| Parameter |
| K | Wakefield loss factor |
| βg | Normalized group velocity |
| vg | Group velocity |
| α | Attenuation constant |
| Q | Quality factor |
| 0 | Electrical conductivity |
| Corrugation spacing parameter |
| S | Corrugation sidewall parameter |
| a | Corrugation minor radius |
| t | Corrugation tooth width |
| g | Corrugation vacuum gap |
| d | Corrugation depth |
| p | Corrugation period |
| rt | Corrugation tooth radius |
| rg | Corrugation vacuum gap radius |
| L | Corrugated waveguide length |
| F | Bunch form factor |
| q0 | Drive bunch charge |
| fr | Bunch repetition rate |
| T | rf pulse decay time constant |
| 8 | Skin depth |
| Pf | rf pulse power envelope |
| P | Instantaneous rf pulse power |
| Eacc | Accelerating field |
| Emax | Peak surface E field |
| Hmax | Peaksurface H field |
| Qdiss | Energy dissipation |
| Pd | Power dissipation distribution |
| W | Average thermal power density |
| ‚ñ≥T | Transient temperature rise |
| C | Speed of light |
| Z0 | Impedance of free space |
| 8 | Initial beam energy |
| R | Transformer ratio |
In the parametric analysis that follows, the corrugation dimensions are expressed in terms of the normalized spacing parameter $\\xi$ and sidewall parameter $\\zeta$ defined as $$ \\begin{array} { l } { \ { \\xi = \\frac { g - t } { p } } , } \\\\ { \ { \\zeta = \\frac { g + t } { p } } . } \\end{array} $$ The spacing parameter $\\xi$ determines the spacing between the corrugation teeth and ranges from $^ { - 1 }$ to 1 for the minimum and maximum radii profiles, where positive values of $\\xi$ result in spacing greater than the tooth width and vice versa for negative values. The sidewall parameter $\\zeta$ controls the sidewall angle of the unequal radii profile, where $\\zeta < 1$ leads to tapered sidewalls and $\\zeta > 1$ leads to undercut sidewalls. These dependencies are illustrated in Fig. 4.",2,NO,0,
IPAC,How is the transformer ratio defined?,It is the ratio of the maximum electric field behind the drive bunch to the maximum electric field within the bunch,Definition,Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf,"$$ Where $\\alpha _ { 0 } : = { \\cal Q } _ { \\scriptscriptstyle L } / { \\cal Q } _ { 0 } , \\alpha _ { \\scriptscriptstyle k } : = \\alpha _ { 0 } \\beta _ { \\scriptscriptstyle k } , \\Psi : = \\mathrm { a t a n } ( - { \\mathrm Q } _ { \\scriptscriptstyle L } \\delta ) .$ The reflection coefficient at AA’ is given by $\\Gamma _ { _ { A d ^ { \\prime } } } = \\Gamma _ { \\boldsymbol { k } } = 2 \\alpha _ { \\boldsymbol { k } } e ^ { i \\Psi } \\cos \\Psi - 1$ and the reflected voltage is given by $$ V _ { k k } ^ { r } = \\sqrt { 2 R P _ { k } } e ^ { i \\phi _ { k } } \\left( 2 \\alpha _ { k } e ^ { i \\Psi } \\cos \\Psi - 1 \\right) $$ Now, we need to add all the transmitted voltages from the other feeds. For such a purpose, let us suppose that the $\\mathrm { j }$ -th feed is active and the other ones are simply replaced by the dummy loads. In this case the cavity voltage is given by the transmitted voltage due to the $\\mathrm { j }$ -th feed transported to the secondary via the multiplication by the turn ratio nj.",1,NO,0,
expert,Is it accurate to only consider the first harmonic?,"the higher nonsynchronous harmonics average out. It can be shown, that their second order (ponderomotive) contribution is also small. ",reasoning,Beam_dynamics_analysis_of_dielectric_laser_acceleration.pdf,"$$ V = q e _ { 1 } \\left[ \\frac { \\lambda _ { g z } } { 2 \\pi } \\cosh \\left( \\frac { \\omega y } { \\beta \\gamma c } \\right) \\sin \\left( \\frac { 2 \\pi s } { \\lambda _ { g z } } \\right) - s \\cos \\varphi _ { s } \\right] . $$ This potential and its adiabatic change with $\\beta$ is illustrated in Fig. 8. The full 6D Hamiltonian reads $$ H = \\frac { 1 } { 2 m _ { e } \\gamma } ( p _ { x } ^ { 2 } + p _ { y } ^ { 2 } + \\Delta P _ { z } ^ { 2 } ) + V , $$ where $\\Delta p _ { z } / \\gamma$ was replaced with $\\Delta P _ { z }$ . The coupled equations of motion are $$ \\begin{array} { r l } & { \\ddot { x } = 0 } \\\\ & { \\ddot { y } = - \\frac { q e _ { 1 } } { m _ { e } \\gamma ^ { 2 } } \\mathrm { s i n h } \\Bigg ( \\frac { \\omega y } { \\beta \\gamma c } \\Bigg ) \\mathrm { s i n } \\Bigg ( \\frac { 2 \\pi s } { \\lambda _ { g z } } \\Bigg ) } \\\\ & { \\ddot { s } = \\frac { q e _ { 1 } } { m _ { e } \\gamma ^ { 3 } } \\Bigg ( \\mathrm { c o s h } \\Bigg ( \\frac { \\omega y } { \\beta \\gamma c } \\Bigg ) \\mathrm { c o s } \\Bigg ( \\frac { 2 \\pi s } { \\lambda _ { g z } } \\Bigg ) - \\mathrm { c o s } \\varphi _ { s } \\Bigg ) . } \\end{array}",4,Yes,1,
expert,Is it accurate to only consider the first harmonic?,"the higher nonsynchronous harmonics average out. It can be shown, that their second order (ponderomotive) contribution is also small. ",reasoning,Beam_dynamics_analysis_of_dielectric_laser_acceleration.pdf,$$ V = q e _ { 1 } \\frac { \\lambda _ { 0 } } { 2 \\pi } \\mathrm { c o s h } \\left( \\frac { \\omega \\tan \\alpha } { c } y \\right) \\cos { \\left[ \\frac { \\omega } { c } ( \\Delta s + x \\tan \\alpha ) \\right] } . $$ The equations of motion become $$ { \\ddot { x } } = { \\frac { q e _ { 1 } } { m _ { e } \\gamma } } \\tan ( \\alpha ) \\cosh \\left[ { \\frac { \\omega \\tan \\alpha } { c } } y \\right] \\sin \\left[ { \\frac { \\omega } { c } } \\left( \\Delta s + x \\tan \\alpha \\right) \\right] $$ $$ { \\ddot { y } } = { \\frac { - i k _ { y } \\lambda _ { g z } q e _ { 1 } } { 2 \\pi m _ { e } \\gamma } } \\sinh \\left[ { \\frac { \\omega \\tan \\alpha } { c } } y \\right] \\cos \\left[ { \\frac { \\omega } { c } } \\left( \\Delta s + x \\tan \\alpha \\right) \\right],4,Yes,1,
expert,Is it accurate to only consider the first harmonic?,"the higher nonsynchronous harmonics average out. It can be shown, that their second order (ponderomotive) contribution is also small. ",reasoning,Beam_dynamics_analysis_of_dielectric_laser_acceleration.pdf,"V. APPLICATIONS We apply our approach to similar experimental parameters as for the subrelativistic experiments at FAU Erlangen [3] and the relativistic experiments at SLAC [1,2]. Although the structures are idealized, the results are qualitatively recovered. As a next step, we show modifications and idealizations of the beam parameters, which outline the way to a microchip accelerator. A. Subrelativistic acceleration A subrelativistic DLA structure needs to be chirped in order to always fulfill the synchronicity condition (6) for the synchronous particle. The proper chirp for each cell and the synchronous velocity are obtained by iterating the two equations $$ \\Delta z ^ { ( n + 1 ) } = \\frac { q e _ { 1 } \\lambda _ { 0 } ^ { 2 } \\cos \\varphi _ { s } ^ { ( n ) } } { m _ { e } c ^ { 2 } } \\sqrt { 1 - { \\beta ^ { ( n ) } } ^ { 2 } } $$ $$ \\beta ^ { ( n + 1 ) } = \\beta ^ { ( n ) } + \\frac { \\Delta z ^ { ( n + 1 ) } } { \\lambda _ { 0 } } .",4,Yes,1,
expert,Is it accurate to only consider the first harmonic?,"the higher nonsynchronous harmonics average out. It can be shown, that their second order (ponderomotive) contribution is also small. ",reasoning,Beam_dynamics_analysis_of_dielectric_laser_acceleration.pdf,"$$ describes the acceleration ramp, where the synchronous phase $\\varphi _ { \\mathrm { s } }$ can be chosen arbitrarily \in each grating cell. The variables $e _ { 1 } , \\lambda _ { g z } , W _ { 0 } , \\beta , \\gamma , \\varphi _ { \\mathrm { s } }$ and all variables \in Eq. (24) are stored as arrays indexed by the grating cell number. The kicks are obtained using Eqs. (7), (18), (19), and (13) and read $$ \\begin{array} { r l } & { \\Delta x ^ { \\prime } = - \ \\frac { q \\lambda _ { 0 } } { p _ { z 0 } c } \\tan ( \\alpha ) \\cosh ( i k _ { y } y ) \\mathrm { R e } \\{ \\underline { { e } } _ { 1 } e ^ { i \\varphi + i \\frac { 2 \\pi x } { \\lambda _ { g x } } } \\} } \\\\ & { \\Delta y ^ { \\prime } = \ \\frac { - i k _ { y } \\lambda _ { 0 } ^ { 2 } q \\beta } { 2 \\pi p _ { z 0 } c } \\mathrm { s i n h } ( i k _ { y } y ) \\mathrm { I m } \\{ \\underline { { e } } _ { 1 } e ^ { i \\varphi + i \\frac { 2 \\pi x } { \\lambda _ { g x } } } \\} } \\\\ & { \\Delta \\delta = \ \\frac { q \\lambda _ { g z } } { \\gamma m _ { e } c ^ { 2 } } \\mathrm { R e } \\{ \\underline { { e } } _ { 1 } ( \\mathrm { c o s h } ( i k _ { y } y ) e ^ { i \\varphi + i \\frac { 2 \\pi x } { \\lambda _ { g x } } } - e ^ { i \\varphi _ { s } } ) \\} , } \\end{array}",5,Yes,1,
expert,Is it accurate to only consider the first harmonic?,"the higher nonsynchronous harmonics average out. It can be shown, that their second order (ponderomotive) contribution is also small. ",reasoning,Beam_dynamics_analysis_of_dielectric_laser_acceleration.pdf,"$$ \\underline { { e } } _ { m } ( x , y ) = \\underline { { e } } _ { m } ( 0 , 0 ) \\cosh ( i k _ { y } y ) e ^ { i k _ { x } x } , $$ where $\\lambda _ { g x } = \\lambda _ { g z } /$ tan $\\alpha$ . A map of the energy gain and transverse kicks for the grating in Fig. 6 can be seen in Fig. 7 for a grating tilt angle $\\alpha = 3 0$ deg. The results labeled numerical are obtained by line integration [Eq. (7)] of the electric field simulated with CST MWS [16] and the analytical results correspond to Eq. (18). The transverse kicks are obtained by Eq. (13) as $$ \\begin{array} { r l r } { { \\vec { \\underline { { f } } } _ { m } ( x , y ) = \\underline { { e } } _ { m } ( 0 , 0 ) \\cosh ( i k _ { y } y ) e ^ { i k _ { x } x } i m \\tan \\alpha \\vec { e } _ { x } } } \\\\ & { } & { + \\underline { { e } } _ { m } ( 0 , 0 ) \\sinh ( i k _ { y } y ) e ^ { i k _ { x } x } ( i k _ { y } \\lambda _ { g z } / 2 \\pi ) \\vec { e } _ { y } } \\end{array}",4,Yes,1,
expert,Is it accurate to only consider the first harmonic?,"the higher nonsynchronous harmonics average out. It can be shown, that their second order (ponderomotive) contribution is also small. ",reasoning,Beam_dynamics_analysis_of_dielectric_laser_acceleration.pdf,"$$ where $W _ { 0 } = \\gamma m _ { e } c ^ { 2 }$ and $p _ { z 0 } = \\beta \\gamma m _ { e } c$ . The particle at the synchronous phase $\\varphi _ { \\mathrm { s } }$ has $\\Delta \\delta = 0$ , i.e., its energy gain is entirely described by the acceleration ramp. The energy gain $\\Delta W$ is given by Eq. (7) and thus the energy gain of the synchronous particle is $$ \\Delta W ( 0 , 0 , \\varphi _ { \\mathrm { s } } ) = q \\lambda _ { g z } \\mathrm { R e } \\{ e ^ { i \\varphi _ { \\mathrm { s } } } \\underline { { e } } _ { 1 } \\} , $$ where we write $e _ { 1 } = \\underline { { e } } _ { 1 } ( x = 0 , y = 0 )$ for brevity. Note that the synchronous phase and the phase of each particle always refer to the laser phase. The sum of the kicks $$ W ( N ) = W _ { \\mathrm { i n i t } } + \\sum _ { n = 1 } ^ { N } \\Delta W ^ { ( n ) } ( 0 , 0 , \\varphi _ { \\mathrm { s } } ^ { ( n ) } )",5,Yes,1,
expert,What are insertion devices?,"They are periodic magnetic structures, such as undulators and wigglers, placed in straight sections to generate radiation.",Definition,Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation,"$$ If the phase of the radiation wave advances by $\\pi$ between $A$ and $B$ , the electromagnetic field of the radiation adds coherently3. The light moves on a straight line $\\overline { { A B } }$ that is slightly shorter than the sinusoidal electron trajectory $\\widetilde { A B }$ $$ { \\frac { \\lambda } { 2 c } } = { \\frac { \\widetilde { A B } } { v } } - { \\frac { \\overline { { A B } } } { c } } . $$ The electron travels on a sinusoidal arc of length $\\widetilde { A B }$ that can be calculated as $$ \\begin{array} { r l } { \\overrightarrow { A B } } & { = \\displaystyle \\int _ { 0 } ^ { \\infty } \\sqrt { 1 + \\left( \\frac { \\mathrm { d } x } { \\mathrm { d } \\xi } \\right) ^ { 2 } } \\mathrm { d } z } \\\\ & { \\approx \\displaystyle \\int _ { 0 } ^ { \\infty } \\left( 1 + \\frac { 1 } { 2 } \\left( \\frac { \\mathrm { d } x } { \\mathrm { d } \\xi } \\right) ^ { 2 } \\right) \\mathrm { d } z } \\\\ & { = \\displaystyle \\int _ { 0 } ^ { \\infty } \\left( 1 - \\frac { K ^ { 2 } } { 2 \\sqrt { 3 \\xi _ { 0 } ^ { 2 } \\gamma ^ { 2 } } } \\mathrm { e } ^ { \\mathrm { i } \\xi } \\mathrm { d } \\xi \\right) \\mathrm { d } z } \\\\ & { = \\displaystyle \\int _ { 0 } ^ { \\infty } \\left( 1 - \\frac { K ^ { 2 } } { 2 \\sqrt { 3 \\xi _ { 0 } ^ { 2 } \\gamma ^ { 2 } } } \\mathrm { e } ^ { \\mathrm { i } \\xi } \\mathrm { d } \\xi \\right) \\mathrm { d } z } \\\\ & { = \\displaystyle \\frac { \\lambda _ { 0 } } { 2 } \\left( 1 + \\frac { K ^ { 2 } } { 4 ( 3 \\xi _ { 0 } ^ { 2 } \\gamma ^ { 2 } ) } \\right) } \\\\ & { \\approx \\displaystyle \\frac { \\lambda _ { 0 } } { 2 } \\left( 1 + \\frac { K ^ { 2 } } { 4 \\gamma ^ { 2 } } \\right) . } \\end{array}",1,NO,0,
expert,What are insertion devices?,"They are periodic magnetic structures, such as undulators and wigglers, placed in straight sections to generate radiation.",Definition,Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation,"$$ j _ { x } + j _ { y } + j _ { z } = 4 . $$ This means that the damping is not uniformly distributed along the three sub-spaces of the phase space (horizontal, vertical and longitudinal), but it is split according to specific partition numbers. These partition numbers are determined by the accelerator lattice, which gives the designers of accelerators some freedom to optimize the damping times. I.10.4 Diffraction limited storage rings The pursuit of higher brilliance and coherence is a driving force in the development of synchrotrons. As we have seen above, while the emission of synchrotron radiation reduces the transverse emittance of the beams in an electron synchrotron, the quantum nature of the radiation imposes a limit on how small the beam will become, and thus set a ceiling on the achievable brilliance. The source size of the $\\mathrm { \\Delta X }$ -ray beam is given by the electron beam size in the undulators. We have seen in Section I.10.3.4 that the vertical emittance is typically significantly smaller than the horizontal emittance. The vertical beam size is indeed typically so small that the X-ray beams are diffraction-limited in this dimension.",1,NO,0,
expert,What are insertion devices?,"They are periodic magnetic structures, such as undulators and wigglers, placed in straight sections to generate radiation.",Definition,Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation,"‚Äì Auger electrons: similarly to fluorescence, this effect starts with the ionization or excitation of an inner-shell electron due to the interaction with the X-ray photon. This leaves a vacancy in the inner shell, which is then filled with an outer-shell electron. However, instead of releasing the excess energy as a photon, the energy is transferred non-radiatively to another outer-shell electron. This transfer of energy gives the second electron enough energy to be ejected from the atom, resulting in the emission of what is known as an Auger electron. These processes are summarized in Fig. I.10.10. Inelastic processes always lead to an energy deposition in the material, often leading to radiation damage, which limits the exposure time in many X-ray experiments. I.10.5.3 Crystal diffraction Imagine many atoms, arranged in a regular lattice, illuminated by a coherent $\\mathrm { \\Delta X }$ -ray source. The elastic scattering on the electron clouds of these atoms will add constructively if all individual waves are in phase. This situation is shown in Fig. I.10.11. Considering a distance $d$ between the crystal planes, and referring to the notation in this figure, we get constructive interference when $$ ( A B + B C ) - ( A C ^ { \\prime } ) = n \\lambda",1,NO,0,
expert,What are insertion devices?,"They are periodic magnetic structures, such as undulators and wigglers, placed in straight sections to generate radiation.",Definition,Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation,"d) . . . requires the rotation of the sample around three orthogonal axes I.10.7.52 Undulator radiation Derive the formula for the fundamental wavelength of undulator radiation emitted at a small angle $\\theta$ : $$ \\lambda = \\frac { \\lambda _ { u } } { 2 \\gamma ^ { 2 } } \\left( 1 + \\frac { K ^ { 2 } } { 2 } + \\gamma ^ { 2 } \\theta ^ { 2 } \\right) $$ from the condition of constructive interference of the radiation emitted by consecutive undulator periods! I.10.7.53 Binding energies In which atom are the core electrons most strongly bound to the nucleus? a) Neon b) Copper c) Lithium d) Osmium e) Helium $f$ ) Iron g) Sodium $h$ ) Gold What about the valence electrons? I.10.7.54 Electron and X-Ray diffraction In comparison to diffractive imaging using electrons, X-ray diffraction. . $a$ ). . . has the advantage that the sample does not need to be in vacuum b). . . gives a stronger diffraction signal for all crystal sizes $c$ ). . . generates the same signal for all atoms in the crystal What are the consequences for the optimum sample thickness for electron diffraction in comparison to X-ray diffraction?",1,NO,0,
expert,What are insertion devices?,"They are periodic magnetic structures, such as undulators and wigglers, placed in straight sections to generate radiation.",Definition,Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation,"How would you measure this radiation? I.10.7.27 Superconducting undulators What is the advantage of using undulators made with superconducting coils, in comparison to permanentmagnet arrays? What are drawbacks? I.10.7.28 In-vacuum undulators What are the advantages of using in-vacuum undulators? What are possible difficulties? I.10.7.29 Instrumentation How would you measure the vertical emittance in a storage ring? I.10.7.30 Top-up operation What are the advantages of top-up operation? What difficulties have to be overcome to establish top-up in a storage ring? (give one advantage and one difficulty for 1P.; give one more advantage and one more difficulty for $\\begin{array} { r } { 1 \\mathrm { P } . \\star . } \\end{array}$ .) I.10.7.31 Fundamental limits The SLS 2.0, a diffraction limited storage ring, aims for an electron energy of $2 . 4 \\mathrm { G e V }$ and an emittance of $1 2 6 \\mathrm { p m }$ . How far is this away from the de Broglie emittance, i.e. the minimum emittance given by the uncertainty principle? I.10.7.32 Applications Why are synchrotrons important for science? I.10.7.33 Applications What applications for industry are there to synchrotrons? I.10.7.34 Orbit correction Which devices are used to measure and correct the orbit inside a synchrotron?",1,NO,0,
expert,What are insertion devices?,"They are periodic magnetic structures, such as undulators and wigglers, placed in straight sections to generate radiation.",Definition,Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation,"$$ Equation (I.10.16) becomes $$ \\begin{array} { r c l } { { \\displaystyle \\frac { \\lambda } { 2 c } } } & { { = } } & { { \\displaystyle \\frac { \\lambda _ { u } } { 2 \\beta c } \\left( 1 + \\frac { K ^ { 2 } } { 4 \\gamma ^ { 2 } } \\right) - \\frac { \\lambda _ { u } } { 2 c } } } \\\\ { { \\Longrightarrow } } & { { \\lambda } } & { { = } } & { { \\displaystyle \\frac { \\lambda _ { u } } { 2 \\gamma ^ { 2 } } ( 1 + K ^ { 2 } / 2 ) , } } \\end{array} $$ where we have used $\\beta = \\textstyle \\sqrt { 1 - \\gamma ^ { - 2 } } \\approx 1 - \\frac { 1 } { 2 } \\gamma ^ { - 2 }$ for $\\gamma \\gg 1$ . Radiation emitted at this wavelength adds up coherently in the forward direction. More generally, the radiation adds up coherently at all odd harmonics $n = 2 m - 1 , m \\in \\mathbb { N }$",1,NO,0,
Expert,What are the filter settings for the DSCR screens?,"The screens use two filters with 10% and 1% attenuation, that give attenuations of 10%, 1%, and 0.1%.",Fact,[ScreenUpgrade]RevSciInst_94_073301(2023).pdf,"The evaluation of the beam size resolution of the screen profile monitors is usually first performed in a laboratory, using calibrated optical targets, and then sometimes checked in the beam itself. However, the in-beam checks can be difficult to execute properly without damaging the scintillators. The simplest way to evaluate the beam size resolution of the screen would be to focus the electron beam to a single point on the screen and record the resulting profile size on the monitor. However, this approach has the disadvantage that the tightly focused beam may damage the screen, degrading its performance and reliability. This article demonstrates a gentler way of determining the resolution of the screen while they are in use. II. MEASUREMENT SETUP The diagnostic screens (DSCRs) used at SwissFEL were developed to use a Scheimpflug geometry to minimize the effect of COTR generated from microbunching that may be present in the SwissFEL electron bunch on the profile measurement.10,14 An optical setup was developed to cover the large range of intensities that the scintillating effect would generate under various measurement regimes of the electron beam. The optical setup uses a Nikon $2 0 0 \\mathrm { m m } \\mathrm { f } / 4$ ED-IF AF Micro lens set at a working distance of $2 5 0 ~ \\mathrm { m m }$ from the scintillating screen. The Ce:YAG scintillating screen is in vacuum, with the light propagating through a $1 5 ^ { \\circ }$ Scheimpflug geometry, through a sapphire vacuum viewport, a mirror, and then into the lens, with a PCO.edge 5.5 camera behind it. The scintillating light has a wavelength range from about 500 to $7 0 0 \\mathrm { n m }$ , with a maximum at $5 5 0 \\mathrm { n m }$ . The design keeps the camera gain at a constant level to maximize the signal-to-noise ratio of the camera electronics and introduces a $1 \\%$ or $1 0 \\%$ neutral density (ND) filter about $2 0 ~ \\mathrm { m m }$ before the lens along the optical path to reduce the intensity of the scintillator light going into the camera. This gives the system the ability to observe the image at $1 0 0 \\%$ , $1 0 \\%$ , $1 \\%$ , or $0 . 1 \\%$ transmission, depending on which combination of ND filters we insert, if any at all. The original chosen filters were Kodak filter foils. The thin foils were thought to have a minimal lensing effect on the optical setup due to their thinness. The optical components are centered on the optical path axis of the scintillated light. The preliminary measurements in an optical laboratory showed that the optical system should have a resolution of about $1 4 \\mu \\mathrm m$ . This diagnostic screen setup was tested at the SwissFEL test facility with a tightly focused, low-charge electron beam and showed a resolution of about $1 6 \\mu \\mathrm m$ .10 A schematic drawing of the setup is shown in Fig. 1.",4,Yes,1,
Expert,What are the filter settings for the DSCR screens?,"The screens use two filters with 10% and 1% attenuation, that give attenuations of 10%, 1%, and 0.1%.",Fact,[ScreenUpgrade]RevSciInst_94_073301(2023).pdf,"However, the first experimental use of these devices after installation to evaluate the emittance of the electron beam at SwissFEL showed that the resolution was significantly worse and was found to be between 20 and $4 0 \\ \\mu \\mathrm { m }$ when using the filters.15–17 An investigation of the filters showed that the thin film deforms and degrades over time and adds a blurring effect, spoiling the optical system resolution. The design was changed to use higher quality ND filters that are made of glass but would affect the optical path. This necessitated the addition of a motorized stage for the lens and camera system to be able to re-focus for every new filter setting, as shown in Fig. 2. This new setup differs from the original in that it allows for changes of the optical path to control the focusing and in the quality of the filters. All other components are unchanged. After the optimization of the camera and lens position to find the best focus for each ND filter combination, we set the control system for the DSCRs so that the proper position would be set for every ND filter combination and resulting transmission. We obtained the screen resolution by measuring the beam size for different electron beam energies, while keeping the same emittance and optics. The measured beam size has two contributions: (1) the true beam size, which can be expressed as $\\sqrt { \\beta \\varepsilon / \\gamma } , ^ { 1 8 }$ where $\\beta$ is the beta-function of the electron beam, $\\pmb { \\varepsilon }$ is the norma/lized emittance, and $\\gamma$ is the relativistic Lorentz factor of the electron beam (with $\\gamma$ being the electron beam energy divided by $m _ { e } c ^ { 2 }$ ), and (2) the screen resolution $\\sigma _ { \\mathrm { s c r } }$ . Since the two components are, in principle, not correlated, the square of the measured beam size can be expressed as the sum of the square of each of the two contributions,",4,Yes,1,
Expert,What are the filter settings for the DSCR screens?,"The screens use two filters with 10% and 1% attenuation, that give attenuations of 10%, 1%, and 0.1%.",Fact,[ScreenUpgrade]RevSciInst_94_073301(2023).pdf,"$$ \\sigma _ { t o t } ^ { 2 } = \\sigma _ { s c r } ^ { 2 } + \\frac { \\beta \\varepsilon } { \\gamma } . $$ It is clear from the above equation that by measuring the electron beam sizes $\\sigma _ { \\mathrm { t o t } }$ for different electron beam energies $\\gamma _ { : }$ , one can reconstruct the screen resolution $\\sigma _ { \\mathrm { s c r } }$ as well as the product of the emittance and beta function $\\beta \\varepsilon$ . This method is inspired by similar ones where certain beam or lattice parameters are varied to obtain the screen resolution.15–17,19,20 It is an implementation of the approach proposed in Ref. 17 for a location without dispersion. III. RESULTS We used the standard $2 0 0 ~ \\mathrm { p C }$ beam and changed the electron beam energy at the end of the SwissFEL linac on the Aramis beamline from 3 to $6 \\ : \\mathrm { G e V }$ . The measurement of the performance of the new system was directly compared with that of the old setup with foils by putting both sets of filters in one optical box and using both for each electron beam energy setting. We recorded ten images for each electron beam energy and filter. The beam size for each image was obtained by fitting a Gaussian function to the image projection. We then fit Eq. (1) to the measured beam sizes to reconstruct the screen resolution and the product of emittance and beta function. Figure 3 shows the single-shot images for different settings. Figure 4 displays the vertical beam sizes averaged over ten shots and the calculated fits under different conditions. As shown in Fig. 4, the measured beam sizes are significantly larger with the foil filter when compared to the glass filter, indicating a worse screen resolution.",4,Yes,1,
Expert,What are the filter settings for the DSCR screens?,"The screens use two filters with 10% and 1% attenuation, that give attenuations of 10%, 1%, and 0.1%.",Fact,[ScreenUpgrade]RevSciInst_94_073301(2023).pdf,"File Name:[ScreenUpgrade]RevSciInst_94_073301(2023).pdf Testing high-resolution transverse profile monitors by measuring the dependence of the electron beam size on the beam energy at SwissFEL Pavle Juranić  ; Eduard Prat  $\\textcircled{1}$ DCheck for updates Articles You May Be Interested In Perspective: Opportunities for ultrafast science at SwissFEL Struct Dyn (January 2018) Physical optics simulations with Pඐඉඛඍ for SwissFEL beamlines AIP Conference Proceedings (July 2016) Optical design of the ARAMIS-beamlines at SwissFEL AIP Conference Proceedings (July 2016) Testing high-resolution transverse profile monitors by measuring the dependence of the electron beam size on the beam energy at SwissFEL Cite as: Rev. Sci. Instrum. 94, 073301 (2023); doi: 10.1063/5.0155444 Submitted: 20 April 2023 $\\cdot \\cdot$ Accepted: 17 June 2023 • Published Online: 5 July 2023 Pavle Jurani´ca) and Eduard Prata) AFFILIATIONS Paul Scherrer Institut, Forschungsstrasse 111, 5232 Villigen, Switzerland a)Authors to whom correspondence should be addressed: pavle.juranic@psi.ch and eduard.prat@psi.ch ABSTRACT Transverse profile monitors are essential devices to characterize particle beams in accelerators. Here, we present an improved design of beam profile monitors at SwissFEL that combines the use of high-quality filters and dynamic focusing. We reconstruct the profile monitor resolution in a gentle way by measuring the electron beam size for different energies. The results show a significant improvement of the new design compared to the previous version, from 20 to $1 4 \\mu \\mathrm m$ .",2,Yes,0,
Expert,What are the filter settings for the DSCR screens?,"The screens use two filters with 10% and 1% attenuation, that give attenuations of 10%, 1%, and 0.1%.",Fact,[ScreenUpgrade]RevSciInst_94_073301(2023).pdf,"V. CONCLUSION The method presented in this article shows the ability to improve the screen resolution by using high-quality filters and dynamic focusing. The profile monitor resolution is reconstructed in a gentle way by measuring the electron beam sizes for different beam energies. Our results show a significant improvement of the beam size resolution (from 20 to $1 4 \\mu \\mathrm m \\dot { }$ ) with the new optical design. These improvements allow for regular evaluations of the resolution and the ability to set the focusing to different values to compensate for the change in optical properties of the setup, enabling a more reliable and consistent performance of the diagnostic for transverse beam profile measurements. ACKNOWLEDGMENTS The authors would like to thank and acknowledge the work of the technical groups that maintain and operate SwissFEL. Of those, special thanks go to Didier Voulot who was instrumental in setting up a script for automatic beam energy scaling in the SwissFEL accelerator that preserved the electron beam optics. Further thanks go to Thomas Schietinger and Rasmus Ischebeck for proofreading the manuscript. AUTHOR DECLARATIONS Conflict of Interest The authors have no conflicts to disclose. Author Contributions Pavle Jurani´c: Conceptualization (equal); Data curation (supporting); Formal analysis (supporting); Funding acquisition (equal); Investigation (equal); Methodology (equal); Project administration (equal); Resources (lead); Software (equal); Supervision (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Eduard Prat: Conceptualization (equal); Data curation (lead); Formal analysis (lead);",4,Yes,1,
Expert,What central wavelength of THz radiation was measured experimentally?,Approximately 881 ?m,Fact,hermann-et-al-2022-inverse-designed-narrowband-thz-radiator-for-ultrarelativistic-electrons.pdf,"$$ The design obtained from the gradient-based technique of adaptive moment estimation $( \\mathrm { A d a m } ) ^ { 2 . 5 }$ is depicted in Figure 1b. The structure features two rows of pillars, shifted by half a period with respect to each other. The rows of pillars are followed by three slabs on each side, which can be easily identified as distributed Bragg reflectors forming a microresonator around the electron channel. The channel width is $2 7 2 \\ \\mu \\mathrm { m } ,$ , even larger than the initially defined clearance of 150 $\\mu \\mathrm { m }$ . These slabs exhibit grooves, which perhaps act as a grating as well as a reflector. We note that these features are good examples of the superiority of inverse design over intuitionbased designs. To fabricate the geometry obtained with inverse design, we used an additive manufacturing process for poly(methyl methacrylate) (PMMA). A stereolithography device, featuring a resolution of $1 4 0 \\ \\mu \\mathrm { m } ,$ , is capable of reproducing the structure with subwavelength accuracy. The so-obtained structure is 6 mm high and $4 5 \\ \\mathrm { m m }$ long (Figure 1d). The holder of the structure was manufactured together with the structure, and filaments connect the pillars and slabs on top of the structure for increased mechanical stability. We selected the Formlabs High Temperature Resin as a material for this study due to its excellent vacuum compatibility after curing in a heated vacuum chamber.24 Afterward, the fabricated Smith‚àíPurcell radiator was inserted into the ACHIP experimental chamber26 at SwissFEL27 (Figure 2a). The photoemitted electron bunch is accelerated to an energy of $3 . 2 ~ \\mathrm { \\ G e V }$ with the normalconducting radio frequency accelerator at SwissFEL. A twostage compression scheme using magnetic chicanes is employed to achieve an electron bunch length of approximately 30 fs at the interaction point. At this location, the transverse beam size was measured to be around $3 0 \\ \\mu \\mathrm { m }$ in the horizontal and $4 0 \\ \\mu \\mathrm { { m } }$ in the vertical direction.",1,Yes,0,
Expert,What central wavelength of THz radiation was measured experimentally?,Approximately 881 ?m,Fact,hermann-et-al-2022-inverse-designed-narrowband-thz-radiator-for-ultrarelativistic-electrons.pdf,"$$ \\lambda = \\frac { a } { m } \\Biggl ( \\frac { 1 } { \\beta } - \\cos { \\theta } \\Biggr ) $$ where $\\beta$ is the normalized velocity of the electrons, a is the periodicity of the structure, and $m$ is the mode order. Smith‚àí Purcell emission from regular metallic grating surfaces has been observed in numerous experiments, first using $3 0 0 ~ \\mathrm { k e V }$ electrons11 and later also using ultrarelativistic electrons.12,13 If electron pulses shorter than the emitted wavelength are used, the fields from individual electrons add coherently, and the radiated energy scales quadratically with the bunch charge.14 The typically used single-sided gratings emit a broadband spectrum,15 which is dispersed by the Smith‚àíPurcell relation (eq 1). To enhance emission at single frequencies, a concept called orotron uses a metallic mirror above the grating to form a resonator.16,17 Dielectrics can sustain fields 1‚àí2 orders of magnitude larger than metals18 and are therefore an attractive material for strong Smith‚àíPurcell interactions. Inverse design is a computational technique that has been successfully employed to advance integrated photonics.19 Algorithms to discover optical structures fulfilling desired functional characteristics are creating a plethora of novel subwavelength geometries: applications include wavelengthdependent beam splitters19,20 and couplers,21 as well as dielectric laser accelerators.22",1,Yes,0,
Expert,What central wavelength of THz radiation was measured experimentally?,Approximately 881 ?m,Fact,hermann-et-al-2022-inverse-designed-narrowband-thz-radiator-for-ultrarelativistic-electrons.pdf,"The geometric acceptance angle of the Michelson interferometer $\\Delta \\theta$ in the plane of the electron beam and the THz radiation defines the accepted bandwidth of the setup. According to the Smith‚àíPurcell relation (eq 1), it is given by $$ \\Delta \\lambda = a \\sin \\theta \\Delta \\theta $$ Around the orthogonal direction $( \\theta \\ : = \\ : 9 0 ^ { \\circ } ,$ ), the accepted bandwidth covers the measured spectrum (Figure 3). We calculated the acceptance with ray tracing including the size of the emitting structure and the apertures of the collimating lens $( 2 5 ~ \\mathrm { m m } )$ and the detector ( $\\cdot 1 2 \\ \\mathrm { m m } ,$ ). A Schottky diode (ACST, Type 3DL 12C LS2500 A2) was used as THz detector, sensitive from 300 to $4 0 0 0 \\ \\mu \\mathrm { { m } }$ . The manufacturer indicates a responsivity of $1 2 0 ~ \\mathrm { V / W }$ at $9 0 0 \\ \\mu \\mathrm { { m } , }$ , which we used to estimate the energy deposited on the detector. The signal from the detector is transmitted via a $2 0 \\mathrm { m }$ long coaxial cable to an oscilloscope outside of the accelerator bunker. For absolute pulse energy measurements, the detector setup including absorption in cables and the vacuum window should be characterized with a calibrated $\\mathrm { T H z }$ source. We calculated the pulse energy for different charges (Figure 4) by averaging over all shots during the oscillating autocorrelation measurement.",1,Yes,0,
Expert,What central wavelength of THz radiation was measured experimentally?,Approximately 881 ?m,Fact,hermann-et-al-2022-inverse-designed-narrowband-thz-radiator-for-ultrarelativistic-electrons.pdf,"An in-vacuum PMMA lens with a diameter of $2 5 \\mathrm { ~ m m }$ collimated parts of the emitted radiation. A Michelson interferometer was used to measure the first-order autocorrelation of the electromagnetic pulse and to obtain its power spectrum via Fourier transform (Figure 2b and Methods). The measured spectrum is centered around 881 $\\mu \\mathrm { m }$ $\\left( 0 . 3 4 ~ \\mathrm { T H z } \\right)$ and has a full width at half-maximum of ${ \\sim } 9 \\%$ (Figure 3). DISCUSSION The observed spectrum agrees well with a 3D finite-differences time-domain (FDTD) simulation of the experiment (Figure 3). In contrast, a finite-differences frequency-domain (FDFD) simulation reveals that the design can in principal emit even more narrowbandly, originating from the high mode density inside the Fabry‚àíPerot cavity formed by the two distributed Bragg reflectors on both sides of the electron channel. The difference between the two simulations can be explained by their distinct grid resolutions. The FDFD simulation considers only a single period of the structure with periodic boundaries, corresponding to an infinitely long structure. Hence, the cell size is small, allowing to use a high grid resolution. The timedomain simulation, on the other hand, calculates the electromagnetic field of the entire 50-period-long structure for each time step. This high memory requirement comes at the cost of a lower spatial resolution. Since the experiment was similarly limited by the fabrication resolution of $1 4 0 \\ \\mu \\mathrm { m } ,$ the FDTD simulation reproduced the measured spectrum much better. We also note that potential absorption losses in the structure can reduce its quality factor and broaden the radiation spectrum. Due to the small contribution from $\\varepsilon ^ { \\prime \\prime } =$ $0 . 0 8 , ^ { 2 4 }$ absorption effects were not considered here but would dominate at higher quality factors.",1,Yes,0,
Expert,What central wavelength of THz radiation was measured experimentally?,Approximately 881 ?m,Fact,hermann-et-al-2022-inverse-designed-narrowband-thz-radiator-for-ultrarelativistic-electrons.pdf,"File Name:hermann-et-al-2022-inverse-designed-narrowband-thz-radiator-for-ultrarelativistic-electrons.pdf Inverse-Designed Narrowband THz Radiator for Ultrarelativistic Electrons Benedikt Hermann,# Urs Haeusler,# Gyanendra Yadav, Adrian Kirchner, Thomas Feurer, Carsten Welsch, Peter Hommelhoff, and Rasmus Ischebeck\\* Cite This: ACS Photonics 2022, 9, 1143−1149 ACCESS 山 Metrics & More 国 Article Recommendations ABSTRACT: THz radiation finds various applications in science and technology. Pump−probe experiments at free-electron lasers typically rely on THz radiation generated by optical rectification of ultrafast laser pulses in electro-optic crystals. A compact and cost-efficient alternative is offered by the Smith−Purcell effect: a charged particle beam passes a periodic structure and generates synchronous radiation. Here, we employ the technique of photonic inverse design to optimize a structure for Smith− Purcell radiation at a single wavelength from ultrarelativistic electrons. The resulting design is highly resonant and emits narrowbandly. Experiments with a 3D-printed model for a wavelength of $9 0 0 \\mu \\mathrm { m }$ show coherent enhancement. The versatility of inverse design offers a simple adaption of the structure to other electron energies or radiation wavelengths. This approach could advance beam-based THz generation for a wide range of applications. KEYWORDS: THz generation, Smith−Purcell radiation, inverse design, light−matter interaction, free-electron light sources $\\mathbf { C }$ aopuprlciecs iof ,TiHnzc rdaidniagtiwoinr aerses ofmimntuenriecsat fonr ,n2uelmeecrtrouns acceleration,3−5 and biomedical and material science.6,7 Freeelectron laser (FEL) facilities demand versatile THz sources for pump−probe experiments.8 Intense, broadband THz pulses up to sub-mJ pulse energy have been demonstrated using optical rectification of high-power femtosecond lasers in lithium niobate crystals.9,10 The Smith−Purcell effect11 offers a compact and cost-efficient alternative for the generation of beam-synchronous THz radiation at electron accelerators. This effect describes the emission of electromagnetic waves from a periodic metallic or dielectric structure excited by electrons moving parallel to its surface. The wavelength of Smith− Purcell radiation at an angle $\\theta$ with respect to the electron beam follows:11",1,Yes,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}",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 } ) .",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.",1,NO,0,
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 } .",1,NO,0,
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 $$ I ( \\omega ) = \\int _ { - \\infty } ^ { \\infty } i ( t ) e ^ { - j \\omega t } d t , $$ $$ i ( t ) = { \\frac { 1 } { 2 \\pi } } \\int _ { - \\infty } ^ { \\infty } I ( \\omega ) e ^ { j \\omega t } d \\omega .",1,NO,0,
expert,What charge distribution maximizes the transformer ratio?,The doorstop charge distribution,Summary,Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf,"$$ 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, $$ E _ { z , n } ( s ) = 2 \\kappa _ { n } \\mathrm { R e } \\Bigg \\{ \\int _ { 0 } ^ { \\infty } q ( s - s ^ { \\prime } ) e ^ { j k _ { n } s ^ { \\prime } } d s ^ { \\prime } \\Bigg \\} .",1,NO,0,
expert,What code was used to simulte the SHINE dechirper,ECHO2D,Summary,Beam_performance_of_the_SHINE_dechirper.pdf,"We next simply consider the quadrupole wake, where the beam is on-axis $( \\mathrm { y } _ { \\mathrm { c } } = 0 )$ . The transfer matrices for the focusing and defocusing quadrupole are given in Eq. (16), where $L$ is the length of the corrugated structure [25]. $$ \\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}",1,Yes,0,
expert,What code was used to simulte the SHINE dechirper,ECHO2D,Summary,Beam_performance_of_the_SHINE_dechirper.pdf,"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.",1,Yes,0,
expert,What code was used to simulte the SHINE dechirper,ECHO2D,Summary,Beam_performance_of_the_SHINE_dechirper.pdf,"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.",2,Yes,0,
expert,What code was used to simulte the SHINE dechirper,ECHO2D,Summary,Beam_performance_of_the_SHINE_dechirper.pdf,"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.",1,Yes,0,
expert,What code was used to simulte the SHINE dechirper,ECHO2D,Summary,Beam_performance_of_the_SHINE_dechirper.pdf,"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].",4,Yes,1,
expert,What code was used to simulte the SHINE dechirper,ECHO2D,Summary,Beam_performance_of_the_SHINE_dechirper.pdf,"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: