| Parameter |
| K | Wakefield loss factor |
| βg | Normalized group velocity |
| vg | Group velocity |
| α | Attenuation constant |
| Q | Quality factor |
| 0 | Electrical conductivity |
| Corrugation spacing parameter |
| S | Corrugation sidewall parameter |
| a | Corrugation minor radius |
| t | Corrugation tooth width |
| g | Corrugation vacuum gap |
| d | Corrugation depth |
| p | Corrugation period |
| rt | Corrugation tooth radius |
| rg | Corrugation vacuum gap radius |
| L | Corrugated waveguide length |
| F | Bunch form factor |
| q0 | Drive bunch charge |
| fr | Bunch repetition rate |
| T | rf pulse decay time constant |
| 8 | Skin depth |
| Pf | rf pulse power envelope |
| P | Instantaneous rf pulse power |
| Eacc | Accelerating field |
| Emax | Peak surface E field |
| Hmax | Peaksurface H field |
| Qdiss | Energy dissipation |
| Pd | Power dissipation distribution |
| W | Average thermal power density |
| ‚ñ≥T | Transient temperature rise |
| C | Speed of light |
| Z0 | Impedance of free space |
| 8 | Initial beam energy |
| R | Transformer ratio |
In the parametric analysis that follows, the corrugation dimensions are expressed in terms of the normalized spacing parameter $\\xi$ and sidewall parameter $\\zeta$ defined as $$ \\begin{array} { l } { \ { \\xi = \\frac { g - t } { p } } , } \\\\ { \ { \\zeta = \\frac { g + t } { p } } . } \\end{array} $$ The spacing parameter $\\xi$ determines the spacing between the corrugation teeth and ranges from $^ { - 1 }$ to 1 for the minimum and maximum radii profiles, where positive values of $\\xi$ result in spacing greater than the tooth width and vice versa for negative values. The sidewall parameter $\\zeta$ controls the sidewall angle of the unequal radii profile, where $\\zeta < 1$ leads to tapered sidewalls and $\\zeta > 1$ leads to undercut sidewalls. These dependencies are illustrated in Fig. 4.",2,NO,0
IPAC,How is the transformer ratio defined?,It is the ratio of the maximum electric field behind the drive bunch to the maximum electric field within the bunch,Definition,Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf,"$$ Where $\\alpha _ { 0 } : = { \\cal Q } _ { \\scriptscriptstyle L } / { \\cal Q } _ { 0 } , \\alpha _ { \\scriptscriptstyle k } : = \\alpha _ { 0 } \\beta _ { \\scriptscriptstyle k } , \\Psi : = \\mathrm { a t a n } ( - { \\mathrm Q } _ { \\scriptscriptstyle L } \\delta ) .$ The reflection coefficient at AA’ is given by $\\Gamma _ { _ { A d ^ { \\prime } } } = \\Gamma _ { \\boldsymbol { k } } = 2 \\alpha _ { \\boldsymbol { k } } e ^ { i \\Psi } \\cos \\Psi - 1$ and the reflected voltage is given by $$ V _ { k k } ^ { r } = \\sqrt { 2 R P _ { k } } e ^ { i \\phi _ { k } } \\left( 2 \\alpha _ { k } e ^ { i \\Psi } \\cos \\Psi - 1 \\right) $$ Now, we need to add all the transmitted voltages from the other feeds. For such a purpose, let us suppose that the $\\mathrm { j }$ -th feed is active and the other ones are simply replaced by the dummy loads. In this case the cavity voltage is given by the transmitted voltage due to the $\\mathrm { j }$ -th feed transported to the secondary via the multiplication by the turn ratio nj.",1,NO,0
expert,How is the transformer ratio defined?,It is the ratio of the maximum electric field behind the drive bunch to the maximum electric field within the bunch,Definition,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,NO,0
expert,How is the transformer ratio defined?,It is the ratio of the maximum electric field behind the drive bunch to the maximum electric field within the bunch,Definition,Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf,"$$ E _ { z , n } ( s \\to \\infty ) = 2 \\kappa _ { n } q _ { 0 } \\mathrm { R e } \\{ e ^ { j k _ { n } s } F ( k _ { n } ) \\} $$ Expanding the real part $$ \\begin{array} { r } { E _ { z , n } ( s \\infty ) = 2 \\kappa _ { n } q _ { 0 } [ \\cos ( k _ { n } s ) \\mathrm { R e } \\{ F ( k _ { n } ) \\} } \\\\ { - \\sin ( k _ { n } s ) \\mathrm { I m } \\{ F ( k _ { n } ) \\} ] . \\qquad } \\end{array} $$ Since we are interested in the maximum value of the longitudinal accelerating field, we define $E _ { \\mathrm { a c c } }$ as the amplitude of $E _ { z , n } \\big ( s \\infty \\big )$ : $$ E _ { \\mathrm { a c c } } = 2 \\kappa q _ { 0 } \\sqrt { \\mathrm { R e } \\{ F ( k _ { n } ) \\} ^ { 2 } + \\mathrm { I m } \\{ F ( k _ { n } ) \\} ^ { 2 } }",augmentation,NO,0
expert,How is the transformer ratio defined?,It is the ratio of the maximum electric field behind the drive bunch to the maximum electric field within the bunch,Definition,Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf,"IV. ELECTROMAGNETIC PARAMETERS Each synchronous eigenmode solution of the periodic structure is characterized by a wakefield loss factor $\\kappa$ , group velocity $v _ { g } ,$ and attenuation constant $\\alpha$ . These parameters determine how the electron beam interacts with the given mode as well as the propagation characteristics of the corresponding wakefield. In this section, equations for the electromagnetic parameters are defined and applied to the structures found in Sec. III. The results are plotted against the corrugation spacing parameter $\\xi$ and period $p$ at each of the three aperture ratios to show how the wave propagation and beam interaction depend on the corrugation geometry and frequency. The loss factor $\\kappa$ describes the energy coupled from a charged particle to the structure and is defined as [16]: $$ \\kappa = \\frac { V ^ { 2 } / U } { 4 ( 1 - \\beta _ { g } ) p } , $$ where $V$ is the induced voltage, $U$ is the stored energy in the unit cell, and $\\beta _ { g }$ is the normalized group velocity $v _ { g } / c$ . The induced voltage is calculated from the time harmonic electric field of the synchronous mode with angular frequency $\\omega$ as",augmentation,NO,0
expert,How is the transformer ratio defined?,It is the ratio of the maximum electric field behind the drive bunch to the maximum electric field within the bunch,Definition,Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf,"$$ W = \\frac { E _ { \\mathrm { a c c } } ^ { 2 } f _ { r } } { 8 \\pi a \\kappa } . $$ Referring to the plot for $\\kappa$ in Fig. 7, the power dissipation density is reduced by minimizing the corrugation period $p$ and maximizing the spacing parameter $\\xi$ . For structures with $p / a \\lesssim 0 . 5$ , the power dissipation density decreases with an increasing aperture ratio. This results in a trade-off between minimizing the peak surface fields and minimizing the thermal loading of the CWG, where choosing a larger aperture ratio (higher $\\mathrm { T M } _ { 0 1 }$ frequency) results in higher peak fields but less thermal power dissipation. Using $\\kappa _ { \\mathrm { m a x } }$ from Eq. (10) in Eq. (16), we obtain the lower bound of the energy dissipation density as $$ \\frac { d Q _ { \\mathrm { d i s s } } ( z \\infty ) } { d S } \\geq \\frac { E _ { \\mathrm { a c c } } ^ { 2 } a } { 4 Z _ { 0 } c } .",augmentation,NO,0
expert,How is the transformer ratio defined?,It is the ratio of the maximum electric field behind the drive bunch to the maximum electric field within the bunch,Definition,Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf,"VI. THERMAL LOADING Thermal loading of the corrugated waveguide places a limit on the maximum repetition rate $f _ { r }$ of the accelerator, where $f _ { r }$ is the number of bunches injected into the structure per second. The thermal loading depends on the electromagnetic properties of the $\\mathrm { T M } _ { 0 1 }$ mode as well as the length of the corrugated waveguide and the conductivity of the wall material. Achieving a high repetition rate requires active cooling of the structure as well as an optimally designed corrugation profile. Here we focus on designing a corrugation that minimizes the steady-state thermal load and transient pulse heating. The thermally induced stresses due to temperature gradients in the wall pose additional design considerations which are discussed further in [26]. Because the group velocity $v _ { g }$ of the electromagnetic wave is less than the electron bunch velocity, the length of the rf pulse behind the bunch grows as it traverses the structure. This causes the thermal energy density deposited in the CWG wall to increase along the direction of propagation. At a distance $z$ from the beginning of the CWG, the field strength of the rf pulse induced by the electron bunch entering at time $t = 0$ is",augmentation,NO,0
expert,How is the transformer ratio defined?,It is the ratio of the maximum electric field behind the drive bunch to the maximum electric field within the bunch,Definition,Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf,"$$ where $$ x ^ { \\prime } = \\frac { x } { \\hat { a } } , \\qquad y ^ { \\prime } = \\frac { y } { \\hat { a } } , \\qquad z ^ { \\prime } = \\frac { z } { \\hat { a } } , \\qquad \\omega ^ { \\prime } = \\frac { \\omega } { \\hat { a } } . $$ Scaling the fields by $\\hat { a } ^ { - 3 / 2 }$ keeps the stored energy $U ^ { \\prime }$ of the scaled structure same as that of the unscaled structure $U$ , which is seen by integrating the total energy in the fields: $$ \\begin{array} { l } { { \\displaystyle U ^ { \\prime } = \\iiint \\frac { \\epsilon _ { 0 } } { 2 } | \\hat { a } ^ { - 3 / 2 } E ( x ^ { \\prime } , y ^ { \\prime } , z ^ { \\prime } ) | ^ { 2 } } } \\\\ { { \\displaystyle \\quad + \\frac { \\mu _ { 0 } } { 2 } | \\hat { a } ^ { - 3 / 2 } H ( x ^ { \\prime } , y ^ { \\prime } , z ^ { \\prime } ) | ^ { 2 } d x d y d z } } \\\\ { { \\displaystyle = \\iiint \\frac { \\epsilon _ { 0 } } { 2 } | E ( x ^ { \\prime } , y ^ { \\prime } , z ^ { \\prime } ) | ^ { 2 } } } \\\\ { { \\displaystyle \\quad + \\frac { \\mu _ { 0 } } { 2 } | H ( x ^ { \\prime } , y ^ { \\prime } , z ^ { \\prime } ) | ^ { 2 } d x ^ { \\prime } d y ^ { \\prime } d z ^ { \\prime } = U , } } \\end{array}",augmentation,NO,0
expert,How is the transformer ratio defined?,It is the ratio of the maximum electric field behind the drive bunch to the maximum electric field within the bunch,Definition,Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf,"$$ Q = \\frac { \\omega U } { P _ { d } } , $$ where $U$ is stored energy and $P _ { d }$ is the power dissipated in the cavity walls. The power dissipation density per unit area is $$ \\frac { d P _ { d } } { d A } = \\frac { 1 } { 2 } \\sqrt { \\frac { \\omega \\mu } { 2 \\sigma } } | { \\cal H } | ^ { 2 } . $$ In the scaled structure, the power dissipation and resulting quality factor become $$ P _ { d } ^ { \\prime } = \\hat { a } ^ { - 3 / 2 } P _ { d } , \\qquad Q ^ { \\prime } = \\hat { a } ^ { 1 / 2 } Q , $$ leading to the scaled attenuation constant from Eq. (9) $$ \\alpha ^ { \\prime } = \\hat { a } ^ { - 3 / 2 } \\alpha . $$ Scaling of the attenuation constant $\\alpha$ with conductivity is accomplished by multiplying $\\alpha$ by $\\sqrt { \\sigma / \\sigma ^ { \\prime } }$ where $\\sigma$ is the conductivity of the unscaled structure and $\\sigma ^ { \\prime }$ is the conductivity of the scaled structure.",augmentation,NO,0
expert,How is the transformer ratio defined?,It is the ratio of the maximum electric field behind the drive bunch to the maximum electric field within the bunch,Definition,Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf,"$$ \\frac { E _ { \\mathrm { m a x } } ^ { 3 0 } t _ { p } ^ { 5 } } { \\mathrm { B D R } } = \\mathrm { c o n s t . } $$ From a design perspective, reducing the BDR is achieved by reducing the peak surface fields and the pulse length. Calculation of the absolute threshold value of the fields that induce breakdown in sub-THz structures is an active area of research [19,22,23] and reliable models have not yet been developed. The modified Poynting vector introduced in [21] has been used to predict rf breakdown in structures operating up to $3 0 ~ \\mathrm { G H z }$ , but there are limited data for its applicability at higher frequencies. For this reason, the BDR and maximum gradient of the CWA must ultimately be determined experimentally. For the purpose of optimization, we choose the peak surface fields $E _ { \\mathrm { m a x } }$ and $H _ { \\mathrm { m a x } }$ as figures of merit which should be minimized to increase the attainable accelerating gradient. Since some evidence suggests that pulse heating is of fundamental importance to the initiation of rf breakdown in high frequency accelerating structures [24], we give additional weight to the minimization of the peak magnetic surface field. This choice leads to a higher overall thermal efficiency which will be discussed further in Sec. VI.",augmentation,NO,0
expert,How is the transformer ratio defined?,It is the ratio of the maximum electric field behind the drive bunch to the maximum electric field within the bunch,Definition,Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf,"$$ and the Fourier transform of the step function $$ \\mathcal { F } \\{ \\theta ( t ) \\} = \\pi \\biggl ( \\frac { 1 } { j \\pi \\omega } + \\delta ( \\omega ) \\biggr ) , $$ the wake impedance becomes $$ \\begin{array} { r } { Z _ { n | | } ( \\omega ) = \\kappa _ { n } \\Bigg [ \\pi [ \\delta ( \\omega - \\omega _ { n } ) + \\delta ( \\omega + \\omega _ { n } ) ] } \\\\ { - j \\Bigg ( \\cfrac { 1 } { ( \\omega - \\omega _ { n } ) } + \\frac { 1 } { ( \\omega + \\omega _ { n } ) } \\Bigg ) \\Bigg ] . } \\end{array} $$ Using $Z _ { n | | } ( \\omega )$ in Eq. (B12) and evaluating the integral yields $$ P _ { w , n } = \\frac { \\kappa _ { n } c } { 2 } ( | I ( \\omega _ { n } ) | ^ { 2 } + | I ( - \\omega _ { n } ) | ^ { 2 } ) .",augmentation,NO,0
expert,How is the transformer ratio defined?,It is the ratio of the maximum electric field behind the drive bunch to the maximum electric field within the bunch,Definition,Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf,"$$ \\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} $$ Here the field strength is defined in units of $\\sqrt { \\mathrm { W } }$ for consistency with the units provided by CST simulation, $F$ is the bunch form factor derived in Appendix B, $q _ { 0 }$ is the drive bunch charge, and $\\Pi ( x )$ is the rectangular window function.",augmentation,NO,0
expert,Is it accurate to only consider the first harmonic?,"the higher nonsynchronous harmonics average out. It can be shown, that their second order (ponderomotive) contribution is also small. ",reasoning,Beam_dynamics_analysis_of_dielectric_laser_acceleration.pdf,"$$ V = q e _ { 1 } \\left[ \\frac { \\lambda _ { g z } } { 2 \\pi } \\cosh \\left( \\frac { \\omega y } { \\beta \\gamma c } \\right) \\sin \\left( \\frac { 2 \\pi s } { \\lambda _ { g z } } \\right) - s \\cos \\varphi _ { s } \\right] . $$ This potential and its adiabatic change with $\\beta$ is illustrated in Fig. 8. The full 6D Hamiltonian reads $$ H = \\frac { 1 } { 2 m _ { e } \\gamma } ( p _ { x } ^ { 2 } + p _ { y } ^ { 2 } + \\Delta P _ { z } ^ { 2 } ) + V , $$ where $\\Delta p _ { z } / \\gamma$ was replaced with $\\Delta P _ { z }$ . The coupled equations of motion are $$ \\begin{array} { r l } & { \\ddot { x } = 0 } \\\\ & { \\ddot { y } = - \\frac { q e _ { 1 } } { m _ { e } \\gamma ^ { 2 } } \\mathrm { s i n h } \\Bigg ( \\frac { \\omega y } { \\beta \\gamma c } \\Bigg ) \\mathrm { s i n } \\Bigg ( \\frac { 2 \\pi s } { \\lambda _ { g z } } \\Bigg ) } \\\\ & { \\ddot { s } = \\frac { q e _ { 1 } } { m _ { e } \\gamma ^ { 3 } } \\Bigg ( \\mathrm { c o s h } \\Bigg ( \\frac { \\omega y } { \\beta \\gamma c } \\Bigg ) \\mathrm { c o s } \\Bigg ( \\frac { 2 \\pi s } { \\lambda _ { g z } } \\Bigg ) - \\mathrm { c o s } \\varphi _ { s } \\Bigg ) . } \\end{array}",4,Yes,1
expert,Is it accurate to only consider the first harmonic?,"the higher nonsynchronous harmonics average out. It can be shown, that their second order (ponderomotive) contribution is also small. ",reasoning,Beam_dynamics_analysis_of_dielectric_laser_acceleration.pdf,$$ V = q e _ { 1 } \\frac { \\lambda _ { 0 } } { 2 \\pi } \\mathrm { c o s h } \\left( \\frac { \\omega \\tan \\alpha } { c } y \\right) \\cos { \\left[ \\frac { \\omega } { c } ( \\Delta s + x \\tan \\alpha ) \\right] } . $$ The equations of motion become $$ { \\ddot { x } } = { \\frac { q e _ { 1 } } { m _ { e } \\gamma } } \\tan ( \\alpha ) \\cosh \\left[ { \\frac { \\omega \\tan \\alpha } { c } } y \\right] \\sin \\left[ { \\frac { \\omega } { c } } \\left( \\Delta s + x \\tan \\alpha \\right) \\right] $$ $$ { \\ddot { y } } = { \\frac { - i k _ { y } \\lambda _ { g z } q e _ { 1 } } { 2 \\pi m _ { e } \\gamma } } \\sinh \\left[ { \\frac { \\omega \\tan \\alpha } { c } } y \\right] \\cos \\left[ { \\frac { \\omega } { c } } \\left( \\Delta s + x \\tan \\alpha \\right) \\right],4,Yes,1
expert,Is it accurate to only consider the first harmonic?,"the higher nonsynchronous harmonics average out. It can be shown, that their second order (ponderomotive) contribution is also small. ",reasoning,Beam_dynamics_analysis_of_dielectric_laser_acceleration.pdf,"V. APPLICATIONS We apply our approach to similar experimental parameters as for the subrelativistic experiments at FAU Erlangen [3] and the relativistic experiments at SLAC [1,2]. Although the structures are idealized, the results are qualitatively recovered. As a next step, we show modifications and idealizations of the beam parameters, which outline the way to a microchip accelerator. A. Subrelativistic acceleration A subrelativistic DLA structure needs to be chirped in order to always fulfill the synchronicity condition (6) for the synchronous particle. The proper chirp for each cell and the synchronous velocity are obtained by iterating the two equations $$ \\Delta z ^ { ( n + 1 ) } = \\frac { q e _ { 1 } \\lambda _ { 0 } ^ { 2 } \\cos \\varphi _ { s } ^ { ( n ) } } { m _ { e } c ^ { 2 } } \\sqrt { 1 - { \\beta ^ { ( n ) } } ^ { 2 } } $$ $$ \\beta ^ { ( n + 1 ) } = \\beta ^ { ( n ) } + \\frac { \\Delta z ^ { ( n + 1 ) } } { \\lambda _ { 0 } } .",4,Yes,1
expert,Is it accurate to only consider the first harmonic?,"the higher nonsynchronous harmonics average out. It can be shown, that their second order (ponderomotive) contribution is also small. ",reasoning,Beam_dynamics_analysis_of_dielectric_laser_acceleration.pdf,"$$ describes the acceleration ramp, where the synchronous phase $\\varphi _ { \\mathrm { s } }$ can be chosen arbitrarily \in each grating cell. The variables $e _ { 1 } , \\lambda _ { g z } , W _ { 0 } , \\beta , \\gamma , \\varphi _ { \\mathrm { s } }$ and all variables \in Eq. (24) are stored as arrays indexed by the grating cell number. The kicks are obtained using Eqs. (7), (18), (19), and (13) and read $$ \\begin{array} { r l } & { \\Delta x ^ { \\prime } = - \ \\frac { q \\lambda _ { 0 } } { p _ { z 0 } c } \\tan ( \\alpha ) \\cosh ( i k _ { y } y ) \\mathrm { R e } \\{ \\underline { { e } } _ { 1 } e ^ { i \\varphi + i \\frac { 2 \\pi x } { \\lambda _ { g x } } } \\} } \\\\ & { \\Delta y ^ { \\prime } = \ \\frac { - i k _ { y } \\lambda _ { 0 } ^ { 2 } q \\beta } { 2 \\pi p _ { z 0 } c } \\mathrm { s i n h } ( i k _ { y } y ) \\mathrm { I m } \\{ \\underline { { e } } _ { 1 } e ^ { i \\varphi + i \\frac { 2 \\pi x } { \\lambda _ { g x } } } \\} } \\\\ & { \\Delta \\delta = \ \\frac { q \\lambda _ { g z } } { \\gamma m _ { e } c ^ { 2 } } \\mathrm { R e } \\{ \\underline { { e } } _ { 1 } ( \\mathrm { c o s h } ( i k _ { y } y ) e ^ { i \\varphi + i \\frac { 2 \\pi x } { \\lambda _ { g x } } } - e ^ { i \\varphi _ { s } } ) \\} , } \\end{array}",5,Yes,1
expert,Is it accurate to only consider the first harmonic?,"the higher nonsynchronous harmonics average out. It can be shown, that their second order (ponderomotive) contribution is also small. ",reasoning,Beam_dynamics_analysis_of_dielectric_laser_acceleration.pdf,"$$ \\underline { { e } } _ { m } ( x , y ) = \\underline { { e } } _ { m } ( 0 , 0 ) \\cosh ( i k _ { y } y ) e ^ { i k _ { x } x } , $$ where $\\lambda _ { g x } = \\lambda _ { g z } /$ tan $\\alpha$ . A map of the energy gain and transverse kicks for the grating in Fig. 6 can be seen in Fig. 7 for a grating tilt angle $\\alpha = 3 0$ deg. The results labeled numerical are obtained by line integration [Eq. (7)] of the electric field simulated with CST MWS [16] and the analytical results correspond to Eq. (18). The transverse kicks are obtained by Eq. (13) as $$ \\begin{array} { r l r } { { \\vec { \\underline { { f } } } _ { m } ( x , y ) = \\underline { { e } } _ { m } ( 0 , 0 ) \\cosh ( i k _ { y } y ) e ^ { i k _ { x } x } i m \\tan \\alpha \\vec { e } _ { x } } } \\\\ & { } & { + \\underline { { e } } _ { m } ( 0 , 0 ) \\sinh ( i k _ { y } y ) e ^ { i k _ { x } x } ( i k _ { y } \\lambda _ { g z } / 2 \\pi ) \\vec { e } _ { y } } \\end{array}",4,Yes,1
expert,Is it accurate to only consider the first harmonic?,"the higher nonsynchronous harmonics average out. It can be shown, that their second order (ponderomotive) contribution is also small. ",reasoning,Beam_dynamics_analysis_of_dielectric_laser_acceleration.pdf,"$$ where $W _ { 0 } = \\gamma m _ { e } c ^ { 2 }$ and $p _ { z 0 } = \\beta \\gamma m _ { e } c$ . The particle at the synchronous phase $\\varphi _ { \\mathrm { s } }$ has $\\Delta \\delta = 0$ , i.e., its energy gain is entirely described by the acceleration ramp. The energy gain $\\Delta W$ is given by Eq. (7) and thus the energy gain of the synchronous particle is $$ \\Delta W ( 0 , 0 , \\varphi _ { \\mathrm { s } } ) = q \\lambda _ { g z } \\mathrm { R e } \\{ e ^ { i \\varphi _ { \\mathrm { s } } } \\underline { { e } } _ { 1 } \\} , $$ where we write $e _ { 1 } = \\underline { { e } } _ { 1 } ( x = 0 , y = 0 )$ for brevity. Note that the synchronous phase and the phase of each particle always refer to the laser phase. The sum of the kicks $$ W ( N ) = W _ { \\mathrm { i n i t } } + \\sum _ { n = 1 } ^ { N } \\Delta W ^ { ( n ) } ( 0 , 0 , \\varphi _ { \\mathrm { s } } ^ { ( n ) } )",5,Yes,1
expert,Is it accurate to only consider the first harmonic?,"the higher nonsynchronous harmonics average out. It can be shown, that their second order (ponderomotive) contribution is also small. ",reasoning,Beam_dynamics_analysis_of_dielectric_laser_acceleration.pdf,"$$ and are depicted as arrows in Fig. 7. For the numerical results, the gradient is determined by finite differences in MATLAB [8]. Note that $- i k _ { y } \\in \\mathbb { R } ^ { + }$ , i.e., the kick in $x$ -direction is in phase with the acceleration while the kick in $y$ -direction is 90 degrees shifted. For a particle that is only slightly displaced from the beam axis by $\\Delta \\vec { x } = ( \\Delta x , \\Delta y )$ , the kick can be written as two-dimensional Taylor expansion $$ \\begin{array} { l } { \\displaystyle \\vec { \\underline { { f } } } _ { m } ( x , y ) = \\vec { \\underline { { f } } } _ { m } ( x _ { 0 } , y _ { 0 } ) + ( \\nabla _ { \\perp } \\underline { { \\vec { f } } } _ { m } ( x _ { 0 } , y _ { 0 } ) ) \\Delta \\vec { x } + O ( | | \\Delta \\vec { x } | | ^ { 2 } ) } \\\\ { \\displaystyle = \\frac { \\lambda _ { g z } } { 2 \\pi } ( \\nabla _ { \\perp } \\underline { { e } } _ { m } ( x _ { 0 } , y _ { 0 } ) } \\\\ { \\displaystyle \\quad \\quad + ( \\nabla _ { \\perp } \\nabla _ { \\perp } ^ { \\mathrm { T } } ) \\underline { { e } } _ { m } ( x _ { 0 } , y _ { 0 } ) \\Delta \\vec { x } ) + O ( | | \\Delta \\vec { x } | | ^ { 2 } ) , \\quad ( 2 0 } \\end{array}",augmentation,Yes,0
expert,Is it accurate to only consider the first harmonic?,"the higher nonsynchronous harmonics average out. It can be shown, that their second order (ponderomotive) contribution is also small. ",reasoning,Beam_dynamics_analysis_of_dielectric_laser_acceleration.pdf,"$$ \\sigma _ { \\Delta W } = \\frac { c _ { 0 } } { \\lambda _ { 0 } } \\sqrt { - 2 \\pi \\lambda _ { g z } m _ { e } \\gamma ^ { 3 } q e _ { 1 } \\sin \\varphi _ { s } } \\sigma _ { \\Delta s } . $$ For a slow change of the potential and filling the bucket only up to a small fraction, the phase space area given by $\\pi \\sigma _ { \\Delta \\varphi } \\sigma _ { \\Delta W }$ is conserved. Moreover, using Eq. (44) a normalized bunch length and energy spread can be written as [19] $$ \\begin{array} { l } { \\displaystyle \\sigma _ { \\Delta W , n } = \\frac { 1 } { \\sqrt [ 4 ] { \\beta ^ { 3 } \\gamma ^ { 3 } } } \\sigma _ { \\Delta _ { W } } } \\\\ { \\displaystyle \\sigma _ { \\Delta \\varphi , n } = \\sqrt [ 4 ] { \\beta ^ { 3 } \\gamma ^ { 3 } } \\sigma _ { \\Delta \\varphi } . } \\end{array}",augmentation,Yes,0
expert,Is it accurate to only consider the first harmonic?,"the higher nonsynchronous harmonics average out. It can be shown, that their second order (ponderomotive) contribution is also small. ",reasoning,Beam_dynamics_analysis_of_dielectric_laser_acceleration.pdf,"Although the experimentally demonstrated gradients in DLA structures are very promising, there are still crucial challenges to create a miniaturized DLA-based particle accelerator. So far the experimentally achieved gradients could only be used to increase the beam’s energy spread and not for coherent acceleration. Moreover, the interaction length with present DLA structures is limited to the Rayleigh range (see Appendix) of the incident electron beam. For low energy electrons, due to the high gradient, the acceleration defocusing even leads to interaction distances significantly shorter than the Rayleigh range. Thus, in order to use DLA for a real accelerator, focusing schemes have to be developed. One option would be alternating phase focusing (APF) as outlined in Fig. 1. Here, drift sections between grating cells lead to jumps in the synchronous phase, which can be designed to provide net focusing. Such schemes can be a way to increase the interaction length in DLAs and make an accelerator on a microchip feasible. A challenge in the creation of a DLA based optical accelerator is related to the complex 3D beam dynamics in DLA structures, which has not been treated systematically in the existing literature yet. In order to facilitate front to end simulations and identify optimized DLA structures, we employ a simple and efficient numerical tracking scheme, which does not require a large amount of computing power, it runs in MATLAB [8] on an ordinary PC.",augmentation,Yes,0
expert,Is it accurate to only consider the first harmonic?,"the higher nonsynchronous harmonics average out. It can be shown, that their second order (ponderomotive) contribution is also small. ",reasoning,Beam_dynamics_analysis_of_dielectric_laser_acceleration.pdf,"We plan to achieve such phase jumps by inserting drift sections as already outlined in Fig. 1. Other options are to modify the accelerating Fourier coefficient in each cell, e.g., by phase masking within the structure or by active phase control of individual parts of the laser pulse. In general, we believe that this paper gives a beam dynamics foundation on which DLA structures providing stable long distance beam transport schemes can be developed. ACKNOWLEDGMENTS The authors wish to thank Ingo Hofmann for proofreading the manuscript. This work is funded by the Gordon and Betty Moore Foundation (Grant No. GBMF4744 to Stanford) and the German Federal Ministry of Education and Research (Grant No. FKZ:05K16RDB). APPENDIX: RAYLEIGH RANGE FORLIGHT AND PARTICLE BEAMS The Rayleigh range for a particle beam can be defined in the same way as for a light beam. The envelope of an externally focused beam is $$ w = w _ { 0 } \\sqrt { 1 + \\left( \\frac { z } { z _ { 0 } } \\right) ^ { 2 } } . $$ Inserting into the envelope equation $$ w ^ { \\prime \\prime } = w ^ { - 3 } $$",augmentation,Yes,0
expert,Is it accurate to only consider the first harmonic?,"the higher nonsynchronous harmonics average out. It can be shown, that their second order (ponderomotive) contribution is also small. ",reasoning,Beam_dynamics_analysis_of_dielectric_laser_acceleration.pdf,"$$ \\mathbf { M } = \\langle \\vec { r } \\vec { r } ^ { T } \\rangle , $$ where the average is taken component-wise. In the absence of nonlinearities, particular emittances are conserved. That is in the case of coupling only the 6D emittance given by $$ \\varepsilon _ { 6 D } = \\sqrt { \\operatorname* { d e t } { \\bf M } } . $$ In case of decoupled planes, the determinants of the diagonal blocks (the emittances of the respective plane) are conserved individually. They read $$ \\begin{array} { l } { \\displaystyle \\varepsilon _ { x , n } = \\frac { 1 } { m _ { e } c } \\sqrt { \\operatorname* { d e t } \\mathbf { M } _ { 1 } } , } \\\\ { \\displaystyle \\varepsilon _ { y , n } = \\frac { 1 } { m _ { e } c } \\sqrt { \\operatorname* { d e t } \\mathbf { M } _ { 2 } } , } \\\\ { \\displaystyle \\varepsilon _ { z , n } = \\frac { 1 } { e } \\sqrt { \\operatorname* { d e t } \\mathbf { M } _ { 3 } } , } \\end{array}",augmentation,Yes,0
expert,Is it accurate to only consider the first harmonic?,"the higher nonsynchronous harmonics average out. It can be shown, that their second order (ponderomotive) contribution is also small. ",reasoning,Beam_dynamics_analysis_of_dielectric_laser_acceleration.pdf,"$$ where $$ \\nabla _ { \\perp } \\nabla _ { \\perp } ^ { \\mathrm { T } } = \\left( { \\begin{array} { c c } { \\partial _ { x } ^ { 2 } } & { \\partial _ { x } \\partial _ { y } } \\\\ { \\partial _ { y } \\partial _ { x } } & { \\partial _ { y } ^ { 2 } } \\end{array} } \\right) $$ is the Hessian. The expansion Eq. (20) about $x _ { 0 } = 0$ , $y _ { 0 } = 0$ of Eq. (18) results in $$ \\underline { { \\vec { f } } } _ { m } ( \\Delta x , \\Delta y ) = \\frac { \\lambda _ { g z } } { 2 \\pi } \\underline { { e } } _ { m } ( 0 , 0 ) \\binom { i k _ { x } - k _ { x } ^ { 2 } \\Delta x } { - k _ { y } ^ { 2 } \\Delta y } , $$ i.e., a position independent (coherent) kick component in $x$ -direction, vanishing for $\\alpha = 0$ . Using this abstract derivation, the results of several papers proposing DLA undulators [12–14] can be recovered.",augmentation,Yes,0
expert,Is it accurate to only consider the first harmonic?,"the higher nonsynchronous harmonics average out. It can be shown, that their second order (ponderomotive) contribution is also small. ",reasoning,Beam_dynamics_analysis_of_dielectric_laser_acceleration.pdf,"$$ If the beam size is significantly smaller than the aperture $( y \\ll \\beta \\gamma c / \\omega )$ , the longitudinal equation decouples and becomes the ordinary differential equation of synchrotron motion. The transverse motion becomes linear in this case, however still dependent on the longitudinal motion via $\\varphi$ . The equation of motion, $$ \\ddot { y } = \\frac { - q e _ { 1 } \\omega } { m _ { e } \\gamma ^ { 3 } \\beta c } \\sin ( \\varphi ) y , $$ is Hill’s equation, with the synchrotron angle being the focusing function. However there is a crucial difference to ordinary magnetic focusing channels. The focusing force scales as $\\gamma ^ { - 3 }$ as expected for acceleration defocusing [19], rather than with $\\gamma ^ { - 1 }$ as would be expected for a magnetic quadrupole focusing channel. The solution to Eq. (39) as function of $z$ for fixed $s = \\lambda _ { g z } \\varphi _ { s } / 2 \\pi$ , i.e., when the bunch length is significantly shorter than the period length, is $$ y = y _ { 0 } \\exp \\left( \\sqrt { \\frac { - q e _ { 1 } \\omega } { m _ { e } \\gamma ^ { 3 } \\beta ^ { 3 } c ^ { 3 } } \\sin \\varphi _ { s } z } \\right)",augmentation,Yes,0
expert,Is it accurate to only consider the first harmonic?,"the higher nonsynchronous harmonics average out. It can be shown, that their second order (ponderomotive) contribution is also small. ",reasoning,Beam_dynamics_analysis_of_dielectric_laser_acceleration.pdf,"With no loss of generality, we restrict ourselves to symmetric grating structures driven from both lateral sides. This makes sure that the axis of symmetry is in the center and the fields have a cosh profile. In the case of nonsymmetric structures or nonsymmetric driving, the fields will have an exponential or an off-axis cosh profile. However, single driver systems can be combined with Bragg mirrors in order to obtain a good approximation to an on-axis cosh profile with a single side driver (see again Fig. 1). Another option is to reshape the structure as e.g., presented in [4], or, just to accept the asymmetry which then leads to a smaller effective aperture. Furthermore, we restrict ourselves to linear dielectrics. Driving the dielectric into its nonlinear regime is discussed in [10] (experimental), whereas the theoretical reader [11] particularly covers quantum aspects of high fields. As it is usually done, e.g., for the synchrotron motion in ion synchrotrons, we take the limit from the tracking difference equations to differential equations. Since the three-dimensional kick must be irrotational due to the Panofsky-Wenzel theorem, it can be derived from a scalar potential. This potential directly allows to determine the 6D Hamiltonian which completely describes the single particle dynamics analytically.",augmentation,Yes,0
expert,Is it accurate to only consider the first harmonic?,"the higher nonsynchronous harmonics average out. It can be shown, that their second order (ponderomotive) contribution is also small. ",reasoning,Beam_dynamics_analysis_of_dielectric_laser_acceleration.pdf,"C. Dynamics in tilted gratings Finally, we address the tilted grating with the same laser parameters and a bunched electron beam with parameters $\\varepsilon _ { x } = \\varepsilon _ { y } = 1 \\ \\mathrm { n m } , \\sigma _ { x } = 1 \\ \\mu \\mathrm { m } , \\sigma _ { y } = 0 . 4 \\mu \\mathrm { m } .$ $\\sigma _ { z } = 3 0 ~ \\mathrm { n m }$ , $\\sigma _ { W } = 1 0 ~ \\mathrm { k e V }$ and a focusing angle of 5 mrad in the y-direction. The grating tilt angle is 70 degrees and again $| \\underline { { e } } _ { 1 } | = 1 \\ \\mathrm { G V / m }$ . Figure 19 shows the evolution of the phase space in all three planes. Evaluating Eq. (54), one finds $\\lambda _ { u } \\approx 1 6 0 \\lambda _ { 0 }$ , i.e., half an oscillation period in the $\\mathbf { \\boldsymbol { x } }$ -direction in the displayed 80 grating cells. As visible in Fig. 19, the horizontal and longitudinal phase spaces are correlated. The projections of the energy spectrum can be seen in Fig. 20 together with the particle loss, which takes place at the physical aperture in y-direction at $\\pm 4 0 0 ~ \\mathrm { n m }$ . Unlike the straight grating with relativistic particles, the tilted grating creates a defocusing force in the y-direction which significantly decreases the Rayleigh range. The energy spread shows a breathing mode, similar to the quadrupole modes in the synchrotron motion. However, since the synchrotron motion is practically frozen due to the high $\\gamma$ , this mode arises entirely due to the correlation with the $\\mathbf { \\boldsymbol { x } }$ -plane. Excluding the defocusing by setting $\\varepsilon _ { y } = 0$ , two coherent oscillation periods are displayed in Fig. 21.",augmentation,Yes,0
expert,Is it accurate to only consider the first harmonic?,"the higher nonsynchronous harmonics average out. It can be shown, that their second order (ponderomotive) contribution is also small. ",reasoning,Beam_dynamics_analysis_of_dielectric_laser_acceleration.pdf,"$$ where the energy momentum differential $\\Delta p _ { \\| } = \\Delta W / ( \\beta c )$ was applied. Moreover, if the phase-synchronicity condition [Eq. (6)] is fulfilled, the kick becomes $$ \\begin{array} { l } { { \\displaystyle \\Delta \\vec { p } _ { \\perp } ( x , y ; s ) = - \\frac { \\lambda _ { g z } ^ { 2 } } { 2 \\pi m } q \\frac { 1 } { \\beta c } \\nabla _ { \\perp } \\mathrm { I m } \\{ e ^ { 2 \\pi i \\frac { s } { \\beta \\lambda _ { 0 } } } \\underline { { e } } _ { m } ( x , y ) \\} } } \\\\ { { \\displaystyle \\ = - \\frac { \\lambda _ { g z } } { m } q \\frac { 1 } { \\beta c } \\mathrm { I m } \\{ e ^ { 2 \\pi i \\frac { s } { \\beta \\lambda _ { 0 } } } \\underline { { \\vec { f } } } _ { m } ( x , y ) \\} , } } \\end{array}",augmentation,Yes,0
expert,Is it accurate to only consider the first harmonic?,"the higher nonsynchronous harmonics average out. It can be shown, that their second order (ponderomotive) contribution is also small. ",reasoning,Beam_dynamics_analysis_of_dielectric_laser_acceleration.pdf,"Both the numerical and the analytical approach can be generalized from ordinary DLA gratings to tilted DLA gratings, which have been proposed as deflectors or laser driven undulators [12–14]. Such a grating is depicted in Fig. 2. However, since our code does not include the radiation fields, a dedicated code as, e.g., [15] can be used to treat the dynamics self-consistently. The analytical kicks reported here can serve as input quantities. Our approach aims at maximal simplicity such that studies of fundamental questions, as, e.g., transverse focusing and deflection, are quickly possible. The paper is organized as follows. Section II presents the determination of the longitudinal and transverse fields and kicks in a single grating period. Here we use CST Studio Suite [16] to calculate the longitudinal kick at the center of the structure. The dependence on the transverse coordinates as well as the transverse kicks are modeled analytically. In Sec. III we present a symplectic 6D tracking method based on one kick per grating period. Analytical descriptions of the coupled longitudinal and transverse beam dynamics as well as the full 6D Hamiltonian are given in Sec. IV. Simplifications and beam matching in linearized fields are also discussed in this section. In Sec. V we address the three crucial examples: subrelativistic acceleration, relativistic acceleration, and deflection by means of DLA gratings. The paper concludes with a summary and an outlook to DLA focusing channels in Sec. VI.",augmentation,Yes,0
expert,Is it accurate to only consider the first harmonic?,"the higher nonsynchronous harmonics average out. It can be shown, that their second order (ponderomotive) contribution is also small. ",reasoning,Beam_dynamics_analysis_of_dielectric_laser_acceleration.pdf,"$$ in the usual units of $\\textrm { m }$ rad and eVs, respectively. The analysis of emittance coupling by means of the eigen-emittances $$ \\varepsilon _ { \\mathrm { e i g } , i } = \\mathrm { e i g s } ( \\mathbf { J } \\mathbf { M } ) , $$ where $\\mathbf { J }$ is the symplectic matrix, is also possible with our code, however beyond the scope of this paper. IV. CONTINUOUS EQUATIONS OF MOTION In order to address the continuous motion in DLA structures we employ positions and momentum as canonically conjugate variables in all directions. The transformation for the energy is $\\Delta p _ { z } = \\Delta W / ( \\beta c )$ . We address the flat and the tilted grating separately and assume for simplicity $\\lvert \\underline { { e } } _ { 1 } \\rvert$ to be constant for all cells and $\\arg ( \\underline { { e } } _ { 1 } ) = 0$ . A. Flat grating Hamilton’s equations can be written as $$ \\dot { x } = \\frac { p _ { x } } { m _ { e } \\gamma }",augmentation,Yes,0
expert,Is it accurate to only consider the first harmonic?,"the higher nonsynchronous harmonics average out. It can be shown, that their second order (ponderomotive) contribution is also small. ",reasoning,Beam_dynamics_analysis_of_dielectric_laser_acceleration.pdf,"For an adiabatic Hamiltonian and if stable orbits exist, a matched locally Gaussian distribution is given by $$ f = C e ^ { - H / \\langle H \\rangle } $$ and a locally elliptic (Hofmann-Pedersen [23]) matched distribution is given by $$ f = C { \\sqrt { H _ { \\operatorname* { m a x } } - H } } . $$ The normalization constant $C$ is determined by integration. Note that in the case of nonperiodic motion $f$ will not be integrable. Thus, we can only write a matched distribution for the longitudinal plane if $\\varphi _ { s } \\in [ \\pi / 2 , \\pi ]$ and for the transverse plane if $\\varphi _ { s } \\in [ \\pi , 3 / 2 \\pi ]$ . The Hamiltonian is not time independent, however its dependence on $\\beta$ and $\\gamma$ is adiabatic. Thus, if $\\varphi _ { s }$ is changing at most adiabatically, the distribution will deform such that the emittance increase is bounded, i.e., also the emittance remains an adiabatic invariant. First, we consider the longitudinal plane and linearized fields. For a given bunch length $\\sigma _ { \\Delta s }$ the matched energy spread is",augmentation,Yes,0
expert,Is it accurate to only consider the first harmonic?,"the higher nonsynchronous harmonics average out. It can be shown, that their second order (ponderomotive) contribution is also small. ",reasoning,Beam_dynamics_analysis_of_dielectric_laser_acceleration.pdf,"For subrelativistic accelerators, the grating needs to be chirped in period length in order to always fulfill Eq. (6) on the energy ramp. The change of period length is given by the energy velocity differential $$ \\frac { \\Delta z } { \\lambda _ { g z } } = \\frac { 1 } { \\beta ^ { 2 } \\gamma ^ { 2 } } \\frac { \\Delta W } { W } $$ and is in the range of ${ \\lesssim } 1 \\%$ for $W _ { \\mathrm { k i n } } = 3 0 ~ \\mathrm { k e V }$ and $\\Delta W / \\lambda _ { g z } = 1 \\mathrm { G e V / m }$ . The thus created “quasiperiodic"" gratings can be seen in good approximation as periodic, however, phase drifts have to be compensated in the structure design [18]. B. Analysis of the transverse field The transverse field probed by a rigidly moving charge can be obtained using the Panofsky-Wenzel theorem [9], which holds for either vanishing fields at infinity or periodic boundary conditions as $$ \\begin{array} { l } { \\nabla ^ { \\prime } \\times \\Delta \\vec { p } ( \\vec { r } _ { \\perp } , s ) = \\displaystyle \\int _ { - T / 2 } ^ { T / 2 } \\mathrm { d } t [ \\nabla \\times \\vec { F } ( \\vec { r } _ { \\perp } , z , t ) ] _ { z = v t - s } } \\\\ { = \\vec { B } | _ { - T / 2 } ^ { T / 2 } = 0 . } \\end{array}",augmentation,Yes,0
IPAC,What are insertion devices?,"They are periodic magnetic structures, such as undulators and wigglers, placed in straight sections to generate radiation.",Definition,Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation,"C-BAND INJECTOR DESIGN We have designed two injectors. One design is plug-free and is shown in Fig. 2. This design focuses on the tuning and high gradient testing of the RF cavity without a high QE photocathode or plug [2]. The design is very similar to the plug-insert design, as shown by the RF parameters in Table 2 . The design uses a solid Cu backplane and thus a Cu photocathode instead of a plug, and has less symmetry due to being an earlier design. A picture of the fabricated injector before brazing is shown in Table: Caption: Table 1: Klystron Conditioning Results for Three Pulse Widths Body: | Stable Filling Patterns |
| Stage 1 7-bucket gap,20 trains 50 mA, chromaticity 5 7-bucket gap,30 trains |
| w/o TMBF,HC Stage 2 7-bucket gap,20 trains 100 mA,chromaticity 5 |
| 7-bucket gap,30 trains w/o TMBF,HC |
| Stage 3 Standard filling pattern 300 mA,chromaticity 2 (7-bucket gap,5 trains) |
The beam vertical oscillation amplitude in the presence of ions at di!erent stages are illustrated in Fig. 2. In stages 1 and 2, the beam is tracked for 5,000 turns using two distinct filling patterns. It has been found that increasing the number of gaps is slightly beneficial to mitigate the ion instability in the early stages. To align with the standard filling pattern, which has 7-bucket gaps, filling patterns with 7-bucket gaps and 20/30 trains are deemed suitable for the early stages. In stage 3, the beam with the standard filling pattern is tracked for 10,000 turns. In all cases, the vertical emittance remains stable at approximately $8 \\mathrm { p m }$ . The maximum oscillation amplitude is less than $5 \\%$ of the nominal beam size for stages 1 and 2. With the aid of TMBF, the maximum oscillation amplitude in stage 3 is even less than $2 . 5 \\%$ of the nominal beam size.",augmentation,NO,0
IPAC,What is a stable closure phase?,"A consistent phase sum around aperture triangles, indicating low noise and beam symmetry.",Fact,Carilli_2024.pdf,"$$ When $| p _ { \\theta } | < p _ { \\theta } ^ { \\mathrm { c r i t } }$ , the polynomial $\\mathcal { P } _ { 8 } ( r )$ has three positive roots: $$ 0 < r _ { * } ^ { \\mathrm { s t } } < r _ { * } ^ { \\mathrm { s e p } } < 1 < r _ { * } ^ { \\mathrm { u n } } . $$ Here, $r _ { * } ^ { \\mathrm { s e p } }$ corresponds to the unstable fixed point with a separatrix that isolates stable trajectories and $r _ { * } ^ { \\mathrm { u n } }$ is the second unstable fixed point. When the absolute value of the angular momentum exceeds the critical value, the two equilibria $r _ { * } ^ { \\mathrm { s t } }$ and $r _ { * } ^ { \\mathrm { s e p } }$ collide and annihilate in a saddle-node bifurcation. For $| a | > 2$ , there is only one unstable equilibrium $r _ { * } ^ { \\mathrm { u n s t } } > 1$ and the global dynamics is unstable, thus we will omit any further consideration.",augmentation,NO,0
IPAC,What is a stable closure phase?,"A consistent phase sum around aperture triangles, indicating low noise and beam symmetry.",Fact,Carilli_2024.pdf,"Table: Caption: Table 1: Averaged Total Pressure at Di!erent Vacuum Condition Stages Body: | Parameters | Values |
| NSLS-II bare lattice | NSLS-IIU CBA lattice |
| Circumference C[m] | 791.958 | 791.7679 | 791.7252 |
| Beam energy E[GeV] | 3 | 3 | 4 |
| Natural emittance Exo [pm-rad] | 2086 | 23.4 | 42.5 |
| Damping partitions (Jx,Jy, Js) | (1,1,2) | (2.24, 1, 0.76) | (2.15,1, 0.85) |
| Ring tunes (vx, Vy) | (33.22,16.26) | (84.67, 28.87) | (84.25,29.20) |
| Natural chromaticities (§x, §y) | (-98.5, -40.2) | (-135, -144) | (-151, -173) |
| Momentum compaction αc | 3.63×10-4 | 7.76×10-5 | 6.77×10-5 |
| Energy loss per turn Uo [keV] | 286.4 | 196 | 656 |
| Energy spread os [%] | 0.0514 | 0.073 | 0.093 |
| (βx, βy) at LS center [m] | (20.1, 3.4) | (2.95,2.99) | (1.63,2.67) |
| (βx,βy)at SS center[m] | (1.8, 1.1) | (1.87, 1.99) | (1.43,2.26) |
| (βx,max,βy,max)[m] | (29.99,27.31) | (13.37,20.82) | (15.13,26.95) |
| (βx,min,βy,min) [m] | (1.84, 1.17) | (0.35, 0.84) | (0.49, 0.70) |
| (βx,avg,βy,avg) [m] | (12.58,13.79) | (3.99, 7.51) | (5.05, 8.09) |
| Length of Long Straight LLs [m] | 9.3 | 8.4 | 8.8 |
| Length of Short Straight Lss [m] | 6.6 | 6.1 | 6.8 |
",augmentation,NO,0
IPAC,What target wavelength was the inverse-designed Smith-Purcell grating optimized for?,Approximately 1.4 ?m,Fact,haeusler-et-al-2022-boosting-the-efficiency-of-smith-purcell-radiators-using-nanophotonic-inverse-design.pdf,"The mid-wave infrared generation is summarized in Figs. 3 and 4. Figure 3 (a) shows the effect of the crystal tuning angle on the DFG process. The angular acceptance of the process is narrow, with a measured FWHM of 0.15 degrees. A plausible reason for the lower than expected efficiency lies in the narrow angular acceptance bandwidth. Phase matching theory indicates that a narrow angular acceptance bandwidth is equivalent to a narrow energy acceptance bandwidth. Indeed, the spectrum shown in Fig. 4 indicates a substantial spectral narrowing with respect to the input bandwidth. The $1 2 \\ \\mathrm { n m }$ FWHM shown in the spectrum corresponds to an energy bandwidth of $0 . 7 3 \\mathrm { m e V }$ , while the input beam has an energy bandwidth of roughly $4 . 3 ~ \\mathrm { m e V }$ . This spectral narrowing implies that a substantial portion of the beam is unable to phase match, greatly reducing the conversion efficiency. Additionally, the narrow angular acceptance indicates that angular spread introduced by deviations from perfect collimation would reduce the efficiency as well. To extend this concept past the proof-of-principle phase, several improvements can be made to increase efficiency. First, the most substantial improvement would come in replacing the lithium niobate crystal with a periodically-poled lithium niobate crystal (PPLN). PPLN is a variety of lithium niobate that has ferroelectric domains that alternate direction. This enables quasi-phase matching, greatly extending the angular and energy bandwidths, as well as allowing higher gain by utilizing the largest element of the nonlinear tensor [8]. In this case, the required periodicity would be around $1 2 \\mu \\mathrm { m }$ . Figure 3 (b) shows the scaling of final DFG output energy with input energy. The conversion efficiency is around $4 \\times 1 0 ^ { - 6 }$ , which is on the order of $1 0 ^ { 3 }$ times smaller than expected from SNLO simulations.",augmentation,NO,0
IPAC,What target wavelength was the inverse-designed Smith-Purcell grating optimized for?,Approximately 1.4 ?m,Fact,haeusler-et-al-2022-boosting-the-efficiency-of-smith-purcell-radiators-using-nanophotonic-inverse-design.pdf,"Since the optimum dispersion $\\eta _ { o p t }$ is obtained, we next calculate the variation of the effective emittance by using the realistic ID field data shown in Fig. 1. This is done by using the individual ID gap data (Fig. 1, left) not by using their average (Fig. 1, right). The results are shown in Fig. 4 and we see that the variation is indeed suppressed by setting the leaked dispersion to the optimum value of $1 5 . 4 \\mathrm { m m }$ . Storage Ring Lattice Design As mentioned above, we are designing the non-achromat optics whose dispersion value at the straight section $\\eta _ { x \\_ S T }$ is tunable within a certain range (a few mm). One of the key points is the design of the LSS matching section, since the dispersion in LSS must be suppressed to an acceptable level regardless of the $\\eta _ { x \\_ S T }$ value. To avoid degrading the momentum acceptance, the optics matching conditions for off-momentum electrons should also be satisfied at least in an approximate way. In Fig. 5 we show examples of the non-achromat optics with $\\eta _ { x \\_ S T } = 1 2 m m$ (solid curves) and with $\\eta _ { x _ { \\scriptscriptstyle - } S T } = 1 5 m m$ (dashed curves). The two optics can be interchanged by changing the strength of quadrupole magnets. To keep the dynamic stability of the ring even after switching the optics, designing a proper matching cell is very important, and work is currently underway to optimize the linear and nonlinear optics design of this section.",augmentation,NO,0
IPAC,What target wavelength was the inverse-designed Smith-Purcell grating optimized for?,Approximately 1.4 ?m,Fact,haeusler-et-al-2022-boosting-the-efficiency-of-smith-purcell-radiators-using-nanophotonic-inverse-design.pdf,"The design angular acceptance of the HRS is $\\pm 6 0$ mrad, and the full-width slit (2ùëÉ) for a resolving power of 24,000 is $1 0 0 \\mu \\mathrm { m }$ with a given $4 ^ { * } \\mathrm { R M S }$ emittance of $3 \\mu \\mathrm { m }$ and an energy spread $( \\Delta E )$ of $1 \\mathrm { e V }$ for a $6 0 \\mathrm { k e V }$ beam. Figure 3 shows the calculated envelope through the HRS system starting from the magnified object slit to the magnified image slit using the TRANSOPTR code [14, 15]; the beam envelope is calculated for a required magnification of 9 in order to achieve a resolving power of 16,000 with a given $4 ^ { * } \\mathrm { R M S }$ emittance of $3 \\mu \\mathrm { m }$ and a $\\Delta E$ of $1 \\mathrm { e V }$ for a $3 0 \\mathrm { k e V }$ beam. The mass dispersion of the pure HRS is $2 . 4 \\mathrm { m }$ , and thus a resolution of 16,000 requires a full slit size of $1 5 0 \\mu \\mathrm { m }$",augmentation,NO,0
IPAC,What target wavelength was the inverse-designed Smith-Purcell grating optimized for?,Approximately 1.4 ?m,Fact,haeusler-et-al-2022-boosting-the-efficiency-of-smith-purcell-radiators-using-nanophotonic-inverse-design.pdf,"Beamline elements must be carefully placed to avoid interferences with other beamlines and the tunnel walls. The solenoids are particularly challenging due to their considerable width in a tight section of the beamline, but there are many other locations where magnets are very close to either the walls or other beamlines. Much work has been done to eliminate such interferences, primarily by adjusting the geometry of the ESR by means of varying drift lengths and dipole angles, but also modifying other beamlines and considering the use of alternative magnets. Figure 5 shows a representation of the geometry layout of the whole ring. OPTICS Figure 6 shows the matched optics for the $1 8 \\mathrm { G e V }$ lattice with two collision points. Table 1 shows the main lattice parameters at $1 8 \\mathrm { G e V }$ with 1 and $2 \\mathrm { I P s }$ . The two lattices are identical with two full interaction regions; however, for the $1 \\mathrm { I P }$ lattice the $\\beta$ functions are additionally squeezed at IP8. This results in a smaller natural chromaticity for the $1 \\mathrm { I P }$ lattice. Table: Caption: Table 1: ESR Lattice Parameters at $1 8 \\mathrm { G e V }$ with 1 and $2 \\mathrm { I P s }$ Body: | Parameter |
| K | Wakefield loss factor |
| βg | Normalized group velocity |
| vg | Group velocity |
| α | Attenuation constant |
| Q | Quality factor |
| 0 | Electrical conductivity |
| Corrugation spacing parameter |
| S | Corrugation sidewall parameter |
| a | Corrugation minor radius |
| t | Corrugation tooth width |
| g | Corrugation vacuum gap |
| d | Corrugation depth |
| p | Corrugation period |
| rt | Corrugation tooth radius |
| rg | Corrugation vacuum gap radius |
| L | Corrugated waveguide length |
| F | Bunch form factor |
| q0 | Drive bunch charge |
| fr | Bunch repetition rate |
| T | rf pulse decay time constant |
| 8 | Skin depth |
| Pf | rf pulse power envelope |
| P | Instantaneous rf pulse power |
| Eacc | Accelerating field |
| Emax | Peak surface E field |
| Hmax | Peaksurface H field |
| Qdiss | Energy dissipation |
| Pd | Power dissipation distribution |
| W | Average thermal power density |
| ‚ñ≥T | Transient temperature rise |
| C | Speed of light |
| Z0 | Impedance of free space |
| 8 | Initial beam energy |
| R | Transformer ratio |
In the parametric analysis that follows, the corrugation dimensions are expressed in terms of the normalized spacing parameter $\\xi$ and sidewall parameter $\\zeta$ defined as $$ \\begin{array} { l } { \\displaystyle { \\xi = \\frac { g - t } { p } } , } \\\\ { \\displaystyle { \\zeta = \\frac { g + t } { p } } . } \\end{array} $$ The spacing parameter $\\xi$ determines the spacing between the corrugation teeth and ranges from $^ { - 1 }$ to 1 for the minimum and maximum radii profiles, where positive values of $\\xi$ result in spacing greater than the tooth width and vice versa for negative values. The sidewall parameter $\\zeta$ controls the sidewall angle of the unequal radii profile, where $\\zeta < 1$ leads to tapered sidewalls and $\\zeta > 1$ leads to undercut sidewalls. These dependencies are illustrated in Fig. 4.",augmentation,Yes,0
IPAC,"When an electron beam scatters off a metallic wire, what particles are produced?","The particle shower contains mostly electrons, positrons, and X-rays",Fact,Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf,"In the past such a dispersion relation from such plasmonic structures has been attributed to the emission from the Au (111) surface state which follows the dispersion relation of $E = \\hbar ^ { 2 } k _ { t } ^ { 2 } / 2 m ^ { * }$ , where $m ^ { * } = 0 . 4 5 m _ { e }$ [25]. This dispersion relation is shown by the dashed red lines in Fig. 4. Our results indicate that the electrons are emitted with a dispersion relation closer to the free electron parabola than the parabola with $m ^ { * } = 0 . 4 5 m _ { e }$ , indicating that the non-uniform distribution in the transverse momentum space may be due to effects other than emission from the Au (111) surface state. One explanation of such a behaviour is the interaction of the emitted electron with the plasmonic fields as well as the incident laser pulse. The incident laser pulse excites the plasmons at the metal-dielectric interface, which travel up to approximately $2 0 \\mu \\mathrm { m }$ at a velocity of about $0 . 9 3 c$ . This journey takes ${ \\sim } 7 0$ fs, shorter than the duration of the 150 fs excitation laser pulse. Consequently, the emitted electrons have the opportunity to interact with both the plasmonic field and the circularly polarized incident laser pulse. These interactions may lead to transfer of momentum between photon/plasmon and the emitted electron [26].",augmentation,NO,0
IPAC,"When an electron beam scatters off a metallic wire, what particles are produced?","The particle shower contains mostly electrons, positrons, and X-rays",Fact,Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf,"COULOMB SCATTERING When a charged particle passes through matter, it is deflected by the Coulomb potentials of the atomic nuclei in the material. The standard deviation of the angular distribution No stochastic straggling Stochastic straggling 30 30 Fresh bunch 20 After absorber 20 G 10 10 0 0 10 10 宝 20 20 Fresh bunch After absorber 30 30 25 0 25 25 0 25 ∆t [mm/c] ∆t [mm/c] due to the scattering can be approximated by $$ \\theta = \\frac { 1 3 . 6 [ \\mathrm { M e V } ] } { \\beta p c } z \\sqrt { \\frac { s } { L _ { \\mathrm { R } } } } \\left[ 1 + 0 . 0 3 8 \\ln \\left( \\frac { s } { L _ { \\mathrm { R } } } \\right) \\right] . $$ In Eq. (3), the variable $s$ describes the path length of the particle inside the absorber; $z$ is the charge of the travelling particle; $L _ { \\mathrm { R } }$ is the radiation length of the material; $c$ is the speed of light; $\\beta$ the relativistic Lorentz factor; and $p$ is the momentum of the impacting particle in $\\mathbf { M e V } \\mathrm { c } ^ { - 1 }$ . The literature states that the scattering angle distribution approximates a Gaussian distribution when the deflection angles are small [9]. An implementation of the particle scattering, according to the equation, can only follow without the logarithmic term. Otherwise, discrepancies of the scattering angle would appear when the simulation step size changes.",augmentation,NO,0
IPAC,"When an electron beam scatters off a metallic wire, what particles are produced?","The particle shower contains mostly electrons, positrons, and X-rays",Fact,Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf,"NET CHARGE DEPOSITION A harp system monitors the beam position and intensity by reading the charge imbalances in metal wires induced by proton and material interactions in there. A large part of the net charge deposition in the wire is caused by emission of weakly bound electrons excited by non-elastic scattering with incident protons. These secondary electrons typically have kinetic energies less than a few hundred electron volts. The secondary electron yield of a metallic wire is defined by the ratio of emitted secondary electrons per incident proton. Sternglass theory presented in Ref. [5] is used to calculate the secondary electron yield, $\\eta _ { S E }$ , $$ \\eta _ { \\mathrm { S E } } = \\frac { P \\cdot \\delta _ { s } } { E _ { i } } \\frac { d E } { d z } . $$ Here, $P$ is the probability of an electron escaping, which is given by $P = 0 . 5$ . $\\delta _ { s }$ is the average depth from which the secondaries arise, which is given by $\\delta _ { s } = 1 ~ \\mathrm { { n m } }$ . $E - i$ is the average kinetic energy lost by the incoming particle per ionization, which is given by $E _ { i } = 2 5 \\mathrm { e V } .$ . Finally, $d E / d z$ is the differential proton stopping power of the wire which depend on proton energy.",1,NO,0
IPAC,"When an electron beam scatters off a metallic wire, what particles are produced?","The particle shower contains mostly electrons, positrons, and X-rays",Fact,Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf,"At injection energy, the vertical beta function at the ES is $6 . 7 \\mathrm { m }$ . Assuming the vertical acceptance of $5 0 \\mathrm { m m }$ ·mrad to be filled, the beam full height at the ES is $3 7 \\mathrm { m m }$ . Taking into account the density $1 9 . 7 \\mathrm { g } / \\mathrm { c m } ^ { 3 }$ of the wires [6], this means that the mass of the wire hit by the beam is $5 . 7 \\mathrm { m g }$ . Assuming further that the beam is distributed uniformly, or at least that the temperature is distributed equally over the beam height, we then obtain the energy needed to reach $1 7 0 0 \\mathrm { K }$ as $\\Delta U = 1 . 2 \\mathrm { J }$ . For $^ { 2 3 8 } \\mathrm { U } ^ { 2 8 + }$ , the kinetic energy per ion at injection is $2 . 7 \\mathrm { G e V }$ , or $4 . 3 5 \\times 1 0 ^ { - 1 0 } \\mathrm { J }$ , meaning that a loss of $2 . 7 \\times 1 0 ^ { 9 }$ ions is needed to break one wire. Thus, a beam loss of $1 0 ^ { 1 0 }$ particles per cycle, as in Fig. 4, has actually the potential of breaking three wires.",2,NO,0
expert,"When an electron beam scatters off a metallic wire, what particles are produced?","The particle shower contains mostly electrons, positrons, and X-rays",Fact,Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf,"To lower the emittance of the beam, the bunch charge is reduced to approximately $1 ~ \\mathrm { p C }$ from the nominal bunch charge at SwissFEL ( $1 0 \\mathrm { p C }$ to $2 0 0 \\ \\mathrm { p C } )$ . The laser aperture and pulse energy at the photo-cathode, as well as the current of the gun solenoid, are empirically tuned to minimize the emittance for the reduced charge. The emittance is measured at different locations along the accelerator with a conventional quadrupole scan [15] and a scintillating YAG:Ce screen. After the second bunch compressor, which is the last location for emittance measurements before the ACHIP chamber, the normalized horizontal and vertical emittances are found to be $9 3 \\mathrm { n m }$ rad and $1 5 7 ~ \\mathrm { n m }$ rad with estimated uncertainties below $10 \\%$ . The difference between the horizontal and vertical emittance could be the result of an asymmetric laser spot on the cathode. The electron energy at this emittance measurement location is $2 . 3 { \\mathrm { G e V . } }$ Subsequently, the beam is accelerated further to $3 . 2 \\mathrm { G e V }$ and directed to the Athos branch by two resonant deflecting magnets (kickers) and a series of dipole magnets [16]. Finally, the beam is transported to the beam stopper upstream of the Athos undulators.",2,NO,0
IPAC,"When an electron beam scatters off a metallic wire, what particles are produced?","The particle shower contains mostly electrons, positrons, and X-rays",Fact,Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf,"This process is termed Secondary Emission (SE) and its theory was developed by E. J. Sternglass [3]. The quantity of electrons generated for each proton is called the Secondary Emission Yield $( S E Y )$ and can be expressed as [5]: $$ S E Y = 0 . 0 1 L _ { s } \\frac { d E } { d x } | _ { e l } \\left[ 1 + \\frac { 1 } { 1 + ( 5 . 4 \\cdot 1 0 ^ { - 6 } E / A _ { p } ) } \\right] $$ This is defined by the kinetic energy of the projectile $( E )$ , the electronic energy loss $\\textstyle { \\big ( } { \\frac { d E } { d x } } | _ { e l } { \\big ) }$ , the mass of projectile $( A _ { p } )$ and the characteristic length of di!usion of low energy electrons $( \\ L _ { s } )$ : $$ L _ { s } = ( 3 . 6 8 \\cdot 1 0 ^ { - 1 7 } N Z ^ { 1 / 2 } ) ^ { - 1 } ,",4,NO,1
IPAC,"When an electron beam scatters off a metallic wire, what particles are produced?","The particle shower contains mostly electrons, positrons, and X-rays",Fact,Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf,"This distribution depends on the radiator tilt angle with respect to the particle trajectory, $\\psi$ , the material properties and the particle energy. The light emission is typically anisotropic. The theoretical angular distribution created by a single particle with $\\beta = 0 . 1 9 5$ striking a smooth glassy carbon screen at $\\psi = 0 / 3 0 / 6 0 ^ { \\circ }$ is presented in Figure 1. It shows two lobes on each side of the particle’s axis of motion. At very low energy they become wide and also asymmetrical with a nonzero tilt angle [6, 7]. EXPERIMENTAL SETUP An OTR imaging system was installed at the EBTF at CERN [2] to measure a high-intensity, low-energy, hollow electron beam, magnetically confined. The measured beam reached up to a $1 . 6 \\mathrm { A }$ in current, and $7 \\mathrm { k e V }$ in energy. The size of the beam could be varied by tuning the ratio of the magnetic fields at the gun and the transport solenoids. The tested beam sizes were ranging in outer radius between 5 and $1 0 \\mathrm { m m }$ , while the inner radius was half the size. The ratio between the outer and inner radius is given by the cathode dimensions - $\\mathrm { R } _ { o u t } = 8 . 0 5 \\mathrm { m m }$ and $\\mathbf { R } _ { i n } = 4 . 0 2 5 \\mathrm { m m }$ .",4,NO,1
IPAC,"When an electron beam scatters off a metallic wire, what particles are produced?","The particle shower contains mostly electrons, positrons, and X-rays",Fact,Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf,"SECONDARY PARTICLE SPECTRA The electrons and positrons produced by muon decay in the collider ring can have TeV energies and emit synchrotron radiation while travelling inside the magnetic fields. Their energy is then dissipated through electromagnetic showers in surrounding materials. In addition, secondary hadrons can be produced in photo-nuclear interactions, in particular neutrons, which dominate the displacement damage in magnet coils. Figure 2 shows the electron/positron, photon and neutron spectra in the dipole coils of a $1 0 \\mathrm { T e V }$ collider. The different blue curves correspond to the different tungsten shielding thicknesses described in the previous section. For comparison, the figure also shows the spectra of decay elec dn/d(log E) (cm‚àí2s‚àí1) 1012 1010 e+/e In coils (2 cm shielding) Lost on beam aperture 108 In coils (3 cm shielding) 106 In coils (4 cm shielding) 104 102 10‚àí3 10‚àí2 10‚àí1 100 101 102 103 104 Energy (GeV) dn/d(log E) (cm‚àí2s‚àí1) 1012 1010 V 108 106 104 102 10‚àí3 10‚àí2 10‚àí1 100 101 102 103 104 Energy (GeV) dn/d(log E) (cm‚àí2s‚àí1) 1012 1010 n 108 106 104 102 10‚àí1410‚àí1210‚àí10 10‚àí8 10‚àí6 10‚àí4 10‚àí2 100 102 Energy (GeV) trons/positrons and synchrotron photons when they impact on the vacuum aperture (red curves). The energy of synchrotron photons emitted by the decay products can reach very high values in a $1 6 \\mathrm { T }$ dipole, up to the TeV regime.",4,NO,1
expert,"When an electron beam scatters off a metallic wire, what particles are produced?","The particle shower contains mostly electrons, positrons, and X-rays",Fact,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",augmentation,NO,0
expert,"When an electron beam scatters off a metallic wire, what particles are produced?","The particle shower contains mostly electrons, positrons, and X-rays",Fact,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,"When an electron beam scatters off a metallic wire, what particles are produced?","The particle shower contains mostly electrons, positrons, and X-rays",Fact,Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf,"The electrons at the ACHIP interaction point at SwissFEL possess a mean energy of $3 . 2 ~ \\mathrm { G e V }$ and are strongly focused by an in-vacuum permanent magnet triplet [11]. A six-dimensional positioning system (hexapod) at the center of the chamber is used to exchange, align, and scan samples or a wire scanner for diagnostics. In this manuscript, we demonstrate that the transverse phase space of a focused electron beam can be precisely characterized with a series of wire scans at different angles and locations along the waist. The transverse phase space $( x - x ^ { \\prime }$ and $y - y ^ { \\prime } )$ is reconstructed with a novel particlebased tomographic algorithm. This technique goes beyond conventional one-dimensional wire scanners since it allows us to assess the four-dimensional transverse phase space. We apply this algorithm to a set of wire scanner measurements performed with nano-fabricated wires at the ACHIP chamber at SwissFEL and reconstruct the dynamics of the transverse phase space of the focused electron beam along the waist. II. EXPERIMENTAL SETUP A. Accelerator setup The generation and characterization of a micrometer sized electron beam in the ACHIP chamber at SwissFEL requires a low-emittance electron beam. The beam size along the accelerator is given by:",augmentation,NO,0
expert,"When an electron beam scatters off a metallic wire, what particles are produced?","The particle shower contains mostly electrons, positrons, and X-rays",Fact,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,"When an electron beam scatters off a metallic wire, what particles are produced?","The particle shower contains mostly electrons, positrons, and X-rays",Fact,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: