ) to operate, hence the packaging requirements to use them are rather stringent both from a thermal-mechanical as well as magnetic standpoint. SQUID magnetometers are most commonly used to measure the magnetic fields produced by laboratory samples, also for brain or heart activity ( magnetoencephalography and magnetocardiography , respectively). Geophysical surveys use SQUIDs from time to time, but the logistics of cooling the SQUID are much more complicated than other magnetometers that operate at room temperature.
Magnetometers based on atomic gasses can perform vector measurements of the magnetic field in the low field regime, where the decay of the atomic coherence becomes faster than the Larmor frequency . The physics of such magnetometers is based on the Hanle effect . Such zero-field optically pumped magnetometers have been tested in various configurations and with different atomic species, notably alkali (potassium, rubidium and cesium), helium and mercury . For the case of alkali, the coherence times were greatly limited due to spin-exchange relaxation. A major breakthrough happened at the beginning of the 2000 decade, Romalis group in Princeton demonstrated that in such a low field regime, alkali coherence times can be greatly enhanced if a high enough density can be reached by high temperature heating, this is the so-called SERF effect .
The main interest of optically-pumped magnetometers is to replace SQUID magnetometers in applications where cryogenic cooling is a drawback. This is notably the case of medical imaging where such cooling imposes a thick thermal insulation, strongly affecting the amplitude of the recorded biomagnetic signals. Several startup companies are currently developing optically pumped magnetometers for biomedical applications: those of TwinLeaf, [ 34 ] quSpin [ 35 ] and FieldLine [ 36 ] being based on alkali vapors, and those of Mag4Health on metastable helium-4. [ 37 ]
At sufficiently high atomic density, extremely high sensitivity can be achieved. Spin-exchange-relaxation-free ( SERF ) atomic magnetometers containing potassium , caesium , or rubidium vapor operate similarly to the caesium magnetometers described above, yet can reach sensitivities lower than 1 fT Hz − 1 ⁄ 2 . The SERF magnetometers only operate in small magnetic fields. The Earth's field is about 50 μT ; SERF magnetometers operate in fields less than 0.5 μT.
Large volume detectors have achieved a sensitivity of 200 aT Hz − 1 ⁄ 2 . [ 38 ] This technology has greater sensitivity per unit volume than SQUID detectors. [ 39 ] The technology can also produce very small magnetometers that may in the future replace coils for detecting radio-frequency magnetic fields. [ citation needed ] This technology may produce a magnetic sensor that has all of its input and output signals in the form of light on fiber-optic cables. [ 40 ] This lets the magnetic measurement be made near high electrical voltages.
The calibration of magnetometers is usually performed by means of coils which are supplied by an electrical current to create a magnetic field. It allows to characterize the sensitivity of the magnetometer (in terms of V/T). In many applications the homogeneity of the calibration coil is an important feature. For this reason, coils like Helmholtz coils are commonly used either in a single axis or a three axis configuration. For demanding applications a high homogeneity magnetic field is mandatory, in such cases magnetic field calibration can be performed using a Maxwell coil , cosine coils, [ 41 ] or calibration in the highly homogenous Earth's magnetic field .
Magnetometers have a very diverse range of applications, including locating objects such as submarines, sunken ships, hazards affecting tunnel boring machines , coal mine hazards, unexploded ordnance, toxic waste drums, as well as a wide range of mineral deposits and geological structures. They also have applications in heart beat monitors, concealed weapons detection, [ 42 ] military weapon systems positioning, sensors in anti-locking brakes, weather prediction (via solar cycles), steel pylons, drill guidance systems, archaeology, plate tectonics, radio wave propagation, and planetary exploration. Laboratory magnetometers determine the magnetic dipole moment of a magnetic sample, typically as a function of temperature , magnetic field , or other parameter. This helps to reveal its magnetic properties such as ferromagnetism , antiferromagnetism , superconductivity , or other properties that affect magnetism .
Depending on the application, magnetometers can be deployed in spacecraft, aeroplanes ( fixed wing magnetometers), helicopters ( stinger and bird ), on the ground ( backpack ), towed at a distance behind quad bikes (ATVs) on a ( sled or trailer ), lowered into boreholes ( tool , probe, or sonde ), or towed behind boats ( tow fish ).
Magnetometers are used to measure or monitor mechanical stress in ferromagnetic materials. Mechanical stress will improve alignment of magnetic domains in microscopic scale that will raise the magnetic field measured close to the material by magnetometers. There are different hypothesis about stress-magnetisation relationship. However the effect of mechanical stress on measured magnetic field near the specimen is claimed to be proven in many scientific publications. There have been efforts to solve the inverse problem of magnetisation-stress resolution in order to quantify the stress based on measured magnetic field. [ 43 ] [ 44 ]
Magnetometers are used extensively in experimental particle physics to measure the magnetic field of pivotal components such as the concentration or focusing beam-magnets.
Magnetometers are also used to detect archaeological sites , shipwrecks , and other buried or submerged objects. Fluxgate gradiometers are popular due to their compact configuration and relatively low cost. Gradiometers enhance shallow features and negate the need for a base station. Caesium and Overhauser magnetometers are also very effective when used as gradiometers or as single-sensor systems with base stations.
The TV program Time Team popularised 'geophys', including magnetic techniques used in archaeological work to detect fire hearths, walls of baked bricks and magnetic stones such as basalt and granite. Walking tracks and roadways can sometimes be mapped with differential compaction in magnetic soils or with disturbances in clays, such as on the Great Hungarian Plain . Ploughed fields behave as sources of magnetic noise in such surveys.
Magnetometers can give an indication of auroral activity before the light from the aurora becomes visible. A grid of magnetometers around the world constantly measures the effect of the solar wind on the Earth's magnetic field, which is then published on the K-index . [ 45 ]
While magnetometers can be used to help map basin shape at a regional scale, they are more commonly used to map hazards to coal mining, such as basaltic intrusions ( dykes , sills , and volcanic plug ) that destroy resources and are dangerous to longwall mining equipment. Magnetometers can also locate zones ignited by lightning and map siderite (an impurity in coal).
The best survey results are achieved on the ground in high-resolution surveys (with approximately 10 m line spacing and 0.5 m station spacing). Bore-hole magnetometers using a Ferret [ clarification needed ] can also assist when coal seams are deep, by using multiple sills or looking beneath surface basalt flows. [ citation needed ]
Modern surveys generally use magnetometers with GPS technology to automatically record the magnetic field and their location. The data set is then corrected with data from a second magnetometer (the base station) that is left stationary and records the change in the Earth's magnetic field during the survey. [ 46 ]
Magnetometers are used in directional drilling for oil or gas to detect the azimuth of the drilling tools near the drill. [ 47 ] They are most often paired with accelerometers in drilling tools so that both the inclination and azimuth of the drill can be found. [ 47 ]
For defensive purposes, navies use arrays of magnetometers laid across sea floors in strategic locations (i.e. around ports) to monitor submarine activity. The Russian Alfa-class titanium submarines were designed and built at great expense to thwart such systems (as pure titanium is non-magnetic). [ 48 ]
Military submarines are degaussed —by passing through large underwater loops at regular intervals—to help them escape detection by sea-floor monitoring systems, magnetic anomaly detectors , and magnetically-triggered mines. However, submarines are never completely de-magnetised. It is possible to tell the depth at which a submarine has been by measuring its magnetic field, which is distorted as the pressure distorts the hull and hence the field. Heating can also change the magnetization of steel. [ clarification needed ]
Submarines tow long sonar arrays to detect ships, and can even recognise different propeller noises. The sonar arrays need to be accurately positioned so they can triangulate direction to targets (e.g. ships). The arrays do not tow in a straight line, so fluxgate magnetometers are used to orient each sonar node in the array.
Fluxgates can also be used in weapons navigation systems, but have been largely superseded by GPS and ring laser gyroscopes .
Magnetometers such as the German Foerster are used to locate ferrous ordnance. Caesium and Overhauser magnetometers are used to locate and help clean up old bombing and test ranges.
UAV payloads also include magnetometers for a range of defensive and offensive tasks. [ example needed ]
Magnetometric surveys can be useful in defining magnetic anomalies which represent ore (direct detection), or in some cases gangue minerals associated with ore deposits (indirect or inferential detection). This includes iron ore , magnetite , hematite , and often pyrrhotite .
Developed countries such as Australia, Canada and USA invest heavily in systematic airborne magnetic surveys of their respective continents and surrounding oceans, to assist with map geology and in the discovery of mineral deposits. Such aeromag surveys are typically undertaken with 400 m line spacing at 100 m elevation, with readings every 10 meters or more. To overcome the asymmetry in the data density, data is interpolated between lines (usually 5 times) and data along the line is then averaged. Such data is gridded to an 80 m × 80 m pixel size and image processed using a program like ERMapper. At an exploration lease scale, the survey may be followed by a more detailed helimag or crop duster style fixed wing at 50 m line spacing and 50 m elevation (terrain permitting). Such an image is gridded on a 10 x 10 m pixel, offering 64 times the resolution.
Where targets are shallow (<200 m), aeromag anomalies may be followed up with ground magnetic surveys on 10 m to 50 m line spacing with 1 m station spacing to provide the best detail (2 to 10 m pixel grid) (or 25 times the resolution prior to drilling).
Magnetic fields from magnetic bodies of ore fall off with the inverse distance cubed ( dipole target), or at best inverse distance squared ( magnetic monopole target). One analogy to the resolution-with-distance is a car driving at night with lights on. At a distance of 400 m one sees one glowing haze, but as it approaches, two headlights, and then the left blinker, are visible.
There are many challenges interpreting magnetic data for mineral exploration. Multiple targets mix together like multiple heat sources and, unlike light, there is no magnetic telescope to focus fields. The combination of multiple sources is measured at the surface. The geometry, depth, or magnetisation direction (remanence) of the targets are also generally not known, and so multiple models can explain the data.
Potent by Geophysical Software Solutions [1] is a leading magnetic (and gravity) interpretation package used extensively in the Australian exploration industry.
Magnetometers assist mineral explorers both directly (i.e., gold mineralisation associated with magnetite , diamonds in kimberlite pipes ) and, more commonly, indirectly, such as by mapping geological structures conducive to mineralisation (i.e., shear zones and alteration haloes around granites).
Airborne Magnetometers detect the change in the Earth's magnetic field using sensors attached to the aircraft in the form of a "stinger" or by towing a magnetometer on the end of a cable. The magnetometer on a cable is often referred to as a "bomb" because of its shape. Others call it a "bird".
Because hills and valleys under the aircraft make the magnetic readings rise and fall, a radar altimeter keeps track of the transducer's deviation from the nominal altitude above ground. There may also be a camera that takes photos of the ground. The location of the measurement is determined by also recording a GPS.
Many smartphones contain miniaturized microelectromechanical systems (MEMS) magnetometers which are used to detect magnetic field strength and are used as compasses . The iPhone 3GS has a magnetometer, a magnetoresistive permalloy sensor, the AN-203 produced by Honeywell. [ 49 ] In 2009, the price of three-axis magnetometers dipped below US$1 per device and dropped rapidly. The use of a three-axis device means that it is not sensitive to the way it is held in orientation or elevation. Hall effect devices are also popular. [ 50 ]
Researchers at Deutsche Telekom have used magnetometers embedded in mobile devices to permit touchless 3D interaction . Their interaction framework, called MagiTact, tracks changes to the magnetic field around a cellphone to identify different gestures made by a hand holding or wearing a magnet. [ 51 ]
Seismic methods are preferred to magnetometers as the primary survey method for oil exploration although magnetic methods can give additional information about the underlying geology and in some environments evidence of leakage from traps. [ 52 ] Magnetometers are also used in oil exploration to show locations of geologic features that make drilling impractical, and other features that give geophysicists a more complete picture of stratigraphy .
A three-axis fluxgate magnetometer was part of the Mariner 2 and Mariner 10 missions. [ 53 ] A dual technique magnetometer is part of the Cassini–Huygens mission to explore Saturn. [ 54 ] This system is composed of a vector helium and fluxgate magnetometers. [ 55 ] Magnetometers were also a component instrument on the Mercury MESSENGER mission. A magnetometer can also be used by satellites like GOES to measure both the magnitude and direction of the magnetic field of a planet or moon.
Systematic surveys can be used to in searching for mineral deposits or locating lost objects. Such surveys are divided into:
Aeromag datasets for Australia can be downloaded from the GADDS database .
Data can be divided in point located and image data, the latter of which is in ERMapper format.
On the base of space measured distribution of magnetic field parameters (e.g. amplitude or direction), the magnetovision images may be generated. Such presentation of magnetic data is very useful for further analyse and data fusion .
Magnetic gradiometers are pairs of magnetometers with their sensors separated, usually horizontally, by a fixed distance. The readings are subtracted to measure the difference between the sensed magnetic fields, which gives the field gradients caused by magnetic anomalies. This is one way of compensating both for the variability in time of the Earth's magnetic field and for other sources of electromagnetic interference, thus allowing for more sensitive detection of anomalies. Because nearly equal values are being subtracted, the noise performance requirements for the magnetometers is more extreme.
Gradiometers enhance shallow magnetic anomalies and are thus good for archaeological and site investigation work. They are also good for real-time work such as unexploded ordnance (UXO) location. It is twice as efficient to run a base station and use two (or more) mobile sensors to read parallel lines simultaneously (assuming data is stored and post-processed). In this manner, both along-line and cross-line gradients can be calculated.
In traditional mineral exploration and archaeological work, grid pegs placed by theodolite and tape measure were used to define the survey area. Some UXO surveys used ropes to define the lanes. Airborne surveys used radio triangulation beacons, such as Siledus.
Non-magnetic electronic hipchain triggers were developed to trigger magnetometers. They used rotary shaft encoders to measure distance along disposable cotton reels.
Modern explorers use a range of low-magnetic signature GPS units, including real-time kinematic GPS.
Magnetic surveys can suffer from noise coming from a range of sources. Different magnetometer technologies suffer different kinds of noise problems.
Heading errors are one group of noise. They can come from three sources:
Some total field sensors give different readings depending on their orientation. Magnetic materials in the sensor itself are the primary cause of this error. In some magnetometers, such as the vapor magnetometers (caesium, potassium, etc.), there are sources of heading error in the physics that contribute small amounts to the total heading error.
Console noise comes from magnetic components on or within the console. These include ferrite in cores in inductors and transformers, steel frames around LCDs, legs on IC chips and steel cases in disposable batteries. Some popular MIL spec connectors also have steel springs.
Operators must take care to be magnetically clean and should check the 'magnetic hygiene' of all apparel and items carried during a survey. Akubra hats are very popular in Australia, but their steel rims must be removed before use on magnetic surveys. Steel rings on notepads, steel capped boots and steel springs in overall eyelets can all cause unnecessary noise in surveys. Pens, mobile phones and stainless steel implants can also be problematic.
The magnetic response (noise) from ferrous object on the operator and console can change with heading direction because of induction and remanence. Aeromagnetic survey aircraft and quad bike systems can use special compensators to correct for heading error noise.
Heading errors look like herringbone patterns in survey images. Alternate lines can also be corrugated.
Recording data and image processing is superior to real-time work because subtle anomalies often missed by the operator (especially in magnetically noisy areas) can be correlated between lines, shapes and clusters better defined. A range of sophisticated enhancement techniques can also be used. There is also a hard copy and need for systematic coverage.
The Magnetometer Navigation (MAGNAV) algorithm was initially running as a flight experiment in 2004. [ 56 ] Later on, diamond magnetometers were developed by the United States Air Force Research Laboratory (AFRL) as a better method of navigation which cannot be jammed by the enemy. [ 57 ] | https://en.wikipedia.org/wiki/Magnetometer |
In physics , the magnetomotive force (abbreviated mmf or MMF , symbol F {\displaystyle {\mathcal {F}}} ) is a quantity appearing in the equation for the magnetic flux in a magnetic circuit , Hopkinson's law. [ 1 ] It is the property of certain substances or phenomena that give rise to magnetic fields : F = Φ R , {\displaystyle {\mathcal {F}}=\Phi {\mathcal {R}},} where Φ is the magnetic flux and R {\displaystyle {\mathcal {R}}} is the reluctance of the circuit. It can be seen that the magnetomotive force plays a role in this equation analogous to the voltage V in Ohm's law , V = IR , since it is the cause of magnetic flux in a magnetic circuit: [ 2 ]
The SI unit of mmf is the ampere , the same as the unit of current [ 3 ] (analogously the units of emf and voltage are both the volt ). Informally, and frequently, this unit is stated as the ampere-turn to avoid confusion with current. This was the unit name in the MKS system . Occasionally, the cgs system unit of the gilbert may also be encountered.
The term magnetomotive force was coined by Henry Augustus Rowland in 1880. Rowland intended this to indicate a direct analogy with electromotive force . [ 4 ] The idea of a magnetic analogy to electromotive force can be found much earlier in the work of Michael Faraday (1791–1867) and it is hinted at by James Clerk Maxwell (1831–1879). However, Rowland coined the term and was the first to make explicit an Ohm's law for magnetic circuits in 1873. [ 5 ]
Ohm's law for magnetic circuits is sometimes referred to as Hopkinson's law rather than Rowland's law as some authors attribute the law to John Hopkinson instead of Rowland. [ 6 ] According to a review of magnetic circuit analysis methods this is an incorrect attribution originating from an 1885 paper by Hopkinson. [ 7 ] Furthermore, Hopkinson actually cites Rowland's 1873 paper in this work. [ 8 ] | https://en.wikipedia.org/wiki/Magnetomotive_force |
Magnetomyography ( MMG ) is a technique for mapping muscle activity by recording magnetic fields produced by electrical currents occurring naturally in the muscles , using arrays of SQUIDs (superconducting quantum interference devices). [ 1 ] It has a better capability than electromyography for detecting slow or direct currents. The magnitude of the MMG signal is in the scale of pico (10^−12) to femto (10^−15) Tesla (T). Miniaturizing MMG offers a prospect to modernize the bulky SQUID to wearable miniaturized magnetic sensors. [ 2 ]
Two key drivers for the development of the MMG method: [ 3 ] 1) poor spatial resolution of the EMG signals when recorded non-invasively on the skin where state-of-the-art EMG measurements are even using needle recording probes, which is possible to accurately assess muscle activity but painful and limited to tiny areas with poor spatial sampling points; 2) poor biocompatibility of the implantable EMG sensors due to the metal-tissue interface. The MMG sensors have the potential to address both shortcomings concurrently because: 1) the size of magnetic field reduces significantly with the distance between the origin and the sensor, thereby with MMG spatial resolution is uplifted; and 2) the MMG sensors do not need electrical contacts to record, hence if fully packaged with biocompatible materials or polymers, they can improve long-term biocompatibility.
At the early 18th century, the electric signals from living tissues have been investigated. These researchers have promoted many innovations in healthcare especially in medical diagnostic. Some example is based on electrical signals produced by human tissues, including Electrocardiogram (ECG), Electroencephalography (EEG) and Electromyogram (EMG). Besides, with the development of technologies, the biomagnetic measurement from the human body, consisting of Magnetocardiogram (MCG), Magnetoencephalography (MEG) and Magnetomyogram (MMG), provided clear evidence that the existence of the magnetic fields from ionic action currents in electrically active tissues can be utilized to record activities. For the first attempt, David Cohen used a point-contact superconducting quantum interference device (SQUID) magnetometer in a shielded room to measure the MCG. They reported that the sensitivity of the recorded MCG was orders of magnitude higher than the previously recorded MCG. The same researcher continued this MEG measurement by using a more sensitive SQUID magnetometer without noise averaging. He compared the EEG and alpha rhythm MEG recorded by both normal and abnormal subjects. It is shown that the MEG has produced some new and different information provided by the EEG. Because the heart can produce a relatively large magnetic field compared to the brain and other organs, the early biomagnetic field research originated from the mathematical modelling of MCG. Early experimental studies also focused on the MCG. In addition, these experimental studies suffer from unavoidable low spatial resolution and low sensitivity due to the lack of sophisticated detection methods. With advances in technology, research has expanded into brain function, and preliminary studies of evoked MEGs began in the 1980s.
These studies provided some details about which neuronal populations were contributing to the magnetic signals generated from the brain. However, the signals from single neurons were too weak to be detected. A group of over 10,000 dendrites is required as a group to generate a detectable MEG signal. At the time, the abundance of physical, technical, and mathematical limitations prevented quantitative comparisons of theories and experiments involving human electrocardiograms and other biomagnetic records. Due to the lack of an accurate micro source model, it is more difficult to determine which specific physiological factors influence the strength of MEG and other biomagnetic signals and which factors dominate the achievable spatial resolution.
In the past three decades, a great deal of research has been conducted to measure and analyze the magnetic field generated by the flow of ex vivo currents in isolated axons and muscle fibers. These measurements have been supported by some complex theoretical studies and the development of ultra-sensitive room temperature amplifiers and neuromagnetic current probes. Nowadays, cell-level magnetic recording technology has become a quantitative measurement technique for operating currents.
Nowadays, the MMG signals can become an important indicator in medical diagnosis, rehabilitation, health monitoring and robotics control. Recent advances in technology have paved the way to remotely and continuously record and diagnosis individuals’ disease of the muscle and the peripheral nerve. [ 4 ] [ 5 ] Motivated by exploring the electrophysiological behavior of the uterus prior to childbirth, MMG was used mainly on health monitoring during pregnancy. [ 6 ] [ 7 ] [ 8 ] In addition, the MMG has the potential to be used in the rehabilitation such as the traumatic nerve injury, spinal cord lesion, and entrapment syndrome. [ 9 ] [ 10 ] [ 11 ] [ 12 ]
The magnitude of the MMG signals is lower than that of the heart and the brain. [ 10 ] The minimum spectral density could reach limit of detection (LOD) of hundreds of fT/√Hz at low frequencies especially between 10 Hz and 100 Hz. In a seminal work of Cohen and Gilver in 1972, they discovered and recorded MMG signals using S uperconducting QU antum I nterference D evices (SQUIDs). They led the development of MMG until now since it is the most sensitive device at moment with the femto-Tesla limit of detection (LOD), and possibly achieve atto-Tesla LOD with averaging. [ 13 ] The state-of-the-art MMG measurement is dominated by SQUIDs. [ 14 ] Nonetheless, their ultra-high cost and cumbersome weight limit the spread of this magnetic sensing technique. In the last several years, optically pumped magnetometers (OPMs) have been rapidly developed to study the innervation of the hand nerves and muscles as proof-of-concept investigations. [ 11 ] [ 15 ] [ 16 ] The OPMs with small physical size have been improved their LODs significantly during recent years, especially from competing manufacturers e.g. QuSpin Inc., FieldLine Inc. and Twinleaf. Below 100 fT/√Hz sensitivity has been achieved with OPMs. [ 17 ] [ 18 ] The MMG has not been a common method yet mainly due to its small magnitude, which can be easily affected by the magnetic noise in surrounding. For instance, the amplitude of the Earth magnetic field is about five million times larger and environmental noise from power lines can reach a level of nano-Tesla. Additionally, current experiments based on SQUIDs and OPMs for MMG sensing are conducted in heavily shielded rooms, which are expensive and bulky for personal daily use. Consequently, the development of miniaturised, low-cost and room temperature biomagnetic sensing methods would constitute an important step towards the wider appreciation of biomagnetism.
A high-performance Hall sensor has been successfully performed with its integrated readout circuit in CMOS technology. [ 2 ] However, Hall sensors require a highly stable DC power supply to excite the Hall effect and a complex interface circuit to process collected weak Hall voltages under surrounding noise. [ 19 ] Recently miniaturised tunneling magnetoresistive sensors [ 20 ] [ 21 ] as well as magnetoelectric sensors [ 22 ] have been proposed for the future of the MMG in the form of wearable devices. They are CMOS compatible and their sensor output can be readout by an analogue front-end. [ 23 ] The miniaturized TMR sensor could be an effective alternative for future MMG measurements with relatively low operating costs. | https://en.wikipedia.org/wiki/Magnetomyography |
Magnetoresistance is the tendency of a material (often ferromagnetic ) to change the value of its electrical resistance in an externally-applied magnetic field . There are a variety of effects that can be called magnetoresistance. Some occur in bulk non-magnetic metals and semiconductors, such as geometrical magnetoresistance, Shubnikov–de Haas oscillations , or the common positive magnetoresistance in metals. [ 1 ] Other effects occur in magnetic metals, such as negative magnetoresistance in ferromagnets [ 2 ] or anisotropic magnetoresistance (AMR). Finally, in multicomponent or multilayer systems (e.g. magnetic tunnel junctions), giant magnetoresistance (GMR), tunnel magnetoresistance (TMR), colossal magnetoresistance (CMR), and extraordinary magnetoresistance (EMR) can be observed.
The first magnetoresistive effect was discovered in 1856 by William Thomson , better known as Lord Kelvin, but he was unable to lower the electrical resistance of anything by more than 5%. Today, systems including semimetals [ 3 ] and concentric ring EMR structures are known. In these, a magnetic field can adjust the resistance by orders of magnitude. Since different mechanisms can alter the resistance, it is useful to separately consider situations where it depends on a magnetic field directly (e.g. geometric magnetoresistance and multiband magnetoresistance) and those where it does so indirectly through magnetization (e.g. AMR and TMR ).
William Thomson (Lord Kelvin) first discovered ordinary magnetoresistance in 1856. [ 4 ] He experimented with pieces of iron and discovered that the resistance increases when the current is in the same direction as the magnetic force and decreases when the current is at 90° to the magnetic force. He then did the same experiment with nickel and found that it was affected in the same way but the magnitude of the effect was greater. This effect is referred to as anisotropic magnetoresistance (AMR).
In 2007, Albert Fert and Peter Grünberg were jointly awarded the Nobel Prize for the discovery of giant magnetoresistance . [ 5 ]
An example of magnetoresistance due to direct action of magnetic field on electric current can be studied on a Corbino disc (see Figure).
It consists of a conducting annulus with perfectly conducting rims. Without a magnetic field, the battery drives a radial current between the rims. When a magnetic field perpendicular to the plane of the annulus is applied, (either into or out of the page) a circular component of current flows as well, due to Lorentz force . Initial interest in this problem began with Boltzmann in 1886, and independently was re-examined by Corbino in 1911. [ 6 ]
In a simple model, supposing the response to the Lorentz force is the same as for an electric field, the carrier velocity v is given by: v = μ ( E + v × B ) , {\displaystyle \mathbf {v} =\mu \left(\mathbf {E} +\mathbf {v\times B} \right),} where μ is the carrier mobility . Solving for the velocity, we find:
v = μ 1 + ( μ B ) 2 ( E + μ E × B + μ 2 ( B ⋅ E ) B ) = μ 1 + ( μ B ) 2 ( E ⊥ + μ E × B ) + μ E ∥ {\displaystyle {\begin{aligned}\mathbf {v} &={\frac {\mu }{1+(\mu B)^{2}}}\left(\mathbf {E} +\mu \mathbf {E\times B} +\mu ^{2}(\mathbf {B\cdot E} )\mathbf {B} \right)\\&={\frac {\mu }{1+(\mu B)^{2}}}\left(\mathbf {E} _{\perp }+\mu \mathbf {E\times B} \right)+\mu \mathbf {E} _{\parallel }\,\end{aligned}}}
where the effective reduction in mobility due to the B -field (for motion perpendicular to this field) is apparent. Electric current (proportional to the radial component of velocity) will decrease with increasing magnetic field and hence the resistance of the device will increase. Critically, this magnetoresistive scenario depends sensitively on the device geometry and current lines and it does not rely on magnetic materials.
In a semiconductor with a single carrier type, the magnetoresistance is proportional to (1 + ( μB ) 2 ) , where μ is the semiconductor mobility (units m 2 ·V −1 ·s −1 , equivalently m 2 ·Wb −1 , or T −1 ) and B is the magnetic field (units teslas ). Indium antimonide , an example of a high mobility semiconductor, could have an electron mobility above 4 m 2 / Wb at 300 K . So in a 0.25 T field, for example the magnetoresistance increase would be 100%.
Thomson's experiments [ 4 ] are an example of AMR, [ 7 ] a property of a material in which a dependence of electrical resistance on the angle between the direction of electric current and direction of magnetization is observed. The effect arises in most cases from the simultaneous action of magnetization and spin–orbit interaction (exceptions related to non-collinear magnetic order notwithstanding) [ 8 ] and its detailed mechanism depends on the material. It can be for example due to a larger probability of s-d scattering of electrons in the direction of magnetization (which is controlled by the applied magnetic field). The net effect (in most materials) is that the electrical resistance has maximum value when the direction of current is parallel to the applied magnetic field. [ 9 ] AMR of new materials is being investigated and magnitudes up to 50% have been observed in some uranium (but otherwise quite conventional) ferromagnetic compounds. [ 10 ] Materials with extreme AMR have been identified [ 11 ] driven by unconventional mechanisms such as a metal-insulator transition triggered by rotating the magnetic moments (while for some directions of magnetic moments, the system is semimetallic, for other directions a gap opens).
In polycrystalline ferromagnetic materials, the AMR can only depend on the angle φ = ψ − θ between the magnetization and current direction and (as long as the resistivity of the material can be described by a rank-two tensor ), it must follow [ 12 ] ρ ( φ ) = ρ ⊥ + ( ρ ∥ − ρ ⊥ ) cos 2 φ {\displaystyle \rho (\varphi )=\rho _{\perp }+(\rho _{\parallel }-\rho _{\perp })\cos ^{2}\varphi } where ρ is the (longitudinal) resistivity of the film and ρ ∥,⟂ are the resistivities for φ = 0° and φ = 90° , respectively. Associated with longitudinal resistivity, there is also transversal resistivity dubbed (somewhat confusingly [ a ] ) the planar Hall effect. In monocrystals, resistivity ρ depends also on ψ and θ individually.
To compensate for the non-linear characteristics and inability to detect the polarity of a magnetic field, the following structure is used for sensors. It consists of stripes of aluminum or gold placed on a thin film of permalloy (a ferromagnetic material exhibiting the AMR effect) inclined at an angle of 45°. This structure forces the current not to flow along the “easy axes” of thin film, but at an angle of 45°. The dependence of resistance now has a permanent offset which is linear around the null point. Because of its appearance, this sensor type is called ' barber pole '.
The AMR effect is used in a wide array of sensors for measurement of Earth's magnetic field (electronic compass ), for electric current measuring (by measuring the magnetic field created around the conductor), for traffic detection and for linear position and angle sensing. The biggest AMR sensor manufacturers are Honeywell , NXP Semiconductors , STMicroelectronics , and Sensitec GmbH .
As theoretical aspects, I. A. Campbell, A. Fert, and O. Jaoul ( CFJ ) [ 13 ] derived an expression of the AMR ratio for Ni-based alloys using the two-current model with s-s and s-d scattering processes, where 's' is a conduction electron, and 'd' is 3d states with the spin-orbit interaction. The AMR ratio is expressed as Δ ρ ρ = ρ ∥ − ρ ⊥ ρ ⊥ = γ ( α − 1 ) , {\displaystyle {\frac {\Delta \rho }{\rho }}={\frac {\rho _{\parallel }-\rho _{\perp }}{\rho _{\perp }}}=\gamma (\alpha -1),} with γ = ( 3 / 4 ) ( A / H ) 2 {\displaystyle \gamma =(3/4)(A/H)^{2}} and α = ρ ↓ / ρ ↑ {\displaystyle \alpha =\rho _{\downarrow }/\rho _{\uparrow }} , where A {\displaystyle A} , H {\displaystyle H} , and ρ σ {\displaystyle \rho _{\sigma }} are a spin-orbit coupling constant (so-called ζ {\displaystyle \zeta } ), an exchange field, and a resistivity for spin σ {\displaystyle \sigma } , respectively. In addition, recently, Satoshi Kokado et al. [ 14 ] [ 15 ] have obtained the general expression of the AMR ratio for 3d transition-metal ferromagnets by extending the CFJ theory to a more general one. The general expression can also be applied to half-metals. | https://en.wikipedia.org/wiki/Magnetoresistance |
A magnetorheological damper or magnetorheological shock absorber is a damper filled with magnetorheological fluid , which is controlled by a magnetic field , usually using an electromagnet . [ 1 ] [ 2 ] [ 3 ] This allows the damping characteristics of the shock absorber to be continuously controlled by varying the power of the electromagnet. Fluid viscosity increases within the damper as electromagnet intensity increases. This type of shock absorber has several applications, most notably in semi-active vehicle suspensions which may adapt to road conditions, as they are monitored through sensors in the vehicle, and in prosthetic limbs . [ 4 ]
Many applications have been proposed using magnetorheological (MR) dampers. While vehicle applications are the most common use of MR dampers, useful medical applications have risen as well, including implants and rehabilitation methods. [ 6 ] Since MR dampers are not yet perfect, they are limited in terms of application. Disadvantages do exist when using a large scale MR damper, for example, particle settling within the carrier fluid may occur that inhibits some possible application.
The technology was originally developed by General Motors Delphi Automotive Division based in the USA and then developed further by BeijingWest Industries in China after BeijingWest Industries bought the technology from General Motors. BeijingWest Industries has subsequently introduced improvements including a redesigned ECU and the introduction of a dual coil system. The first car to use the technology was the 2002.5 Cadillac Seville STS, and the first sports car to use the technology was the 2003 C5 Corvette .
These types of systems are available from OEMs for several vehicles, including the Acura MDX , Audi TT and R8 , Buick Lucerne , Cadillac ATS , CTS-V , DTS , XLR , SRX , STS , Chevrolet Corvette , Camaro ZL1 , Ferrari 458 Italia , 599GTB , F12 Berlinetta , Mustang Mach-E , Shelby GT 350 , Holden HSV E-Series ,and Lamborghini Huracán . [ 2 ] [ 7 ] These systems were produced by the Delphi Corporation and now by BWI Group under the proprietary name MagneRide . [ 8 ] [ 9 ]
MillenWorks has also included them in several military vehicles including the MillenWorks Light Utility Vehicle , and in retrofits to the US Army Stryker and HMMWV for testing by TARDEC . [ 10 ] [ 11 ]
MRF-based dampers are excellent candidates for stability augmentation of the lead-lag (in-plane bending) mode of rotor blades in helicopters. [ 12 ] MRF-based squeeze film dampers are being designed for use in the rotary wing industry to isolate vibrations from the aircraft structure and crew. [ 13 ]
A magnetorheological damper is controlled by algorithms specifically designed for the purpose. There are plenty of alternatives, such as skyhook or groundhook algorithms. [ 14 ] The idea of the algorithms is to control the yield point shear stress of the magnetorheological fluid with electric current . When the fluid is in the presence of an applied magnetic field , the suspended metal particles align according to the field lines . Viscosity of the fluid increases according to the intensity of the magnetic field. When this occurs at the right instant, the properties of the damper change helps in attenuating an undesired shock or vibration. The relative efficacy of magnetorheological dampers to active and passive control strategies is usually comparable. [ 15 ] | https://en.wikipedia.org/wiki/Magnetorheological_damper |
Magnetorheological elastomers (MREs) (also called magnetosensitive elastomers) are a class of solids that consist of polymeric matrix with embedded micro- or nano-sized ferromagnetic particles such as carbonyl iron . As a result of this composite microstructure, the mechanical properties of these materials can be controlled by the application of magnetic field. [ 1 ]
MREs are typically prepared by curing process for polymers. The polymeric material (e.g. silicone rubber) in its liquid state is mixed with iron powder and several other additives to enhance their mechanical properties. [ 2 ] The entire mixture is then cured at high temperature. Curing in the presence of a magnetic field causes the iron particles to arrange in chain like structures resulting in an anisotropic material. If magnetic field is not applied, then iron-particles are randomly distributed in the solid resulting in an isotropic material. Recently, in 2017, an advanced technology, 3D printing has also been used to configure the magnetic particles inside the polymer matrix. [ 3 ]
MREs can be classified according to several parameters like: particles type, matrix, structure and distribution of particles: [ citation needed ]
In order to understand magneto-mechanical behaviour of MREs, theoretical studies need to be performed which couple the theories of electromagnetism with mechanics . Such theories are called theories of magneto-mechanics. [ 4 ] [ 5 ]
Magnetopolymers with large remanence are typically formed by combining hard-magnetic particles with a polymer matrix. The orientation of the magnetic particles is typically controlled with an external magnetic field during the polymerization process, and then mechanically fixed after the material is synthesized. Because the Curie temperature of these magnetopolymers exceeds the temperature at which the polymer matrix would break down, they must be degaussed in order to be remagnetized. This means that the functionality of these magnetopolymers is limited and they can only be permanently programmed during manufacturing.
Programmable magnetopolymers embed athermal ferromagnetic particles in droplets of low melting point materials in polymer matrices. [ 6 ] [ 7 ] [ 8 ] Above the droplet melting point, the particles have rotational freedom. The uniqueness of these composites exists in their easily reprogrammable magnetization profiles. This behaviour follows from the fact that particles (1) are athermal, (2) have Curie temperatures above the droplet melting point, and (3) are fixated in solid droplets while possessing full rotational freedom in molten droplets. This easy reprogramming is a critical characteristic for such materials to be used in a wide range of applications. [ 7 ]
MREs have been used for vibration isolation applications since their stiffness changes within a magnetic field [ 9 ] [ 10 ] | https://en.wikipedia.org/wiki/Magnetorheological_elastomer |
A magnetorheological fluid ( MR fluid , or MRF ) is a type of smart fluid in a carrier fluid, usually a type of oil. When subjected to a magnetic field , the fluid greatly increases its apparent viscosity , to the point of becoming a viscoelastic solid. [ 1 ] Importantly, the yield stress of the fluid when in its active ("on") state can be controlled very accurately by varying the magnetic field intensity. The upshot is that the fluid's ability to transmit force can be controlled with an electromagnet , which gives rise to its many possible control-based applications.
MR fluid is different from a ferrofluid which has smaller particles. MR fluid particles are primarily on the micrometre -scale and are too dense for Brownian motion to keep them suspended (in the lower density carrier fluid). Ferrofluid particles are primarily nanoparticles that are suspended by Brownian motion and generally will not settle under normal conditions. As a result, these two fluids have very different applications.
The magnetic particles, which are typically micrometer or nanometer scale spheres or ellipsoids, are suspended within the carrier oil and distributed randomly in suspension under normal circumstances, as below.
When a magnetic field is applied, however, the microscopic particles (usually in the 0.1–10 μm range) align themselves along the lines of magnetic flux , [ 2 ] see below.
To understand and predict the behavior of the MR fluid it is necessary to model the fluid mathematically, a task slightly complicated by the varying material properties (such as yield stress ).
As mentioned above, smart fluids are such that they have a low viscosity in the absence of an applied magnetic field, but become quasi-solid with the application of such a field. In the case of MR fluids (and ER ), the fluid actually assumes properties comparable to a solid when in the activated ("on") state, up until a point of yield (the shear stress above which shearing occurs). This yield stress (commonly referred to as apparent yield stress) is dependent on the magnetic field applied to the fluid, but will reach a maximum point after which increases in magnetic flux density have no further effect, as the fluid is then magnetically saturated. The behavior of a MR fluid can thus be considered similar to a Bingham plastic , a material model which has been well-investigated.
However, MR fluid does not exactly follow the characteristics of a Bingham plastic. For example, below the yield stress (in the activated or "on" state), the fluid behaves as a viscoelastic material, with a complex modulus that is also known to be dependent on the magnetic field intensity. MR fluids are also known to be subject to shear thinning , whereby the viscosity above yield decreases with increased shear rate. Furthermore, the behavior of MR fluids when in the "off" state is also non-Newtonian and temperature dependent, however it deviates little enough for the fluid to be ultimately considered as a Bingham plastic for a simple analysis.
Thus our model of MR fluid behavior in the shear mode becomes:
Where τ {\displaystyle \tau } = shear stress; τ y {\displaystyle \tau _{y}} = yield stress; H {\displaystyle H} = Magnetic field intensity η {\displaystyle \eta } = Newtonian viscosity; d v d z {\displaystyle {\frac {dv}{dz}}} is the velocity gradient in the z-direction.
Low shear strength has been the primary reason for limited range of applications. In the absence of external pressure the maximum shear strength is about 100 kPa. If the fluid is compressed in the magnetic field direction and the compressive stress is 2 MPa, the shear strength is raised to 1100 kPa. [ 3 ] If the standard magnetic particles are replaced with elongated magnetic particles, the shear strength is also improved. [ 4 ]
Ferroparticles settle out of the suspension over time due to the inherent density difference between the particles and their carrier fluid. The rate and degree to which this occurs is one of the primary attributes considered in industry when implementing or designing an MR device. Surfactants are typically used to offset this effect, but at a cost of the fluid's magnetic saturation, and thus the maximum yield stress exhibited in its activated state.
MR fluids often contain surfactants including, but not limited to: [ 5 ]
These surfactants serve to decrease the rate of ferroparticle settling, of which a high rate is an unfavorable characteristic of MR fluids. The ideal MR fluid would never settle, but developing this ideal fluid is as highly improbable as developing a perpetual motion machine according to our current understanding of the laws of physics. Surfactant-aided prolonged settling is typically achieved in one of two ways: by addition of surfactants, and by addition of spherical ferromagnetic nanoparticles. Addition of the nanoparticles results in the larger particles staying suspended longer since the non-settling nanoparticles interfere with the settling of the larger micrometre-scale particles due to Brownian motion . Addition of a surfactant allows micelles to form around the ferroparticles. A surfactant has a polar head and non-polar tail (or vice versa), one of which adsorbs to a ferroparticle, while the non-polar tail (or polar head) sticks out into the carrier medium, forming an inverse or regular micelle , respectively, around the particle. This increases the effective particle diameter. Steric repulsion then prevents heavy agglomeration of the particles in their settled state, which makes fluid remixing (particle redispersion) occur far faster and with less effort. For example, magnetorheological dampers will remix within one cycle with a surfactant additive, but are nearly impossible to remix without them.
While surfactants are useful in prolonging the settling rate in MR fluids, they also prove detrimental to the fluid's magnetic properties (specifically, the magnetic saturation), which is commonly a parameter which users wish to maximize in order to increase the maximum apparent yield stress. Whether the anti-settling additive is nanosphere-based or surfactant-based, their addition decreases the packing density of the ferroparticles while in its activated state, thus decreasing the fluids on-state/activated viscosity, resulting in a "softer" activated fluid with a lower maximum apparent yield stress. While the on-state viscosity (the "hardness" of the activated fluid) is also a primary concern for many MR fluid applications, it is a primary fluid property for the majority of their commercial and industrial applications and therefore a compromise must be met when considering on-state viscosity, maximum apparent yields stress, and settling rate of an MR fluid.
An MR fluid is used in one of three main modes of operation, these being flow mode, shear mode and squeeze-flow mode. These modes involve, respectively, fluid flowing as a result of pressure gradient between two stationary plates; fluid between two plates moving relative to one another; and fluid between two plates moving in the direction perpendicular to their planes. In all cases the magnetic field is perpendicular to the planes of the plates, so as to restrict fluid in the direction parallel to the plates.
The applications of these various modes are numerous. Flow mode can be used in dampers and shock absorbers, by using the movement to be controlled to force the fluid through channels, across which a magnetic field is applied. Shear mode is particularly useful in clutches and brakes - in places where rotational motion must be controlled. Squeeze-flow mode, on the other hand, is most suitable for applications controlling small, millimeter-order movements but involving large forces. This particular flow mode has seen the least investigation so far.
Overall, between these three modes of operation, MR fluids can be applied successfully to a wide range of applications. However, some limitations exist which are necessary to mention here.
Although smart fluids are rightly seen as having many potential applications, they are limited in commercial feasibility for the following reasons:
Commercial applications do exist, as mentioned, but will continue to be few until these problems (particularly cost) are overcome.
Studies published beginning in the late 2000s which explore the effect of varying the aspect ratio of the ferromagnetic particles have shown several improvements over conventional MR fluids. Nanowire-based fluids show no sedimentation after qualitative observation over a period of three months. This observation has been attributed to a lower close-packing density due to decreased symmetry of the wires compared to spheres, as well as the structurally supportive nature of a nanowire lattice held together by remnant magnetization. [ 6 ] [ 7 ] Further, they show a different range of loading of particles (typically measured in either volume or weight fraction) than conventional sphere- or ellipsoid-based fluids. Conventional commercial fluids exhibit a typical loading of 30 to 90 wt%, while nanowire-based fluids show a percolation threshold of ~0.5 wt% (depending on the aspect ratio). [ 8 ] They also show a maximum loading of ~35 wt%, since high aspect ratio particles exhibit a larger per particle excluded volume as well as inter-particle tangling as they attempt to rotate end-over-end, resulting in a limit imposed by high off-state apparent viscosity of the fluids. This range of loadings suggest a new set of applications are possible which may have not been possible with conventional sphere-based fluids.
Newer studies have focused on dimorphic magnetorheological fluids, which are conventional sphere-based fluids in which a fraction of the spheres, typically 2 to 8 wt%, are replaced with nanowires. These fluids exhibit a much lower sedimentation rate than conventional fluids, yet exhibit a similar range of loading as conventional commercial fluids, making them also useful in existing high-force applications such as damping. Moreover, they also exhibit an improvement in apparent yield stress of 10% across those amounts of particle substitution. [ 9 ]
Another way to increase the performance of magnetorheological fluids is to apply a pressure to them. In particular the properties in term of yield strength can be increased up to ten times in shear mode [ 10 ] and up five times in flow mode. [ 11 ] The motivation of this behaviour is the increase in the ferromagnetic particles friction, as described by the semiempirical magneto-tribological model by Zhang et al. Even though applying a pressure strongly improves the magnetorheological fluids behaviour, particular attention must be paid in terms of mechanical resistance and chemical compatibility of the sealing system used.
The application set for MR fluids is vast, and it expands with each advance in the dynamics of the fluid.
Magnetorheological dampers of various applications have been and continue to be developed. These dampers are mainly used in heavy industry with applications such as heavy motor damping, operator seat/cab damping in construction vehicles, and more.
As of 2006, materials scientists and mechanical engineers are collaborating to develop stand-alone seismic dampers which, when positioned anywhere within a building, will operate within the building's resonance frequency , absorbing detrimental shock waves and oscillations within the structure, giving these dampers the ability to make any building earthquake-proof, or at least earthquake-resistant. [ 12 ]
MR fluids' technology can applied among high-end auxiliary equipment that has flexible fixtures at CNC machining. It can hold irregular surfaces and difficult-to-grasp products. [ 13 ]
The U.S. Army Research Office is currently funding research into using MR fluid to enhance body armor. In 2003, researchers stated they were five to ten years away from making the fluid bullet resistant. [ 14 ] In addition, HMMWVs, and various other all-terrain vehicles employ dynamic MR shock absorbers and/or dampers.
Magnetorheological finishing , a magnetorheological fluid-based optical polishing method, has proven to be highly precise. It was used in the construction of the Hubble Space Telescope 's corrective lens.
If the shock absorbers of a vehicle's suspension are filled with magnetorheological fluid instead of a plain oil or gas, and the channels which allow the damping fluid to flow between the two chambers is surrounded with electromagnets , the viscosity of the fluid, and hence the critical frequency of the damper , can be varied depending on driver preference or the weight being carried by the vehicle - or it may be dynamically varied in order to provide stability control across vastly different road conditions. This is in effect a magnetorheological damper . For example, the MagneRide active suspension system permits the damping factor to be adjusted once every millisecond in response to conditions. General Motors (in a partnership with Delphi Corporation ) has developed this technology for automotive applications. It made its debut in both Cadillac (Seville STS build date on or after 1/15/2002 with RPO F55) as "Magneride" (or "MR") and Chevrolet passenger vehicles (All Corvettes made since 2003 with the F55 option code) as part of the driver selectable "Magnetic Selective Ride Control (MSRC)" system in model year 2003. Other manufacturers have paid for the use of it in their own vehicles, for example Audi and Ferrari offer the MagneRide on various models.
General Motors and other automotive companies are seeking to develop a magnetorheological fluid based clutch system for push-button four wheel drive systems. This clutch system would use electromagnets to solidify the fluid which would lock the driveshaft into the drive train .
Porsche has introduced magnetorheological engine mounts in the 2010 Porsche GT3 and GT2. At high engine revolutions, the magnetorheological engine mounts get stiffer to provide a more precise gearbox shifter feel by reducing the relative motion between the power train and chassis/body.
As of September 2007, Acura (Honda) has begun an advertising campaign highlighting its use of MR technology in passenger vehicles manufactured for the 2007 MDX model year.
Magnetorheological dampers are under development for use in military and commercial helicopter cockpit seats, as safety devices in the event of a crash. [ 15 ] [ 16 ] They would be used to decrease the shock delivered to a passenger's spinal column, thereby decreasing the rate of permanent injury during a crash.
Magnetorheological dampers are utilized in semi-active human prosthetic legs. Much like those used in military and commercial helicopters, a damper in the prosthetic leg decreases the shock delivered to the patients leg when jumping, for example. This results in an increased mobility and agility for the patient.
The company XeelTech and CK Materials Lab in Korea use magnetorheological fluid to generate the haptic feedback of their HAPTICORE rotary switches . The MR actuators are primarily used as input devices with adaptive haptic feedback to enable new possibilities in user interface design . The HAPTICORE technology functions like a miniature MR brake. By changing the magnetic field created by a small electromagnet inside the rotary knob, the friction between the outer shell and the stator is modified in such a way that the user perceives the braking effect as haptic feedback.
By modifying the rheological state of the fluid in near real time, a variety of mechanical rotary knob and cam switch haptic patterns such as ticks, grids, and barriers or limits can be simulated. In addition, it is also possible to generate new forms of haptic feedback, such as speed-adaptive and direction-dependent haptic feedback modes. This technology is used, for example, in HMIs of industrial equipment, household appliances or computer peripherals . [ 17 ] | https://en.wikipedia.org/wiki/Magnetorheological_fluid |
The magnetorotational instability (MRI) is a fluid instability that causes an accretion disk orbiting a massive central object to become turbulent . It arises when the angular velocity of a conducting fluid in a magnetic field decreases as the distance from the rotation center increases. It is also known as the Velikhov–Chandrasekhar instability or Balbus–Hawley instability in the literature, not to be confused with the electrothermal Velikhov instability . The MRI is of particular relevance in astrophysics where it is an important part of the dynamics in accretion disks .
Gases or liquids containing mobile electrical charges are subject to the influence of a magnetic field. In addition to hydrodynamical forces such as pressure and gravity, an element of magnetized fluid also feels the Lorentz force J × B , {\displaystyle {\boldsymbol {J}}\times {\boldsymbol {B}}\ ,} where J {\displaystyle {\boldsymbol {J}}} is the current density and B {\displaystyle {\boldsymbol {B}}} is the magnetic field vector. If the fluid is in a state of differential rotation about a fixed origin, this Lorentz force can be surprisingly disruptive, even if the magnetic field is very weak. In particular, if the angular velocity of rotation Ω {\displaystyle \Omega } decreases with radial distance R , {\displaystyle R\ ,} the motion is unstable: a fluid element undergoing a small displacement from circular motion experiences a destabilizing force that increases at a rate which is itself proportional to the displacement. This process is known as the Magnetorotational Instability , or "MRI".
In astrophysical settings, differentially rotating systems are very common and magnetic fields are ubiquitous. In particular, thin disks of gas are often found around forming stars or in binary star systems, where they are known as accretion disks. Accretion disks are also commonly present in the centre of galaxies, and in some cases can be extremely luminous: quasars , for example, are thought to originate from a gaseous disk surrounding a very massive black hole . Our modern understanding of the MRI arose from attempts to understand the behavior of accretion disks in the presence of magnetic fields; it is now understood that the MRI is likely to occur in a very wide variety of different systems.
The MRI was first noticed in a non-astrophysical context by Evgeny Velikhov in 1959 when considering the stability of Couette flow of an ideal hydromagnetic fluid. [ 1 ] His result was later generalized by Subrahmanyan Chandrasekhar in 1960. [ 2 ] [ 3 ] This mechanism was proposed by David Acheson and Raymond Hide (1973) to perhaps play a role in the context of the Earth's geodynamo problem. [ 4 ] Although there was some follow-up work in later decades (Fricke, 1969; Acheson and Hide 1972; Acheson and Gibbons 1978), the generality and power of the instability were not fully appreciated until 1991, when Steven A. Balbus and John F. Hawley gave a relatively simple elucidation and physical explanation of this important process. [ 5 ]
In a magnetized, perfectly conducting fluid, the magnetic forces behave in some very important respects as though the elements of fluid were connected with elastic bands: trying to displace such an element perpendicular to a magnetic line of force causes an attractive force proportional to the displacement, like a spring under tension. Normally, such a force is restoring, a strongly stabilizing influence that would allow a type of magnetic wave to propagate. If the fluid medium is not stationary but rotating, however, attractive forces can actually be destabilizing. The MRI is a consequence of this surprising behavior.
Consider, for example, two masses, m i ("inner") and m o ("outer") connected by a spring under tension, both masses in orbit around a central body, M c . In such a system, the angular velocity of circular orbits near the center is greater than the angular velocity of orbits farther from the center, but the angular momentum of the inner orbits is smaller than that of the outer orbits. If m i is allowed to orbit a little bit closer to the center than m o , it will have a slightly higher angular velocity. The connecting spring will pull back on m i , and drag m o forward. This means that m i experiences a retarding torque, loses angular momentum, and must fall inward to an orbit of smaller radius, corresponding to a smaller angular momentum. m o , on the other hand, experiences a positive torque, acquires more angular momentum, and moves outward to a higher orbit. The spring stretches yet more, the torques become yet larger, and the motion is unstable! Because magnetic forces act like a spring under tension connecting fluid elements, the behavior of a magnetized fluid is almost exactly analogous to this simple mechanical system. This is the essence of the MRI .
To see this unstable behavior more quantitatively, consider the equations of motion for a fluid element mass in circular motion with an angular velocity Ω . {\displaystyle \Omega \ .} In general Ω {\displaystyle \Omega } will be a function of the distance from the rotation axis R , {\displaystyle R\ ,} and we assume that the orbital radius is r = R 0 . {\displaystyle r=R_{0}\ .} The centripetal acceleration required to keep the mass in orbit is − R Ω 2 ( R ) {\displaystyle -R\Omega ^{2}(R)} ; the minus sign indicates a direction toward the center. If this force is gravity from a point mass at the center, then the centripetal acceleration is simply − G M / R 2 , {\displaystyle -GM/R^{2},} where G {\displaystyle G} is the gravitational constant and M {\displaystyle M} is the central mass.
Let us now consider small departures from the circular motion of the orbiting mass element caused by some perturbing force. We transform variables into a rotating frame moving with the orbiting mass element at angular velocity Ω ( R 0 ) = Ω 0 , {\displaystyle \Omega (R_{0})=\Omega _{0}\ ,} with origin located at the unperturbed, orbiting location of the mass element. As usual when working in a rotating frame, we need to add to the equations of motion a Coriolis force − 2 Ω 0 × v {\displaystyle -2{\boldsymbol {\Omega }}_{0}\times {\boldsymbol {v}}} plus a centrifugal force R Ω 0 2 . {\displaystyle R\Omega _{0}^{2}\ .} The velocity v {\displaystyle v} is the velocity as measured in the rotating frame. Furthermore, we restrict our attention to a small neighborhood near R 0 , {\displaystyle R_{0}\ ,} say R 0 + x , {\displaystyle R_{0}+x\ ,} with x {\displaystyle x} much smaller than R 0 . {\displaystyle R_{0}\ .} Then the sum of the centrifugal and centripetal forces is
to linear order in x . {\displaystyle x\ .} With our x {\displaystyle x} axis pointing radial outward from the unperturbed location of the fluid element and our y {\displaystyle y} axis pointing in the direction of increasing azimuthal angle (the direction of the unperturbed orbit), the x {\displaystyle x} and y {\displaystyle y} equations of motion for a small departure from a circular orbit R = R 0 {\displaystyle R=R_{0}} are:
where f x {\displaystyle f_{x}} and f y {\displaystyle f_{y}} are the forces per unit mass in the x {\displaystyle x} and y {\displaystyle y} directions, and a dot indicates a time derivative (i.e., x ˙ {\displaystyle {\dot {x}}} is the x {\displaystyle x} velocity, x ¨ {\displaystyle {\ddot {x}}} is the x {\displaystyle x} acceleration, etc.). Provided that f x {\displaystyle f_{x}} and f y {\displaystyle f_{y}} are either 0 or linear in x and y, this is a system of coupled second-order linear differential equations that can be solved analytically.
In the absence of external forces, f x = 0 {\displaystyle f_{x}=0} and f y = 0 {\displaystyle f_{y}=0} , the equations of motion have solutions with the time dependence e i ω t , {\displaystyle e^{i\omega t}\ ,} where the angular frequency ω {\displaystyle \omega } satisfies the equation
where κ 2 {\displaystyle \kappa ^{2}} is known as the epicyclic frequency . In the Solar System , for example, deviations from a sun-centered circular orbit that are familiar ellipses when viewed by an external viewer at rest, appear instead as small radial and azimuthal oscillations of the orbiting element when viewed by an observer moving with the undisturbed circular motion.
These oscillations trace out a small retrograde ellipse (i.e. rotating in the opposite sense of the large circular orbit), centered on the undisturbed orbital location of the mass element.
The epicyclic frequency may equivalently be written ( 1 / R 3 ) ( d R 4 Ω 2 / d R ) , {\displaystyle (1/R^{3})(dR^{4}\Omega ^{2}/dR)\ ,} which shows that it is proportional to the radial derivative of the angular momentum per unit mass, or specific angular momentum. The specific angular momentum must increase outward if stable epicyclic oscillations are to exist, otherwise displacements would grow exponentially, corresponding to instability. This is a very general result known as the Rayleigh criterion (Chandrasekhar 1961) for stability. For orbits around a point mass, the specific angular momentum is proportional to R 1 / 2 , {\displaystyle R^{1/2}\ ,} so the Rayleigh criterion is well satisfied.
Consider next the solutions to the equations of motion if the mass element is subjected to an external restoring force, f x = − K x , {\displaystyle f_{x}=-Kx\ ,} f y = − K y {\displaystyle f_{y}=-Ky} where K {\displaystyle K} is an arbitrary constant (the "spring constant"). If we now seek solutions for the modal displacements in x {\displaystyle x} and y {\displaystyle y} with time dependence e i ω t , {\displaystyle e^{i\omega t}\ ,} we find a much more complex equation for ω : {\displaystyle \omega \ :}
Even though the spring exerts an attractive force, it may destabilize. For example, if the spring constant K {\displaystyle K} is sufficiently weak, the dominant balance will be between the final two terms on the left side of the equation. Then, a decreasing outward angular velocity profile will produce negative values for ω 2 , {\displaystyle \omega ^{2}\ ,} and both positive and negative imaginary values for ω . {\displaystyle \omega \ .} The negative imaginary root results not in oscillations, but in exponential growth of very small displacements. A weak spring therefore causes the type of instability described qualitatively at the end of the previous section. A strong spring on the other hand, will produce oscillations, as one intuitively expects.
The conditions inside a perfectly conducting fluid in motion is often a good approximation to astrophysical gases. In the presence of a magnetic field B , {\displaystyle {\boldsymbol {B}}\ ,} a moving conductor responds by trying to eliminate the Lorentz force on the free charges. The magnetic force acts in such a way as to locally rearrange these charges to produce an internal electric field of E = − v × B . {\displaystyle {\boldsymbol {E=-{v\times B}}}\ .} In this way, the direct Lorentz force on the charges E + v × B {\displaystyle {\boldsymbol {E+v\times B}}} vanishes. (Alternatively, the electric field in the local rest frame of the moving charges vanishes.) This induced electric field can now itself induce further changes in the magnetic field B {\displaystyle {\boldsymbol {B}}} according to Faraday's law ,
Another way to write this equation is that if in time δ t {\displaystyle \delta t} the fluid makes a displacement ξ = v δ t , {\displaystyle {\boldsymbol {\xi }}={\boldsymbol {v}}\delta t\ ,} then the magnetic field changes by
The equation of a magnetic field in a perfect conductor in motion has a special property: the combination of Faraday induction and zero Lorentz force makes the field lines behave as though they were painted, or "frozen," into the fluid. In particular, if B {\displaystyle {\boldsymbol {B}}} is initially nearly constant and ξ {\displaystyle \xi } is a divergence-free displacement, then our equation reduces to
because of the vector calculus identity ∇ × ( ξ × B ) = ξ ( ∇ ⋅ B ) − B ( ∇ ⋅ ξ ) + ( B ⋅ ∇ ) ξ − ( ξ ⋅ ∇ ) B . {\displaystyle \nabla \times (\mathbf {\xi } \times \mathbf {B} )=\mathbf {\xi } (\nabla \cdot \mathbf {B} )-\mathbf {B} (\nabla \cdot \mathbf {\xi } )+(\mathbf {B} \cdot \nabla )\mathbf {\xi } -(\mathbf {\xi } \cdot \nabla )\mathbf {B} \ .} Out of these 4 terms, ∇ ⋅ B = 0 {\displaystyle \nabla \cdot \mathbf {B} =0} is one of Maxwell's equations . By the divergence-free assumption, ∇ ⋅ ξ = 0 {\displaystyle \nabla \cdot \mathbf {\xi } =0} . ( ξ ⋅ ∇ ) B = 0 {\displaystyle (\mathbf {\xi } \cdot \nabla )\mathbf {B} =0} because B is assumed to be nearly constant. Equation 8 shows that B {\displaystyle {\boldsymbol {B}}} changes only when there is a shearing displacement along the field line.
To understand the MRI, it is sufficient to consider the case in which B {\displaystyle {\boldsymbol {B}}} is uniform in vertical z {\displaystyle z} direction, and ξ {\displaystyle \xi } varies as e i k z . {\displaystyle e^{ikz}\ .} Then
where it is understood that the real part of this equation expresses its physical content. (If ξ {\displaystyle {\boldsymbol {\xi }}} is proportional to cos ( k z ) , {\displaystyle \cos(kz)\ ,} for example, then δ B {\displaystyle \delta {\boldsymbol {B}}} is proportional to − sin ( k z ) . {\displaystyle -\sin(kz)\ .} )
A magnetic field exerts a force per unit volume on an electrically neutral, conducting fluid equal to J × B . {\displaystyle {\boldsymbol {J}}\times {\boldsymbol {B}}\ .} Ampere's circuital law gives μ 0 J = ∇ × B , {\displaystyle \mu _{0}{\boldsymbol {J=\nabla \times B}}\ ,} because Maxwell's correction is neglected in the MHD approximation. The force per unit volume becomes
where we have used the same vector calculus identity. This equation is fully general, and makes no assumptions about the strength or direction of the magnetic field.
The first term on the right is analogous to a pressure gradient. In our problem it may be neglected because it exerts no force in the plane of the disk, perpendicular to z . {\displaystyle z\ .} The second term acts like a magnetic tension force, analogous to a taut string. For a small disturbance δ B , {\displaystyle \delta {\boldsymbol {B}}\ ,} it exerts an acceleration given by force divided by mass, or equivalently, force per unit volume divided by mass per unit volume:
Thus, a magnetic tension force gives rise to a return force which is directly proportional to the displacement. This means that the oscillation frequency ω {\displaystyle \omega } for small displacements in the plane of rotation of a disk with a uniform magnetic field in the vertical direction satisfies an equation ("dispersion relation") exactly analogous to equation 5 , with the "spring constant" K = k 2 B 2 / μ 0 ρ : {\displaystyle K={k^{2}B^{2}/\mu _{0}\rho }\ :}
As before, if d Ω 2 / d R < 0 , {\displaystyle d\Omega ^{2}/dR<0\ ,} there is an exponentially growing root of this equation for wavenumbers k {\displaystyle k} satisfying ( k 2 B 2 / μ 0 ρ ) < − R d Ω 2 / d R . {\displaystyle (k^{2}B^{2}/\mu _{0}\rho )<-Rd\Omega ^{2}/dR\ .} This corresponds to the MRI.
Notice that the magnetic field appears in equation 12 only as the product k B . {\displaystyle kB\ .} Thus, even if B {\displaystyle B} is very small, for very large wavenumbers k {\displaystyle k} this magnetic tension can be important. This is why the MRI is so sensitive to even very weak magnetic fields: their effect is amplified by multiplication by k . {\displaystyle k\ .} Moreover, it can be shown that MRI is present regardless of the magnetic field geometry, as long as the field is not too strong.
In astrophysics, one is generally interested in the case for which the disk is supported by rotation against the gravitational attraction of a central mass. A balance between the Newtonian gravitational force and the radial centripetal force immediately gives
where G {\displaystyle G} is the Newtonian gravitational constant, M {\displaystyle M} is the central mass, and R {\displaystyle R} is radial location in the disk. Since R d Ω 2 / d R = − 3 Ω 2 < 0 , {\displaystyle Rd\Omega ^{2}/dR=-3\Omega ^{2}<0\ ,} this so-called Keplerian disk is unstable to the MRI . Without a weak magnetic field, the flow would be stable.
For a Keplerian disk, the maximum growth rate is γ = 3 Ω / 4 , {\displaystyle \gamma =3\Omega /4\ ,} which occurs at a wavenumber satisfying ( k 2 B 2 / μ 0 ρ ) = 15 Ω 2 / 16 . {\displaystyle (k^{2}B^{2}/\mu _{0}\rho )=15\Omega ^{2}/16\ .} γ {\displaystyle \gamma } is very rapid, corresponding to an amplification factor of more than 100 per rotation period.
The nonlinear development of the MRI into fully developed turbulence may be followed via large scale numerical computation.
Interest in the MRI is based on the fact that it appears to give an explanation for the origin of turbulent flow in astrophysical accretion disks (Balbus and Hawley, 1991).
A promising model for the compact, intense X-ray sources discovered in the 1960s was that of a neutron star or black hole drawing in ("accreting") gas from its surroundings (Prendergast and Burbidge, 1968). Such gas always accretes with a finite amount of angular momentum relative to the central object, and so it must first form a rotating disk — it cannot accrete directly onto the object without first losing its angular momentum. But how an element of gaseous fluid managed to lose its angular momentum and spiral onto the central object was not at all obvious.
One explanation involved shear-driven turbulence (Shakura and Sunyaev, 1973). There would be significant shear in an accretion disk (gas closer to the centre rotates more rapidly than outer disk regions), and shear layers often break down into turbulent flow. The presence of shear-generated turbulence, in turn, produces the powerful torques needed to transport angular momentum from one (inner) fluid element to another (farther out).
The breakdown of shear layers into turbulence is routinely observed in flows with velocity gradients, but without systematic rotation. This is an important point, because rotation produces strongly stabilizing Coriolis forces, and this is precisely what occurs in accretion disks . As can be seen in equation 5 , the K = 0 limit produces Coriolis-stabilized oscillations, not exponential growth. These oscillations are present under much more general conditions as well: a recent laboratory experiment (Ji et al., 2006) has shown stability of the flow profile expected in accretion disks under conditions in which otherwise troublesome dissipation effects are (by a standard measure known as the Reynolds number) well below one part in a million. All of this changes, however, are when even a very weak magnetic field is present. The MRI produces torques that are not stabilized by Coriolis forces. Large scale numerical simulations of the MRI indicate that the rotational disk flow breaks down into turbulence (Hawley et al., 1995), with strongly enhanced angular momentum transport properties. This is just what is required for the accretion disk model to work. The formation of stars (Stone et al., 2000), the production of X-rays in neutron star and black hole systems (Blaes, 2004), and the creation of active galactic nuclei (Krolik, 1999) and gamma ray bursts (Wheeler, 2004) are all thought to involve the development of the MRI at some level.
Thus far, we have focused rather exclusively on the dynamical breakdown of laminar flow into turbulence triggered by a weak magnetic field, but it is also the case that the resulting highly agitated flow can act back on this same magnetic field. Embedded magnetic field lines are stretched by the turbulent flow, and it is possible that systematic field amplification could result. The process by which fluid motions are converted to magnetic field energy is known as a dynamo (Moffatt, 1978); the two best studied examples are the Earth's liquid outer core and the layers close to the surface of the Sun. Dynamo activity in these regions is thought to be responsible for maintaining the terrestrial and solar magnetic fields. In both of these cases thermal convection is likely to be the primary energy source, though in the case of the Sun differential rotation may also play an important role. Whether the MRI is an efficient dynamo process in accretion disks is currently an area of active research (Fromang and Papaloizou, 2007).
There may also be applications of the MRI outside of the classical accretion disk venue. Internal rotation in stars (Ogilvie, 2007), and even planetary dynamos (Petitdemange et al., 2008) may, under some circumstances, be vulnerable to the MRI in combination with convective instabilities. These studies are also ongoing.
Finally, the MRI can, in principle, be studied in the laboratory (Ji et al., 2001), though these experiments are very difficult to implement. A typical set-up involves either concentric spherical shells or coaxial cylindrical shells. Between (and confined by) the shells, there is a conducting liquid metal such as sodium or gallium. The inner and outer shells are set in rotation at different rates, and viscous torques compel the trapped liquid metal to differentially rotate. The experiment then investigates whether the differential rotation profile is stable or not in the presence of an applied magnetic field.
A claimed detection of the MRI in a spherical shell experiment (Sisan et al., 2004), in which the underlying state was itself turbulent, awaits confirmation at the time of this writing (2009). A magnetic instability that bears some similarity to the MRI can be excited if both vertical and azimuthal magnetic fields are present in the undisturbed state (Hollerbach and Rüdiger, 2005). This is sometimes referred to as the helical-MRI, (Liu et al., 2006) though its precise relation to the MRI described above has yet to be fully elucidated. Because it is less sensitive to stabilizing ohmic resistance than is the classical MRI, this helical magnetic instability is easier to excite in the laboratory, and there are indications that it may have been found (Stefani et al., 2006). The detection of the classical MRI in a hydrodynamically quiescent background state has yet to be achieved in the laboratory, however.
The spring-mass analogue of the standard MRI has been demonstrated in rotating Taylor–Couette / Keplerian-like flow (Hung et al. 2019) . | https://en.wikipedia.org/wiki/Magnetorotational_instability |
In astronomy and planetary science , a magnetosphere is a region of space surrounding an astronomical object in which charged particles are affected by that object's magnetic field . [ 1 ] [ 2 ] It is created by a celestial body with an active interior dynamo .
In the space environment close to a planetary body with a dipole magnetic field such as Earth, the field lines resemble a simple magnetic dipole . Farther out, field lines can be significantly distorted by the flow of electrically conducting plasma , as emitted from the Sun (i.e., the solar wind ) or a nearby star. [ 3 ] [ 4 ] Planets having active magnetospheres, like the Earth, are capable of mitigating or blocking the effects of solar radiation or cosmic radiation . [ 5 ] Interactions of particles and atmospheres with magnetospheres are studied under the specialized scientific subjects of plasma physics , space physics , and aeronomy .
Study of Earth's magnetosphere began in 1600, when William Gilbert discovered that the magnetic field on the surface of Earth resembled that of a terrella , a small, magnetized sphere. In the 1940s, Walter M. Elsasser proposed the model of dynamo theory , which attributes Earth's magnetic field to the motion of Earth's iron outer core . Through the use of magnetometers , scientists were able to study the variations in Earth's magnetic field as functions of both time and latitude and longitude.
Beginning in the late 1940s, rockets were used to study cosmic rays . In 1958, Explorer 1 , the first of the Explorer series of space missions, was launched to study the intensity of cosmic rays above the atmosphere and measure the fluctuations in this activity. This mission observed the existence of the Van Allen radiation belt (located in the inner region of Earth's magnetosphere), with the follow-up Explorer 3 later that year definitively proving its existence. Also during 1958, Eugene Parker proposed the idea of the solar wind , with the term 'magnetosphere' being proposed by Thomas Gold in 1959 to explain how the solar wind interacted with the Earth's magnetic field. The later mission of Explorer 12 in 1961 led by the Cahill and Amazeen observation in 1963 of a sudden decrease in magnetic field strength near the noon-time meridian, later was named the magnetopause . By 1983, the International Cometary Explorer observed the magnetotail , or the distant magnetic field. [ 4 ]
The structure of magnetospheres are dependent on several factors: the type of astronomical object, the nature of sources of plasma and momentum , the period of the object's spin, the nature of the axis about which the object spins, the axis of the magnetic dipole, and the magnitude and direction of the flow of solar wind .
The planetary distance where the magnetosphere can withstand the solar wind pressure is called the Chapman–Ferraro distance. This is usefully modeled by the formula wherein R P {\displaystyle R_{\rm {P}}} represents the radius of the planet, B s u r f {\displaystyle B_{\rm {surf}}} represents the magnetic field on the surface of the planet at the equator, V S W {\displaystyle V_{\rm {SW}}} represents the velocity of the solar wind, ρ {\displaystyle \rho } is the particle density of solar wind, and μ 0 {\displaystyle \mu _{0}} is the vacuum permeability constant:
A magnetosphere is classified as "intrinsic" when R C F ≫ R P {\displaystyle R_{\rm {CF}}\gg R_{\rm {P}}} , or when the primary opposition to the flow of solar wind is the magnetic field of the object. Mercury , Earth, Jupiter , Ganymede , Saturn , Uranus , and Neptune , for example, exhibit intrinsic magnetospheres. A magnetosphere is classified as "induced" when R C F ≪ R P {\displaystyle R_{\rm {CF}}\ll R_{\rm {P}}} , or when the solar wind is not opposed by the object's magnetic field. In this case, the solar wind interacts with the atmosphere or ionosphere of the planet (or surface of the planet, if the planet has no atmosphere). Venus has an induced magnetic field, which means that because Venus appears to have no internal dynamo effect , the only magnetic field present is that formed by the solar wind's wrapping around the physical obstacle of Venus (see also Venus' induced magnetosphere ). When R C F ≈ R P {\displaystyle R_{\rm {CF}}\approx R_{\rm {P}}} , the planet itself and its magnetic field both contribute. It is possible that Mars is of this type. [ 6 ]
When viewed from the Sun, a celestial body's orbital motion can compress its otherwise symmetrical magnetosphere slightly, and stretch it out in the direction opposite its motion (in Earth's example, from west to east). This is known as dawn-dusk asymmetry . [ 7 ] [ 8 ] [ 9 ]
The bow shock forms the outermost layer of the magnetosphere; the boundary between the magnetosphere and the surrounding medium. For stars, this is usually the boundary between the stellar wind and interstellar medium ; for planets, the speed of the solar wind there decreases as it approaches the magnetopause. [ 10 ] Due to interactions with the bow shock, the stellar wind plasma gains a substantial anisotropy , leading to various plasma instabilities upstream and downstream of the bow shock. [ 11 ]
The magnetosheath is the region of the magnetosphere between the bow shock and the magnetopause. It is formed mainly from shocked solar wind, though it contains a small amount of plasma from the magnetosphere. [ 12 ] It is an area exhibiting high particle energy flux , where the direction and magnitude of the magnetic field varies erratically. This is caused by the collection of solar wind gas that has effectively undergone thermalization . It acts as a cushion that transmits the pressure from the flow of the solar wind and the barrier of the magnetic field from the object. [ 4 ]
The magnetopause is the area of the magnetosphere wherein the pressure from the planetary magnetic field is balanced with the pressure from the solar wind. [ 3 ] It is the convergence of the shocked solar wind from the magnetosheath with the magnetic field of the object and plasma from the magnetosphere. Because both sides of this convergence contain magnetized plasma, the interactions between them are complex. The structure of the magnetopause depends upon the Mach number and beta ratio of the plasma, as well as the magnetic field. [ 13 ] The magnetopause changes size and shape as the pressure from the solar wind fluctuates. [ 14 ]
Opposite the compressed magnetic field is the magnetotail, where the magnetosphere extends far beyond the astronomical object. It contains two lobes, referred to as the northern and southern tail lobes. Magnetic field lines in the northern tail lobe point towards the object while those in the southern tail lobe point away. The tail lobes are almost empty, with few charged particles opposing the flow of the solar wind. The two lobes are separated by a plasma sheet, an area where the magnetic field is weaker, and the density of charged particles is higher. [ 15 ]
Over Earth's equator , the magnetic field lines become almost horizontal, then return to reconnect at high latitudes. However, at high altitudes, the magnetic field is significantly distorted by the solar wind and its solar magnetic field. On the dayside of Earth, the magnetic field is significantly compressed by the solar wind to a distance of approximately 65,000 kilometers (40,000 mi). Earth's bow shock is about 17 kilometers (11 mi) thick [ 16 ] and located about 90,000 kilometers (56,000 mi) from Earth. [ 17 ] The magnetopause exists at a distance of several hundred kilometers above Earth's surface. Earth's magnetopause has been compared to a sieve because it allows solar wind particles to enter. Kelvin–Helmholtz instabilities occur when large swirls of plasma travel along the edge of the magnetosphere at different velocities from the magnetosphere, causing the plasma to slip past. This results in magnetic reconnection , and as the magnetic field lines break and reconnect, solar wind particles are able to enter the magnetosphere. [ 18 ] On Earth's nightside, the magnetic field extends in the magnetotail, which lengthwise exceeds 6,300,000 kilometers (3,900,000 mi). [ 3 ] Earth's magnetotail is the primary source of the polar aurora . [ 15 ] Also, NASA scientists have suggested that Earth's magnetotail might cause "dust storms" on the Moon by creating a potential difference between the day side and the night side. [ 19 ]
Many astronomical objects generate and maintain magnetospheres. In the Solar System this includes the Sun, Mercury , Earth , Jupiter , Saturn , Uranus , Neptune , [ 20 ] and Ganymede . The magnetosphere of Jupiter is the largest planetary magnetosphere in the Solar System, extending up to 7,000,000 kilometers (4,300,000 mi) on the dayside and almost to the orbit of Saturn on the nightside. [ 21 ] Jupiter's magnetosphere is stronger than Earth's by an order of magnitude , and its magnetic moment is approximately 18,000 times larger. [ 22 ] Venus , Mars , and Pluto , on the other hand, have no intrinsic magnetic field. This may have had significant effects on their geological history. It is hypothesized that Venus and Mars may have lost their primordial water to photodissociation and the solar wind. A strong magnetosphere, were it present, would greatly slow down this process. [ 20 ] [ 23 ]
Alfvén Mach number
Magnetospheres generated by exoplanets are thought to be common, though the first discoveries did not come until the 2010s. In 2014, a magnetic field around HD 209458 b was inferred from the way hydrogen was evaporating from the planet. [ 25 ] [ 26 ] In 2019, the strength of the surface magnetic fields of 4 hot Jupiters were estimated and ranged between 20 and 120 gauss compared to Jupiter's surface magnetic field of 4.3 gauss. [ 27 ] [ 28 ] In 2020, a radio emission in the 14-30 MHz band was detected from the Tau Boötis system, likely associated with cyclotron radiation from the poles of Tau Boötis b which might be a signature of a planetary magnetic field. [ 29 ] [ 30 ] In 2021 a magnetic field generated by the hot Neptune HAT-P-11b became the first to be confirmed. [ 31 ] The first unconfirmed detection of a magnetic field generated by a terrestrial exoplanet was found in 2023 on YZ Ceti b . [ 32 ] [ 33 ] [ 34 ] [ 35 ] | https://en.wikipedia.org/wiki/Magnetosphere |
Magnetostatics is the study of magnetic fields in systems where the currents are steady (not changing with time). It is the magnetic analogue of electrostatics , where the charges are stationary. The magnetization need not be static; the equations of magnetostatics can be used to predict fast magnetic switching events that occur on time scales of nanoseconds or less. [ 1 ] Magnetostatics is even a good approximation when the currents are not static – as long as the currents do not alternate rapidly. Magnetostatics is widely used in applications of micromagnetics such as models of magnetic storage devices as in computer memory .
Starting from Maxwell's equations and assuming that charges are either fixed or move as a steady current J {\displaystyle \mathbf {J} } , the equations separate into two equations for the electric field (see electrostatics ) and two for the magnetic field . [ 2 ] The fields are independent of time and each other. The magnetostatic equations, in both differential and integral forms, are shown in the table below.
Where ∇ with the dot denotes divergence , and B is the magnetic flux density , the first integral is over a surface S {\displaystyle S} with oriented surface element d S {\displaystyle d\mathbf {S} } . Where ∇ with the cross denotes curl , J is the current density and H is the magnetic field intensity , the second integral is a line integral around a closed loop C {\displaystyle C} with line element l {\displaystyle \mathbf {l} } . The current going through the loop is I enc {\displaystyle I_{\text{enc}}} .
The quality of this approximation may be guessed by comparing the above equations with the full version of Maxwell's equations and considering the importance of the terms that have been removed. Of particular significance is the comparison of the J {\displaystyle \mathbf {J} } term against the ∂ D / ∂ t {\displaystyle \partial \mathbf {D} /\partial t} term. If the J {\displaystyle \mathbf {J} } term is substantially larger, then the smaller term may be ignored without significant loss of accuracy.
A common technique is to solve a series of magnetostatic problems at incremental time steps and then use these solutions to approximate the term ∂ B / ∂ t {\displaystyle \partial \mathbf {B} /\partial t} . Plugging this result into Faraday's Law finds a value for E {\displaystyle \mathbf {E} } (which had previously been ignored). This method is not a true solution of Maxwell's equations but can provide a good approximation for slowly changing fields. [ citation needed ]
If all currents in a system are known (i.e., if a complete description of the current density J ( r ) {\displaystyle \mathbf {J} (\mathbf {r} )} is available) then the magnetic field can be determined, at a position r , from the currents by the Biot–Savart equation : [ 3 ] : 174 B ( r ) = μ 0 4 π ∫ J ( r ′ ) × ( r − r ′ ) | r − r ′ | 3 d 3 r ′ {\displaystyle \mathbf {B} (\mathbf {r} )={\frac {\mu _{0}}{4\pi }}\int {{\frac {\mathbf {J} (\mathbf {r} ')\times \left(\mathbf {r} -\mathbf {r} '\right)}{|\mathbf {r} -\mathbf {r} '|^{3}}}\mathrm {d} ^{3}\mathbf {r} '}}
This technique works well for problems where the medium is a vacuum or air or some similar material with a relative permeability of 1. This includes air-core inductors and air-core transformers . One advantage of this technique is that, if a coil has a complex geometry, it can be divided into sections and the integral evaluated for each section. Since this equation is primarily used to solve linear problems, the contributions can be added. For a very difficult geometry, numerical integration may be used.
For problems where the dominant magnetic material is a highly permeable magnetic core with relatively small air gaps, a magnetic circuit approach is useful. When the air gaps are large in comparison to the magnetic circuit length, fringing becomes significant and usually requires a finite element calculation. The finite element calculation uses a modified form of the magnetostatic equations above in order to calculate magnetic potential . The value of B {\displaystyle \mathbf {B} } can be found from the magnetic potential.
The magnetic field can be derived from the vector potential . Since the divergence of the magnetic flux density is always zero, B = ∇ × A , {\displaystyle \mathbf {B} =\nabla \times \mathbf {A} ,} and the relation of the vector potential to current is: [ 3 ] : 176 A ( r ) = μ 0 4 π ∫ J ( r ′ ) | r − r ′ | d 3 r ′ . {\displaystyle \mathbf {A} (\mathbf {r} )={\frac {\mu _{0}}{4\pi }}\int {{\frac {\mathbf {J(\mathbf {r} ')} }{|\mathbf {r} -\mathbf {r} '|}}\mathrm {d} ^{3}\mathbf {r} '}.}
Strongly magnetic materials (i.e., ferromagnetic , ferrimagnetic or paramagnetic ) have a magnetization that is primarily due to electron spin . In such materials the magnetization must be explicitly included using the relation B = μ 0 ( M + H ) . {\displaystyle \mathbf {B} =\mu _{0}(\mathbf {M} +\mathbf {H} ).}
Except in the case of conductors, electric currents can be ignored. Then Ampère's law is simply ∇ × H = 0. {\displaystyle \nabla \times \mathbf {H} =0.}
This has the general solution H = − ∇ Φ M , {\displaystyle \mathbf {H} =-\nabla \Phi _{M},} where Φ M {\displaystyle \Phi _{M}} is a scalar potential . [ 3 ] : 192 Substituting this in Gauss's law gives ∇ 2 Φ M = ∇ ⋅ M . {\displaystyle \nabla ^{2}\Phi _{M}=\nabla \cdot \mathbf {M} .}
Thus, the divergence of the magnetization, ∇ ⋅ M , {\displaystyle \nabla \cdot \mathbf {M} ,} has a role analogous to the electric charge in electrostatics [ 4 ] and is often referred to as an effective charge density ρ M {\displaystyle \rho _{M}} .
The vector potential method can also be employed with an effective current density J M = ∇ × M . {\displaystyle \mathbf {J_{M}} =\nabla \times \mathbf {M} .} | https://en.wikipedia.org/wiki/Magnetostatics |
Magnetostriction is a property of magnetic materials that causes them to change their shape or dimensions during the process of magnetization . The variation of materials' magnetization due to the applied magnetic field changes the magnetostrictive strain until reaching its saturation value, λ. The effect was first identified in 1842 by James Joule when observing a sample of iron . [ 1 ]
Magnetostriction applies to magnetic fields, while electrostriction applies to electric fields.
Magnetostriction causes energy loss due to frictional heating in susceptible ferromagnetic cores, and is also responsible for the low-pitched humming sound that can be heard coming from transformers, where alternating currents produce a changing magnetic field. [ 2 ]
Internally, ferromagnetic materials have a structure that is divided into domains , each of which is a region of uniform magnetization. When a magnetic field is applied, the boundaries between the domains shift and the domains rotate; both of these effects cause a change in the material's dimensions. The reason that a change in the magnetic domains of a material results in a change in the material's dimensions is a consequence of magnetocrystalline anisotropy ; it takes more energy to magnetize a crystalline material in one direction than in another. If a magnetic field is applied to the material at an angle to an easy axis of magnetization, the material will tend to rearrange its structure so that an easy axis is aligned with the field to minimize the free energy of the system. Since different crystal directions are associated with different lengths, this effect induces a strain in the material. [ 3 ]
The reciprocal effect, the change of the magnetic susceptibility (response to an applied field) of a material when subjected to a mechanical stress, is called the Villari effect . Two other effects are related to magnetostriction: the Matteucci effect is the creation of a helical anisotropy of the susceptibility of a magnetostrictive material when subjected to a torque and the Wiedemann effect is the twisting of these materials when a helical magnetic field is applied to them.
The Villari reversal is the change in sign of the magnetostriction of iron from positive to negative when exposed to magnetic fields of approximately 40 kA/m .
On magnetization, a magnetic material undergoes changes in volume which are small: of the order 10 −6 .
Like flux density , the magnetostriction also exhibits hysteresis versus the strength of the magnetizing field. The shape of this hysteresis loop (called "dragonfly loop") can be reproduced using the Jiles-Atherton model . [ 4 ]
Magnetostrictive materials can convert magnetic energy into kinetic energy , or the reverse, and are used to build actuators and sensors . The property can be quantified by the magnetostrictive coefficient, λ, which may be positive or negative and is defined as the fractional change in length as the magnetization of the material increases from zero to the saturation value. The effect is responsible for the familiar " electric hum " ( Listen ⓘ ) which can be heard near transformers and high power electrical devices.
Cobalt exhibits the largest room-temperature magnetostriction of a pure element at 60 microstrains . Among alloys, the highest known magnetostriction is exhibited by Terfenol-D , (Ter for terbium , Fe for iron , NOL for Naval Ordnance Laboratory , and D for dysprosium ). Terfenol-D, Tb x Dy 1− x Fe 2 , exhibits about 2,000 microstrains in a field of 160 kA/m (2 kOe) at room temperature and is the most commonly used engineering magnetostrictive material. [ 5 ] Galfenol , Fe x Ga 1− x , and Alfer , Fe x Al 1− x , are newer alloys that exhibit 200-400 microstrains at lower applied fields (~200 Oe) and have enhanced mechanical properties from the brittle Terfenol-D. Both of these alloys have <100> easy axes for magnetostriction and demonstrate sufficient ductility for sensor and actuator applications. [ 6 ]
Another very common magnetostrictive composite is the amorphous alloy Fe 81 Si 3.5 B 13.5 C 2 with its trade name Metglas 2605SC. Favourable properties of this material are its high saturation-magnetostriction constant, λ, of about 20 microstrains and more, coupled with a low magnetic-anisotropy field strength, H A , of less than 1 kA/m (to reach magnetic saturation ). Metglas 2605SC also exhibits a very strong ΔE-effect with reductions in the effective Young's modulus up to about 80% in bulk. This helps build energy-efficient magnetic MEMS . [ citation needed ]
Cobalt ferrite , CoFe 2 O 4 (CoO·Fe 2 O 3 ), is also mainly used for its magnetostrictive applications like sensors and actuators, thanks to its high saturation magnetostriction (~200 parts per million). [ 7 ] In the absence of rare-earth elements, it is a good substitute for Terfenol-D . [ 8 ] Moreover, its magnetostrictive properties can be tuned by inducing a magnetic uniaxial anisotropy. [ 9 ] This can be done by magnetic annealing, [ 10 ] magnetic field assisted compaction, [ 11 ] or reaction under uniaxial pressure. [ 12 ] This last solution has the advantage of being ultrafast (20 min), thanks to the use of spark plasma sintering .
In early sonar transducers during World War II, nickel was used as a magnetostrictive material. To alleviate the shortage of nickel, the Japanese navy used an iron - aluminium alloy from the Alperm family.
Single-crystal alloys exhibit superior microstrain, but are vulnerable to yielding due to the anisotropic mechanical properties of most metals. It has been observed that for polycrystalline alloys with a high area coverage of preferential grains for microstrain, the mechanical properties ( ductility ) of magnetostrictive alloys can be significantly improved. Targeted metallurgical processing steps promote abnormal grain growth of {011} grains in galfenol and alfenol thin sheets, which contain two easy axes for magnetic domain alignment during magnetostriction. This can be accomplished by adding particles such as boride species [ 13 ] and niobium carbide ( NbC ) [ 14 ] during initial chill casting of the ingot .
For a polycrystalline alloy, an established formula for the magnetostriction, λ, from known directional microstrain measurements is: [ 15 ]
λ s = 1/5(2λ 100 +3λ 111 )
During subsequent hot rolling and recrystallization steps, particle strengthening occurs in which the particles introduce a “pinning” force at grain boundaries that hinders normal ( stochastic ) grain growth in an annealing step assisted by a H 2 S atmosphere. Thus, single-crystal-like texture (~90% {011} grain coverage) is attainable, reducing the interference with magnetic domain alignment and increasing microstrain attainable for polycrystalline alloys as measured by semiconducting strain gauges . [ 16 ] These surface textures can be visualized using electron backscatter diffraction (EBSD) or related diffraction techniques.
For actuator applications, maximum rotation of magnetic moments leads to the highest possible magnetostriction output. This can be achieved by processing techniques such as stress annealing and field annealing. However, mechanical pre-stresses can also be applied to thin sheets to induce alignment perpendicular to actuation as long as the stress is below the buckling limit. For example, it has been demonstrated that applied compressive pre-stress of up to ~50 MPa can result in an increase of magnetostriction by ~90%. This is hypothesized to be due to a "jump" in initial alignment of domains perpendicular to applied stress and improved final alignment parallel to applied stress. [ 17 ]
These materials generally show non-linear behavior with a change in applied magnetic field or stress. For small magnetic fields, linear piezomagnetic constitutive [ 18 ] behavior is enough. Non-linear magnetic behavior is captured using a classical macroscopic model such as the Preisach model [ 19 ] and Jiles-Atherton model. [ 20 ] For capturing magneto-mechanical behavior, Armstrong [ 21 ] proposed an "energy average" approach. More recently, Wahi et al. [ 22 ] have proposed a computationally efficient constitutive model wherein constitutive behavior is captured using a "locally linearizing" scheme. | https://en.wikipedia.org/wiki/Magnetostriction |
Magnetotactic bacteria (or MTB ) are a polyphyletic group of bacteria that orient themselves along the magnetic field lines of Earth's magnetic field . [ 1 ] Discovered in 1963 by Salvatore Bellini and rediscovered in 1975 by Richard Blakemore, this alignment is believed to aid these organisms in reaching regions of optimal oxygen concentration. [ 2 ] To perform this task, these bacteria have organelles called magnetosomes that contain magnetic crystals . The biological phenomenon of microorganisms tending to move in response to the environment's magnetic characteristics is known as magnetotaxis . However, this term is misleading in that every other application of the term taxis involves a stimulus-response mechanism. In contrast to the magnetoreception of animals, the bacteria contain fixed magnets that force the bacteria into alignment—even dead cells are dragged into alignment, just like a compass needle. [ 3 ]
The first description of magnetotactic bacteria was in 1963 by Salvatore Bellini of the University of Pavia . [ 4 ] [ 5 ] While observing bog sediments under his microscope, Bellini noticed a group of bacteria that evidently oriented themselves in a unique direction. He realized these microorganisms moved according to the direction of the North Pole , and hence called them "magnetosensitive bacteria". The publications were academic (peer-reviewed by the Istituto di Microbiologia ' s editorial committee under responsibility of the Institute's Director Prof. L. Bianchi, as usual in European universities at the time) and communicated in Italian with English, French and German short summaries in the official journal of a well-known institution, yet unexplainedly seem to have attracted little attention until they were brought to the attention of Richard Frankel in 2007. Frankel translated them into English and the translations were published in the Chinese Journal of Oceanography and Limnology . [ 6 ] [ 7 ] [ 8 ] [ 9 ]
Richard Blakemore, then a microbiology graduate student [ 10 ] at the University of Massachusetts at Amherst, working in the Woods Hole Oceanographic Institution in whose collections the pertinent publications of the Institute of Microbiology of the University of Pavia were extant, observed microorganisms following the direction of Earth's magnetic field. [ when? ] Blakemore did not mention Bellini's research in his own report, which he published in Science , but was able to observe magnetosome chains using an electron microscope. [ 8 ] [ 11 ] Bellini's terms for this behavior, namely Italian : batteri magnetosensibili , French : bactéries magnétosensibles or bactéries aimantées , German : magnetisch empfindliche Bakterien and English: magnetosensitive bacteria (Bellini's first publication, last page), went forgotten, and Blakemore's "magnetotaxis" was adopted by the scientific community.
These bacteria have been the subject of many experiments. They have even been aboard the Space Shuttle to examine their magnetotactic properties in the absence of gravity , but a definitive conclusion was not reached. [ 12 ]
The sensitivity of magnetotactic bacteria to the Earth's magnetic field arises from the fact these bacteria precipitate chains of crystals of magnetic minerals within their cells. To date [update] , all magnetotactic bacteria are reported to precipitate either magnetite or greigite . These crystals, and sometimes the chains of crystals, can be preserved in the geological record as magnetofossils . The oldest unambiguous magnetofossils come from the Cretaceous chalk beds of southern England, [ 13 ] though less certain reports of magnetofossils extend to 1.9 billion years old Gunflint chert . [ 14 ] There have also been claims of their existence on Mars based on the shape of magnetite particles within the Martian meteorite ALH84001 , but these claims are highly contested. [ 15 ]
Several different morphologies (shapes) of MTB exist, differing in number, layout and pattern of the bacterial magnetic particles (BMPs) they contain. [ 16 ] The MTBs can be subdivided into two categories, according to whether they produce particles of magnetite ( Fe 3 O 4 ) or of greigite ( Fe 3 S 4 ), although some species [ which? ] are capable of producing both. Magnetite possesses a magnetic moment with three times the magnitude of greigite. [ 15 ]
Magnetite-producing magnetotactic bacteria are usually found in an oxic-anoxic transition zone (OATZ), the transition zone between oxygen-rich and oxygen-starved water or sediment. Many MTB are able to survive only in environments with very limited oxygen, and some can exist only in completely anaerobic environments . It has been postulated that the evolutionary advantage of possessing a system of magnetosomes is linked to the ability to efficiently navigate within this zone of sharp chemical gradients by simplifying a potential three-dimensional search for more favorable conditions to a single dimension. (See § Magnetism for a description of this mechanism.) Some types of magnetotactic bacteria can produce magnetite even in anaerobic conditions, using nitric oxide , nitrate , or sulfate as a final acceptor for electrons . The greigite mineralizing MTBs are usually strictly anaerobic. [ 17 ]
It has been suggested MTB evolved in the early Archean Eon, as the increase in atmospheric oxygen meant that there was an evolutionary advantage for organisms to have magnetic navigation. [ 18 ] Magnetosomes first evolved as a defense mechanism in response to the increase of reactive oxygen species (ROS) that resulted from the Great Oxygenation Event . [ 19 ] Organisms began to store iron in some form, and this intracellular iron was later adapted to form magnetosomes for magnetotaxis. These early MTB may have participated in the formation of the first eukaryotic cells. [ 14 ] Biogenic magnetite similar to that found in magnetotactic bacteria has been also found in higher organisms, from euglenoid algae to trout . [ 20 ] Reports in humans and pigeons are far less advanced. [ 21 ]
Magnetotactic bacteria organize their magnetosomes in linear chains. The magnetic dipole moment of the cell is therefore the sum of the dipole moment of each BMP, which is then sufficient to passively orient the cell and overcome the casual thermal forces found in a water environment. [ 17 ] In the presence of more than one chain, the inter-chain repulsive forces will push these structures to the edge of the cell, inducing turgor . [ 15 ]
Nearly all of the genes relevant to magnetotaxis in MTB [ which? ] are located in an approximately 80 kilobase region in the genome called the magnetosome island. [ 22 ] There are three main operons in the magnetosome island: the mamAB operon, the mamGFDC operon, and the mms6 operon. There are 9 genes that are essential for the formation and function of modern magnetosomes: mamA, mamB, mamE, mamI, mamK, mamM, mamO, mamP, and mamQ. [ 23 ] In addition to these 9 genes that are well conserved across all MTB, there are more than 30 total genes that contribute to magnetotaxis in MTB. [ 23 ] These non-essential genes account for the variation in magnetite/greigite crystal size and shape, as well as the specific alignment of magnetosomes in the cell.
The diversity of MTB is reflected by the high number of different morphotypes found in environmental samples of water or sediment. Commonly observed morphotypes include spherical or ovoid cells ( cocci ), rod-shaped ( bacilli ), and spiral bacteria of various dimensions. One of the more distinctive morphotypes is an apparently multicellular bacterium [ 24 ] referred to as the many-celled magnetotactic prokaryote (MMP).
Regardless of their morphology, all MTB studied so far are motile by means of flagella and are gram-negative bacteria of various phyla. Despite the majority of known species [ which? ] being Pseudomonadota , e.g. Magnetospirillum magneticum , an alphaproteobacterium , members of various phyla possess the magnetosome gene cluster , such as Candidatus Magnetobacterium bavaricum , a Nitrospira . [ 25 ] The arrangement of flagella differs and can be polar, bipolar, or in tufts. [ 26 ] The first phylogenetic analysis on magnetotactic bacteria using 16S rRNA gene sequence comparisons was performed by P. Eden et al. in 1991.
Another trait that shows considerable diversity is the arrangement of magnetosomes inside the bacterial cell. In the majority of MTB, the magnetosomes are aligned in chains of various lengths and numbers along the cell's long axis, which is magnetically the most efficient orientation. However, dispersed aggregates or clusters of magnetosomes occur in some MTB, usually at one side of the cell, which often corresponds to the site of flagellar insertion. Besides magnetosomes, large inclusion bodies containing elemental sulfur , polyphosphate , or poly-β-hydroxybutyrate are common in MTB.
The most abundant type of MTB occurring in environmental samples, especially sediments, are coccoid cells possessing two flagellar bundles on a somewhat flattened side. This "bilophotrichous" type of flagellation gave rise to the tentative genus "Bilophococcus" for these bacteria. In contrast, two of the morphologically more conspicuous MTB, regularly observed in natural samples, but never isolated in pure culture , are the MMP and a large rod containing copious amounts of hook-shaped magnetosomes ( Magnetobacterium bavaricum ).
The physical development of a magnetic crystal is governed by two factors: one is moving to align the magnetic force of the molecules in conjunction with the developing crystal, while the other reduces the magnetic force of the crystal, allowing an attachment of the molecule while experiencing an opposite magnetic force. In nature, this causes the existence of a magnetic domain , surrounding the perimeter of the domain, with a thickness of approximately 150 nm of magnetite, within which the molecules gradually change orientation. For this reason, the iron is not magnetic in the absence of an applied field. Likewise, extremely small magnetic particles do not exhibit signs of magnetisation at room temperature; their magnetic force is continuously altered by the thermal motions inherent in their composition. [ 15 ] Instead, individual magnetite crystals in MTB are of a size between 35 and 120 nm, that is; large enough to have a magnetic field and at the same time small enough to remain a single magnetic domain . [ 17 ]
The inclination of the Earth's magnetic field in the two respective hemispheres selects one of the two possible polarities of the magnetotactic cells (with respect to the flagellated pole of the cell), orienting the biomineralisation of the magnetosomes .
Aerotaxis is the response by which bacteria migrate to an optimal oxygen concentration in an oxygen gradient. Various experiments have clearly shown that magnetotaxis and aerotaxis work in conjunction in magnetotactic bacteria. It has been shown that, in water droplets, one-way swimming magnetotactic bacteria can reverse their swimming direction and swim backwards under reducing conditions (less than optimal oxygen concentration ), as opposed to oxic conditions (greater than optimal oxygen concentration). The behaviour that has been observed in these bacterial strains has been referred to as magneto-aerotaxis .
Two different magneto-aerotactic mechanisms—known as polar and axial—are found in different MTB strains. [ 27 ] Some strains that swim persistently in one direction along the magnetic field (either north-seeking [NS] or south-seeking [SS])—mainly the magnetotactic cocci —are polar magneto-aerotactic. These magnetotactic bacteria will travel along the lines of the earth's magnetic field according to their orientation, but will swerve as a group and reverse direction if exposed to a local, more powerful and oppositely-oriented magnetic field. In this way, they continue to travel in the same magnetic direction, but relative instead to the local field . Those MTB that swim in either direction along magnetic field lines with frequent, spontaneous reversals of swimming direction without turning around—for example, freshwater spirilla —are axial magneto-aerotactic and the distinction between NS and SS does not apply to these bacteria. The magnetic field provides both an axis and a direction of motility for polar magneto-aerotactic bacteria, whereas it only provides an axis of motility for axial types of bacteria. In both cases, magnetotaxis increases the efficiency of aerotaxis in vertical concentration gradients by reducing a three-dimensional search to a single dimension.
Scientists have also proposed an extension of the described model of magneto-aerotaxis to a more complex redoxtaxis . In this case, the unidirectional movement of MTB in a drop of water would be only one aspect of a sophisticated redox-controlled response. One hint for the possible function of polar magnetotaxis could be that most of the representative microorganisms are characterised by possessing either large sulfur inclusions or magnetosomes consisting of iron-sulfides. Therefore, it may be speculated that the metabolism of these bacteria, being either chemolithoautotrophic or mixotrophic , is strongly dependent on the uptake of reduced sulfur compounds, which occurs in many habitats only in deeper regions at or below the OATZ due to the rapid chemical oxidation of these reduced chemical species by oxygen or other oxidants in the upper layers.
Microorganisms belonging to the genus Thioploca , for example, use nitrate, which is stored intracellularly, to oxidize sulfide, and have developed vertical sheaths in which bundles of motile filaments are located. It is assumed that Thioploca use these sheathes to move efficiently in a vertical direction in sediment, thereby accumulating sulfide in deeper layers and nitrate in upper layers. [ 28 ] For some MTB, it might also be necessary to perform excursions to anoxic zones of their habitat to accumulate reduced sulfur compounds.
The biomineralisation of magnetite ( Fe 3 O 4 ) requires regulating mechanisms to control the concentration of iron, the crystal nucleation , the redox potential and the acidity ( pH ). This is achieved by means of compartmentalisation in structures known as magnetosomes that allow the biochemical control of the above-mentioned processes. After the genome of several MTB species had been sequenced , a comparative analysis of the proteins involved in the formation of the BMP became possible. Sequence homology with proteins belonging to the ubiquitous cation diffusion facilitator (CDF) family and the "Htr-like" serine proteases has been found. While the first group is exclusively dedicated to the transport of heavy metals, the second group consists of heat shock proteins (HSPs) involved in the degradation of badly folded proteins. Other than the serine protease domain, some proteins found in the magnetosomial membrane (MM) also contain PDZ domains, while several other MM proteins contain tetratricopeptide repeat (TPR) domains. [ 16 ]
The TPR domains are characterized by a folding consisting of two α-helices and include a highly conserved consensus sequence of 8 amino acids (of the 34 possible), [ 29 ] which is the most common in nature. Apart from these amino acids, the remainder of the structure is found to be specialised in relation to its functional significance. The more notable compounds that comprise TPR domains include:
Examples of both the TPR-TPR interactions, as well as TPR-nonTPR interactions, have been reported. [ 30 ]
The PDZ domains are structures that consist of 6 β-filaments and 2 α-helices that recognise the C-terminal amino acids of proteins in a sequence-specific manner. Usually, the third residue from the C-terminal is phosphorylated , preventing interaction with the PDZ domain. The only conserved residues in these structures are those involved in the recognition of the carboxy terminal . PDZ domains are quite widespread in nature, since they constitute the basic structure upon which multiproteinic complexes are assembled. This is especially true for those associated with membrane proteins , such as the inward rectifier K + channels or the β 2 - adrenergic receptors. [ 31 ]
The formation of the magnetosome requires at least three steps:
The first formation of an invagination in the cytoplasmic membrane is triggered by a GTPase . It is supposed this process can take place amongst eukaryotes , as well.
The second step requires the entrance of ferric ions into the newly formed vesicles from the external environment. Even when cultured in a Fe 3+ deficient medium, MTB succeed at accumulating high intracellular concentrations of this ion. It has been suggested that they accomplish this by secreting , upon need, a siderophore , a low- molecular-weight ligand displaying an elevated affinity for Fe 3+ ions. The "Fe 3+ -siderophore" complex is subsequently moved in the cytoplasm , where it is cleaved. The ferric ions must then be converted into the ferrous form (Fe 2+ ), to be accumulated within the BMP; this is achieved by means of a transmembrane transporter , which exhibits sequence homology with a Na + /H + antiporter . Furthermore, the complex is a H + /Fe 2+ antiporter, which transports ions via the proton gradient . These transmembrane transporters are localised both in the cytoplasmic membrane and in the MM, but in an inverted orientation; this configuration allows them to generate an efflux of Fe 2+ ions at the cytoplasmic membrane, and an influx of this same ion at the MM. This step is strictly controlled by a cytochrome -dependent redox system, which is not yet fully explained and appears to be species-specific. [ as of? ]
During the final stage of the process, the magnetite crystal nucleation is by action of transmembrane proteins with acidic and basic domains. One of these proteins, called Mms6 , has also been employed for the artificial synthesis of magnetite, where its presence allows the production of crystals homogeneous in shape and size.
It is likely that many other proteins associated with the MM could be involved in other roles, such as generation of supersaturated concentrations of iron, maintenance of reducing conditions, oxidisation of iron, and partial reduction and dehydration of hydrated iron compounds. [ 32 ]
Several clues led to the hypothesis that different genetic sets exist for the biomineralisation of magnetite and greigite. In cultures of Magnetospirillum magnetotacticum , iron can not be replaced with other transition metals (Ti, Cr, Co, Cu, Ni, Hg, Pb) commonly found in the soil. In a similar manner, oxygen and sulfur are not interchangeable as nonmetallic substances of the magnetosome within the same species. [ 17 ]
From a thermodynamic point of view, in the presence of a neutral pH and a low redox potential, the inorganic synthesis of magnetite is favoured when compared to those of other iron oxides . [ 33 ] It would thus appear microaerophilic or anaerobic conditions create a suitable potential for the formation of BMPs. Moreover, all iron absorbed by the bacteria is rapidly converted into magnetite, indicating the formation of crystals is not preceded by the accumulation of intermediate iron compounds; this also suggests the structures and the enzymes necessary for biomineralisation are already present within the bacteria. These conclusions are also supported by the fact that MTB cultured in aerobic conditions (and thus nonmagnetic) contain amounts of iron comparable to any other species of bacteria. [ 34 ]
Symbiosis with magnetotactic bacteria has been proposed as the explanation for magnetoreception in some marine protists . [ 35 ] Besides, some species of protists can prey on MTB so that magnetosomes can accumulate in the cells. So protists can obtain the ability of magnetic response. [ 36 ] Research is underway on whether a similar relationship may underlie magnetoreception in vertebrates as well. [ 37 ]
In certain types of applications, bacterial magnetite offers several advantages compared to chemically synthesized magnetite. [ 38 ] Bacterial magnetosome particles, unlike those produced chemically, have a consistent shape, a narrow size distribution within the single magnetic domain range , and a membrane coating consisting of lipids and proteins . The magnetosome envelope allows for easy couplings of bioactive substances to its surface, a characteristic important for many applications.
Magnetotactic bacterial cells have been used to determine south magnetic poles in meteorites and rocks containing fine-grained magnetic minerals and for the separation of cells after the introduction of magnetotactic bacterial cells into granulocytes and monocytes by phagocytosis . Magnetotactic bacterial magnetite crystals have been used in studies of magnetic domain analysis and in many commercial applications including: the immobilisation of enzymes ; the formation of magnetic antibodies , and the quantification of immunoglobulin G ; the detection and removal of Escherichia coli cells with a fluorescein isothiocyanate conjugated monoclonal antibody, immobilised on magnetotactic bacterial magnetite particles; and the introduction of genes into cells, a technology in which magnetosomes are coated with DNA and "shot" using a particle gun into cells that are difficult to transform using more standard methods.
However, the prerequisite for any large-scale commercial application is mass cultivation of magnetotactic bacteria or the introduction and expression of the genes responsible for magnetosome synthesis into a bacterium, e.g., E. coli , that can be grown relatively cheaply to extremely large yields. Although some progress has been made, the former has not been achieved with the available pure cultures. | https://en.wikipedia.org/wiki/Magnetotactic_bacteria |
Magnetotropism is the movement or plant growth in response to the stimulus provided by the magnetic field in plants (specifically agricultural plants) around the world. As a natural environmental factor in the Earth, variations of magnetic field level causes many biological effects, including germination rate, flowering time, photosynthesis , biomass accumulation, activation of cryptochrome , and shoot growth. [ 1 ]
As an adaptive behavior, magnetotropism is recognizing as a method to improve agriculture success, using the well-studied plant model, Arabidopsis thaliana , a typical small plant which is native in the Europe and Asia with well-known genomic functions. In 2012, Xu et al. conducted a Near-Null Magnetic Field experiment under white light and long-day conditions using the homemade equipment of combining three couples of Helmholtz coils in vertical, north–south, east–west direction compensating near-null magnetic field. Xu noted that under the near-null magnetic field, Arabidopsis thaliana delays the flowering time by altering the transcription level of three cryptochrome related florigen genes: PHYB , CO, and FT ; Arabidopsis thaliana also induced longer hypocotyl length under white light in the Near-Null magnetic field compared to standard geomagnetic field and either dark or white light conditions. [ 2 ] Furthermore, the biomass accumulation reduces in the near-null magnetic field while Arabidopsis thaliana switches from vegetative growth to reproductive growth. [ 3 ] Not until recently, Agliassa conducted a similar experiment continuing Xu et al. ’s discovery found out that Arabidopsis thaliana delay flowering by shortening stem length and reduction of leaf size. This expression shows that the near-null magnetic field has caused downregulation of several flowering genes, including FT genes in the meristem and leaves, which is cryptochrome related. [ 4 ]
Although preliminary experiments have shown a wide range of effects due to the magnetic field, the mechanism has not yet been elucidated. Having known that the delay of flowering is downregulating in cryptochrome related genes affected by the near-null magnetic field under blue light, cryptochrome is taking as a potential magneto-sensor by a few considerations. Based on the radical pair model, cryptochrome would be the magneto-sensor in the light-dependent magnetoreception since cryptochrome has evolved a significant role of plant behavior, including blue-light reception and regulation, de-etiolation , circadian rhythm , and photolyase . [ 5 ] In the photoactivation process, blue light hits cryptochrome and accepts a photon to Flavin while tryptophan receives a photon by another tryptophan donor simultaneously. Due to the geomagnetic field , this combination would rotate from south pole to north pole of the Earth and convert the two single photons back to its inactive resting states under aerobic environment. [ 6 ] Based on a few behavior changes due to variations of the magnetic field, many plant scientists have paid attention to cryptochrome being the candidate for the magneto-sensory receptor. So far, the interactions between signals and magnetoreceptor molecules have not yet discovered, thus leaving potential space for future research while understanding magnetotropism would be significant for improving life forms and ecology such as agriculture . | https://en.wikipedia.org/wiki/Magnetotropism |
In astronomy , magnitude is a measure of the brightness of an object , usually in a defined passband . An imprecise but systematic determination of the magnitude of objects was introduced in ancient times by Hipparchus .
Magnitude values do not have a unit. The scale is logarithmic and defined such that a magnitude 1 star is exactly 100 times brighter than a magnitude 6 star. Thus each step of one magnitude is 100 5 ≈ 2.512 {\displaystyle {\sqrt[{5}]{100}}\approx 2.512} times brighter than the magnitude 1 higher. The brighter an object appears, the lower the value of its magnitude, with the brightest objects reaching negative values.
Astronomers use two different definitions of magnitude: apparent magnitude and absolute magnitude . The apparent magnitude ( m ) is the brightness of an object and depends on an object's intrinsic luminosity , its distance , and the extinction reducing its brightness. The absolute magnitude ( M ) describes the intrinsic luminosity emitted by an object and is defined to be equal to the apparent magnitude that the object would have if it were placed at a certain distance, 10 parsecs for stars. A more complex definition of absolute magnitude is used for planets and small Solar System bodies , based on its brightness at one astronomical unit from the observer and the Sun.
The Sun has an apparent magnitude of −27 and Sirius , the brightest visible star in the night sky, −1.46. Venus at its brightest is -5. The International Space Station (ISS) sometimes reaches a magnitude of −6.
Amateur astronomers commonly express the darkness of the sky in terms of limiting magnitude , i.e. the apparent magnitude of the faintest star they can see with the naked eye. At a dark site, it is usual for people to see stars of 6th magnitude or fainter.
Apparent magnitude is really a measure of illuminance , which can also be measured in photometric units such as lux . [ 1 ]
The Greek astronomer Hipparchus produced a catalogue which noted the apparent brightness of stars in the second century BCE. In the second century CE, the Alexandrian astronomer Ptolemy classified stars on a six-point scale, and originated the term magnitude . [ 2 ] To the unaided eye, a more prominent star such as Sirius or Arcturus appears larger than a less prominent star such as Mizar , which in turn appears larger than a truly faint star such as Alcor . In 1736, the mathematician John Keill described the ancient naked-eye magnitude system in this way:
The fixed Stars appear to be of different Bignesses, not because they really are so, but because they are not all equally distant from us. [ note 1 ] Those that are nearest will excel in Lustre and Bigness; the more remote Stars will give a fainter Light, and appear smaller to the Eye. Hence arise the Distribution of Stars , according to their Order and Dignity, into Classes ; the first Class containing those which are nearest to us, are called Stars of the first Magnitude; those that are next to them, are Stars of the second Magnitude ... and so forth, 'till we come to the Stars of the sixth Magnitude, which comprehend the smallest Stars that can be discerned with the bare Eye. For all the other Stars , which are only seen by the Help of a Telescope, and which are called Telescopical, are not reckoned among these six Orders. Altho' the Distinction of Stars into six Degrees of Magnitude is commonly received by Astronomers ; yet we are not to judge, that every particular Star is exactly to be ranked according to a certain Bigness, which is one of the Six; but rather in reality there are almost as many Orders of Stars , as there are Stars , few of them being exactly of the same Bigness and Lustre. And even among those Stars which are reckoned of the brightest Class, there appears a Variety of Magnitude; for Sirius or Arcturus are each of them brighter than Aldebaran or the Bull's Eye, or even than the Star in Spica ; and yet all these Stars are reckoned among the Stars of the first Order: And there are some Stars of such an intermedial Order, that the Astronomers have differed in classing of them; some putting the same Stars in one Class, others in another. For Example: The little Dog was by Tycho placed among the Stars of the second Magnitude, which Ptolemy reckoned among the Stars of the first Class: And therefore it is not truly either of the first or second Order, but ought to be ranked in a Place between both. [ 3 ]
Note that the brighter the star, the smaller the magnitude: Bright "first magnitude" stars are "1st-class" stars, while stars barely visible to the naked eye are "sixth magnitude" or "6th-class".
The system was a simple delineation of stellar brightness into six distinct groups but made no allowance for the variations in brightness within a group.
Tycho Brahe attempted to directly measure the "bigness" of the stars in terms of angular size, which in theory meant that a star's magnitude could be determined by more than just the subjective judgment described in the above quote. He concluded that first magnitude stars measured 2 arc minutes (2′) in apparent diameter ( 1 ⁄ 30 of a degree, or 1 ⁄ 15 the diameter of the full moon), with second through sixth magnitude stars measuring 1 + 1 ⁄ 2 ′, 1 + 1 ⁄ 12 ′, 3 ⁄ 4 ′, 1 ⁄ 2 ′, and 1 ⁄ 3 ′, respectively. [ 4 ] The development of the telescope showed that these large sizes were illusory—stars appeared much smaller through the telescope. However, early telescopes produced a spurious disk-like image of a star that was larger for brighter stars and smaller for fainter ones. Astronomers from Galileo to Jaques Cassini mistook these spurious disks for the physical bodies of stars, and thus into the eighteenth century continued to think of magnitude in terms of the physical size of a star. [ 5 ] Johannes Hevelius produced a very precise table of star sizes measured telescopically, but now the measured diameters ranged from just over six seconds of arc for first magnitude down to just under 2 seconds for sixth magnitude. [ 5 ] [ 6 ] By the time of William Herschel astronomers recognized that the telescopic disks of stars were spurious and a function of the telescope as well as the brightness of the stars, but still spoke in terms of a star's size more than its brightness. [ 5 ] Even into the early nineteenth century, the magnitude system continued to be described in terms of six classes determined by apparent size. [ 7 ]
However, by the mid-nineteenth century astronomers had measured the distances to stars via stellar parallax , and so understood that stars are so far away as to essentially appear as point sources of light. Following advances in understanding the diffraction of light and astronomical seeing , astronomers fully understood both that the apparent sizes of stars were spurious and how those sizes depended on the intensity of light coming from a star (this is the star's apparent brightness, which can be measured in units such as watts per square metre) so that brighter stars appeared larger.
Early photometric measurements (made, for example, by using a light to project an artificial “star” into a telescope's field of view and adjusting it to match real stars in brightness) demonstrated that first magnitude stars are about 100 times brighter than sixth magnitude stars.
Thus in 1856 Norman Pogson of Oxford proposed that a logarithmic scale of 5 √ 100 ≈ 2.512 be adopted between magnitudes, so five magnitude steps corresponded precisely to a factor of 100 in brightness. [ 8 ] [ 9 ] Every interval of one magnitude equates to a variation in brightness of 5 √ 100 or roughly 2.512 times. Consequently, a magnitude 1 star is about 2.5 times brighter than a magnitude 2 star, about 2.5 2 times brighter than a magnitude 3 star, about 2.5 3 times brighter than a magnitude 4 star, and so on.
This is the modern magnitude system, which measures the brightness, not the apparent size, of stars. Using this logarithmic scale, it is possible for a star to be brighter than “first class”, so Arcturus or Vega are magnitude 0, and Sirius is magnitude −1.46. [ citation needed ]
As mentioned above, the scale appears to work 'in reverse', with objects with a negative magnitude being brighter than those with a positive magnitude. The more negative the value, the brighter the object.
Objects appearing farther to the left on this line are brighter, while objects appearing farther to the right are dimmer. Thus zero appears in the middle, with the brightest objects on the far left, and the dimmest objects on the far right.
Two of the main types of magnitudes distinguished by astronomers are:
The difference between these concepts can be seen by comparing two stars. Betelgeuse (apparent magnitude 0.5, absolute magnitude −5.8) appears slightly dimmer in the sky than Alpha Centauri A (apparent magnitude 0.0, absolute magnitude 4.4) even though it emits thousands of times more light, because Betelgeuse is much farther away.
Under the modern logarithmic magnitude scale, two objects, one of which is used as a reference or baseline, whose flux (i.e., brightness, a measure of power per unit area) in units such as watts per square metre (W m −2 ) are F 1 and F ref , will have magnitudes m 1 and m ref related by
Astronomers use the term "flux" for what is often called "intensity" in physics, in order to avoid confusion with the specific intensity . Using this formula, the magnitude scale can be extended beyond the ancient magnitude 1–6 range, and it becomes a precise measure of brightness rather than simply a classification system. Astronomers now measure differences as small as one-hundredth of a magnitude. Stars that have magnitudes between 1.5 and 2.5 are called second-magnitude; there are some 20 stars brighter than 1.5, which are first-magnitude stars (see the list of brightest stars ). For example, Sirius is magnitude −1.46, Arcturus is −0.04, Aldebaran is 0.85, Spica is 1.04, and Procyon is 0.34. Under the ancient magnitude system, all of these stars might have been classified as "stars of the first magnitude".
Magnitudes can also be calculated for objects far brighter than stars (such as the Sun and Moon ), and for objects too faint for the human eye to see (such as Pluto ).
Often, only apparent magnitude is mentioned since it can be measured directly. Absolute magnitude can be calculated from apparent magnitude and distance from:
because intensity falls off proportionally to distance squared. This is known as the distance modulus , where d is the distance to the star measured in parsecs , m is the apparent magnitude, and M is the absolute magnitude.
If the line of sight between the object and observer is affected by extinction due to absorption of light by interstellar dust particles , then the object's apparent magnitude will be correspondingly fainter. For A magnitudes of extinction, the relationship between apparent and absolute magnitudes becomes
Stellar absolute magnitudes are usually designated with a capital M with a subscript to indicate the passband. For example, M V is the magnitude at 10 parsecs in the V passband. A bolometric magnitude (M bol ) is an absolute magnitude adjusted to take account of radiation across all wavelengths; it is typically smaller (i.e. brighter) than an absolute magnitude in a particular passband, especially for very hot or very cool objects. Bolometric magnitudes are formally defined based on stellar luminosity in watts , and are normalised to be approximately equal to M V for yellow stars.
Absolute magnitudes for Solar System objects are frequently quoted based on a distance of 1 AU. These are referred to with a capital H symbol. Since these objects are lit primarily by reflected light from the Sun, an H magnitude is defined as the apparent magnitude of the object at 1 AU from the Sun and 1 AU from the observer. [ 10 ]
The following is a table giving apparent magnitudes for celestial objects and artificial satellites ranging from the Sun to the faintest object visible with the James Webb Space Telescope (JWST) :
Any magnitude systems must be calibrated to define the brightness of magnitude zero. Many magnitude systems, such as the Johnson UBV system, assign the average brightness of several stars to a certain number to by definition, and all other magnitude measurements are compared to that reference point. [ 15 ] Other magnitude systems calibrate by measuring energy directly, without a reference point, and these are called "absolute" reference systems. Current absolute reference systems include the AB magnitude system, in which the reference is a source with a constant flux density per unit frequency, [ 16 ] and the STMAG system, in which the reference source is instead defined to have constant flux density per unit wavelength. [ citation needed ]
Another logarithmic measure for intensity is the level, in decibel . Although it is more commonly used for sound intensity, it is also used for light intensity. It is a parameter for photomultiplier tubes and similar camera optics for telescopes and microscopes. Each factor of 10 in intensity corresponds to 10 decibels. In particular, a multiplier of 100 in intensity corresponds to an increase of 20 decibels and also corresponds to a decrease in magnitude by 5. Generally, the change in level is related to a change in magnitude by
For example, an object that is 1 magnitude larger (fainter) than a reference would produce a signal that is 4 dB smaller (weaker) than the reference, which might need to be compensated by an increase in the capability of the camera by as many decibels. | https://en.wikipedia.org/wiki/Magnitude_(astronomy) |
Magnonics is an emerging field of modern magnetism , which can be considered a sub-field of modern solid state physics . [ 1 ] Magnonics combines the study of waves and magnetism. Its main aim is to investigate the behaviour of spin waves in nano-structure elements. In essence, spin waves are a propagating re-ordering of the magnetisation in a material and arise from the precession of magnetic moments . Magnetic moments arise from the orbital and spin moments of the electron, most often it is this spin moment that contributes to the net magnetic moment.
Following the success of the modern hard disk , there is much current interest in future magnetic data storage and using spin waves for things such as 'magnonic' logic and data storage. [ 2 ] Similarly, spintronics looks to utilize the inherent spin degree of freedom to complement the already successful charge property of the electron used in contemporary electronics . Modern magnetism is concerned with furthering the understanding of the behaviour of the magnetisation on very small (sub-micrometre) length scales and very fast (sub-nanosecond) timescales and how this can be applied to improving existing or generating new technologies and computing concepts. A magnon torque device was invented and later perfected at the National University of Singapore 's Electrical & Computer Engineering department, which is based on such potential uses, with results published on November 29, 2019, in Science .
A magnonic crystal is a magnetic metamaterial with alternating magnetic properties. Like conventional metamaterials, their properties arise from geometrical structuring, rather than their bandstructure or composition directly. Small spatial inhomogeneities create an effective macroscopic behaviour, leading to properties not readily found in nature. By alternating parameters such as the relative permeability or saturation magnetisation, there exists the possibility to tailor 'magnonic' bandgaps in the material. By tuning the size of this bandgap, only spin wave modes able to cross the bandgap would be able to propagate through the media, leading to selective propagation of certain spin wave frequencies. See Surface magnon polariton .
Spin waves can propagate in magnetic media with magnetic ordering such as ferromagnets and antiferromagnets . The frequencies of the precession of the magnetisation depend on the material and its magnetic parameters, in general precession frequencies are in the microwave from 1–100 GHz, exchange resonances in particular materials can even see frequencies up to several THz. This higher precession frequency opens new possibilities for analogue and digital signal processing.
Spin waves themselves have group velocities on the order of a few km per second. The damping of spin waves in a magnetic material also causes the amplitude of the spin wave to decay with distance, meaning the distance freely propagating spin waves can travel is usually only several 10's of μm. The damping of the dynamical magnetisation is accounted for phenomenologically by the Gilbert damping constant in the Landau-Lifshitz-Gilbert equation (LLG equation), the energy loss mechanism itself is not completely understood, but is known to arise microscopically from magnon -magnon scattering , magnon- phonon scattering and losses due to eddy currents . The Landau-Lifshitz-Gilbert equation is the ' equation of motion ' for the magnetisation. All of the properties of the magnetic systems such as the applied bias field, the sample's exchange, anisotropy and dipolar fields are described in terms of an 'effective' magnetic field that enters the Landau–Lifshitz–Gilbert equation. The study of damping in magnetic systems is an ongoing modern research topic.
The LL equation was introduced in 1935 by Landau and Lifshitz to model the precessional motion of magnetization M {\displaystyle \mathbf {M} } in a solid with an effective magnetic field H e f f {\displaystyle \mathbf {H} _{\mathrm {eff} }} and with damping. [ 3 ] Later, Gilbert modified the damping term, which in the limit of small damping yields identical results. The LLG equation is,
The constant α {\displaystyle \alpha } is the Gilbert phenomenological damping parameter and depends on the solid, and γ {\displaystyle \gamma } is the electron gyromagnetic ratio . Here m = M / M S . {\displaystyle {\textbf {m}}={\textbf {M}}/{\mathrm {M} _{S}}\,.}
Research in magnetism, like the rest of modern science, is conducted with a symbiosis of theoretical and experimental approaches. Both approaches go hand-in-hand, experiments test the predictions of theory and theory provides explanations and predictions of new experiments. The theoretical side focuses on numerical modelling and simulations, so called micromagnetic modelling . Programs such as OOMMF or NMAG are micromagnetic solvers that numerically solve the LLG equation with appropriate boundary conditions. [ 4 ] Prior to the start of the simulation, magnetic parameters of the sample and the initial groundstate magnetisation and bias field details are stated. [ 5 ]
Experimentally, there are many techniques that exist to study magnetic phenomena, each with its own limitations and advantages. [ citation needed ] The experimental techniques can be distinguished by being time-domain (optical and field pumped TR-MOKE), field-domain ( ferromagnetic resonance (FMR)) and frequency-domain techniques (Brillouin light scattering (BLS), vector network analyser - ferromagnetic resonance (VNA-FMR)). Time-domain techniques allow the temporal evolution of the magnetisation to be traced indirectly by recording the polarisation response of the sample. The magnetisation can be inferred by the so-called 'Kerr' rotation. Field-domain techniques such as FMR tickle the magnetisation with a CW microwave field. By measuring the absorption of the microwave radiation through the sample, as an external magnetic field is swept provides information about magnetic resonances in the sample. Importantly, the frequency at which the magnetisation precesses depends on the strength of the applied magnetic field. As the external field strength is increased, so does the precession frequency. Frequency-domain techniques such as VNA-FMR, examine the magnetic response due to excitation by an RF current, the frequency of the current is swept through the GHz range and the amplitude of either the transmitted or reflected current can be measured.
Modern ultrafast lasers allow femtosecond (fs) temporal resolution for time-domain techniques, such tools are now standard in laboratory environments. [ citation needed ] Based on the magneto-optic Kerr effect , TR-MOKE is a pump-probe technique where a pulsed laser source illuminates the sample with two separate laser beams. The 'pump' beam is designed to excite or perturb the sample from equilibrium, it is very intense designed to create highly non-equilibrium conditions within the sample material, exciting the electron, and thereby subsequently the phonon and the spin system. Spin-wave states at high energy are excited and subsequently populate the lower lying states during their relaxation path's. A much weaker beam called a 'probe' beam is spatially overlapped with the pump beam on the magnonic material's surface. The probe beam is passed along a delay line, which is a mechanical way of increasing the probe path length. By increasing the probe path length, it becomes delayed with respect to the pump beam and arrives at a later time on the sample surface. Time-resolution is built in the experiment by changing the delay distance. As the delay line position is stepped, the reflected beam properties are measured. The measured Kerr rotation is proportional to the dynamic magnetisation as the spin-waves propagate in the media. The temporal resolution is limited by the temporal width of the laser pulse only. This allows to connect ultrafast optics with a local spin-wave excitation and contact free detection in magnonic metamaterials, photomagnonics . [ 6 ] [ 7 ]
Since 2009 "Magnonics" conferences are organised every second year. The next conference takes place in July-August 2025 in Cala Millor, Mallorca, Spain. | https://en.wikipedia.org/wiki/Magnonics |
Magnotech is a type of biosensor using magnetic nanoparticles to measure target molecules in blood and saliva in a matter of minutes. The technology is based on magnetic nanoparticles that are actuated by magnetic fields. [ 1 ]
A cartridge is inserted into a hand-held analyzer. The cartridge is constructed entirely from plastic components, has no moving parts or embedded electronics, and is disposable. It automatically fills itself from a single drop of blood or saliva. Once filled, no other fluid movement is required. The entire assay process within the cartridge is executed by controlled movement of the magnetic nanoparticles, using magnetic fields generated by the hand-held analyzer. The analyzer unit contains the electromagnets, an optical detection system, control electronics, software and the read-out display. Tests have shown that the cardiac marker Troponin I can be measured in blood plasma in around five minutes.
Magnotech was used in the Minicare product of Philips Handheld Diagnostics, which was commercially launched in 2016. In 2018 the technology was spun out into Minicare BV, which was acquired by Siemens Healthineers in July 2019. [ 2 ] Magnotech technology is used in Siemens' Atellica VTLi Patient-Side Immunoassay Analyzer, a test for high-sensitivity cardiac troponin I. [ 3 ]
The technology behind Magnotech was initiated by Philips Research Fellow, Menno Prins. In 2014 he became full professor at Eindhoven University of Technology. | https://en.wikipedia.org/wiki/Magnotech |
In alchemy , the Magnum Opus or Great Work is a term for the process of working with the prima materia to create the philosopher's stone . It has been used to describe personal and spiritual transmutation in the Hermetic tradition , attached to laboratory processes and chemical color changes, used as a model for the individuation process, and as a device in art and literature. The magnum opus has been carried forward in New Age and neo-Hermetic movements which sometimes attached new symbolism and significance to the processes. The original process philosophy has four stages: [ 1 ] [ 2 ]
The origin of these four phases can be traced at least as far back as the first century. Zosimus of Panopolis wrote that it was known to Mary the Jewess . [ 3 ] The development of black, white, yellow, and red can also be found in the Physika kai Mystika of Pseudo-Democritus, which is often considered to be one of the oldest books on alchemy. [ 4 ] After the 15th century, many writers tended to compress citrinitas into rubedo and consider only three stages. [ 5 ] Other color stages are sometimes mentioned, most notably the cauda pavonis (peacock's tail) in which an array of colors appear.
The magnum opus had a variety of alchemical symbols attached to it. Birds like the raven, swan, and phoenix could be used to represent the progression through the colors. Similar color changes could be seen in the laboratory, where for example, the blackness of rotting, burnt, or fermenting matter would be associated with nigredo.
Alchemical authors sometimes elaborated on the three or four color model by enumerating a variety of chemical steps to be performed. Though these were often arranged in groups of seven or twelve stages, there is little consistency in the names of these processes, their number, their order, or their description. [ 6 ]
Various alchemical documents were directly or indirectly used to justify these stages. The Tabula Smaragdina is the oldest document [ 7 ] said to provide a "recipe". Others include the Mutus Liber , the twelve keys of Basil Valentine , the emblems of Steffan Michelspacher, and the twelve gates of George Ripley . [ 8 ] Ripley's steps are given as: [ 9 ]
In another example from the sixteenth century, Samuel Norton gives the following fourteen stages: [ 10 ]
Some alchemists also circulated steps for the creation of practical medicines and substances, that have little to do with the magnum opus. The cryptic and often symbolic language used to describe both adds to the confusion, but it's clear that there is no single standard step-by-step recipe given for the creation of the philosopher's stone. [ 11 ] | https://en.wikipedia.org/wiki/Magnum_opus_(alchemy) |
Magnus Gens is a Swedish engineer known for his development of a moose crash test dummy in his 2001 master's thesis . In 2022, the thesis earned him the Ig Nobel Prize for safety engineering , which honors unusual but important research.
In 1994, Gens began working on his master's thesis for the KTH Royal Institute of Technology in Stockholm which involved the creation of a crash test dummy to emulate an automobile collision with a moose in order to improve safety in vehicles . [ 2 ] During the process, he worked alongside the Swedish National Road and Transport Research Institute ( Swedish : Statens väg- och transportforskningsinstitut , VTI) and the auto manufacturer Saab . [ 3 ] Gens also consulted with a veterinarian and the Kolmården Zoo in order to become acquainted with the animal's physical characteristics. [ 4 ] The vehicle crash tests were performed on two relatively-new Saab 9-5s and one older Volvo 245 at the Saab facility in Trollhättan . [ 5 ] [ 6 ]
In 2001, Gens published his master's thesis, Moose Crash Test Dummy , with the Swedish National Road and Transport Research Institute. [ 3 ] The moose itself was built using 116 rubber plates which were fastened together with steel tubes and wiring. [ 7 ] The thesis provided data on how moose hit vehicles and the dummy is designed to be hit several times before a replacement is necessary. [ 6 ] Prior to publication, VTI had been asked to provide horse and camel analogs for testing and similar testing for kangaroo–vehicle collisions had begun in Australia. [ 8 ] [ 9 ]
Gens's thesis has been the basis of tests in several countries. Moose crash test dummies based on his design have been in a large number of automobile safety tests in Sweden and Spain. [ 11 ] Saab's participation in the study helped to start its reputation as a "moose-proof vehicle manufacturer". [ 12 ] In 2008, the television show MythBusters obtained Gens's permission to use a modified version of his model in testing a moose auto collision theory in the episode " Alaska Special ". [ 13 ]
In 2022, Gens was awarded the Ig Nobel Prize , an award for "research that makes people laugh, but also think", in safety engineering . [ 14 ] The cash prize was a ten trillion Zimbabwean dollar banknote. [ 15 ]
Although initially frustrated that his work did not receive much traction at publication, he has expressed hope that renewed attention to the paper will bring more attention to automobile accidents involving wildlife. [ 16 ] As a result of the award, Gens was offered an open invitation to lecture at Harvard University . [ 17 ] | https://en.wikipedia.org/wiki/Magnus_Gens |
The Magnus Hirschfeld Medal is awarded by the German Society for Social-Scientific Sexuality Research (DGSS) [ 1 ] for outstanding service to sexual science , granted in the categories "Sexual Research" and "Sexual Reform". It is named in honour of German sexology pioneer Magnus Hirschfeld [ 2 ] (though DGSS diverges from some of Hirschfeld's theories). | https://en.wikipedia.org/wiki/Magnus_Hirschfeld_Medal |
The Magnus effect is a phenomenon that occurs when a spinning object is moving through a fluid . A lift force acts on the spinning object and its path may be deflected in a manner not present when it is not spinning. The strength and direction of the Magnus force is dependent on the speed and direction of the rotation of the object. [ 1 ]
The Magnus effect is named after Heinrich Gustav Magnus , the German physicist who investigated it. The force on a rotating cylinder is an example of Kutta–Joukowski lift, [ 2 ] named after Martin Kutta and Nikolay Zhukovsky (or Joukowski), mathematicians who contributed to the knowledge of how lift is generated in a fluid flow. [ 3 ]
The most readily observable case of the Magnus effect is when a spinning sphere (or cylinder) curves away from the arc it would follow if it were not spinning. It is often used by football ( soccer ) and volleyball players, baseball pitchers, and cricket bowlers. Consequently, the phenomenon is important in the study of the physics of many ball sports . It is also an important factor in the study of the effects of spinning on guided missiles —and has some engineering uses, for instance in the design of rotor ships and Flettner airplanes .
Topspin in ball games is defined as spin about a horizontal axis perpendicular to the direction of travel that moves the top surface of the ball in the direction of travel. Under the Magnus effect, topspin produces a downward swerve of a moving ball, greater than would be produced by gravity alone. Backspin produces an upwards force that prolongs the flight of a moving ball. [ 4 ] Likewise side-spin causes swerve to either side as seen during some baseball pitches, e.g. slider . [ 5 ] The overall behaviour is similar to that around an aerofoil (see lift force ), but with a circulation generated by mechanical rotation rather than shape of the foil. [ 6 ]
In baseball, this effect is used to generate the downward motion of a curveball, in which the baseball is rotating forward (with 'topspin'). Participants in other sports played with a ball also take advantage of this effect.
The Magnus effect or Magnus force acts on a rotating body moving relative to a fluid. Examples include a " curve ball " in baseball or a tennis ball hit obliquely. The rotation alters the boundary layer between the object and the fluid. The force is perpendicular to the relative direction of motion and oriented towards the direction of rotation, i.e. the direction the "nose" of the ball is turning towards. [ 7 ] The magnitude of the force depends primarily on the rotation rate, the relative velocity, and the geometry of the body; the magnitude also depends upon the body's surface roughness and viscosity of the fluid. Accurate quantitative predictions of the force are difficult, [ 7 ] : 20 but as with other examples of aerodynamic lift there are simpler, qualitative explanations :
The diagram shows lift being produced on a back-spinning ball. The wake and trailing air-flow have been deflected downwards; according to Newton's third law of motion there must be a reaction force in the opposite direction. [ 1 ] [ 8 ]
The air's viscosity and the surface roughness of the object cause the air to be carried around the object. This adds to the air velocity on one side of the object and decreases the velocity on the other side. Bernoulli's principle states that under certain conditions increased flow speed is associated with reduced pressure, implying that there is lower air pressure on one side than the other. This pressure difference results in a force perpendicular to the direction of travel. [ 9 ]
On a cylinder, the force due to rotation is an example of Kutta–Joukowski lift . It can be analysed in terms of the vortex produced by rotation. The lift per unit length of the cylinder L ′ {\displaystyle L^{\prime }} , is the product of the freestream velocity v ∞ {\displaystyle v_{\infty }} , the fluid density ρ ∞ {\displaystyle \rho _{\infty }} and circulation Γ {\displaystyle \Gamma } due to viscous effects: [ 2 ]
where the vortex strength (assuming that the surrounding fluid obeys the no-slip condition ) is given by
where ω is the angular velocity of the cylinder (in rad/s) and r is the radius of the cylinder.
In wind tunnel studies, (rough surfaced) baseballs show the Magnus effect, but smooth spheres do not. [ 10 ] Further study has shown that certain combinations of conditions result in turbulence in the fluid on one side of the rotating body but laminar flow on the other side. [ 11 ] In these cases are called the inverse Magnus effect: the deflection is opposite to that of the typical Magnus effect. [ 12 ]
Potential flow is a mathematical model of the steady flow of a fluid with no viscosity or vorticity present. For potential flow around a circular cylinder, it provides the following results:
The flow pattern is symmetric about a horizontal axis through the centre of the cylinder. At each point above the axis and its corresponding point below the axis, the spacing of streamlines is the same so velocities are also the same at the two points. Bernoulli's principle shows that, outside the boundary layers , pressures are also the same at corresponding points. There is no lift acting on the cylinder. [ 13 ]
Streamlines are closer spaced immediately above the cylinder than below, so the air flows faster past the upper surface than past the lower surface. Bernoulli's principle shows that the pressure adjacent to the upper surface is lower than the pressure adjacent to the lower surface. The Magnus force acts vertically upwards on the cylinder. [ 14 ]
Streamlines immediately above the cylinder are curved with radius little more than the radius of the cylinder. This means there is low pressure close to the upper surface of the cylinder. Streamlines immediately below the cylinder are curved with a larger radius than streamlines above the cylinder. This means there is higher pressure acting on the lower surface than on the upper. [ 15 ]
Air immediately above and below the cylinder is curving downwards, accelerated by the pressure gradient. A downwards force is acting on the air.
Newton's third law predicts that the Magnus force and the downwards force acting on the air are equal in magnitude and opposite in direction.
The effect is named after German physicist Heinrich Gustav Magnus who demonstrated the effect with a rapidly rotating brass cylinder and an air blower in 1852. [ 16 ] [ 17 ] [ 7 ] : 18 Isaac Newton was the first to observe and explain the effect in 1672 after observing tennis players at Cambridge college. [ 18 ] [ 19 ] In 1742, Benjamin Robins , a British mathematician, ballistics researcher, and military engineer, explained deviations in the trajectories of musket balls due to their rotation. [ 20 ] [ 21 ] [ 22 ] [ 23 ]
Pioneering wind tunnel research on the Magnus effect was carried out with smooth rotating spheres in 1928. [ 24 ] Lyman Briggs later studied baseballs in a wind tunnel, [ 10 ] and others have produced images of the effect. [ 25 ] [ 26 ] [ 12 ] The studies show that a turbulent wake behind the spinning ball causes aerodynamic drag, plus there is a noticeable angular deflection in the wake, and this deflection is in the direction of spin.
The Magnus effect explains commonly observed deviations from the typical trajectories or paths of spinning balls in sport , notably association football , table tennis , [ 27 ] tennis , [ 28 ] volleyball , golf , baseball , and cricket .
The curved path of a golf ball known as slice or hook is largely due to the ball's spin axis being tilted away from the horizontal due to the combined effects of club face angle and swing path, causing the Magnus effect to act at an angle, moving the ball away from a straight line in its trajectory. [ 29 ] Backspin (upper surface rotating backwards from the direction of movement) on a golf ball causes a vertical force that counteracts the force of gravity slightly, and enables the ball to remain airborne a little longer than it would were the ball not spinning: this allows the ball to travel farther than a ball not spinning about its horizontal axis. [ citation needed ]
In table tennis , the Magnus effect is easily observed, because of the small mass and low density of the ball. An experienced player can place a wide variety of spins on the ball. Table tennis rackets usually have a surface made of rubber to give the racket maximum grip on the ball to impart a spin.
In cricket , the Magnus effect contributes to the types of motion known as drift , dip and lift in spin bowling , depending on the axis of rotation of the spin applied to the ball. The Magnus effect is not responsible for the movement seen in conventional swing bowling , [ 30 ] : Fig. 4.19 in which the pressure gradient is not caused by the ball's spin, but rather by its raised seam, and the asymmetric roughness or smoothness of its two halves; however, the Magnus effect may be responsible for so-called "Malinga Swing", [ 31 ] [ 32 ] as observed in the bowling of the swing bowler Lasith Malinga .
In airsoft , a system known as hop-up is used to create a backspin on a fired BB , which greatly increases its range, using the Magnus effect in a similar manner as in golf.
In baseball , pitchers often impart different spins on the ball, causing it to curve in the desired direction due to the Magnus effect. The PITCHf/x system measures the change in trajectory caused by Magnus in all pitches thrown in Major League Baseball . [ 33 ]
The match ball for the 2010 FIFA World Cup has been criticised for the different Magnus effect from previous match balls. The ball was described as having less Magnus effect and as a result flies farther but with less controllable swerve. [ 34 ]
The Magnus effect can also be found in advanced external ballistics . First, a spinning bullet in flight is often subject to a crosswind , which can be simplified as blowing from either the left or the right. In addition to this, even in completely calm air a bullet experiences a small sideways wind component due to its yawing motion. This yawing motion along the bullet's flight path means that the nose of the bullet points in a slightly different direction from the direction the bullet travels. In other words, the bullet "skids" sideways at any given moment, and thus experiences a small sideways wind component in addition to any crosswind component. [ 35 ]
The combined sideways wind component of these two effects causes a Magnus force to act on the bullet, which is perpendicular both to the direction the bullet is pointing and the combined sideways wind. In a very simple case where we ignore various complicating factors, the Magnus force from the crosswind would cause an upward or downward force to act on the spinning bullet (depending on the left or right wind and rotation), causing deflection of the bullet's flight path up or down, thus influencing the point of impact.
Overall, the effect of the Magnus force on a bullet's flight path itself is usually insignificant compared to other forces such as aerodynamic drag . However, it greatly affects the bullet's stability, which in turn affects the amount of drag, how the bullet behaves upon impact, and many other factors. The stability of the bullet is affected, because the Magnus effect acts on the bullet's centre of pressure instead of its centre of gravity . [ 36 ] This means that it affects the yaw angle of the bullet; it tends to twist the bullet along its flight path, either towards the axis of flight (decreasing the yaw thus stabilising the bullet) or away from the axis of flight (increasing the yaw thus destabilising the bullet). The critical factor is the location of the centre of pressure, which depends on the flowfield structure, which in turn depends mainly on the bullet's speed (supersonic or subsonic), but also the shape, air density and surface features. If the centre of pressure is ahead of the centre of gravity, the effect is destabilizing; if the centre of pressure is behind the centre of gravity, the effect is stabilising. [ 37 ]
Some aircraft have been built to use the Magnus effect to create lift with a rotating cylinder instead of a wing, allowing flight at lower horizontal speeds. [ 2 ] The earliest attempt to use the Magnus effect for a heavier-than-air aircraft was in 1910 by a US member of Congress, Butler Ames of Massachusetts. The next attempt was in the early 1930s by three inventors in New York state. [ 38 ]
Rotor ships use mast-like cylinders, called Flettner rotors , for propulsion. These are mounted vertically on the ship's deck. When the wind blows from the side, the Magnus effect creates a forward thrust. Thus, as with any sailing ship, a rotor ship can only move forwards when there is a wind blowing. The effect is also used in a special type of ship stabilizer consisting of a rotating cylinder mounted beneath the waterline and emerging laterally. By controlling the direction and speed of rotation, strong lift or downforce can be generated. [ 39 ] The largest deployment of the system to date is in the motor yacht Eclipse . | https://en.wikipedia.org/wiki/Magnus_effect |
Magnussen model is a popular method for computing reaction rates as a function of both mean concentrations and turbulence levels (Magnussen and Hjertager). [ 1 ] Originally developed for combustion , it can also be used for liquid reactions by tuning some of its parameters. The model consists of rates calculated by two primary means. An Arrhenius , or kinetic rate, R K _ i ′ , k {\displaystyle R_{K\_i',k}} , for species i ′ {\displaystyle i'} in reaction k {\displaystyle k} , is governed by the local mean species concentrations and temperature in the following way:
This expression describes the rate at which species i ′ {\displaystyle i'} is consumed in reaction k {\displaystyle k} . The constants A k {\displaystyle A_{k}} and E k {\displaystyle E_{k}} , the Arrhenius pre-exponential factor and activation energy,
respectively, are adjusted for specific reactions, often as the result of experimental measurements. The stoichiometry for species i ′ {\displaystyle i'} in reaction k {\displaystyle k} is represented by the factor ν i ′ , k {\displaystyle \nu _{i',k}} , and is positive or negative, depending upon whether the species serves as a product or reactant. The molecular weight of the species i ′ {\displaystyle i'} appears as the factor M i ′ {\displaystyle M_{i'}} . The temperature, T {\displaystyle T} , appears in the exponential term and also as a factor in the rate expression, with an optional exponent, β k {\displaystyle \beta _{k}} . Concentrations of other species, j ′ {\displaystyle j'} , involved in the reaction, [ C j ′ ] {\displaystyle \left[C_{j'}\right]} , appear as factors with optional exponents associated with each. Other factors and terms not appearing in the equation, can be added to include effects such as the presence of non-reacting
species in the rate equation. Such so-called third-body reactions are typical of the effect of a catalyst on a reaction, for example. Many of the factors are often collected into a single rate constant, K i ′ , k {\displaystyle K_{i',k}} .
Magnussen, B. F., and B. H. Hjertager, “On Mathematical Mod-
els of Turbulent Combustion with Special Emphasis on Soot For-
mation and Combustion,” Proc. 16th Int. Symp. on Combustion,
The Combustion Institute, Pittsburgh, PA (1976).
This engineering-related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Magnussen_model |
Magway is a UK startup noted for its e-commerce and freight delivery system that aims to transport goods in pods that fit in new and existing 90 cm (35 in)-diameter pipes, underground and overground, reducing road congestion and air pollution . [ 1 ] It uses linear magnetic motors to shuttle pods, designed to accommodate a standard delivery crate (or tote), at approximately 31 miles per hour (50 km/h). [ 2 ]
Founded in 2017 by Rupert Cruise, an engineer on Elon Musk 's Hyperloop project, and Phill Davies, a business expert, Magway secured a £0.65 million grant in 2018, through Innovate UK’s 'Emerging and Enabling Technologies' competition, to develop an operational demonstrator. In 2019, £1.58 million was raised through crowdfunding to fund a pilot scheme, [ 3 ] and in 2020, Magway was awarded £1.9 million [ 1 ] from the UK Government 's 'Driving the Electric Revolution Challenge' , an initiative launched to coincide with the first meeting of a new Cabinet committee focused on climate change . In September 2020, Magway completed its first full loop of test track in a warehouse in Wembley. [ 4 ]
Primarily focused on two freight routes from large consolidation centres near London ( Milton Keynes , Buckinghamshire and Hatfield, Hertfordshire ) into Park Royal , a west London distribution centre , future plans involve installing 850 kilometres (530 mi) of track in decommissioned London gas pipelines, to deliver e-commerce goods from distribution centres direct to consumers in the capital. [ 5 ] The design of the pipes is similar to the current underground pipe system in small tunnels that distribute water, gas, and electricity in the city. [ 6 ] The pods are powered by electromagnetic wave from magnetic motors that are similar to those used in roller coasters. [ 7 ] A proposed route that runs from Milton Keynes to London will have the capacity to transport more than 600 million parcels annually. [ 6 ] Outside of urban areas, Magway plans to build its pipe system alongside motorways. [ 8 ] | https://en.wikipedia.org/wiki/Magway_Ltd |
In mathematics, a Maharam algebra is a complete Boolean algebra with a continuous submeasure (defined below). They were introduced by Dorothy Maharam ( 1947 ).
A continuous submeasure or Maharam submeasure on a Boolean algebra is a real-valued function m such that
A Maharam algebra is a complete Boolean algebra with a continuous submeasure.
Every probability measure is a continuous submeasure, so as the corresponding Boolean algebra of measurable sets modulo measure zero sets is complete, it is a Maharam algebra.
Michel Talagrand ( 2008 ) solved a long-standing problem by constructing a Maharam algebra that is not a measure algebra , i.e. , that does not admit any countably additive strictly positive finite measure.
This algebra -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Maharam_algebra |
The Mahathir Science Award is an award for outstanding contributions in science and technology that address issues related to the tropics. [ 1 ] [ 2 ] The Foundation was established 17 August 2004 in honour of the former Prime Minister of Malaysia Mahathir Mohamad . [ 3 ] [ 4 ] It is presented by the Mahathir Science Award Foundation.
This science awards article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Mahathir_Science_Award |
Mahesha Thakura was the ruler of Mithila in the 16th century. He made his capital at Bhaur which is in the northwest of Sarisab-Pahi and Rajgram. He was also wrote some treatises and commentaries on astronomy and Indian philosophy . He was gifted the Kingdom of Mithila for his scholarly wisdom by the Mughal emperor . He established the Khandwala dynasty in Mithila, later known as Raj Darbhanga, in 1527. [ 1 ] [ page needed ]
Mahesha Thakura was the middle son of Rajpandita Chandrapati Thakura. His mother name was Dhira. [ 2 ] Chandrapati Thakura was Rajpandita (Royal Priest) in Akbar empire. He belonged to Shandilya Gotra in Maithil Brahmin. His mool was Kharaure Bhaur. Chandrapati Thakura was living in Garh Mandla which is presently in Madhya Pradesh . [ 3 ]
Mahesha Thakura was a priest at the court of Dalapatishah in Garha Mandla. He was a priest even during the time of Rani Durgavati . Since he was the scholar of philosophy as well as Karmakanda , he used to narrate the Puranas to the queen Rani Durgavati every day. It is said that during the reign of Rani Durgavati, Mahesha Thakura left Garha Mandla and went to Mithila to establish his kingdom in the region. This kingdom was later called as Darbhanga Raj . [ 3 ]
It is said that the Mughal emperor Akbar was very influenced by the wisdom of Raghunandana Dasa and gifted him the throne of Mithila. Raghunandan Dasa, in turn, gifted the throne of Mithila to his teacher Mahesha Thakura as Gurudakshina . [ 4 ] [ 5 ]
Some scholars claim that Mahesha Thakura's father Chandrapati Thakura was the priest at the court of the Mughal emperor Akbar and the emperor asked Chandrapati Thakura to advise any name of his son for the caretaker of Mithila. Then Chandrapati Thakura advised Akbar his middle son Mahesha Thakura as the caretaker of Mithila. [ 6 ] It said that the Mughal emperor Akbar was also very influenced with the wisdom of Mahesha Thakura so he granted the throne of Mithila to Mahesha Thakura as the caretaker. Mahesha Thakura then became the ruler of Mithila and established Khadwala Dynasty in Mithila on the day of Ramnavami . [ 7 ] [ 8 ] [ 9 ]
Mahesha Thakura established the Khandwala Dynasty, which continued for nearly 400 years ( from 16th century CE to 20th century CE ) in the Mithila region till the independence of India . He is well known for the institution of Dhaut Pariksha at his court to examine the scholarship of the scholars in his kingdom. [ 10 ]
Apart from being the ruler of the Mithila region, Mahesha Thakura was also a renowned scholar of Sanskrit literature, Indian philosophy and astronomy. He was the author several treatises and commentaries. He wrote a commentary Aloka Pradipa on the Nyaya Aloka commentary text of the 15th century eminent Naiyayika Pakshadhara Mishra . Similarly he also wrote a commentary text Darpan on the Tattavachintamani text of the Naiyayika Gangesha Upadhyaya .
Mahesha Thakura also wrote the texts Dayasara and Tethitattava Chintamani . He wrote an astronomical text known as Atīcārādinirṇayaḥ . [ 11 ] | https://en.wikipedia.org/wiki/Mahesha_Thakura |
In mathematics , Mahler's compactness theorem , proved by Kurt Mahler ( 1946 ), is a foundational result on lattices in Euclidean space , characterising sets of lattices that are 'bounded' in a certain definite sense. Looked at another way, it explains the ways in which a lattice could degenerate ( go off to infinity ) in a sequence of lattices. In intuitive terms it says that this is possible in just two ways: becoming coarse-grained with a fundamental domain that has ever larger volume; or containing shorter and shorter vectors. It is also called his selection theorem , following an older convention used in naming compactness theorems, because they were formulated in terms of sequential compactness (the possibility of selecting a convergent subsequence).
Let X be the space
that parametrises lattices in R n {\displaystyle \mathbb {R} ^{n}} , with its quotient topology . There is a well-defined function Δ on X , which is the absolute value of the determinant of a matrix – this is constant on the cosets , since an invertible integer matrix has determinant 1 or −1.
Mahler's compactness theorem states that a subset Y of X is relatively compact if and only if Δ is bounded on Y , and there is a neighbourhood N of 0 in R n {\displaystyle \mathbb {R} ^{n}} such that for all Λ in Y , the only lattice point of Λ in N is 0 itself.
The assertion of Mahler's theorem is equivalent to the compactness of the space of unit-covolume lattices in R n {\displaystyle \mathbb {R} ^{n}} whose systole is larger or equal than any fixed ε > 0 {\displaystyle \varepsilon >0} .
Mahler's compactness theorem was generalized to semisimple Lie groups by David Mumford ; see Mumford's compactness theorem . | https://en.wikipedia.org/wiki/Mahler's_compactness_theorem |
In mathematics , Mahler's inequality , named after Kurt Mahler , states that the geometric mean of the term-by-term sum of two finite sequences of positive numbers is greater than or equal to the sum of their two separate geometric means:
when x k , y k > 0 for all k .
By the inequality of arithmetic and geometric means , we have:
and
Hence,
Clearing denominators then gives the desired result.
This mathematical analysis –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Mahler's_inequality |
In mathematics, Mahler's theorem , introduced by Kurt Mahler ( 1958 ), expresses any continuous p -adic function as an infinite series of certain special polynomials . It is the p -adic counterpart to the Stone-Weierstrass theorem for continuous real-valued functions on a closed interval.
Let ( Δ f ) ( x ) = f ( x + 1 ) − f ( x ) {\displaystyle (\Delta f)(x)=f(x+1)-f(x)} be the forward difference operator . Then for any p -adic function f : Z p → Q p {\displaystyle f:\mathbb {Z} _{p}\to \mathbb {Q} _{p}} , Mahler's theorem states that f {\displaystyle f} is continuous if and only if its Newton series converges everywhere to f {\displaystyle f} , so that for all x ∈ Z p {\displaystyle x\in \mathbb {Z} _{p}} we have
where
is the n {\displaystyle n} th binomial coefficient polynomial. Here, the n {\displaystyle n} th forward difference is computed by the binomial transform , so that ( Δ n f ) ( 0 ) = ∑ k = 0 n ( − 1 ) n − k ( n k ) f ( k ) . {\displaystyle (\Delta ^{n}f)(0)=\sum _{k=0}^{n}(-1)^{n-k}{\binom {n}{k}}f(k).} Moreover, we have that f {\displaystyle f} is continuous if and only if the coefficients ( Δ n f ) ( 0 ) → 0 {\displaystyle (\Delta ^{n}f)(0)\to 0} in Q p {\displaystyle \mathbb {Q} _{p}} as n → ∞ {\displaystyle n\to \infty } .
It is remarkable that as weak an assumption as continuity is enough in the p -adic setting to establish convergence of Newton series. By contrast, Newton series on the field of complex numbers are far more tightly constrained, and require Carlson's theorem to hold. | https://en.wikipedia.org/wiki/Mahler's_theorem |
In mathematics , the Mahler measure M ( p ) {\displaystyle M(p)} of a polynomial p ( z ) {\displaystyle p(z)} with complex coefficients is defined as
M ( p ) = | a | ∏ | α i | ≥ 1 | α i | = | a | ∏ i = 1 n max { 1 , | α i | } , {\displaystyle M(p)=|a|\prod _{|\alpha _{i}|\geq 1}|\alpha _{i}|=|a|\prod _{i=1}^{n}\max\{1,|\alpha _{i}|\},} where p ( z ) {\displaystyle p(z)} factorizes over the complex numbers C {\displaystyle \mathbb {C} } as p ( z ) = a ( z − α 1 ) ( z − α 2 ) ⋯ ( z − α n ) . {\displaystyle p(z)=a(z-\alpha _{1})(z-\alpha _{2})\cdots (z-\alpha _{n}).}
The Mahler measure can be viewed as a kind of height function . Using Jensen's formula , it can be proved that this measure is also equal to the geometric mean of | p ( z ) | {\displaystyle |p(z)|} for z {\displaystyle z} on the unit circle (i.e., | z | = 1 {\displaystyle |z|=1} ): M ( p ) = exp ( ∫ 0 1 ln ( | p ( e 2 π i θ ) | ) d θ ) . {\displaystyle M(p)=\exp \left(\int _{0}^{1}\ln(|p(e^{2\pi i\theta })|)\,d\theta \right).}
By extension, the Mahler measure of an algebraic number α {\displaystyle \alpha } is defined as the Mahler measure of the minimal polynomial of α {\displaystyle \alpha } over Q {\displaystyle \mathbb {Q} } . In particular, if α {\displaystyle \alpha } is a Pisot number or a Salem number , then its Mahler measure is simply α {\displaystyle \alpha } .
The Mahler measure is named after the German-born Australian mathematician Kurt Mahler .
The Mahler measure M ( p ) {\displaystyle M(p)} of a multi-variable polynomial p ( x 1 , … , x n ) ∈ C [ x 1 , … , x n ] {\displaystyle p(x_{1},\ldots ,x_{n})\in \mathbb {C} [x_{1},\ldots ,x_{n}]} is defined similarly by the formula [ 2 ]
M ( p ) = exp ( ∫ 0 1 ∫ 0 1 ⋯ ∫ 0 1 log ( | p ( e 2 π i θ 1 , e 2 π i θ 2 , … , e 2 π i θ n ) | ) d θ 1 d θ 2 ⋯ d θ n ) . {\displaystyle M(p)=\exp \left(\int _{0}^{1}\int _{0}^{1}\cdots \int _{0}^{1}\log {\Bigl (}{\bigl |}p(e^{2\pi i\theta _{1}},e^{2\pi i\theta _{2}},\ldots ,e^{2\pi i\theta _{n}}){\bigr |}{\Bigr )}\,d\theta _{1}\,d\theta _{2}\cdots d\theta _{n}\right).} It inherits the above three properties of the Mahler measure for a one-variable polynomial.
The multi-variable Mahler measure has been shown, in some cases, to be related to special values
of zeta-functions and L {\displaystyle L} -functions . For example, in 1981, Smyth [ 3 ] proved the formulas m ( 1 + x + y ) = 3 3 4 π L ( χ − 3 , 2 ) {\displaystyle m(1+x+y)={\frac {3{\sqrt {3}}}{4\pi }}L(\chi _{-3},2)} where L ( χ − 3 , s ) {\displaystyle L(\chi _{-3},s)} is a Dirichlet L-function , and m ( 1 + x + y + z ) = 7 2 π 2 ζ ( 3 ) , {\displaystyle m(1+x+y+z)={\frac {7}{2\pi ^{2}}}\zeta (3),} where ζ {\displaystyle \zeta } is the Riemann zeta function . Here m ( P ) = log M ( P ) {\displaystyle m(P)=\log M(P)} is called the logarithmic Mahler measure .
From the definition, the Mahler measure is viewed as the integrated values of polynomials over the torus (also see Lehmer's conjecture ). If p {\displaystyle p} vanishes on the torus ( S 1 ) n {\displaystyle (S^{1})^{n}} , then the convergence of the integral defining M ( p ) {\displaystyle M(p)} is not obvious, but it is known that M ( p ) {\displaystyle M(p)} does converge and is equal to a limit of one-variable Mahler measures, [ 4 ] which had been conjectured by Boyd . [ 5 ] [ 6 ]
This is formulated as follows: Let Z {\displaystyle \mathbb {Z} } denote the integers and define Z + N = { r = ( r 1 , … , r N ) ∈ Z N : r j ≥ 0 for 1 ≤ j ≤ N } {\displaystyle \mathbb {Z} _{+}^{N}=\{r=(r_{1},\dots ,r_{N})\in \mathbb {Z} ^{N}:r_{j}\geq 0\ {\text{for}}\ 1\leq j\leq N\}} . If Q ( z 1 , … , z N ) {\displaystyle Q(z_{1},\dots ,z_{N})} is a polynomial in N {\displaystyle N} variables and r = ( r 1 , … , r N ) ∈ Z + N {\displaystyle r=(r_{1},\dots ,r_{N})\in \mathbb {Z} _{+}^{N}} define the polynomial Q r ( z ) {\displaystyle Q_{r}(z)} of one variable by
Q r ( z ) := Q ( z r 1 , … , z r N ) {\displaystyle Q_{r}(z):=Q(z^{r_{1}},\dots ,z^{r_{N}})}
and define q ( r ) {\displaystyle q(r)} by q ( r ) := min { H ( s ) : s = ( s 1 , … , s N ) ∈ Z N , s ≠ ( 0 , … , 0 ) and ∑ j = 1 N s j r j = 0 } {\displaystyle q(r):=\min \left\{H(s):s=(s_{1},\dots ,s_{N})\in \mathbb {Z} ^{N},s\neq (0,\dots ,0)~{\text{and}}~\sum _{j=1}^{N}s_{j}r_{j}=0\right\}}
where H ( s ) = max { | s j | : 1 ≤ j ≤ N } {\displaystyle H(s)=\max\{|s_{j}|:1\leq j\leq N\}} .
Theorem (Lawton) — Let Q ( z 1 , … , z N ) {\displaystyle Q(z_{1},\dots ,z_{N})} be a polynomial in N variables with complex coefficients. Then the following limit is valid (even if the condition that r i ≥ 0 {\displaystyle r_{i}\geq 0} is relaxed): lim q ( r ) → ∞ M ( Q r ) = M ( Q ) {\displaystyle \lim _{q(r)\to \infty }M(Q_{r})=M(Q)}
Boyd provided more general statements than the above theorem. He pointed out that the classical Kronecker's theorem , which characterizes monic polynomials with integer coefficients all of whose roots are inside the unit disk, can be regarded as characterizing those polynomials of one variable whose measure is exactly 1, and that this result extends to polynomials in several variables. [ 6 ]
Define an extended cyclotomic polynomial to be a polynomial of the form Ψ ( z ) = z 1 b 1 … z n b n Φ m ( z 1 v 1 … z n v n ) , {\displaystyle \Psi (z)=z_{1}^{b_{1}}\dots z_{n}^{b_{n}}\Phi _{m}(z_{1}^{v_{1}}\dots z_{n}^{v_{n}}),} where Φ m ( z ) {\displaystyle \Phi _{m}(z)} is the m -th cyclotomic polynomial , the v i {\displaystyle v_{i}} are integers, and the b i = max ( 0 , − v i deg Φ m ) {\displaystyle b_{i}=\max(0,-v_{i}\deg \Phi _{m})} are chosen minimally so that Ψ ( z ) {\displaystyle \Psi (z)} is a polynomial in the z i {\displaystyle z_{i}} . Let K n {\displaystyle K_{n}} be the set of polynomials that are products of monomials ± z 1 c 1 … z n c n {\displaystyle \pm z_{1}^{c_{1}}\dots z_{n}^{c_{n}}} and extended cyclotomic polynomials.
Theorem (Boyd) — Let F ( z 1 , … , z n ) ∈ Z [ z 1 , … , z n ] {\displaystyle F(z_{1},\dots ,z_{n})\in \mathbb {Z} [z_{1},\ldots ,z_{n}]} be a polynomial with integer coefficients. Then M ( F ) = 1 {\displaystyle M(F)=1} if and only if F {\displaystyle F} is an element of K n {\displaystyle K_{n}} .
This led Boyd to consider the set of values L n := { m ( P ( z 1 , … , z n ) ) : P ∈ Z [ z 1 , … , z n ] } , {\displaystyle L_{n}:={\bigl \{}m(P(z_{1},\dots ,z_{n})):P\in \mathbb {Z} [z_{1},\dots ,z_{n}]{\bigr \}},} and the union L ∞ = ⋃ n = 1 ∞ L n {\textstyle {L}_{\infty }=\bigcup _{n=1}^{\infty }L_{n}} . He made the far-reaching conjecture [ 5 ] that the set of L ∞ {\displaystyle {L}_{\infty }} is a closed subset of R {\displaystyle \mathbb {R} } . An immediate consequence of this conjecture would be the truth of Lehmer's conjecture, albeit without an explicit lower bound. As Smyth's result suggests that L 1 ⫋ L 2 {\displaystyle L_{1}\subsetneqq L_{2}} , Boyd further conjectures that L 1 ⫋ L 2 ⫋ L 3 ⫋ ⋯ . {\displaystyle L_{1}\subsetneqq L_{2}\subsetneqq L_{3}\subsetneqq \ \cdots .}
An action α M {\displaystyle \alpha _{M}} of Z n {\displaystyle \mathbb {Z} ^{n}} by automorphisms of a compact metrizable abelian group may be associated via duality to any countable module N {\displaystyle N} over the ring R = Z [ z 1 ± 1 , … , z n ± 1 ] {\displaystyle R=\mathbb {Z} [z_{1}^{\pm 1},\dots ,z_{n}^{\pm 1}]} . [ 7 ] The topological entropy (which is equal to the measure-theoretic entropy ) of this action, h ( α N ) {\displaystyle h(\alpha _{N})} , is given by a Mahler measure (or is infinite). [ 8 ] In the case of a cyclic module M = R / ⟨ F ⟩ {\displaystyle M=R/\langle F\rangle } for a non-zero polynomial F ( z 1 , … , z n ) ∈ Z [ z 1 , … , z n ] {\displaystyle F(z_{1},\dots ,z_{n})\in \mathbb {Z} [z_{1},\ldots ,z_{n}]} the formula proved by Lind, Schmidt , and Ward gives h ( α N ) = log M ( F ) {\displaystyle h(\alpha _{N})=\log M(F)} , the logarithmic Mahler measure of F {\displaystyle F} . In the general case, the entropy of the action is expressed as a sum of logarithmic Mahler measures over the generators of the principal associated prime ideals of the module. As pointed out earlier by Lind in the case n = 1 {\displaystyle n=1} of a single compact group automorphism, this means that the set of possible values of the entropy of such actions is either all of [ 0 , ∞ ] {\displaystyle [0,\infty ]} or a countable set depending on the solution to Lehmer's problem . Lind also showed that the infinite-dimensional torus T ∞ {\displaystyle \mathbb {T} ^{\infty }} either has ergodic automorphisms of finite positive entropy or only has automorphisms of infinite entropy depending on the solution to Lehmer's problem. [ 9 ] | https://en.wikipedia.org/wiki/Mahler_measure |
In mathematics, the Mahler polynomials g n ( x ) are polynomials introduced by Mahler [ 1 ] in his work on the zeros of the incomplete gamma function .
Mahler polynomials are given by the generating function
Which is close to the generating function of the Touchard polynomials .
The first few examples are (sequence A008299 in the OEIS )
This polynomial -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Mahler_polynomial |
Mahmoud Hashem Abdel-Kader is a physical chemist and Professor of Photochemistry at Cairo University /NILES Institute. [ 1 ] [ 2 ] He founded the European Universities in Egypt [ 3 ]
Mahmoud Abdel-Kader received his BSc in Chemistry from Alexandria University in 1969, and was then associated with the Faculty of Science (chemistry) at Tanta University (initially a branch of Alexandria University, from 1972 on an independent university), where he performed "Spectroscopic Studies on Some Hydroxybenzanilides" [ 4 ] and served as a teaching and research assistant (1970–1973). He was granted a DAAD scholarship in 1974 to perform doctoral studies in Germany and received his Ph.D. (Dr. rer. nat.) in " Spectroscopy and Photochemistry" from Stuttgart University in Germany in 1979. [ 5 ] His doctoral studies were supervised by two German physicochemists, Theodor Förster († 1974) and his former scholar Horst E.A. Kramer. It included physicochemical investigations on the isomerization of a merocyanine (polymethine dye) of the stilbazolium betaine type and its corresponding acid [ 6 ] [ 7 ]
After a 3-years period as lecturer in physical chemistry at Tanta University (1979–1982) [ 4 ] and a post-doctoral research period at the University of Karlsruhe, now the Karlsruhe Institute of Technology (Department of Physical Chemistry, 1982 to 1983), he was appointed as Visiting Senior Researcher at the École Polytechnique Fédérale de Lausanne (Switzerland) from 1983 to 1984. He joined the Arabian Gulf University in Bahrain (Professor of Physical Chemistry/Photochemistry at the Faculty of Applied Sciences, 1985–1992), then the United Arab Emirates University (Professor of Physical Chemistry/Photochemistry at the Faculty of Science, 1992–1995). [ 8 ] Mahmoud Abdel-Kader served as Visiting Professor at the Georgia Institute of Technology in Atlanta (USA) and at the Institute for Laser Technology in Medicine and Metrology of Ulm University (Germany). [ 1 ]
He joined Cairo University in 1992 and acted as Department Chairman and Vice Dean of the National Institute of Laser-Enhanced Sciences (NILES) [ 9 ] [ 10 ] until August 2002. He had been involved in the establishment of the German University in Cairo (GUC), where he served as first University President (until 2017). [ 2 ] [ 4 ]
Mahmoud Abdel-Kader's research interests are in:
Mahmoud Abdel-Kader is regarded as one of the experts in the field of modern photodynamic therapy [ 17 ] (PDT) and the 2014-volume "Photodynamic Therapy: from Theory to Application", which he edited and to which he contributed as author, a summary in the various fields of PDT. [ 17 ]
He has supervised approximately 90 master's theses and doctoral dissertations , and has published over 100 scientific communications in peer-reviewed journals and in conference proceedings. [ 4 ] He is an inventor of 8 patents and has given more than 80 invited talks and plenary lectures [ 18 ] at both national and international meetings.
Internationally, Mahmoud Abdel-Kader [ 4 ] is mainly known in the photochemistry -related research field. [ 19 ] He was elected Officer of the European Society for Photobiology in 1997, [ 20 ] then served as "Chair outside Europe" until 2001. In September 2024 he was awarded an Honorary Doctorate of Science by The University of East London for his contributions to chemistry. [ 21 ]
In Egypt, Mahmoud Abdel-Kader has received various honors and awards: [ 4 ] | https://en.wikipedia.org/wiki/Mahmoud_Hashem_Abdel-Kader |
The Shell in situ conversion process ( Shell ICP ) is an in situ shale oil extraction technology to convert kerogen in oil shale to shale oil . It is developed by the Shell Oil Company .
Shell's in situ conversion process has been under development since the early 1980s. [ 1 ] In 1997, the first small scale test was conducted on the 30-by-40-foot (9.1 by 12.2 m) Mahogany property test site, located 200 miles (320 km) west of Denver on Colorado's Western Slope in the Piceance Creek Basin . Since 2000, additional research and development activities have carried on as a part of the Mahogany Research Project. [ 2 ] The oil shale heating at Mahogany started early 2004. [ 3 ] From this test site, Shell has recovered 1,700 barrels (270 m 3 ) of shale oil. [ 4 ] [ 5 ]
The process heats sections of the vast oil shale field in situ , releasing the shale oil and oil shale gas from the rock so that it can be pumped to the surface and made into fuel . In this process, a freeze wall is first to be constructed to isolate the processing area from surrounding groundwater. [ 1 ] To maximize the functionality of the freeze walls, adjacent working zones will be developed in succession. 2,000 feet (610 m) wells, eight feet apart, are drilled and filled with a circulating super-chilled liquid to cool the ground to −60 °F (−50 °C). [ 4 ] [ 6 ] [ 7 ] Water is then removed from the working zone. Heating and recovery wells are drilled at 40 feet (12 m) intervals within the working zone. Electrical heating elements are lowered into the heating wells and used to heat oil shale to between 650 °F (340 °C) and 700 °F (370 °C) over a period of approximately four years. [ 2 ] [ 6 ] Kerogen in oil shale is slowly converted into shale oil and gases, which then flow to the surface through recovery wells. [ 4 ] [ 6 ]
A RAND study in 2005 estimated that production of 100,000 barrels per day (16,000 m 3 /d) of oil (5.4 million tons/year) would theoretically require a dedicated power generating capacity of 1.2 gigawatts (10 billion kWh/year), assuming deposit richness of 25 US gallons (95 L; 21 imp gal) per ton, with 100% pyrolysis efficiency, and 100% extraction of pyrolysis products. [ 1 ] If this amount of electricity were to be generated by a coal-fired power plant, it would consume five million ton of coal annually (about 2.2 million toe ). [ 8 ]
In 2006, Shell estimated that over the project life cycle, for every unit of energy consumed, three to four units would be produced. [ 4 ] [ 6 ] Such an " energy returned on energy invested " would be significantly better than that achieved in the Mahogany trials. For the 1996 trial, Shell applied 440,000 kWh (which would require about 96 toe energy input in a coal-fired plant), to generate 250 barrels (40 m 3 ) of oil (37 toe output). [ 9 ]
Shell's underground conversion process requires significant development on the surface. The separation between drilled wells is less than five meters and wells must be connected by electrical wiring and by piping to storage and processing facilities. Shell estimates that the footprint of extraction operations would be similar to that for conventional oil and gas drilling. [ 4 ] [ 6 ] However, the dimensions of Shell's 2005 trial indicate that a much larger footprint is required. Production of 50,000 bbl/day would require that land be developed at a rate on the order of 1 square kilometre (0.39 sq mi) per year. [ 10 ]
Extensive water use and the risk of groundwater pollution are the technology's greatest challenges. [ 11 ]
In 2006, Shell received a Bureau of Land Management lease to pursue a large demonstration with a capacity of 1,500 barrels per day (240 m 3 /d); Shell has since dropped those plans and is planning a test based on ICP that would produce a total of minimum 1,500 barrels (240 m 3 ), together with nahcolite , over a seven-year period. [ 12 ] [ 13 ]
In Israel, IEI, a subsidiary of IDT Corp. is planning a shale pilot based on ICP technology. The project would produce a total of 1,500 barrels. However, IEI has also announced that any subsequent projects would not use ICP technology, but would instead utilize horizontal wells and hot gas heating methods. [ 14 ]
In Jordan, Shell subsidiary JOSCO plans to use ICP technology to achieve commercial production by the "late 2020s." [ 15 ] In October, 2011, it was reported that JOSCO had drilled more than 100 test holes over the prior two years, apparently for the sake of testing shale samples. [ 16 ]
The Mahogany Oil Shale Project has been abandoned by Shell in 2013 due to unfavorable project economics [ 17 ] | https://en.wikipedia.org/wiki/Mahogany_Research_Project |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.