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IPAC
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What was the observed bandwidth (FWHM) of the THz radiation?
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Approximately 9%
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Fact
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hermann-et-al-2022-inverse-designed-narrowband-thz-radiator-for-ultrarelativistic-electrons.pdf
|
$$ In equation (1), $\\lambda$ is the wavelength of terahertz radiation, $\\lambda _ { u }$ is the period length of the undulator, $\\gamma$ is the electron beam relativistic energy factor, and $K$ is the undulator magnetic field strength parameter. $$ \\begin{array} { r } { \\left( \\frac { d W } { d \\omega } \\right) \\propto s i n c ^ { 2 } \\left[ \\frac { \\pi N _ { u } \\Delta \\omega } { \\omega _ { 0 } } \\right] \\left| \\frac { \\frac { s i n \\left( N _ { b } \\omega \\Delta t \\right) } { 2 } } { \\frac { s i n \\left( \\omega \\Delta t \\right) } { 2 } } \\right| ^ { 2 } e x p ^ { 2 } \\left[ - \\frac { \\left( \\omega \\sigma _ { t } \\right) ^ { 2 } } { 2 } \\right] . } \\end{array} $$ In Equation (2), $N _ { u }$ is the number of undulator cycles, $N _ { b }$ denotes the number of micro-bunches, $\\sigma _ { t }$ indicates the length of the micro-bunch, and $\\Delta t$ represents the time spacing of the micro-bunches. The first term of Eq. (2). signifies the contribution of the coherent radiation of the undulator to the bandwidth, while the second term represents the contribution of the periodic structure of the pre-bunched electron beam to the bandwidth. These two terms manifest as narrow bands in the spectrum. The third term represents the contribution of the electron beam length to the spectrum, which results in a broadband spectrum primarily affecting the intensity of radiation.
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augmentation
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NO
| 0
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IPAC
|
What was the observed bandwidth (FWHM) of the THz radiation?
|
Approximately 9%
|
Fact
|
hermann-et-al-2022-inverse-designed-narrowband-thz-radiator-for-ultrarelativistic-electrons.pdf
|
The primary objective of the electron beam test was to validate the TS performance. Initially, we confirmed the production of the expected Čerenkov radiation by the electron bunch as it traversed the $3 0 0 \\mathrm { - m m }$ long CWG. Subsequently, the TS was positioned with two of the horns of the $\\mathrm { T M } _ { 0 1 }$ and the $\\mathrm { T E } _ { 1 1 }$ couplers facing the TPX window. On the other side of TPX window was the interferometer, measuring the spectrum of the two overlapping sub-THz waves emitted from the horns. To prevent stray waves from the other TS horns entering the window, a 2-inch diameter aluminum tube was utilized. Fig. 5 presents two Čerenkov radiation spectra measurements: a) without the wire grid polarizer and b) with the polarizer between the TPX window and the interferometer. The polarizer was oriented vertically and was expected to completely attenuate the horizontally polarized wave from the $\\mathrm { T M } _ { 0 1 }$ mode coupler antenna, leaving the vertically polarized wave from the $\\mathrm { T E } _ { 1 1 }$ coupler unaffected. However, in practice, a minor portion of this mode reached the detector due to polarization-altering reflections within the aluminum tube. The measurements indicate that the ratio of the total energy contained in the sub-THz $\\mathrm { H E } _ { 1 1 }$ mode to that of $\\mathrm { T M } _ { 0 1 }$ mode is 0.093. Considering that $\\mathrm { T M } _ { 0 1 }$ mode pulse energy is divided between four ports in the $\\mathrm { T M } _ { 0 1 }$ mode coupler and $\\mathrm { H E } _ { 1 1 }$ mode pulse energy is divided between two ports in the $\\mathrm { T E } _ { 1 1 }$ mode coupler and accounting for the beam offset of $1 5 0 \\mu \\mathrm { m }$ used in these measurements, we calculated a ratio of 0.091 using Eq.3 and Table 1 from [6]. This agreement between measurement and theory is noteworthy, considering potential uncertainties in defining the reference trajectory of the electron beam.
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4
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NO
| 1
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Expert
|
What was the observed bandwidth (FWHM) of the THz radiation?
|
Approximately 9%
|
Fact
|
hermann-et-al-2022-inverse-designed-narrowband-thz-radiator-for-ultrarelativistic-electrons.pdf
|
$$ \\lambda = \\frac { a } { m } \\Biggl ( \\frac { 1 } { \\beta } - \\cos { \\theta } \\Biggr ) $$ where $\\beta$ is the normalized velocity of the electrons, a is the periodicity of the structure, and $m$ is the mode order. Smith‚àí Purcell emission from regular metallic grating surfaces has been observed in numerous experiments, first using $3 0 0 ~ \\mathrm { k e V }$ electrons11 and later also using ultrarelativistic electrons.12,13 If electron pulses shorter than the emitted wavelength are used, the fields from individual electrons add coherently, and the radiated energy scales quadratically with the bunch charge.14 The typically used single-sided gratings emit a broadband spectrum,15 which is dispersed by the Smith‚àíPurcell relation (eq 1). To enhance emission at single frequencies, a concept called orotron uses a metallic mirror above the grating to form a resonator.16,17 Dielectrics can sustain fields 1‚àí2 orders of magnitude larger than metals18 and are therefore an attractive material for strong Smith‚àíPurcell interactions. Inverse design is a computational technique that has been successfully employed to advance integrated photonics.19 Algorithms to discover optical structures fulfilling desired functional characteristics are creating a plethora of novel subwavelength geometries: applications include wavelengthdependent beam splitters19,20 and couplers,21 as well as dielectric laser accelerators.22
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1
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NO
| 0
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Expert
|
What was the observed bandwidth (FWHM) of the THz radiation?
|
Approximately 9%
|
Fact
|
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 >
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1
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NO
| 0
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Expert
|
What was the observed bandwidth (FWHM) of the THz radiation?
|
Approximately 9%
|
Fact
|
hermann-et-al-2022-inverse-designed-narrowband-thz-radiator-for-ultrarelativistic-electrons.pdf
|
File Name:hermann-et-al-2022-inverse-designed-narrowband-thz-radiator-for-ultrarelativistic-electrons.pdf Inverse-Designed Narrowband THz Radiator for Ultrarelativistic Electrons Benedikt Hermann,# Urs Haeusler,# Gyanendra Yadav, Adrian Kirchner, Thomas Feurer, Carsten Welsch, Peter Hommelhoff, and Rasmus Ischebeck\\* Cite This: ACS Photonics 2022, 9, 1143−1149 ACCESS 山 Metrics & More 国 Article Recommendations ABSTRACT: THz radiation finds various applications in science and technology. Pump−probe experiments at free-electron lasers typically rely on THz radiation generated by optical rectification of ultrafast laser pulses in electro-optic crystals. A compact and cost-efficient alternative is offered by the Smith−Purcell effect: a charged particle beam passes a periodic structure and generates synchronous radiation. Here, we employ the technique of photonic inverse design to optimize a structure for Smith− Purcell radiation at a single wavelength from ultrarelativistic electrons. The resulting design is highly resonant and emits narrowbandly. Experiments with a 3D-printed model for a wavelength of $9 0 0 \\mu \\mathrm { m }$ show coherent enhancement. The versatility of inverse design offers a simple adaption of the structure to other electron energies or radiation wavelengths. This approach could advance beam-based THz generation for a wide range of applications. KEYWORDS: THz generation, Smith−Purcell radiation, inverse design, light−matter interaction, free-electron light sources $\\mathbf { C }$ aopuprlciecs iof ,TiHnzc rdaidniagtiwoinr aerses ofmimntuenriecsat fonr ,n2uelmeecrtrouns acceleration,3−5 and biomedical and material science.6,7 Freeelectron laser (FEL) facilities demand versatile THz sources for pump−probe experiments.8 Intense, broadband THz pulses up to sub-mJ pulse energy have been demonstrated using optical rectification of high-power femtosecond lasers in lithium niobate crystals.9,10 The Smith−Purcell effect11 offers a compact and cost-efficient alternative for the generation of beam-synchronous THz radiation at electron accelerators. This effect describes the emission of electromagnetic waves from a periodic metallic or dielectric structure excited by electrons moving parallel to its surface. The wavelength of Smith− Purcell radiation at an angle $\\theta$ with respect to the electron beam follows:11
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1
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NO
| 0
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IPAC
|
What was the observed bandwidth (FWHM) of the THz radiation?
|
Approximately 9%
|
Fact
|
hermann-et-al-2022-inverse-designed-narrowband-thz-radiator-for-ultrarelativistic-electrons.pdf
|
File Name:THz_SASE_FEL_AT_PITZ__LASING_AT_A_WAVELENGTH_OF_100#U00b5m__M._Krasilnikov#U2020,_Z._Aboulbanine1,_G..pdf THz SASE FEL AT PITZ: LASING AT A WAVELENGTH OF $\\mathbf { 1 0 0 } \\mu \\mathbf { m } ^ { * }$ . Krasilnikov†, Z. Aboulbanine1, G. Adhikari2, N. Aftab, A. Asoyan3, H. Davtyan3 G. Georgiev, J. Good, A. Grebinyk, M. Gross, A. Hoffmann, E. Kongmon4, X.-K. Li, A. Lueangaramwong5, D. Melkumyan, S. Mohanty, R. Niemczyk6, A. Oppelt, H. Qian7, C. Richard, E. Schneidmiller, F. Stephan, G. Vashchenko, T. Weilbach8, M. Yurkov, Deutsches Elektronen-Synchrotron DESY, Germany W. Hillert, J. Rossbach, University of Hamburg, Germany 1now at Oak Ridge National Laboratory, USA 2now at SLAC National Accelerator laboratory, USA 3on leave from CANDLE Synchrotron Research Institute, Armenia 4on leave from Chiang Mai University, Thailand 5now at Diamond Light Source Ltd, UK 6now at Helmholtz-Zentrum Dresden Rossendorf, Germany 7now at Zhangjiang Lab, China 8now at Paul Scherrer Institute, Switzerland Abstract Development of an accelerator-based tunable THz source prototype for pump-probe experiments at the European XFEL is ongoing at the Photo Injector Test facility at DESY in Zeuthen (PITZ). The proof-of-principle experiments on the THz SASE FEL are performed utilizing the LCLS-I undulator (on loan from SLAC) installed in the PITZ beamline. The first lasing at a center wavelength of $1 0 0 ~ { \\mu \\mathrm { m } }$ was observed in the summer of 2022. The lasing of the narrowband THz source was achieved using an electron beam with an energy of ${ \\sim } 1 7 \\mathrm { M e V }$ and a bunch charge up to several nC. Optimization of beam transport and matching resulted in the measurement of THz radiation with a pulse energy of tens of $\\mu \\mathrm { J }$ , measured with pyroelectric detectors. The THz FEL gain curves were measured by means of specially designed short coils along the undulator. The results of the first characterization of the THz source at PITZ will be presented.
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1
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NO
| 0
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Expert
|
What was the observed bandwidth (FWHM) of the THz radiation?
|
Approximately 9%
|
Fact
|
hermann-et-al-2022-inverse-designed-narrowband-thz-radiator-for-ultrarelativistic-electrons.pdf
|
RESULTS The goal of our inverse design optimization was a narrowband dielectric Smith‚àíPurcell radiator for ultrarelativistic electrons $\\mathit { \\check { E } } = 3 . 2 \\ \\mathrm { G e V }$ , $\\gamma \\approx 6 0 0 0 ,$ ). To simplify the collection of the THz radiation, a periodicity of $a = \\lambda$ was chosen, resulting in an emission perpendicular to the electron propagation direction, $\\theta \\ : = \\ : 9 0 ^ { \\circ }$ . The optimization was based on a 2D finite-difference frequency-domain (FDFD) simulation of a single unit cell of the grating (Figure 1a). Periodic boundaries in direction of the electron propagation ensure the desired periodicity, and perfectly matched layers in the transverse xdirection imitate free space. The design region extends $4 . 5 \\mathrm { m m }$ to each side of a $1 5 0 \\ \\mu \\mathrm { m }$ wide vacuum channel, large enough to facilitate the full transmission of the electron beam with a width of $\\sigma _ { x } = 3 0 \\ \\mu \\mathrm { m }$ (RMS). The electric current spectral density $\\scriptstyle \\mathbf { J } ( x , y , \\omega )$ of a single electron bunch acts here as the source term of our simulation and is given by
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augmentation
|
NO
| 0
|
Expert
|
What was the observed bandwidth (FWHM) of the THz radiation?
|
Approximately 9%
|
Fact
|
hermann-et-al-2022-inverse-designed-narrowband-thz-radiator-for-ultrarelativistic-electrons.pdf
|
Ultrarelativistic Optimization. The simulation of ultrarelativistic electrons poses challenges that have so far prevented inverse design in this regime.33 Here, we report on two main challenges. First, the electron velocity is close to the speed of light $( \\beta = 0 . 9 9 9 9 9 9 9 8 5$ for $E = 3 . 2 \\mathrm { G e V } ,$ ), which requires a high mesh resolution. If the numerical error is too large due to a low mesh resolution, the simulation may not be able to distinguish between $\\beta < 1$ and $\\beta > 1$ . In that case, the simulation could show Cherenkov radiation in vacuum instead of Smith‚àíPurcell radiation. Not only does a higher mesh resolution require more computational memory and time, but it may also hamper the inverse design optimization if the number of design parameters becomes too large. Hence, we parametrized our structures at a low resolution (mesh spacing $\\lambda / { 3 0 } \\mathrm { \\dot { } }$ ), which is still above the fabrication accuracy of $\\lambda / 5$ , and computed the fields at a high resolution (mesh spacing $\\lambda / { 1 5 0 } \\dot$ ).
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augmentation
|
NO
| 0
|
Expert
|
What was the observed bandwidth (FWHM) of the THz radiation?
|
Approximately 9%
|
Fact
|
hermann-et-al-2022-inverse-designed-narrowband-thz-radiator-for-ultrarelativistic-electrons.pdf
|
$$ \\epsilon _ { r } ( x , y ) = \\epsilon _ { \\mathrm { m i n } } + ( \\epsilon _ { \\mathrm { m a x } } - \\epsilon _ { \\mathrm { m i n } } ) { \\cdot } \\frac { 1 } { 2 } ( 1 + \\operatorname { t a n h } \\alpha \\phi ( x , y ) ) $$ where large values of $\\alpha$ yield a close-to-binary design with few values between $\\varepsilon _ { \\operatorname* { m i n } } = 1$ and $\\varepsilon _ { \\operatorname* { m a x } } = 2 . 7 9$ . To avoid small or sharp features in the final design, we convolved $\\phi ( x , y )$ with a uniform 2D circular kernel with radius $6 0 \\mu \\mathrm m$ before projection onto the sigmoid function tanh $( \\alpha \\tilde { \\phi } )$ with the convolved design parameter $\\tilde { \\phi }$ . By increasing $\\alpha$ from 20 to 1000 as the optimization progresses, we found improved convergence. We further accelerated convergence by applying mirror and point symmetry with respect to the center of a unit cell of the grating, which reduces the parameter space by a factor of 4. An exemplary design evolution is shown in Figure 6.
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augmentation
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NO
| 0
|
Expert
|
What was the observed bandwidth (FWHM) of the THz radiation?
|
Approximately 9%
|
Fact
|
hermann-et-al-2022-inverse-designed-narrowband-thz-radiator-for-ultrarelativistic-electrons.pdf
|
During and after our experiments, the structure did not show any signs of performance degradation or visible damage. It was used continuously for eight hours with a bunch charge of approximately $1 0 ~ \\mathrm { p C }$ at a pulse repetition rate of $1 \\ \\mathrm { H z }$ . CONCLUSION The here-presented beam-synchronous radiation source can be added to the beamline of an FEL to enrich capabilities for pump‚àíprobe experiments. For ultrarelativistic electrons, a second beamline may be used to compensate for the longer path length of the THz radiation and achieve simultaneous arrival with the X-ray radiation created in the undulator of the FEL (Figure 5a). Smith‚àíPurcell radiation represents a costefficient alternative to the broadband generation of THz by optical rectification, which requires an external laser system and precise synchronization to the accelerator. Our inverse design approach to Smith‚àíPurcell emitters can produce beamsynchronous narrowband THz radiation, which could propel pump‚àíprobe studies with THz excitations in solids, for instance, resonant control of strongly correlated electron systems, high-temperature superconductors, or vibrational modes of crystal lattices (phonons).28,29 Further improvement of our THz structure can be achieved by higher fabrication accuracy and the use of a fully 3Doptimized geometry with a higher quality factor, resulting in more narrowband emission and higher pulse energy. Moreover, the inverse design suite could be extended to composite structures of more than one material, which could provide extra stability for complicated 3D designs. In the case of highly resonant structures, materials with low absorption, for example, polytetrafluoroethylene (PTFE),24 are a necessity. The measured THz pulse energy can be increased by a factor of almost 300 by raising the driving bunch charge from the used $1 1 . 8 ~ \\mathrm { p C }$ up to the $2 0 0 ~ \\mathrm { p C }$ available at SwissFEL. Whether the currently used material can withstand such high fields and radiation remains to be investigated. Combining 3D optimization, longer structures, larger collection optics, and higher bunch charges will result in a THz pulse energy multiple orders of magnitude larger than observed in the presented experiment $( 0 . 6 ~ \\mathrm { p J } )$ .
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augmentation
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NO
| 0
|
Expert
|
What was the observed bandwidth (FWHM) of the THz radiation?
|
Approximately 9%
|
Fact
|
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}
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augmentation
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NO
| 0
|
Expert
|
What was the observed bandwidth (FWHM) of the THz radiation?
|
Approximately 9%
|
Fact
|
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.
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augmentation
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NO
| 0
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expert
|
What was the purpose of performing parameter sweeps of the corrugation geometry?
|
To determine an optimal geometry for colinear wakefield acceleration
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Summary
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Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf
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$$ Here we notice the linear scaling of the energy dissipation with the minor radius, $a$ , which helps smaller diameter structures achieve less heating per pulse and thus higher bunch repetition rates. At a gradient of $E _ { \\mathrm { a c c } } = 9 0 ~ \\mathrm { M V } \\mathrm { m } ^ { - 1 }$ , a minor radius of $a = 1 ~ \\mathrm { m m }$ , and a repetition rate of $f _ { r } = 2 0 ~ \\mathrm { k H z }$ , the minimum theoretical thermal power dissipation density on the wall of the corrugated waveguide is roughly $3 6 ~ \\mathrm { W / c m ^ { 2 } }$ . This is well within the cooling capability of single phase cooling systems using water as a working fluid, see for example [27]. In addition to the steady-state thermal load, the transient heating of the corrugation plays an important role in limiting the attainable accelerating gradient. The transient temperature rise due to pulse heating causes degradation of the surface which eventually leads to nucleation sites where electric breakdown may occur [20]. Acceptable transient temperature rise is cited in the literature as $4 0 \\mathrm { K }$ [20], above which the structure begins to incur damage. The transient $\\Delta T$ at the surface is calculated from a Green’s function solution of the thermal diffusion equation in one dimension with Neumann boundary conditions as [20]:
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1
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Yes
| 0
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expert
|
What was the purpose of performing parameter sweeps of the corrugation geometry?
|
To determine an optimal geometry for colinear wakefield acceleration
|
Summary
|
Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf
|
$$ V = \\Biggl | \\int _ { 0 } ^ { p } E _ { z } ( z ) e ^ { j \\omega _ { c } ^ { z } } d z \\Biggr | . $$ The group velocity ${ \\boldsymbol { v } } _ { g }$ is calculated from the time averaged electromagnetic field power flow $P _ { z }$ , the unit cell length $p$ , and the stored energy $U$ in the unit cell, where $P _ { z }$ is found by integration of the Poynting vector, $$ v _ { g } = \\frac { P _ { z } } { U } p . $$ Loss in the structure due to the conductivity of the wall material causes the fields to decay as $\\exp ( - \\alpha z )$ , where the attenuation constant $\\alpha$ in $\\mathrm { { N p m ^ { - 1 } } }$ is calculated in terms of the quality factor $\\boldsymbol { Q }$ of the unit cell as [17]: $$ \\alpha = \\frac { \\omega } { 2 Q v _ { g } } .
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1
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Yes
| 0
|
expert
|
What was the purpose of performing parameter sweeps of the corrugation geometry?
|
To determine an optimal geometry for colinear wakefield acceleration
|
Summary
|
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 } }
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1
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Yes
| 0
|
expert
|
What was the purpose of performing parameter sweeps of the corrugation geometry?
|
To determine an optimal geometry for colinear wakefield acceleration
|
Summary
|
Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf
|
After determining the minor radius, $a$ , of $1 \\ \\mathrm { m m }$ , the frequency and corresponding aperture ratio of the synchronous $\\mathrm { T M } _ { 0 1 }$ accelerating mode must be chosen. We have shown in Figs. 10 and 12 that the peak surface fields and associated pulse heating increase with aperture ratio while the total power dissipation decreases, as shown by its dependence on the loss factor $\\kappa$ in Eq. (16) and Fig. 7. In addition to these considerations, the frequency must be compatible with the electromagnetic output couplers used to extract rf energy from the structure. An important feature of A-STAR is its ability to measure the trajectory of the bunch in the CWA using the $\\mathrm { H E M } _ { 1 1 }$ mode which is excited when the beam propagates off-axis. Due to mode conversion, the design of the coupler that extracts the $\\mathrm { H E M } _ { 1 1 }$ mode becomes increasingly challenging as the $\\mathrm { H E M } _ { 1 1 }$ wavelength shrinks with respect to the fixed aperture of the waveguide. For the $1 \\mathrm { - m m }$ minor radius cylindrical waveguide, the limiting factor in the $\\mathbf { H E M } _ { 1 1 }$ coupler design was converted to the $\\mathrm { T E } _ { 3 1 }$ mode which has a cutoff frequency of $2 0 0 \\ : \\mathrm { G H z }$ . To address this, the synchronous $\\mathbf { H E M } _ { 1 1 }$ mode was chosen to be $1 0 \\mathrm { G H z }$ below the $\\mathrm { T E } _ { 3 1 }$ cutoff frequency, resulting in a 190-GHz $\\mathrm { H E M } _ { 1 1 }$ mode and 180-GHz $\\mathrm { T M } _ { 0 1 }$ mode with an aperture ratio of $a / \\lambda = 0 . 6 0$ .
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2
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Yes
| 0
|
expert
|
What was the purpose of performing parameter sweeps of the corrugation geometry?
|
To determine an optimal geometry for colinear wakefield acceleration
|
Summary
|
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.
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1
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Yes
| 0
|
expert
|
What was the purpose of performing parameter sweeps of the corrugation geometry?
|
To determine an optimal geometry for colinear wakefield acceleration
|
Summary
|
Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf
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Maintaining the fundamental $\\mathrm { T M } _ { 0 1 }$ and $\\mathrm { H E } _ { 1 1 }$ frequencies within a $\\pm 5$ GHz-bandwidth specified by the design of the output couplers requires dimensional tolerances of roughly $\\pm 1 0 ~ { \\mu \\mathrm { m } } ,$ as shown by Fig. 5. The most sensitive dimension to manufacturing error is the corrugation depth, which must be carefully controlled to produce the desired frequency. Mode conversion due to the straightness of the CWG is not expected to change the acceleration properties over the short length scale between the drive and witness bunch. However, such effects may become relevant in the operation of the output couplers and are a subject of future analysis. Table: Caption: TABLE II. A-STAR key operating parameters. Body: <html><body><table><tr><td colspan="2">Parameter</td></tr><tr><td>a</td><td>1 mm Corrugation minor radius</td></tr><tr><td>d 264 μm</td><td>Corrugation depth</td></tr><tr><td>g 180 μm</td><td>Corrugation vacuum gap</td></tr><tr><td>t 160 μm</td><td>Corrugation tooth width</td></tr><tr><td>80 μm rt.g</td><td>Corrugation corner radius</td></tr><tr><td>P 340 μm</td><td>Corrugation period</td></tr><tr><td>0.06</td><td>Spacing parameter</td></tr><tr><td>L</td><td>50 cm Waveguide module length</td></tr><tr><td>R 5</td><td>Transformer ratio</td></tr><tr><td>|F| 0.382</td><td>Bunch form factor</td></tr><tr><td>q0 10 nC</td><td>Bunch charge</td></tr><tr><td>90 MVm-1 Eacc</td><td>Accelerating gradient</td></tr><tr><td>325 MV m-1 Emax</td><td>Peak surface E field</td></tr><tr><td>610 kA m-1 Hmax</td><td>Peak surface H field</td></tr><tr><td>74°</td><td>Phase advance</td></tr><tr><td>fr 20 kHz</td><td>Repetition rate</td></tr><tr><td>Pdiss 1050 W</td><td>Power dissipation per module</td></tr><tr><td>W 55 W/cm²</td><td>Power density upper bound</td></tr><tr><td>△T 9.5K</td><td>Pulse heating</td></tr></table></body></html>
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expert
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What was the purpose of performing parameter sweeps of the corrugation geometry?
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To determine an optimal geometry for colinear wakefield acceleration
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Summary
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Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf
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$$ which reduces to $$ E _ { \\mathrm { a c c } } = 2 \\kappa q _ { 0 } | F ( k _ { n } ) | $$ For the doorstep distribution of Eq. (25) with transformer ratio $\\mathcal { R }$ and wave number $k _ { n } = \\omega _ { n } / c$ , the form factor $| F ( k ) |$ is calculated from Eq. (B20) as $$ \\begin{array} { r l r } { | F ( k ) | = \\frac { 2 k _ { n } } { \\mathcal { R } ^ { 2 } + \\pi - 2 } \\{ \\frac { \\mathcal { R } ^ { 2 } } { k ^ { 2 } } + \\frac { 2 k _ { n } } { k ^ { 3 } } [ \\frac { k _ { n } } { k } [ 1 - \\cos ( k l - \\frac { \\pi k } { 2 k _ { n } } ) ] } \\\\ & { } & { + \\sin ( k l ) - \\sin ( \\frac { \\pi k } { 2 k _ { n } } ) ] } \\\\ & { } & { - \\frac { 2 } { k ^ { 2 } } \\sqrt { \\mathcal { R } ^ { 2 } - 1 } [ \\cos ( k l ) + \\frac { k _ { n } } { k } \\sin ( k l - \\frac { \\pi k } { 2 k _ { n } } ) ] \\} ^ { 1 / 2 } , } \\end{array}
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augmentation
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Yes
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expert
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What was the purpose of performing parameter sweeps of the corrugation geometry?
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To determine an optimal geometry for colinear wakefield acceleration
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Summary
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Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf
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APPENDIX B: BUNCH FORM FACTOR DERIVATION When calculating a bunch’s energy loss to a particular mode of the corrugated waveguide, the shape of the bunch described by the bunch peak current distribution $i ( t )$ is accounted for by scaling the loss factor $\\kappa$ by the Fourier transform ${ \\cal I } ( \\omega _ { n } )$ of the current, where $\\omega _ { n }$ is the angular frequency of the synchronous mode. The form factor $F ( k _ { n } )$ of the bunch is defined as ${ \\cal I } ( \\omega _ { n } ) / q _ { 0 }$ , where $k _ { n }$ is the wave number of the synchronous mode and $q _ { 0 }$ is the total charge of the bunch. Here, time $t$ begins when the head of the bunch passes a fixed observation point in the corrugated waveguide. We begin by considering the kinetic energy lost by an element of charge idt as it moves a distance cdt in an electric field $E _ { z }$ : $$ d ^ { 2 } U _ { \\mathrm { l o s s } } = ( i d t ) ( c d t ) E _ { z } .
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augmentation
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Yes
| 0
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expert
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What was the purpose of performing parameter sweeps of the corrugation geometry?
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To determine an optimal geometry for colinear wakefield acceleration
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Summary
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Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf
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$$ where $$ 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}
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augmentation
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Yes
| 0
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expert
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What was the purpose of performing parameter sweeps of the corrugation geometry?
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To determine an optimal geometry for colinear wakefield acceleration
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Summary
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Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf
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$$ Since the current density $i ( t )$ is a purely real function, $I ( - \\omega ) = I ^ { * } ( \\omega )$ where $*$ denotes complex conjugation, leading to $$ P _ { \\nu } = \\frac { c } { 2 \\pi } \\int _ { - \\infty } ^ { \\infty } | I ( \\omega ) | ^ { 2 } \\operatorname { R e } \\{ Z _ { | | } ( \\omega ) \\} d \\omega . $$ Equation (B12) represents the power being converted from kinetic energy to electromagnetic energy in the frequency domain. Considering a single mode denoted by the subscript $n$ , the wake impedance is $$ Z _ { n | | } ( \\omega ) = \\int _ { - \\infty } ^ { \\infty } 2 \\kappa _ { n } \\cos ( \\omega _ { n } t ) \\theta ( t ) e ^ { - j \\omega t } d t . $$ Using the Fourier transform property $$ \\mathcal { F } \\{ f ( t ) \\cos ( a t ) \\} = \\frac { F ( \\omega - a ) + F ( \\omega + a ) } { 2 } ,
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augmentation
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Yes
| 0
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expert
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What was the purpose of performing parameter sweeps of the corrugation geometry?
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To determine an optimal geometry for colinear wakefield acceleration
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Summary
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Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf
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The A-STAR design is made up of $0 . 5 \\mathrm { - m }$ long CWG modules connected in series by $4 0 \\mathrm { - m m }$ long transition sections which contain the rf output couplers, vacuum pumping ports, and bellows. The addition of the transition sections increases the overall length of the accelerator by less than $10 \\%$ . The transformer ratio $\\mathcal { R }$ is determined by the longitudinal charge density of the drive bunch $q ( s )$ , where it has been shown in [12] that $\\mathcal { R }$ can be maximized by using a “doorstep” type charge distribution defined as Table: Caption: TABLE III. A-STAR synchronous electromagnetic mode characteristics. The loss factor $\\kappa$ for the $\\mathrm { H E M } _ { 1 1 }$ mode scales with the square of the beam offset and is given for the offset of $1 ~ { \\mu \\mathrm { m } }$ . The attenuation coefficient $\\alpha$ is given for a structure with the conductivity of $4 \\times 1 0 ^ { 7 } \\ \\mathrm { S m ^ { - 1 } }$ . Body: <html><body><table><tr><td></td><td>TM01</td><td>HEM11</td><td>Units</td></tr><tr><td>f</td><td>180</td><td>190</td><td>GHz</td></tr><tr><td>K</td><td>1.18 × 1016</td><td>2.19 × 1010</td><td>VC-1 m-1</td></tr><tr><td>βg</td><td>0.57</td><td>0.62</td><td>None</td></tr><tr><td>α</td><td>2.31</td><td>1.96</td><td>Np m-1</td></tr></table></body></html>
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augmentation
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Yes
| 0
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expert
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What was the purpose of performing parameter sweeps of the corrugation geometry?
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To determine an optimal geometry for colinear wakefield acceleration
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Summary
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Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf
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$$ q ( s ) = N \\times { \\left\\{ \\begin{array} { l l } { 1 } & { 0 < s < \\pi / ( 2 k _ { n } ) } \\\\ { k _ { n } s + ( 1 - \\pi / 2 ) } & { \\pi / ( 2 k _ { n } ) < s < l } \\\\ { 0 } & { { \\mathrm { e l s e } } } \\end{array} \\right. } $$ 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.
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augmentation
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Yes
| 0
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expert
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What was the purpose of performing parameter sweeps of the corrugation geometry?
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To determine an optimal geometry for colinear wakefield acceleration
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Summary
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Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf
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$$ The integrals in $t$ and $t ^ { \\prime }$ produce Dirac delta functions leaving $$ \\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 \\} .
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augmentation
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Yes
| 0
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expert
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What was the purpose of performing parameter sweeps of the corrugation geometry?
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To determine an optimal geometry for colinear wakefield acceleration
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Summary
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Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf
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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.
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augmentation
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Yes
| 0
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expert
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What was the purpose of performing parameter sweeps of the corrugation geometry?
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To determine an optimal geometry for colinear wakefield acceleration
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Summary
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Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf
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$$ Making the substitution $u = s - s ^ { \\prime }$ , $$ 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\\} . $$ We can now write the field in terms of the previously derived form factor $F ( k _ { n } )$ given in Eq. (B20):
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augmentation
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Yes
| 0
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expert
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What was the purpose of performing parameter sweeps of the corrugation geometry?
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To determine an optimal geometry for colinear wakefield acceleration
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Summary
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Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf
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$$ where the integrals are over all space. Applying the normalized fields with $U = 1$ to Eq. (8) for the group velocity shows that group velocity is independent of scaling $$ \\begin{array} { l } { { v _ { g } ^ { \\prime } = \\hat { a } p \\iint \\displaystyle \\frac { 1 } { 2 } \\mathrm { R e } \\big \\{ E ^ { \\prime } ( x , y ) \\times H ^ { \\prime * } ( x , y ) \\big \\} d x d y } } \\\\ { { \\mathrm { ~ } = p \\iint \\displaystyle \\frac { 1 } { 2 } \\mathrm { R e } \\big \\{ E ( x ^ { \\prime } , y ^ { \\prime } ) \\times H ^ { * } ( x ^ { \\prime } , y ^ { \\prime } ) \\big \\} d x ^ { \\prime } d y ^ { \\prime } = v _ { g } . } } \\end{array} $$ Using Eq. (7), the induced voltage $V ^ { \\prime }$ in the scaled structure is $$ V ^ { \\prime } = \\biggr | \\int _ { 0 } ^ { \\hat { a } p } \\hat { a } ^ { - 3 / 2 } E _ { z } ( z ^ { \\prime } ) e ^ { j \\omega _ { c } ^ { \\prime } } d z \\biggr | ,
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augmentation
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Yes
| 0
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expert
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What was the purpose of performing parameter sweeps of the corrugation geometry?
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To determine an optimal geometry for colinear wakefield acceleration
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Summary
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Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf
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$$ 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 . $$ Scaling of the attenuation constant $\\alpha$ with conductivity is accomplished by multiplying $\\alpha$ by $\\sqrt { \\sigma / \\sigma ^ { \\prime } }$ where $\\sigma$ is the conductivity of the unscaled structure and $\\sigma ^ { \\prime }$ is the conductivity of the scaled structure.
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augmentation
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Yes
| 0
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expert
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What was the purpose of performing parameter sweeps of the corrugation geometry?
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To determine an optimal geometry for colinear wakefield acceleration
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Summary
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Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf
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APPENDIX A: SCALING AND NORMALIZATION Here, we derive the scaling laws for the loss factor $\\kappa$ , group velocity $\\beta _ { g } ,$ and attenuation constant $\\alpha$ . We will assume that $\\sigma$ satisfies the conditions of a good conductor so that the field solutions are independent of conductivity. The time harmonic eigenmode solutions $E$ and $\\pmb { H }$ produced by CST are normalized such that the stored energy $U$ in the unit cell is 1 J and the frequency is $\\omega$ . Uniformly scaling the geometry by a constant $\\hat { \\boldsymbol a }$ while holding the stored energy fixed results in the scaled eigenmode solutions: $$ \\begin{array} { r l } & { E ^ { \\prime } ( x , y , z ) e ^ { j \\omega ^ { \\prime } t } = \\hat { a } ^ { - 3 / 2 } E ( x ^ { \\prime } , y ^ { \\prime } , z ^ { \\prime } ) e ^ { j \\omega _ { \\hat { a } } ^ { t } } } \\\\ & { H ^ { \\prime } ( x , y , z ) e ^ { j \\omega ^ { \\prime } t } = \\hat { a } ^ { - 3 / 2 } H ( x ^ { \\prime } , y ^ { \\prime } , z ^ { \\prime } ) e ^ { j \\omega _ { \\hat { a } } ^ { t } } , } \\end{array}
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augmentation
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Yes
| 0
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expert
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What was the purpose of performing parameter sweeps of the corrugation geometry?
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To determine an optimal geometry for colinear wakefield acceleration
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Summary
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Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf
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$$ Here, the electric field $E _ { z }$ is the wakefield left behind by the current in the head of the bunch which has already passed the observation point. The wakefield produced by a current impulse $q _ { 0 } \\delta ( t )$ is the Green’s function $h ( t )$ which is expressed as an expansion over the normal modes of the corrugation unit cell as $$ h ( t ) = \\sum _ { n = 0 } ^ { \\infty } 2 \\kappa _ { n } \\cos { ( \\omega _ { n } t ) } \\theta ( t ) , $$ where $\\theta ( t )$ is the Heaviside theta function $$ \\theta ( t ) = \\left\\{ \\begin{array} { l l } { 0 } & { t < 0 } \\\\ { 1 / 2 } & { t = 0 } \\\\ { 1 } & { t > 0 } \\end{array} \\right. $$ and $\\kappa _ { n }$ is the loss factor given in Eq. (6) in units of $\\mathrm { { V } m ^ { - 1 } C ^ { - 1 } }$ . The fields in the unit cell are time harmonic, oscillating with frequency $\\omega _ { n }$ . Because the structure is approximated to be periodic, the oscillating fields are part of an infinitely long traveling wave that never decays. In terms of the Green’s function $h ( t )$ , the wakefield $E _ { z } ( t )$ due to the total current distribution $i ( t )$ is then constructed with the convolution integral
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augmentation
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Yes
| 0
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expert
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What was the purpose of performing parameter sweeps of the corrugation geometry?
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To determine an optimal geometry for colinear wakefield acceleration
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Summary
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Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf
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Table: Caption: TABLE I. Parameters and variables used throughout the paper. Body: <html><body><table><tr><td colspan="2">Parameter</td></tr><tr><td>K</td><td>Wakefield loss factor</td></tr><tr><td>βg</td><td>Normalized group velocity</td></tr><tr><td>vg</td><td>Group velocity</td></tr><tr><td>α</td><td>Attenuation constant</td></tr><tr><td>Q</td><td>Quality factor</td></tr><tr><td>0</td><td>Electrical conductivity</td></tr><tr><td></td><td>Corrugation spacing parameter</td></tr><tr><td>S</td><td>Corrugation sidewall parameter</td></tr><tr><td>a</td><td>Corrugation minor radius</td></tr><tr><td>t</td><td>Corrugation tooth width</td></tr><tr><td>g</td><td>Corrugation vacuum gap</td></tr><tr><td>d</td><td>Corrugation depth</td></tr><tr><td>p</td><td>Corrugation period</td></tr><tr><td>rt</td><td>Corrugation tooth radius</td></tr><tr><td>rg</td><td>Corrugation vacuum gap radius</td></tr><tr><td>L</td><td>Corrugated waveguide length</td></tr><tr><td>F</td><td>Bunch form factor</td></tr><tr><td>q0</td><td>Drive bunch charge</td></tr><tr><td>fr</td><td>Bunch repetition rate</td></tr><tr><td>T</td><td>rf pulse decay time constant</td></tr><tr><td>8</td><td>Skin depth</td></tr><tr><td>Pf</td><td>rf pulse power envelope</td></tr><tr><td>P</td><td>Instantaneous rf pulse power</td></tr><tr><td>Eacc</td><td>Accelerating field</td></tr><tr><td>Emax</td><td>Peak surface E field</td></tr><tr><td>Hmax</td><td>Peaksurface H field</td></tr><tr><td>Qdiss</td><td>Energy dissipation</td></tr><tr><td>Pd</td><td>Power dissipation distribution</td></tr><tr><td>W</td><td>Average thermal power density</td></tr><tr><td>△T</td><td>Transient temperature rise</td></tr><tr><td>C</td><td>Speed of light</td></tr><tr><td>Z0</td><td>Impedance of free space</td></tr><tr><td>8</td><td>Initial beam energy</td></tr><tr><td>R</td><td>Transformer ratio</td></tr></table></body></html> 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.
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augmentation
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Yes
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IPAC
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When an electron beam scatters off a metallic wire, what particles are produced?
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The particle shower contains mostly electrons, positrons, and X-rays
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Fact
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Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf
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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].
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augmentation
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NO
| 0
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IPAC
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When an electron beam scatters off a metallic wire, what particles are produced?
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The particle shower contains mostly electrons, positrons, and X-rays
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Fact
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Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf
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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.
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augmentation
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NO
| 0
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IPAC
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When an electron beam scatters off a metallic wire, what particles are produced?
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The particle shower contains mostly electrons, positrons, and X-rays
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Fact
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Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf
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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.
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When an electron beam scatters off a metallic wire, what particles are produced?
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The particle shower contains mostly electrons, positrons, and X-rays
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Fact
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Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf
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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.
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expert
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When an electron beam scatters off a metallic wire, what particles are produced?
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The particle shower contains mostly electrons, positrons, and X-rays
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Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf
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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.
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When an electron beam scatters off a metallic wire, what particles are produced?
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The particle shower contains mostly electrons, positrons, and X-rays
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Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf
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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 } ,
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When an electron beam scatters off a metallic wire, what particles are produced?
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The particle shower contains mostly electrons, positrons, and X-rays
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Fact
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Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf
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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 $\\mathbf { R } _ { i n } = 4 . 0 2 5 \\mathrm { m m }$ .
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When an electron beam scatters off a metallic wire, what particles are produced?
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The particle shower contains mostly electrons, positrons, and X-rays
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Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf
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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.
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When an electron beam scatters off a metallic wire, what particles are produced?
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The particle shower contains mostly electrons, positrons, and X-rays
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Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf
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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
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expert
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When an electron beam scatters off a metallic wire, what particles are produced?
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The particle shower contains mostly electrons, positrons, and X-rays
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Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf
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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).
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When an electron beam scatters off a metallic wire, what particles are produced?
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The particle shower contains mostly electrons, positrons, and X-rays
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Fact
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Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf
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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:
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expert
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When an electron beam scatters off a metallic wire, what particles are produced?
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The particle shower contains mostly electrons, positrons, and X-rays
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Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf
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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.
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expert
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When an electron beam scatters off a metallic wire, what particles are produced?
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The particle shower contains mostly electrons, positrons, and X-rays
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Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf
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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 $9 0 ^ { \\circ }$ .
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expert
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When an electron beam scatters off a metallic wire, what particles are produced?
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The particle shower contains mostly electrons, positrons, and X-rays
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Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf
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ACKNOWLEDGMENTS We would like to express our gratitude to the SwissFEL operations crew, the PSI expert groups, and the entire ACHIP collaboration for their support with these experiments. We would like to thank Thomas Schietinger for careful proofreading of the manuscript. This research is supported by the Gordon and Betty Moore Foundation through Grant No. GBMF4744 (ACHIP) to Stanford University. APPENDIX A: ERROR ESTIMATION 1. Position errors The uncertainty of the position of the wire scanner with respect to the electron beam is affected by the readout precision of the hexapod $( < 1 ~ \\mathrm { n m } )$ , vibrational motion of the hexapod $\\phantom { + } < 1 0 ~ \\mathrm { { n m } } )$ and position jitter of the electron beam, which at SwissFEL is typically a few-percent of the beam size. The orbit of the electron beam is measured with BPMs along the accelerator. Unfortunately, the BPMs along the Athos branch of SwissFEL have not been calibrated (the measurement took place during the commissioning phase of Athos). Nevertheless, we tried correcting the orbit shot-by-shot based on five BPMs and the magnetic lattice around the interaction point. However, it does not reduce the measured beam emittance, as their position reading is not precise enough to correct orbit jitter at the wire scanner location correctly. Therefore, we do not include corrections to the wire positions based on BPMs. The reconstructed beam phase space represents the average distribution for many shots including orbit fluctuations. After the calibration of the BPMs in Athos we plan to characterize the effect of orbit jitter to wire scan measurements in detail.
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expert
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When an electron beam scatters off a metallic wire, what particles are produced?
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The particle shower contains mostly electrons, positrons, and X-rays
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Fact
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Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf
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$$ \\sigma ( z ) = \\sqrt { \\beta ( z ) \\varepsilon _ { n } ( z ) / \\gamma ( z ) } , $$ 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 $0 . 1 \\%$ .
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expert
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When an electron beam scatters off a metallic wire, what particles are produced?
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The particle shower contains mostly electrons, positrons, and X-rays
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Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf
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$$ Afterwards, the histogram of the particles’ transported and rotated $x$ coordinates is calculated. Note that the bin width needs to be smaller than the width of the wire, to ensure an accurate convolution with the wire profile. This becomes important when the beam size or beam features are smaller than the wire width. Next, the convolution of the histogram and the wire profile is interpolated linearly to the measured wire positions $\\xi$ . Now, the reconstruction can be directly compared to the measurement: $$ \\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.
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expert
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When an electron beam scatters off a metallic wire, what particles are produced?
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The particle shower contains mostly electrons, positrons, and X-rays
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Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf
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B. ACHIP chamber The ACHIP chamber at SwissFEL is a multi-purpose test chamber, designed and built for DLA research. It is located in the switch-yard of SwissFEL, where the electron beam has an energy of around $3 . 2 \\mathrm { G e V . }$ The electron beam is focused by an in-vacuum quadrupole triplet and matched back by a second symmetric quadrupole triplet. All six magnets can be remotely retracted from the beam line for standard SwissFEL operation. The positioning system allows the alignment of the quadrupoles with respect to the electron beam. The magnetic center of the quadrupole is found by observing and reducing transverse kicks with a downstream screen or beam position monitor. At the center of the chamber a hexapod allows positioning different samples in the electron beam path. Figure 2 shows the interior of the ACHIP chamber including the permanent magnets and the hexapod. Further details about the design of the experimental chamber can be found in [11,12] and the first results of the beam characterization can be found in [17]. C. Nanofabricated wire scanner Nanofabricated wires are installed on the hexapod for the characterization of the focused beam profile. The wire scan device consists of nine free-standing $1 \\mu \\mathrm m$ wide metallic (Au) stripes. The nine radial wires are supported by a spiderweb-shaped structure attached to a silicon frame. A scanning electron microscope image of the wire scanner sample is shown in Fig. 3. We chose nine homogeneously spaced wires for our design, since this configuration allows us to access any wire angle within the tilt limits of the hexapod. The sample was fabricated at the Laboratory for Micro and Nanotechnology at PSI by means of electron beam lithography. The $1 \\mu \\mathrm m$ wide stripes of gold are electroplated on a $2 5 0 ~ \\mathrm { n m }$ thick $\\mathrm { S i } _ { 3 } \\mathrm { N } _ { 4 }$ membrane, which is removed afterwards with a KOH bath. The fabrication process and performance for this type of wire scanner are described in detail in [9]. The hexapod moves the wire scan device on a polygon path to scan each of the nine wires orthogonally through the electron beam. Hereby, projections along different angles $\\mathbf { \\eta } ^ { ( \\theta ) }$ of the transverse electron density can be measured. The two-dimensional transverse beam profile can be obtained using tomographic reconstruction techniques. The hexapod can position the wire scanner within a range of $2 0 \\ \\mathrm { c m }$ along the beam direction $( z )$ . By repeating the wire scan measurement at different locations around the waist, the transverse phase space and emittance of the beam can be inferred.
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expert
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When an electron beam scatters off a metallic wire, what particles are produced?
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The particle shower contains mostly electrons, positrons, and X-rays
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Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf
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A. Resolution limit The ultimate resolution limit of the presented tomographic characterization of the transverse beam profile depends on the roughness of the wire profile. With the current fabrication process, this is on the order of $1 0 0 ~ \\mathrm { { n m } }$ estimated from electron microscope images of the freestanding gold wires. This is one to two orders of magnitude below the resolution of standard profile monitors for ultrarelativistic electron beams (YAG:Ce screens) [5,6]. B. Comparison to other profile monitors The scintillating screens (YAG:Ce) at SwissFEL achieve an optical resolution of $8 \\ \\mu \\mathrm { m }$ , and the smallest measured beam sizes are $1 5 \\ \\mu \\mathrm { m }$ [6]. At the Pegasus Laboratory at UCLA beam sizes down to $5 \\mu \\mathrm { m }$ were measured with a $2 0 \\ \\mu \\mathrm { m }$ thick YAG:Ce screen in combination with an invacuum microscope objective [5]. Optical transition radiation (OTR) based profile monitors are only limited by the optics and camera resolution [23]. At the Accelerator Test Facility 2 at KEK this technique was used to measure a beam size of $7 5 0 ~ \\mathrm { n m }$ [7]. However, OTR profile monitors are not suitable for compressed electron bunches (e.g., at FELs) due to the emission of coherent OTR [24].
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When an electron beam scatters off a metallic wire, what particles are produced?
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The particle shower contains mostly electrons, positrons, and X-rays
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Fact
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Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf
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APPENDIX B: TERMINATION CRITERIONFOR RECONSTRUCTION ALGORITHM The algorithm to reconstruct the phase space from wire scan measurements iteratively approximates the distribution that fits best to all measurements (see Sec. III). The iteration is stopped when a criterion based on the relative change from the current to the previous iteration is reached. We define $p _ { k }$ as the average probability for a particle to be added or removed to the ensemble in iteration $k$ . $$ p _ { k } = \\frac { 1 } { n _ { p } n _ { \\theta } n _ { z } } \\sum _ { i , \\theta , z } \\lvert \\Delta _ { z , \\theta } ^ { i } \\rvert $$ The iteration terminates when the relative change of $p _ { k }$ reaches a tolerance limit $\\tau$ : $$ \\frac { \\left| p _ { k } - p _ { k - 1 } \\right| } { \\left| p _ { k } \\right| } < \\tau $$ For the case of the presented data set $\\tau = 0 . 0 0 5$ is found to provide stable convergence and a consistent solution. Around 110 iterations are required to reach the termination criterion.
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expert
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When an electron beam scatters off a metallic wire, what particles are produced?
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The particle shower contains mostly electrons, positrons, and X-rays
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Fact
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Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf
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We developed a reconstruction algorithm based on a macroparticle distribution (instead of the intensity on grid), where each macroparticle, from now on called particle, represents a point in the four-dimensional phase space. The complexity of this algorithm is proportional to $n _ { p }$ (number of particles) and is independent on the dimension of the reconstruction domain. The particle density is then given by applying a Gaussian kernel to each coordinate of the particle ensemble: $$ 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 } }$ .
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augmentation
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NO
| 0
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Expert
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When does the Aramis gas detector not give shot-to-shot calibrated pulse energy data?
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When the photon energy or the gain voltage on the detector is changed.
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Fact
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[FELFastPulseEnergy]_JSR_30(2023).pdf
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Another component of the gas detector system developed by DESY and used at various facilities, including SwissFEL, is the huge aperture open multiplier (HAMP), which is a large multiplier used for single-shot relative flux measurements that are not an absolute evaluation of the pulse energy. The response of this device to the ions generated from the photoionization depends on the potential that they are operated under, and the energy and charge of the photoionized ions that are impacting the HAMP surface. Furthermore, this response changes with time, as the multiplier coating slowly depletes over years of use. It is theoretically possible to evaluate the absolute single-shot pulse energy from the HAMP measurements if one can characterize the multiplier for every gas type and pressure, photon energy and voltage setting, year after year. Furthermore, the multiplier itself must be set with a voltage that has the signal generated by the ion impact to be in the linear regime. A constant monitoring of the signal amplitude must be implemented that feeds back on the multiplier voltage to ensure the operation of this device in a reliable manner. It was developed to deal with hard X-rays and lower fluxes which are encountered at most hard $\\mathbf { X }$ -ray FEL facilities.
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4
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Yes
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Expert
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When does the Aramis gas detector not give shot-to-shot calibrated pulse energy data?
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When the photon energy or the gain voltage on the detector is changed.
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Fact
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[FELFastPulseEnergy]_JSR_30(2023).pdf
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This manuscript describes the developments in hardware characterization, feedback and monitoring programs, and processing algorithms that allow the photon pulse energy monitor (PBIG) at SwissFEL to deliver absolute pulse energy evaluations on a shot-to-shot basis (Juranic´ et al., 2018). The PBIG is the renamed DESY-developed and constructed pulse energy monitor, and the methods proposed here can be adapted to any similar device at FELs around the world. 2. Measurement setup 2.1. Detector reliability The precursor to effective data processing and evaluation of pulse-resolved pulse energy is the reliability of the input data for this evaluation. The XGMD slow absolute energy measurement must be calibrated against another device, and the fast HAMP measurement has to be operating so it can react linearly to the incoming pulse energies, and hence the data collected for eventual algorithmic processing are not dominated by noise or empty measurements. The XMGD average pulse energy measurements are linear and were calibrated in previous work (Juranic et al., 2019). The copper plate from which the current is measured by a Keithley 6514 calibrated multimeter has a quantum efficiency of 1, and the multimeter has a linear measurement range for current measurements that spans more than ten orders of magnitude. This device provides the calibrated long-scale average signal that will be used to evaluate the shot-to-shot pulse energy from the HAMPs.
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2
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Yes
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Expert
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When does the Aramis gas detector not give shot-to-shot calibrated pulse energy data?
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When the photon energy or the gain voltage on the detector is changed.
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Fact
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[FELFastPulseEnergy]_JSR_30(2023).pdf
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2.2. Algorithm for data-processing The core of the data processing and evaluation of the absolute pulse energy on a shot-to-shot basis is the evaluation of the ratio between the slow signals and the fast signals. The slow absolute evaluation from the XGMD has an integration time of about $1 0 { \\mathrm { ~ s } } .$ , updated every second as the Keithley multimeter updates its readout. The fast signal reads out the relative pulse energy from the integral of the ion peaks at the repetition rate of SwissFEL, up to $1 0 0 \\mathrm { H z }$ . To be able to compare these two evaluations with each other directly on a pulse-by-pulse basis, we first create a rolling buffer of pulseresolved measurements that is as long as or longer than the XGMD evaluation integration time. The rolling buffer always maintains the same number of elements, adding a new element with each new processed FEL pulse, while dropping the oldest element in the buffer. The rolling buffer is updated at the repetition rate of the FEL, and is used to continuously evaluate the conversion constant $C _ { i }$ so that $$ C _ { i } \\ = \\ I _ { \\mathrm { X G M D } } / I _ { \\mathrm { H A M P } } ,
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2
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Yes
| 0
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Expert
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When does the Aramis gas detector not give shot-to-shot calibrated pulse energy data?
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When the photon energy or the gain voltage on the detector is changed.
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Fact
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[FELFastPulseEnergy]_JSR_30(2023).pdf
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$$ where $I _ { \\mathrm { X G M D } }$ and ${ \\cal I } _ { \\mathrm { H A M P } }$ are the evaluations of the XGMD and HAMP signal data in the buffer, respectively. This constant is then used in further evaluations. A weighted average algorithm is used to evaluate the current conversion constant so that $$ C = W C _ { i } + \\left( 1 - W \\right) C _ { i - 1 } , $$ where $W$ is the weighting factor, equal to the period of the FEL divided by the chosen buffer length time constant, and $C _ { i - 1 }$ is the previous conversion constant. A 10 s time constant and $1 0 0 \\mathrm { H z }$ repetition rate would yield a weighting factor of 0.001. The role of this weighting factor and the data buffer is to ensure that the conversion constant between the XGMD and HAMP readouts is not affected by single-shot losses of pulse energies and remains stable unless the relationship between the two devices is altered due to a change in photon energy or multiplier voltage gain. The FEL radiation can vary significantly on a shot-to-shot basis owing to the stochastic nature of the self-amplified spontaneous emission (SASE), so such a large buffer is necessary to establish a suitable conversion constant between the two devices. The last step of the data processing is to evaluate the single pulse energy, which is equal to C IHAMP .
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4
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Yes
| 1
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Expert
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When does the Aramis gas detector not give shot-to-shot calibrated pulse energy data?
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When the photon energy or the gain voltage on the detector is changed.
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Fact
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[FELFastPulseEnergy]_JSR_30(2023).pdf
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Though the setup described is fast, an even better setup would be one where the evaluation of the pulse energy would depend completely on values measured from the HAMPs, their gain voltage and a photon energy. This is theoretically possible, but would require a long-term project to gather sufficient data to correlate these parameters to the absolutely measured pulse energy on a shot-to-shot basis, and a setup that ensures every data point measured is valid. The scheme described in this manuscript creates such a system. The data gathered by the fast pulse energy measurement are currently evaluated using a comparison against the slow pulse energy measurement. However, with enough time and data points, one could use this data to create a machinelearning algorithm that would enable the evaluation of the pulse energy directly, without having to compare the HAMP values with the slow calibrated XGMD signals. In that respect, the effort described here is the first step to eventually create a wholly calibrated fast pulse energy measurement for all possible beam parameters. Acknowledgements The authors would like to thank Florian Lo¨ hl, Nicole Hiller and Sven Reiche for fruitful discussions about the imple mentation and execution of the fast pulse energy measurement, as well as Antonios Foskolos and Mariia Zykova for their help with the measurements.
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4
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Yes
| 1
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IPAC
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When doing tomographic reconstruction, when would it be beneficial to use a macroparticle distribution rather than the intensity on the grid?
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when the number of dimensions is large
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Reasoning
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Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf
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$$ Let $\\mathbf { Q } _ { i }$ represent the $i t h$ tuning parameter and $P _ { i }$ , the ùëñùë°‚Ñé projected distribution function. We define $\\pi ( \\mathbf { X } ) _ { i }$ as: $$ \\pi ( \\mathbf { X } ) _ { i } = P _ { i } ( M ( \\mathbf { X } , \\mathbf { Q } _ { i } ) ) . $$ Defining $\\pi ( \\mathbf { X } )$ is the core of MCMC Tomography. Our initial beam distribution is the resulting distribution created from the Markov Chain once it has reached equilibrium. Angle Calculation Given the transfer map, $M ( \\mathbf { X } , \\mathbf { Q } ) \\colon \\mathbb { R } ^ { 2 } \\to \\mathbb { R } ^ { 2 }$ , projections at location B are projections of the distribution at location A given a certain scaling and rotation [6]. In addition, to allow for complete data acquisition from all angles around the object, one would need to take a projection of at least 180 degrees around the sampled distribution; However, not all beamlines allow for the full range of 180 degrees.
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augmentation
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NO
| 0
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IPAC
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When doing tomographic reconstruction, when would it be beneficial to use a macroparticle distribution rather than the intensity on the grid?
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when the number of dimensions is large
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Reasoning
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Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf
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File Name:BEAM_TOMOGRAPHY_USING_MCMC#U2217.pdf BEAM TOMOGRAPHY USING MCMC A. D. Tran†, Y. Hao, Michigan State University, East Lansing, MI, USA B. Mustapha, Argonne National Laboratory, Argonne, IL, USA Abstract Beam tomography is a method to reconstruct the higher dimensional beam from its lower dimensional projections. Previous methods to reconstruct the beam required large computer memory for high resolution; others needed differential simulations, and others did not consider beam elements’ coupling. This work develops a direct 4D reconstruction algorithm using Markov Chain Monte Carlo (MCMC). INTRODUCTION Tomography is a method to reconstruct a higherdimensional object from its lower-dimensional projections. Beam tomography is defined here as tomography in an accelerator to reconstruct the beam phase space from indirect projection measurements. This is a simple mapping for a two-dimensional reconstruction from a one-dimensional projection, while for a higher-dimensional reconstruction, it can be done indirectly [1]. Current techniques for direct higher-dimension tomography in accelerators use algebraic reconstruction technique (ART) [2], machine learning (ML) [3], or maximum entropy technique (MENT) [4]. ART and MENT are limited by computer memory, while ML uses a differentiable simulation. This paper develops a direct 4D tomography reconstruction using MCMC as an alternative method without these limitations. MCMC TOMOGRAPHY THEORY We will consider a linear system for our study and limit our study to 2D. Beam tomography aims at retrieving the beam distribution in phase space at location A, e.g., $f ( \\mathbf { X } ) =$ $f ( x , x ^ { \\prime } , y , y ^ { \\prime } )$ using the lower dimension measurement at location $ { \\mathbf { B } } , P ( x , y )$ or its projections. Let $M ( \\mathbf { X } , \\mathbf { Q } )$ : $\\mathbb { R } ^ { 3 } \\mathbb { R } ^ { 3 }$ be the transfer map between A and B with $\\mathbf { Q } = \\mathrm { a s }$ the vector of the accelerator tuning parameters such as the strength of quadrupoles and steering magnets.
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augmentation
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NO
| 0
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IPAC
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When doing tomographic reconstruction, when would it be beneficial to use a macroparticle distribution rather than the intensity on the grid?
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when the number of dimensions is large
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Reasoning
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Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf
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$$ We solve for $\\sigma _ { i } j ( 0 )$ using a pseudo inverse. This method can be used separately for the $\\mathbf { \\boldsymbol { x } }$ and y phase spaces and can be applied to the $6 t h$ quad by setting $M _ { 6 } = D _ { 7 } Q _ { 7 } D _ { 6 } Q _ { 6 }$ . Table: Caption: Table 2: Quad Scan Results Body: <html><body><table><tr><td></td><td>Quad 7</td><td>Quad 6</td></tr><tr><td>norm e x cm*mrad</td><td>0.0104</td><td>0.0090</td></tr><tr><td> norm ey cm*mrad</td><td>0.0031</td><td>0.0028</td></tr></table></body></html> We note, in Table 2, that the normalized emittance should be the same since that is invariant. The difference in beam emittance between quad-6 and quad-7 scans gives an estimate of the error of $\\approx 1 0 \\%$ . PRELIMINARY EXPERIMENTAL RESULTS We attempt to apply MCMC Tomography to experimental data. Using set A and set B, as noted in the Data Collection section, we used our algorithm on the first 25 data points of each set, showing the results in Fig. 4 and Table 3. Table: Caption: Table 3: Twiss parameters Body: <html><body><table><tr><td></td><td>Set A</td><td>Set B</td></tr><tr><td>Angular range x °</td><td>158.5</td><td>52.7</td></tr><tr><td>Angular range y°</td><td>149.3</td><td>33.1</td></tr><tr><td>ax</td><td>-1.15</td><td>-0.11</td></tr><tr><td>ay</td><td>-3.66</td><td>-7.04</td></tr><tr><td>βx cm/mrad</td><td>0.42</td><td>0.24</td></tr><tr><td>βy cm/mrad</td><td>1.72</td><td>3.87</td></tr><tr><td>Ex cm*mrad</td><td>0.0043</td><td>0.0078</td></tr><tr><td>Ey cm*mrad</td><td>0.0010</td><td>0.0042</td></tr></table></body></html> We achieved preliminary results on the reconstruction, with the emittance being within the same order of magnitude as that from the quad scan but with a significant error. For one, the auto-encoder analysis for set B resulted in a smaller angular range despite the advantage of a higher transmission. The reconstruction from set B resulted in a larger emittance than set A because its angular range is smaller. More errors may be due to inaccurate beamline model since the quadrupole may have misalignments, or the beam may have shifted during the data collection period. This may explain the slight shifts in Fig. 5.
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augmentation
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NO
| 0
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IPAC
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When doing tomographic reconstruction, when would it be beneficial to use a macroparticle distribution rather than the intensity on the grid?
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when the number of dimensions is large
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Reasoning
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Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf
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$$ Algorithm The new algorithm is based on the use of a fourdimensional array $C$ the ‚Äùnear particle‚Äù-array. The cells in the CEG are identified by $( j , k , l )$ of $C$ with In the next step, the macro-particles are stored in the array $C _ { j , k , l , m }$ according to the following procedure. The particle with index $p$ identifies the CEG cell of indexes $( j _ { p } , k _ { p } , l _ { p } )$ . The indexes $( j _ { p } , k _ { p } , l _ { p } )$ are assigned to the corresponding indexes $( j , k , l )$ of $C _ { j , k , l , m }$ . The number of macro-particles $N _ { c }$ located in the CEG cell identified by (ùëó,ùëò,ùëô) is ùëÅùëê = ùê∂ùëó,ùëò,ùëô,0. When a new particle is identified to this cell, then we update $C _ { j , k , l , 0 }$ to $N _ { c } + 1$ , and assign the particle identification number $p$ to $C _ { j , k , l , ( N _ { c } + 1 ) }$ . The fourth index $m$ range from zero to the number of macro-particles the $\\mathrm { C E G } _ { j , k , l }$ contains. The zeroth cell, if $m = 0$ , in the array $C _ { j , k , l , m }$ contains the number of particles in the according CEG. For $m > 0$ the particle $p$ index is stored.
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augmentation
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NO
| 0
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IPAC
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When doing tomographic reconstruction, when would it be beneficial to use a macroparticle distribution rather than the intensity on the grid?
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when the number of dimensions is large
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Reasoning
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Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf
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$$ where $N$ is the number of particles and $\\boldsymbol { e } _ { s , i }$ is the spherical wave scattered by the particle with index $i$ . Under heterodyne conditions $| \\sum e _ { s , i } | \\ll | e _ { 0 } |$ [8, 10], the last term (homodyne term) can be neglected and the intensity distribution is determined by the heterodyne term $\\sum 2 \\Re \\{ e _ { 0 } e _ { s , i } ^ { * } \\}$ only. It is given by the sum of many singleparticle interference images as in Eq. (6), resulting in a random speckle pattern. Despite such random appearance, Fourier analysis of heterodyne speckles preserves and enables 2D coherence mapping since the power spectrum $I ( { \\bf q } )$ takes the form [8, 10, 12]: $$ I ( \\mathbf { q } ) = N \\cdot I _ { 0 } \\cdot S \\left( \\mathbf { q } \\right) \\cdot \\left| \\mu \\left( \\frac { z \\mathbf { q } } { k } \\right) \\right| ^ { 2 } \\cdot T ( q , z ) ,
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augmentation
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NO
| 0
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IPAC
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When doing tomographic reconstruction, when would it be beneficial to use a macroparticle distribution rather than the intensity on the grid?
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when the number of dimensions is large
|
Reasoning
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Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf
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$$ \\frac { \\sigma ( \\bar { \\rho } ( x _ { I } ) } { \\rho _ { I } } = \\sqrt { \\frac { 2 } { 3 } } \\frac { 1 } { \\sqrt { N _ { P I } } } , $$ where ${ { N _ { P I } } }$ is the number of macroparticles in grid cell $I$ . This density fluctuation level represents the shot noise level of a group of macroparticles from the random sampling of a smooth function without any amplification. Figure 2 shows the final current profile and the relative current fluctuation from the linear deposition of the macroparticles (real number of electrons) after transporting through the strong hadron cooling accelerator in the high precision simulation including both the space-charge e"ect and the CSR e"ect. Here, the relative current fluctuation is defined as $( I _ { s } - I _ { f i t } ) / I _ { f i t }$ . where $I _ { s }$ is the current from simulation and $I _ { f i t }$ the current from fitting using a polynomial function. A relative current modulation with a wavelength of about $2 8 0 \\mu \\mathrm { m }$ is seen from the relative current fluctuation. In order to view this modulation more clearly, Fig. 3 shows the zoom-in current profile and relative current fluctuation for a small section of the electron beam. The relative RMS current fluctuation after removing the modulation is about $7 . 5 \\times 1 0 ^ { - 4 }$ , which is at the same level as the relative current fluctuation from direct random sampling of the smooth fitting function. This suggests that the initial high frequency shot noise level has not been amplified through the nominal strong hadron cooling accelerator. Figure 4 shows the power spectral density of the relative current fluctuation (after removing the $2 8 0 \\mu \\mathrm { m }$ modulation) of the electron beam through the nominal accelerator and of the direct random sampling of the smooth fitting function. The relative current fluctuations in both cases show the same level of power spectral density, which is consistent with the direct relative current fluctuations.
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augmentation
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NO
| 0
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IPAC
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When doing tomographic reconstruction, when would it be beneficial to use a macroparticle distribution rather than the intensity on the grid?
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when the number of dimensions is large
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Reasoning
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Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf
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File Name:BEAM_TOMOGRAPHY_WITH_COUPLING_USING_MAXIMUM_ENTROPY.pdf BEAM TOMOGRAPHY WITH COUPLING USING MAXIMUM ENTROPY TECHNIQUE‚àó A. D. Tranp, Y. Hao, Michigan State University, East Lansing, MI, USA Abstract Current analytical beam tomography methods require an accurate representation of the beam transport matrix between the reconstruction and measurement locations. In addition, these methods need the transport matrix to be linear as the technique depends on a simple mapping of the projections between the two areas, a rotation, and a scaling. This work will explore expanding beam tomography for transversely coupled beam and non-linear beam transports. INTRODUCTION Tomography is a method to reconstruct a higher dimensional distribution from its lower dimensional projections. The basic principle is that multiple projections of a distribution are taken at different orientations, which can then be used to reconstruct the original distribution. Phase space tomography uses a similar technique to reconstruct a beam phase space. It is used in various accelerators such as SNS [1] and TRIUMP [2]. Measurements taken in accelerators are projections of the beam distribution by nature, providing many opportunities to use tomography. However, the use of tomography is limited by the need to accurately map points from the measurement to the reconstruction location. This is usually a linear map, but some methods include particle tracking [3] or machine learning [4]. In this paper, we expand upon these methods to add coupling elements using purely transfer matrices.
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augmentation
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NO
| 0
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expert
|
When doing tomographic reconstruction, when would it be beneficial to use a macroparticle distribution rather than the intensity on the grid?
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when the number of dimensions is large
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Reasoning
|
Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf
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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 ) } .
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4
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NO
| 1
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expert
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When doing tomographic reconstruction, when would it be beneficial to use a macroparticle distribution rather than the intensity on the grid?
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when the number of dimensions is large
|
Reasoning
|
Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf
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In the last step of each iteration, a small random value is added to each coordinate according to the Gaussian kernel defined in Eq. (2). This smoothes the distribution on the scale of $\\rho$ . For the reconstruction of the measurement presented in Sec. IV, $\\rho _ { x , y }$ was set to $8 0 \\ \\mathrm { n m }$ . The iterative algorithm is terminated by a criterion based on the relative change of the average of the difference $\\Delta _ { z , \\theta } ^ { i }$ (further details in Appendix B). The measurement range along $z$ ideally covers the waist and the spacing between measurements is reduced close to the waist, since the phase advance is the largest here. Since the algorithm does not where $P _ { z , \\theta } ^ { m }$ and $P _ { z , \\theta } ^ { r }$ are the measured and reconstructed projections for the current iteration at position $z$ and angle $\\theta$ . The difference between both profiles quantifies over- and underdense regions in the projection. Then, $\\Delta _ { z , \\theta } ( \\xi )$ is interpolated back to the particle coordinates along the wire scan direction, yielding $\\Delta _ { z , \\theta } ^ { i }$ for the ith particle. Afterwards, we calculate the average over all measured $z$ and $\\theta$ :
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4
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NO
| 1
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IPAC
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When doing tomographic reconstruction, when would it be beneficial to use a macroparticle distribution rather than the intensity on the grid?
|
when the number of dimensions is large
|
Reasoning
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Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf
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Solving the VFPE for simulating the bunch longitudinal phase space evolution helps in understanding instabilities caused by factors like beam-beam interactions, wakefield effects, and micro-bunching instabilities. Conversely, phase space density tomography is the inverse problem which is mainly used as an diagnostic tool. It involves reconstructing the distribution of particles in phase space based on measured data. This approach is critical for understanding the real dynamics of a beam. The work of [1] has proved that the longitudinal phase space density of an electron bunch in synchrotrons can be reconstructed utilizing a collection of bunch profile measurements from a single-shot electro-optical (EO) sampling system [2]. The study relies on the progressive rotation of the phase space during turn-by-turn bunch profile measurements and the simplification of the dynamics by a rigid rotation assumption. Considering this, tomography of the phase space density is comparable to a patient rotation in a static CT scanner [3]. Therefore, out-of-the-box tomography methods, for example Filter Back Projection (FBP), can be used for phase-space reconstruction when the phase space remains constant for at least half of the synchrotron oscillation period. However, this approach may encounter challenges when the phase space deforms within each rotation, potentially resulting in significant distortions or inaccuracies in the reconstructed phase space density from the input sequence of measurements.
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4
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NO
| 1
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IPAC
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When doing tomographic reconstruction, when would it be beneficial to use a macroparticle distribution rather than the intensity on the grid?
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when the number of dimensions is large
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Reasoning
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Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf
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INTRODUCTION Phase space tomography [1, 2] is a powerful technique for characterising a beam’s charge distribution in phase space in one or more degrees of freedom. Tomography in two transverse degrees of freedom provides a detailed understanding of the beam substructure, and also allows for characterization of the betatron coupling. However, applying the technique for multiple degrees of freedom generally requires significant computational resources. Storage of a 4D phase space distribution with $N$ data points along each axis requires a data structure with $N ^ { 4 }$ values, and the memory resources required to manipulate the input data can be much larger. High-dimensional tomography methods may be of particular use for characterizing and operating advanced accelerators, such as high-brightness Free Electron Laser (FEL) drivers and injectors for machines using novel acceleration methods. Recent simulation work [3, 4] has demonstrated a technique for 5D tomography, revealing the transverse phase space as a function of longitudinal position. Techniques leading to a reduction in the computational resources required for high-dimensional tomography are therefore of widespread interest. Tomography Section (3.36 m) Photoinjector + Laser S-Baud Linac =I Quadrupole YAG Screen RF Structure Beam Dump In principle, images can be stored in a compressed form (for example, as discrete cosine transforms) to reduce the size of the data structures involved in tomography, while retaining sufficient information to reconstruct the phase space to a good resolution. However, conventional tomography algorithms are formulated on the basis that the input data are direct projections of the initial phase space (e.g. beam images obtained for a range of betatron phase advances). Therefore, it is not obvious how compressed data can be used in the context of an established tomography algorithm.
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5
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NO
| 1
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IPAC
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When doing tomographic reconstruction, when would it be beneficial to use a macroparticle distribution rather than the intensity on the grid?
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when the number of dimensions is large
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Reasoning
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Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf
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RESULTS The error is compared to the original and reconstructed distribution using the Kullback–Leibler (KL) divergence. As seen in Figure 3, the error decreases as the number of samples and the number of algorithm iterations increases. Compared to Figure 4, the model converges better using a rotation matrix since it constrains the particles within the grid. When using an FRIB-like lattice, we have scaling and shearing in 4D. This results in noisier projections and projections outside our grid, leading to the method failing after a certain number of samples, as seen in Figure 4. NONLINEARITIES The method presented in the paper can be expanded to include nonlinearities by using the square matrix method [11] to approximate the mapping between the reconstructed Gridesize = 32 Gridesize = 645040KL-err.2 KL-error1.05： 28 ： 1.5 1.2010 · ： ： ： 05 10 15 5 10 15iters iters Gridesize $= 3 2$ Gridesize $= 6 4$ 1 1I S40 | S 1 L 1 0 | | ： · 6 ： · 44 4.810三 营 1 三 =00 5 10 15 20 0 5 10 15 20iters iters and measurement locations. The square matrix method has been shown to approximate the inverse of a Hénon map, which represents a linear lattice with a single sextupole kick [12]. An inverse by this method is not valid everywhere but exists within its dynamic aperture enabling our tomography method to converge if all particles stayed within it. This will be the subject of future research.
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when the number of dimensions is large
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Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf
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ACKNOWLEDGMENTS We would like to express our gratitude to the SwissFEL operations crew, the PSI expert groups, and the entire ACHIP collaboration for their support with these experiments. We would like to thank Thomas Schietinger for careful proofreading of the manuscript. This research is supported by the Gordon and Betty Moore Foundation through Grant No. GBMF4744 (ACHIP) to Stanford University. APPENDIX A: ERROR ESTIMATION 1. Position errors The uncertainty of the position of the wire scanner with respect to the electron beam is affected by the readout precision of the hexapod $( < 1 ~ \\mathrm { n m } )$ , vibrational motion of the hexapod $\\phantom { + } < 1 0 ~ \\mathrm { { n m } } )$ and position jitter of the electron beam, which at SwissFEL is typically a few-percent of the beam size. The orbit of the electron beam is measured with BPMs along the accelerator. Unfortunately, the BPMs along the Athos branch of SwissFEL have not been calibrated (the measurement took place during the commissioning phase of Athos). Nevertheless, we tried correcting the orbit shot-by-shot based on five BPMs and the magnetic lattice around the interaction point. However, it does not reduce the measured beam emittance, as their position reading is not precise enough to correct orbit jitter at the wire scanner location correctly. Therefore, we do not include corrections to the wire positions based on BPMs. The reconstructed beam phase space represents the average distribution for many shots including orbit fluctuations. After the calibration of the BPMs in Athos we plan to characterize the effect of orbit jitter to wire scan measurements in detail.
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When doing tomographic reconstruction, when would it be beneficial to use a macroparticle distribution rather than the intensity on the grid?
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when the number of dimensions is large
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Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf
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APPENDIX B: TERMINATION CRITERIONFOR RECONSTRUCTION ALGORITHM The algorithm to reconstruct the phase space from wire scan measurements iteratively approximates the distribution that fits best to all measurements (see Sec. III). The iteration is stopped when a criterion based on the relative change from the current to the previous iteration is reached. We define $p _ { k }$ as the average probability for a particle to be added or removed to the ensemble in iteration $k$ . $$ p _ { k } = \\frac { 1 } { n _ { p } n _ { \\theta } n _ { z } } \\sum _ { i , \\theta , z } \\lvert \\Delta _ { z , \\theta } ^ { i } \\rvert $$ The iteration terminates when the relative change of $p _ { k }$ reaches a tolerance limit $\\tau$ : $$ \\frac { \\left| p _ { k } - p _ { k - 1 } \\right| } { \\left| p _ { k } \\right| } < \\tau $$ For the case of the presented data set $\\tau = 0 . 0 0 5$ is found to provide stable convergence and a consistent solution. Around 110 iterations are required to reach the termination criterion.
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When doing tomographic reconstruction, when would it be beneficial to use a macroparticle distribution rather than the intensity on the grid?
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when the number of dimensions is large
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Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf
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At the SLAC Final Focus Test Beam experiment a laserCompton monitor was used to characterize a $7 0 \\ \\mathrm { n m }$ wide beam along one dimension [25]. The cost and complexity of this system, especially for multiangle measurements, are its main drawbacks. Concerning radiation hardness of the nanofabricated wire scanner, tests with a single wire and a bunch charge of $2 0 0 \\ \\mathrm { p C }$ at a beam energy of $3 0 0 \\mathrm { M e V }$ at SwissFEL did not show any sign of degradation after repeated measurements [9]. VI. CONCLUSION In summary, we have presented and validated a novel technique for the reconstruction of the transverse phase space of a strongly focused, ultrarelativistic electron beam. The method is based on a series of wire scans at different angles and positions along the waist. An iterative tomographic algorithm has been developed to reconstruct the transverse phase space. The technique is validated with experimental data obtained in the ACHIP chamber at SwissFEL. The method could be applied to other facilities and experiments, where focused high-brightness electron beams need to be characterized, for instance at plasma acceleration or DLA experiments for matching of an externally injected electron beam, emittance measurements at future compact low-emittance FELs [3], or for the characterization of the final-focus system at a high-energy collider test facility. For the latter application, the damage threshold of the free-standing nano-fabricated gold wires needs to be identified and radiation protection for the intense shower of scattered particles needs to be considered. Nevertheless, the focusing optics could be characterized with the presented method using a reduced bunch charge.
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When doing tomographic reconstruction, when would it be beneficial to use a macroparticle distribution rather than the intensity on the grid?
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when the number of dimensions is large
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Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf
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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 }$ .
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When doing tomographic reconstruction, when would it be beneficial to use a macroparticle distribution rather than the intensity on the grid?
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Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf
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V. DISCUSSION The reconstructed phase space represents the average distribution of many shots, since shot-to-shot fluctuations in the density cannot be characterized with multishot measurements like wire scans. Errors induced by total bunch charge fluctuations and position jitter of the electron beam could be corrected for by evaluating beam-synchronous BPM data. Since the BPMs in the Athos branch were still uncalibrated, their precision was insufficient to correct orbit jitter in our measurement. This issue is considered further in Appendix A. The expected waist is located at the center of the chamber $z = 0 \\mathrm { c m } )$ , whereas the reconstructed waist is found $6 . 2 \\mathrm { c m }$ downstream. In addition, the $\\beta$ -function at the waist $( \\beta ^ { * } )$ was measured to be around $3 . 6 \\ \\mathrm { c m }$ in both planes, which is in disagreement with the design optics $( \\beta _ { x } ^ { * } = 1 ~ \\mathrm { c m }$ , $\\beta _ { y } ^ { * } = 1 . 8 ~ \\mathrm { c m } ,$ ). This indicates that the beam is mismatched at the chamber entrance and improving the matching of the electron beam to the focusing lattice could provide even smaller (submicrometer) beams in the ACHIP chamber.
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when the number of dimensions is large
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Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf
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File Name:Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf Electron beam transverse phase space tomography using nanofabricated wire scanners with submicrometer resolution Benedikt Hermann ,1,3,\\* Vitaliy A. Guzenko,1 Orell R. Hürzeler,1 Adrian Kirchner,2 Gian Luca Orlandi ,1 Eduard Prat ,1 and Rasmus Ischebeck1 1Paul Scherrer Institut, 5232 Villigen PSI, Switzerland 2Friedrich-Alexander-Universität Erlangen-Nürnberg, 91054 Erlangen, Germany 3Institute of Applied Physics, University of Bern, 3012 Bern, Switzerland (Received 27 October 2020; accepted 28 January 2021; published 15 February 2021) Characterization and control of the transverse phase space of high-brightness electron beams is required at free-electron lasers or electron diffraction experiments for emittance measurement and beam optimization as well as at advanced acceleration experiments. Dielectric laser accelerators or plasma accelerators with external injection indeed require beam sizes at the micron level and below. We present a method using nano-fabricated metallic wires oriented at different angles to obtain projections of the transverse phase space by scanning the wires through the beam and detecting the amount of scattered particles. Performing this measurement at several locations along the waist allows assessing the transverse distribution at different phase advances. By applying a novel tomographic algorithm the transverse phase space density can be reconstructed. Measurements at the ACHIP chamber at SwissFEL confirm that the transverse phase space of micrometer-sized electron beams can be reliably characterized using this method.
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When doing tomographic reconstruction, when would it be beneficial to use a macroparticle distribution rather than the intensity on the grid?
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when the number of dimensions is large
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Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf
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B. ACHIP chamber The ACHIP chamber at SwissFEL is a multi-purpose test chamber, designed and built for DLA research. It is located in the switch-yard of SwissFEL, where the electron beam has an energy of around $3 . 2 \\mathrm { G e V . }$ The electron beam is focused by an in-vacuum quadrupole triplet and matched back by a second symmetric quadrupole triplet. All six magnets can be remotely retracted from the beam line for standard SwissFEL operation. The positioning system allows the alignment of the quadrupoles with respect to the electron beam. The magnetic center of the quadrupole is found by observing and reducing transverse kicks with a downstream screen or beam position monitor. At the center of the chamber a hexapod allows positioning different samples in the electron beam path. Figure 2 shows the interior of the ACHIP chamber including the permanent magnets and the hexapod. Further details about the design of the experimental chamber can be found in [11,12] and the first results of the beam characterization can be found in [17]. C. Nanofabricated wire scanner Nanofabricated wires are installed on the hexapod for the characterization of the focused beam profile. The wire scan device consists of nine free-standing $1 \\mu \\mathrm m$ wide metallic (Au) stripes. The nine radial wires are supported by a spiderweb-shaped structure attached to a silicon frame. A scanning electron microscope image of the wire scanner sample is shown in Fig. 3. We chose nine homogeneously spaced wires for our design, since this configuration allows us to access any wire angle within the tilt limits of the hexapod. The sample was fabricated at the Laboratory for Micro and Nanotechnology at PSI by means of electron beam lithography. The $1 \\mu \\mathrm m$ wide stripes of gold are electroplated on a $2 5 0 ~ \\mathrm { n m }$ thick $\\mathrm { S i } _ { 3 } \\mathrm { N } _ { 4 }$ membrane, which is removed afterwards with a KOH bath. The fabrication process and performance for this type of wire scanner are described in detail in [9]. The hexapod moves the wire scan device on a polygon path to scan each of the nine wires orthogonally through the electron beam. Hereby, projections along different angles $\\mathbf { \\eta } ^ { ( \\theta ) }$ of the transverse electron density can be measured. The two-dimensional transverse beam profile can be obtained using tomographic reconstruction techniques. The hexapod can position the wire scanner within a range of $2 0 \\ \\mathrm { c m }$ along the beam direction $( z )$ . By repeating the wire scan measurement at different locations around the waist, the transverse phase space and emittance of the beam can be inferred.
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Where is the ACHIP chamber located in SwissFEL?
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 It is located in the switch-yard to the Athos beamline
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Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf
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VACUUM CHAMBERS DESIGN About 500 vacuum chambers of length ranging between 150 and $1 5 0 0 \\mathrm { m m }$ are needed for the 12 arcs. The chambers are assembled together with flat silver-plated copper gaskets (VATseal type), having sealing lips protruding by $2 0 0 \\mu \\mathrm { m }$ and which deform to roughly $1 5 0 ~ { \\mu \\mathrm { m } }$ after tightening, in between. The main chamber types are described in this section. Bending Magnet Chambers The most complicated chambers of the arcs, in terms of fabrication, are the dipole magnet chambers (CB series). Most of these chambers are produced in-house and the rest of the arc chambers are provided by the company FMB GmbH [7]. The inner cross section portion of the vacuum chambers, in which the electron beam travels, has an octagonal shape of $1 8 ~ \\mathrm { m m }$ inner diameter and a minimum of $1 \\mathrm { m m }$ wall thickness (Fig. 3). This cross-sectional area is 4 times smaller in comparison to SLS1, significantly increasing the Synchrotron Radiation (SR) power deposition on surfaces. An antechamber leads from the octagonal chamber by a slit with a $3 \\ \\mathrm { m m }$ height allowing the dipole-generated SR to escape. A slit with a $1 0 ~ \\mathrm { m m }$ height in the first dipole chamber of every arc allows undulator light originating farther away to be extracted. This slit height corresponds to a maximum vertical opening angle of 1 mrad.
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 It is located in the switch-yard to the Athos beamline
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Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf
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The last critical system for the ICS-IP chamber is the vacuum system. There are three Pfeiffer turbopumps mounted on the sides of the chamber that create a UHV environment inside the chamber that is ${ \\sim } 1 0 ^ { - 8 }$ torr. Figure 2 shows a CAD representation of the exterior of the ICS-IP chamber and how the cameras, turbopumps, and UHV feedthroughs are secured to the chamber. Chamber Design & Installation The ICS-IP vacuum chamber was designed by the by the CXFEL team and fabricated by Kurt J. Lesker. Detailed dimensional drawings for every panel of the chamber were provided to Kurt J. Lesker with a suggested welding sequence of the panels. The acceptable tolerances were discussed and agreed upon with the manufacturer. All of the individual vacuum chamber panels were made with 316 stainless steel and the tunnel section was made with 316LN stainless steel. The tunnel is encompassed by a large dipole magnet; therefore, 316LN stainless steel was selected for its nonmagnetic properties to minimize any perturbations to the magnetic field created by the dipole magnet. The chamber was designed with removable lids and flange ports to allow for easy installation of the internal components. Figure 3 shows the lids and flange ports that can be removed and installed on the chamber.
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 It is located in the switch-yard to the Athos beamline
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Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf
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INTRODUCTION SwissFEL is a compact cost-effective FEL driven by a low energy $( 5 . 8 \\mathrm { G e V } )$ , low charge $( 1 0 ~ \\mathrm { p C } - 2 0 0 ~ \\mathrm { p C } )$ and low-emittance electron beam, which produces hard X-rays with pulse energies above $1 \\mathrm { m J }$ , pulse duration of $\\leq 1 - 3 0$ fs and jitter requirements for the electron beam below 10 fs [1]. To meet the stringent requirements for high sensitivity and timing stability, four Bunch Arrival-Time Monitors (BAM) based on electro-optical detection scheme [2] have been installed. The principle is illustrated in Fig. 1. A pulse train from a mode-locked laser is distributed via length-stabilized single-mode fiber links with dispersion compensation to counteract the pulse broadening. The arrival-time is encoded in the amplitude of one reference laser pulse in a Mach-Zehnder electro-optical modulator (EOM). The electron bunch produces a fast transient in a pick-up, which is sampled at its zero crossing by the stable optical reference signal. The BAMs at the location of the laser heater (injector section) and at LINAC1 (upstream of the second bunch compressor) are routinely used during SwissFEL operation. Two further BAMs, near the energy collimator and downstream of the hard X-ray undulator line (BAM1 and BAM2 on Fig. 2) do not have stabilized optical links. They are used as a testbed in the current correlation measurements. All four systems are equally built [3, 4].
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 It is located in the switch-yard to the Athos beamline
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Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf
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SwissFEL presents multiple advantages as the host facility of the ${ \\bf P } ^ { 3 }$ experiment. First and foremost, the SwissFEL linac can produce $6 \\mathrm { G e V } \\mathrm { e } ^ { - }$ beams, corresponding to the nominal drive energy of FCC-ee, and has the required room and infrastructure for a relatively large installation like a $\\mathrm { e ^ { + } }$ source. Table 1 compares the baseline drive $\\mathrm { e } ^ { - }$ beam parameters of ${ \\mathrm { P } } ^ { 3 }$ and FCC-ee. Most parameters are equivalent since the same beam dynamics behavior is desired in both facilities. However, due to the radiation protection limits of SwissFEL, the differences are prominent in terms of bunch charge, repetition rate and the number of bunches per pulse. A dedicated radiation protection bunker will be built inside the SwissFEL tunnel as additional protection for personnel and nearby accelerator equipment. Table: Caption: Table 1: Primary e- of FCC-ee Linac and SwissFEL Body: <html><body><table><tr><td></td><td>FCC-ee [6]</td><td>p3</td></tr><tr><td>Energy [GeV]</td><td>6</td><td></td></tr><tr><td>Ot [ps]</td><td>3.33</td><td></td></tr><tr><td>Ox,Oy [mm]</td><td>0.5</td><td></td></tr><tr><td>Target length [mm]</td><td>17.5</td><td></td></tr><tr><td>Qbunch [nC]</td><td>1.7 - 2.4</td><td>0.201</td></tr><tr><td>Reptition rate [Hz]</td><td>200</td><td>11</td></tr><tr><td>Bunches per pulse</td><td>2</td><td>11</td></tr></table></body></html> PHYSICS STUDIES According to Geant4 [7] simulations, the $\\mathrm { e + }$ production scheme described in Table 1 will yield a secondary $\\mathrm { e + }$ distribution of $2 7 5 4 ~ \\mathrm { p C }$ , which amounts to 13.77 secondary $\\mathrm { e + }$ per primary e-. At the target exit face, the secondary $\\mathrm { e + }$ beam will have a moderate beam size $( \\sigma _ { x } ~ \\approx 1 ~ \\mathrm { { m m } } )$ ) and bunch lentgh $( \\sigma _ { t } ~ \\approx 3 . 3$ ps), but a very high energy spread $( \\Delta \\mathrm { E } _ { R M S } \\approx 1 1 5 ~ \\mathrm { M e V } )$ and transverse momentum $( \\sigma _ { p x } \\approx 8 \\mathrm { M e V / c } )$ .
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Where is the ACHIP chamber located in SwissFEL?
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 It is located in the switch-yard to the Athos beamline
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Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf
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File Name:CXLS_INVERSE_COMP_TON_SCATTERING.pdf CXLS INVERSE COMPTON SCATTERING INTERACTION POINT CHAMBER\\* A. Gardeck†, A. Dupre, A. Semaan, J. Houkal, D. Smith, H. Loos, R. Rednour, J. Vela, R. Kaindl, S. Teitelbaum, W. S. Graves, M. R. Holl‡, Arizona State University, Tempe, AZ, USA Abstract The Inverse Compton Scattering Interaction Point (ICS-IP) vacuum chamber provides a UHV environment where the electron and IR laser beams are overlapped in space and time to generate hard x-rays between 4 and 20 keV. The chamber has over two dozen motorized stages that position YAG screens with ${ \\sim } 1 0 \\ \\mathrm { n m }$ precision utilizing the EPICS framework for instrumentation interface. Using agile programming methods, MATLAB GUIs were created to control all the motors inside the chamber. Each YAG screen has a linear array of laser drilled holes ranging from microns to millimeters (depending on the diameter of the beam being measured), which are imaged by cameras mounted on top of the chamber. An IR lens focuses a $\\sim 3 0 \\mathrm { m m }$ collimated laser beam to ${ \\sim } 1 0 \\mu \\mathrm { m }$ with a ${ \\sim } 2 1 0 \\mathrm { m m }$ focal length. The lens is secured to a 3-axis stage assembly to enable precise beam axis positioning. Beam pointing to the interaction point (IP) is adjusted using a motorized IR mirror. The focused IR laser pulse is convolved with an electron bunch at the IP to generate $\\mathbf { \\boldsymbol { x } }$ -ray pulses at $1 \\mathrm { { k H z } }$ . A Montel x-ray optic, mounted on a six degree of freedom Nano-positioner, receives and collimates each divergent x-ray pulse coming from the IP. When freely diverging x-rays are desired, the Montel x-ray optic is retracted from the beam path. We present the systems integration of the chamber, diagnostics elements, and control software and comment on its performance during commissioning.
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 It is located in the switch-yard to the Athos beamline
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Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf
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RF−stationsBACCA D−chicane RF−station movable D−cFhLicAanSeH0 RF−stations old seed laser FLASH1 beam dump THz undulator 1 1 □ T 0= 中 ilsnanyesjsewetrcetmor RF g1u.n3 (G1H.3zGSHCzR/wFarm) matchuipngraded 1.3GHz SCRmFatching (w/ up1g.r3.GrfH−zd iSstCriRbFution) XSeed expemriamtcehnitng FLASHA2PPLE−III undulatorbeam dump ‘‘Albert Einstein’’ 560 MeV to 1360 MeV FEL user halls 5.6 MeV 143 MeV 560 MeV pre−ionization laser (25 TW) ‘‘Kai Siegbahn’’ FLASHForward Exp. PolariX−TDS FLASH3 PETRA of a laser trip, the other laser can take over its sub-train with still reasonable variability. FLASH is usually operated with bunch repetition frequencies of $4 0 \\mathrm { k H z }$ to 1 MHz. But the lasers are capable of creating full-length trains with bunch repetition frequency of $3 \\mathrm { M H z }$ at $1 0 \\mathrm { { H z } }$ . The superconducting L-band modules (ACC1/2/3/4/5/6/7) are strings of 8 nine-cell niobium $1 . 3 \\mathrm { G H z }$ cavities embedded in a common cryostate with separate couplers per cavity and an embedded superconducting quadrupole/steerer pack. The 3rd harmonic linearizer (ACC39) is a string of 4 scaled down nine-cell niobium $3 . 9 \\mathrm { G H z }$ cavities in a seperate customized cryostate. These modules are from various phases of the development of SRF at DESY and are potentially all slightly different in all imaginable aspects. Hence the distribution of the modules puts certain constraints on the achievable $E$ -profile and the beamoptics. The original modules ACC2 and ACC3 have been replaced by high-gradient modules which where carefully refurbished spares from the XFEL production line [9, 24]. They constitute the main part of the FLASH $2 0 2 0 +$ energy upgrade. The laser-heater and the 1st bunch compressor are operated at $1 4 3 \\mathrm { M e V }$ and the 2nd bunch compressor is usually operated at ${ 5 6 0 } \\mathrm { M e V }$ , but for specialized operation at highest energies can be operated above ${ 5 8 0 } \\mathrm { M e V }$ due to the excellent performance of ACC2/3. The laser heater consists of a small dedicated in-coupling chicane for the $5 3 2 \\mathrm { n m }$ laserheater laser, and an undulator for the laser/bunch interaction, both in the dispersion free region downstream of ACC39. The over-folding of the $E$ -modulation is performed in CBC1. CBC1 is a conventional 4-dipole chicane with flat vacuum chamber and variable $M _ { 5 6 }$ from $1 2 0 \\mathrm { m m }$ to $2 5 0 \\mathrm { m m }$ , run routinely in 2023/24 between $1 5 0 \\mathrm { m m }$ to $1 7 0 \\mathrm { m m }$ . CBC2 is a 4-dipole chicane with round vacuum chamber and corrector quadrupoles/skew-quadrupoles to ameliorate transverse-tolongitudinal correlations inside the bunches [21, 22]. Both chicanes are followed by optical matching sections to rematch bunches into the design optical functions and measure the transverse bunch emittances [11]. The remaining 4 SRF modules, driven pairwise by independent RF stations, constitute the FLASH “main linac” and are capable of accelerating the beam from ${ 5 8 5 } \\mathrm { M e V }$ to $1 3 6 5 \\mathrm { M e V }$
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Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf
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• The deuteron beam impinges on a liquid lithium target flowing at high speeed $( 1 5 \\mathrm { m } \\mathrm { s } ^ { - 1 } ,$ ) and high temperature $( 3 0 0 ^ { \\circ } \\mathrm { C } )$ . This serves to absorb the 5 MW beam power, as well as permitting an upgrade to a second accelerator, with a total maximum power of $1 0 \\mathrm { M W }$ . The main lithium loop evacuates the heat and a purification system controls the impurities and corrosion in the loop (Fig. 4). In order to avoid the potential direct contact between lithium and water, the heat is transferred outside by a series combination of three isolated cooling loops: a lithium-oil heat exchanger, an oil-oil heat exchanger, and finally an oil-water one. • The main experimental area of the facility is located in the high neutron flux area just behind the lithium target (Fig. 5). There, a High Flux Test Module (HFTM) is placed, containing several types of material specimen under test with a fusion-prototypic neutron field. Both the HFTM and the liquid lithium target are enclosed within the so-called Test Cell, which provides shielding and a confinement barrier, interfacing with the building. Both target and modules are to be removed periodically. In addition, other test modules are presently under consideration, either for other fusion or non-fusion applications. In addition to the test cell area, some of those could be located in a room downstream the main neutron flux, or in an area in the floor below the accelerator, using a parasitic fraction of less than $0 . 1 \\%$ of the HEBT beam.
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expert
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Where is the ACHIP chamber located in SwissFEL?
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 It is located in the switch-yard to the Athos beamline
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Fact
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Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf
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ACKNOWLEDGMENTS We would like to express our gratitude to the SwissFEL operations crew, the PSI expert groups, and the entire ACHIP collaboration for their support with these experiments. We would like to thank Thomas Schietinger for careful proofreading of the manuscript. This research is supported by the Gordon and Betty Moore Foundation through Grant No. GBMF4744 (ACHIP) to Stanford University. APPENDIX A: ERROR ESTIMATION 1. Position errors The uncertainty of the position of the wire scanner with respect to the electron beam is affected by the readout precision of the hexapod $( < 1 ~ \\mathrm { n m } )$ , vibrational motion of the hexapod $\\phantom { + } < 1 0 ~ \\mathrm { { n m } } )$ and position jitter of the electron beam, which at SwissFEL is typically a few-percent of the beam size. The orbit of the electron beam is measured with BPMs along the accelerator. Unfortunately, the BPMs along the Athos branch of SwissFEL have not been calibrated (the measurement took place during the commissioning phase of Athos). Nevertheless, we tried correcting the orbit shot-by-shot based on five BPMs and the magnetic lattice around the interaction point. However, it does not reduce the measured beam emittance, as their position reading is not precise enough to correct orbit jitter at the wire scanner location correctly. Therefore, we do not include corrections to the wire positions based on BPMs. The reconstructed beam phase space represents the average distribution for many shots including orbit fluctuations. After the calibration of the BPMs in Athos we plan to characterize the effect of orbit jitter to wire scan measurements in detail.
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1
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NO
| 0
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expert
|
Where is the ACHIP chamber located in SwissFEL?
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 It is located in the switch-yard to the Athos beamline
|
Fact
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Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf
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V. DISCUSSION The reconstructed phase space represents the average distribution of many shots, since shot-to-shot fluctuations in the density cannot be characterized with multishot measurements like wire scans. Errors induced by total bunch charge fluctuations and position jitter of the electron beam could be corrected for by evaluating beam-synchronous BPM data. Since the BPMs in the Athos branch were still uncalibrated, their precision was insufficient to correct orbit jitter in our measurement. This issue is considered further in Appendix A. The expected waist is located at the center of the chamber $z = 0 \\mathrm { c m } )$ , whereas the reconstructed waist is found $6 . 2 \\mathrm { c m }$ downstream. In addition, the $\\beta$ -function at the waist $( \\beta ^ { * } )$ was measured to be around $3 . 6 \\ \\mathrm { c m }$ in both planes, which is in disagreement with the design optics $( \\beta _ { x } ^ { * } = 1 ~ \\mathrm { c m }$ , $\\beta _ { y } ^ { * } = 1 . 8 ~ \\mathrm { c m } ,$ ). This indicates that the beam is mismatched at the chamber entrance and improving the matching of the electron beam to the focusing lattice could provide even smaller (submicrometer) beams in the ACHIP chamber.
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2
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NO
| 0
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expert
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Where is the ACHIP chamber located in SwissFEL?
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 It is located in the switch-yard to the Athos beamline
|
Fact
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Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf
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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:
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4
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NO
| 1
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expert
|
Where is the ACHIP chamber located in SwissFEL?
|
 It is located in the switch-yard to the Athos beamline
|
Fact
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Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf
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A. Resolution limit The ultimate resolution limit of the presented tomographic characterization of the transverse beam profile depends on the roughness of the wire profile. With the current fabrication process, this is on the order of $1 0 0 ~ \\mathrm { { n m } }$ estimated from electron microscope images of the freestanding gold wires. This is one to two orders of magnitude below the resolution of standard profile monitors for ultrarelativistic electron beams (YAG:Ce screens) [5,6]. B. Comparison to other profile monitors The scintillating screens (YAG:Ce) at SwissFEL achieve an optical resolution of $8 \\ \\mu \\mathrm { m }$ , and the smallest measured beam sizes are $1 5 \\ \\mu \\mathrm { m }$ [6]. At the Pegasus Laboratory at UCLA beam sizes down to $5 \\mu \\mathrm { m }$ were measured with a $2 0 \\ \\mu \\mathrm { m }$ thick YAG:Ce screen in combination with an invacuum microscope objective [5]. Optical transition radiation (OTR) based profile monitors are only limited by the optics and camera resolution [23]. At the Accelerator Test Facility 2 at KEK this technique was used to measure a beam size of $7 5 0 ~ \\mathrm { n m }$ [7]. However, OTR profile monitors are not suitable for compressed electron bunches (e.g., at FELs) due to the emission of coherent OTR [24].
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augmentation
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NO
| 0
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expert
|
Where is the ACHIP chamber located in SwissFEL?
|
 It is located in the switch-yard to the Athos beamline
|
Fact
|
Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf
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$$ \\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 \\%$ .
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augmentation
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NO
| 0
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expert
|
Where is the ACHIP chamber located in SwissFEL?
|
 It is located in the switch-yard to the Athos beamline
|
Fact
|
Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf
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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.
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augmentation
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NO
| 0
|
expert
|
Where is the ACHIP chamber located in SwissFEL?
|
 It is located in the switch-yard to the Athos beamline
|
Fact
|
Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf
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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).
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augmentation
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NO
| 0
|
expert
|
Where is the ACHIP chamber located in SwissFEL?
|
 It is located in the switch-yard to the Athos beamline
|
Fact
|
Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf
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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.
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augmentation
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NO
| 0
|
expert
|
Where is the ACHIP chamber located in SwissFEL?
|
 It is located in the switch-yard to the Athos beamline
|
Fact
|
Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf
|
In the last step of each iteration, a small random value is added to each coordinate according to the Gaussian kernel defined in Eq. (2). This smoothes the distribution on the scale of $\\rho$ . For the reconstruction of the measurement presented in Sec. IV, $\\rho _ { x , y }$ was set to $8 0 \\ \\mathrm { n m }$ . The iterative algorithm is terminated by a criterion based on the relative change of the average of the difference $\\Delta _ { z , \\theta } ^ { i }$ (further details in Appendix B). The measurement range along $z$ ideally covers the waist and the spacing between measurements is reduced close to the waist, since the phase advance is the largest here. Since the algorithm does not where $P _ { z , \\theta } ^ { m }$ and $P _ { z , \\theta } ^ { r }$ are the measured and reconstructed projections for the current iteration at position $z$ and angle $\\theta$ . The difference between both profiles quantifies over- and underdense regions in the projection. Then, $\\Delta _ { z , \\theta } ( \\xi )$ is interpolated back to the particle coordinates along the wire scan direction, yielding $\\Delta _ { z , \\theta } ^ { i }$ for the ith particle. Afterwards, we calculate the average over all measured $z$ and $\\theta$ :
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augmentation
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NO
| 0
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expert
|
Where is the ACHIP chamber located in SwissFEL?
|
 It is located in the switch-yard to the Athos beamline
|
Fact
|
Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf
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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 } . $$ where we choose $\\rho _ { x ^ { \\prime } , y ^ { \\prime } } = \\rho _ { x , y } / z _ { \\mathrm { m a x } }$ , with $z _ { \\mathrm { m a x } }$ the range of the measurement along z. Choosing the right kernel size is important for an appropriate reconstruction of the beam. It is dimensioned such that $\\rho _ { x , x ^ { \\prime } , y , y ^ { \\prime } }$ represents the length scale below which we expect only random fluctuations in the particle distribution, which are not reproducible from shot to shot. Note that despite the Gaussian kernel, this reconstruction does not assume a Gaussian distribution of the beam, but is able to reconstruct arbitrary distributions that vary on a length scale given by $\\rho _ { x , x ^ { \\prime } , y , y ^ { \\prime } }$ .
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augmentation
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NO
| 0
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expert
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Where is the ACHIP chamber located in SwissFEL?
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 It is located in the switch-yard to the Athos beamline
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Fact
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Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf
|
APPENDIX B: TERMINATION CRITERIONFOR RECONSTRUCTION ALGORITHM The algorithm to reconstruct the phase space from wire scan measurements iteratively approximates the distribution that fits best to all measurements (see Sec. III). The iteration is stopped when a criterion based on the relative change from the current to the previous iteration is reached. We define $p _ { k }$ as the average probability for a particle to be added or removed to the ensemble in iteration $k$ . $$ p _ { k } = \\frac { 1 } { n _ { p } n _ { \\theta } n _ { z } } \\sum _ { i , \\theta , z } \\lvert \\Delta _ { z , \\theta } ^ { i } \\rvert $$ The iteration terminates when the relative change of $p _ { k }$ reaches a tolerance limit $\\tau$ : $$ \\frac { \\left| p _ { k } - p _ { k - 1 } \\right| } { \\left| p _ { k } \\right| } < \\tau $$ For the case of the presented data set $\\tau = 0 . 0 0 5$ is found to provide stable convergence and a consistent solution. Around 110 iterations are required to reach the termination criterion.
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augmentation
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NO
| 0
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expert
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Where is the ACHIP chamber located in SwissFEL?
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 It is located in the switch-yard to the Athos beamline
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Fact
|
Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf
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The ensemble of particles is iteratively optimized so that their projections match with the set of measured projections. The algorithm starts from a homogeneous particle distribution. One iteration consists of the following operations. (i) Transport $T ( z )$ (ii) Rotation $R ( \\theta )$ (iii) Histogram of the transported and rotated coordinates (iv) Convolution with wire profile (v) Interpolation to measured wire positions (vi) Comparison of reconstruction and measurement (vii) Redistribution of particles In the case of ultrarelativistic electrons transverse space charge effects can be neglected since they scale as $\\mathcal { O } ( \\gamma ^ { - 2 } )$ and hence $T ( z )$ becomes the ballistic transport matrix: $$ 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 ) } .
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augmentation
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NO
| 0
|
expert
|
Where is the ACHIP chamber located in SwissFEL?
|
 It is located in the switch-yard to the Athos beamline
|
Fact
|
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 ) } , $$ The sign of $\\Delta ^ { i }$ indicates if a particle is located in an over- or underdense region represented by the current particle distribution. According to the magnitude of $\\Delta ^ { i }$ the new particle ensemble is generated. A particle is copied or removed from the previous distribution with a probability based on $| \\Delta ^ { i } |$ . This process is implemented by drawing a pseudorandom number $\\chi ^ { i } \\in [ 0 , 1 [$ for each particle. In case $\\chi ^ { i } < | \\Delta ^ { i } | / s _ { \\mathrm { m a x } }$ , particle $i$ is copied or removed from the distribution (depending on the sign of $\\Delta ^ { i }$ ). Otherwise, the particle remains in the ensemble. Here, $s _ { \\mathrm { m a x } }$ is the maximum of all measured BLM signals and is used to normalize $\\Delta ^ { i }$ for the comparison with $\\chi ^ { i } \\in [ 0 , 1 [$ . This process makes sure that particles in highly underdense (overdense) regions are created (removed) with an increased probability.
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augmentation
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NO
| 0
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IPAC
|
Which effects, relevant in synchrotrons, can occur when an X-ray photon interacts with an electron bound to an atom?
|
Photoelectric absorption, Thomson scattering and Compton scattering.
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Summary
|
Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation
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$$ \\eta _ { s } = \\alpha _ { s } - 1 / \\gamma ^ { 2 } $$ where it is clear to see that if $\\eta _ { s } < 0$ , the particles that have higher momentum will have a higher revolution frequency, and if $\\eta _ { s } > 0$ the particles that have lower momentum will have a lower revolution frequency therefore at transition the revolution frequency of the particles is independent of the particles energy. This effect, in turn, reduces the bunch length increasing the peak current and space charge effects. At transition, $\\eta _ { s } = 0$ and the bunch length is at a minimum. The synchrotron tune begins to slow and the beam becomes nonadiabatic as transition is approached. The adiabticity condition, $$ \\Omega = \\frac { 1 } { \\omega _ { s } ^ { 2 } } \\left| \\frac { d \\omega _ { s } } { d t } \\right| \\ll 1 $$ where is the angular frequency and $t$ is time [12]. In Equ. 4, it is clear that there is no change in the action provided that $\\Omega \\ll 1$ [13]. The time period in which the beam becomes nonadiabatic is defined as [14]
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augmentation
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NO
| 0
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IPAC
|
Which effects, relevant in synchrotrons, can occur when an X-ray photon interacts with an electron bound to an atom?
|
Photoelectric absorption, Thomson scattering and Compton scattering.
|
Summary
|
Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation
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$$ where $A _ { i }$ with $i = 1$ and 2 symbolizes the energy spread $( \\sigma _ { E } / E ) ^ { 2 }$ and horizontal emittance $\\varepsilon _ { x }$ , respectively. $\\dot { E }$ is the time derivative of energy $E , J _ { 1 }$ is longitudinal damping partition number, $J _ { 2 }$ is horizontal damping partition number, $P _ { \\gamma }$ is the synchrotron radiation power, $C _ { q }$ is the quantum constant with $3 . 8 3 2 \\times 1 0 ^ { - 1 3 } \\mathrm { m } , \\gamma$ is the Lorentz factor, $G _ { 1 } { = } I _ { 3 } / I _ { 2 }$ and $G _ { 2 } { = } I _ { 5 } / I _ { 2 }$ . $I _ { 2 }$ , $I _ { 3 }$ and $I _ { 5 }$ are 2nd, 3rd and 5th synchrotron ramping integrals, respectively. Equation (1) includes adiabatic damping and quantum excitation. The first term on the right-hand side represents adiabatic damping process, which comes from the e!ects of beam energy ramping and radiation damping. The second term on the right-hand side indicates quantum excitation and is independent of the emittance.
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augmentation
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NO
| 0
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IPAC
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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
|
$$ …where the first-order longitudinal path-lengthening term is cancelled out in the long run by synchrotron oscillations. In general, path-lengthening effects manifest as an apparent speeding up of all particles with a non-zero emittance, which changes the effective Lorentz factor and thus the spin tune. This mechanism complements that of the momentum offset $\\delta$ and can be observed in (right) showing the time development of the spin tune spread, where the local oscillations are due to the path-lengthening effect and the overall linear trend is due to the effective spin tune. Simulations at the origin $\\langle \\xi _ { x } = 0$ , $\\xi _ { y } = 0$ , $\\alpha _ { 1 } = 0$ ) show a downward trend without local oscillations due to the effect of the $\\delta ^ { 2 }$ term in eq. ( 3 ). Measurements of the error in the spin tune measured at different points in the vector-space $\\vec { \\xi } = \\left( \\xi _ { x } , \\xi _ { y } , \\alpha _ { 1 } \\right)$ have shown that $\\Delta \\nu _ { s }$ can be modelled as a scalar potential with a constant gradient, and that the set of all points with $\\Delta \\nu _ { s } = 0$ forms a plane in this space. The plane thus represents the second order optical configurations where the path-lengthening effect cancels out the original spin tune error.
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augmentation
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NO
| 0
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expert
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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
|
d) . . . requires the rotation of the sample around three orthogonal axes I.10.7.52 Undulator radiation Derive the formula for the fundamental wavelength of undulator radiation emitted at a small angle $\\theta$ : $$ \\lambda = \\frac { \\lambda _ { u } } { 2 \\gamma ^ { 2 } } \\left( 1 + \\frac { K ^ { 2 } } { 2 } + \\gamma ^ { 2 } \\theta ^ { 2 } \\right) $$ from the condition of constructive interference of the radiation emitted by consecutive undulator periods! I.10.7.53 Binding energies In which atom are the core electrons most strongly bound to the nucleus? a) Neon b) Copper c) Lithium d) Osmium e) Helium $f$ ) Iron g) Sodium $h$ ) Gold What about the valence electrons? I.10.7.54 Electron and X-Ray diffraction In comparison to diffractive imaging using electrons, X-ray diffraction. . $a$ ). . . has the advantage that the sample does not need to be in vacuum b). . . gives a stronger diffraction signal for all crystal sizes $c$ ). . . generates the same signal for all atoms in the crystal What are the consequences for the optimum sample thickness for electron diffraction in comparison to X-ray diffraction?
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