Source string | Question string | Answer string | Question_type string | Referenced_file(s) string | chunk_text string | expert_annotation string | specific to paper string | Label int64 |
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expert | Which effects, relevant in synchrotrons, can occur when an X-ray photon interacts with an electron bound to an atom? | Photoelectric absorption, Thomson scattering and Compton scattering. | Summary | Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation | Suggest a way to lower the emittance at the existing machine in order to test the instrumentation. What are some issues with your suggestion? I.10.7.24 Upgrade The SLS 2.0 Upgrade, amongst other things, considers an increase of the electron energy from 2.4 to $2 . 7 \\mathrm { G e V . }$ ‚Äì What can be the rationale for this change? Assume that the lattice is the same for both energies. ‚Äì Are there detrimental aspects to an energy increase? I.10.7.25 Neutron star A proton with energy $E _ { p } = 1 0 \\mathrm { T e V }$ moves through the magnetic field of a neutron star with strength $B = 1 0 ^ { 8 } \\mathrm { T }$ . ‚Äì Calculate the diameter of the proton trajectory and the revolution frequency. ‚Äì How large is the power emitted by synchrotron radiation? ‚Äì How much energy does the proton lose per revolution? I.10.7.26 Cosmic electron A cosmic electron with an energy of $1 \\mathrm { G e V }$ enters an interstellar region with a magnetic field of $1 \\ \\mathrm { n T }$ . Calculate: ‚Äì The radius of curvature, ‚Äì The critical energy of the emitted synchrotron radiation, ‚Äì The energy emitted in one turn. | 1 | NO | 0 |
expert | Which effects, relevant in synchrotrons, can occur when an X-ray photon interacts with an electron bound to an atom? | Photoelectric absorption, Thomson scattering and Compton scattering. | Summary | Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation | This undulator is placed in a storage ring, with an electron beam energy of $E = 4 { \\mathrm { G e V } } ,$ and a beam current of $4 0 0 \\mathrm { m A }$ . The beam is focused to a waist of $\\sigma _ { x } = \\sigma _ { y } = 2 0 \\mu \\mathrm { m }$ inside the undulator. ‚Äì What range can be reached with the fundamental photon energy? ‚Äì What brilliance can be reached at the fundamental photon energy? ‚Äì Is there a significant flux higher harmonics? I.10.7.19 Undulator radiation Assume an undulator of $1 5 \\mathrm { m m }$ period and $5 \\mathrm { m }$ length. The pole tip field is $B _ { t } = 1 . 5 \\ : \\mathrm { T }$ , and the gap can be varied between 8 and $1 6 \\mathrm { m m }$ . This undulator is placed in a storage ring, with an electron beam energy of $E = 3 . 2 \\mathrm { G e V } ,$ and a beam current of $5 0 0 \\mathrm { m A }$ . The beam is focused to a waist of $\\sigma _ { x } = \\sigma _ { y } = 2 0 \\mu \\mathrm { m }$ inside the undulator. | 1 | NO | 0 |
expert | Which effects, relevant in synchrotrons, can occur when an X-ray photon interacts with an electron bound to an atom? | Photoelectric absorption, Thomson scattering and Compton scattering. | Summary | Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation | ‚Äì Fourtihogneneexrtartaiocnti:oFnr.oAmccthoerd2i0n1g0lsyonewiatrhdes.r tAhlseoskonuorwcne assizdeiffnraocrtitohneliamnitgeudlsatrorage rings (DLSsRpsr),etahde sewfearciel itoiepstifematiuzreds iagsn ifaicra natsl ytrhed urcaedihaotiriozno nitsa lceomnicttearnnce,di.ncreasing the coherent flux siVgenirfyi casnotloy.n Wdeewdillclaotoekd atftahceislietinesd, etawilhinerSe ctihoen I.u1n0i.4q.uEe xapmuprlepsoisnec luodfe MA iXnItVh in Lutnhd,e Sewledcetnr,oan datcheceulpecroamtionr g SwLaSs 2t.0o inseVrilvlie geans, Sa wiltizgehrlta nsdo. Synchrotronesleacretrtohne dset-ofraactgoestraindgasr,dwfohrerreseetarhceh eulseincgtrconhserecinrtcXu-lratyebaetamas. Tnhsetyanarte operated by nationaleonreErguryo paenadn trhese raracdh alatbiorna tlorises s,is wrheoplmeankieshthed mbay vaRiFl apbloewtoera. cBadEeSmSiYc I aind indusftrioalm researchers.BeSrylnicnh, roGtreornms arney naonwds utphpel eNmaetnitoednabl ySfryenecehlercotrtornonl asLeirgsh(t FSEoLus)r,cwe h(icNhSLmSa)ke usetorfoan linear acceler ator to generate u ltrabr ight electron be ams that radi ate c oherent ly in lo ng undulators. FaEnLds are treated in Chapte r II I.7. The key properties of synchrotron radiation are: ‚Äì Broad spectrum available, ‚Äì High flux, ‚Äì High spectral brightness, ‚Äì High degree of transverse coherence, ‚Äì Polarization can be controlled, ‚Äì Pulsed time structure, ‚Äì Stability, ‚Äì Power can be computed from first principles. We will now navigate through the electromagnetic theory to understand how synchrotron radiation is generated when relativistic electrons are subjected to magnetic fields, noting in particular undulators, insertion devices present in every synchrotron radiation source. We will then look at the effect of the emission of synchrotron radiation on the particle bunches in a storage ring, and come to the surprising conclusion that this actually improves the emittance of the beam. We will then explore recent technological advancements in accelerator physics, which allow improving the transverse coherence of the $\\mathrm { \\Delta } X$ -ray beams significantly. Finally, we will look at the interaction of $\\mathrm { \\Delta } X$ -rays with matter, and give an overview of scientific uses of synchrotron radiation. | 1 | NO | 0 |
expert | Which effects, relevant in synchrotrons, can occur when an X-ray photon interacts with an electron bound to an atom? | Photoelectric absorption, Thomson scattering and Compton scattering. | Summary | Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation | ‚Äì Vacuum system: as a result of the smaller inner bore of the magnets, the vacuum chamber diameter needs to be reduced to a point where a conventional pumping system becomes difficult to implement. A key enabling technology is the use of a distributed getter pump system, where the entire vacuum chamber is coated with a non-evaporable getter (NEG); ‚Äì Generation of hard X-rays: the strong field in longitudinal gradient bends, peaking at 4. . . 6 Tesla, results in very hard X-rays, up to a photon energy of $8 0 \\mathrm { k e V }$ ; ‚Äì Momentum compaction factor: when designing a magnetic lattice that employs LGBs and reverse bends, one can achieve a situation where a higher-energy particle takes a shorter path. This can then result in a negative momentum compaction factor of the ring (like in proton synchrotrons below transition energy). The Paul Scherrer Institut is upgrading its storage ring in the year 2024, making use of the principles outlined in this section [5]. I.10.5 Interaction of $\\mathbf { X }$ -rays with matter In the subsequent sections, we will look at the interaction of X-rays with matter, and the use of X-rays for experiments. To understand the processes that lead to absorption, scattering, and diffraction, we will proceed in three steps, and look at the interaction of $\\mathrm { \\Delta X }$ -rays with: | 1 | NO | 0 |
expert | Which effects, relevant in synchrotrons, can occur when an X-ray photon interacts with an electron bound to an atom? | Photoelectric absorption, Thomson scattering and Compton scattering. | Summary | Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation | I.10.2 Generation of radiation by charged particles An accelerated charge emits electromagnetic radiation. An oscillating charge emits radiation at the oscillation frequency, and a charged particle moving on a circular orbit radiates at the revolution frequency. As soon as the particles approach the speed of light, however, this radiation is shifted towards higher frequencies, and it is concentrated in a forward cone, as shown in Fig. I.10.3. I.10.2.1 Non-relativistic particles moving in a dipole field Let us first look at non-relativistic particles. In a constant magnetic field with magnitude $B$ , a particle with charge $e$ and momentum $p = m v$ will move on a circular orbit with radius $\\rho$ $$ \\rho = \\frac { p } { e B } . $$ This is an accelerated motion, and the particle emits radiation. For non-relativistic particles, this radiation is called cyclotron radiation, and the total emitted power is $$ P = \\sigma _ { t } \\frac { B ^ { 2 } v ^ { 2 } } { \\mu _ { 0 } c } , $$ where $\\sigma _ { t }$ is the Thomson cross section $$ \\sigma _ { t } = \\frac { 8 \\pi } { 3 } \\left( \\frac { e ^ { 2 } } { 4 \\pi \\varepsilon _ { 0 } m c ^ { 2 } } \\right) ^ { 2 } . | augmentation | NO | 0 |
expert | Which effects, relevant in synchrotrons, can occur when an X-ray photon interacts with an electron bound to an atom? | Photoelectric absorption, Thomson scattering and Compton scattering. | Summary | Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation | applications in Section I.10.6. The total radiated power per particle, obtained by integrating over the spectrum, is $$ P _ { \\gamma } = \\frac { e ^ { 2 } c } { 6 \\pi \\varepsilon _ { 0 } } \\frac { \\beta ^ { 4 } \\gamma ^ { 4 } } { \\rho ^ { 2 } } . $$ The energy lost by a particle on a circular orbit, i.e. in an accelerator consisting only of dipole magnets, is $$ U _ { 0 } = \\frac { e ^ { 2 } \\beta ^ { 4 } \\gamma ^ { 4 } } { 3 \\varepsilon _ { 0 } \\rho } , $$ where we have used $T = 2 \\pi \\rho / c$ , assuming $v \\approx c$ . Of course, real accelerators contain also other types of magnets. The energy lost per turn for a particle in an arbitrary accelerator lattice can be calculated by the following ring integral $$ U _ { 0 } = \\frac { C _ { \\gamma } } { 2 \\pi } E _ { \\mathrm { n o m } } ^ { 4 } \\oint \\frac { 1 } { \\rho ^ { 2 } } d s , | augmentation | NO | 0 |
expert | Which effects, relevant in synchrotrons, can occur when an X-ray photon interacts with an electron bound to an atom? | Photoelectric absorption, Thomson scattering and Compton scattering. | Summary | Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation | File Name:Ischebeck_-_2024_-_I.10_‚Äî_Synchrotron_radiation.pdf Chapter I.10 Synchrotron radiation Rasmus Ischebeck Paul Scherrer Institut, Villigen, Switzerland Electrons circulating in a storage ring emit synchrotron radiation. The spectrum of this powerful radiation spans from the far infrared to the $\\boldsymbol { \\mathrm { \\Sigma } } _ { \\mathrm { X } }$ -rays. Synchrotron radiation has evolved from being a mere byproduct of particle acceleration to a powerful tool leveraged in diverse scientific and engineering fields. Indeed, synchrotrons are the most brilliant X-ray sources on Earth, and they find use in a wide range of fields in research. In this chapter, we will look at the generation of radiation of charged particles in an accelerator, at the influence of this on the beam dynamics, and on the physics behind applications of synchrotron radiation for research. I.10.1 Introduction It is difficult to overstate the importance of X-rays for medicine, research and industry. Already a few years after their discovery by Wilhelm Conrad R√∂ntgen, their ability to penetrate matter established Xrays as an important diagnostics tool in medicine. Experiments with $\\mathrm { \\Delta X }$ -rays have come a long way since the inception of the first $\\mathrm { \\Delta } X$ -ray tubes. The short wavelength of $\\mathrm { \\Delta X }$ -rays allowed Rosalynd Franklin and Raymond Gosling to take diffraction images that would lead to the discovery of the structure of DNA. Today, X-ray diffraction is an indispensable tool in structural biology and in pharmaceutical research. Industrial applications of X-rays range from cargo inspection to sterilization and crack detection. | augmentation | NO | 0 |
expert | Which effects, relevant in synchrotrons, can occur when an X-ray photon interacts with an electron bound to an atom? | Photoelectric absorption, Thomson scattering and Compton scattering. | Summary | Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation | $$ with a horizontal damping time $$ \\tau _ { x } = \\frac { 2 } { j _ { x } } \\frac { E _ { 0 } } { U _ { 0 } } T _ { 0 } . $$ All effects related to the dispersion are summarized in the horizontal partition number $j _ { x }$ $$ j _ { x } = 1 - { \\frac { I _ { 4 } } { I _ { 2 } } } . $$ The second synchrotron radiation integral is defined in Equation I.10.12. For the sake of completeness, we now define all five synchrotron radiation integrals $$ \\begin{array} { r c l } { { I _ { 1 } } } & { { = } } & { { \\displaystyle \\oint \\frac { \\eta _ { x } } { \\rho } d s } } \\\\ { { } } & { { } } & { { } } \\\\ { { I _ { 2 } } } & { { = } } & { { \\displaystyle \\oint \\frac { 1 } { \\rho ^ { 2 } } d s } } \\\\ { { } } & { { } } & { { } } \\\\ { { I _ { 3 } } } & { { = } } & { { \\displaystyle \\oint \\frac { 1 } { | \\rho | ^ { 3 } } d s } } \\\\ { { } } & { { } } & { { } } \\\\ { { I _ { 4 } } } & { { = } } & { { \\displaystyle \\oint \\frac { \\eta _ { x } } { \\rho } \\left( \\frac { 1 } { \\rho ^ { 2 } } + 2 k _ { 1 } \\right) d s , \\qquad k _ { 1 } = \\frac { e } { P _ { 0 } } \\frac { \\partial B _ { y } } { \\partial x } } } \\\\ { { } } & { { } } & { { } } \\\\ { { I _ { 5 } } } & { { = } } & { { \\displaystyle \\oint \\frac { \\hat { \\mathcal { H } } _ { x } } { | \\rho | ^ { 3 } } d s , ~ \\qquad \\mathcal { H } _ { x } = \\gamma _ { x } \\eta _ { x } ^ { 2 } + 2 \\alpha _ { x } \\eta _ { x } \\eta _ { \\rho x } + \\beta _ { x } \\eta _ { p x } ^ { 2 } . } } \\end{array} | augmentation | NO | 0 |
expert | Which effects, relevant in synchrotrons, can occur when an X-ray photon interacts with an electron bound to an atom? | Photoelectric absorption, Thomson scattering and Compton scattering. | Summary | Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation | I.10.7.55 Practical applications of synchrotron radiation The Italian Light Source Elettra is a 3rd generation synchrotron source with $2 5 9 \\mathrm { m }$ circumference, and can operate at beam energies of either $2 . 0 \\mathrm { G e V }$ or $2 . 4 \\mathrm { G e V } ,$ with beam currents of $3 1 0 \\mathrm { m A }$ and $1 6 0 \\mathrm { m A }$ , respectively. The Machine Director is feeling thirsty, and would like to use Elettra to make a splendid espresso. By assuming that all radiation emitted as SR from the dipole magnets can be converted into heat, calculate how much time is needed for the $2 . 0 \\mathrm { G e V }$ beam to heat up the espresso water from $2 0 ^ { \\circ } \\mathrm { C }$ to $8 8 ^ { \\circ } \\mathrm { C }$ . One espresso is $3 0 \\mathrm { m L }$ . The radius of curvature in the dipoles is $5 . 5 \\mathrm { m }$ . Neglect potential insertion devices! Hint: the specific heat capacity of water is $\\begin{array} { r } { c _ { w } = 4 . 1 8 6 \\frac { \\mathrm { ~ J ~ } } { \\mathrm { g K } } } \\end{array}$ | augmentation | NO | 0 |
expert | Which effects, relevant in synchrotrons, can occur when an X-ray photon interacts with an electron bound to an atom? | Photoelectric absorption, Thomson scattering and Compton scattering. | Summary | Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation | $$ Shifting our view to a broader perspective, we now consider the properties of the entire electron bunch. By definition, the emittance is given as the ensemble average of the action. The change in emittance follows thus from the change in action $$ \\begin{array} { r c l } { d \\varepsilon _ { y } } & { = } & { \\langle d J _ { y } \\rangle } \\\\ & { = } & { - \\langle \\alpha _ { y } \\underbrace { \\langle g p _ { y } \\rangle } _ { = - \\alpha _ { y } \\varepsilon _ { y } } + \\beta _ { y } \\underbrace { \\langle p _ { y } ^ { 2 } \\rangle } _ { = \\gamma _ { \\mathrm { t r } } \\varepsilon _ { y } } \\frac { \\partial p _ { \\mathrm { t } } } { \\partial P _ { 0 } } } \\\\ & & { - \\langle - \\alpha _ { y } ^ { 2 } \\varepsilon _ { y } + \\beta _ { y } \\gamma _ { y } \\varepsilon _ { y } \\rangle \\frac { \\partial p _ { \\mathrm { t } } } { \\partial P _ { 0 } } } \\\\ & { = } & { - \\varepsilon _ { y } \\langle \\underbrace { \\delta _ { y } \\gamma _ { y } } _ { \\mathrm { 1 } } - \\alpha _ { y } ^ { 2 } \\rangle \\frac { d p _ { \\mathrm { f } } } { P _ { 0 } } } \\\\ & & { - \\varepsilon _ { y } \\frac { d p _ { \\mathrm { f } } } { D _ { 0 } } , } \\end{array} | augmentation | NO | 0 |
expert | Which effects, relevant in synchrotrons, can occur when an X-ray photon interacts with an electron bound to an atom? | Photoelectric absorption, Thomson scattering and Compton scattering. | Summary | Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation | The total radiated power depends on the fourth power of the Lorentz factor $\\gamma$ , or for a given particle energy, it is inversely proportional to the fourth power of the mass of this particle. This means that synchrotron radiation, and its effect on the beam, are negligible for all proton accelerators except for the highest-energy one. For electron storage rings, conversely, this radiation dominates power losses of the beam, the evolution of the emittance in the ring, and therefore the beam dynamics of the accelerator. Before we will look at this in detail, we will treat one particular case where the electrons pass through a sinusoidal magnetic field. Such a field, generated by wigglers and undulators2, gives rise to strong radiation in the forward direction, which makes it particularly useful for applications of $\\mathrm { \\Delta } \\mathrm { X }$ -rays. I.10.2.3 Coherent generation of X-rays in undulators Wiggler and undulator magnets are devices that impose a periodic magnetic field on the electron beam. These insertion devices have been specially designed to excite the emission of electromagnetic radiation in particle accelerators. Let us assume a cartesian coordinate system with an electron travelling in $z$ direction. A planar insertion device, with a mangetic field in the vertical direction $y$ , has the following field on axis | augmentation | NO | 0 |
expert | Which effects, relevant in synchrotrons, can occur when an X-ray photon interacts with an electron bound to an atom? | Photoelectric absorption, Thomson scattering and Compton scattering. | Summary | Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation | $$ When deriving the equations for the beam dynamics in the horizontal phase space, we need to consider: ‚Äì Change in momentum: the emission of radiation leads to a recoil of the electron. This change in momentum is the same that we considered in the vertical phase space; ‚Äì Dispersion: the emission of radiation results in a change in the energy deviation, denoted as $\\delta$ . This deviation brings about subsequent changes in the horizontal coordinate $x$ and its associated momentum $p _ { x }$ . When we explored the beam dynamics in the vertical phase space, we ignored the second factor, as we assumed that the vertical dispersion is zero. This assumption streamlined the analysis, but it can certainly not be made in the horizontal dimension. While the details of the interplay between the emission of synchrotron radiation and the damping of the emittance are unique to each plane, the outcomes are similar. The horizontal emittance decays exponentially $$ \\frac { d \\varepsilon _ { x } } { d t } = - \\frac { 2 } { \\tau _ { x } } \\varepsilon _ { x } $$ $$ \\Rightarrow \\varepsilon _ { x } ( t ) = \\varepsilon _ { x } ( 0 ) \\exp \\left( - 2 \\frac { t } { \\tau _ { x } } \\right) | augmentation | NO | 0 |
expert | Which effects, relevant in synchrotrons, can occur when an X-ray photon interacts with an electron bound to an atom? | Photoelectric absorption, Thomson scattering and Compton scattering. | Summary | Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation | This method contrasts with traditional filling schemes, where the beam intensity peaks right after a fill and then continuously diminishes. Top-up injection maintains a nearly constant beam current, equilibrating thermal load and thereby improving the stability of the beam over extended periods. Such consistency is particularly advantageous for user experiments, because the electron beam emits in an X-ray beam that is constant in intensity and pointing, offering more uniform conditions and reliable data. Furthermore, the ability to maintain optimal beam conditions without ramping the lattice during acceleration enhances overall time available for experiments. For this reason, virtually all modern synchrotrons make use of top-up injection (see Fig. I.10.7). I.10.3.5.3 Robinson theorem If we take the sum of all three partition damping numbers, noting that $\\begin{array} { r } { j _ { x } = 1 - \\frac { I _ { 4 } } { I _ { 2 } } } \\end{array}$ , $\\begin{array} { r } { j _ { z } = 2 + \\frac { I _ { 4 } } { I _ { 2 } } } \\end{array}$ , and using $j _ { y } = 1$ as the vertical damping does not depend on the synchrotron radiation integrals, we can derive the Robinson theorem, which states that the sum of the partition numbers is 4 | augmentation | NO | 0 |
expert | Which effects, relevant in synchrotrons, can occur when an X-ray photon interacts with an electron bound to an atom? | Photoelectric absorption, Thomson scattering and Compton scattering. | Summary | Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation | I.10.7.2 Brilliance Estimate the brilliance $\\boldsymbol { B }$ of the sun on its surface, for photons in the visible spectrum. What is the brilliance of the sun on the surface of the Earth? For simplicity, ignore the influence of the Earth‚Äôs atmosphere. Table: Caption: Sun Body: <html><body><table><tr><td>Radiated power</td><td>3.828 ¬∑ 1026</td><td>W</td></tr><tr><td>Surface area</td><td>6.09 ¬∑1012</td><td>km¬≤</td></tr><tr><td>Distance to Earth</td><td>1.496 ¬∑ 108</td><td>km</td></tr><tr><td>Angular size,seen from Earth</td><td>31.6.. .32.7</td><td>minutes of arc</td></tr><tr><td>Age</td><td>4.6 ¬∑ 109</td><td>years</td></tr></table></body></html> I.10.7.3 Synchrotron radiation Synchrotron radiation. . . (check all that apply: more than one answer may be correct) a) . . . is used by scientists in numerous disciplines, including semiconductor physics, material science and molecular biology b) . . . can be calculated from Maxwell‚Äôs equations, without the need of material constants c) . . . is emitted at much longer wavelengths, as compared to cyclotron radiation d) . . . is emitted uniformly in all directions, when seen in the reference frame of the particle e) . . . is emitted in forward direction in the laboratory frame, and uniformly in all directions, when seen in the reference frame of the electron bunches I.10.7.4 Crab Nebula On July 5, 1054, astronomers observed a new star, which remained visible for about two years, and it was brighter than all stars in the sky (with the exception of the Sun). Indeed, it was a supernova, and the remnants of this explosion, the Crab Nebula, are still visible today. It was discovered in the 1950‚Äôs that a significant portion of the light emitted by the Crab Nebula originates from synchrotron radiation (Fig. I.10.17). | augmentation | NO | 0 |
expert | Which effects, relevant in synchrotrons, can occur when an X-ray photon interacts with an electron bound to an atom? | Photoelectric absorption, Thomson scattering and Compton scattering. | Summary | Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation | $$ Equation (I.10.16) becomes $$ \\begin{array} { r c l } { { \\displaystyle \\frac { \\lambda } { 2 c } } } & { { = } } & { { \\displaystyle \\frac { \\lambda _ { u } } { 2 \\beta c } \\left( 1 + \\frac { K ^ { 2 } } { 4 \\gamma ^ { 2 } } \\right) - \\frac { \\lambda _ { u } } { 2 c } } } \\\\ { { \\Longrightarrow } } & { { \\lambda } } & { { = } } & { { \\displaystyle \\frac { \\lambda _ { u } } { 2 \\gamma ^ { 2 } } ( 1 + K ^ { 2 } / 2 ) , } } \\end{array} $$ where we have used $\\beta = \\textstyle \\sqrt { 1 - \\gamma ^ { - 2 } } \\approx 1 - \\frac { 1 } { 2 } \\gamma ^ { - 2 }$ for $\\gamma \\gg 1$ . Radiation emitted at this wavelength adds up coherently in the forward direction. More generally, the radiation adds up coherently at all odd harmonics $n = 2 m - 1 , m \\in \\mathbb { N }$ | augmentation | NO | 0 |
expert | Which material is preferred for a short pulse colinear accelerator: copper, aluminum or stainless steal? | Stainless steel | Reasoning | Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf | $$ \\begin{array} { l } { \\displaystyle P ^ { 1 / 2 } ( z , t ) = \\sqrt { \\frac { 2 \\kappa q _ { 0 } ^ { 2 } | F | ^ { 2 } v _ { g } } { 1 - \\beta _ { g } } } e ^ { \\frac { - \\alpha ( v _ { g } t - \\beta _ { g } z ) } { 1 - \\beta _ { g } } } \\cos { \\left[ \\omega \\left( t - \\frac { z } { c } \\right) \\right] } } \\\\ { \\displaystyle \\times \\Pi \\bigg ( \\frac { 2 v _ { g } t - z ( 1 + \\beta _ { g } ) } { 2 z ( 1 - \\beta _ { g } ) } \\bigg ) . } \\end{array} $$ Here the field strength is defined in units of $\\sqrt { \\mathrm { W } }$ for consistency with the units provided by CST simulation, $F$ is the bunch form factor derived in Appendix B, $q _ { 0 }$ is the drive bunch charge, and $\\Pi ( x )$ is the rectangular window function. | 1 | Yes | 0 |
expert | Which material is preferred for a short pulse colinear accelerator: copper, aluminum or stainless steal? | Stainless steel | Reasoning | Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf | $$ Equation (B5) can now be written in terms of the Fourier transformed functions as $$ \\begin{array} { c } { { P _ { w } = \\displaystyle \\frac { c } { ( 2 \\pi ) ^ { 3 } } \\mathrm { R e } \\Bigg \\{ \\int _ { - \\infty } ^ { \\infty } \\int _ { - \\infty } ^ { \\infty } I ( \\omega _ { 2 } ) e ^ { j \\omega _ { 2 } t } d \\omega _ { 2 } \\int _ { - \\infty } ^ { \\infty } } } \\\\ { { \\times \\int _ { - \\infty } ^ { \\infty } I ( \\omega _ { 1 } ) e ^ { j \\omega _ { 1 } ( t - t ^ { \\prime } ) } d \\omega _ { 1 } \\int _ { - \\infty } ^ { \\infty } Z _ { | | } ( \\omega ) e ^ { j \\omega t ^ { \\prime } } d \\omega d t ^ { \\prime } d t \\Bigg \\} . } } \\end{array} | 1 | Yes | 0 |
expert | Which material is preferred for a short pulse colinear accelerator: copper, aluminum or stainless steal? | Stainless steel | Reasoning | Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf | $$ \\Pi ( x ) = { \\left\\{ \\begin{array} { l l } { 1 } & { | x | < 1 / 2 } \\\\ { 0 } & { { \\mathrm { e l s e } } } \\end{array} \\right. } $$ The derivative of the one-dimensional energy dissipation distribution $Q _ { \\mathrm { d i s s } } ( z )$ along the corrugated structure is obtained by multiplying $P$ from Eq. (12) by the attenuation constant $\\alpha$ and integrating the product over time from $t = 0$ to $t = \\infty$ giving $$ \\frac { d Q _ { \\mathrm { d i s s } } ( z ) } { d z } = \\frac { E _ { \\mathrm { a c c } } ^ { 2 } } { 4 \\kappa } ( 1 - e ^ { - 2 \\alpha z } ) , $$ where we have made the substitution $E _ { \\mathrm { a c c } } = 2 \\kappa q _ { 0 } | \\boldsymbol { F } |$ as derived in Appendix B. The total energy dissipated in the CWG of the length $L$ is obtained by integrating Eq. (14) over the length $L$ giving | 1 | Yes | 0 |
expert | Which material is preferred for a short pulse colinear accelerator: copper, aluminum or stainless steal? | Stainless steel | Reasoning | Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf | $$ Q _ { \\mathrm { d i s s } } = \\frac { E _ { \\mathrm { a c c } } ^ { 2 } } { 8 \\alpha \\kappa } ( e ^ { - 2 \\alpha L } + 2 \\alpha L - 1 ) . $$ According to Eq. (14), the amount of energy deposited on the CWG wall per unit length reaches a maximum after the electron bunch propagates a distance $z \\gg 1 / \\alpha$ . It is further convenient to approximate the CWG as a smooth cylinder of radius $a$ and elementary area $d S = 2 \\pi a d z$ , leading to the energy dissipation density on the cylinder wall: $$ \\frac { d Q _ { \\mathrm { d i s s } } ( z \\infty ) } { d S } = \\frac { E _ { \\mathrm { a c c } } ^ { 2 } } { 8 \\pi a \\kappa } . $$ Since the undulating wall of the CWG has a larger surface area per unit length than the smooth cylinder, Equation (16) is an upper bound on the average energy dissipation density in the CWG wall. From Eq. (16), we define the upper bound of the average thermal power dissipation density as | 1 | Yes | 0 |
expert | Which material is preferred for a short pulse colinear accelerator: copper, aluminum or stainless steal? | Stainless steel | Reasoning | Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf | The condition for vertical sidewalls is $\\zeta = 1$ and $d > p / 2$ . Preventing a self-intersecting geometry requires both the width of the tooth and vacuum gap to be less than the corrugation period, as well as a sufficiently large corrugation depth when $\\zeta > 1$ to ensure positive length of the inner tangent line defining the sidewall. These conditions can be expressed as $$ \\zeta - 2 < \\xi < 2 - \\zeta , $$ $$ d > { \\frac { p } { 2 } } \\left( \\zeta + { \\sqrt { \\zeta ^ { 2 } - 1 } } \\right) \\quad { \\mathrm { f o r ~ } } \\zeta > 1 . $$ III. SIMULATION Electromagnetic simulation of the $\\mathrm { T M } _ { 0 1 }$ accelerating mode was performed using the eigenmode solver in CST Microwave Studio [13]. In this analysis, only the fundamental $\\mathrm { T M } _ { 0 1 }$ mode was considered since it accounts for the largest portion of the accelerating gradient. It will be shown in Sec. VII that the exclusion of higher order modes (HOMs) is a very good approximation for the corrugated structures under consideration. A tetrahedral mesh and magnetic symmetry planes were used to accurately model the rounded corners of the corrugation and minimize computation time. Since the simulation only considers a single period of the geometry, the run time was short (approximately $1 \\mathrm { ~ m ~ }$ on a four-core desktop PC) allowing large parametric sweeps to be run rapidly. The eigenmode solver models the corrugated waveguide as a periodic structure of infinite length by employing a periodic boundary condition derived from beam-wave synchronicity: | 1 | Yes | 0 |
expert | Which material is preferred for a short pulse colinear accelerator: copper, aluminum or stainless steal? | Stainless steel | Reasoning | Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf | $$ where $\\tau = ( 1 - \\beta _ { g } ) / 2 \\alpha v _ { g }$ is the decay time constant of the rf pulse and $R _ { s } = \\sqrt { \\pi f \\mu / \\sigma }$ is the surface resistance. This result is valid when $\\alpha L > 0 . 4 2 7$ such that the maximum $\\Delta T$ occurs before the end of the pulse. For pure copper at room temperature, the maximum temperature rise in $\\mathrm { \\bf K }$ becomes $$ \\Delta T _ { \\mathrm { m a x } , c u } = 2 4 2 \\frac { H _ { \\mathrm { m a x } } ^ { 2 } } { \\sigma ^ { 1 / 4 } } \\sqrt { \\frac { f ( 1 - \\beta _ { g } ) } { \\alpha _ { 0 } \\beta _ { g } } } $$ where $H _ { \\mathrm { m a x } }$ is the peak surface field in $\\mathrm { \\mathbf { M A m } ^ { - 1 } }$ , $f$ is the frequency in $\\mathrm { G H z }$ , and $\\alpha _ { 0 }$ is the attenuation constant in $\\mathrm { { N p } \\mathrm { { m } ^ { - 1 } } }$ for a pure copper structure with $\\sigma { = } 5 . 8 { \\times } 1 0 ^ { 7 } \\mathrm { S m ^ { - 1 } }$ . Here, $\\sigma$ is the effective electrical conductivity of the structure in $S \\mathrm { m } ^ { - 1 }$ which may be reduced from its nominal value due to surface roughness. The pulse heating depends primarily on the peak magnetic field and group velocity, having only a weak dependence on the electrical conductivity of the material. Higher group velocities lead to less pulse heating due to the shortening of the effective pulse length. Figure 12 shows how the pulse heating varies with the geometry of the maximum radii corrugation. The temperature rise, $\\Delta T$ , increases with increasing corrugation period $p / a$ and decreases with increasing spacing parameter $\\xi . \\ \\Delta T$ also increases with increasing aperture ratio. The optimal corrugation design for minimal pulse heating has a small period, large spacing parameter, and small aperture ratio. | 1 | Yes | 0 |
expert | Which material is preferred for a short pulse colinear accelerator: copper, aluminum or stainless steal? | Stainless steel | Reasoning | Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf | File Name:Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf Design of a cylindrical corrugated waveguide for a collinear wakefield accelerator A. Siy ,1,2,\\\\* N. Behdad,1 J. Booske,1 G. Waldschmidt,2 and A. Zholents 2,† 1University of Wisconsin, Madison, Wisconsin 53715, USA 2Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439, USA (Received 30 May 2022; accepted 7 November 2022; published 7 December 2022) We present the design of a cylindrical corrugated waveguide for use in the A-STAR accelerator under development at Argonne National Laboratory. A-STAR is a high gradient, high bunch repetition rate collinear wakefield accelerator that uses a $1 - \\\\mathrm { m m }$ inner radius corrugated waveguide to produce a $9 0 \\\\ \\\\mathrm { M V } \\\\mathrm { m } ^ { - 1 }$ , 180-GHz accelerating field when driven by a $1 0 \\\\mathrm { - n C }$ drive bunch. To select a corrugation geometry for A-STAR, we analyze three types of corrugation profiles in the overmoded regime with $a / \\\\lambda$ ranging from 0.53 to 0.67, where $a$ is the minor radius of the corrugated waveguide and $\\\\lambda$ is the free-space wavelength. We find that the corrugation geometry that optimizes the accelerator performance is a rounded profile with vertical sidewalls and a corrugation period $p \\\\ll a$ . Trade-offs between the peak surface fields and thermal loading are presented along with calculations of pulse heating and steady-state power dissipation. In addition to the $\\\\mathrm { T M } _ { 0 1 }$ accelerating mode, properties of the $\\\\mathrm { H E M } _ { 1 1 }$ mode and contributions from higher order modes are discussed. | augmentation | Yes | 0 |
expert | Which material is preferred for a short pulse colinear accelerator: copper, aluminum or stainless steal? | Stainless steel | Reasoning | Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf | $$ \\kappa _ { \\mathrm { t o t } } = \\sum \\kappa _ { n } = \\frac { 2 } { L } \\int _ { 0 } ^ { \\infty } { \\mathrm { R e } } \\{ Z _ { | | } ( f ) \\} d f , $$ where $Z _ { | | }$ is the longitudinal wakefield impedance and $L$ is the length of the structure. The HOM content can be characterized by the sum of HOM loss factors over the sum of all loss factors: $$ \\mathrm { H O M \\ r a t i o } = \\frac { \\kappa _ { \\mathrm { t o t } } - \\kappa } { \\kappa _ { \\mathrm { t o t } } } , $$ where $\\kappa$ is the loss factor of the $\\mathrm { T M } _ { 0 1 }$ mode. In this characterization, the HOM ratio goes to 0 as the HOMs vanish, at which point the loss is due exclusively to the $\\mathrm { T M } _ { 0 1 }$ mode. Figure 14 shows that the HOM content primarily depends on the corrugation period, where periods larger than $0 . 4 a$ lead to significant HOM coupling. The HOMs also increase modestly with aperture ratio and corrugation spacing. The HOM ratio shown here assumes that all modes are excited equally which is not the case for a finite length bunch with a limited charge spectrum. The actual HOM energy content must account for the bunch shape by inclusion of the form factor discussed in Appendix B. | augmentation | Yes | 0 |
expert | Which material is preferred for a short pulse colinear accelerator: copper, aluminum or stainless steal? | Stainless steel | Reasoning | Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf | $$ The integrals in $t$ and $t ^ { \\prime }$ produce Dirac delta functions leaving $$ \\begin{array} { l } { \\displaystyle P _ { w } = \\frac { c } { 2 \\pi } \\mathrm { R e } \\Bigg \\{ \\int _ { - \\infty } ^ { \\infty } d \\omega \\int _ { - \\infty } ^ { \\infty } d \\omega _ { 2 } \\int _ { - \\infty } ^ { \\infty } d \\omega _ { 1 } } \\\\ { \\displaystyle \\times I ( \\omega _ { 2 } ) I ( \\omega _ { 1 } ) Z _ { | | } ( \\omega ) \\delta ( \\omega _ { 1 } + \\omega _ { 2 } ) \\delta ( \\omega - \\omega _ { 1 } ) \\Bigg \\} . } \\end{array} $$ Using the sifting property of the delta function to evaluate the integral Eq. (B10) becomes $$ P _ { \\ w } = \\frac { c } { 2 \\pi } \\mathrm { R e } \\Bigg \\{ \\int _ { - \\infty } ^ { \\infty } I ( - \\omega ) I ( \\omega ) Z _ { | | } ( \\omega ) d \\omega \\Bigg \\} . | augmentation | Yes | 0 |
expert | Which material is preferred for a short pulse colinear accelerator: copper, aluminum or stainless steal? | Stainless steel | Reasoning | Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf | $$ We will now consider the effect of the bunch charge density $q ( s )$ on the accelerating field $E _ { z } ( s )$ in order to understand how $E _ { \\mathrm { a c c } }$ and the peak surface fields depend on $q ( s )$ . To begin, we write $E _ { z , n }$ due to a single mode as a convolution $$ E _ { z , n } ( s ) = \\int _ { - \\infty } ^ { \\infty } q ( s - s ^ { \\prime } ) 2 \\kappa _ { n } \\cos ( k _ { n } s ^ { \\prime } ) \\theta ( s ^ { \\prime } ) d s ^ { \\prime } . $$ Since $q ( s )$ is a real function, $$ E _ { z , n } ( s ) = 2 \\kappa _ { n } \\mathrm { R e } \\Bigg \\{ \\int _ { 0 } ^ { \\infty } q ( s - s ^ { \\prime } ) e ^ { j k _ { n } s ^ { \\prime } } d s ^ { \\prime } \\Bigg \\} . | augmentation | Yes | 0 |
expert | Which material is preferred for a short pulse colinear accelerator: copper, aluminum or stainless steal? | Stainless steel | Reasoning | Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf | $$ q ( s ) = N \\times { \\left\\{ \\begin{array} { l l } { 1 } & { 0 < s < \\pi / ( 2 k _ { n } ) } \\\\ { k _ { n } s + ( 1 - \\pi / 2 ) } & { \\pi / ( 2 k _ { n } ) < s < l } \\\\ { 0 } & { { \\mathrm { e l s e } } } \\end{array} \\right. } $$ where $s$ is the longitudinal displacement from the head of the bunch, $k _ { n } = \\omega _ { n } / c$ is the wave number of the $\\mathrm { T M } _ { 0 1 }$ mode, $l = ( \\sqrt { \\mathcal { R } ^ { 2 } - 1 } + \\pi / 2 - 1 ) / k _ { n }$ is the bunch length, and $N = 2 k _ { n } q _ { 0 } / ( \\mathcal { R } ^ { 2 } + \\pi - 2 )$ is a normalization constant such that $\\textstyle \\int q ( s ) d s = q _ { 0 }$ is the total charge of the bunch. The accelerating wakefield behind the drive bunch is given by the convolution of the charge density $q ( s )$ with the Green’s function of the structure $h ( s )$ and can be calculated from Eqs. (26) and (27), and Eq. (B3), resulting in the accelerating field shown in Fig. 16 for the A-STAR design. | augmentation | Yes | 0 |
expert | Which material is preferred for a short pulse colinear accelerator: copper, aluminum or stainless steal? | Stainless steel | Reasoning | Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf | $$ Making the substitution $u = s - s ^ { \\prime }$ , $$ E _ { z , n } ( s ) = 2 \\kappa _ { n } \\operatorname { R e } \\Biggl \\{ \\int _ { - \\infty } ^ { s } q ( u ) e ^ { j k _ { n } ( s - u ) } d u \\Biggr \\} . $$ Since we are only interested in the fields behind the bunch, we take the limit as $s \\infty$ , noting that the result will be valid outside the bunch where $q ( s ) = 0$ : $$ E _ { z , n } ( s \\to \\infty ) = 2 \\kappa _ { n } \\operatorname { R e } \\left\\{ e ^ { j k _ { n } s } \\int _ { - \\infty } ^ { \\infty } q ( u ) e ^ { - j k _ { n } u } d u \\right\\} . $$ We can now write the field in terms of the previously derived form factor $F ( k _ { n } )$ given in Eq. (B20): | augmentation | Yes | 0 |
expert | Which material is preferred for a short pulse colinear accelerator: copper, aluminum or stainless steal? | Stainless steel | Reasoning | Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf | $$ which can be written as $$ V ^ { \\prime } = \\biggr \\vert \\int _ { 0 } ^ { p } \\hat { a } ^ { - 1 / 2 } E _ { z } ( z ^ { \\prime } ) e ^ { j \\omega _ { c } ^ { z ^ { \\prime } } } d z ^ { \\prime } \\biggr \\vert = \\frac { V } { \\hat { a } ^ { 1 / 2 } } . $$ Since we have normalized the fields with $U = 1 \\mathrm { ~ J ~ }$ and shown that the group velocity $\\beta _ { g }$ is independent of scaling, Equation (6) is used to write the loss factor for the scaled structure as $$ \\kappa ^ { \\prime } = \\frac { V ^ { \\prime 2 } / U } { 4 ( 1 - \\beta _ { g } ) \\hat { a } p } = \\frac { \\kappa } { \\hat { a } ^ { 2 } } . $$ The quality factor $\\boldsymbol { Q }$ of the corrugation unit cell is defined as | augmentation | Yes | 0 |
expert | Which material is preferred for a short pulse colinear accelerator: copper, aluminum or stainless steal? | Stainless steel | Reasoning | Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf | VII. HOM CONSIDERATIONS In addition to the fundamental $\\mathrm { T M } _ { 0 1 }$ mode, the wakefield contains contributions from higher order modes (HOMs). Since the HOMs span a range of wavelengths, they may interfere either constructively or destructively with the accelerating mode at the position of the witness bunch leading to a potential reduction in the accelerating gradient. It is desirable to minimize coupling to HOMs to maintain maximum acceleration [12]. Figure 13 shows the wakefield impedance simulated with CST’s wakefield solver for structures with $p / a = 0 . 4$ (left panel) and $p / a = 0 . 7$ (right panel), where the HOMs are seen as additional peaks in the impedance spectrum. Characterization of the HOMs for the maximum radii structures was carried out in CST’s wakefield solver by simulating $2 0 \\mathrm { - m m }$ long corrugated waveguides with minor radius $a = 1$ and an on-axis Gaussian bunch with standard deviation length of $\\sigma _ { s } = 0 . 2 ~ \\mathrm { m m }$ . This bunch length resolves the wake impedance up to $5 0 0 ~ \\mathrm { G H z }$ , capturing a large portion of the HOM spectrum which falls off with frequency. The sum of the loss factors for all modes is calculated as | augmentation | Yes | 0 |
expert | Which material is preferred for a short pulse colinear accelerator: copper, aluminum or stainless steal? | Stainless steel | Reasoning | Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf | In evaluating the peak surface fields for the various corrugation geometries, we have normalized the fields over the accelerating gradient given in Eq. (B29) in Appendix B to allow a comparison of the results. Typical electric and magnetic field distributions within the corrugation unit cell are shown in Fig. 8, where the electric field is generally concentrated around the tooth tip and the magnetic field is highest in the vacuum gap. The simulation results in Figs. 9 and 10 show that the peak electric and magnetic fields always increase with increasing aperture ratio, meaning higher choices of frequency for the $\\mathrm { T M } _ { 0 1 }$ synchronous mode result in higher peak fields for a given accelerating gradient. This observation is consistent with the results reported in [25] and is seen in unequal radii geometries as well. Unlike the rounded geometries, the peak fields of the minimum radii rectangular geometry shown in Fig. 9 have a strong dependence on the corrugation period and higher overall values due to field enhancement at the corrugation corners. At a period of $p / a = 0 . 4$ , the peak electric fields of the minimum radii geometry are roughly double those of the rounded designs making minimum radii rectangular corrugations unsuitable for high gradient CWA structures. | augmentation | Yes | 0 |
expert | Which material is preferred for a short pulse colinear accelerator: copper, aluminum or stainless steal? | Stainless steel | Reasoning | Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf | IX. CONCLUSION Through simulation, we have shown how the electromagnetic parameters characterizing the $\\mathrm { T M } _ { 0 1 }$ synchronous mode of a cylindrical CWG used as a slow-wave structure depend on the corrugation period, spacing, sidewall angle, and frequency of the accelerating mode. In analyzing the structures, we found that minimizing the corrugation period plays a key role in reducing the peak electromagnetic fields, thermal loading, and coupling to HOMs. Taking into account electromagnetic and manufacturing considerations, we found the most practical corrugation profile has vertical sidewalls and a corrugation tooth width similar to the width of the vacuum gap. Using the results of our analysis, we have designed a prototype CWG for the A-STAR CWA under development at Argonne National Laboratory. The calculated parameters of A-STAR suggest that a CWA based on a metallic corrugated waveguide is a promising approach to realize a new generation of high repetition rates and compact XFEL light sources. ACKNOWLEDGMENTS This manuscript is based upon work supported by Laboratory Directed Research and Development (LDRD) funding from Argonne National Laboratory (ANL), provided by the Director, Office of Science, of the U.S. Department of Energy under Contract No. DEAC02-06CH11357. Useful discussions with W. Jansma, S. Lee, A. Nassiri, B. Popovic, J. Power, S. Sorsher, K. Suthar, E. Trakhtenberg, and J. Xu of ANL are gratefully acknowledged. | augmentation | Yes | 0 |
expert | Which material is preferred for a short pulse colinear accelerator: copper, aluminum or stainless steal? | Stainless steel | Reasoning | Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf | Comparing the maximum radii and unequal radii rounded corrugation peak fields in Figs. 10 and 11, we note that the two geometry types are identical when the spacing parameter $\\xi = 0$ and the sidewall parameter $\\zeta = 1$ . In both structure types, the minimum $E _ { \\mathrm { m a x } }$ occurs for a negative spacing parameter $\\xi$ , corresponding to a corrugation tooth width wider than the vacuum gap. Increasing the corrugation spacing beyond the minimum point decreases $H _ { \\mathrm { m a x } }$ while increasing $E _ { \\mathrm { m a x } }$ . The sidewall angle determined by $\\zeta$ shifts the plots on the $\\xi$ axis but does not significantly affect the minimum value of the peak fields. While changing the sidewall parameter offers little to no benefit in reducing the peak fields, the practical implications of using values of $\\zeta \\neq 1$ have several disadvantages. For tapered corrugations with $\\zeta < 1$ , the corrugation depth must be greater requiring a thicker vacuum chamber wall and additional manufacturing complexity. Undercut corrugations with $\\zeta > 1$ are also impractical to manufacture for the dimensions of interest in a compact wakefield accelerator. For these reasons, we suggest the maximum radii corrugation with $\\xi$ close to zero as a good candidate for a wakefield accelerator design. Further refinement of the geometry requires experimental determination of where rf breakdown is most likely to occur in order to reduce the peak fields in those regions. | augmentation | Yes | 0 |
expert | Which material is preferred for a short pulse colinear accelerator: copper, aluminum or stainless steal? | Stainless steel | Reasoning | Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf | $$ where the bunch length $l$ is $$ l = \\frac { \\frac { \\pi } { 2 } + \\sqrt { \\mathcal { R } ^ { 2 } - 1 } - 1 } { k _ { n } } . $$ Evaluating the form factor at $k = k _ { n }$ produces $$ | F ( k _ { n } ) | = \\frac { 2 \\mathcal { R } } { \\mathcal { R } ^ { 2 } + \\pi - 2 } . $$ This result leads to the accelerating gradient $E _ { \\mathrm { a c c } }$ scaling with the inverse of the transformer ratio $\\mathcal { R }$ . [1] A. Zholents, S. Baturin, D. Doran, W. Jansma, M. Kasa, A. Nassiri, P. Piot, J. Power, A. Siy, S. Sorsher, K. Suthar, W. Tan, E. Trakhtenberg, G. Waldschmidt, and J. Xu, A compact high repetition rate free-electron laser based on the Advanced Wakefield Accelerator Technology, in Proceedings of the 11th International Particle Accelerator Conference, IPAC-2020, CAEN, France (2020), https:// ipac2020.vrws.de/html/author.htm. [2] A. Zholents et al., A conceptual design of a compact wakefield accelerator for a high repetition rate multi user X-ray Free-Electron Laser Facility, in Proceedings of the 9th International Particle Accelerator Conference, IPAC’18, Vancouver, BC, Canada (JACoW Publishing, Geneva, Switzerland, 2018), pp. 1266–1268, 10.18429/ JACoW-IPAC2018-TUPMF010. [3] G. Voss and T. Weiland, The wake field acceleration mechanism, DESY Technical Report No. DESY-82-074, 1982. [4] R. J. Briggs, T. J. Fessenden, and V. K. Neil, Electron autoacceleration, in Proceedings of the 9th International Conference on the High-Energy Accelerators, Stanford, CA, 1974 (A.E.C., Washington, DC, 1975), p. 278 [5] M. Friedman, Autoacceleration of an Intense Relativistic Electron Beam, Phys. Rev. Lett. 31, 1107 (1973). [6] E. A. Perevedentsev and A. N. Skrinsky, On the use of the intense beams of large proton accelerators to excite the accelerating structure of a linear accelerator, in Proceedings of 6th All-Union Conference Charged Particle Accelerators, Dubna (Institute of Nuclear Physics, Novosibirsk, USSR, 1978), Vol. 2, p. 272; English version is available in Proceedings of the 2nd ICFA Workshop on Possibilities and Limitations of Accelerators and Detectors, Les Diablerets, Switzerland, 1979 (CERN, Geneva, Switzerland,1980), p. 61 | augmentation | Yes | 0 |
expert | Which material is preferred for a short pulse colinear accelerator: copper, aluminum or stainless steal? | Stainless steel | Reasoning | Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf | DOI: 10.1103/PhysRevAccelBeams.25.121601 I. INTRODUCTION A sub-terahertz accelerator (A-STAR) is being developed at Argonne National Laboratory to reduce the cost and footprint of a future hard x-ray free-electron laser (XFEL) facility [1,2]. A-STAR is a collinear wakefield accelerator (CWA) that uses a cylindrical corrugated waveguide (CWG) as a slow-wave structure, analogous to other CWA configurations [3–8] and drive beam decelerator in CLIC [9]. In operation, a high-charge drive electron bunch passing through the CWA generates an electromagnetic field, known as the wakefield, which accelerates a low charge witness electron bunch following close behind the drive bunch. The ratio of the maximum electric field behind the drive bunch to the maximum electric field within the bunch is known as the transformer ratio $\\mathcal { R }$ and is limited to 2 for symmetric drive bunches [10]. The A-STAR design uses a 10-nC asymmetrical drive bunch [10,11] to achieve a transformer ratio of 5 and an accelerating gradient of $9 0 \\ \\mathrm { M V } \\mathrm { m } ^ { - 1 }$ , where the accelerating field is a $1 8 0 – \\mathrm { G H z }$ $\\mathrm { T M } _ { 0 1 }$ mode propagating with a group velocity of $0 . 5 7 c$ , where $c$ is the speed of light. The accelerator ends when the drive bunch exhausts almost all of its energy at which point the witness bunch reaches a maximum energy approaching $\\mathcal { E } _ { 0 } ( 1 + \\mathcal { R } )$ , where $\\mathcal { E } _ { 0 }$ is the initial energy of the beam. The entire CWA is composed of many $0 . 5 \\mathrm { - m }$ long modules connected in series, as shown in Fig. 1. | augmentation | Yes | 0 |
expert | Which material is preferred for a short pulse colinear accelerator: copper, aluminum or stainless steal? | Stainless steel | Reasoning | Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf | $$ \\phi = \\frac { 3 6 0 f p } { c } , $$ where $\\phi$ is the periodic boundary condition phase advance in degrees, $f$ is the frequency of the electromagnetic mode, $p$ is the corrugation period, and $c$ is the speed of light. The electron bunch velocity is considered to be equal to $c$ . The structures were simulated at three fixed frequencies in order to characterize frequency-dependent behavior of the $\\mathrm { T M } _ { 0 1 }$ mode. Throughout the paper, we will refer to results for the simulated frequencies by their respective aperture ratios which we define as $a / \\lambda$ , where $a$ is the minor radius of the CWG and $\\lambda$ is the free-space wavelength of the synchronous mode. This normalization allows the results to be applied to structures of any size and frequency. Parametric analysis began by treating the corrugation depth $d$ as a dependent variable determined by the aperture ratio, eliminating it from the parameter sweeps. This was done by using an iterative optimization process to find the corrugation depths required to achieve predetermined frequencies, producing aperture ratios of 0.53, 0.60, and 0.67 for each combination of $p , \\xi$ , and $\\zeta$ in the study. The resulting corrugation depths are plotted in Figs. 5 and 6. In all cases, the corrugation depth decreases with increasing aperture ratio, where shallower corrugations produce higher synchronous $\\mathrm { T M } _ { 0 1 }$ frequencies. The sidewall parameter $\\zeta$ is found to modify the effective corrugation depth where reducing $\\zeta$ has an effect similar to reducing $d$ . Undercut corrugation profiles with $\\zeta > 1$ can only be found when the conditions in Eqs. (3) and (4) are satisfied which requires the period and aperture ratio to be sufficiently small. For this reason, the dotted line solutions in Fig. 6 only occur above the set values of the corrugation depth. In the remainder of the analysis, we will pay special attention to the maximum radii corrugation and unequal radii corrugation with $\\zeta = 1$ which are good candidates for wakefield acceleration due to their manufacturability and electromagnetic characteristics. | augmentation | Yes | 0 |
Expert | Which non-redundant mask showed better results? | The 7-hole mask with 2.4?mm diameter gave the best results, providing stable closure phases, low residuals, and reliable beam size fits. | Reasoning | Carilli_2024.pdf | $$ \\begin{array} { r l r } { \\gamma ( u , v ) = } & { { } } & { \\mathrm { e x p } [ - \\frac { ( u ^ { 2 } + v ^ { 2 } ) + 2 \\rho ( u v ) + \\eta ( u ^ { 2 } - v ^ { 2 } ) } { 2 \\sigma ^ { 2 } } ] } \\\\ { \\| V _ { i j } \\| = } & { { } } & { \\gamma ( u _ { i j } , v _ { i j } ) \\| G _ { i } \\| \\| G _ { j } \\| } \\\\ { \\| V _ { \\mathrm { a u t o } } \\| = } & { { } } & { \\displaystyle \\sum _ { i } \\| G _ { i } \\| ^ { 2 } } \\end{array} $$ The fitting to the data is done using the Levenberg-Marquardt algorithm. The derived gains from the self-calibration rocess are shown in Figure 9, and listed in Table I. | 1 | Yes | 0 |
Expert | Which non-redundant mask showed better results? | The 7-hole mask with 2.4?mm diameter gave the best results, providing stable closure phases, low residuals, and reliable beam size fits. | Reasoning | Carilli_2024.pdf | These images show the expected behaviour, with the diffraction pattern covering more of the CCD for the $3 \\mathrm { m m }$ hole image vs. the 5mm hole. Note that the total counts in the field is very large (millions of photons), and hence the Airy disk is visible beyond the first null, right to the edge of the field. This extent may be relevant for the closure phase analysis below. Figure 4 shows the corresponding image for a 5-hole mask with 3 mm holes. The interference pattern is clearly more complex given the larger number of non-redundant baselines sampled $\\mathrm { \\Delta N _ { b a s e l i n e s } = ( N _ { h o l e s } * ( N _ { h o l e s } - 1 ) ) / 2 = 1 0 }$ for $\\mathrm { N } _ { \\mathrm { h o l e s } } = 5$ ). B. Fourier Domain Data are acquired as CCD two-dimensional arrays of size $1 2 9 6 \\times 9 6 6$ . We first remove the constant offset which is due to a combination of the bias and the dark current. We use a fixed estimate of this offset obtained by examination of the darkest areas of the CCD and the FFT of the image. We find a bias of 3.7 counts per pixel. Errors in this procedure accumulate in the central Fourier component, corresponding to the zero spacing, or total flux (u,v = 0,0), and contribute to the overall uncertainty of the beam reconstruction. | 2 | Yes | 0 |
Expert | Which non-redundant mask showed better results? | The 7-hole mask with 2.4?mm diameter gave the best results, providing stable closure phases, low residuals, and reliable beam size fits. | Reasoning | Carilli_2024.pdf | Gaussian random noise is then added to the complex visibilities at the rms level of $\\sim 1 0 \\%$ of the visibility amplitudes, and a second test was done with $1 \\%$ rms noise. Since the noise is incorporated in the complex visibilities, it affects both phase and amplitude. In each case, a series of 30 measurement sets with independent noise (changing ‚Äôsetseed‚Äô parameter), are generated to imitate the 30 frames taken in our measured time series. We employ ‚ÄôUVMODELFIT‚Äô in CASA to then fit for the source amplitude, major axis, minor axis, and major axis position angle. Starting guesses are given that are close to, but not identical with, the model parameters (within $2 0 \\%$ ), although the results are insensitive to the starting guesses (within reason). We first run uvmodelfit on the data with no noise, and recover the expected model parameters to better than $1 0 ^ { - 3 }$ precision. These low level differences arise from numerical pixelization. Figure 32 shows the results for the two simulation ‚Äôtime series‚Äô, and Table IV lists the values for the mean and rms/root(30). Also listed are the results from the measurements in Nikolic et al. (2024), and the input model. Two results are of note. | 1 | Yes | 0 |
Expert | Which non-redundant mask showed better results? | The 7-hole mask with 2.4?mm diameter gave the best results, providing stable closure phases, low residuals, and reliable beam size fits. | Reasoning | Carilli_2024.pdf | Notice that, for the 6-hole mask Figure 8, the u,v data points corresponding to the vertical and horizontal 16mm baseline have roughly twice the visibility amplitude as neighboring points (and relative to the 5-hole mask). This is because these are now redundantly sampled, meaning the 16mm horizontal baseline now includes photons from 0-1 and 2-5, and 16mm vertical baseline includes 0-2 and 1-5. C. Self-calibration The self-calibration and source size fitting is described in more detail in Nikolic et al. (2024). For completeness, we summarize the gain fitting procedure and equations herein, since it is relevant to the results presented below. For computational and mathematical convenience (see Nikolic et al. 2024), the coherence is modelled as a twodimensional Gaussian function parametrised in terms of the overall width $( \\sigma )$ and the distortion in the ‚Äò $+ \\mathbf { \\nabla } ^ { \\prime } \\left( \\eta \\right)$ and ‚ÄòX‚Äô $( \\rho )$ directions. Dispersion in e.g., the $u$ direction is $\\sigma / \\sqrt { 1 + \\eta }$ while in the $v$ direction it is $\\sigma / { \\sqrt { 1 - \\eta } }$ , which shows that values $\\eta$ or $\\rho$ close to $1$ indicate that one of the directions is poorly constrained. | 4 | Yes | 1 |
Expert | Which non-redundant mask showed better results? | The 7-hole mask with 2.4?mm diameter gave the best results, providing stable closure phases, low residuals, and reliable beam size fits. | Reasoning | Carilli_2024.pdf | We extract the correlated power on each of the baselines by calculating the complex sum of pixels within a circular aperture of 7 pixels, centered at the calculated position of the baseline. With the padding used here 1 mm on the mask corresponds to 2.54 pixels in the Fourier transformed interferogram. An illustration of this procedure on the example frame is shown in Figure 18. We experimented with different u,v apertures (3,5,7,9 pixels), and found that 7 pixels provided the highest S/N while avoiding overlap with the neighboring u,v sample (Section V B). The interferometric phases of the visibilities are derived by a vector average over the selected apertures in the uv-plane of the images of the Real and Imaginary part of the Fourier transform, using the standard relation: phase = arctan(Im/Re). For reference, Figure 6 shows the intensity image and visibility amplitudes for a three hole mask with 3 mm holes and 1 ms integrations, Figure 7 shows the same for one of the 2-hole mask with 3 ms integrations, and Figure 8 shows the same for the 6-hole mask and 1 ms integrations. The u,v pixel locations of the Fourier components are dictated by the mask geometry (ie. the Fourier conjugate of the hole separations or ‚Äôbaselines‚Äò), and determined by the relative positions of the peaks of the sampled u,v points to the autocorrelation. These are set by the sampled baselines in the mask, the Fourier conjugate of which are the spatial frequencies. We find that the measured u,v data points are consistent with the mask machining to within $0 . 1 \\mathrm { m m } ,$ and that the u,v pixel locations for the common u,v sampled points between the 2-hole, 3-hole, and 5-hole mask agree to within 0.1 pixel. | 5 | Yes | 1 |
Expert | Which non-redundant mask showed better results? | The 7-hole mask with 2.4?mm diameter gave the best results, providing stable closure phases, low residuals, and reliable beam size fits. | Reasoning | Carilli_2024.pdf | To investigate decoherence caused by redundant sampling, we assume a gain for hole 5 equal to the mean between the gains of the two holes in close proximity to hole 5 (holes 3 and 4 see Figure 2 and Table I, mean gain of 3 and $4 =$ $\\mathrm { G } _ { 5 } = 9 . 2 5$ ). This gain assumes that the illumination pattern in that corner of the mask is relatively uniform. In this case, the decoherence becomes the ratio of the measured visibility amplitude (V6Hmeasured), to the sum of the expected visibility amplitudes of the redundant samples (ie. assuming no phase difference and decoherence). The expected amplitudes are given by: $\\mathrm { V _ { i , j } = \\gamma _ { i , j } G _ { i } G _ { j } }$ , where the gains were derived from the 5-hole non-redundant mask (Table I; and assuming $\\mathrm { G } _ { 5 } = 9 . 2 5$ ), and the coherence is also measured for the given baseline using the 5-hole non-redundant mask (see Table II). For example, for redundant sample [0-1 + 2-5], the decoherence is: | augmentation | Yes | 0 |
Expert | Which non-redundant mask showed better results? | The 7-hole mask with 2.4?mm diameter gave the best results, providing stable closure phases, low residuals, and reliable beam size fits. | Reasoning | Carilli_2024.pdf | Next we pad and center the data so that the centre of the Airy disk-like envelope of the fringes is in the centre of a larger two-dimensional array of size $2 0 4 8 \\times 2 0 4 8$ . To find the correct pixel to center to we first smooth the image with a wide (50 pixel) Gaussian kernel, then select the pixel with highest signal value. The Gaussian filtering smooths the fringes creating an image corresponding approximately to the Airy disk. Without the filtering the peak pixel selected would be affected by the fringe position and the photon noise, rather than the envelope. Off-sets of the Airy disk from the image center lead to phase slopes across the u,v apertures. To calculate the coherent power between the apertures, we make use of the van Cittert–Zernike theorem that the coherence and the image intensity are related by a Fourier transform. We therefore compute the two-dimensional Fourier transform of the padded CCD frame using the FFT algorithm. Amplitude and phase images of an example Fourier transform are shown in Figure 5. Distinct peaks can be seen in the FFT corresponding to each vector baseline defined by the aperture separations in the mask. | augmentation | Yes | 0 |
Expert | Which non-redundant mask showed better results? | The 7-hole mask with 2.4?mm diameter gave the best results, providing stable closure phases, low residuals, and reliable beam size fits. | Reasoning | Carilli_2024.pdf | I. INTRODUCTION We consider the measurement of the ALBA synchrotron electron beam size and shape using optical interferometry with aperture masks. Monitoring the emittance of the electron beam is important for optimal operation of the synchrotron light source, and potentially for future improved performance and real-time adjustments. There are a number of methods to monitor the size of the electron beam, including: (i) LOCO, which is a guiding magnetic lattice analysis incorporating the beam position monitors, (ii) X-ray pinholes (Elleaume et al 1995), and (iii) Synchrotron Radiation Interferometry (SRI). Herein, we consider optical SRI, which can be done in real time without affecting the main beam. Previous measurements using SRI at ALBA have involved a two hole Young’s slit configuration, with rotation of the mask in subsequent measurements to determine the two dimensional size of the electron beam, assuming a Gaussian profile (Torino & Iriso 2016; Torino & Iriso 2015). Such a two hole experiment is standard in synchrotron light sources (Mitsuhasi 2012; Kube 2007), and has been implemented at large particle accelerators, including the LHC (Butti et al. 2022). Four hole square masks have been considered for instantaneous two dimensional size characaterization, but such a square mask has redundant spacings which can lead to decoherence, and require a correction for variation of illumination across the mask (Masaki & Takano 2003; Novokshonov et al. 2017; see Section VI). Non-redundant masks have been used in synchrotron X-ray interferometry, but only for linear (one dimensional grazing incidence) masks (Skopintsev et al. 2014). | augmentation | Yes | 0 |
Expert | Which non-redundant mask showed better results? | The 7-hole mask with 2.4?mm diameter gave the best results, providing stable closure phases, low residuals, and reliable beam size fits. | Reasoning | Carilli_2024.pdf | In most cases, we employ non-redundant masks. A non-redundant aperture mask has a hole geometry such that each interferometric baseline, or separation between holes, is sampled uniquely in the Fourier domain (herein, called, the u,v plane), by a single pair of holes (Bucher & Haniff 1993; Labeyrie 1996). Non-redundant masks are extensively used in astronomical interferometric imaging, in situations where the interferometric phases may be corrupted by atmospheric turbulence, or other phenomena that may be idiosyncratic to a given aperture (often referred to as ’element based phase errors’). In such cases, redundant sampling of a u,v point by multiple baselines with different phase errors would lead to decoherence of the summed fringes in the image (focal) plane. Similarly, a full aperture (ie. no mask), which has very many redundant baselines, will show blurring of the image due to this ’seeing’ caused by phase structure across the aperture. Our 5-hole mask is an adaptation of Gonzales-Mejia (2011) non-redundant array, with the five holes selected to maximize the longer baselines, given the source is only marginally resolved. The full 6-hole mask includes a square for the four corner holes, leading to two redundant baselines (horizontal 16 mm 2-5 and 0-1; vertical 16 mm 1-5 and 0-2). These will be used for testing of the effects of redundant sampling in Section VI. | augmentation | Yes | 0 |
Expert | Which non-redundant mask showed better results? | The 7-hole mask with 2.4?mm diameter gave the best results, providing stable closure phases, low residuals, and reliable beam size fits. | Reasoning | Carilli_2024.pdf | One curious result is the close correlation between the decoherence of the two redundant baselines with time, as can be seen in Figure 29 and Figure 28. Some correlation is expected, since the phase fluctations at hole 5 are common to both baselines. But we are surprised by the degree of correlation. Perhaps vibrations of optical components might be more susceptible to such close correlation as opposed to laboratory ’seeing’ ? Further experiments are required to understand the origin of visibility phase fluctuations in the SRI measurements. We conclude that redundant sampling of the visibilities leads to decoherence at the level $\\sim 5 \\%$ , with a comparable magnitude for the scatter for the time series. A 5% decoherence is comparable to that seen comparing 1 ms vs. 3 ms time averaging of interferograms (Figure 22), and likewise the larger rms scatter of the time series is similar to that seen comparing 1 ms and 3 ms averaging. A 5% decoherence for a redundantly sampled baseline would be caused by a $\\sim 2 0 ^ { o }$ phase difference between the two redundant visibilities. These results necessitate the use of a non-redundant mask to avoid decoherence caused by hole-based phase perturbations due to eg. turbulence in the lab atmosphere or vibration of optical components (Torino & Iriso 2015). Likewise, a filled-aperture imaging system will display image smearing due to these phase perturbations. | augmentation | Yes | 0 |
Expert | Which non-redundant mask showed better results? | The 7-hole mask with 2.4?mm diameter gave the best results, providing stable closure phases, low residuals, and reliable beam size fits. | Reasoning | Carilli_2024.pdf | V. PROCESSING CHOICES The analysis presented herein is meant as supporting material for other papers that present the science results. Our main focus is to justify the choices made in this new type of analysis of laboratory optical interferometric data. A. Centering: phase slopes For reference, Figure 14 shows the centers found with and without smoothing of the input image. Centering will affect mean phases and phase slopes across apertures. We have found that smoothing before centering, ie. centering on the Airy disk not the peak pixel, leads to the minimum phase slopes across the u,v sampled points, as seen in Figure 5. The scatter plot shows similar overall scatter with and without Airy disk centering, but there is a systematic shift, which leads to phase slopes across apertures. Figure 15 shows a cut in the Y direction across the phase distribution for different centering. The phase slopes are clearly reduced with centering on the Airy disk. Closure phase could be affected by centering of the image on the CCD – the outer parts of the Airy disk, beyond the first null are sampled differently. For reference, the counts beyond the first null without bias subtraction contribute about $4 0 \\%$ to $4 5 \\%$ to the total counts in the field with 3 mm holes and 1ms integations hole data. | augmentation | Yes | 0 |
Expert | Which non-redundant mask showed better results? | The 7-hole mask with 2.4?mm diameter gave the best results, providing stable closure phases, low residuals, and reliable beam size fits. | Reasoning | Carilli_2024.pdf | In this report, we explore various configurations of a multi-hole, two-dimensional mask, emphasizing non-redundant masks, for an instantaneous measurement of the 2D electron beam size. Non-redundant masks have been used extensively in optical astronomical interferometric imaging to determine eg. the size of stellar photospheres, and or exoplanet searches (see Monnier 2003, Labeyrie 1996, Haniff et al. 1989), including recent observations with the perture mask on the JWST (Hinkley et al. 2022; Lau et al. 2023). The beam size measurements will be presented in a parallel paper (Nikolic et al. 2024). The purpose of this report is to review the experimental setup, and discuss the adopted standard processing of the data for this approach to synchrotron light source size measurements. We then present the details of why various processing decisions were made, based on the experimental data. In general, the ALBA SRI facility is ideal to explore various aspects of interferometry, including the effects of redundancy, shape-orientation-size conservation for three apertures (Thyagarjan & Carilli 2022), and image plane self-calibration (Carilli, Nikolic, Thyagarjan 2023; Carilli et al. 2024). II. BASICS OF INTERFEROMETRIC IMAGING AND NOMENCLATURE The spatial coherence (or visibility), $V _ { a b } ( \\nu )$ , corresponds to the cross correlation of two quasi-monochromatic voltages of frequency $\\nu$ of the same polarization measured by two spatially distinct elements in the aperture plane of an interferometer. The visibility relates to the intensity distribution of an incoherent source, $I ( \\hat { \\mathbf { s } } , \\nu )$ , via a Fourier transform (van Cittert 1934, Zernike 1938, Born & Wolf 1999; Thomson, Moran, Swenson 2023): | augmentation | Yes | 0 |
Expert | Which non-redundant mask showed better results? | The 7-hole mask with 2.4?mm diameter gave the best results, providing stable closure phases, low residuals, and reliable beam size fits. | Reasoning | Carilli_2024.pdf | D. 3ms vs 1ms coherences: 5 hole data We consider the affect of the integration time on coherence and closure phase on the 5-hole data (see Section VII for further analysis with other masks). Figure 22 shows the coherence at 3 ms vs 1 ms integrations. The 3 ms coherences are lower by about 2 - 10%. The rms of 3 ms coherences are much higher by factors 2 to 7. The explanation of the Figure 22 is Figure 23, which shows the time series of coherences for 3 ms vs 1 ms. Two things occur: (i) the coherence goes down by up to 8%, and (ii) the rms goes way up with 3 ms, by up to a factor 7. The increased rms in 3 ms data appears to be due to ’dropouts’, or records when the coherence drops by up to $2 0 \\%$ . Figure 24 shows the closure phases for $3 \\mathrm { m s }$ averaging vs. 1 ms averaging. The differences in closure phases are small, within a fraction of a degree. The rms scatter is slightly larger for $3 \\mathrm { m s }$ , but again, not dramatically. Hence, closure phase seems to be more robust to averaging time, than coherence itself. | augmentation | Yes | 0 |
Expert | Which non-redundant mask showed better results? | The 7-hole mask with 2.4?mm diameter gave the best results, providing stable closure phases, low residuals, and reliable beam size fits. | Reasoning | Carilli_2024.pdf | $$ \\phi _ { a b c } ( \\nu ) = \\phi _ { a b } ( \\nu ) + \\phi _ { b c } ( \\nu ) + \\phi _ { c a } ( \\nu ) . $$ In this summation, the element-based phase errors cancel, and the measured closure phase equals the true closure phase, independent of calibration. Closure phase is image shift invariant, and it relates to the symmetry properties of the source (Section IV D). Closure phase is conserved under element-based complex gain calibration. Thyagarajan & Carilli (2022) present a geometric understanding of how closure phase manifests itself in the image plane. In essence, the shape, orientation, and size (SOS) of the triangle enclosed by the fringes of a three element interference pattern, are invariant to element-based phase errors, the only degree of freedom being an unknown translation of the grid pattern of triangles due to the element-based phase errors. A straight-forward means of visualizing how SOS conservation works is given in Figure 4 in Thyagarajan & Carilli (2022): for any three element interferometer, the only possible image corruption due to an element-based phase screen is a tilt of the aperture plane, leading to a shift in the image plane. No higher order decoherence or image blurring is possible, since three points always define a plane parallel to which the wavefronts are coherent. This is not true for an image made with four or more elements, since multiple phase-planes can occur for different triads, and higher order decoherence (ie. image blurring) occurs. SOS conservation then raises the possibility of an image-plane self-calibration process (IPSC; Carilli, Nikolic, Thyagarajan 2023). We consider IPSC in a separate report (Carilli et al. 2024). | augmentation | Yes | 0 |
Expert | Which non-redundant mask showed better results? | The 7-hole mask with 2.4?mm diameter gave the best results, providing stable closure phases, low residuals, and reliable beam size fits. | Reasoning | Carilli_2024.pdf | $$ V _ { a b } ( \\nu ) = \\int _ { \\mathrm { s o u r c e } } A _ { a b } ( \\hat { \\bf s } , \\nu ) I ( \\hat { \\bf s } , \\nu ) e ^ { - i 2 \\pi { \\bf u } _ { a b } \\cdot \\hat { \\bf s } } \\mathrm { d } \\Omega , $$ where, $a$ and $b$ denote a pair of array elements (eg. holes in a mask), $\\hat { \\pmb s }$ denotes a unit vector in the direction of any location in the image, $A _ { a b } ( \\hat { \\mathbf { s } } , \\nu )$ is the spatial response (the ‘power pattern’) of each element (in the case of circular holes in the mask, the power pattern is the Airy disk), ${ \\mathbf { u } } _ { a b } = { \\mathbf { x } } _ { a b } ( \\nu / c )$ is referred to as the “baseline” vector which is the vector spacing $\\left( { \\bf x } _ { a b } \\right)$ between the element pair expressed in units of wavelength, and $\\mathrm { d } \\Omega$ is the differential solid angle element on the image (focal) plane. | augmentation | Yes | 0 |
Expert | Which non-redundant mask showed better results? | The 7-hole mask with 2.4?mm diameter gave the best results, providing stable closure phases, low residuals, and reliable beam size fits. | Reasoning | Carilli_2024.pdf | Figure 13 shows the closure phases for all ten triads in the uv-sampling, and the values are listed in Table III. All the closure phases are stable (RMS variations $\\leq 0 . 7 ^ { o }$ ), and all the values are close to zero, typically $\\leq 1 ^ { o }$ . The only triads with closure phases of about $2 ^ { o }$ involve the baseline 0-2. This is the vertical baseline of $1 6 \\mathrm { m m }$ length, and hence has a fringe that projects (lengthwise) in the horizontal direction. The origin of closures phases that appear to be very small, but statistically different from zero, is under investigation. For the present, we conclude the closure phases are $< 2 ^ { o }$ . Closure phase is a measure of source symmetry. X-ray pin-hole measurements imply that the beam is Gaussian in shape to high accuracy (Elleaume et al. 1995). A closure phase close to zero is typically assumed to imply a source that is point-symmetric in the image plane (a closure phase $\\leq 2 ^ { o }$ implies brightness asymmetries $\\leq 1 \\%$ of the total flux, for a well resolved source), as would be the case for an elliptical Gaussian. However, the fact that the source is only marginally resolved (Section III), can also lead to small closure phases, regardless of source structure on scales much smaller than the resolution. A simple test using uv-data for a very complex source that is only marginally resolved, shows that for closed triads composed of baselines with coherences $\\ge 7 0 \\%$ , the closure phase is $< 2 ^ { o }$ . In this case, even small, but statistically non-zero, closure phases provide information on source structure. | augmentation | Yes | 0 |
Expert | Which non-redundant mask showed better results? | The 7-hole mask with 2.4?mm diameter gave the best results, providing stable closure phases, low residuals, and reliable beam size fits. | Reasoning | Carilli_2024.pdf | First, the $1 \\%$ rms noise on the visibilities results in fitted quantities (amplitude, bmaj, bmin, pa), that are consistent with the model parameters, to within the scatter. Also, the rms scatter for the fit paramaters are of similar magnitude as those found for the real data. Second, the $1 0 \\%$ rms visibility noise leads to $\\sim 1 0 \\times$ higher scatter in the fitting results. Moreover, the minor axis fitting shows a skewed distribution toward values higher than the input model (ie. 21 points above the model line, and 9 below). We suspect that this skewness arises due to a Poisson-like bias when fitting for a positive definite quantity, when the errors become significant compared to the value itself. This skewness is not seen in the $1 \\%$ error analysis. C. Systematic Errors We investigate the effect of systematic errors using real data for visibility amplitudes from the ALBA 5-hole data. Two simple tests are performed: adjust the amplitudes systematically low by 5%, and high by 5%, then run the Gaussian fitting routine in Nikolic et al. (2024). The fitted source size for the 5% low amplitudes increases by $6 . 4 \\%$ , while the size decreases by 6.9% for the 5% high amplitudes. This is qualitatively consistent with the expected increase in source size for lower coherences, and vice versa. Quantitatively, for small offsets, the source size appears to be roughly linear with systematic offset for the visibility amplitudes. However, the fitting routine includes a joint fit for the gains of each hole. These gains also change slightly with systematic errors, with up to 2% lower gains for lower amplitudes, and similarly higher gains for higher amplitudes. | augmentation | Yes | 0 |
Expert | Which non-redundant mask showed better results? | The 7-hole mask with 2.4?mm diameter gave the best results, providing stable closure phases, low residuals, and reliable beam size fits. | Reasoning | Carilli_2024.pdf | In radio interferometry, the voltages at each element are measured by phase coherent receivers and amplifiers, and visibilities are generated through subsequent cross correlation of these voltages using digital multipliers (Thomson, Moran, Swenson 2023; Taylor, Carilli, Perley 1999). In the case of optical aperture masking, interferometry is performed by focusing the light that passes through the mask ( $=$ the aperture plane element array), using reimaging optics (effectively putting the mask in the far-field, or Fraunhofer diffraction), and generating an interferogram on a CCD detector at the focus. The visibilities can then be generated via a Fourier transform of these interferograms or by sinusoidal fitting in the image plane. However, the measurements can be corrupted by distortions introduced by the propagation medium, or the relative illumination of the holes, or other effects in the optics, that can be described, in many instances, as a multiplicative element-based complex voltage gain factor, $G _ { a } ( \\nu )$ . Thus, the corrupted measurements are given by: $$ V _ { a b } ^ { \\prime } ( \\nu ) = G _ { a } ( \\nu ) V _ { a b } ( \\nu ) G _ { b } ^ { \\star } ( \\nu ) , | augmentation | Yes | 0 |
Expert | Which non-redundant mask showed better results? | The 7-hole mask with 2.4?mm diameter gave the best results, providing stable closure phases, low residuals, and reliable beam size fits. | Reasoning | Carilli_2024.pdf | $$ where, $\\star$ denotes a complex conjugation. The process of calibration determines these complex voltage gain factors. In general, calibration of interferometers can be done with one or more bright sources (‘calibrators’), whose visibilities are accurately known (Thomson, Moran, Swenson 2023). Equation (2) is then inverted to derive the complex voltage gains, $G _ { a } ( \\nu )$ (Schwab1980, Schwab1981, Readhead & Wilkinson 1978; Cornwell & Wilkinson 1981). If these gains are stable over the calibration cycle time, they can then be applied to the visibility measurements of the target source, to obtain the true source visibilities, and hence the source brightness distribution via a Fourier transform. In the case of SRI at ALBA, we have employed self-calibration assuming a Gaussian shape for the synchrotron source, the details of which are presented in the parallel paper (Nikolic et al. 2024). Our process has considered only the gain amplitudes, corresponding to the square root of the flux through an aperture (recall, power $\\propto$ voltage2), dictated by the illumination pattern across the mask. We do not consider the visibility phases. Future work will consider full phase and amplitude self-calibration to constrain more complex source geometries. Closure phase is a quantity defined early in the history of astronomical interferometry, as a measurement of the properties of the source brightness distribution that is robust to element-based phase corruptions (Jennison 1958). Closure phase is the sum of three visibility phases measured cyclically on three interferometer baseline vectors forming a closed triangle, i.e., closure phase is the argument of the bispectrum $=$ product of three complex visbilities in a closed triad of elements: | augmentation | Yes | 0 |
Expert | Which physical effect is utilized to generate THz radiation in the design? | The Smith-Purcell effect | Definition | hermann-et-al-2022-inverse-designed-narrowband-thz-radiator-for-ultrarelativistic-electrons.pdf | ACS PHOTONICS READ Quasi-BIC Modes in All-Dielectric Slotted Nanoantennas for Enhanced $\\mathbf { E r ^ { 3 + } }$ Emission Boris Kalinic, Giovanni Mattei, et al.JANUARY 18, 2023 ACS PHOTONICS READ Get More Suggestions > | 1 | Yes | 0 |
Expert | Which physical effect is utilized to generate THz radiation in the design? | The Smith-Purcell effect | Definition | hermann-et-al-2022-inverse-designed-narrowband-thz-radiator-for-ultrarelativistic-electrons.pdf | We drove the structure with electron bunches with a duration of approximately 30 fs (RMS), which is much shorter than the resonant wavelength corresponding to a period of 3 ps. Hence, we expect to see the coherent addition of radiated fields. To experimentally verify this, we varied the bunch charge. Figure 4 shows the detected pulse energy for six bunch charge settings ranging from $0 ~ \\mathrm { p C }$ to $1 1 . 8 ~ \\mathrm { p C }$ The scaling is well approximated by a quadratic fit, which confirms the expected coherent enhancement of the $\\mathrm { T H z }$ pulse energy.14 We observe a slight deviation for the highest charge measurement from the quadratic fit, which might be a result of detector saturation (see Methods). We note that the quadratic scaling would enable $\\mathrm { T H z }$ pulse energies orders of magnitude larger by driving the structure at higher bunch charges. The THz pulse emitted perpendicular to the Smith-Purcell radiator possesses a pulse-front tilt of close to $4 5 ^ { \\circ }$ since it is driven by ultrarelativistic electrons. Depending on the length of the radiator and the application, the tilt can be compensated for with a diffraction grating. | 1 | Yes | 0 |
Expert | Which physical effect is utilized to generate THz radiation in the design? | The Smith-Purcell effect | Definition | hermann-et-al-2022-inverse-designed-narrowband-thz-radiator-for-ultrarelativistic-electrons.pdf | The objective function $G$ , quantifying the performance of a design $\\phi ,$ is given by the line integral of the Poynting vector $\\begin{array} { r } { { \\bf S } ( x , y ) = \\mathrm { R e } \\left\\{ \\frac { 1 } { 2 } { \\bf E } \\times { \\bf H } ^ { * } \\right\\} } \\end{array}$ in the $x$ -direction along the length of one period, evaluated at a point $x _ { S }$ outside the design region: $$ G ( \\phi ) = \\int _ { 0 } ^ { a } S _ { x } ( x _ { S } , y ) \\mathrm { d } y $$ The optimization problem can then be stated as $$ \\begin{array} { r l } & { \\operatorname* { m a x } _ { \\phi } G ( \\phi ) \\quad \\mathrm { s u b j e c t t o } \\quad \\nabla \\times \\mathbf { E } = - i \\omega \\mu \\mathbf { H } \\quad \\mathrm { a n d } } \\\\ & { \\quad \\nabla \\times \\epsilon ( \\phi ) ^ { - 1 } \\nabla \\times \\mathbf { H } - \\omega ^ { 2 } \\mu \\mathbf { H } = \\nabla \\times \\epsilon ( \\phi ) ^ { - 1 } \\mathbf { J } } \\end{array} | augmentation | Yes | 0 |
Expert | Which physical effect is utilized to generate THz radiation in the design? | The Smith-Purcell effect | Definition | hermann-et-al-2022-inverse-designed-narrowband-thz-radiator-for-ultrarelativistic-electrons.pdf | Our work naturally extends to the field of subrelativistic electrons. Here, simultaneous arrival of THz radiation and electron bunches is readily achieved by compensating for the higher velocity of the radiation with a longer path length (Figure 5b). Besides its application for pump‚àíprobe experiments, our structure can be more generally applied as a radiation source at wavelengths that are otherwise difficult to generate. An advantage lies in the tunability that arises from changing the periodicity, either by replacing the entire structure or using a design with variable periodicity (Figure 5c), or from tuning the electron velocity. For the visible to UV regime, the idea of a compact device with the electron source integrated on a nanofabricated chip has recently sparked interest.30,31 METHODS Structure Parametrization. Our inverse design process was carried out with an open-source Python package32 suitable for 2D-FDFD gradient-based optimizations25 of the chosen objective function $G ( \\phi )$ with respect to the design parameter $\\phi$ . A key step lies in the parametrization of the structure $\\varepsilon ( \\phi )$ through the variable $\\phi$ in a way that ensures robust convergence of the algorithm and fabricability of the final design. In the most rudimentary case, $\\varepsilon ( x , y ) \\stackrel { \\cdot } { = } \\phi ( x , y )$ is a two-dimensional array with entries $\\in [ 1 , 2 . 7 9 ]$ for each pixel of the design area. Instead of setting bounds on the values of $\\phi ,$ we leave $\\phi$ unbounded and apply a sigmoid function of the shape | augmentation | Yes | 0 |
Expert | Which physical effect is utilized to generate THz radiation in the design? | The Smith-Purcell effect | Definition | hermann-et-al-2022-inverse-designed-narrowband-thz-radiator-for-ultrarelativistic-electrons.pdf | The second difficulty arises from the long-range evanescent waves of ultrarelativistic electrons. The spectral density of the electric field of a line charge decays with $\\bar { \\exp ( - \\kappa | x | ) }$ , where $\\kappa =$ $2 \\pi / \\beta \\gamma \\lambda$ , with $\\beta \\approx 1$ and $\\gamma \\approx 6 0 0 0$ for $E = 3 . 2$ GeV.34 This means the evanescent waves will reach the boundaries of our simulation cell in the $x$ -direction. Generalized perfectly matched layers $\\left( \\mathrm { P M L s } \\right) ^ { 3 5 }$ are chosen, such that they can absorb both propagating and evanescent waves. A detailed look at Figure 1b reveals that our implementation of generalized PMLs is not fully capable of absorbing evanescent waves. Hence, we make use of symmetry to further reduce the effect of evanescent waves at the boundaries of the simulation cell. Note that the evanescent electric field for $\\beta \\approx 1$ is almost entirely polarized along the transverse direction $x .$ . This means if the simulation cell is mirror symmetric with respect to the electron channel, antiperiodic boundaries can be applied after the PMLs to cancel out the effect of evanescent waves at the boundaries. This turned out to work well for us, although the structure is not mirror symmetric with respect to the electron axis. | augmentation | Yes | 0 |
Expert | Which physical effect is utilized to generate THz radiation in the design? | The Smith-Purcell effect | Definition | hermann-et-al-2022-inverse-designed-narrowband-thz-radiator-for-ultrarelativistic-electrons.pdf | A bunch length of 30 fs (RMS) was measured for similar machine settings in a separate shift with a transverse deflecting cavity (TDC) in the Aramis beamline of the accelerator. Therefore, we expect the longitudinal dimension of the electron beam at the ACHIP chamber to be on the order of $1 0 \\ \\mu \\mathrm m ,$ , almost 2 orders of magnitude shorter than the period of the structure and radiated wavelength. The transverse beam size at the interaction point was $3 0 \\mu \\mathrm { m }$ in the horizontal and $4 0 \\ \\mu \\mathrm m$ in the vertical direction (for a charge of $9 . 5 \\ \\mathrm { p C } ,$ ), as measured with a scintillating YAG screen imaged with an out-of-vacuum microscope onto a CCD camera. After position and angular alignment of the structure using an in-vacuum hexapod, the beam could be transmitted without substantial losses through the $2 7 2 \\ \\mu \\mathrm { m }$ wide channel of the THz generating structure. Structure Fabrication. The structure was fabricated with a commercial PMMA stereolithography device Formlabs Form 2. The resolution of the device is $1 4 0 \\ \\mu \\mathrm { { m } , }$ , which provides subwavelength feature sizes for the geometry with a periodicity of $9 0 0 \\mu \\mathrm { m }$ . The height of the structure $( 6 ~ \\mathrm { { m m } ) }$ was limited by the stability of the structure rods during the fabrication process. The high temperature resin used for this study can be heated to $2 3 5 ~ ^ { \\circ } \\mathrm { C }$ . A sufficiently low outgassing rate for the installation at SwissFEL was achieved after baking the device for $s \\mathrm { ~ h ~ }$ under vacuum conditions at $1 7 5 ~ ^ { \\circ } \\mathrm { C } . ^ { 2 4 }$ Thanks to the rapid improvements in SLA technology and other free-form manufacturing techniques, the geometry could certainly be fabricated also at shorter wavelengths and higher resolution for future experiments. An increased manufacturing quality is required to achieve an even narrower emission bandwidth. | augmentation | Yes | 0 |
Expert | Which physical effect is utilized to generate THz radiation in the design? | The Smith-Purcell effect | Definition | hermann-et-al-2022-inverse-designed-narrowband-thz-radiator-for-ultrarelativistic-electrons.pdf | Michelson Interferometer and THz Detector. For the spectrum measurements, we installed a Michelson interferometer outside the vacuum chamber. The THz pulse was first sent through an in-vacuum lens made of PMMA with a diameter of $2 5 \\ \\mathrm { m m }$ and a focal length of $1 0 0 ~ \\mathrm { { m m } }$ . The lens collimates radiation in the vertical plane, but it does not map the entire radiation of the $4 5 \\ \\mathrm { m m }$ long structure onto the detector. The angular acceptance in the horizontal plane is calculated via ray tracing (see Figure 3). A fused silica vacuum window with about $5 0 \\%$ transmission for the design wavelength of the structure $( 9 0 0 ~ \\mu \\mathrm { m } )$ is used as extraction port. The beam splitter is made of $3 . 5 \\ \\mathrm { m m }$ -thick plano‚àíplano high-resistivity float-zone silicon (HRFZ-Si) manufactured by TYDEX. It provides a splitting ratio of $5 4 / 4 6$ for wavelengths ranging from 0.1 to $1 ~ \\mathrm { m m }$ . Translating one of the mirrors of the interferometer allowed us to measure the first-order autocorrelation, from which the power spectrum is obtained via Fourier transform. | augmentation | Yes | 0 |
Expert | Which physical effect is utilized to generate THz radiation in the design? | The Smith-Purcell effect | Definition | hermann-et-al-2022-inverse-designed-narrowband-thz-radiator-for-ultrarelativistic-electrons.pdf | A typical autocorrelation measurement for a charge of 9.4 pC is depicted in Figure 2b. The shape of the autocorrelation is not perfectly symmetric in amplitude and stage position. The amplitude asymmetry could be a result of a nonlinear detector response (onset of saturation). This is in agreement with the slight deviation of the pulse energy from the quadratic fit (Figure 4). Since the length of only one arm is changed and the radiation might not be perfectly collimated, the position scan of the mirror is not creating a perfectly symmetric autocorrelation signal. AUTHOR INFORMATION Corresponding Author Rasmus Ischebeck − Paul Scherrer Institut, 5232 Villigen, PSI, Switzerland; $\\circledcirc$ orcid.org/0000-0002-5612-5828; Email: rasmus.ischebeck@psi.ch Authors Benedikt Hermann − Paul Scherrer Institut, 5232 Villigen, PSI, Switzerland; Institute of Applied Physics, University of Bern, 3012 Bern, Switzerland; Galatea Laboratory, Ecole Polytechnique Fédérale de Lausanne (EPFL), 2000 Neuchâtel, Switzerland; $\\circledcirc$ orcid.org/0000-0001-9766-3270 Urs Haeusler − Department Physik, Friedrich-AlexanderUniversität Erlangen-Nürnberg (FAU), 91058 Erlangen, Germany; Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, United Kingdom; $\\circledcirc$ orcid.org/0000- 0002-6818-0576 Gyanendra Yadav − Department of Physics, University of Liverpool, Liverpool L69 7ZE, United Kingdom; Cockcroft Institute, Warrington WA4 4AD, United Kingdom Adrian Kirchner − Department Physik, Friedrich-AlexanderUniversität Erlangen-Nürnberg (FAU), 91058 Erlangen, Germany | augmentation | Yes | 0 |
IPAC | Which types of facilities require beam profile measurements with micrometer accuracy? | Dielectric laser accelerators, and future compact free-electron lasers. | Summary | Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf | Multi-particle tracking method, instead, can simulate the non-linear space charge and it is adopted in some previous studies [3]. TraceWin is adopted in our design for the CSNSII Linac and it is also used for the beam commissioning study. BEAM SIZE MEASUREMENT AT CSNS-MEBT Figure 1 illustrates a schematic layout [4] of the CSNSMEBT [5], which contains two bunchers, ten quadrupoles and beam diagnotic devices including: four wire scanners (PR), one emittance monitor (EM), seven beam position monitors (BPM) and two current transformers (CT). In this study, four wire scanners are used to measure the beam size at beam intensity of $7 \\mathrm { m A }$ , $1 5 ~ \\mathrm { m A }$ , $2 5 \\mathrm { m A }$ , respectively. In addition in order to test the coupling between the longitudinal and the horizontal direction, the measurements have been done with the bunchers turned ON or OFF. If the beam from upstream is stable enough, the parameters of the beam at the MEBT entrance should be the same regardless of the bunchers’ status. BEAM PARAMETERS FITTED WITH PARTICLE TRACKING Beam Size Fitting A common way to obtained the beam size is to do Gaussian fitting to the the beam profile measured by the wire scanner or wire grid. The fitting is simply done by: | augmentation | NO | 0 |
IPAC | Which types of facilities require beam profile measurements with micrometer accuracy? | Dielectric laser accelerators, and future compact free-electron lasers. | Summary | Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf | This also leads to having unusable data points when individual pre-amplifiers for a channel fail giving disconnected data points within a profile. During data analysis, the channels that were marked to be inoperative were set to the average value of the overall IPM data set to eliminate the poor MCP issue. Out of all 64,000 turns, both horizontal and vertical IPMs store the data locally but only return the first 1000 turns for analysis. This allows to calculate the sigma $\\sigma$ that represents the beam size. The IPMs were used to study the change in beam size in the MI by changing the MCP voltage to determine its e!ects as both were functioning compared to the vertical IPM not working in the RR. The R-square of the fits were also calculated to analyze the quality of the fits and this determined which voltage range was the best fit. Once an ideal MCP voltage range was determined, the beam size and the emittance were analyzed by using intensity as the dependent. Afterwards, the emittance of the beam was calculated by using $\\sigma$ in Eq. (1) where $\\beta$ is a Twiss parameter, $D$ is dispersion, and $\\frac { \\delta p } { p _ { 0 } }$ is the momentum spread. | augmentation | NO | 0 |
IPAC | Which types of facilities require beam profile measurements with micrometer accuracy? | Dielectric laser accelerators, and future compact free-electron lasers. | Summary | Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf | File Name:BEAM_LOSS_MONITORING_THROUGH_EMITTANCE_GROWTH.pdf BEAM LOSS MONITORING THROUGH EMITTANCE GROWTH CONTROL AND FEEDBACK WITH DESIGN F. Osswald†, E. Traykov, M. Heine, IPHC, CNRS/IN2P3, Université de Strasbourg, France T. Durand1, SUBATECH, CNRS/IN2P3, IMT Atlantique, Université de Nantes, France J. Michaud, Université Paris-Saclay, CNRS/IN2P3, IJCLab, Orsay, France JC. Thomas, GANIL, CEA/DRF-CNRS/IN2P3, Caen, France 1also at GIP ARRONAX, Saint-Herblain, France Abstract Beam intensities and powers being increasingly strong, installations increasingly large, the need to reduce losses and costs (i.e. dimensions) becomes essential. Improvements are possible by increasing the acceptance in the two transverse planes. We investigate the solution to control the beam line acceptance by measuring the emittance growth and a feedback with the design, e.g. pole shape and highorder modes of the fields. This is possible with detection of very low intensities of the halo and beam loss monitoring. INTRODUCTION A new focusing unit based on a quadrupole doublet structure has been constructed at the Institut Pluridisciplinaire Hubert Curien (IPHC). The prototype with a $0 . 5 \\mathrm { ~ m ~ }$ long quadrupole doublet structure was developed to study some key issues for the transport of low energy ion beams with the electrostatic quadrupole technology. The typical application is the transport of radioactive ion beams (RIB), as SPIRAL 2 and DERICA projects [1-2]. Despite the low current intensity and standard loss level of $1 0 ^ { - 4 }$ , cumulative contamination can limit access and reduce operability [3]. | augmentation | NO | 0 |
IPAC | Which types of facilities require beam profile measurements with micrometer accuracy? | Dielectric laser accelerators, and future compact free-electron lasers. | Summary | Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf | To obtain the beam parameters at each section, the beam sizes are measured with three or four wire scanners and data of wire scanners is analysed. At each section, four wire scanners are located, and beam parameters are calculated by using the transfer matrix formalism. Figure 3 shows the result of the beam parameter calculation and beam matching at the LEBT section, and the result of the MEBT section is shown in Fig. 4. The beam parameters calculated from the wire scanners are compared to the result of Allison scanner, and the results are consistent within about 10 percent. In addition to previous physics applications, the tool with a quadscan method is under development. As changing the quadrupole strength, the transverse rms. beam size is measured with a wire scanner located in the downstream of the quadrupole. Figure 5 shows the result of the horizontal quadscan at the MEBT section, and the vertical quadscan result is shown in Fig. 6. The beam parameters obtained by three different physics applications agree well, and the machine setting at each section is carried out with the beam test results. At the beam commissioning, the beam trajectory is distorted by machine errors, and the orbit correction based on the singular value decomposition (SVD) method [8] is carried with the physics application tool. At the LEBT section, the orbit correction is carried out by using steering magnets and wire scanners [9] because the beam generated by an ECR-IS is in continuous-wave (CW) mode, and one case of beam test result of the orbit correction at the LEBT section is shown in Fig. 7. Because of working time of the wire scanners, about 10 minutes are taken for one iteration. After the RFQ, the beam is bunched, and the beam position can be read by a beam-position-monitor (BPM) in real time through the EPICS system. Figure 8 shows the result of the orbit correction at the MEBT section, and the test result at the front end of SCL3 section is shown in Fig. 9. For one iteration, about three seconds are needed to read the beam data and correct the beam orbit at each section. As the beam commissioning at the SCL3 section proceeds, the beam test of the orbit correction at the SCL3 section will be also continued. | augmentation | NO | 0 |
IPAC | Which types of facilities require beam profile measurements with micrometer accuracy? | Dielectric laser accelerators, and future compact free-electron lasers. | Summary | Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf | The Q-scan curve obtained for the y-direction is shown in Fig. 3. Where $\\sqrt { | K | }$ is a value proportional to the focusing force of the quadrupole magnet. Fitting using Eq. (3) results in an emittance $8 \\%$ lower than the simulation input. This is because the beam in the y-direction is shaved o! about $1 \\%$ by the beam pipe, resulting in an underestimation of emittance. The Q-scan curve obtained for the $\\mathbf { \\boldsymbol { x } }$ and $\\textbf { Z }$ -direction is shown in Fig. 4. By varying the focusing force of both the quadrupole magnet and the buncher, the Q-scan curve is fitted with a bivariate function as in Eq. (4). Where f $\\mathrm { ( E _ { 0 } L T ) }$ is a value proportional to the focusing force of the buncher. The results of the fitting showed that the diagnostic error of emittance was within $1 \\%$ . 1 司 。 。。 O 1 0° oQoo 。 C 。 。 。 [9 8000o。8Q0000 。 C0 Q00000 。 C-0.2 r .3 <元 T 0.5 980000000.6 10.0.8 8 9 VK[/m]6 Requirements for Beam Monitor The requirement of emittance error is less than $10 \\%$ for the acceleration test [9]. On the other hand, the above evaluation results do not include the resolution of the BPM. The expected measured beam width $( \\sigma _ { \\mathrm { e x p . } } )$ ) can be expressed using the expected actual beam width $( \\sigma _ { \\mathrm { s i m . } } )$ and the monitor resolution $( \\sigma _ { \\mathrm { B P M } } )$ by the following relation, | augmentation | NO | 0 |
IPAC | Which types of facilities require beam profile measurements with micrometer accuracy? | Dielectric laser accelerators, and future compact free-electron lasers. | Summary | Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf | Beam Size For this study a precise and reliable measurement of the beam size is critical. The beam images are recorded on luminescent screens with digital cameras. Different methods to compute the $1 \\sigma$ beam sizes from the beam profiles were investigated (Fig. 4). RMS beam sizes with $5 \\%$ amplitude or $5 \\%$ area cut-off [4] depend on the image section, which is used for the analysis and wrong results are produced, if the beam spot is cut on one side. Fitting a Gaussian or uniform distribution to the profiles does not well represent the data and depend on the image section. Skew Gaussian and Super Gaussian distributions proposed in [5] yield a better result, but are also not optimal. The best agreement with the data and the least sensitive to the choice of the image section is a combination of these two fit functions, a Skew Super Gaussian distribution $$ I = \\frac { I _ { 0 } } { \\sqrt { 2 \\pi } \\sigma _ { 0 } } \\exp \\left( \\frac { - \\mathrm { a b s } ( x - x _ { 0 } ) ^ { n } } { 2 \\big ( \\sigma _ { 0 } ( 1 + \\mathrm { s i g n } ( x - x _ { 0 } ) E ) \\big ) ^ { n } } \\right) + I _ { b g } | augmentation | NO | 0 |
IPAC | Which types of facilities require beam profile measurements with micrometer accuracy? | Dielectric laser accelerators, and future compact free-electron lasers. | Summary | Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf | Quantum gas jet due to its small dimensions can significantly improve the position resolution and at the same time issues related to space charge can be mitigated. The jet can be scanned slowly across the beam or, to avoid problems with loss of alignment, the beam can be steered to produce a scan through the jet. The profile resolution depends only on the jet thickness and a diameter of less than $1 0 0 ~ { \\mu \\mathrm { m } }$ would be sufficient for most applications. This is very challenging to achieve due to the mechanical constraints of typical nozzle/skimmer systems. The measurement of the beam intensity at each jet position is done by collecting the ions. BEAM PROFILE MEASURMENT RESULTS OF ELECTRON BEAM USING PINHOLES The beam profile measurements were performed for a $3 . 7 \\mathrm { k e V }$ electron beam with a filament current of $2 . 6 \\mathrm { A }$ , using different pinholes having a diameter varying from $5 0 0 ~ { \\mu \\mathrm { m } }$ to $5 0 ~ { \\mu \\mathrm { m } }$ . Fig. 2 shows the example image obtained for the beam profile measurements after subtracting the background. The rectangular box indicates the region of interest (ROI), the image generated due to the interaction between the gas jet and the electron beam. | augmentation | NO | 0 |
IPAC | Which types of facilities require beam profile measurements with micrometer accuracy? | Dielectric laser accelerators, and future compact free-electron lasers. | Summary | Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf | The horizontal and vertical MWs in MI-8 line measure the number of counts of a proton beam via the wire planes. A Gaussian fit was also applied to the number of counts collected on the wire planes and calculated the beam size using the same method as the IPMs. An example of MWs in the RR profile is shown in Fig. 2. The emittance was also calculated using Eq. (2) by using the corresponding Twiss parameters for each MWs. IPM - MCP VOLTAGE SCAN Di!erent MCP voltage levels were set as dependent using the IPMs in the MI to see if there is a change in the measured profile. This range varied between 1170V-1220V and three data sets were collected at each MCP voltage level in both cases. This study was done by using the IPMs in the MI since both the horizontal and vertical work. This was done in order to determine if the MCP voltage had a significant e!ect on the measurements and to decide which MCP voltage level was advantageous to use for the horizontal IPM in the RR to be compared to the MWs. The horizontal IPM was used to measure the beam size showed high uncertainties and the beam size was observed to be much larger than the average. Therefore, the horizontal IPM was not shown in this paper. | augmentation | NO | 0 |
expert | Which types of facilities require beam profile measurements with micrometer accuracy? | Dielectric laser accelerators, and future compact free-electron lasers. | Summary | Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf | assume a specific shape (e.g., Gaussian) of the distribution, asymmetries, double-peaks, or halos of the distribution can be reconstructed (an example is shown in Appendix C). Properties of the transverse phase space including, transverse emittance in both planes, astigmatism and Twiss parameters can be calculated from the reconstructed distribution. To obtain the full 4D emittance, cross-plane information, such as correlations in $x - y ^ { \\prime }$ or $x ^ { \\prime } - y$ need to be assessed. For this purpose, the phase advance has to be scanned independently in both planes. This can be achieved with a multiple quadrupole scan as explained for instance in [20,21] but is not achieved by measuring beam projections along a waist, as the phase advance in both planes is correlated. The presented phase space reconstruction algorithm could also be adapted to use two-dimensional profile measurements from a screen at different phase advances to characterize the four-dimensional transverse phase space. The python-code related to the described tomographic reconstruction technique is made available on github [22]. A. Reconstruction of a simulated measurement To verify the reconstruction algorithm, we generate a test distribution and calculate a set of wire scan projections (nine projections along different angles at seven locations along the waist). The algorithm then reconstructs the distribution based on these simulated projections. For this test, we choose a Gaussian beam distribution with Twiss parameters $\\beta _ { x } ^ { * } = 2 . 0 ~ \\mathrm { c m }$ , $\\beta _ { y } ^ { * } = 3 . 0 ~ \\mathrm { c m }$ and a transverse emittance of 200 nm rad in both planes. An astigmatism of $- 1 \\ \\mathrm { c m }$ (longitudinal displacement of the horizontal waist) is artificially introduced. Moreover, noise is added to the simulated wire scan profiles to obtain a signal-to-noise ratio similar to the experimental data show in Sec. IV. The Gaussian kernel size for the reconstruction $\\rho _ { x , y }$ [see Eq. (2)] is $8 0 \\mathrm { n m }$ , which is around one order of magnitude smaller than the beam size in this test. Figure 4 compares the original and reconstructed transverse phase space at $z = 0$ cm. Good agreement ( $\\text{‰}$ error) is achieved for the emittances and astigmatism, which is manifested as a tilt in the $x - x ^ { \\prime }$ plane. For this numerical experiment, the algorithm terminates according to the criterion described in Appendix B after around 100 iterations. The run-time on a single-core of a standard personal computer is around two minutes. Parallelizing the computation on several cores would reduce the computation time by few orders of magnitude. | 1 | NO | 0 |
expert | Which types of facilities require beam profile measurements with micrometer accuracy? | Dielectric laser accelerators, and future compact free-electron lasers. | Summary | Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf | fluctuations, or density variations of the electron beam. The effect of these error sources is discussed further in Appendix A. The evolution of the reconstructed transverse phase space along the waist is depicted in Fig. 6. The expected rotation of the transverse phase space around the waist is clearly observed. The position of the waist is found to be at around $z = 6 . 2$ cm downstream of the center of the chamber. IV. RESULTS We have measured projections of the transverse electron beam profile at the ACHIP chamber at SwissFEL with the accelerator setup, wire scanner and BLM detector described in Sec. II. All nine wire orientations are used at six different locations along the waist of the electron beam. This results in a total of 54 projections of the electron beam’s transverse phase space. Lowering the number of projections limits the possibility to observe inhomogeneities of the charge distribution. The distance between measurement locations is increased along $z$ , since the expected waist location was around $z = 0 \\ \\mathrm { c m }$ . All 54 individual profiles are shown in Fig. 5. In each subplot, the orange dashed curve represents the projection of the reconstructed phase space for the respective angle $\\theta$ and longitudinal position z. The reconstruction represents the average distribution over many shots and agrees with most of the measured data points. Discrepancies arise due to shot-to-shot position jitter, charge | 4 | NO | 1 |
expert | Which types of facilities require beam profile measurements with micrometer accuracy? | Dielectric laser accelerators, and future compact free-electron lasers. | Summary | Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf | Table: Caption: TABLE I. Normalized emittance $\\varepsilon _ { n }$ , Twiss $\\beta$ -function at the waist $\\beta ^ { * }$ , and corresponding beam size $\\sigma ^ { * }$ of the reconstructed transverse phase space distribution. Body: <html><body><table><tr><td></td><td>εn (nm rad)</td><td>β*(cm)</td><td>0* (μm)</td></tr><tr><td></td><td>186±15</td><td>3.7 ± 0.2</td><td>1.04 ± 0.06</td></tr><tr><td>y</td><td>278±18</td><td>3.7 ±0.2</td><td>1.26 ± 0.05</td></tr></table></body></html> Figure 7 shows the beam size evolution around the waist. We quantify the normalized emittance and $\\beta$ -function of the distribution by fitting a 2D Gauss function to the distribution in the $( x , x ^ { \\prime } )$ and $( y , y ^ { \\prime } )$ phase space. The 1- $\\mathbf { \\sigma } \\cdot \\sigma _ { \\mathbf { \\lambda } }$ ellipse of the fit is drawn in blue in all subplots of Fig. 6. We use the following definition for the normalized emittance: $$ \\varepsilon _ { n } = \\gamma A _ { 1 \\sigma } / \\pi , $$ where $A _ { 1 \\sigma }$ is the area of the $_ { 1 - \\sigma }$ ellipse in transverse phase space. The values for the reconstructed emittance, minimal $\\beta$ -function $( \\beta ^ { * } )$ and beam size at the waist are summarized in Table I. The measurement range $( 8 \\mathrm { c m } )$ along the waist with $\\beta ^ { * } = 3 . 7$ cm covers a phase advance of around $9 0 ^ { \\circ }$ . | 1 | NO | 0 |
IPAC | Which types of facilities require beam profile measurements with micrometer accuracy? | Dielectric laser accelerators, and future compact free-electron lasers. | Summary | Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf | File Name:DEVELOPMENTS_AND_CHARACTERIZATION_OF_A_GAS_JET.pdf DEVELOPMENTS AND CHARACTERIZATION OF A GAS JET IONIZATION IMAGING OPTICAL COLUMN P. Denham→, A. Ody, P. Musumeci, University of California Los Angeles, Los Angeles, CA USA N. Burger, G. Andonian, T. Hodgetts, D. Gavryushkin, RadiaBeam Technologies, Santa Monica, CA, USA N.M. Cook, RadiaSoft, Boulder, CO USA Abstract Standard methods of measuring the transverse beam profile are not adaptable for su!ciently high-intensity beams. Therefore, the development of non-invasive techniques for extracting beam parameters is necessary. Here we present experimental progress on developing a transverse profile diagnostic that reconstructs beam parameters based on images of an ion distribution generated by beam-induced ionization. Laser-based ionization is used as an initial step to validate the electrostatic column focusing characteristics, and di"erent modalities, including velocity map imaging. This paper focuses on ion imaging performance measurements and ion intensity’s dependence on gas density and incident beam current for low-energy electron beams $( < 1 0 \\mathrm { M e V } )$ . INTRODUCTION Advancements in particle accelerator technology have enabled next-generation facilities to achieve unprecedented levels of beam intensity, power output, and beam brightness. For instance, at FACET, the electron beam can reach an energy of up to $2 0 \\ \\mathrm { G e V }$ and a peak current of 3.2 kA, making it one of the highest-intensity beams in the world [1]. However, conventional diagnostic methods for measuring transverse parameters from beams of this caliber have become increasingly challenging. Additionally, conventional techniques, such as intercepting the beam using phosphor or scintillator screens, or wire scanners, can damage the equipment, particularly when the beam is focused. Consequently, there is a pressing need for non-invasive techniques to extract beam parameters without intercepting the beam [2]. This is especially crucial in high-energy physics, where precise control over the beam is essential for experiments involving particle collisions and beam-target interactions. | 1 | NO | 0 |
expert | Which types of facilities require beam profile measurements with micrometer accuracy? | Dielectric laser accelerators, and future compact free-electron lasers. | Summary | Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf | $$ \\sigma ( z ) = \\sqrt { \\beta ( z ) \\varepsilon _ { n } ( z ) / \\gamma ( z ) } , $$ where $\\beta$ denotes the Twiss (or Courant-Snyder) parameter of the magnetic lattice, $\\gamma$ is the relativistic Lorentz factor of the electrons and $\\varepsilon _ { n }$ is the normalized emittance of the beam. With an optimized lattice a minimal $\\beta$ -function of around $1 \\ \\mathrm { c m }$ in the horizontal and $1 . 8 ~ \\mathrm { c m }$ in the vertical plane is expected from simulations [11,12]. In order to reduce chromatic effects of the focusing quadrupoles [14], we minimize the projected energy spread by accelerating the beam in most parts of the machine close to on-crest acceleration. From simulations, we expect an optimized projected energy spread of $4 2 \\mathrm { k e V }$ for a $3 { \\mathrm { G e V - } }$ beam with a charge of $1 \\ \\mathrm { p C }$ [11], which corresponds to a relative energy spread of $1 . 4 \\times 1 0 ^ { - 5 }$ . For this uncompressed and low-energy-spread beam we expect chromatic enlargement of the focused beam size on the order of $0 . 1 \\%$ . | augmentation | NO | 0 |
expert | Which types of facilities require beam profile measurements with micrometer accuracy? | Dielectric laser accelerators, and future compact free-electron lasers. | Summary | Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf | D. Beam loss monitor Electrons scatter off the atomic nuclei of the metallic wire and a particle shower containing mainly x-rays, electrons and positrons is generated. The intensity of the secondary particle shower depends on the electron density integrated along the wire and is measured with a downstream beam loss monitor (BLM). The BLM consists of a scintillating fiber wrapped around the beam pipe. The fiber is connected to a photomultiplier tube (PMT). The signal of the PMT is read-out beam synchronously in a shot-by-shot manner. To avoid saturation of the PMT, the gain voltage needs to be set appropriately. SwissFEL is equipped with a series of BLMs, which are normally used to detect unwanted beam losses and are connected to an interlock system. For the purpose of wire scan measurements, individual BLMs can be excluded from the machine protection system. Details about the BLMs at SwissFEL can be found in [18]. For the wire scan measurement reported here, a BLM located $1 0 \\mathrm { ~ m ~ }$ downstream of the interaction with the wire was used. III. TRANSVERSE PHASE SPACE RECONSTRUCTION ALGORITHM Inferring a density distribution from a series of projection measurements is a problem arising in many scientific and medical imaging applications. Standard tomographic reconstruction techniques, e.g., filtered back projection or algebraic reconstruction technique [19] use an intensity on a grid to represent the density to be reconstructed. The complexity of these algorithms scales as $O ( n ^ { d } )$ , where $n$ is the number of pixels per dimension and $d$ is the number of dimensions of the reconstructed density. Typically, for real space density reconstruction, $d$ is 2 (slice reconstruction) or 3 (volume reconstruction). In the case of transverse phase space tomography $d$ equals 4 $( x , x ^ { \\prime } , y , y ^ { \\prime } )$ , leading to very long reconstruction times. | augmentation | NO | 0 |
expert | Which types of facilities require beam profile measurements with micrometer accuracy? | Dielectric laser accelerators, and future compact free-electron lasers. | Summary | Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf | APPENDIX C: RECONSTRUCTION OF NON-GAUSSIAN BEAMS Our particle based tomographic reconstruction algorithm does not assume any specific shape for the density profile. Therefore, asymmetric density variations, such as tails of a localized core can be reconstructed. To demonstrate this capability of our tomographic technique, we show here a measurement of a non-Gaussian beam shape and compare the result to a 2D Gaussian fit. This measurement was performed with different machine settings than the measurement presented in Sec. IV. The electron bunch carried a charge of around $1 0 ~ \\mathrm { p C }$ . The transverse beam profile was characterized with nine wire scans at different angles at one z position. Therefore we can only reconstruct the twodimensional $( x , y )$ beam profile. The measurement and the tomographic reconstruction are shown in Fig. 8. For comparison, we add the result of a single two-dimensional Gaussian fit to all nine measured projections (Fig. 9). The core and tails observed in the measurement are well represented by the tomographic reconstruction, whereas the Gaussian fit overestimates the core region by trying to approximate the tails. [1] E. Esarey, C. Schroeder, and W. Leemans, Physics of laser-driven plasma-based electron accelerators, Rev. Mod. Phys. 81, 1229 (2009). | augmentation | NO | 0 |
expert | Which types of facilities require beam profile measurements with micrometer accuracy? | Dielectric laser accelerators, and future compact free-electron lasers. | Summary | Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf | The reconstructed normalized emittances are up to a factor of two larger than the normalized emittances measured after the second bunch compressor. This emittance increase can be attributed to various reasons. Within a distance of $1 0 3 \\mathrm { ~ m ~ }$ the electron beam is accelerated from $2 . 3 { \\mathrm { G e V } }$ (conventional emittance measurement) to around $3 . 2 { \\mathrm { ~ G e V } }$ and is directed to the Athos branch with a fast kicker and a series of bending magnets. Chromatic effects in the lattice, transverse offsets in the accelerating cavities or leaking dispersion from dispersive sections in the switch-yard can lead to a degradation of the emittance along the accelerator. These effects were not precisely characterized and corrected before the measurement, since the priority was to validate a new method for transverse phase space characterization of a strongly focused ultrarelativistic electron beam. Another possible explanation for the discrepancy of the emittances: the conventional emittance measurement uses the horizontal and vertical beam profiles measured for different phase advances (quadrupole currents) with a scintillating screen (single-shot). A Gaussian fit to the beam profiles at each phase advance is used to estimate the emittance [15]. In contrast, the tomographic wire scan technique presented here reconstructs the transverse phase space averaged over many shots. Afterwards, a Gaussian fit estimates the area of the distribution in the transverse phase space. Both large shot-to-shot jitter and non-Gaussian beams can give rise to differences between the results of the two techniques. The wire scan acquisition time could be reduced by using fewer projection angles. This could be done, if less detailed information on the beam distribution is acceptable, e.g., if only projected beam sizes are of interest, two projection angles are sufficient. The optimal number of angles depends on the internal beam structure and the beam quantities of interest. | augmentation | NO | 0 |
expert | Which types of facilities require beam profile measurements with micrometer accuracy? | Dielectric laser accelerators, and future compact free-electron lasers. | Summary | Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf | The ensemble of particles is iteratively optimized so that their projections match with the set of measured projections. The algorithm starts from a homogeneous particle distribution. One iteration consists of the following operations. (i) Transport $T ( z )$ (ii) Rotation $R ( \\theta )$ (iii) Histogram of the transported and rotated coordinates (iv) Convolution with wire profile (v) Interpolation to measured wire positions (vi) Comparison of reconstruction and measurement (vii) Redistribution of particles In the case of ultrarelativistic electrons transverse space charge effects can be neglected since they scale as $\\mathcal { O } ( \\gamma ^ { - 2 } )$ and hence $T ( z )$ becomes the ballistic transport matrix: $$ T ( z ) = { \\left( \\begin{array} { l l } { 1 } & { z } \\\\ { 0 } & { 1 } \\end{array} \\right) } $$ for $( x , x ^ { \\prime } )$ and $\\left( { y , y ^ { \\prime } } \\right)$ . The rotation matrix is then applied to $( x , y )$ : $$ R ( \\theta ) = { \\binom { \\cos \\theta } { - \\sin \\theta } } \\quad \\sin \\theta { \\Big ) } . | augmentation | NO | 0 |
expert | Which types of facilities require beam profile measurements with micrometer accuracy? | Dielectric laser accelerators, and future compact free-electron lasers. | Summary | Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf | We developed a reconstruction algorithm based on a macroparticle distribution (instead of the intensity on grid), where each macroparticle, from now on called particle, represents a point in the four-dimensional phase space. The complexity of this algorithm is proportional to $n _ { p }$ (number of particles) and is independent on the dimension of the reconstruction domain. The particle density is then given by applying a Gaussian kernel to each coordinate of the particle ensemble: $$ G _ { \\kappa } = \\frac { 1 } { \\sqrt { 2 \\pi } \\rho _ { \\kappa } } \\exp { \\left( - \\frac { \\kappa ^ { 2 } } { 2 \\rho _ { \\kappa } ^ { 2 } } \\right) } , \\qquad \\kappa \\in \\{ x , x ^ { \\prime } , y , y ^ { \\prime } \\} $$ $$ \\Delta ^ { i } = \\frac { 1 } { n _ { \\theta } n _ { z } } \\sum _ { \\theta , z } \\Delta _ { z , \\theta } ^ { i } . $$ where we choose $\\rho _ { x ^ { \\prime } , y ^ { \\prime } } = \\rho _ { x , y } / z _ { \\mathrm { m a x } }$ , with $z _ { \\mathrm { m a x } }$ the range of the measurement along z. Choosing the right kernel size is important for an appropriate reconstruction of the beam. It is dimensioned such that $\\rho _ { x , x ^ { \\prime } , y , y ^ { \\prime } }$ represents the length scale below which we expect only random fluctuations in the particle distribution, which are not reproducible from shot to shot. Note that despite the Gaussian kernel, this reconstruction does not assume a Gaussian distribution of the beam, but is able to reconstruct arbitrary distributions that vary on a length scale given by $\\rho _ { x , x ^ { \\prime } , y , y ^ { \\prime } }$ . | augmentation | NO | 0 |
expert | Which types of facilities require beam profile measurements with micrometer accuracy? | Dielectric laser accelerators, and future compact free-electron lasers. | Summary | Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf | $$ Afterwards, the histogram of the particles’ transported and rotated $x$ coordinates is calculated. Note that the bin width needs to be smaller than the width of the wire, to ensure an accurate convolution with the wire profile. This becomes important when the beam size or beam features are smaller than the wire width. Next, the convolution of the histogram and the wire profile is interpolated linearly to the measured wire positions $\\xi$ . Now, the reconstruction can be directly compared to the measurement: $$ \\Delta _ { z , \\theta } ( \\xi ) = \\frac { P _ { z , \\theta } ^ { m } ( \\xi ) - P _ { z , \\theta } ^ { r } ( \\xi ) } { \\operatorname* { m a x } _ { \\xi } P _ { z , \\theta } ^ { r } ( \\xi ) } , $$ The sign of $\\Delta ^ { i }$ indicates if a particle is located in an over- or underdense region represented by the current particle distribution. According to the magnitude of $\\Delta ^ { i }$ the new particle ensemble is generated. A particle is copied or removed from the previous distribution with a probability based on $| \\Delta ^ { i } |$ . This process is implemented by drawing a pseudorandom number $\\chi ^ { i } \\in [ 0 , 1 [$ for each particle. In case $\\chi ^ { i } < | \\Delta ^ { i } | / s _ { \\mathrm { m a x } }$ , particle $i$ is copied or removed from the distribution (depending on the sign of $\\Delta ^ { i }$ ). Otherwise, the particle remains in the ensemble. Here, $s _ { \\mathrm { m a x } }$ is the maximum of all measured BLM signals and is used to normalize $\\Delta ^ { i }$ for the comparison with $\\chi ^ { i } \\in [ 0 , 1 [$ . This process makes sure that particles in highly underdense (overdense) regions are created (removed) with an increased probability. | augmentation | NO | 0 |
expert | Who first observed synchrotron radiation and when? | It was first observed on April 24, 1947, by Herb Pollock, Robert Langmuir, Frank Elder, and Anatole Gurewitsch at General Electric¬Ç√Ñ√¥s Research Lab in Schenectady, New York. | Fact | Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation | I.10.7.2 Brilliance Estimate the brilliance $\\boldsymbol { B }$ of the sun on its surface, for photons in the visible spectrum. What is the brilliance of the sun on the surface of the Earth? For simplicity, ignore the influence of the Earth‚Äôs atmosphere. Table: Caption: Sun Body: <html><body><table><tr><td>Radiated power</td><td>3.828 ¬∑ 1026</td><td>W</td></tr><tr><td>Surface area</td><td>6.09 ¬∑1012</td><td>km¬≤</td></tr><tr><td>Distance to Earth</td><td>1.496 ¬∑ 108</td><td>km</td></tr><tr><td>Angular size,seen from Earth</td><td>31.6.. .32.7</td><td>minutes of arc</td></tr><tr><td>Age</td><td>4.6 ¬∑ 109</td><td>years</td></tr></table></body></html> I.10.7.3 Synchrotron radiation Synchrotron radiation. . . (check all that apply: more than one answer may be correct) a) . . . is used by scientists in numerous disciplines, including semiconductor physics, material science and molecular biology b) . . . can be calculated from Maxwell‚Äôs equations, without the need of material constants c) . . . is emitted at much longer wavelengths, as compared to cyclotron radiation d) . . . is emitted uniformly in all directions, when seen in the reference frame of the particle e) . . . is emitted in forward direction in the laboratory frame, and uniformly in all directions, when seen in the reference frame of the electron bunches I.10.7.4 Crab Nebula On July 5, 1054, astronomers observed a new star, which remained visible for about two years, and it was brighter than all stars in the sky (with the exception of the Sun). Indeed, it was a supernova, and the remnants of this explosion, the Crab Nebula, are still visible today. It was discovered in the 1950‚Äôs that a significant portion of the light emitted by the Crab Nebula originates from synchrotron radiation (Fig. I.10.17). | 1 | NO | 0 |
expert | Who first observed synchrotron radiation and when? | It was first observed on April 24, 1947, by Herb Pollock, Robert Langmuir, Frank Elder, and Anatole Gurewitsch at General Electric¬Ç√Ñ√¥s Research Lab in Schenectady, New York. | Fact | Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation | The size of an atom is on the order of $1 \\ \\mathring { \\mathrm { A } } = 1 0 ^ { - 1 0 } \\ \\mathrm { m }$ , while the pixels of an X-ray detector are around $1 0 0 ~ { \\mu \\mathrm { m } }$ in size. A magnification of $1 0 ^ { 6 }$ would thus be required, and it turns out that no X-ray lens can provide this9. Unlike lenses for visible light, where glasses of different index of refraction and different dispersion can be combined to compensate lens errors, this is not possible for X-rays. Scientist use thus diffractive imaging, where a computer is used to reconstruct the distribution of atoms in the molecule from the diffraction pattern. When a crystal is placed in a coherent X-ray beam, constructive interference occurs if the Bragg condition (Equation I.10.48) for the incoming and outgoing rays is fulfilled for any given crystal plane. The resulting diffraction pattern appears as a series of spots or fringes, commonly captured on a detector. As an example, the diffraction pattern of a complex biomolecule is shown in Fig. I.10.13. The crystal is then rotated to change the incoming angle, to allow for diffraction from other crystal planes to be recorded. Note that the detector records the number of photons, i.e., the intensity of the diffracted wave, but all phase information is lost. | 1 | NO | 0 |
expert | Who first observed synchrotron radiation and when? | It was first observed on April 24, 1947, by Herb Pollock, Robert Langmuir, Frank Elder, and Anatole Gurewitsch at General Electric¬Ç√Ñ√¥s Research Lab in Schenectady, New York. | Fact | Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation | $$ where we have used the Twiss parameter identity $\\alpha _ { y } ^ { 2 } = \\beta _ { y } \\gamma _ { y }$ . The change in emittance is thus proportional to the emittance, with a proportionality factor $- d p / P _ { 0 }$ . We thus have an exponentially decreasing emittance (the factor 2 is by convention) $$ \\varepsilon _ { y } ( t ) = \\varepsilon _ { y } ( 0 ) \\cdot \\exp \\left( - 2 \\frac { t } { \\tau _ { y } } \\right) . $$ This result underscores the value of the chosen variable transformation. By using action and angle variables, we can get an understanding of a key characteristic of the electron bunch: its emittance. This variable transformation is not just a mathematical maneuver; it serves as a powerful tool, offering clarity and depth to our exploration. Note that we assume the momentum of the photon to be much smaller than the reference momentum. As a result, we see a slow (i.e. an adiabatic) damping of the emittance. To proceed our determination of the vertical damping time, i.e. the decay constant of the emittance, we need to quantify the energy lost by a particle due to synchrotron radiation for each turn in the storage | 1 | NO | 0 |
expert | Who first observed synchrotron radiation and when? | It was first observed on April 24, 1947, by Herb Pollock, Robert Langmuir, Frank Elder, and Anatole Gurewitsch at General Electric¬Ç√Ñ√¥s Research Lab in Schenectady, New York. | Fact | Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation | $$ Figure I.10.2 shows the development of the peak brilliance of $\\mathrm { \\Delta X }$ -ray sources during the last century. Scientists working in synchrotron radiation facilities have gotten accustomed to an extremely high flux, as well as an excellent stability of their X-ray source. The flux is controlled on the permille level, and the position stability is measured in micrometers. Synchrotron radiation was first observed on April 24, 1947 by Herb Pollock, Robert Langmuir, Frank Elder, and Anatole Gurewitsch, when they saw a gleam of bluish-white light emerging from the transparent vacuum tube of their new $7 0 \\mathrm { M e V }$ electron synchrotron at General Electric‚Äôs Research Laboratory in Schenectady, New York1. It was first considered a nuisance because it caused the particles to lose energy, but it was recognised in the 1960s as radiation with exceptional properties that overcame the shortcomings of X-ray tubes. Furthermore, it was discovered that the emission of radiation improved the emittance of the beams in electron storage rings, and additional series of dipole magnets were installed at the Cambridge Electron Accelerator (CEA) at Harvard University to provide additional damping of betatron and synchrotron oscillations. The evolution of synchrotron sources has proceeded in four generations, where each new generation made use of unique new features in science and engineering to increase the coherent flux available to experiments: | 5 | NO | 1 |
expert | Who first observed synchrotron radiation and when? | It was first observed on April 24, 1947, by Herb Pollock, Robert Langmuir, Frank Elder, and Anatole Gurewitsch at General Electric¬Ç√Ñ√¥s Research Lab in Schenectady, New York. | Fact | Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation | $$ d \\varepsilon _ { y } = - \\varepsilon _ { y } \\frac { U _ { 0 } } { E _ { \\mathrm { { n o m } } } } . $$ Using the revolution period $T _ { 0 }$ $$ \\frac { d \\varepsilon _ { y } } { d t } = - \\varepsilon _ { y } \\frac { U _ { 0 } } { E _ { \\mathrm { n o m } } T _ { 0 } } . $$ The damping time is thus $$ \\tau _ { y } = 2 \\frac { E _ { \\mathrm { { n o m } } } } { U _ { 0 } } T _ { 0 } . $$ We use the (classical) result from Equation I.10.9 for the power radiated by a particle of charge $e$ and energy $E _ { \\mathrm { n o m } }$ . Integrating around the ring, we have the energy loss per turn $$ \\begin{array} { l l l } { { U _ { 0 } } } & { { = } } & { { \\displaystyle \\oint P _ { \\gamma } d t } } \\\\ { { } } & { { = } } & { { \\displaystyle \\oint \\frac { 1 } { c } P _ { \\gamma } d s } } \\\\ { { } } & { { = } } & { { \\displaystyle \\frac { C _ { \\gamma } } { 2 \\pi } E _ { \\mathrm { n o m } } ^ { 4 } \\oint \\frac { 1 } { \\rho ^ { 2 } } d s . } } \\end{array} | augmentation | NO | 0 |
expert | Who first observed synchrotron radiation and when? | It was first observed on April 24, 1947, by Herb Pollock, Robert Langmuir, Frank Elder, and Anatole Gurewitsch at General Electric¬Ç√Ñ√¥s Research Lab in Schenectady, New York. | Fact | Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation | File Name:Ischebeck_-_2024_-_I.10_‚Äî_Synchrotron_radiation.pdf Chapter I.10 Synchrotron radiation Rasmus Ischebeck Paul Scherrer Institut, Villigen, Switzerland Electrons circulating in a storage ring emit synchrotron radiation. The spectrum of this powerful radiation spans from the far infrared to the $\\boldsymbol { \\mathrm { \\Sigma } } _ { \\mathrm { X } }$ -rays. Synchrotron radiation has evolved from being a mere byproduct of particle acceleration to a powerful tool leveraged in diverse scientific and engineering fields. Indeed, synchrotrons are the most brilliant X-ray sources on Earth, and they find use in a wide range of fields in research. In this chapter, we will look at the generation of radiation of charged particles in an accelerator, at the influence of this on the beam dynamics, and on the physics behind applications of synchrotron radiation for research. I.10.1 Introduction It is difficult to overstate the importance of X-rays for medicine, research and industry. Already a few years after their discovery by Wilhelm Conrad R√∂ntgen, their ability to penetrate matter established Xrays as an important diagnostics tool in medicine. Experiments with $\\mathrm { \\Delta X }$ -rays have come a long way since the inception of the first $\\mathrm { \\Delta } X$ -ray tubes. The short wavelength of $\\mathrm { \\Delta X }$ -rays allowed Rosalynd Franklin and Raymond Gosling to take diffraction images that would lead to the discovery of the structure of DNA. Today, X-ray diffraction is an indispensable tool in structural biology and in pharmaceutical research. Industrial applications of X-rays range from cargo inspection to sterilization and crack detection. | augmentation | NO | 0 |
expert | Who first observed synchrotron radiation and when? | It was first observed on April 24, 1947, by Herb Pollock, Robert Langmuir, Frank Elder, and Anatole Gurewitsch at General Electric¬Ç√Ñ√¥s Research Lab in Schenectady, New York. | Fact | Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation | $$ Computing the photon flux $\\dot { N } _ { \\gamma }$ for an undulator is even more elaborate than the calculation for a single dipole, and we just cite the result [2] $$ { \\dot { N } } _ { \\gamma } = 1 . 4 3 \\cdot 1 0 ^ { 1 4 } N I _ { b } Q _ { n } ( K ) , $$ where $$ Q _ { n } ( K ) = \\frac { 1 + K ^ { 2 } / 2 } { n } F _ { n } ( K ) . $$ We denote the harmonic number by $n = 2 m - 1$ with $m \\in \\mathbb { N }$ , the number of periods in the undulator by $N$ , the beam current in A by $I _ { b }$ , the undulator parameter by $K$ , and $F _ { n } ( K )$ is given by $$ \\begin{array} { r c l } { { F _ { n } ( K ) } } & { { = } } & { { \\displaystyle \\frac { n ^ { 2 } K ^ { 2 } } { ( 1 + K ^ { 2 } / 2 ) ^ { 2 } } \\left( J _ { ( n + 1 ) / 2 } ( Y ) - J _ { ( n - 1 ) / 2 } ( Y ) \\right) ^ { 2 } } } \\\\ { { } } & { { } } & { { } } \\\\ { { Y } } & { { = } } & { { \\displaystyle \\frac { n K ^ { 2 } } { 4 ( 1 + K ^ { 2 } / 2 ) } , } } \\end{array} | augmentation | NO | 0 |
expert | Who first observed synchrotron radiation and when? | It was first observed on April 24, 1947, by Herb Pollock, Robert Langmuir, Frank Elder, and Anatole Gurewitsch at General Electric¬Ç√Ñ√¥s Research Lab in Schenectady, New York. | Fact | Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation | $$ For a synchrotron consisting of only dipoles $$ \\oint { \\frac { 1 } { \\rho ^ { 2 } } } d s = { \\frac { 2 \\pi \\rho } { \\rho ^ { 2 } } } = { \\frac { 2 \\pi } { \\rho } } . $$ More generally, we use the second synchrotron radiation integral as defined in Equation I.10.12, and we can write the energy loss per turn as a function of $I _ { 2 }$ $$ U _ { 0 } = \\frac { C _ { \\gamma } } { 2 \\pi } E _ { \\mathrm { n o m } } ^ { 4 } I _ { 2 } . $$ Notice that $I _ { 2 }$ is a property of the lattice (actually, a property of the reference trajectory), and does not depend on the properties of the beam. The emittance evolves as $$ \\varepsilon _ { y } ( t ) = \\varepsilon _ { y } ( 0 ) \\exp \\left( - 2 \\frac { t } { \\tau _ { y } } \\right) . $$ From this, it follows that the emittance decreases exponentially, asymptotically approaching zero. This phenomenon is termed radiation damping. While radiation damping plays a key role in influencing the emittance of the beam in a synchrotron, there exist other factors and effects that counterbalance its influence. These countering mechanisms ensure that the emittance does not perpetually decline due to the sole influence of radiation damping, but that it reaches a non-zero equilibrium value. Before diving into these balancing effects, we turn our attention to the horizontal plane, examining its unique characteristics and dynamics in the context of our ongoing analysis. | augmentation | NO | 0 |
expert | Who first observed synchrotron radiation and when? | It was first observed on April 24, 1947, by Herb Pollock, Robert Langmuir, Frank Elder, and Anatole Gurewitsch at General Electric¬Ç√Ñ√¥s Research Lab in Schenectady, New York. | Fact | Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation | $$ Equation (I.10.16) becomes $$ \\begin{array} { r c l } { { \\displaystyle \\frac { \\lambda } { 2 c } } } & { { = } } & { { \\displaystyle \\frac { \\lambda _ { u } } { 2 \\beta c } \\left( 1 + \\frac { K ^ { 2 } } { 4 \\gamma ^ { 2 } } \\right) - \\frac { \\lambda _ { u } } { 2 c } } } \\\\ { { \\Longrightarrow } } & { { \\lambda } } & { { = } } & { { \\displaystyle \\frac { \\lambda _ { u } } { 2 \\gamma ^ { 2 } } ( 1 + K ^ { 2 } / 2 ) , } } \\end{array} $$ where we have used $\\beta = \\textstyle \\sqrt { 1 - \\gamma ^ { - 2 } } \\approx 1 - \\frac { 1 } { 2 } \\gamma ^ { - 2 }$ for $\\gamma \\gg 1$ . Radiation emitted at this wavelength adds up coherently in the forward direction. More generally, the radiation adds up coherently at all odd harmonics $n = 2 m - 1 , m \\in \\mathbb { N }$ | augmentation | NO | 0 |
expert | Who first observed synchrotron radiation and when? | It was first observed on April 24, 1947, by Herb Pollock, Robert Langmuir, Frank Elder, and Anatole Gurewitsch at General Electric¬Ç√Ñ√¥s Research Lab in Schenectady, New York. | Fact | Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation | $$ Shifting our view to a broader perspective, we now consider the properties of the entire electron bunch. By definition, the emittance is given as the ensemble average of the action. The change in emittance follows thus from the change in action $$ \\begin{array} { r c l } { d \\varepsilon _ { y } } & { = } & { \\langle d J _ { y } \\rangle } \\\\ & { = } & { - \\langle \\alpha _ { y } \\underbrace { \\langle g p _ { y } \\rangle } _ { = - \\alpha _ { y } \\varepsilon _ { y } } + \\beta _ { y } \\underbrace { \\langle p _ { y } ^ { 2 } \\rangle } _ { = \\gamma _ { \\mathrm { t r } } \\varepsilon _ { y } } \\frac { \\partial p _ { \\mathrm { t } } } { \\partial P _ { 0 } } } \\\\ & & { - \\langle - \\alpha _ { y } ^ { 2 } \\varepsilon _ { y } + \\beta _ { y } \\gamma _ { y } \\varepsilon _ { y } \\rangle \\frac { \\partial p _ { \\mathrm { t } } } { \\partial P _ { 0 } } } \\\\ & { = } & { - \\varepsilon _ { y } \\langle \\underbrace { \\delta _ { y } \\gamma _ { y } } _ { \\mathrm { 1 } } - \\alpha _ { y } ^ { 2 } \\rangle \\frac { d p _ { \\mathrm { f } } } { P _ { 0 } } } \\\\ & & { - \\varepsilon _ { y } \\frac { d p _ { \\mathrm { f } } } { D _ { 0 } } , } \\end{array} | augmentation | NO | 0 |
expert | Who first observed synchrotron radiation and when? | It was first observed on April 24, 1947, by Herb Pollock, Robert Langmuir, Frank Elder, and Anatole Gurewitsch at General Electric¬Ç√Ñ√¥s Research Lab in Schenectady, New York. | Fact | Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation | applications in Section I.10.6. The total radiated power per particle, obtained by integrating over the spectrum, is $$ P _ { \\gamma } = \\frac { e ^ { 2 } c } { 6 \\pi \\varepsilon _ { 0 } } \\frac { \\beta ^ { 4 } \\gamma ^ { 4 } } { \\rho ^ { 2 } } . $$ The energy lost by a particle on a circular orbit, i.e. in an accelerator consisting only of dipole magnets, is $$ U _ { 0 } = \\frac { e ^ { 2 } \\beta ^ { 4 } \\gamma ^ { 4 } } { 3 \\varepsilon _ { 0 } \\rho } , $$ where we have used $T = 2 \\pi \\rho / c$ , assuming $v \\approx c$ . Of course, real accelerators contain also other types of magnets. The energy lost per turn for a particle in an arbitrary accelerator lattice can be calculated by the following ring integral $$ U _ { 0 } = \\frac { C _ { \\gamma } } { 2 \\pi } E _ { \\mathrm { n o m } } ^ { 4 } \\oint \\frac { 1 } { \\rho ^ { 2 } } d s , | augmentation | NO | 0 |
expert | Who first observed synchrotron radiation and when? | It was first observed on April 24, 1947, by Herb Pollock, Robert Langmuir, Frank Elder, and Anatole Gurewitsch at General Electric¬Ç√Ñ√¥s Research Lab in Schenectady, New York. | Fact | Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation | ‚Äì Auger electrons: similarly to fluorescence, this effect starts with the ionization or excitation of an inner-shell electron due to the interaction with the X-ray photon. This leaves a vacancy in the inner shell, which is then filled with an outer-shell electron. However, instead of releasing the excess energy as a photon, the energy is transferred non-radiatively to another outer-shell electron. This transfer of energy gives the second electron enough energy to be ejected from the atom, resulting in the emission of what is known as an Auger electron. These processes are summarized in Fig. I.10.10. Inelastic processes always lead to an energy deposition in the material, often leading to radiation damage, which limits the exposure time in many X-ray experiments. I.10.5.3 Crystal diffraction Imagine many atoms, arranged in a regular lattice, illuminated by a coherent $\\mathrm { \\Delta X }$ -ray source. The elastic scattering on the electron clouds of these atoms will add constructively if all individual waves are in phase. This situation is shown in Fig. I.10.11. Considering a distance $d$ between the crystal planes, and referring to the notation in this figure, we get constructive interference when $$ ( A B + B C ) - ( A C ^ { \\prime } ) = n \\lambda | augmentation | NO | 0 |
expert | Who first observed synchrotron radiation and when? | It was first observed on April 24, 1947, by Herb Pollock, Robert Langmuir, Frank Elder, and Anatole Gurewitsch at General Electric¬Ç√Ñ√¥s Research Lab in Schenectady, New York. | Fact | Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation | I.10.2 Generation of radiation by charged particles An accelerated charge emits electromagnetic radiation. An oscillating charge emits radiation at the oscillation frequency, and a charged particle moving on a circular orbit radiates at the revolution frequency. As soon as the particles approach the speed of light, however, this radiation is shifted towards higher frequencies, and it is concentrated in a forward cone, as shown in Fig. I.10.3. I.10.2.1 Non-relativistic particles moving in a dipole field Let us first look at non-relativistic particles. In a constant magnetic field with magnitude $B$ , a particle with charge $e$ and momentum $p = m v$ will move on a circular orbit with radius $\\rho$ $$ \\rho = \\frac { p } { e B } . $$ This is an accelerated motion, and the particle emits radiation. For non-relativistic particles, this radiation is called cyclotron radiation, and the total emitted power is $$ P = \\sigma _ { t } \\frac { B ^ { 2 } v ^ { 2 } } { \\mu _ { 0 } c } , $$ where $\\sigma _ { t }$ is the Thomson cross section $$ \\sigma _ { t } = \\frac { 8 \\pi } { 3 } \\left( \\frac { e ^ { 2 } } { 4 \\pi \\varepsilon _ { 0 } m c ^ { 2 } } \\right) ^ { 2 } . | augmentation | NO | 0 |
expert | Who first observed synchrotron radiation and when? | It was first observed on April 24, 1947, by Herb Pollock, Robert Langmuir, Frank Elder, and Anatole Gurewitsch at General Electric¬Ç√Ñ√¥s Research Lab in Schenectady, New York. | Fact | Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation | The total radiated power depends on the fourth power of the Lorentz factor $\\gamma$ , or for a given particle energy, it is inversely proportional to the fourth power of the mass of this particle. This means that synchrotron radiation, and its effect on the beam, are negligible for all proton accelerators except for the highest-energy one. For electron storage rings, conversely, this radiation dominates power losses of the beam, the evolution of the emittance in the ring, and therefore the beam dynamics of the accelerator. Before we will look at this in detail, we will treat one particular case where the electrons pass through a sinusoidal magnetic field. Such a field, generated by wigglers and undulators2, gives rise to strong radiation in the forward direction, which makes it particularly useful for applications of $\\mathrm { \\Delta } \\mathrm { X }$ -rays. I.10.2.3 Coherent generation of X-rays in undulators Wiggler and undulator magnets are devices that impose a periodic magnetic field on the electron beam. These insertion devices have been specially designed to excite the emission of electromagnetic radiation in particle accelerators. Let us assume a cartesian coordinate system with an electron travelling in $z$ direction. A planar insertion device, with a mangetic field in the vertical direction $y$ , has the following field on axis | augmentation | NO | 0 |
expert | Who first observed synchrotron radiation and when? | It was first observed on April 24, 1947, by Herb Pollock, Robert Langmuir, Frank Elder, and Anatole Gurewitsch at General Electric¬Ç√Ñ√¥s Research Lab in Schenectady, New York. | Fact | Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation | The scattering amplitude $I _ { 0 }$ can be calculated from classic electromagnetism. For non-relativistic electrons, it is sufficient to consider the electric component of the incoming wave. The Thomson scattering cross section is equal to $$ \\sigma _ { T } = { \\frac { 8 \\pi } { 3 } } \\left( { \\frac { e ^ { 2 } } { 4 \\pi \\varepsilon _ { 0 } m _ { e } c ^ { 2 } } } \\right) ^ { 2 } = 0 . 6 \\cdot 1 0 ^ { - 2 8 } \\mathrm { { m } } = 0 . 6 \\mathrm { { b a r n } , } $$ independent of the wavelength of the incoming photon. This is in contrast to Compton scattering, where we consider photons with an energy above a few $1 0 \\mathrm { k e V . }$ In this case, we have to consider quantum mechanical effects, and the photon transfers energy and momentum to the electron. The wavelength change of the scattered photon can be determined from the conservation of energy and momentum $$ \\Delta \\lambda = \\frac { h } { m _ { e } c } ( 1 - \\cos { \\vartheta } ) , | augmentation | NO | 0 |
expert | Who first observed synchrotron radiation and when? | It was first observed on April 24, 1947, by Herb Pollock, Robert Langmuir, Frank Elder, and Anatole Gurewitsch at General Electric¬Ç√Ñ√¥s Research Lab in Schenectady, New York. | Fact | Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation | $$ When deriving the equations for the beam dynamics in the horizontal phase space, we need to consider: ‚Äì Change in momentum: the emission of radiation leads to a recoil of the electron. This change in momentum is the same that we considered in the vertical phase space; ‚Äì Dispersion: the emission of radiation results in a change in the energy deviation, denoted as $\\delta$ . This deviation brings about subsequent changes in the horizontal coordinate $x$ and its associated momentum $p _ { x }$ . When we explored the beam dynamics in the vertical phase space, we ignored the second factor, as we assumed that the vertical dispersion is zero. This assumption streamlined the analysis, but it can certainly not be made in the horizontal dimension. While the details of the interplay between the emission of synchrotron radiation and the damping of the emittance are unique to each plane, the outcomes are similar. The horizontal emittance decays exponentially $$ \\frac { d \\varepsilon _ { x } } { d t } = - \\frac { 2 } { \\tau _ { x } } \\varepsilon _ { x } $$ $$ \\Rightarrow \\varepsilon _ { x } ( t ) = \\varepsilon _ { x } ( 0 ) \\exp \\left( - 2 \\frac { t } { \\tau _ { x } } \\right) | augmentation | NO | 0 |
expert | Who first observed synchrotron radiation and when? | It was first observed on April 24, 1947, by Herb Pollock, Robert Langmuir, Frank Elder, and Anatole Gurewitsch at General Electric¬Ç√Ñ√¥s Research Lab in Schenectady, New York. | Fact | Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation | Suggest a way to lower the emittance at the existing machine in order to test the instrumentation. What are some issues with your suggestion? I.10.7.24 Upgrade The SLS 2.0 Upgrade, amongst other things, considers an increase of the electron energy from 2.4 to $2 . 7 \\mathrm { G e V . }$ ‚Äì What can be the rationale for this change? Assume that the lattice is the same for both energies. ‚Äì Are there detrimental aspects to an energy increase? I.10.7.25 Neutron star A proton with energy $E _ { p } = 1 0 \\mathrm { T e V }$ moves through the magnetic field of a neutron star with strength $B = 1 0 ^ { 8 } \\mathrm { T }$ . ‚Äì Calculate the diameter of the proton trajectory and the revolution frequency. ‚Äì How large is the power emitted by synchrotron radiation? ‚Äì How much energy does the proton lose per revolution? I.10.7.26 Cosmic electron A cosmic electron with an energy of $1 \\mathrm { G e V }$ enters an interstellar region with a magnetic field of $1 \\ \\mathrm { n T }$ . Calculate: ‚Äì The radius of curvature, ‚Äì The critical energy of the emitted synchrotron radiation, ‚Äì The energy emitted in one turn. | augmentation | NO | 0 |
expert | Who first observed synchrotron radiation and when? | It was first observed on April 24, 1947, by Herb Pollock, Robert Langmuir, Frank Elder, and Anatole Gurewitsch at General Electric¬Ç√Ñ√¥s Research Lab in Schenectady, New York. | Fact | Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation | $$ All synchrotron radiation integrals are a function of the lattice, independent of the properties of the stored beam. Again, Equation I.10.32 would predict an emittance that decays exponentially, approaching zero. The reason that this does not happen in reality is that there are effects that increase the horizontal emittance and thus result in a non-zero equilibrium emittance. We will soon look at these effects, but not before examining the longitudinal phase space. I.10.3.3 Longitudinal damping We will now look at the effect of synchrotron radiation on the longitudinal phase space $( z , \\delta )$ . Electrons that have a larger energy than the reference particle radiate more, while those that have smaller energy radiate less. This leads to a damping of the oscillations in the longitudinal phase space (the so-called synchrotron oscillations), and the longitudinal emittance, i.e. the phase space volume of the beam, decays exponentially. This phase space is again coupled to the horizontal phase space, for the reasons mentioned above. Finding the damping time, one follows a derivation similar as in the vertical phase space: ‚Äì Write down the equations of motion of a single electron in the longitudinal phase space, including losses through synchrotron radiation; | augmentation | NO | 0 |
expert | Who first observed synchrotron radiation and when? | It was first observed on April 24, 1947, by Herb Pollock, Robert Langmuir, Frank Elder, and Anatole Gurewitsch at General Electric¬Ç√Ñ√¥s Research Lab in Schenectady, New York. | Fact | Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation | How would you measure this radiation? I.10.7.27 Superconducting undulators What is the advantage of using undulators made with superconducting coils, in comparison to permanentmagnet arrays? What are drawbacks? I.10.7.28 In-vacuum undulators What are the advantages of using in-vacuum undulators? What are possible difficulties? I.10.7.29 Instrumentation How would you measure the vertical emittance in a storage ring? I.10.7.30 Top-up operation What are the advantages of top-up operation? What difficulties have to be overcome to establish top-up in a storage ring? (give one advantage and one difficulty for 1P.; give one more advantage and one more difficulty for $\\begin{array} { r } { 1 \\mathrm { P } . \\star . } \\end{array}$ .) I.10.7.31 Fundamental limits The SLS 2.0, a diffraction limited storage ring, aims for an electron energy of $2 . 4 \\mathrm { G e V }$ and an emittance of $1 2 6 \\mathrm { p m }$ . How far is this away from the de Broglie emittance, i.e. the minimum emittance given by the uncertainty principle? I.10.7.32 Applications Why are synchrotrons important for science? I.10.7.33 Applications What applications for industry are there to synchrotrons? I.10.7.34 Orbit correction Which devices are used to measure and correct the orbit inside a synchrotron? | augmentation | NO | 0 |
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