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IPAC
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What charge distribution maximizes the transformer ratio?
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The doorstop charge distribution
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Summary
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Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf
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Optimization Results for 16 fC Final Bunch Charge For the low bunch charge simulations performed for UED applications, the final desired bunch charge was $1 6 ~ \\mathrm { f C }$ . In these optimizations, the location of the aperture was variable. In this case, the simulation outputs the beam distribution at a set of locations along the beamline. At each of these locations, a set of survivor particles with the desired final charge is selected. The emittance of these particles is computed to determine the location at which the minimum survivor emittance is achieved. The optimization objectives are then this minimum emittance and the survivor bunch length at this location. Table 2 summarizes the optimization parameters and their ranges used in these simulations. In these simulations, the final number of macroparticles was set to be 2000. The initial distribution for these simulations used $p = 1$ and $n _ { c } =$ 3, such that the initial distribution is a Gaussian distribution both transversely and longitudinally. Table: Caption: Table 2: Optimization parameters and ranges for optimizations with $1 6 ~ \\mathrm { f C }$ final bunch charge. As in the $2 5 0 \\mathrm { p C }$ optimizations, the solenoid field is given as a fraction of the maximum design solenoid field and the gun phase is relative to the phase that maximizes the gradient at the cathode. The rightmost column lists the parameters corresponding to the case with a final 55 fs bunchlength. Body: <html><body><table><tr><td>Parameter</td><td>Range</td><td>0 t=55 fs</td></tr><tr><td>Bunch charge Q (fC)</td><td>16 -80</td><td>20</td></tr><tr><td>Initial σx,y (μm)</td><td>0.1-100</td><td>3.9</td></tr><tr><td>Initial σt (ps)</td><td>0.025 - 5</td><td>0.032</td></tr><tr><td>Fractional solenoid strength</td><td>0-2</td><td>0.98</td></tr><tr><td>Gun phase (deg)</td><td>-40-90</td><td>7.4</td></tr></table></body></html>
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augmentation
|
NO
| 0
|
IPAC
|
What charge distribution maximizes the transformer ratio?
|
The doorstop charge distribution
|
Summary
|
Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf
|
Table: Caption: Body: <html><body><table><tr><td>h/D</td><td>0.4</td><td>0.6</td><td>0.8</td><td>1</td><td>2</td></tr><tr><td>u</td><td>4.06</td><td>4.5</td><td>4.93</td><td>5.29</td><td>6.58</td></tr></table></body></html> The main ohmic resistance of the coil is given by the length of the conductor. The $\\mathbf { k }$ -factor accounts for an additional resistance that occurs as the coil turns get closer together. On the one hand, the tightening of the turns reduces the total length of the conductor and thus the resistance, but on the other hand the k-factor increases it. There is therefore an optimal geometry for a given coil volume that minimises the resistance while maintaining the value of the inductance. Figure 5 shows the quality factor (green) of the coil as a function of the number of turns for a given volume. For each value of the number of turns, the corresponding height and diameter (red and blue plots) give a coil with the right inductance value. As expected, this curve shows a maximum corresponding to the best coil geometry. In practice, the measured Qfactor for the whole circuit is much lower than this optimum value and is around 650 instead of the theoretical value of 3526. This difference is mainly due to feedthroughs and other connections resistance. The coil is coated with $1 5 \\mu \\mathrm { m }$ silver and its geometry is maintained with PEEK supports, see Fig. 6.
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augmentation
|
NO
| 0
|
IPAC
|
What charge distribution maximizes the transformer ratio?
|
The doorstop charge distribution
|
Summary
|
Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf
|
$$ where $\\tilde { \\rho } ( \\boldsymbol { r } ^ { \\prime } , \\boldsymbol { k } )$ is the volumetric charge distribution on the Fourier space. HYBRID PHOTOINJECTOR SPACECHARGE ANALYSIS The hybrid photoinjector use a new way to create bright beams. This device combines a photocathode with a $2 . 5 \\mathrm { g u n }$ cell SW section and a TW section through an input coupling cell [17]. It has advantages over a standard split SW-TW system, including eliminating rf reflections and avoiding the bunch lengthening e!ect. The rf coupling between the SW and TW sections creates a $9 0 ^ { \\circ }$ phase shift, which produces a strong velocity bunching e!ect resulting in very short bunch lengths [20]. In the framework of beam dynamics optimization the process of shaping beams during photocathode injection has been studied using two di!erent transverse laser distributions. The first distribution is a uniform flattop distribution in $r$ , while the second is a truncated Gaussian with a hard radial edge achieved through collimation at a radius of $0 . 5 \\ : m m$ . This study showed that using a truncated Gaussian transverse laser distribution provides two significant operational advantages. The use of the truncated Gaussian transverse laser distribution provides a significantly emittance lowering compared to previous designs. In initial studies, a uniform transverse laser illumination yielded an optimized rms normalized emittance of approximately 0.75 ùëïùëï ùëïùëàùëñùëë. However, when using the truncated Gaussian laser profile on the photocathode, the normalized emittance decreased dramatically to 0.46 ùëïùëï ùëïùëàùëñùëë. The simulation of this case (performed by using the General
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augmentation
|
NO
| 0
|
IPAC
|
What charge distribution maximizes the transformer ratio?
|
The doorstop charge distribution
|
Summary
|
Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf
|
$$ f ( z ) \\sin \\left( m \\phi \\right) = \\frac { n - \\frac { 1 } { 2 } } { N } , n = 1 , 2 , . . . , N $$ Field Analysis The field requirements for the magnet will be achieved by stacking concentric layers of quadrupole windings. The field of the designed model was evaluated in MatLab, CST Studio®, and COMSOL with sufficient agreement. A plot of $B _ { r }$ of the coil-dominated magnet and the normalized integrated harmonics can be seen in Fig. 2. Every nonquadrupole component up to $n = 1 0$ contributed $0 . 1 \\%$ of the entire field, which is well within the design criterion of $1 \\%$ maximum non-uniformity. While the coil-dominated design has a lower ratio of integrated strength per amp-turn, from the comparison shown in Table: Caption: Table 1: Operation Comparison Body: <html><body><table><tr><td>Parameter</td><td>FSQC</td><td>CD Type C</td></tr><tr><td>Operating Current</td><td>105A</td><td>450 A</td></tr><tr><td>Turns per Coil</td><td>2150</td><td>176</td></tr><tr><td>Amp-Turn</td><td>225.75kA</td><td>316.80kA</td></tr><tr><td>WarmBoreRadius</td><td>0.1 m</td><td>0.1 m</td></tr><tr><td>Quad Gradient</td><td>18.3 T/m</td><td>18.3 T/m</td></tr><tr><td>Integrated Strength</td><td>14.1T</td><td>14.7T</td></tr><tr><td>Effective Length</td><td>0.79 m</td><td>0.8 m</td></tr><tr><td>Non-Uniformity</td><td>1.0%</td><td>0.1%</td></tr><tr><td>MaxField in Coil</td><td>3.8T</td><td>2.9T</td></tr><tr><td>Inductance</td><td>41H</td><td>1.32 H</td></tr><tr><td>Stored Energy</td><td>213.3kJ</td><td>134.3 kJ</td></tr></table></body></html> Table 1, when considering the reduction in inductance and stored energy we consider this an acceptable trade. FABRICATION The quadrupole is wound from a four wire NbTi twisted cable. The cable is wound on a cylindrical 6061-T6 aluminum bobbin with machined pathways or grooves for the conductor. Each bobbin consists of four coil quadrants and allows for all the quadrants to be wound in a continuous winding, a picture of the bobbin can be seen in Fig. 3.
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augmentation
|
NO
| 0
|
IPAC
|
What charge distribution maximizes the transformer ratio?
|
The doorstop charge distribution
|
Summary
|
Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf
|
$$ Hence, if the stabilizing effect of the main cavities is small we expect the mode 0 growth rate to scale as $Q _ { L } / R _ { s } ^ { 2 }$ ; for a fixed cavity geometry (and $R _ { s } / Q _ { L } )$ the growth rate scales inversely with the HHC shunt impedance. We illustrate this scaling for “optimal” stretching in Fig. 1, in which the HHC settings are chosen to flatten the potential such that it is approximately quartic, which for the APS-U leads to $\\sigma _ { t } \\approx 5 0$ ps. The top plot shows how the growth rate varies with $R _ { s }$ for fixed $Q _ { L } = 6 0 0 \\times 1 0 ^ { 3 }$ , and also the required feedback damping rate to stabilize the system. When the growth rates are small the two approximately agree, but they quickly diverge at small $R _ { s }$ . Table: Caption: Table 1: APS-U Ring and Main Cavity Parameters Body: <html><body><table><tr><td>Ring</td><td>Value</td><td>Main Cavity</td><td>Value</td></tr><tr><td>ac</td><td>4.04 × 10-5</td><td>Rs</td><td>10.1 MΩ</td></tr><tr><td>T</td><td>3.628 μs</td><td>QL</td><td>7380</td></tr><tr><td>08</td><td>0.135 %</td><td>Total V</td><td>4.6 MV</td></tr></table></body></html> Similar behavior is seen for the “overstretched” bunch in the top of Fig. 2, wherein the HHC is set to maximize Touschek lifetime, and the final distribution has two humps along $z$ and $\\sigma _ { t } \\approx 9 0$ ps. The growth rates are approximately the same as for optimal stretching, but the required feedback is approximately twice as large. Interestingly, both theory and simulation indicate that this difference is largely due to a sudden “jump” in the required feedback near $R _ { s } \\approx 1 8 \\mathrm { M } \\Omega$ .
|
augmentation
|
NO
| 0
|
IPAC
|
What charge distribution maximizes the transformer ratio?
|
The doorstop charge distribution
|
Summary
|
Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf
|
Typical voltage laws are shown in Fig. 2 along with the corresponding adiabaticity evolution. The final captured beam distribution is shown in Fig.4 for the case of a linear increase of RF voltage from $0 . 1 0 4 5 \\mathrm { k V }$ to $1 . 0 4 5 \\mathrm { k V } .$ . Figure 5 shows the variation of emittance with initial voltage $U _ { 1 }$ for the case of iso-adiabatic and linear voltage laws with fixed $U _ { 2 }$ and ramp turns. For each $U _ { 1 }$ , the tracking was repeated for a set of 30 random distributions. The points in the figure show the mean and the error bars the standard deviation for each set. The error bars are larger in the $1 0 0 \\%$ emittance case compared with the $9 9 . 9 \\%$ emittance case because of the relatively small number of particles at the edge of the distribution. It is clear from Fig. 5 that the lowest $1 0 0 \\%$ emittance is obtained if the voltage is ramped linearly from zero volts. On the other hand, in the iso-adiabatic case, the emittance is at its highest level for the lowest value of $U _ { 1 }$ tested - this is to be expected the since $\\alpha$ increases as $U _ { 1 }$ is reduced. The increase in the mean $1 0 0 \\%$ emittance when $U _ { 1 } > 5 0 \\mathrm { V }$ is not consistent with the fact that $\\alpha$ is decreasing at the same time. This may be because the instantaneous, non-adiabatic rise of the voltage to $U _ { 1 }$ at the start of tracking is not accounted for in the $\\alpha$ parameter (the same argument applies to the linear ramp case). Note, when $U _ { 1 } = 2 5 0 \\mathrm { V }$ , the bucket height is approximately equal to the coasting beam energy spread.
|
augmentation
|
NO
| 0
|
expert
|
What charge distribution maximizes the transformer ratio?
|
The doorstop charge distribution
|
Summary
|
Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf
|
$$ Here we have used the convolution’s commutative property to switch the roles of $i$ and $h$ \in the convolution integral and written the Fourier transform of Green’s function $h ( t )$ as the longitudinal wake impedance $Z _ { | | } ( \\omega )$ . The subscripts added to the $\\omega$ variables indicate that they are independent, allowing Eq. (B8) to be rearranged: $$ \\begin{array} { c c c } { { P _ { w } = \ \\frac { c } { ( 2 \\pi ) ^ { 3 } } \\mathrm { R e } \\left\\{ \\int _ { - \\infty } ^ { \\infty } d \\omega \\int _ { - \\infty } ^ { \\infty } d \\omega _ { 2 } \\int _ { - \\infty } ^ { \\infty } d \\omega _ { 1 } \\int _ { - \\infty } ^ { \\infty } d t \\int _ { - \\infty } ^ { \\infty } d t ^ { \\prime } \\right. } } \\\\ { { \\left. \\times I ( \\omega _ { 2 } ) I ( \\omega _ { 1 } ) Z _ { | | } ( \\omega ) e ^ { j t ( \\omega _ { 1 } + \\omega _ { 2 } ) } e ^ { j t ^ { \\prime } ( \\omega - \\omega _ { 1 } ) } \\right\\} . } } & { { ( \\mathrm { B 9 } ) } } \\end{array}
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1
|
NO
| 0
|
expert
|
What charge distribution maximizes the transformer ratio?
|
The doorstop charge distribution
|
Summary
|
Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf
|
$$ and the Fourier transform of the step function $$ \\mathcal { F } \\{ \\theta ( t ) \\} = \\pi \\biggl ( \\frac { 1 } { j \\pi \\omega } + \\delta ( \\omega ) \\biggr ) , $$ the wake impedance becomes $$ \\begin{array} { r } { Z _ { n | | } ( \\omega ) = \\kappa _ { n } \\Bigg [ \\pi [ \\delta ( \\omega - \\omega _ { n } ) + \\delta ( \\omega + \\omega _ { n } ) ] } \\\\ { - j \\Bigg ( \\cfrac { 1 } { ( \\omega - \\omega _ { n } ) } + \\frac { 1 } { ( \\omega + \\omega _ { n } ) } \\Bigg ) \\Bigg ] . } \\end{array} $$ Using $Z _ { n | | } ( \\omega )$ \in Eq. (B12) and evaluating the integral yields $$ P _ { w , n } = \\frac { \\kappa _ { n } c } { 2 } ( | I ( \\omega _ { n } ) | ^ { 2 } + | I ( - \\omega _ { n } ) | ^ { 2 } ) .
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1
|
NO
| 0
|
IPAC
|
What charge distribution maximizes the transformer ratio?
|
The doorstop charge distribution
|
Summary
|
Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf
|
File Name:START-TO-END_SIMULATION_OF_HIGH-GRADIENT,.pdf START-TO-END SIMULATION OF HIGH-GRADIENT, HIGH-TRANSFORMER RATIO STRUCTURE WAKEFIELD ACCELERATION WITH TDC-BASED SHAPING Gwanghui $\\mathrm { { H a ^ { * } } }$ , Northern Illinois University, DeKalb, IL, USA Abstract In collinear wakefield acceleration, two figures of merits, gradient and transformer ratio, play pivotal roles. A highgradient acceleration requires a high-charge beam. However, shaping current profile of such high-charge beam is challenging, due to the degradation by CSR. Recently proposed method, utilizing transverse deflecting cavities (TDC) for shaping, has shown promising simulation results for accurate shaping of high-charge beams. This is attributed to its dispersion-less feature. We plan to experimentally demonstrate high-gradient $( > 1 0 0 \\mathrm { M V / m } )$ and high-transformer ratio $( > 5 )$ collinear structure wakefield acceleration. The experiment is planned at Argonne Wakefield Accelerator Facility. We present results from start-to-end simulations for the experiment. INTRODUCTION One of the challenges in collinear wakefield acceleration (CWA) is preparing a properly shaped, high-charge drive bunch [1, 2]. Since direct shaping on the longitudinal phase space is not feasible except for shaping the laser pulse, most longitudinal shaping methods rely on introducing correlations between transverse and longitudinal planes [3]. These correlations are typically introduced by dispersion from dipole magnets. However, when a beam passes through a dipole magnet, it generates CSR that deteriorates both beam and shaping quality. This issue is particularly problematic for CWA, which has high-charge requirements.
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1
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NO
| 0
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expert
|
What charge distribution maximizes the transformer ratio?
|
The doorstop charge distribution
|
Summary
|
Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf
|
$$ Again, using the fact that the current distribution is a purely real function, we obtain $$ P _ { \\boldsymbol { w } , n } = \\kappa _ { n } c | I ( \\omega _ { n } ) | ^ { 2 } . $$ Assuming the loss factor $\\kappa _ { n }$ is uniform throughout the corrugated waveguide of length $L$ , the total energy lost by the bunch to the wakefield mode is $$ U _ { \\mathrm { l o s s } , n } = \\kappa _ { n } L | I ( \\omega _ { n } ) | ^ { 2 } $$ In terms of the bunch form factor, $F ( k )$ is defined as $$ F ( k ) = { \\frac { 1 } { q _ { 0 } } } \\int _ { - \\infty } ^ { \\infty } q ( s ) e ^ { - j k s } d s , $$ where $s$ is the longitudinal displacement from the head of the bunch and $k$ is the wave number, the energy loss is $$ U _ { \\mathrm { l o s s } , n } = \\kappa _ { n } q _ { 0 } ^ { 2 } | { \\cal F } ( k _ { n } ) | ^ { 2 } .
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1
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NO
| 0
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expert
|
What charge distribution maximizes the transformer ratio?
|
The doorstop charge distribution
|
Summary
|
Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf
|
$$ E _ { z } ( t ) = \\int _ { - \\infty } ^ { \\infty } h ( t - t ^ { \\prime } ) i ( t ^ { \\prime } ) d t ^ { \\prime } . $$ Inserting Eq. (B4) into Eq. (B1) and integrating over the time axis of the bunch produce the power being deposited into the wakefield $$ P _ { w } = \\frac { d U _ { \\mathrm { l o s s } } } { d t } = c \\int _ { - \\infty } ^ { \\infty } i ( t ) \\int _ { - \\infty } ^ { \\infty } h ( t - t ^ { \\prime } ) i ( t ^ { \\prime } ) d t ^ { \\prime } d t . $$ Defining the Fourier transform and its inverse $$ I ( \\omega ) = \\int _ { - \\infty } ^ { \\infty } i ( t ) e ^ { - j \\omega t } d t , $$ $$ i ( t ) = { \\frac { 1 } { 2 \\pi } } \\int _ { - \\infty } ^ { \\infty } I ( \\omega ) e ^ { j \\omega t } d \\omega .
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1
|
NO
| 0
|
expert
|
What charge distribution maximizes the transformer ratio?
|
The doorstop charge distribution
|
Summary
|
Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf
|
$$ We will now consider the effect of the bunch charge density $q ( s )$ on the accelerating field $E _ { z } ( s )$ \in order to understand how $E _ { \\mathrm { a c c } }$ and the peak surface fields depend on $q ( s )$ . To begin, we write $E _ { z , n }$ due to a single mode as a convolution $$ E _ { z , n } ( s ) = \\int _ { - \\infty } ^ { \\infty } q ( s - s ^ { \\prime } ) 2 \\kappa _ { n } \\cos ( k _ { n } s ^ { \\prime } ) \\theta ( s ^ { \\prime } ) d s ^ { \\prime } . $$ Since $q ( s )$ is a real function, $$ E _ { z , n } ( s ) = 2 \\kappa _ { n } \\mathrm { R e } \\Bigg \\{ \\int _ { 0 } ^ { \\infty } q ( s - s ^ { \\prime } ) e ^ { j k _ { n } s ^ { \\prime } } d s ^ { \\prime } \\Bigg \\} .
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1
|
NO
| 0
|
expert
|
What charge distribution maximizes the transformer ratio?
|
The doorstop charge distribution
|
Summary
|
Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf
|
File Name:Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf Design of a cylindrical corrugated waveguide for a collinear wakefield accelerator A. Siy ,1,2,\\* N. Behdad,1 J. Booske,1 G. Waldschmidt,2 and A. Zholents 2,† 1University of Wisconsin, Madison, Wisconsin 53715, USA 2Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439, USA (Received 30 May 2022; accepted 7 November 2022; published 7 December 2022) We present the design of a cylindrical corrugated waveguide for use in the A-STAR accelerator under development at Argonne National Laboratory. A-STAR is a high gradient, high bunch repetition rate collinear wakefield accelerator that uses a $1 - \\mathrm { m m }$ inner radius corrugated waveguide to produce a $9 0 \\ \\mathrm { M V } \\mathrm { m } ^ { - 1 }$ , 180-GHz accelerating field when driven by a $1 0 \\mathrm { - n C }$ drive bunch. To select a corrugation geometry for A-STAR, we analyze three types of corrugation profiles in the overmoded regime with $a / \\lambda$ ranging from 0.53 to 0.67, where $a$ is the minor radius of the corrugated waveguide and $\\lambda$ is the free-space wavelength. We find that the corrugation geometry that optimizes the accelerator performance is a rounded profile with vertical sidewalls and a corrugation period $p \\ll a$ . Trade-offs between the peak surface fields and thermal loading are presented along with calculations of pulse heating and steady-state power dissipation. In addition to the $\\mathrm { T M } _ { 0 1 }$ accelerating mode, properties of the $\\mathrm { H E M } _ { 1 1 }$ mode and contributions from higher order modes are discussed.
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augmentation
|
NO
| 0
|
expert
|
What charge distribution maximizes the transformer ratio?
|
The doorstop charge distribution
|
Summary
|
Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf
|
$$ \\phi = \\frac { 3 6 0 f p } { c } , $$ where $\\phi$ is the periodic boundary condition phase advance in degrees, $f$ is the frequency of the electromagnetic mode, $p$ is the corrugation period, and $c$ is the speed of light. The electron bunch velocity is considered to be equal to $c$ . The structures were simulated at three fixed frequencies in order to characterize frequency-dependent behavior of the $\\mathrm { T M } _ { 0 1 }$ mode. Throughout the paper, we will refer to results for the simulated frequencies by their respective aperture ratios which we define as $a / \\lambda$ , where $a$ is the minor radius of the CWG and $\\lambda$ is the free-space wavelength of the synchronous mode. This normalization allows the results to be applied to structures of any size and frequency. Parametric analysis began by treating the corrugation depth $d$ as a dependent variable determined by the aperture ratio, eliminating it from the parameter sweeps. This was done by using an iterative optimization process to find the corrugation depths required to achieve predetermined frequencies, producing aperture ratios of 0.53, 0.60, and 0.67 for each combination of $p , \\xi$ , and $\\zeta$ in the study. The resulting corrugation depths are plotted in Figs. 5 and 6. In all cases, the corrugation depth decreases with increasing aperture ratio, where shallower corrugations produce higher synchronous $\\mathrm { T M } _ { 0 1 }$ frequencies. The sidewall parameter $\\zeta$ is found to modify the effective corrugation depth where reducing $\\zeta$ has an effect similar to reducing $d$ . Undercut corrugation profiles with $\\zeta > 1$ can only be found when the conditions in Eqs. (3) and (4) are satisfied which requires the period and aperture ratio to be sufficiently small. For this reason, the dotted line solutions in Fig. 6 only occur above the set values of the corrugation depth. In the remainder of the analysis, we will pay special attention to the maximum radii corrugation and unequal radii corrugation with $\\zeta = 1$ which are good candidates for wakefield acceleration due to their manufacturability and electromagnetic characteristics.
|
augmentation
|
NO
| 0
|
expert
|
What charge distribution maximizes the transformer ratio?
|
The doorstop charge distribution
|
Summary
|
Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf
|
$$ 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 $$ \\mathcal { F } \\{ f ( t ) \\cos ( a t ) \\} = \\frac { F ( \\omega - a ) + F ( \\omega + a ) } { 2 } ,
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augmentation
|
NO
| 0
|
expert
|
What charge distribution maximizes the transformer ratio?
|
The doorstop charge distribution
|
Summary
|
Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf
|
$$ Q _ { \\mathrm { d i s s } } = \\frac { E _ { \\mathrm { a c c } } ^ { 2 } } { 8 \\alpha \\kappa } ( e ^ { - 2 \\alpha L } + 2 \\alpha L - 1 ) . $$ According to Eq. (14), the amount of energy deposited on the CWG wall per unit length reaches a maximum after the electron bunch propagates a distance $z \\gg 1 / \\alpha$ . It is further convenient to approximate the CWG as a smooth cylinder of radius $a$ and elementary area $d S = 2 \\pi a d z$ , leading to the energy dissipation density on the cylinder wall: $$ \\frac { d Q _ { \\mathrm { d i s s } } ( z \\infty ) } { d S } = \\frac { E _ { \\mathrm { a c c } } ^ { 2 } } { 8 \\pi a \\kappa } . $$ Since the undulating wall of the CWG has a larger surface area per unit length than the smooth cylinder, Equation (16) is an upper bound on the average energy dissipation density in the CWG wall. From Eq. (16), we define the upper bound of the average thermal power dissipation density as
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augmentation
|
NO
| 0
|
expert
|
What charge distribution maximizes the transformer ratio?
|
The doorstop charge distribution
|
Summary
|
Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf
|
Comparing the maximum radii and unequal radii rounded corrugation peak fields in Figs. 10 and 11, we note that the two geometry types are identical when the spacing parameter $\\xi = 0$ and the sidewall parameter $\\zeta = 1$ . In both structure types, the minimum $E _ { \\mathrm { m a x } }$ occurs for a negative spacing parameter $\\xi$ , corresponding to a corrugation tooth width wider than the vacuum gap. Increasing the corrugation spacing beyond the minimum point decreases $H _ { \\mathrm { m a x } }$ while increasing $E _ { \\mathrm { m a x } }$ . The sidewall angle determined by $\\zeta$ shifts the plots on the $\\xi$ axis but does not significantly affect the minimum value of the peak fields. While changing the sidewall parameter offers little to no benefit in reducing the peak fields, the practical implications of using values of $\\zeta \\neq 1$ have several disadvantages. For tapered corrugations with $\\zeta < 1$ , the corrugation depth must be greater requiring a thicker vacuum chamber wall and additional manufacturing complexity. Undercut corrugations with $\\zeta > 1$ are also impractical to manufacture for the dimensions of interest in a compact wakefield accelerator. For these reasons, we suggest the maximum radii corrugation with $\\xi$ close to zero as a good candidate for a wakefield accelerator design. Further refinement of the geometry requires experimental determination of where rf breakdown is most likely to occur in order to reduce the peak fields in those regions.
|
augmentation
|
NO
| 0
|
expert
|
What charge distribution maximizes the transformer ratio?
|
The doorstop charge distribution
|
Summary
|
Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf
|
With the minor radius and frequency selected, the corrugation profile is chosen to maximize the accelerating gradient as well as provide a high repetition rate. The $1 \\mathrm { - m m }$ minor radius of the CWG results in corrugation dimensions in the hundreds of $\\mu \\mathrm { m }$ which presents unique manufacturing challenges. Several fabrication methods have been investigated for constructing the CWG, with electroforming copper on an aluminum mandrel producing the most promising results [14]. Electroforming at these scales requires that neither the corrugation tooth width nor the vacuum gap is made excessively small since this would result in either a flimsy mandrel or a flimsy final structure. A sensible choice is to make the tooth width similar to the vacuum gap, resulting in $\\xi \\approx 0$ , while using the shortest practical corrugation period. The maximum radii and unequal radii geometries have similar characteristics when $\\xi \\approx 0$ and we have selected the maximum radii design for A-STAR. The final corrugation dimensions are shown in Table II and the electromagnetic characteristics of the $\\mathrm { T M } _ { 0 1 }$ and $\\mathbf { H E M } _ { 1 1 }$ modes are given in Table III.
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augmentation
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NO
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expert
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What charge distribution maximizes the transformer ratio?
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The doorstop charge distribution
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Summary
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Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf
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$$ \\kappa _ { \\mathrm { m a x } } = \\frac { Z _ { 0 } c } { 2 \\pi a ^ { 2 } } , $$ where $Z _ { 0 }$ is the impedance of free space. In practical corrugated waveguide designs, the loss factor is always less than $\\kappa _ { \\mathrm { m a x } }$ due to manufacturing constraints on the minimum corrugation size. In these structures, simulations are required to accurately determine the loss factor. V. PEAK FIELD MINIMIZATION The maximum attainable accelerating gradient in the CWA is limited by several factors, including pulse heating and rf breakdown due to the peak surface fields and modified Poynting vector [19–21] exceeding certain threshold values. The corrugated waveguide must be optimized to maximize the accelerating field of the $\\mathrm { T M } _ { 0 1 }$ mode while minimizing these factors. Data collected from existing accelerator structures operating up to $3 0 \\mathrm { G H z }$ show that the breakdown rate (BDR), measured in breakdowns per pulse per meter, scales approximately with the magnitude of the peak electromagnetic field $E _ { \\mathrm { m a x } }$ as well as the duration of the rf pulse $t _ { p }$ according to [21]:
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augmentation
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NO
| 0
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expert
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What charge distribution maximizes the transformer ratio?
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The doorstop charge distribution
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Summary
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Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf
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VI. THERMAL LOADING Thermal loading of the corrugated waveguide places a limit on the maximum repetition rate $f _ { r }$ of the accelerator, where $f _ { r }$ is the number of bunches injected into the structure per second. The thermal loading depends on the electromagnetic properties of the $\\mathrm { T M } _ { 0 1 }$ mode as well as the length of the corrugated waveguide and the conductivity of the wall material. Achieving a high repetition rate requires active cooling of the structure as well as an optimally designed corrugation profile. Here we focus on designing a corrugation that minimizes the steady-state thermal load and transient pulse heating. The thermally induced stresses due to temperature gradients in the wall pose additional design considerations which are discussed further in [26]. Because the group velocity $v _ { g }$ of the electromagnetic wave is less than the electron bunch velocity, the length of the rf pulse behind the bunch grows as it traverses the structure. This causes the thermal energy density deposited in the CWG wall to increase along the direction of propagation. At a distance $z$ from the beginning of the CWG, the field strength of the rf pulse induced by the electron bunch entering at time $t = 0$ is
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augmentation
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NO
| 0
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expert
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What code was used to simulte the SHINE dechirper
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ECHO2D
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Summary
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Beam_performance_of_the_SHINE_dechirper.pdf
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We next simply consider the quadrupole wake, where the beam is on-axis $( \\mathrm { y } _ { \\mathrm { c } } = 0 )$ . The transfer matrices for the focusing and defocusing quadrupole are given in Eq. (16), where $L$ is the length of the corrugated structure [25]. $$ \\begin{array} { r } { \\boldsymbol { R } _ { \\mathrm { f } } = \\left[ \\begin{array} { c c } { \\cos k _ { \\mathrm { q } } L } & { \\frac { \\sin k _ { \\mathrm { q } } L } { k _ { \\mathrm { q } } } } \\\\ { - k _ { \\mathrm { q } } \\sin k _ { \\mathrm { q } } L } & { \\cos k _ { \\mathrm { q } } L } \\end{array} \\right] , \\boldsymbol { R } _ { \\mathrm { d } } = \\left[ \\begin{array} { c c } { \\cosh k _ { \\mathrm { q } } L } & { \\frac { \\sin k _ { \\mathrm { q } } L } { k _ { \\mathrm { q } } } } \\\\ { k _ { \\mathrm { q } } \\sinh k _ { \\mathrm { q } } L } & { \\cosh k _ { \\mathrm { q } } L } \\end{array} \\right] . } \\end{array}
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1
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Yes
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expert
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What code was used to simulte the SHINE dechirper
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ECHO2D
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Summary
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Beam_performance_of_the_SHINE_dechirper.pdf
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This paper begins by reviewing the dechirper parameters for a small metallic pipe. The wakefield effects are studied with an ultra-short electron bunch in the Shanghai high repetition rate XFEL and extreme light facility (SHINE). Then, the process in dechirper is studied analytically and verified by numerical simulations. The longitudinal wakefield generated by the corrugated structure was adopted as the dechirper was calculated and simulated for SHINE. The following chapter focuses on the transverse wakefield, discussing emittance dilution effects on different arrangements of two orthogonally oriented dechirpers, mainly for the case of an on-axis beam. We also propose using ‘fourdechirpers’ as a novel approach for controlling the beam emittance dilution effect during dechirping and compare it with the conventional scheme. We then close with a brief conclusion. 2 Background The layout of the SHINE linac and the beam parameters along the beamline are shown in Fig. 1. The electron beam generated by the VHF gun is accelerated to $1 0 0 \\ \\mathrm { M e V }$ before entering the laser heater, to suppress potential subsequent microbunching by increasing the uncorrelated energy spread of the beam. The overall linac system consists of four accelerating sections (L1, L2, L3 and L4) and two bunch compressors (BC1 and BC2). A higher harmonic linearizer (HL), which works in the deceleration phase, is also placed upstream of BC1 for the purpose of linear compression.
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1
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Yes
| 0
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expert
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What code was used to simulte the SHINE dechirper
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ECHO2D
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Summary
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Beam_performance_of_the_SHINE_dechirper.pdf
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File Name:Beam_performance_of_the_SHINE_dechirper.pdf Beam performance of the SHINE dechirper You-Wei $\\mathbf { G o n g } ^ { 1 , 2 } ( \\mathbb { D } )$ • Meng Zhang3 • Wei-Jie $\\mathbf { F a n } ^ { 1 , 2 } ( \\mathbb { D } )$ • Duan $\\mathbf { G } \\mathbf { u } ^ { 3 } \\boldsymbol { \\oplus }$ Ming-Hua Zhao1 Received: 14 August 2020 / Revised: 11 January 2021 / Accepted: 13 January 2021 / Published online: 17 March 2021 $\\circledcirc$ China Science Publishing & Media Ltd. (Science Press), Shanghai Institute of Applied Physics, the Chinese Academy of Sciences, Chinese Nuclear Society 2021 Abstract A corrugated structure is built and tested on many FEL facilities, providing a ‘dechirper’ mechanism for eliminating energy spread upstream of the undulator section of X-ray FELs. The wakefield effects are here studied for the beam dechirper at the Shanghai high repetition rate XFEL and extreme light facility (SHINE), and compared with analytical calculations. When properly optimized, the energy spread is well compensated. The transverse wakefield effects are also studied, including the dipole and quadrupole effects. By using two orthogonal dechirpers, we confirm the feasibility of restraining the emittance growth caused by the quadrupole wakefield. A more efficient method is thus proposed involving another pair of orthogonal dechirpers.
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2
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Yes
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expert
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What code was used to simulte the SHINE dechirper
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ECHO2D
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Summary
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Beam_performance_of_the_SHINE_dechirper.pdf
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The SHINE linac beam specifications are listed in Table 1. After two stages of bunch compressors, the bunch length is shortened to $1 0 ~ { \\mu \\mathrm { m } }$ , with a time-dependent energy chirp of approximately $0 . 2 5 \\%$ $( 2 0 \\mathrm { M e V } )$ at the exit of the SHINE linac. Compared with normal conducting RF structures, the wakefield generated by the L-band superconducting structure is relatively weak because of its large aperture [15]. Therefore, it is impossible to compensate the correlated energy spread of the beam by adopting the longitudinal wakefield of the accelerating module, which becomes a key design feature of superconducting linacdriven FELs. In the case of the SHINE linac, the electron bunch length is less than $1 0 ~ { \\mu \\mathrm { m } }$ after passing through the second bunch compressor. Therefore, the beam energy spread cannot be effectively compensated by chirping the RF phase of the main linac. The SHINE linac adopts the corrugated structure (Fig. 2) to dechirp the energy spread. This is achieved by deliberately selecting the structural parameters so as to control the wavelength and strength of the field, as verified by beam experiments on many FEL facilities.
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1
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Yes
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expert
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What code was used to simulte the SHINE dechirper
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ECHO2D
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Summary
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Beam_performance_of_the_SHINE_dechirper.pdf
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As described in Eq. (567), the distance factor is affected by the dechirper parameters, especially by the ratio $t / p$ . The wakefields induced by the Gaussian bunch with different $t /$ $p$ values are shown in Fig. 3. Over the initial $2 0 ~ { \\mu \\mathrm { m } }$ , all the induced wakefields have the same slope coefficient and differ mainly in terms of the maximal chirp. As $t / p$ increases, the wakefield decreases progressively until it settles when $t / p$ reaches 0.5. Therefore, $t / p = 0 . 5$ is selected for SHINE as the dechirper parameter for which deviations are tolerable. Equation (1) is suitable only for dechirpers with a flat geometry, with corrugations in the $y -$ and $z$ -directions and with $x$ extending to infinity horizontally. However, in practice, it assumes the presence of a resistive wall in the $x$ - direction, as defined by the width $w$ . The wake calculated in the time domain by the wakefield solver ECHO2D [22] is adopted to simulate the actual situation. This is expressed as a sum of discrete modes, with odd mode numbers m corresponding to the horizontal mode wavenumbers $k x =$ $m \\pi / \\nu$ $( m = 1 , 3 , 5 . . . )$ . To obtain the exact simulated wakefield, it has been verified that $w \\gg a$ should be satisfied, and that more than one mode contribute to the impedance of the structure [17].
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4
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Yes
| 1
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expert
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What code was used to simulte the SHINE dechirper
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ECHO2D
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Summary
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Beam_performance_of_the_SHINE_dechirper.pdf
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As previously mentioned, $t / p = 0 . 5$ was adopted. The longitudinal wakefields corresponding to different widths are shown in the middle subplot of Fig. 3. The longitudinal wakefield appears to increase with $w$ , but settles at a maximum value when $w = 1 5 \\mathrm { m m }$ . For our calculation, setting $a = 1 \\mathrm { m m }$ and $w = 1 5 \\mathrm { m m }$ yields a sufficiently large ratio $w / a = 1 5$ . The scenarios in Eq. (1) and ECHO2D can all be regarded as flat geometries. The main parameters chosen for SHINE are summarized in Table 2. Assuming that the beam goes through an actual periodic structure, the beam entering the finite-length pipe still displays a transient response, characterized by the catch-up distance $z = a ^ { 2 } / 2 \\sigma _ { z }$ . Based on the parameters in Table 2, the catch-up distance in SHINE is $5 0 ~ \\mathrm { c m }$ , which is small compared to the structure length, suggesting that the transient response of the structure can be ignored. Table: Caption: Table 2 Corrugated structural parameters for SHINE Body: <html><body><table><tr><td>Parameter</td><td>Value</td></tr><tr><td>Half-gap, a (mm)</td><td>1.0</td></tr><tr><td>Period,p (mm)</td><td>0.5</td></tr><tr><td>Depth,h (mm)</td><td>0.5</td></tr><tr><td>Longitudinal gap,t (mm)</td><td>0.25</td></tr><tr><td>Width,w (mm)</td><td>15.0</td></tr><tr><td>Plate length,L (m)</td><td>10.0</td></tr></table></body></html>
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1
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Yes
| 0
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expert
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What code was used to simulte the SHINE dechirper
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ECHO2D
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Summary
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Beam_performance_of_the_SHINE_dechirper.pdf
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Keywords Corrugated structure $\\mathbf { \\nabla } \\cdot \\mathbf { \\varepsilon }$ Energy spread $\\cdot$ Wakefield $\\mathbf { \\nabla } \\cdot \\mathbf { \\varepsilon }$ Shanghai high repetition rate XFEL and extreme light facility 1 Introduction Eliminating residual energy chirps is essential for optimizing the beam brightness in the undulator of a free electron laser (FEL). There are currently two traditional ways to eliminate chirps in superconducting linear accelerator (linac)-driven X-ray FEL facilities. One involves exploiting the resistive-wall wakefield induced by the beam pipe. The other option, which involves running the beam ‘off-crest,’ is inefficient and costly, especially for ultrashort bunches in FEL facilities [1]. Recently, corrugated metallic structures have attracted much interest within the accelerator community, as they use a wakefield to remove linear energy chirps passively before the beam enters the undulator. The idea of using a corrugated structure as a dechirper in an X-ray FEL was first proposed by Karl and Gennady [1]. Several such structures, XFELs [2], PALXFEL [3], pint-sized facility [4, 5], LCLS [6] and SwissFEL [7] have been built and tested. The feasibility of employing a corrugated structure to precisely control the beam phase space has been demonstrated in various applications. It has also been utilized as a longitudinal beam phase-space linearizer for bunch compression [8, 9], to linearize energy profiles for FEL lasing [10], and as a passive deflector for longitudinal phase-space reconstruction [11]. Meanwhile, many other novel applications of light sources have also been proposed in recent years. Bettoni et al. verified the possibility of using them to generate a two-color beam [12]. A new role for generating fresh-slice multi-color generations in FELs was demonstrated in LCLS [13]. The generation of terahertz waves was also proposed recently [14].
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augmentation
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Yes
| 0
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expert
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What code was used to simulte the SHINE dechirper
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ECHO2D
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Summary
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Beam_performance_of_the_SHINE_dechirper.pdf
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Table: Caption: Table 1 Beam parameters upon exiting the SHINE linac Body: <html><body><table><tr><td>Parameter</td><td>Value</td></tr><tr><td>Energy,E (GeV)</td><td>8</td></tr><tr><td>Charge per bunch, Q (PC)</td><td>100</td></tr><tr><td>Beam current,I (kA)</td><td>1.5</td></tr><tr><td>Bunch length (RMS),σ(μm)</td><td>10</td></tr><tr><td>βx (m)</td><td>60.22</td></tr><tr><td>βy (m)</td><td>43.6</td></tr><tr><td>αx</td><td>1.257</td></tr><tr><td>αy</td><td>1.264</td></tr><tr><td>Enx (mm·mrad)</td><td>0.29</td></tr><tr><td>Eny (mm·mrad)</td><td>0.29</td></tr></table></body></html> 3 Longitudinal Wakefield effect Round pipes and rectangular plates are usually adopted as dechirpers. Round pipes perform better on the longitudinal wakefield by a factor of $1 6 / \\pi ^ { 2 }$ relative to a rectangular plate of comparable dimensions. However, SHINE uses a rectangular plate nonetheless, as its gap can be adjusted by changing the two plates. The corrugated structure is made of aluminum with small periodic sags and crests, with the parameters defined in Fig. 2. The surface impedance of a pipe with small, periodic corrugations has been described in detail [16–18]. The high-frequency longitudinal impedance for the dechirper can be determined by starting from the general impedance expression. Taking $q$ as the conjugate variable in the Fourier transform, we have $$ Z _ { 1 } ( k ) = \\frac { 2 \\zeta } { c } \\int _ { - \\infty } ^ { \\infty } \\mathrm { d } q q \\mathrm { c s c h } ^ { 3 } ( 2 q a ) f ( q ) e ^ { - i q x } ,
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augmentation
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Yes
| 0
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expert
|
What code was used to simulte the SHINE dechirper
|
ECHO2D
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Summary
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Beam_performance_of_the_SHINE_dechirper.pdf
|
$$ where $f ( q ) = n / d$ , and with $$ \\begin{array} { l } { n = q [ \\cosh [ q ( 2 a - y - y _ { 0 } ) ] - 2 \\cosh [ q ( y - y _ { 0 } ) ] } \\\\ { \\qquad + \\cosh [ q ( 2 a + y + y _ { 0 } ) ] ] } \\\\ { \\qquad - i k \\zeta [ \\sinh [ q ( 2 a - y - y _ { 0 } ) ] + \\sinh [ q ( 2 a + y + y _ { 0 } ) ] ] , } \\end{array} $$ $$ d = [ q \\mathrm { s e c h } ( q a ) - i k \\zeta \\mathrm { c s c h } ( q a ) ] [ q \\mathrm { c s c h } ( q a ) - i k \\zeta \\mathrm { s e c h } ( q a ) ] . $$ We use $( x _ { 0 } , \\ y _ { 0 } )$ and $( x , y )$ to represent the driving and testing particles, respectively. In Eq. (1), the surface impedance is written as $\\zeta$ , which is related to the wavenumber $k$ . In Ref. [18], the impedance at large $k$ is expanded, keeping terms to leading order $1 / k$ and to the next order $1 / k ^ { 3 / 2 }$ . Then, we compare this equation to the round case for a disk-loaded structure in a round geometry, with the same expression in parameters as rectangular plates. The longitudinal impedances at large $q$ for the round and rectangular plates are given by [18–21]
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augmentation
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Yes
| 0
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expert
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What code was used to simulte the SHINE dechirper
|
ECHO2D
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Summary
|
Beam_performance_of_the_SHINE_dechirper.pdf
|
$$ \\begin{array} { l } { \\displaystyle { Z _ { \\mathrm { { r } } } ( k ) = \\frac { 4 i } { k c a ^ { 2 } } \\left[ 1 + \\frac { 1 + i } { \\sqrt { 2 k S _ { 0 \\mathrm { { r } } } } } \\right] ^ { - 1 } , } } \\\\ { \\displaystyle { Z _ { \\mathrm { { l } } } ( k ) = \\frac { 4 i } { k c a ^ { 2 } } \\left[ 1 + \\frac { 1 + i } { \\sqrt { 2 k S _ { 0 \\mathrm { { l } } } } } \\right] ^ { - 1 } . } } \\end{array} $$ The distance scale factors $S _ { \\mathrm { 0 r } }$ and $S _ { 0 1 }$ for the round and flat are strongly influenced by the dechirper parameters: $$ \\begin{array} { l } { { \\displaystyle S _ { 0 \\mathrm { r } } = \\frac { a ^ { 2 } t } { 2 \\pi \\alpha ^ { 2 } p ^ { 2 } } , } } \\\\ { { \\displaystyle \\alpha ( x ) = 1 - 0 . 4 6 5 \\sqrt { ( x ) } - 0 . 0 7 0 ( x ) , } } \\\\ { { \\displaystyle S _ { 0 1 } = 9 S _ { 0 \\mathrm { r } } / 4 . } } \\end{array}
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augmentation
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Yes
| 0
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expert
|
What code was used to simulte the SHINE dechirper
|
ECHO2D
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Summary
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Beam_performance_of_the_SHINE_dechirper.pdf
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$$ After calculating the inverse Fourier transformation, the distance s between the test and driving particles yields the longitudinal wake at the origin of $s = 0 ^ { + }$ , according to $w _ { \\mathrm { l } } \\sim e ^ { \\sqrt { s / s _ { 0 1 } } }$ . The relationship between the longitudinal point wake and the distance about the test charge behind the driving charge is expressed as Eq. (8) [19]. $$ w _ { 1 } ( s ) = - \\frac { \\pi Z _ { 0 } c } { 1 6 a ^ { 2 } } e ^ { - \\sqrt { s / s _ { 0 1 } } } . $$ The wakefield of the short bunch is obtained by convoluting the wake with the bunch shape $\\lambda ( s )$ . For a pencil beam, the original wake $w _ { 0 }$ on the axis becomes [19] $$ w _ { 0 } = \\frac { \\pi Z _ { 0 } c } { 1 6 a ^ { 2 } } . $$ Equation (8) shows that the required dechirper length $L$ is determined by the half-gap for a given dechirper strength. The half-gap $a = 1 \\mathrm { m m }$ was chosen as the baseline for the following reasons. On the one hand, it ensures that a sufficiently large proportion of the beam is included in the clear region for beam propagation, an essential requirement for controlling beam loss in a superconducting linac. On the other hands, the aperture size is constrained by the transverse emittance dilution effect, which is discussed in the following section. In [26], it is assumed that the corrugation dimensions are no greater than the gap size, i.e., $t , p \\leq a$ . This ensures that the structure is ‘steeply corrugated,’ such that short-range wakes can be neglected.
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augmentation
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Yes
| 0
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expert
|
What code was used to simulte the SHINE dechirper
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ECHO2D
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Summary
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Beam_performance_of_the_SHINE_dechirper.pdf
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The effect of a high group velocity in the radiation pulse also merits discussion. At the end of the structure length, the pulse length can be expressed [1] as $l _ { \\mathrm { p } } = 2 h t L / a p$ . For the structural parameters of SHINE, we have $l _ { \\mathrm { p } } = 5 \\mathrm { m }$ which is much longer than the actual bunch length of the particle. This effect does not have to be taken. During RF acceleration and beam transportation, the electron beam traveling from the VHF gun to the linac is affected by several beam-dynamic processes. These include the space-charge effect in the injector, the wakefield effect from SC structures, coherent synchrotron radiation (CSR) and non-linear effects during bunch compression [23]. Non-linearities in both the accelerating fields and the longitudinal dispersion can distort the longitudinal phase space. The typical final double-horn current distribution after the SHINE linac is shown in Fig. 4. The particles are concentrated within the first $2 0 ~ { \\mu \\mathrm { m } }$ with a linear energy spread. The wakefield for the actual simulated bunch distribution is shown in Fig. 5. Compared with the Gaussian and rectangular bunch distributions, as the head-tail wakefield effect of the beam, the double-horn bunch distribution distorts the expected chirp from the Gaussian bunch. The high peak current at the head of the beam complicates the situation further. The maximal chirp generated at different positions is also related to the feature in the bunch distribution. The particles in the double-horn bunch descend steeply over $1 5 ~ { \\mu \\mathrm { m } }$ , but the particles in the Gaussian and rectangular bunches hold a gender distribution. Nevertheless, the chirp induced by the double-horn beam distribution in less than $5 \\%$ differences in the maximal chirp and shows great correspondence on the tail. This proves that the analytical method is also perfectly suitable for the actual bunch in SHINE.
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augmentation
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Yes
| 0
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expert
|
What code was used to simulte the SHINE dechirper
|
ECHO2D
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Summary
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Beam_performance_of_the_SHINE_dechirper.pdf
|
According to the middle subplot in Fig. 5, the wakefield generated by the same structural parameters in the corrugated structure depends mainly on the shape of the bunch. As shown in the bottom of Fig. 5, with the longitudinal wakefield by the actual bunch, the energy chirp in the positive slope after L4 in SHINE can be well compensated. We can conclude that the longitudinal wake generated by the corrugated structure over $1 0 \\mathrm { ~ m ~ }$ is adequate and effective at canceling the energy chirp passively. 4 Transverse Wakefield effect For the part of the beam near the axis of plates, $w _ { \\mathrm { y d } }$ and $w _ { y \\mathbf { q } }$ are defined as the transverse quadrupole and dipole wakes, where the driving and test particle coordinates $y _ { 0 }$ and ${ \\boldsymbol { y } } \\ll { \\boldsymbol { a } }$ . For a driving particle at $( x _ { 0 } , \\ y _ { 0 } )$ and a test particle at $( x , y )$ , the transverse wake is given by [24] $$ \\begin{array} { r } { \\begin{array} { r c l } { w _ { y } = y _ { 0 } w _ { y \\mathrm { d } } + y w _ { y \\mathrm { q } } , } \\\\ { w _ { x } = ( x _ { 0 } - x ) w _ { y \\mathrm { q } } . } \\end{array} } \\end{array}
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augmentation
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Yes
| 0
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expert
|
What code was used to simulte the SHINE dechirper
|
ECHO2D
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Summary
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Beam_performance_of_the_SHINE_dechirper.pdf
|
$$ Expanding the surface impedance $\\zeta ~ [ 1 8 ]$ in the first two orders, the short-range vertical dipole and quadrupole wakes near the axis are given by [19] $$ \\begin{array} { r l } & { w _ { y \\mathrm { d } } \\approx \\displaystyle \\frac { Z _ { 0 } \\mathrm { c } \\pi ^ { 3 } } { 6 4 a ^ { 4 } } { \\mathit { s } } _ { 0 \\mathrm { d } } \\bigg [ 1 - \\big ( 1 + \\sqrt { { s } / { s } _ { 0 \\mathrm { d } } } \\big ) e ^ { \\sqrt { { s } / { s } _ { 0 \\mathrm { d } } } } \\bigg ] , } \\\\ & { w _ { y \\mathrm { q } } \\approx \\displaystyle \\frac { Z _ { 0 } \\mathrm { c } \\pi ^ { 3 } } { 6 4 a ^ { 4 } } { \\mathit { s } } _ { 0 \\mathrm { q } } \\bigg [ 1 - \\big ( 1 + \\sqrt { { s } / { s } _ { 0 \\mathrm { q } } } \\big ) e ^ { \\sqrt { { s } / { s } _ { 0 \\mathrm { q } } } } \\bigg ] , } \\\\ & { { \\mathit { s } } _ { 0 \\mathrm { d } } = s _ { 0 \\mathrm { r } } \\bigg ( \\displaystyle \\frac { 1 5 } { 1 4 } \\bigg ) ^ { 2 } , { \\mathit { s } } _ { 0 \\mathrm { q } } = s _ { 0 \\mathrm { r } } \\bigg ( \\displaystyle \\frac { 1 5 } { 1 6 } \\bigg ) ^ { 2 } . } \\end{array}
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augmentation
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Yes
| 0
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expert
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What code was used to simulte the SHINE dechirper
|
ECHO2D
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Summary
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Beam_performance_of_the_SHINE_dechirper.pdf
|
$$ where $k _ { \\mathrm { q } } ( s )$ is the effective quadrupole strength, which changes with $s$ within the bunch length $l$ . For the case where the beam is near the axis, a short uniformly distributed bunch was deduced in Ref. [25] to calculate the emittance growth after passing through the dechirper. As mentioned above, Eq. (9) is substituted into Eq. (50) of Ref. [25] to completely eliminate $2 0 \\mathrm { M e V }$ from the invariant: $$ \\begin{array} { r } { \\left( \\frac { \\epsilon _ { y } } { \\epsilon _ { y 0 } } \\right) = \\left[ 1 + \\left( \\frac { 1 0 ^ { 7 } \\pi ^ { 2 } l \\beta _ { y } } { 6 \\sqrt { 5 } a ^ { 2 } E } \\right) ^ { 2 } \\left( 1 + \\frac { 4 y _ { \\mathrm { c } } ^ { 2 } } { \\sigma _ { y } ^ { 2 } } \\right) \\right] ^ { 1 / 2 } . } \\end{array} $$ Based on the SHINE parameters, Fig. 7 shows the growth in emittance for different beam offsets. The value of $y _ { \\mathrm { c } }$ is proven to be a significant factor for determining the projected emittance. When the beam is near the axis and the gap $\\mathrm { ~ a ~ } \\geqslant \\mathrm { ~ 1 ~ m m ~ }$ , the effect on the growth in emittance induced by the dipole wakefield is tolerable. Hence, as a point of technique in beamline operation, maintaining the beam on-axis is an effective way to restrain emittance growth.
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augmentation
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Yes
| 0
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expert
|
What code was used to simulte the SHINE dechirper
|
ECHO2D
|
Summary
|
Beam_performance_of_the_SHINE_dechirper.pdf
|
To improve the beam quality in SHINE and maintain the projected emittance, we attempted to divide the dechirper into four sections of uniform length $2 . 5 \\mathrm { ~ m ~ }$ (hereafter named ‘four-dechirpers’). The two-dechirper and four-dechirper layouts are depicted in Fig. 9 based on the FODO design. The blue ellipse represents the bunch on-axis. The transverse direction points perpendicular to the page, while the black arrow under the e-beam defines the longitudinal direction. The corrugated structures are orthogonal, distributed between the quadrupole magnets. One FODO structure is formed in the two-dechirper and two are formed in the four-dechirper. The hypothesis on the beta functions is validated using a thick-lens calculation. The final transfer matrix is thus expressed as a $2 \\times 2$ matrix $M _ { \\mathrm { f } }$ , and the original and final Twiss parameters, given by $( \\alpha _ { 0 } , \\beta _ { 0 } , \\gamma _ { 0 } )$ and $( \\alpha , \\beta , \\gamma )$ , respectively, are related as $\\gamma = ( 1 + \\alpha ^ { 2 } ) / \\beta$ . As shown in Eq. (17) (where $< >$ [ denotes the numerical average obtained by integrating over the bunch length), the quadrupole wake transforms exactly like a magnetic quadrupole for any slice position in $s$ . By computing the transfer matrix with the structural parameters, the average of the final Twiss parameter and the emittance growth can be calculated as
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augmentation
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Yes
| 0
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expert
|
What code was used to simulte the SHINE dechirper
|
ECHO2D
|
Summary
|
Beam_performance_of_the_SHINE_dechirper.pdf
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$$ \\epsilon _ { \\mathrm { f } } / \\epsilon _ { 0 } = ( \\langle \\gamma _ { \\mathrm { f } } \\rangle \\langle \\beta _ { \\mathrm { f } } \\rangle - \\langle \\alpha _ { \\mathrm { f } } \\rangle ^ { 2 } ) ^ { 1 / 2 } , $$ where the subscripts f o represent the final (original) situation. Then, the other plane is also suitable. In contrast to the conventional FODO design, we utilized the two- and four-dechirpers, including the quadrupole wake generated in the corrugated structure. This destroys the periodicity in the Twiss parameters and causes the changes in the projected emittance in the final. The projected emittance growth for different magnet lengths $L$ and magnet strengths $K$ of the quadrupole magnets is demonstrated in Fig. 10. However, the minimum projected emittances in the two- and four-dechirpers are $0 . 0 1 7 5 \\%$ and $0 . 0 0 2 3 8 \\%$ , respectively. These values are comparatively small. The projected four-dechirper emittance still performs better. In the case of the symmetric feature in the FODO structure, the conclusion reached for the $x$ -direction does not apply to the $y$ -direction. The optimized working point (red dot) is selected for the quadrupole magnets, where the function $\\beta _ { x }$ is minimal and shows the best performance in terms of the emittance growth. The above calculation confirms the validity of dividing the dechirpers into four.
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augmentation
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Yes
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expert
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What code was used to simulte the SHINE dechirper
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ECHO2D
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Summary
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Beam_performance_of_the_SHINE_dechirper.pdf
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The $\\beta$ functions for both models are plotted in Fig. 9. In [28], the emittance growth caused by the quadrupole wakefield is fully compensated only if $\\beta _ { x } = \\beta _ { y }$ . In practice, however, the beta functions always fluctuate, and the beam suffers from the residual quadrupole wakefield. For a period FODO cell, the difference between the maximum and minimum $\\beta$ values is given by Eq. (18) [29], where $K$ and $L$ denote the quadrupole strength and length separately, and $l$ the length for each separated dechirper (5 and $2 . 5 \\mathrm { ~ m ~ }$ for the two- and four-dechirpers, respectively). $$ \\beta _ { \\mathrm { m a x } } - \\beta _ { \\mathrm { m i n } } = { 4 l } / { \\sqrt { 6 4 - K ^ { 2 } L ^ { 2 } l ^ { 2 } } } . $$ Figure 11 compares the $\\beta$ functions for two- and fourdechirpers by scanning the magnet strength $K$ and the magnet length $L$ . The minimum differences are $2 . 5 0 \\mathrm { ~ m ~ }$ and 1.25 for the two- and four-dechirpers, respectively. This implies a better compensation of the quadrupole wakefieldinduced emittance growth in the four-dechirper schemes. In practical engineering applications, four-dechirpers are considered appropriate to simplify the system.
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augmentation
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Yes
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IPAC
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What differences between time-domain and frequency-domain simulations affect predicted performance?
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Time-domain (2D) simulations include finite structure length and transient effects, while frequency-domain (3D) assume infinite periodicity and ideal conditions, leading to differences in predicted spectral purity and power.
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Reasoning
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haeusler-et-al-2022-boosting-the-efficiency-of-smith-purcell-radiators-using-nanophotonic-inverse-design.pdf
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Table: Caption: Table 2: Model Parameters Body: <html><body><table><tr><td>Inverter Stage Qty</td><td>Switching Freq, max (kHz)</td><td>Output Inductors (mH)</td><td>Output Capacitors (mF)</td><td>Load (ohms)</td></tr><tr><td>3</td><td>1</td><td>1</td><td>10</td><td>10</td></tr></table></body></html> It is important to note that the switching frequency, output inductance, and output capacitance values do not match the values of the actual supply though they are of the same magnitude. They were tuned in the preliminary model to give a smooth, $6 0 \\mathrm { { H z } }$ AC waveform output, as shown in Fig. 4. Simulation Procedure Once the model parameters were finalized, the next steps were to simulate four different scenarios, with the associated frequency spectrum as the simulation output: • Base case, no performance degradation • Degrading inductor • Degrading capacitor • Loss of a switch Figure 5 shows the frequemcy spectrum of the base case, while Fig. 6, Fig.7, and Fig. 8 show the spectrums of the degrading inductor, degrading capacitor, and the loss of a switch respectively. The corresponding values of degraded inductance and capacitance are listed for the associated simulations. “Degrading” is defined as a drop in component value to 80 percent of nameplate or less. [4]. prevent inadvertent filtering of the desired signals. Work on the next step is ongoing, however, as is shown in Fig. 9.
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augmentation
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NO
| 0
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IPAC
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What differences between time-domain and frequency-domain simulations affect predicted performance?
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Time-domain (2D) simulations include finite structure length and transient effects, while frequency-domain (3D) assume infinite periodicity and ideal conditions, leading to differences in predicted spectral purity and power.
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Reasoning
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haeusler-et-al-2022-boosting-the-efficiency-of-smith-purcell-radiators-using-nanophotonic-inverse-design.pdf
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The longitudinal analysis is then completed by calculating the normalized longitudinal impedances $Z / n$ [9] (see Fig. 4), where $n = f / f _ { r e \\nu }$ is the mode number, with $f _ { r e \\nu }$ denoting the revolution frequency of the accelerator. The wake loss factors for SFL and SFP are $4 . 8 3 \\times 1 0 ^ { - 2 } \\mathrm { V / p C }$ and $1 . 3 1 \\times 1 0 ^ { - 2 } \\mathrm { V / p C }$ , respectively. A comparison between the real parts of $Z / n$ shows that the SFL type is almost 100 times higher than the SFP one, while the ratio of the wake loss factors is about 3.69. Table: Caption: Table 2: $R _ { s }$ , $\\mathsf { Q }$ and $\\operatorname { R e } ( Z / n )$ comparison between the SFL and SFP dominant resonance. Body: <html><body><table><tr><td></td><td>fr [GHz]</td><td>Rs [Ω]</td><td>Q</td><td>Re(Z/n) [Ω]</td></tr><tr><td>SFL</td><td>2.9388</td><td>1247.7</td><td>287</td><td>0.4914</td></tr><tr><td>SFP</td><td>4.8793</td><td>22.64</td><td>56</td><td>5.4 × 10-3</td></tr></table></body></html> Mechanical Tolerances and Parametric Simulations The previously presented EM analysis on the SFP nominal model has allowed the evaluation of the variations of the longitudinal impedance for different geometric tolerances. Assuming that only one parameter varies at a time, we can now estimate the effects introduced by the unavoidable manufacturing and assembly tolerances. The considered parameter variations and the corresponding effects can be listed and discussed as follows.
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augmentation
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NO
| 0
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IPAC
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What differences between time-domain and frequency-domain simulations affect predicted performance?
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Time-domain (2D) simulations include finite structure length and transient effects, while frequency-domain (3D) assume infinite periodicity and ideal conditions, leading to differences in predicted spectral purity and power.
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Reasoning
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haeusler-et-al-2022-boosting-the-efficiency-of-smith-purcell-radiators-using-nanophotonic-inverse-design.pdf
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e s METHOD Ohmic losses from surface currents can reduce the efficiency of the cavity, resulting in heat generation caused by the Joule effect. This heat causes an increase in temperature and subsequent deformation of the cavity. These local displacements cause changes in the inductance and capacitance of the RF system, depending on whether they occur in the drift tube zone or in the cavity’s external walls. As a result, the frequency of the system decreases in each of the studied cases. To compare the maximum temperature, displacement, and frequency shift differences between the two prototypes, a series of simulations are performed in CST using nominal parameters of a duty cycle of $0 . 1 ~ \\%$ and a cooling water temperature of $2 5 ~ ^ { \\circ } \\mathrm { C }$ . We summarize in Table 1 a selection of thermal and mechanical properties of the materials that were considered in this study. For this purpose, the CST software employs the finite element method [2]. The steps followed, as shown in Fig. 3, are: 1. Analyze the electromagnetic fields generated in the cavity and calculate their resonant frequency. 2. Calculate the temperature increase in the different parts of the structure caused by the surface heat distribution obtained from the electromagnetic simulation, taking into account the material properties and cooling system. 3. Obtain the displacements resulting from the temperature changes. 4. Study the frequency shift caused by these displacements in an electromagnetic analysis of the cavity.
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augmentation
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NO
| 0
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IPAC
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What differences between time-domain and frequency-domain simulations affect predicted performance?
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Time-domain (2D) simulations include finite structure length and transient effects, while frequency-domain (3D) assume infinite periodicity and ideal conditions, leading to differences in predicted spectral purity and power.
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Reasoning
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haeusler-et-al-2022-boosting-the-efficiency-of-smith-purcell-radiators-using-nanophotonic-inverse-design.pdf
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MODELING FOR SIMULINK Cavity All measurements to create and validate the models were taken at the FoS RF system described in Ref. [8, 9]. In the first step, the modeling process is based on an RLC parallel resonant circuit (Fig. 1) as the equivalent lumped-element circuit of cavity and amplifiers near resonance [10]. From the describing integro-di!erential equation $$ C \\dot { V } _ { \\mathrm { g a p } } ( t ) + \\frac { 1 } { R _ { \\mathrm { p } } } V _ { \\mathrm { g a p } } ( t ) + \\frac { 1 } { L _ { \\mathrm { p } } } \\int V _ { \\mathrm { g a p } } ( t ) \\mathrm { d } t = S V _ { \\mathrm { d r i v e r } } ( t ) $$ the transfer function $$ G ( s ) = { \\frac { V _ { \\mathrm { g a p } } ( s ) } { V _ { \\mathrm { d r i v e r } } ( s ) } } = { \\frac { { \\frac { S } { C } } s } { s ^ { 2 } + { \\frac { 1 } { C R _ { \\mathrm { p } } } } s + { \\frac { 1 } { C L _ { \\mathrm { p } } } } } }
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augmentation
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NO
| 0
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IPAC
|
What differences between time-domain and frequency-domain simulations affect predicted performance?
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Time-domain (2D) simulations include finite structure length and transient effects, while frequency-domain (3D) assume infinite periodicity and ideal conditions, leading to differences in predicted spectral purity and power.
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Reasoning
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haeusler-et-al-2022-boosting-the-efficiency-of-smith-purcell-radiators-using-nanophotonic-inverse-design.pdf
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BENCHMARKING Fig. 5 shows FFTs of the driving and spill signals from machine measurements (left) and simulations (right). These plots compare the extracted spill/loss signal with the driving TFB/kicker signal, effectively comparing the “output” and “input” signals in frequency space. The signal used was a frequency-modulated chirp, from .3–.35 fractions of the time taken for one revolution, shown in Fig. 6. These chirps lasted for a set number of turns, and were repeated at a frequency marked at the red line, which is prominent in both the TFB/exciter and spill/loss frequency plots. For machine measurements, spill signals were measured using N2 gas scintillators [13] as they have been found to perform better at lower intensities than secondary emission monitors [1]. The driving signal was measured via an OASIS oscilloscope connected to the TFB plates [14]. Previous works characterising slow extraction have utilised fixed-amplitude frequency response functions, which describe how the frequency characteristics of the chirp signal propagate to the spill signal. One prominent feature is a “low-pass filter” effect, where low-frequency current ripples (e.g., chirp repetition rate) propagate to the extraction frequencies more than higher frequencies [15], with a pronounced cut-off frequency [16]. To compare the accuracy of the simulation’s frequency characteristics, this low-pass filter effect will be compared between simulations and machine data.
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augmentation
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NO
| 0
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IPAC
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What differences between time-domain and frequency-domain simulations affect predicted performance?
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Time-domain (2D) simulations include finite structure length and transient effects, while frequency-domain (3D) assume infinite periodicity and ideal conditions, leading to differences in predicted spectral purity and power.
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Reasoning
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haeusler-et-al-2022-boosting-the-efficiency-of-smith-purcell-radiators-using-nanophotonic-inverse-design.pdf
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Table: Caption: Table 5: Transient Analysis – Validation Body: <html><body><table><tr><td>Parameter</td><td>HF model</td><td>LDV (averaged)</td></tr><tr><td>Max. disp.</td><td>39.5 μm</td><td>32.7 μm</td></tr><tr><td>Max. velocity</td><td>0.10 m/s</td><td>0.26 m/s</td></tr></table></body></html> The punctual vibration measurements on several locations have been carried out using the single-point LDV as shown in Fig. 5. The electric pulse was triggered every 10 seconds to avoid a significant overlap of vibrations (the overlap was seen for shorter durations - 1 s and 2 s). The measurements were studied in different frequency ranges. The results from the campaign are shown in Fig. 6, for the frequency up to $3 5 0 \\mathrm { H z }$ . The pulse response waveform has been split in four 1-second timeframes. Fast Fourier Transform (FFT) for each of these frames was calculated and then averaged over three consecutive pulses. In Fig. 6, the waveform split of the first pulse was shown as an example. Future LDV measurements are also considered under vacuum conditions, an initial performance demonstration based on measurement through a standard vacuum feedthrough window has shown satisfactory results. -80 P 50 100 150 200 250 300 350 Frequency [Hz] ×10-1 ×10-4 ×10-5 ×10-5 2 2 -2.5 0 -5.0 -5 -2 -7.5 16 0 1 1 2 2 3 3 4 Time[s]
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augmentation
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NO
| 0
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Expert
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What differences between time-domain and frequency-domain simulations affect predicted performance?
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Time-domain (2D) simulations include finite structure length and transient effects, while frequency-domain (3D) assume infinite periodicity and ideal conditions, leading to differences in predicted spectral purity and power.
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Reasoning
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haeusler-et-al-2022-boosting-the-efficiency-of-smith-purcell-radiators-using-nanophotonic-inverse-design.pdf
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A 200-period-long version of the inverse-designed structure was fabricated by electron beam lithography $\\bar { ( } 1 0 0 \\ \\mathrm { k V } )$ and cryogenic reactive-ion etching of $1 - 5 \\Omega \\cdot \\mathrm { c m }$ phosphorus-doped silicon to a depth of $1 . 3 \\big ( 1 \\big ) \\mathsf { \\bar { \\mu } m }$ .35 The surrounding substrate was etched away to form a $5 0 ~ \\mu \\mathrm { m }$ high mesa (Figure 2a). We note that unlike in most previous works the etching direction is here perpendicular to the radiation emission, enabling the realization of complex 2D geometries. The radiation generation experiment was performed inside a scanning electron microscope (SEM) with an 11 nA beam of $3 0 \\mathrm { \\ k e V }$ electrons. The generated photons were collected with an objective (NA 0.58), guided out of the vacuum chamber via a $3 0 0 ~ \\mu \\mathrm { m }$ core multimode fiber and detected with a spectrometer (Figure 2b and Methods). RESULTS We compare the emission characteristics of the inversedesigned structure to two other designs: First, a rectangular 1D grating with groove width and depth of half the periodicity $a _ { \\mathrm { { ; } } }$ , similar to the one used in refs 6 and 36. And second, a dual pillar structure with two rows of pillars, $\\pi$ -phase shifted with respect to each other, and with a DBR on the back. This design was successfully used in dielectric laser acceleration, the inverse effect of SPR. $\\mathbf { \\lambda } ^ { 3 0 , 3 2 , 3 3 , 3 5 , 3 7 - } 3 9$ It further represents the manmade design closest to our result of a computer-based optimization.
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1
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NO
| 0
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IPAC
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What differences between time-domain and frequency-domain simulations affect predicted performance?
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Time-domain (2D) simulations include finite structure length and transient effects, while frequency-domain (3D) assume infinite periodicity and ideal conditions, leading to differences in predicted spectral purity and power.
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Reasoning
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haeusler-et-al-2022-boosting-the-efficiency-of-smith-purcell-radiators-using-nanophotonic-inverse-design.pdf
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The forecasting of all the projections in all the modules takes less than one second whereas HPSim takes around 10 minutes with similar computing infrastructure, resulting in a speed up by a factor of $\\sim 6 0 0$ . The exceptional computational speed of the method makes it extremely well-suited for various real-time accelerator applications. The method can be used as a virtual diagnostic in which CVAE-LSTM predicts a detailed evolution of the beam’s phase space through the entire LANSCE accelerator based on the current RF module settings and using only 4 initial steps from the much slower HPSim physics-based model as its initial points. In general, the application of such an approach to any large accelerator will provide a substantial benefit for simulating beam dynamics and for accelerator optimization. Uncertainty analysis is a byproduct of probabilistic models (like VAE) and it plays an important role in understanding uncertainties associated with the accelerator operation. In our proposed methods, just by sampling the latent space for the first few modules, the LSTM and decoder can be used to generate phase space projections in all the modules. A detailed investigation of the uncertainty analysis aspect is a part of future research work.
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1
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NO
| 0
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IPAC
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What differences between time-domain and frequency-domain simulations affect predicted performance?
|
Time-domain (2D) simulations include finite structure length and transient effects, while frequency-domain (3D) assume infinite periodicity and ideal conditions, leading to differences in predicted spectral purity and power.
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Reasoning
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haeusler-et-al-2022-boosting-the-efficiency-of-smith-purcell-radiators-using-nanophotonic-inverse-design.pdf
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The vertical quadrupole wake potential was calculated by integrating the derivative of the longitudinal wake potential as shown in Eq. (3). Since calculating the derivative of the longitudinal wake potential along the vertical direction involves subtracting two large numbers, the accuracy of the quadrupole wake potential can be compromised. 0.08ECH03DGdfidL0.06 0.02 -0.02-0.04-0.06-0.08-0.10 50 100 150 200 250 300s (cm) Figure 12 shows the quadrupole wake potential, indicating significant discrepancies between the results obtained from the two codes, especially for $\\mathrm { s } > 1 . 5 \\mathrm { ~ m ~ }$ . A similar problem was encountered when the quadrupole wake potential for the ESR cavity was calculated. The author of ECHO3D was contacted and is looking into the issue. The impedances calculated from the two codes, however, share a lot of similarities, including the frequencies for the spikes and the amplitude of the spikes, as shown in Fig. 13. In addition, the quadrupole wake potential calculated by GdfidL (Fig. 13 left) is less noisy than those calculated from ECHO3D (Fig. 13 right). 40 40 Re(Zq 30 30 20 20 cal -10 -20 -20 -30 -30 0 5 10 15 20 25 0 5 10 15 20 25 f (GHz) f(GHz)
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1
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NO
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Expert
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What differences between time-domain and frequency-domain simulations affect predicted performance?
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Time-domain (2D) simulations include finite structure length and transient effects, while frequency-domain (3D) assume infinite periodicity and ideal conditions, leading to differences in predicted spectral purity and power.
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Reasoning
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haeusler-et-al-2022-boosting-the-efficiency-of-smith-purcell-radiators-using-nanophotonic-inverse-design.pdf
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$$ { \\bf J } ( { \\bf r } , \\omega ) = \\frac { q } { 2 \\pi } { ( 2 \\pi \\sigma _ { x } ^ { 2 } ) } ^ { - 1 / 2 } \\mathrm { e } ^ { - x ^ { 2 } / 2 \\sigma _ { x } ^ { 2 } } \\mathrm { e } ^ { - i k _ { y } y } \\widehat { { \\bf y } } $$ with $k _ { y } = \\omega / \\nu$ . Using this expression, the electromagnetic field was calculated via Maxwell’s equations for linear, nonmagnetic materials. As this is a 2D problem, the transverse-electric mode $E _ { z }$ decouples from the transverse-magnetic mode $H _ { z } ,$ where only the latter is relevant here. A typical 2D-FDFD simulation took 1 s on a common laptop, and the algorithm needed about 500 iterations to converge to a stable maximum. Simulated Radiation Power. From the simulated electromagnetic field, we calculate the total energy $W$ radiated by a single electron per period $a$ of the grating. In the time domain, this would correspond to integrating the energy flux $\\mathbf { \\boldsymbol { s } } ( \\mathbf { \\boldsymbol { r } } , \\ t )$ through the area surrounding the grating over the time it takes for the particle to pass over one period of the grating. In the frequency domain, one needs to integrate $\\mathbf { \\Delta } \\mathbf { S } ( \\mathbf { r } , \\omega )$ through the area around one period over all positive frequencies, that is,36
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1
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NO
| 0
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Expert
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What differences between time-domain and frequency-domain simulations affect predicted performance?
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Time-domain (2D) simulations include finite structure length and transient effects, while frequency-domain (3D) assume infinite periodicity and ideal conditions, leading to differences in predicted spectral purity and power.
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Reasoning
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haeusler-et-al-2022-boosting-the-efficiency-of-smith-purcell-radiators-using-nanophotonic-inverse-design.pdf
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For a further study of the different structures, we performed 2D time-domain and 3D frequency-domain simulations. While both time and frequency domain are in principal legitimate ways to calculate the radiation spectrum from single electrons, they differ in computational complexity and precession. The time-domain simulation (Figure 3b and Videos S1, S2, and S3) can capture the instantaneous response to a structure of finite length. This is computationally expensive because the field of the entire grating needs to be calculated at each point in time. The frequency-domain simulation (Figure 3c), on the other hand, calculates the radiation density at each frequency of the spectrum. This is computationally less complex because it is sufficient to consider a single unit cell with periodic boundaries, which allowed us to perform 3D simulations. It can therefore take into account the limited height of the electron beam and the structure, which is on the order of the wavelength. This is particularly relevant here, because the inverse design yielded a double-sided grating that forms a resonator. The mirrors of the resonator are plane parallel and therefore do not form a stable resonator. Both the 2D time-domain and 3D frequency-domain simulations show similar results. For the inverse design, they predict a total radiation of 108(14) pW, a quantum efficiency of $1 . 1 ( 2 ) \\% ,$ and a peak spectral radiation density of 1.8(2) $\\mathrm { { \\ p W / n m } }$ . In terms of total power, this corresponds to an increase by $8 0 \\%$ compared to the dual pillar design and a colossal boost of $9 8 0 \\%$ with respect to the rectangular grating. The contrast in terms of peak efficiency within the experimentally accessible range from 1200 to $1 6 0 0 ~ \\mathrm { { n m } }$ is even more drastic. It reaches an increase by $2 9 0 \\%$ compared to the dual pillars and $1 6 5 0 \\%$ relative to the rectangular grating.
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1
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NO
| 0
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IPAC
|
What differences between time-domain and frequency-domain simulations affect predicted performance?
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Time-domain (2D) simulations include finite structure length and transient effects, while frequency-domain (3D) assume infinite periodicity and ideal conditions, leading to differences in predicted spectral purity and power.
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Reasoning
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haeusler-et-al-2022-boosting-the-efficiency-of-smith-purcell-radiators-using-nanophotonic-inverse-design.pdf
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Table: Caption: Table 1: Resonance frequencies, shunt impedances and Qfactors of the dominant modes calculates by the impedance and eigenmode solvers, respectively. Body: <html><body><table><tr><td>#</td><td colspan="2">fo/MHz 二</td><td colspan="2">Rs/Ω 1</td><td colspan="2">Q</td></tr><tr><td></td><td>Imp.</td><td>Eig.</td><td>Imp.</td><td>Eig.</td><td>Imp.</td><td>Eig.</td></tr><tr><td>1</td><td>97.81</td><td>97.32</td><td>3.23</td><td>3.14</td><td>1001</td><td>1005</td></tr><tr><td>2</td><td>131.9</td><td>131.3</td><td>11.6</td><td>12.9</td><td>1733</td><td>1802</td></tr><tr><td>3</td><td>157.4</td><td>156.7</td><td>46.2</td><td>50.0</td><td>2346</td><td>2486</td></tr><tr><td>4</td><td>185.0</td><td>184.3</td><td>82.4</td><td>89.0</td><td>3080</td><td>3332</td></tr><tr><td>5</td><td>215.1</td><td>214.3</td><td>101</td><td>109</td><td>3915</td><td>4309</td></tr><tr><td>6</td><td>246.8</td><td>245.8</td><td>105</td><td>112</td><td>4771</td><td>5322</td></tr><tr><td>7</td><td>278.6</td><td>277.6</td><td>94.9</td><td>99.4</td><td>5702</td><td>6465</td></tr><tr><td>8</td><td>312.3</td><td>311.2</td><td>82.5</td><td>84.4</td><td>6520</td><td>7482</td></tr><tr><td>9</td><td>346.0</td><td>344.7</td><td>68.4</td><td>68.2</td><td>7332</td><td>8503</td></tr><tr><td>10</td><td>380.2</td><td>378.7</td><td>54.8</td><td>51.7</td><td>7967</td><td>9301</td></tr><tr><td>11</td><td>413.7</td><td>412.2</td><td>37.1</td><td>32.5</td><td>8672</td><td>10237</td></tr><tr><td>12</td><td>448.3</td><td>446.9</td><td>17.3</td><td>15.2</td><td>6397</td><td>7840</td></tr><tr><td>13</td><td>482.9</td><td>481.5</td><td>15.8</td><td>11.6</td><td>8762</td><td>10272</td></tr></table></body></html> To estimate the accuracy of the results, a comparison between the $2 ^ { \\mathrm { n d } }$ and $3 ^ { \\mathrm { { r d } } }$ order solution of the impedance solver is shown in Fig. 4. This comparison further substantiates the conclusion of a good accuracy up to ${ 5 0 0 } \\mathrm { M H z }$ . Moreover, the comparison reveals that the impedance error is due to spatial resolution, which implies that the mesh resolution for higher frequencies is insufficient. A similar behaviour is observed for the eigenmode solver. Referring to the above comparison, the limitation of the two frequency domain solvers becomes evident. The presented $3 ^ { \\mathrm { r d } }$ order calculation of the impedance solver requires about $2 0 0 \\mathrm { G B }$ of RAM, with the available memory of the used machine being 256 GB. Similarly, the simulation of the eigenmode solver requires 250 GB. Ultimately, these results emphasize the demand for further improvements in numerical methods for impedance calculations. Relying on time-consuming wakefield simulations in the time domain is not a viable option. Therefore, further improvements are necessary, in particular, for the impedance and eigenmode solvers. For the impedance solver, potential improvements could be achieved by employing techniques such as multigrid methods, domain decomposition, or concatenation methods [6].
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1
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NO
| 0
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Expert
|
What differences between time-domain and frequency-domain simulations affect predicted performance?
|
Time-domain (2D) simulations include finite structure length and transient effects, while frequency-domain (3D) assume infinite periodicity and ideal conditions, leading to differences in predicted spectral purity and power.
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Reasoning
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haeusler-et-al-2022-boosting-the-efficiency-of-smith-purcell-radiators-using-nanophotonic-inverse-design.pdf
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3D Simulations. 3D finite-element-method (FEM) frequency-domain simulations were performed in COMSOL to analyze effects originating from the finite height of the structure and beam. The structures were assumed to be $1 . 5 \\mu \\mathrm { m }$ high on a flat silicon substrate (Figure 1b). The spectral current density had a Gaussian beam profile of width $\\sigma = 2 0$ nm: $$ \\mathbf { J } ( \\mathbf { r } , \\omega ) = \\frac { - e } { 2 \\pi } \\big ( 2 \\pi \\sigma ^ { 2 } \\big ) ^ { - 1 } \\mathrm { e } ^ { - \\big ( x ^ { 2 } + z ^ { 2 } \\big ) / 2 \\sigma ^ { 2 } } \\mathrm { e } ^ { - i k _ { y } y } \\widehat { \\mathbf { y } } $$ Experimental Setup. The experiment was performed within an FEI/Philips XL30 SEM providing an $1 1 \\mathrm { \\ n A }$ electron beam with $3 0 \\mathrm { \\ k e V }$ mean electron energy. The structure was mounted to an electron optical bench with full translational and rotational control. The generated photons were collected with a microfocus objective SchaÃàfter+Kirchhoff 5M-A4.0-00-STi with a numerical aperture of 0.58 and a working distance of $1 . 6 ~ \\mathrm { m m }$ . The objective can be moved relative to the structure with five piezoelectric motors for the three translation axes and the two rotation axes transverse to the collection direction. The front lens of the objective was shielded with a fine metal grid to avoid charging with secondary electrons in the SEM, which would otherwise deflect the electron beam, reducing its quality. The collected photons were focused with a collimator into a ${ 3 0 0 } { - } \\mu \\mathrm { m }$ -core multimode fiber guiding the photons outside the SEM, where they were detected with a NIRQuest $^ { \\cdot + }$ spectrometer.
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augmentation
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NO
| 0
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Expert
|
What differences between time-domain and frequency-domain simulations affect predicted performance?
|
Time-domain (2D) simulations include finite structure length and transient effects, while frequency-domain (3D) assume infinite periodicity and ideal conditions, leading to differences in predicted spectral purity and power.
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Reasoning
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haeusler-et-al-2022-boosting-the-efficiency-of-smith-purcell-radiators-using-nanophotonic-inverse-design.pdf
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KEYWORDS: light‚àímatter interaction, free-electron light sources, Smith‚àíPurcell radiation, inverse design, nanophotonics T ehle Smith‚àíPurcell effect describes the emission of ctromagnetic radiation from a charged particle propagating freely near a periodic structure. The wavelength $\\lambda$ of the far-field radiation follows1 $$ \\lambda = \\frac { a } { m } ( \\beta ^ { - 1 } - \\cos { \\theta } ) $$ where $a$ is the periodicity of the structure, $\\beta = \\nu / c$ is the velocity of the particle, $\\theta$ is the angle of emission with respect to the particle propagation direction, and $m$ is the integer diffraction order. The absence of a lower bound on the electron velocity in eq 1 makes Smith‚àíPurcell radiation (SPR) an interesting candidate for an integrated, tunable free-electron light source in the low-energy regime.2‚àí8 While the power efficiency of this process is still several orders of magnitude smaller than conventional light sources, it can be enhanced by super-radiant emission from coherent electrons.9 For this, prebunching of the electrons is a possible avenue ,10‚àí13 but also self-bunching due to the interaction with the excited nearfield of the grating is observed above a certain current threshold.14‚àí16 The use of coherent electrons is particularly interesting in combination with resonant structures, such as near bound states in the continuum.5,17
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What differences between time-domain and frequency-domain simulations affect predicted performance?
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Time-domain (2D) simulations include finite structure length and transient effects, while frequency-domain (3D) assume infinite periodicity and ideal conditions, leading to differences in predicted spectral purity and power.
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Reasoning
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haeusler-et-al-2022-boosting-the-efficiency-of-smith-purcell-radiators-using-nanophotonic-inverse-design.pdf
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allows to design the spectrum $( \\omega )$ , spatial distribution $\\mathbf { \\Pi } ( \\mathbf { r } )$ , and polarization (e) of radiation by favoring one kind $| \\mathbf { e } { \\cdot } \\mathbf { E } ( \\mathbf { r } , \\omega ) |$ and penalizing others, $- | \\mathbf { e } ^ { \\prime } { \\boldsymbol { \\cdot } } \\mathbf { E } ( \\mathbf { r } ^ { \\prime } , \\omega ^ { \\prime } ) |$ , with possibly orthogonal polarization $\\mathbf { e ^ { \\prime } }$ . Lifting the periodicity constraint opens the space to complex metasurfaces, which would for example enable designs for focusing or holograms.18,22‚àí27,40 Future efforts could also target the electron dynamics to achieve (self-)bunching and, hence, coherent enhancement of radiation. In that case, the objective function would aim at the field inside the electron channel rather than the far-field emission. This would favor higher quality factors at the cost of lower out-coupling efficiencies. However, direct inclusion of the electron dynamics through an external multiphysics package proves challenging as our inverse design implementation requires differentiability of the objective function with respect to the design parameters. Instead, one may choose to use an analytical expression for the desired electron trajectory or an approximate form for the desired field pattern.
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Expert
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What differences between time-domain and frequency-domain simulations affect predicted performance?
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Time-domain (2D) simulations include finite structure length and transient effects, while frequency-domain (3D) assume infinite periodicity and ideal conditions, leading to differences in predicted spectral purity and power.
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Reasoning
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haeusler-et-al-2022-boosting-the-efficiency-of-smith-purcell-radiators-using-nanophotonic-inverse-design.pdf
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DESIGN The inverse design optimization was carried out via an opensource Python package34 based on a 2D frequency-domain (FD) simulation. At the center of the optimization process is the objective function $G$ , which formulates the desired performance of the design, defined by the design variable $\\phi$ (Methods). Here, we aimed for maximum radiation in negative $x$ -direction at the design angular frequency $\\omega$ corresponding to $\\lambda = 1 . 4 \\mu \\mathrm { m }$ (Figure 1). To this end, the Poynting vector S was numerically measured in the far field of the structure and integrated over one period $a$ , giving the objective function $$ G ( \\phi ) = - \\int _ { 0 } ^ { a } \\mathrm { d } y \\ S _ { x } ( x _ { \\mathrm { f a r f i e l d } } , y ) $$ The resulting design is depicted in Figure 1a and reveals two gratings on each side of the vacuum channel, which are similar in shape but $\\pi$ -phase shifted with respect to each other. The back of the double-sided grating results in a structure that resembles a distributed Bragg reflector (DBR). This way, the radiation to the left is $4 6 9 \\times$ higher than to the right.
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Expert
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What differences between time-domain and frequency-domain simulations affect predicted performance?
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Time-domain (2D) simulations include finite structure length and transient effects, while frequency-domain (3D) assume infinite periodicity and ideal conditions, leading to differences in predicted spectral purity and power.
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Reasoning
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haeusler-et-al-2022-boosting-the-efficiency-of-smith-purcell-radiators-using-nanophotonic-inverse-design.pdf
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Collection Range. The measured Gaussian spectrum from Figure 3a can be explained by the limited numerical aperture of the collection fiber. Smith‚àíPurcell radiation that is emitted in the nonperpendicular direction is offset from the optical axis for collection. This leads to a loss in collection efficiency, which we modeled with the function $\\exp \\{ - 2 r ^ { 2 } / ( { f } \\mathrm { { \\cdot } N A } ) ^ { 2 } \\} ,$ where $r$ is the offset measured at the collimator, $f = 1 2 ~ \\mathrm { m m }$ is the focal length of the collimator, and NA is the numerical aperture of the fiber. We found good agreement with the experimental data for $\\mathrm { N A } = 0 . 1 1$ , which is below the 0.22 stated by the manufacturer and might have been a result of misalignment. ASSOCIATED CONTENT $\\bullet$ Supporting Information The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsphotonics.1c01687. Dependence of radiation on electron beam height within the structure; Determination of effective current; Dependence on beam-grating distance (PDF) 2D time-domain simulation of the inverse design structure (MP4) 2D time-domain simulation of the dual pillar structure with DBR (MP4)
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What differences between time-domain and frequency-domain simulations affect predicted performance?
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Time-domain (2D) simulations include finite structure length and transient effects, while frequency-domain (3D) assume infinite periodicity and ideal conditions, leading to differences in predicted spectral purity and power.
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Reasoning
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haeusler-et-al-2022-boosting-the-efficiency-of-smith-purcell-radiators-using-nanophotonic-inverse-design.pdf
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METHODS Inverse Design. The inverse design optimization was carried out via an open-source Python package34 based on a 2D finite-difference frequency-domain (FDFD) simulation at the design angular frequency $\\omega$ corresponding to $\\lambda = 1 . 4 \\mu \\mathrm { m }$ . The simulation cell used for this purpose is presented in Figure 5. The design $\\varepsilon _ { \\mathrm { r } } ( \\phi )$ was parametrized with the variable $\\phi ( \\mathbf { r } )$ . Sharp features $\\left( < 1 0 0 \\ \\mathrm { \\ n m } \\right)$ in the design were avoided by convolving $\\phi ( \\mathbf { r } )$ with a 2D circular kernel of uniform weight. Afterward the convolved design $\\tilde { \\phi }$ was projected onto a sigmoid function of the form tanh $( \\gamma \\tilde { \\phi } )$ . This results in a closeto-binary design where the relative permittivity $\\varepsilon _ { \\mathrm { { r } } } ( { \\bf { r } } )$ only takes the values of silicon $\\left( \\varepsilon _ { \\mathrm { r } } = 1 2 . 2 \\right) ^ { 4 \\mathrm { f } }$ or vacuum $\\left( \\varepsilon _ { \\mathrm { r } } \\ = \\ 1 \\right)$ ). We observed good results by starting the optimization with small values $\\gamma = 2 0$ and slowly increasing $\\gamma$ to 1000.
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What differences between time-domain and frequency-domain simulations affect predicted performance?
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Time-domain (2D) simulations include finite structure length and transient effects, while frequency-domain (3D) assume infinite periodicity and ideal conditions, leading to differences in predicted spectral purity and power.
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Reasoning
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haeusler-et-al-2022-boosting-the-efficiency-of-smith-purcell-radiators-using-nanophotonic-inverse-design.pdf
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Even in the regime of incoherent electrons, Smith‚àíPurcell radiation can be greatly enhanced by optimizing beam parameters (velocity and diameter) and grating properties (material and shape). The latter are generally limited by the chosen method of fabrication. Typical gratings for the generation of near-infrared, visible, or ultraviolet light are fabricated by reactive-ion etching or focused-ion-beam milling of silicon or fused silica.2‚àí7,18 Coating the grating with a metal such as gold, silver, or aluminum can lead to plasmonic enhancement.19‚àí22 While a simple rectangular grating has been the most common choice in Smith‚àíPurcell experiments, other designs have been investigated, such as metasurfaces and aperiodic structures.18,22‚àí28 Here, we explored the optimization technique of nanophotonic inverse design29‚àí33 to generate SPR much more efficiently. In contrast to other photonic designs created manually and optimized for a small set of parameters, inverse design finds an optimal design without any prior knowledge of its shape, purely based on the desired performance. We applied the technique to maximize SPR from $3 0 { \\mathrm { \\ k e V } }$ electrons $\\zeta = 0 . 3 2 8 )$ passing through a silicon nanostructure and radiating around $\\lambda = 1 . 4 \\mu \\mathrm { m }$ in the transverse direction ( $\\cdot \\theta$ $= 9 0 ^ { \\circ } )$ ). The resulting nanostructure forms an asymmetric cavity around the electron beam, which leads to a highly concentrated emission into a well-defined direction. We compared the emission characteristics to those of a structure with a double row of pillars and a distributed Bragg reflector as well as that of a rectangular grating (Figure 1). Like most previously used gratings, these radiate broadbandly, both spectrally and spatially (Figure 1c). This impedes their application as a light source because part of the electron energy is converted to radiation that cannot be collected or is spectrally irrelevant. By contrast, the here presented inverse design can resolve these problems with unprecedented efficiency.
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IPAC
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What does LYSO:Ce stand for?
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Cerium-doped Lutetium-Yttrium Oxyorthosilicate
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Definition
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Addesa_2022_J._Inst._17_P08028.pdf
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Table: Caption: Table 1: Parameters of the Proposed LANSCE Injector Body: <html><body><table><tr><td></td></tr><tr><td>Ions</td><td>H+/H</td></tr><tr><td>Ion sources extraction voltage</td><td>100 keV</td></tr><tr><td>RF Frequency</td><td>201.25 MHz</td></tr><tr><td>RFQ energy</td><td>3 MeV</td></tr><tr><td>Number ofRFQ cells</td><td>187</td></tr><tr><td>RFQ length</td><td>4.2 m</td></tr><tr><td>DTL Energy</td><td>100 MeV</td></tr><tr><td>Repetition rate</td><td>120 Hz</td></tr><tr><td>Average current</td><td>1.25 mA</td></tr><tr><td>Beam pulse</td><td>625-1000 μs</td></tr></table></body></html> Table: Caption: Table 2: Normalized Transverse RMS Beam Emittance (π mm mrad), Charge Per Bunch $\\left( \\mathrm { Q } / \\mathrm { b } \\right)$ , and Relative Emittance Growth, $\\varepsilon / \\varepsilon _ { \\mathrm { 0 } }$ in the Existing LANSCE Linac Body: <html><body><table><tr><td>Beam (Facility)</td><td>Sour ce</td><td>0.75 MeV</td><td>100 MeV</td><td>800 MeV</td><td>Q/b pC</td><td>ε/£0</td></tr><tr><td>H (Lujan /pRad/ UCN)</td><td>0.18</td><td>0.22</td><td>0.45</td><td>0.7</td><td>50</td><td>3.2</td></tr><tr><td>H (WNR)</td><td>0.18</td><td>0.27</td><td>0.58</td><td>1.2</td><td>125</td><td>4.6</td></tr><tr><td>H+ (IPF), DTL only</td><td>0.03</td><td>0.05</td><td>0.26</td><td></td><td>20</td><td>5.2</td></tr><tr><td>H+ (Area A, 1995)</td><td>0.05</td><td>0.08</td><td>0.3</td><td>0.7</td><td>82</td><td>8.7</td></tr></table></body></html> 50ms(x20=1sec) 8.33ms 625μs 625us 4mAH+ ? A PF HμA PEF PARM l PF Table 2 illustrates the emittance growth of various beams in the existing LANSCE accelerator, including a highpower $8 0 0 { ~ \\mathrm { k W } ~ \\mathrm { H } ^ { + } }$ beam delivered to Area A until 1999. Significant emittance growth is observed in DTL, especially in $\\mathrm { H } ^ { - }$ beam transported to WNR, and in $\\mathrm { H ^ { + } }$ beam. In the present LANSCE front end, the two-cavity bunching system provides $80 \\%$ capture into Drift Tube Linac.
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IPAC
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What does LYSO:Ce stand for?
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Cerium-doped Lutetium-Yttrium Oxyorthosilicate
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Definition
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Addesa_2022_J._Inst._17_P08028.pdf
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SUMMARY AND OUTLOOK This paper describes the current status of the far-field EOSD setup at KARA. The optics have now been adapted to easily switch from EOS to EOSD. The spectrometer setup has been improved. The effort to make the balanced detection on KALYPSO to work is in progress. ACKNOWLEDGEMENTS [2] S. Funkner et al., “Revealing the dynamics of ultrarelativistic non-equilibrium many-electron systems with phase space tomography”, Sci Rep, vol. 13.1, pp. 1-11, March 2023. doi:10.1038/s41598-023-31196-5 [3] L. Rota et al., “KALYPSO: Linear array detector for highrepetition rate and real-time beam diagnostics”, Nucl. Instrum. Methods Phys. Res., Sect. A, 936, pp. 10–13, 2019. doi:10.1016/j.nima.2018.10.093 [4] L. Rota et al., “A high-throughput readout architecture based on PCI-Express Gen3 and DirectGMA technology”, J. Instrum.,11, p02007, 2016. doi:10.1088/1748-0221/11/02/P02007 [5] C. Widmann et al., “Measuring the Coherent Synchrotron Radiation Far Field with Electro-Optical Techniques”, in Proc. IPAC’22, Bangkok, Thailand, Jun. 2022, pp. 292–295. doi:10.18429/JACoW-IPAC2022-MOPOPT024 [6] Menlo Systems GmbH, TDS Spectrometer TERA K15 with emitter TERA15-FC, https://www.menlosystems.com [7] L. L. Grimm, “Design and Set-Up of a Spectrometer for the Electro-Optical Far-Field Setup at KARA for Detection Using KALYPSO.”, Bachelor thesis, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany, 2023. [8] M. M. Patil et al., “Ultra-Fast Line-Camera KALYPSO for fs-Laser-Based Electron Beam Diagnostics”, in Proc. IBIC’21, Pohang, Korea, Sep. 2021, pp. 1–6. doi:10.18429/JACoW-IBIC2021-MOOB01
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IPAC
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What does LYSO:Ce stand for?
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Cerium-doped Lutetium-Yttrium Oxyorthosilicate
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Definition
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Addesa_2022_J._Inst._17_P08028.pdf
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For over 30 years the PSB has been directly delivering beams to ISOLDE [4], a radioactive isotope facility at CERN. To satisfy the demands of ISOLDE for high-intensity beams, the PSB operated before LS2 in the space charge dominated regime with considerable beam losses at injection, also caused by the multi-turn injection scheme. One of the most important upgrades within LIU was the replacement of Linac2, which delivered protons at a kinetic energy of $5 0 \\mathrm { M e V }$ , by Linac4 (L4) that delivers $\\mathrm { H } ^ { - }$ ions at an increased kinetic energy of $1 6 0 \\mathrm { M e V } .$ . The increase of the injection energy in the PSB allows doubling the beam intensity while maintaining similar space charge detuning and transverse emittances. To convert the $\\mathrm { H } ^ { - }$ ions of L4 to protons, the conventional proton multi-turn injection was replaced by a new charge exchange injection system. In this system, the incoming $\\mathrm { H } ^ { - }$ pass through a thin foil which strips their electrons. The remaining protons are put into orbit around the PSB while the partially or unstripped particles end up in the $\\mathrm { H ^ { 0 } / H ^ { - } }$ dump. The installation of a charge exchange system allows the production of high intensity and high brightness beams with an almost loss-free injection. Furthermore, adjusting closed orbit bumps in the horizontal plane allows the tailoring of the beam emittances in terms of phase space painting, which helps reducing the phase space density and thus space charge forces at high intensities [5].
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augmentation
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IPAC
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What does LYSO:Ce stand for?
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Cerium-doped Lutetium-Yttrium Oxyorthosilicate
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Definition
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Addesa_2022_J._Inst._17_P08028.pdf
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$$ with $\\mathrm { E _ { b e a m } = 6 5 0 0 G e V }$ and $1 8 2 . 5 \\mathrm { G e V }$ and the bending radius $\\rho = 2 8 0 3 . 9 5 \\mathrm { m }$ and $1 0 7 6 0 \\mathrm { m }$ respectively for the LHC and the FCC. A correction factor is used to take into account the distance between the last dipole and the position of the pressure computation to evaluate de photon flux. The evolution of the electron density at a point, averaged over the time interval between successive bunch passages, can be accurately described by a simple cubic map [4]. The DYVACS code is implemented in MATHEMATICA and the solution to the set of Eq. (1) is given in [1]. Therefore, for each time step that are defined: $\\bullet$ ion flux (from ionization and desorption); • $\\Gamma _ { e }$ electron flux (from ionization and electron cloud); • $\\Gamma _ { p h }$ photon flux (due to synchrotron radiation); are calculated. Then, $n _ { j }$ and the partial pressures of $\\mathrm { H } _ { 2 }$ , $\\mathrm { C H } _ { 4 }$ , CO and $\\mathrm { C O } _ { 2 }$ were determined.
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expert
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What does LYSO:Ce stand for?
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Cerium-doped Lutetium-Yttrium Oxyorthosilicate
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Definition
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Addesa_2022_J._Inst._17_P08028.pdf
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As example, the emission spectrum weighted for the transmittance is shown in figure 8 for the same crystal $\\# 6 6$ . The resulting spectrum provides the information necessary to optimize the coupling of the crystals with the light detection sensor. 4 Scintillation properties The light output $( L O )$ and the decay time $( \\tau )$ of the crystal samples from each producer were measured with dedicated setup and methods at the INFN — Sezione di Roma and Sapienza University laboratory (Roma, Italy). The results are shown as the average values over the 15 samples of each producer. Details about the reproducibility of the measurements are provided. $L O$ and $\\tau$ are key parameters for LYSO:Ce crystal timing applications. The highest possible $L O$ in the shortest possible time frame leads to the best timing performance for which a figure of merit can be defined as the ratio $L O / \\tau$ . Results for the figure of merit are also shown for all the producers. Finally, the dependency of $L O$ and $\\tau$ on the relative $\\mathrm { C e } ^ { 3 + }$ concentration has been investigated in section 4.3 with the aim to explore the possibility to use $\\mathrm { C e } ^ { 3 + }$ concentration as a quality indicator of the scintillation and timing performance of the crystals.
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expert
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What does LYSO:Ce stand for?
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Cerium-doped Lutetium-Yttrium Oxyorthosilicate
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Definition
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Addesa_2022_J._Inst._17_P08028.pdf
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4.1 Experimental setup, methods and tools Setup description. The experimental setup used for the measurement of the scintillation properties is shown in figure 9. It consists of a $5 1 \\mathrm { m m }$ diameter end window PMT (ET Enterprised model 9256B) placed inside a cylindrical box with a rectangular frame. The frame works as a guide to insert the bar holder which keeps the crystal bar vertical on the PMT photocathode window and is equipped with different transverse section holes for the housing of the 3 bar types. The crystal bars are inserted into the holder without any wrapping. One crystal end face is in contact with the PMT window while the other one is free and in contact with air. No grease is applied to enhance the PMT-crystal optical contact. This precaution was taken to optimize the reproducibility of the measurement. The setup is enclosed in a black painted box whose temperature is kept stable at $2 0 ^ { \\circ } \\mathrm { C }$ (within $0 . 1 { - } 0 . 2 \\ ^ { \\circ } \\mathrm { C }$ over $2 4 \\mathrm { h }$ ) by the use of a chiller. The PMT signal is readout by the DRS4 evaluation board [17], working at a sampling rate of $2 \\mathrm { G S } / \\mathrm { s }$ ; this allows an integration window for the PMT signal extending up to $5 0 0 \\mathrm { n s }$ . The single photoelectron (SPE) response is calibrated using a pulsed, fast, blue LED. The LED light is brought inside the box using an optical fiber.
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expert
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What does LYSO:Ce stand for?
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Cerium-doped Lutetium-Yttrium Oxyorthosilicate
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Definition
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Addesa_2022_J._Inst._17_P08028.pdf
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Optical transmission spectra and photoluminescence properties were also studied for all producers. In particular, the evaluation of the relative concentration of the main crystal luminescence center $( \\mathrm { C e } ^ { 3 + } )$ was obtained from the transmission spectra. Its correlation with the light output $( L O )$ and decay time $( \\tau )$ of the crystals has been investigated in the attempt to establish a method to characterize the timing performance of the crystals. The data do not match the expectations showing a poor linear correlation of the $( \\mathrm { C e } ^ { 3 + } )$ relative concentration with both scintillation parameters. This has been mainly ascribed to the possible presence of different co-dopants, impurities and defects which may have an important role in the scintillation dynamics. $L O$ and $\\tau$ were measured for all the crystal samples, together with the figure of merit for timing application defined as $L O / \\tau$ . all producers’ samples show similar scintillation properties. The spread of the $L O$ value for different producers is at the level of $8 \\%$ while for $\\tau$ , ranging from 38 to $4 5 \\mathrm { n s }$ , it is within $5 \\%$ . The uniformity of the crystal samples provided by each producer with respect to these scintillation parameters is comparable with the reproducibility of the measurements: $4 \\%$ for the $L O$ and $1 \\%$ for $\\tau$ .
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expert
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What does LYSO:Ce stand for?
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Cerium-doped Lutetium-Yttrium Oxyorthosilicate
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Definition
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Addesa_2022_J._Inst._17_P08028.pdf
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6 crystals were measured in order to check the consistency of the measurement within the same producer. In total, 31 crystal bars were measured by the ICP-MS technique. The results showing the Yttrium content and its linear correlation with the measured mass density are reported in figure 4 (right). Measurements from all the crystals of the subsample analyzed are shown and correspond to a data point. The linear correlation of the Yttrium fraction of a crystal bar with its density is clearly demonstrated and the linear regression coefficient is $R = 0 . 9 5$ . In addition, a linear fit with $\\chi ^ { 2 }$ minimization has been applied to the data. The linear fit parameters correspond, within the error, to the empirical linear relation of the Yttrium content and the density of the crystal which can be determined by the densities of pure LSO $( x = 0$ , density $\\underline { { \\mathbf { \\sigma } } } = 7 . 4 \\ : \\mathrm { g / c m } ^ { 3 } .$ ) and pure YSO $\\langle x = 1$ , density $= 4 . 5 \\mathrm { g } / \\mathrm { c m } ^ { 3 } .$ ) crystals.
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expert
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What does LYSO:Ce stand for?
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Cerium-doped Lutetium-Yttrium Oxyorthosilicate
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Definition
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Addesa_2022_J._Inst._17_P08028.pdf
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the ratio between the amplitude of the Gaussian function and the sample width can be used for a relative estimation of the concentration of $\\mathrm { C e } ^ { 3 + }$ centers in the sample $( N _ { \\mathrm { C e } ^ { 3 + } } )$ . The fit function is effective for all the spectra, regardless of the Cerium doping and possible co-doping used by different crystal producers, as illustrated in figure 6. Transmission spectra were measured for 39 crystals from different producers with at least two crystals from each producer. For producer 4, 5 and 6, samples from different ingots and with different declared Cerium concentration were studied. The corresponding $N _ { \\mathrm { C e } ^ { 3 + } }$ value are reported in table 3. A total of 23 crystals were measured in both transversal directions, $w$ and $t$ , and often more than one measurement was taken for a given direction, thus having a total of 75 optical transmission spectra analyzed. This was made in order to check both the reproducibility of the transmission spectrum measurement and the overall stability of the $( N _ { \\mathrm { C e } ^ { 3 + } } )$ measurement procedure.
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expert
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What does LYSO:Ce stand for?
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Cerium-doped Lutetium-Yttrium Oxyorthosilicate
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Definition
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Addesa_2022_J._Inst._17_P08028.pdf
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6 Scintillation properties at low temperature Due to its radiation hardness against photons and hadrons, LYSO:Ce can be employed for timing purposes in the harsh environment of the new generation particle colliders such as the HL-LHC. Here, to mitigate the impact of the radiation damage on the performance of the detector components, especially the silicon ones, the operating temperature is usually lowered below $0 ^ { \\circ } \\mathrm { C }$ by some tens of degrees. This will be, for example, the case of the barrel part of the timing detector of CMS-phase II. In BTL, LYSO crystals are coupled to Silicon PhotoMultipliers (SiPM). Radiation exposure increases the noise due to the SiPM dark count rate and lowers the $L O$ of the crystals deteriorating the time resolution. For this reason the detector will be operated at low temperature, between $- 4 5 ^ { \\circ } \\mathrm { C }$ and $- 3 5 ^ { \\circ } \\mathrm { C }$ . With the aim to extend and complete the set of information collected in this paper, additional measurements of $L O$ and $\\tau$ in this range of temperatures for crystal bars from each of the 12 producers were performed. The experimental setup and the results are presented in this section.
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expert
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What does LYSO:Ce stand for?
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Cerium-doped Lutetium-Yttrium Oxyorthosilicate
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Definition
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Addesa_2022_J._Inst._17_P08028.pdf
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A Absorbance analytical expression in the approximation of multiple reflection between parallel crystal faces The absorbance is defined as: $$ A = 2 - \\log _ { 1 0 } T ( \\% ) $$ where $T$ corresponds, in the present study, to the measured optical transmission (transmittance). The transmittance is defined as the ratio $I / I _ { 0 }$ of light intensities at the exit $( I )$ and the entrance $( I _ { 0 } )$ of the measured sample. When accounting for multiple reflections on the crystal faces, the numerator is given by the sum of the $I _ { j }$ contributions exiting the crystal and displayed in figure 22: $$ T = \\frac { I } { I _ { 0 } } = \\operatorname* { l i m } _ { n \\to \\infty } \\frac { \\sum _ { j = 1 } ^ { n } I _ { j } } { I _ { 0 } } = \\operatorname* { l i m } _ { n \\to \\infty } { ( 1 - R ) ^ { 2 } e ^ { - \\alpha d } \\left[ 1 + R ^ { 2 } e ^ { - 2 \\alpha d } + R ^ { 4 } e ^ { - 4 \\alpha d } + . . . R ^ { 2 n } e ^ { - 2 n \\alpha d } \\right] }
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augmentation
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expert
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What does LYSO:Ce stand for?
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Cerium-doped Lutetium-Yttrium Oxyorthosilicate
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Definition
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Addesa_2022_J._Inst._17_P08028.pdf
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6.2 Results At least one crystal bar of the smallest geometry for each of the 12 producers was measured. Six measurement points have been acquired with temperatures ranging from $2 0 ^ { \\circ } \\mathrm { C }$ down to $- 3 0 ^ { \\circ } \\mathrm { C }$ . Lowering the temperature, both the $L O$ and $\\tau$ increase slowly. In figure 19 (top) an example of $L O$ as a function of the temperature and normalized to the corresponding value at $T = 2 0 ^ { \\circ } \\mathrm { C }$ is shown. The $L O$ is linear with the temperature for all producers. The temperature coefficient is on average $- 0 . 1 5 \\% / { } ^ { \\circ } \\mathrm { C }$ ranging between $- 0 . 2 8 \\ : \\% / ^ { \\circ } \\mathrm { C }$ and $- 0 . 0 8 \\ : \\% / ^ { \\circ } \\mathrm { C }$ as shown in figure 19 (bottom). The $L O$ relative variation as a function of the temperature is equal to the light yield (LY) relative variation because the $L O$ can be factorized as $\\mathrm { L Y } \\times \\mathrm { L C E } \\times \\mathrm { Q E }$ and the LCE and the QE can be assumed constant with the temperature and therefore cancel out in the ratio.
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expert
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What does LYSO:Ce stand for?
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Cerium-doped Lutetium-Yttrium Oxyorthosilicate
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Definition
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Addesa_2022_J._Inst._17_P08028.pdf
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Nevertheless, the figure of merit at $- 3 0 ^ { \\circ } \\mathrm { C }$ compared with the results obtained at $2 0 ^ { \\circ } \\mathrm { C }$ shows that lowering the operating temperature of the crystals can help to improve their timing performance. This holds true for all the producers and with a relative standard deviation of $\\simeq 2 \\%$ . The most important crystal features measured in this study are summarized in table 5 and table 6 for each producer. All producers showed similar characteristics within $\\simeq 1 0 \\%$ , except for the $\\mathrm { C e } ^ { 3 + }$ relative concentration and the LY temperature coefficient. For these crystal properties the spread among the producers is at the level of $5 0 \\%$ . Despite this, their impact on the key performance for HEP and especially for timing application is limited. The $\\mathrm { C e } ^ { 3 + }$ relative concentration has shown a poor correlation with LO and $\\tau$ while the spread in the LY temperature coefficients does not reflect in the figure of merit $\\mathrm { L Y } / \\tau$ . 8 Conclusions
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augmentation
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expert
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What does LYSO:Ce stand for?
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Cerium-doped Lutetium-Yttrium Oxyorthosilicate
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Definition
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Addesa_2022_J._Inst._17_P08028.pdf
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After irradiation, all the crystals exhibited phosphorescence light with an approximate decay time of $2 { - } 3 \\mathrm { h }$ as estimated from the presence of a transient noise in the baseline of the PMT signal acquired $\\sim$ every hour for $1 2 \\mathrm { h }$ , displayed in figure 16. For this reason, the samples were measured again at least $1 6 \\mathrm { h }$ after the irradiation to evaluate the ratio of the $L O$ and the $\\tau$ after and before irradiation. The results are shown in figure 17. The average light output loss amounts to $9 \\%$ with a relative standard deviation of $3 \\%$ among the different producers (figure 17, top). The scintillation $\\tau$ (figure 17, bottom) after irradiation remains unchanged within the measurement uncertainties compared to the pre-irradiation value for most of the producers. The average ratio of $\\tau$ after and before the irradiation is $1 \\%$ with a standard deviation of $2 \\%$ . In general, the scintillation mechanism of LYSO:Ce is not damaged by $\\gamma$ -ray irradiation [21]. The $L O$ decrease depends on the $\\gamma$ -induced transparency loss which is due to the creation of absorbing centers. The $L O$ can be further recovered through a air annealing of the crystal at $\\sim 3 0 0 ^ { \\circ } \\mathrm { C }$ for some hours. Slow (few days) spontaneous recovery can also be observed at room temperature [18].
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augmentation
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NO
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expert
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What does LYSO:Ce stand for?
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Cerium-doped Lutetium-Yttrium Oxyorthosilicate
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Definition
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Addesa_2022_J._Inst._17_P08028.pdf
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In this case the PMT signal acquisition is triggered on the PMT signal itself using an optimal threshold. The charge is integrated in a 450 ns time window after the baseline subtraction. An example of charge spectra used to extract the $5 1 1 \\mathrm { k e V }$ photo-peak values is presented together with the corresponding fitting functions in figure 10, bottom. Decay time measurement. The acquisition with a fast sampling digitizer allows the extraction of the scintillation $\\tau$ directly from the acquired waveform of the PMT signal. An average over all PMT signals with an associated total charge above roughly $1 0 0 \\mathrm { k e V }$ in the $^ { 2 2 } \\mathrm { N a }$ runs is performed. The average waveform is passed through a Butterworth filter with a cut-off frequency of $2 0 \\mathrm { M H z }$ to reduce oscillations due the imperfect impedance matching between the PMT anode output and the DRS4 buffer input. $\\tau$ is extracted from a fit which includes a single exponential decay function and a Gaussian turn-on. An example of this fit is shown in figure 11. From the average waveform it is also possible to estimate the amount of light emitted in a time window smaller than $4 5 0 \\mathrm { n s }$ , integrating the waveform in different time windows.
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augmentation
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NO
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expert
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What does LYSO:Ce stand for?
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Cerium-doped Lutetium-Yttrium Oxyorthosilicate
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Definition
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Addesa_2022_J._Inst._17_P08028.pdf
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$\\tau$ dependency on the temperature is linear down to $- 3 0 ^ { \\circ } \\mathrm { C }$ only for 6 producers over 12 (regression coefficient $\\mathrm { R > 0 . 8 5 }$ ) and in general the variation with temperature is smaller than for the $L O$ . In figure 20 (top) the linear dependency of $\\tau$ for producer 5 is shown as an example. For the other producers, no linear relation between the temperature and $\\tau$ can be assumed $( \\mathrm { R } < 0 . 7 5 )$ . In figure 20 (bottom), $\\tau$ vs. $T$ is shown for crystals from this subset of producers; in particular for producer 2 $( R = 0 . 4 1 )$ ), 4 $R = 0 . 7 3 )$ and 7 $R = 0 . 7 6 )$ ). For these producers, additional measurement points at low temperature would be needed for a more rigorous description of $\\tau$ dependency down to $- 3 0 ^ { \\circ } \\mathrm { C }$ . In figure 21 the ratio of the figure of merit $( L O / \\tau )$ measured at $- 3 0 ^ { \\circ } \\mathrm { C }$ and at $2 0 ^ { \\circ } \\mathrm { C }$ is also shown. Its average value and standard deviation are 1.05 and 0.02 respectively. For all producers the ratio is ${ > } 1$ . This demonstrates that lowering the operating temperature of the crystal can help to improve their timing performance.
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augmentation
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NO
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expert
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What does LYSO:Ce stand for?
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Cerium-doped Lutetium-Yttrium Oxyorthosilicate
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Definition
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Addesa_2022_J._Inst._17_P08028.pdf
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The reproducibility of the $L O$ and $\\tau$ measurements was estimated repeating them daily over one month using a reference crystal and it was found to be $4 \\%$ and better than $1 \\%$ , respectively. 4.2 Measurement results The $L O$ and $\\tau$ measurement results are averaged over the 15 crystals provided by each producer and are displayed in figure 12. The $L O$ (figure 12, top) is expressed in photons/MeV and represents the number of scintillation photons produced per MeV of energy deposit which impinge on the photosensor and are successfully detected. It is corrected for the quantum efficiency of the sensor and corresponds to the intrinsic crystal light yield (LY) times the light collection efficiency (LCE). The latter depends on the optical surface quality of the crystal and the transparency of the bulk as well as the crystal-sensor coupling (which is, however, the same for all the crystals). The quantum efficiency correction factor is obtained by the quantum efficiency of the PMT, as provided by the producer, weighted over the LYSO spectrum and corresponds to about $2 5 \\%$ . The relative standard deviation of the $L O$ values for different producers is about $8 \\%$ . The $L O$ standard deviation (error bars in figure 12, top) for samples of the same producer is mostly comparable with the reproducibility of the measurement $( 4 \\% )$ , although some show higher values revealing a less uniform $L O$ among the provided samples. The standard deviation value of producer 1 can be explained by 2 outlier crystals.
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augmentation
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NO
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expert
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What does LYSO:Ce stand for?
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Cerium-doped Lutetium-Yttrium Oxyorthosilicate
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Definition
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Addesa_2022_J._Inst._17_P08028.pdf
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File Name:Addesa_2022_J._Inst._17_P08028.pdf Comparative characterization study of LYSO:Ce crystals for timing applications To cite this article: F.M. Addesa etal2022 JINST17 P08028 View the article online for updates and enhancements. You may also like Comparison of acrylic polymer adhesive tapes and silicone optical grease in light sharing detectors for positron emission tomography Devin J Van Elburg, Scott D Noble, Simone Hagey et al. - Measurement of intrinsic rise times for various L(Y)SO and LuAG scintillators with a general study of prompt photons to achieve 10 ps in TOF-PET Stefan Gundacker, Etiennette Auffray, Kristof Pauwels et al. - Analytical calculation of the lower bound on timing resolution for PET scintillation detectors comprising high-aspect-ratio crystal elements Joshua W Cates, Ruud Vinke and Craig S Levin Join the Society Led by Scientists, for Scientists Like You! Comparative characterization study of LYSO:Ce crystals for timing applications F.M. Addesa,ùëé,ùëè,‚àó P. Barria,ùëè R. Bianco,ùëè M. Campana,ùëè F. Cavallari,ùëè A. Cemmi,ùëê M. Cipriani,ùëë I. Dafinei,ùëè B. D‚ÄôOrsi,ùëè D. del Re,ùëè M. Diemoz,ùëè G. D‚ÄôImperio,ùëè E. Di Marco,ùëè I. Di Sarcina,ùëê M. Enculescu,ùëí E. Longo,ùëè M.T. Lucchini, ùëì F. Marchegiani,ùëî P. Meridiani,ùëè S. Nisi,ùëî G. Organtini,ùëè F. Pandolfi,ùëè R. Paramatti,ùëè V. Pettinacci,ùëè C. Quaranta,ùëè S. Rahatlou,ùëè C. Rovelli,ùëè F. Santanastasio,ùëè L. Soffi,ùëè R. Tramontanoùëè and C.G. Tullyùëé
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augmentation
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NO
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expert
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What does LYSO:Ce stand for?
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Cerium-doped Lutetium-Yttrium Oxyorthosilicate
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Definition
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Addesa_2022_J._Inst._17_P08028.pdf
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Table: Caption: Table 3. $\\mathrm { C e } ^ { 3 + }$ relative concentration $( N _ { \\mathrm { C e } ^ { 3 + } } )$ reported per crystal sample. The uncertainty of the $N _ { \\mathrm { C e } ^ { 3 + } }$ corresponds to the stability of the fit procedure $( 6 \\% )$ . In the last column of the table, information about the laboratory in which the measurement was performed is also given. Body: <html><body><table><tr><td>Prod.</td><td>Sample #</td><td>Nce3+</td><td>Lab.</td><td>Prod.</td><td>Sample #</td><td>Nce3+</td><td>Lab.</td></tr><tr><td>1</td><td>1</td><td>1.7540</td><td>CERN</td><td>6</td><td>3</td><td>0.8835</td><td>NIMP</td></tr><tr><td>1</td><td>2</td><td>1.4990</td><td>CERN</td><td>6</td><td>4</td><td>0.5733</td><td>NIMP</td></tr><tr><td>1</td><td>3</td><td>1.2230</td><td>NIMP</td><td>6</td><td>5</td><td>0.4932</td><td>NIMP</td></tr><tr><td>1</td><td>4</td><td>1.2450</td><td>NIMP</td><td>7</td><td>1</td><td>0.5195</td><td>CERN</td></tr><tr><td>2</td><td>1</td><td>2.1010</td><td>CERN</td><td>7</td><td>2</td><td>0.5799</td><td>CERN</td></tr><tr><td>2</td><td>2</td><td>1.4590</td><td>CERN</td><td>7</td><td>3</td><td>0.5386</td><td>NIMP</td></tr><tr><td>2</td><td>3</td><td>1.5520</td><td>NIMP</td><td>8</td><td>1</td><td>0.8030</td><td>CERN</td></tr><tr><td>3</td><td>1</td><td>0.3244</td><td>CERN</td><td>8</td><td>2</td><td>0.5434</td><td>CERN</td></tr><tr><td>3</td><td>2</td><td>0.3231</td><td>CERN</td><td>8</td><td>3</td><td>0.4948</td><td>NIMP</td></tr><tr><td>3</td><td>3</td><td>0.3240</td><td>NIMP</td><td>8</td><td>4</td><td>0.5140</td><td>NIMP</td></tr><tr><td>4</td><td>1</td><td>1.9800</td><td>CERN</td><td>9</td><td>1</td><td>0.9132</td><td>CERN</td></tr><tr><td>4</td><td>2</td><td>1.2480</td><td>NIMP</td><td>9</td><td>2</td><td>1.0730</td><td>CERN</td></tr><tr><td>4</td><td>3</td><td>1.5990</td><td>CERN</td><td>9</td><td>3</td><td>0.6914</td><td>NIMP</td></tr><tr><td>4</td><td>4</td><td>0.6741</td><td>NIMP</td><td>9</td><td>4</td><td>0.7214</td><td>NIMP</td></tr><tr><td>5</td><td>1</td><td>0.3481</td><td>CERN</td><td>10</td><td>1</td><td>0.4885</td><td>NIMP</td></tr><tr><td>5</td><td>2</td><td>0.2560</td><td>NIMP</td><td>11</td><td>1</td><td>1.0490</td><td>NIMP</td></tr><tr><td>5</td><td>3</td><td>0.3779</td><td>CERN</td><td>11</td><td>2</td><td>0.8990</td><td>NIMP</td></tr><tr><td>5</td><td>4</td><td>0.4304</td><td>NIMP</td><td>12</td><td>1</td><td>0.8548</td><td>NIMP</td></tr><tr><td>6</td><td>1</td><td>1.2850</td><td>CERN</td><td>12</td><td>2</td><td>0.9264</td><td>NIMP</td></tr><tr><td>6</td><td>2</td><td>1.1040</td><td>CERN</td><td></td><td></td><td></td><td></td></tr></table></body></html> The reproducibility of the transmission spectrum measurement was evaluated repeating the measurement of the same kind of spectrum (along $w$ or $t$ ) several times and it was found to be within $1 \\%$ . The overall measurement process stability, depending on the reliability of the fit function, was evaluated at the level of $6 \\%$ using the $N _ { \\mathrm { C e } ^ { 3 + } w , t }$ values obtained for crystals for which both the transverse spectra were available. In particular, it corresponds to the standard deviation of the distribution of $N _ { \\mathrm { C e } ^ { 3 + } w , t }$ divided by the corresponding average value over the two transverse spectra $ { \\langle N _ { \\mathrm { C e } ^ { 3 + } } \\rangle }$ .
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augmentation
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expert
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What does LYSO:Ce stand for?
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Cerium-doped Lutetium-Yttrium Oxyorthosilicate
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Definition
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Addesa_2022_J._Inst._17_P08028.pdf
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7 Discussion A set of 15 small crystal bars $( 3 m m \\times 3 m m \\times 5 7 m m )$ from 12 different producers were studied and compared with respect to a set of properties and performance fundamental for HEP applications with a special focus on timing applications. All producers are shown to have mastered the cutting technology producing samples with uniform dimensions at the level of per mille, and within the requested specifications at a level better than $1 \\%$ . From the dimensions and the mass measurement, the crystal density value was derived for every sample. It ranges from 7.1 to $7 . 4 \\mathrm { g } / \\mathrm { c m } ^ { 3 }$ and its relative standard deviation among the samples of the same producer is well below $1 \\%$ . The mass density study is complemented, for at least one crystal per producer, by inductively coupled plasma mass spectrometry (ICP-MS) measurements from which the Yttrium molar fraction was evaluated. The Yttrium fraction is indeed expected to linearly correlate with the mass density. The expectation has been confirmed by data $R = 0 . 9 5$ ) and the spread of the Yttrium fraction among the different producers is about $30 \\%$ .
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augmentation
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NO
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IPAC
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What does OTR mean?
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Optical Transition Radiation
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Definition
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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:ONLINE_FIT_OF_AN_ANALYTICAL_RESPONSE_MATRIX_MODEL_FOR.pdf ONLINE FIT OF AN ANALYTICAL RESPONSE MATRIX MODEL FOR ORBIT CORRECTION AND OPTICAL FUNCTION MEASUREMENT S. Kötter ∗, E. Blomley, E. Bründermann, A. Santamaria Garcia, M. Schuh, A-S. Müller Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany Abstract At the Karlsruhe Research Accelerator (KARA), an analytical online model of the orbit response matrix (ORM) has been implemented. The model, called the bilinearexponential model with dispersion ( $\\mathrm { B E + d }$ model), is derived from the Mais-Ripken parameterization of coupled betatron motion. The online fit continuously adapts the model to changing beam optics without dedicated measurements using only orbit correction results as input. This gives access to an up-to-date ORM for orbit correction as well as estimates for the coupled beta function, betatron phase, and the tunes. After comparing such beta function fit results to an optics simulation and evaluating orbit correction with the model, problems of the approach are discussed. INTRODUCTION KARA is a $2 . 5 \\mathrm { G e V }$ synchrotron light source and accelerator test facility at the Institute for Beam Physics and Technology (IBPT) of the Karlsruhe Institute of Technology (KIT). Here, a new orbit correction software is under development. The goal is a program that performs well with different experimental operation modes, such as negative alpha optics [1], and to investigate novel orbit correction approaches in general. A first iteration was derived from a program used at the Dortmunder Elektronenspeicherring-Anlage (DELTA) [2]. It relies on a conic solver for convex constrained optimization for calculating orbit corrections that allows orbit and steerer strength constraints, and can also correct the orbit length by modulating the frequency of the radio frequency (RF) accelerating cavity. At KARA, an analytical online model of the ORM based on the $\\mathrm { \\ B E { + } d }$ model that had been proposed in [3] was added to the software. Its ring buffer is loaded with tuples of orbit and steerer strength changes resulting from orbit corrections, and gives access to estimates for the coupled beta function, the betatron phase, and the tunes, as well as an analytical representation of the ORM. Similarly to the local optics from closed orbits (LOCO) approach [4], the method measures the linear optics of the storage ring without turn-by-turn capable beam position monitors (BPMs). An advantage of the $\\mathrm { B E + d }$ model fit is that it requires no detailed lattice information to do so. Another usecase is orbit correction where it can be used as a replacement for a measured ORM. Compared to an online fit of the ORM itself, the fit of the analytical model is expected to require less measurements for the same signal-to-noise ratio. The reason is that the analytical model has only a fraction of the degrees of freedom of the naive matrix.
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augmentation
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IPAC
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What does OTR mean?
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Optical Transition Radiation
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Definition
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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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insulation, pressure relief, • materials, ventilation, oxygen detectors and alarm systems (Fig. 2), and interlock devices. Administrative controls Some administrative controls for ODH areas are warning signs, training programs, and safety device testing. One critical administrative control for areas with ODH class 2 or higher is the buddy rule, multiple personnel in continuous communication. Table 3 presents the warning signs and managerial tasks necessary for each ODH class. Table: Caption: Table 3: ODH Warning Signs and Management Measures Body: <html><body><table><tr><td>ODH class</td><td>O (per hour)</td><td>Warning signs</td><td>Management measure</td></tr><tr><td>ODH 0</td><td><10-7</td><td>注意（NOTICE) OXYGEN DEFICIENCY HAZARD（ODH）0 此區域可能有缺氧危害，如氧氣偵測器警報響起，請儘速離開。 This area may have oxygen deficiency hazards.If oxygen detector alarms,please leave as soon as possible.</td><td>Warning signs</td></tr><tr><td>ODH 1</td><td>> 10-7 but <10-5</td><td>警告(CAUTION) OXYGEN DEFICIENCY HAZARD(ODH）1 此區域可能有訣氣危書，如氧氣綽測器警報響起，請儘速離開。 进入前，人員守事(Prior toentryallpersonelmust have the folloving): 安全教育訓隸(oxygen deficiency hazard training)</td><td>Warning signs ODH training</td></tr><tr><td>ODH 2</td><td>> 10- but <10-3</td><td>危險（DANGER) OXYGEN DEFICIENCY HAZARD（ODH)2 可能有，ec pleaseleave as soon as possble. 进入前，人員需道守下列事顶(Prior to entry，al1personnelmust have the 同作璨nultiplepersonelincontinuo 人氧氣慎测器(personal oxygen detector) uouscomnunfcation)</td><td>Warning signs ODH training Multiperson teams Personal oxygen detectors</td></tr></table></body></html> ODH Training All individuals must undergo ODH and safety training covering: • the activities at the NSRRC involving oxygen deficiency, • the definition of ODH, • the effects of exposure to an oxygen-deficient atmosphere, • the ODH classification scheme, • required control measures, personal protective equipment, and emergency procedures and evacuation (Fig. 3).
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augmentation
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NO
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IPAC
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What does OTR mean?
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Optical Transition Radiation
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Definition
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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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As the compaction is reduced, the areas of stable longitudinal phase space are modified and new stable fixed points, so-called alpha buckets, are formed at non-zero $\\delta$ and at a phase of $\\pi$ with respect to the RF bucket. For a given lattice, there exists a maximally-stable configuration which particles can populate with significantly longer lifetimes. Accessing these areas of phase space could be utilized in the injection or storage of particles in the IOTA ring to support greater beam currents and lifetimes [4]. Low-alpha lattices are a fundamental requirement for steady-state microbunching (SSMB), a highly active area of research with great promise as a next-generation light source technology [5, 6]. In SSMB, very short substructure is created within a bunch stored in a ring, which persists and is reinforced through successive turns. Through the use of a radiator placed at a strategic location, it is conceptually possible to create high power, high frequency radiation comparable to that from a free-electron laser with the high repetition rate of a storage ring. OPTICAL STOCHASTIC CRYSTALLIZATION OSC is a state-of-the-art beam cooling technology first demonstrated experimentally at IOTA in 2021 [7]. It extends the well-established stochastic cooling technique from microwave to optical bandwidths, enabling significantly increased cooling rates. The ‘transit-time’ method of OSC [8] utilizes undulators for both the ‘pickup’ and ‘kicker’ components, which respectively produce radiation from a bunch and enables subsequent downstream interactions between the particles and their radiation. The radiation contains information about the longitudinal distribution of the bunch particles to enable corrective energy exchanges in the kicker. Between the undulators, the beam is directed through a dispersive section to convert momentum discrepancies to a longitudinal spread, whilst the light passes through optics to refocus and optionally amplify the radiation. The system is phased such that a particle at the reference momentum will arrive in time with its own radiation and thus feel no corrective kicks; particles with an energy discrepancy will gain or lose energy to the radiation fields so that they move closer to the reference energy. Over time and multiple passes through the system, the bunch is effectively cooled. The cooling rate is dependent on the bandwidth of the system; that is, how narrow the bunch is sampled to ensure particles are not impacted by others spatially nearby in the kicker. Additionally, the mechanism relies on sufficient randomization of particles between the kicker and the pickup to ensure collective effects are not enforced. The fundamental mechanism was demonstrated very successfully without the use of an optical amplifier, and a second phase of the program including an amplifier is currently being designed and scheduled to operate in 2025.
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augmentation
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NO
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IPAC
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What does OTR mean?
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Optical Transition Radiation
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Definition
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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:HIGH_ORDER_MODE_ANALYSIS_IN_ENERGY_RECOVERY_LINAC_BASED.pdf HIGH ORDER MODE ANALYSIS IN ENERGY RECOVERY LINAC BASED ON AN ENERGY BUDGET MODEL S. Samsam∗, M. Rossetti Conti, A.R. Rossi, A. Bacci, V. Petrillo1, I. Drebot, M. Ruijter, D. Sertore, R. Paparella, A. Bosotti, D. Giove and L. Serafini INFN - Sezione di Milano, Milano and LASA, Segrate (MI), Italy A. Passarelli, M. R. Masullo, INFN - Sezione di Napoli, Napoli, Italy 1also at Università degli Studi, Milano, Italy Abstract Energy Recovery linear accelerator (ERL) light source facilities based on superconducting radiofrequency (SRF) are deemed of the most resplendent techniques in the future of accelerator physics. Running in a continuous waves mode with a high repetition rate for a long timescale, we discuss High order modes (HOMs) analysis in a two-pass two-way ERL scheme where acceleration and deceleration of electron bunches are supported by a standing wave structure of the RF cavity. The analysis reported in this paper is based on differential equations that describe the beam dynamics (BD) to overcome the limitations imposed by high currents and insure energy recuperation over millions of interactions. INTRODUCTION ERLs have a relatively fascinating history in the field of particle accelerator physics [1–3]. The concept of energy recovery in accelerators has been around for a long time since 1965 [4], with the first successful implementation of energy recovery occurring in the late 80s with the construction of the TRISTAN collider in Japan [5]. However, the ERL concept takes this idea one step further by recovering the energy of the beam in a more efficient way. The first ERL facility; the IR-FEL, was constructed at the Thomas Jefferson National Accelerator Facility (Jefferson Lab) in the early 2000s and demonstrated the feasibility of the ERL concept for the generation of intense high-quality electron beams [3, 6]. Since then, several other ERL facilities have been built, including the ERL Test Facility (ERLTF) at Brookhaven National Laboratory and the Cornell-BNL ERL Test Accelerator (CBETA) [7–10]. ERL technology has many advantages over traditional linear accelerators. For example, ERLs can provide continuous-wave (CW) operation, which means that the accelerator can run for extended periods of time, enabling a wide range of experiments [11]. Additionally, ERLs can create beams of variable energy, making them ideal for a wide range of applications in fields such as nuclear physics, materials science, and particle detection [12–14].
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augmentation
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NO
| 0
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expert
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What does OTR mean?
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Optical Transition Radiation
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Definition
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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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expert
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What does OTR mean?
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Optical Transition Radiation
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Definition
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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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IPAC
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What does OTR mean?
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Optical Transition Radiation
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Definition
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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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CONCLUSION The RSFM analysis built into the online model produces reliable beta function and tune estimates and gives access to an analytical ORM representation that can be used for orbit correction. The deviation of the fitted beta function estimates from an OCELOT optics model in the peaks and oscillations appearing while correcting the RF frequency can probably be attributed to a non-linear dependence of the transverse orbit measurement on the steerer strengths. Most BPM-HSM pairs show either a second- or third-order dependence. OUTLOOK The problems arising from the linear assumption inherent to matrix-based orbit correction approaches are usually countered with regularization. As cutting of singular values does not work sufficiently well in our case, Thikonov regularization could be tried. However, it might be advisable to switch to a non-linear orbit response model instead as was shown in Refs. [15] and [16]. Such an approach would probably not only remove the problem of the oscillations during RF frequency correction but would also work better with non-linear and experimental optics such as negative alpha optics [1].
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IPAC
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What does OTR mean?
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Optical Transition Radiation
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Definition
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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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NO
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IPAC
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What does OTR mean?
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Optical Transition Radiation
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Definition
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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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Of particular interest are investigations into TR from targets with rough surfaces. It was recently found that the spectral density of the radiation energy is influenced by the optical constants of the material, the surface roughness, and the angle at which electrons strike the material [5]. There, a significant amount of unpolarized radiation was observed for targets with rough surfaces and larger incidence angles. It is speculated that at grazing angles, reflection radiation might predominate over TR [6]. Using a $1 0 \\mathrm { k e V }$ RHEED electron gun capable of producing a direct current (DC) beam of up to $1 0 0 ~ \\mu \\mathrm { A }$ , coupled with a Proxivision image intensifier and an iDS CMOS camera, positioned at a right angle to the direction of the electron beam, the behavior of different targets, placed in a sample holder attached to a linear bellow drive, was observed. This setup allowed movements perpendicular to the beam and observation directions, and includes a Faraday cup, housed in a vacuum chamber at a pressure of approximately $2 . 4 { \\cdot } 1 0 ^ { - 5 }$ mbar, to measure the beam current. This was used to analyze OTR emitted from carbon steel targets with varying degrees of roughness.
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NO
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What does OTR mean?
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Optical Transition Radiation
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Definition
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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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DISCUSSION AND FUTURE PLANS End-to-end OTR simulations will be an important next step to demonstrate the viability of the MLA and DMD methods. Measurements with a laser source will also provide a reliable cross-check value across the DMD and MLA systems. Despite the di!raction limit, the result will be reproducible if DMD pinhole diameters are matched to the MLA apertures. Beam measurements with OTR are planned at CLEAR (CERN, CH) in the near future. Following this, it would be straightforward to adapt this technology to image other, non-interceptive, radiation sources; this would make the technique non-invasive. A noninvasive single-shot method of measuring emittance would have applications across all accelerator sectors. This is particularly the case for novel acceleration where this system could be used to non-invasively monitor both pre-injection, and post-plasma accelerated electron beams. Finally, work will commence to leverage existing experience of machine learning techniques to increase the insight a single image can provide, from advanced analysis, to machine control. ACKNOWLEDGEMENT This work is supported by the AWAKE-UK phase II project funded by STFC under grant ST/T001941/1 and the STFC Cockcroft Institute core grant ST/V001612/1.
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expert
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What does OTR mean?
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Optical Transition Radiation
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Definition
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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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augmentation
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NO
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expert
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What does OTR mean?
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Optical Transition Radiation
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Definition
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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 $$ For the case of the presented data set $\\tau = 0 . 0 0 5$ is found to provide stable convergence and a consistent solution. Around 110 iterations are required to reach the termination criterion.
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augmentation
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NO
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expert
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What does OTR mean?
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Optical Transition Radiation
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Definition
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Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf
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$$ 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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augmentation
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NO
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expert
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What does OTR mean?
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Optical Transition Radiation
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Definition
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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 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
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expert
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What does OTR mean?
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Optical Transition Radiation
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Definition
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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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augmentation
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NO
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expert
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What does OTR mean?
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Optical Transition Radiation
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Definition
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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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augmentation
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NO
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expert
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What does OTR mean?
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Optical Transition Radiation
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Definition
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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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augmentation
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NO
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expert
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What does OTR mean?
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Optical Transition Radiation
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Definition
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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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2. Amplitude errors Jitter to the BLM signal is introduced by read-out noise of the PMT $( < 1 \\% )$ , charge fluctuations of the machine and halo-particles scattering at other elements of the accelerator. The charge measured by the BPMs fluctuated by $1 . 3 \\%$ (rms) during the measurement. The signal-to-noise ratio (SNR) of the measurements varies from 25 to 45 depending on the respective projected beam size. We define the SNR as: $s _ { \\mathrm { m a x } } / \\sigma _ { \\mathrm { n o i s e } }$ , where $s _ { \\mathrm { m a x } }$ is the maximum of the signal and $\\sigma _ { \\mathrm { n o i s e } }$ refers to the standard deviation of the background. 3. Uncertainty of the reconstruction Due to the error sources mentioned above the measured projections are not fully compatible with each other, i.e., the reconstructed distribution cannot match to all measured data points. The error of the reconstructed phase space density and the derived quantities is estimated by a procedure similar to the main reconstruction algorithm. The reconstructed distribution is now taken as input. Instead of averaging over all projections, the iteration is performed for each projection individually. Hence, a set of $n _ { z } \\times n _ { \\theta }$ distributions is generated, in which each distribution matches best to one measured projection. All derived quantities, such as the emittance or $\\beta$ -function, are computed for each distribution and the error is taken as the standard deviation of this set.
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augmentation
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NO
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expert
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What does OTR mean?
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Optical Transition Radiation
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Definition
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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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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
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expert
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What does OTR mean?
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Optical Transition Radiation
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Definition
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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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augmentation
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NO
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expert
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What effect does reducing the corrugation period have?
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reduces peak surface fields, heating & HOMs
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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 } { { \ U ^ { \\prime } = \\iiint \\frac { \\epsilon _ { 0 } } { 2 } | \\hat { a } ^ { - 3 / 2 } E ( x ^ { \\prime } , y ^ { \\prime } , z ^ { \\prime } ) | ^ { 2 } } } \\\\ { { \ \\quad + \\frac { \\mu _ { 0 } } { 2 } | \\hat { a } ^ { - 3 / 2 } H ( x ^ { \\prime } , y ^ { \\prime } , z ^ { \\prime } ) | ^ { 2 } d x d y d z } } \\\\ { { \ = \\iiint \\frac { \\epsilon _ { 0 } } { 2 } | E ( x ^ { \\prime } , y ^ { \\prime } , z ^ { \\prime } ) | ^ { 2 } } } \\\\ { { \ \\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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Yes
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expert
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What effect does reducing the corrugation period have?
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reduces peak surface fields, heating & HOMs
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Summary
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Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf
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Comparing the maximum radii and unequal radii rounded corrugation peak fields in Figs. 10 and 11, we note that the two geometry types are identical when the spacing parameter $\\xi = 0$ and the sidewall parameter $\\zeta = 1$ . In both structure types, the minimum $E _ { \\mathrm { m a x } }$ occurs for a negative spacing parameter $\\xi$ , corresponding to a corrugation tooth width wider than the vacuum gap. Increasing the corrugation spacing beyond the minimum point decreases $H _ { \\mathrm { m a x } }$ while increasing $E _ { \\mathrm { m a x } }$ . The sidewall angle determined by $\\zeta$ shifts the plots on the $\\xi$ axis but does not significantly affect the minimum value of the peak fields. While changing the sidewall parameter offers little to no benefit in reducing the peak fields, the practical implications of using values of $\\zeta \\neq 1$ have several disadvantages. For tapered corrugations with $\\zeta < 1$ , the corrugation depth must be greater requiring a thicker vacuum chamber wall and additional manufacturing complexity. Undercut corrugations with $\\zeta > 1$ are also impractical to manufacture for the dimensions of interest in a compact wakefield accelerator. For these reasons, we suggest the maximum radii corrugation with $\\xi$ close to zero as a good candidate for a wakefield accelerator design. Further refinement of the geometry requires experimental determination of where rf breakdown is most likely to occur in order to reduce the peak fields in those regions.
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Yes
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expert
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What effect does reducing the corrugation period have?
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reduces peak surface fields, heating & HOMs
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Summary
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Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf
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The condition for vertical sidewalls is $\\zeta = 1$ and $d > p / 2$ . Preventing a self-intersecting geometry requires both the width of the tooth and vacuum gap to be less than the corrugation period, as well as a sufficiently large corrugation depth when $\\zeta > 1$ to ensure positive length of the inner tangent line defining the sidewall. These conditions can be expressed as $$ \\zeta - 2 < \\xi < 2 - \\zeta , $$ $$ d > { \\frac { p } { 2 } } \\left( \\zeta + { \\sqrt { \\zeta ^ { 2 } - 1 } } \\right) \\quad { \\mathrm { f o r ~ } } \\zeta > 1 . $$ III. SIMULATION Electromagnetic simulation of the $\\mathrm { T M } _ { 0 1 }$ accelerating mode was performed using the eigenmode solver in CST Microwave Studio [13]. In this analysis, only the fundamental $\\mathrm { T M } _ { 0 1 }$ mode was considered since it accounts for the largest portion of the accelerating gradient. It will be shown in Sec. VII that the exclusion of higher order modes (HOMs) is a very good approximation for the corrugated structures under consideration. A tetrahedral mesh and magnetic symmetry planes were used to accurately model the rounded corners of the corrugation and minimize computation time. Since the simulation only considers a single period of the geometry, the run time was short (approximately $1 \\mathrm { ~ m ~ }$ on a four-core desktop PC) allowing large parametric sweeps to be run rapidly. The eigenmode solver models the corrugated waveguide as a periodic structure of infinite length by employing a periodic boundary condition derived from beam-wave synchronicity:
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