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Expert
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What is the order of resolution of the PSSS spectrometer at SwissFEL?
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The resolution varies depending on the photon energy, but is the range of dE/E between 2e-5 to 6e-5.
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Fact
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PSSS_performance_JSR_28_1978(2021).pdf
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Several different spectrometer designs have been used at FELs for these kinds of spectral characterizations (Inubushi et al., 2012; Boesenberg et al., 2017; Rich et al., 2016; Svetina et al., 2016; Makita et al., 2015; Tono et al., 2013). Experiments at the Linac Coherent Light Source (LCLS) used bent Si crystals with transmission gratings (Makita et al., 2015). The bent Si crystals approach achieved high-resolution measurements (better than $0 . 2 \\ : \\mathrm { e V }$ at $8 . 3 \\mathrm { k e V }$ ), but were limited in spectral range and lost about half of the photon flux due to poor transmission (Zhu et al., 2012) while the transmission gratings had a poorer resolution $( 1 . 2 \\mathrm { e V }$ at $6 { \\mathrm { k e V } _ { , } }$ but much better transmission (Karvinen et al., 2012). The SPring-8 Angstrom Compact Free Electron Laser (SACLA) used a transmission grating in combination with an elliptical mirror and a flat Si crystal to deliver online spectra with tunability in both resolution and spectral range (Katayama et al., 2016). The Swiss-FEL photon single-shot spectrometer (PSSS) (Rehanek et al., 2017) combines a transmission grating with bent Si crystals to create a spectrometer that has a good resolution, large spectral range, and good transmission for online spectral measurements of photon energies between 4 and $1 3 \\mathrm { k e V } .$ Using this setup, the first order of the diffracted beam is used for spectral or intensity monitoring, while the zeroth order is transmitted downstream of the experiments.
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4
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Yes
| 1
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Expert
|
What is the order of resolution of the PSSS spectrometer at SwissFEL?
|
The resolution varies depending on the photon energy, but is the range of dE/E between 2e-5 to 6e-5.
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Fact
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PSSS_performance_JSR_28_1978(2021).pdf
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This work presents the achievements and the characterized capabilities of the PSSS as a single-shot online $\\mathbf { X }$ -ray spectrometer. We demonstrate that the PSSS can deliver a full width at half-maximum (FWHM) resolution of $\\Delta E / E \\simeq$ $5 \\times 1 0 ^ { - 5 }$ and a spectral window of up to $0 . 7 \\%$ of the photon energy over the working range of the device. 2. Setup The working principle of the PSSS is shown in Fig. 1. The diamond grating diffracts the incoming FEL beam in the horizontal plane, sending the first order to the bent crystal spectrometer while the zeroth order continues further downstream with $8 0 \\%$ or more of the incoming flux. Monitoring the spectra online in this fashion reduces the heat load on the spectrometer optics (Boesenberg et al., 2017). The first order is Bragg-reflected from the bent Si crystal in the spectrometer and projected onto a detector, as shown in Fig. 1. The detector is a PCO:Edge 5.5 camera with an objective that is focused onto a Ce:YAG scintillator. The diffraction gratings have pitches of $1 0 0 \\mathrm { n m }$ , $1 5 0 \\mathrm { n m }$ and $2 0 0 \\mathrm { n m }$ . The grating pitches are chosen such that the first-order diffracted beam is always far enough from the zeroth order so that the crystals can be put safely into it and do not block or affect the propagation of the main beam to the experimental station downstream. The first-order efficiency can be enhanced by tilting the diamond gratings up to $6 0 ^ { \\circ }$ . For the bent Si crystals, three Si(220) crystals with bending radii of $7 5 \\mathrm { m m }$ , $1 4 5 ~ \\mathrm { m m }$ and $2 0 0 \\mathrm { m m }$ , and one Si(111) crystal with a bending radius of $1 5 5 \\mathrm { m m }$ can be chosen. All of the Si crystals are $1 0 \\mu \\mathrm { m }$ thick. More information about the PSSS construction are given by Rehanek et al. (2017) and Juranic´ et al. (2018).
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5
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Yes
| 1
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Expert
|
What is the order of resolution of the PSSS spectrometer at SwissFEL?
|
The resolution varies depending on the photon energy, but is the range of dE/E between 2e-5 to 6e-5.
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Fact
|
PSSS_performance_JSR_28_1978(2021).pdf
|
Fig. $4 ( a )$ shows the dependence of the separation of the zeroth- and first-order beams as a function of photon energy for the three available diamond gratings with 100, 150 and $2 0 0 \\mathrm { n m }$ pitches. The region between $1 4 ^ { \\circ }$ and $6 0 ^ { \\circ }$ is where noninvasive operation of the PSSS is possible, corresponding to between $3 \\mathrm { m m }$ and $8 \\mathrm { m m }$ beam separation. Fig. $4 ( b )$ shows the calculated transmission of the diamond gratings as a function of photon energy, calculated with the Henke tables (Henke et al., 1993; http://henke.lbl.gov/optical_constants/tgrat2.html). The transmitted beam has a transmission between $8 0 \\%$ at $4 { \\mathrm { k e V } }$ and $9 8 \\%$ at $1 3 \\mathrm { k e V }$ photon energy. The transmission efficiency of the gratings has been measured and reported elsewhere (Juranic et al., 2019). 3.1.2. Si crystal alignment, energy calibration and detector sensitivity. The average integrated intensity of the spectra on the detector shows a very strong dependence on the vertical position of the bent Si crystal in the beam, as shown in Fig. $3 ( a )$ . The integrated intensity drops by about $5 0 \\%$ for a $1 1 0 \\mu \\mathrm { m }$ displacement of the crystal for an optimum position, highlighting the sensitivity of the device to misalignments and shifts in the beam position.
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1
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Yes
| 0
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Expert
|
What is the order of resolution of the PSSS spectrometer at SwissFEL?
|
The resolution varies depending on the photon energy, but is the range of dE/E between 2e-5 to 6e-5.
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Fact
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PSSS_performance_JSR_28_1978(2021).pdf
|
Additional profile monitors situated both before and after the Bragg crystal chambers allow for the destructive observation of the diffracted beam and to see the Bragg diffraction in transmission. These monitors are Ce:YAG scintillators with a camera/lens unit (Juranic´ et al., 2018). Fig. $2 ( a )$ shows the diffracted beam on the profile monitor, while Fig. $2 ( b )$ shows the raw image of the spectrum on the PCO.Edge camera of the spectrometer. The RMS size of the photon beam in the horizontal and vertical directions at the PSSS ranges from about 150 to $4 0 0 ~ { \\mu \\mathrm { m } }$ , depending on the photon energy and operating mode. The PSSS setup requires precise alignment of the Si bent crystals to the beam. The vertical position of the crystal is the most important parameter to maximize the signal once the correct Bragg angles were selected for a chosen energy window. The setup is typically conducted in the non-invasive mode: the diamond gratings upstream diffract the beam, and the analyser crystals are placed in the first diffraction order. An exemplary measurement, conducted at $1 2 \\mathrm { k e V }$ photon energy and with a pulse energy of approximately $1 1 0 \\mu \\mathrm { J } ,$ is shown in Fig. $3 ( a )$ .
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5
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Yes
| 1
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Expert
|
What is the order of resolution of the PSSS spectrometer at SwissFEL?
|
The resolution varies depending on the photon energy, but is the range of dE/E between 2e-5 to 6e-5.
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Fact
|
PSSS_performance_JSR_28_1978(2021).pdf
|
The sensitivity across the detector was investigated by scanning the detector position perpendicular to the Bragg reflection and comparing the integrated intensity against the simultaneous measurements taken with the online gas-based pulse energy monitor (Juranic´ et al., 2018). The field of view of the detector is about $4 \\mathrm { m m }$ , so the spectra becomes cut off as one approaches that limit, and the integrated intensity drops off as a part of the spectrum is cut out, as shown in Figs. 3(c) and $3 ( d )$ . 3. PSSS performance and discussion 3.1. Operational parameters 3.1.1. Si crystals and transmission gratings. The first step of the PSSS commissioning process was to determine the performance of different Si crystals and transmission gratings. From the Bragg angles [Fig. $3 ( b ) ]$ , we can see the reachable energy windows for the different silicon crystals. The Si(220) reflection can be used over the complete range of the PSSS (4 to $1 3 \\mathrm { \\ k e V } ,$ ), while the Si(111) reflections can be used from $4 { \\mathrm { k e V } }$ to $8 \\mathrm { k e V }$ due to the limited range of the detector rotation stage due to other beamline components, limiting us to Bragg reflections from $1 4 ^ { \\circ }$ to $6 0 ^ { \\circ }$ .
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4
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Yes
| 1
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Expert
|
What is the order of resolution of the PSSS spectrometer at SwissFEL?
|
The resolution varies depending on the photon energy, but is the range of dE/E between 2e-5 to 6e-5.
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Fact
|
PSSS_performance_JSR_28_1978(2021).pdf
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Table: Caption: Table 1 Bragg angle offsets due to miscuts for the four bent crystals. Body: <html><body><table><tr><td>Crystal</td><td>Offset (°)</td></tr><tr><td>Si(111),R= 155 mm</td><td>-0.217</td></tr><tr><td>Si(220),R= 75 mm</td><td>-0.898</td></tr><tr><td>Si(220), R= 145 mm</td><td>1.149</td></tr><tr><td>Si(220),R= 200 mm</td><td>0.537</td></tr></table></body></html> 3.1.3. FEL beam profile. Previous work has noted that the spectral intensity distribution can depend on the part of the FEL beam profile that is being Bragg reflected by the crystals (Makita et al., 2015; Rehanek et al., 2017). The homogeneity of the beam profile across the sampled portion of the beam being Bragg reflected should be as good as possible to ensure good spectral intensity measurements. Fig. $5 ( a )$ shows the profile of the transmitted beam with a Bragg crystal positioned on the main beam (without the use of a diamond grating) that was acquired with a profile monitor downstream of the Bragg crystals (attenuated to avoid saturation). The diffracted portion of the beam is revealed by the small intensity drop in the beam center. The amount of the Bragg reflection is estimated as the maximum difference between the sides and the Bragg dip in the middle of the profile, as shown in Fig. $5 ( b )$ . The dip in signal due to the Bragg reflection is about $5 \\%$ near the maximum. From the tiny amount of the diffraction and the uniformity of the transmitted beam profile, we anticipate that the influence of the intensity on the measured spectral distribution of the beam is negligible as long as the Bragg crystal is centered.
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4
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Yes
| 1
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Expert
|
What is the order of resolution of the PSSS spectrometer at SwissFEL?
|
The resolution varies depending on the photon energy, but is the range of dE/E between 2e-5 to 6e-5.
|
Fact
|
PSSS_performance_JSR_28_1978(2021).pdf
|
1. Introduction The pulse-to-pulse measurement of spectra of self-amplified spontaneous emission (SASE) X-ray free-electron lasers (FELs) (Bergmann et al., 2017) is of fundamental importance for several experimental techniques ranging from resonant inelastic X-ray scattering (RIXS) (Lemke et al., 2013; Chergui, 2016; Obara et al., 2017; Park et al., 2019; Kimberg & Rohringer, 2016; Błachucki et al., 2014; Kayser et al., 2019) to protein crystallography (Tono et al., 2015; Moreno-Chicano et al., 2019). The SASE process changes the spectral properties of the X-ray pulse on a pulse-to-pulse basis, which requires a device for online, non-invasive measurements of the X-ray spectra for both experimental spectral normalization and performance optimization (Rehanek et al., 2017). A good example of the use of an online spectrometer is in X-ray absorption spectroscopy (XAS), where measurements have been reported using both SASE and sample-transmitted spectra (Boutet & Hunter, 2018; Katayama et al., 2013; Brenner et al., 2019). Such spectrometers are also useful in high-pressure or high-energy density science, where scans have to be performed with a small number of shots, preventing monochromator scans (Harmand et al., 2015). A large advantage in recording absorption spectra with the full SASE mode compared with the use of monochromatic light is that extreme intensity fluctuations are avoided, if the SASE spectrum does not contain the photon energy chosen by the monochromator (Boutet & Hunter, 2018). The SASE spectrum also carries useful information to set up FEL operational parameters and develop new operating modes (Rehanek et al., 2017) and can be used to estimate pulse durations from the measurements of spectral spike widths (Malyzhenkov et al., 2020; Huang et al., 2017; Makita et al., 2015).
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augmentation
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Yes
| 0
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Expert
|
What is the order of resolution of the PSSS spectrometer at SwissFEL?
|
The resolution varies depending on the photon energy, but is the range of dE/E between 2e-5 to 6e-5.
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Fact
|
PSSS_performance_JSR_28_1978(2021).pdf
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The precise energy calibration of the spectrometer was performed by inserting several filter foils into the beam and identifying the transmission edges. By fitting the observed position on the camera to the expected Bragg angles, the geometry, miscut of the crystals and mounting tolerances were taken into account. The used foils were Ti $K$ -edge $4 . 9 6 6 \\mathrm { k e V } ,$ $1 0 \\mu \\mathrm { m }$ thickness), Mn ( $K$ -edge $6 . 5 4 \\mathrm { k e V } _ { ; }$ , $2 0 \\mu \\mathrm { m }$ thickness), Fe ( $K$ -edge $7 . 1 1 \\mathrm { k e V } ,$ , $1 0 \\mu \\mathrm { m }$ thickness), Ni ( $K$ -edge $8 . 3 3 \\mathrm { k e V } ,$ $1 2 . 5 \\mu \\mathrm { m }$ thickness) and $\\mathrm { c u }$ ( $K \\cdot$ -edge $8 . 9 8 \\mathrm { k e V } ,$ , $2 0 \\mu \\mathrm { m }$ thickness). The photon energy of the FEL was set to the absorption edges of the foils, and the Bragg angle of the PSSS was scanned to find the motor positions that matched the photon energies of the absorption edges for all crystals. The measured points were then used to fit a theoretical Bragg curve with an additional free parameter to take the miscut of the crystals into account. These fits were then used to create a look-up table for all relevant motor positions across the energy window for each crystal. The resulting points and Bragg curves are shown in Fig. $3 ( b )$ . Note that we also show the Bragg curves without miscuts for Si(111) and Si(220) (dashed lines).
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augmentation
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Yes
| 0
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Expert
|
What is the order of resolution of the PSSS spectrometer at SwissFEL?
|
The resolution varies depending on the photon energy, but is the range of dE/E between 2e-5 to 6e-5.
|
Fact
|
PSSS_performance_JSR_28_1978(2021).pdf
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The difference between the measured Bragg angle values and those expected from the calculations are explained by the miscuts in the manufacturing process of the Si crystals (Rehanek et al., 2017). The offset between the measured crystal angles and the ideal Bragg angles is obvious in Fig. 3(b), where the three different Si(220) crystals have slightly different Bragg curves, offset from each other by a constant. The angular offsets of the Bragg angle for the four crystals were determined from these fits, and are shown in Table 1. Fig. $3 ( c )$ shows the average spectra plotted as a function of the sensor position perpendicular to the Bragg reflection. The sensitivity seems to be homogeneous over the scanned region, though the spectra, and the integrated intensity, start being clipped and reduced as the spectrum is moved out of the sensor’s field of view. Fig. $3 ( d )$ indicates that the best sensor position for the spectral center to minimize this clipping is between $- 2 . 5 \\mathrm { m m }$ and $1 \\mathrm { m m }$ , giving about a $3 . 5 \\mathrm { { m m } }$ effective field of view to reliably observe the spectrum.
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augmentation
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Yes
| 0
|
Expert
|
What is the order of resolution of the PSSS spectrometer at SwissFEL?
|
The resolution varies depending on the photon energy, but is the range of dE/E between 2e-5 to 6e-5.
|
Fact
|
PSSS_performance_JSR_28_1978(2021).pdf
|
3.2. Experience with the PSSS The PSSS went into full operation for users and machine operators after the implementation of a user-friendly graphical user interface for spectral measurements based on look-up tables created from the calibration data. To further help with the optimization of the FEL spectral settings, a fast algorithm was developed to evaluate the center of energy and the FWHM of a Gaussian fit to the smoothed spectrum on a shot-to-shot basis. Further tools created by the accelerator scientists use this data for feedbacks for the machine, and the PSSS is being used regularly to correct drifts and instabilities of the mean photon energy and spectral width via a feedback system and an optimizer to the SwissFEL accelerator settings. The PSSS has been used even when the end-stations use monochromators for an experiment, as the PSSS spectral bandwidth evaluation can be used to optimize the smallest bandwidth the FEL can achieve so that the maximum amount of photons possible pass through a monochromator’s bandpass, increasing the signal at the experiment. A good example of such an optimization feedback, and its effect on stabilizing the photon energy, is shown in Fig. 7. Overall, the device has been extremely helpful for machine optimization and experimental work.
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augmentation
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Yes
| 0
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IPAC
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What is the primary advantage of synchrotron radiation over traditional X-ray tubes?
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Synchrotron radiation provides much higher brightness, broader spectral coverage, and superior collimation compared to traditional X-ray tubes.
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Reasoning
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Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation
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INTRODUCTION Synchrotron radiation (SR) is produced in almost all accelerator facilities, as it is an e!ect of the path of charged particles being bent by magnetic fields. Whilst in many cases it is preferred to minimise the SR produced (and therefore the energy lost to it) [1], it can be very useful for diagnostics. Some sections of this emitted radiation are coherent. Coherent synchrotron radiation (CSR) occurs at frequencies where the wavelength is equal to or greater than the bunch length. The spectral content of the CSR image is directly influenced by the charge distribution of the bunch, making CSR a good choice for bunch length diagnostics [2]. Whilst incoherent radiation is also emitted, the spectral images produced are lower in frequency and do not vary with bunch length. $$ S ( \\omega ) \\approx N ^ { 2 } \\int _ { \\Delta \\omega } S _ { p } ( \\omega ) F ( \\omega ) ~ d \\omega $$ Equation 1 gives the synchrotron radiation spectrum $( S ( \\omega ) )$ for a bunch. Here, $N$ is the number of particles per bunch, $\\Delta \\omega$ is the frequency bandwidth, $S _ { p } ( \\omega )$ is the spectrum for a single particle, and $F ( \\omega )$ is the bunch form factor, given by Eq. 2 [3].
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augmentation
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NO
| 0
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IPAC
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What is the primary advantage of synchrotron radiation over traditional X-ray tubes?
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Synchrotron radiation provides much higher brightness, broader spectral coverage, and superior collimation compared to traditional X-ray tubes.
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Reasoning
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Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation
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INTRODUCTION Compared to conventional high-gain harmonic generation (HGHG) [1-4], the EEHG scheme is significantly less sensitive to energy spread, which is typically large in SRs. EEHG enables the possibility for synchrotron light source (SLS) based FELs to produce intense coherent radiation (CR) pulses with short durations [5-10]. Such fully coherent ultrafast photon pulses up to soft X-ray wavelength could offer unique opportunities to conduct high resolution phase-contrast spectroscopy on organic materials that are important in medicine, biology, and bio-renewable energy materials [11]. Also, extending the pump-probe approach to soft X-ray could allow detailed studies of excited-state dynamics in organic molecules or biomolecular structures on a nanosecond to femtosecond time scale. Based on current development of using two straight sections (SS) of the NSLS-II storage ring (SR) to seed the coherent soft X-ray emission, a compact EEHG design is presently studied as a standardized beamline option for current and future $4 ^ { \\mathrm { t h } }$ generation SLSs. With the improved longitudinal coherence and output stability, those EEHG beamlines could open new opportunities for studying excited-state dynamics in organic molecules, together with the tremendous increase of computing power, allows understanding the excited-state behavior even of very complex organic molecules in more detail [12-13].
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augmentation
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NO
| 0
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IPAC
|
What is the primary advantage of synchrotron radiation over traditional X-ray tubes?
|
Synchrotron radiation provides much higher brightness, broader spectral coverage, and superior collimation compared to traditional X-ray tubes.
|
Reasoning
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Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation
|
INTRODUCTION Understanding the structure and reaction dynamics of matter are crucial for advances in the fields of chemistry, biology, physics, and material science [1,2]. For decades synchrotron light sources and later also $\\mathbf { \\boldsymbol { x } }$ -ray free-electron lasers (FELs) were the sources of brilliant $\\mathbf { \\boldsymbol { x } }$ -rays for the determination of the structure of matter. However, the size and cost of these facilities is large compared to that of electron diffraction setups, which are an alternative tool for the analysis of the structure of matter. Moreover, x-rays have a smaller scattering cross-section than relativistic electrons, typically a longer wavelength, and are only sensitive to a samples electron distribution, while electron diffraction is sensitive to both the nuclei and the electrons. Electron diffraction is typically done at $\\mathrm { k e V }$ beam energies, where little radiation shielding is required, and systems with table-top footprint are commercially available. Moving towards MeV electron beams allows for higher beam brightness and, thus, better transverse beam coherence, and allows for stronger bunch compression, leading to shorter electron pulses and better time resolution. Also, the electrons propagate at the speed of light at MeV energies, leading to a vanishing velocity mismatch between optical pump and electron probe in thick samples during pump-probe experiments.
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augmentation
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NO
| 0
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expert
|
What is the primary advantage of synchrotron radiation over traditional X-ray tubes?
|
Synchrotron radiation provides much higher brightness, broader spectral coverage, and superior collimation compared to traditional X-ray tubes.
|
Reasoning
|
Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation
|
This method contrasts with traditional filling schemes, where the beam intensity peaks right after a fill and then continuously diminishes. Top-up injection maintains a nearly constant beam current, equilibrating thermal load and thereby improving the stability of the beam over extended periods. Such consistency is particularly advantageous for user experiments, because the electron beam emits in an X-ray beam that is constant in intensity and pointing, offering more uniform conditions and reliable data. Furthermore, the ability to maintain optimal beam conditions without ramping the lattice during acceleration enhances overall time available for experiments. For this reason, virtually all modern synchrotrons make use of top-up injection (see Fig. I.10.7). I.10.3.5.3 Robinson theorem If we take the sum of all three partition damping numbers, noting that $\\begin{array} { r } { j _ { x } = 1 - \\frac { I _ { 4 } } { I _ { 2 } } } \\end{array}$ , $\\begin{array} { r } { j _ { z } = 2 + \\frac { I _ { 4 } } { I _ { 2 } } } \\end{array}$ , and using $j _ { y } = 1$ as the vertical damping does not depend on the synchrotron radiation integrals, we can derive the Robinson theorem, which states that the sum of the partition numbers is 4
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1
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NO
| 0
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expert
|
What is the primary advantage of synchrotron radiation over traditional X-ray tubes?
|
Synchrotron radiation provides much higher brightness, broader spectral coverage, and superior collimation compared to traditional X-ray tubes.
|
Reasoning
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Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation
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$$ The critical angle is defined as $$ \\vartheta _ { c } = \\frac { 1 } { \\gamma } \\left( \\frac { \\omega _ { c } } { \\omega } \\right) ^ { 1 / 3 } . $$ Higher frequencies have a smaller critical angle. For frequencies much larger than the critical frequency, and for angles much larger than the critical angle, the synchrotron radiation emission is negligible. The total spectrum, integrated over all emission angles, is given by $$ \\frac { d I } { d \\omega } = \\int \\int _ { 4 \\pi } \\frac { d ^ { 3 } I } { d \\omega d \\Omega } d \\Omega = \\frac { \\sqrt { 3 } e ^ { 2 } } { 4 \\pi \\varepsilon _ { 0 } c } \\gamma \\frac { \\omega } { \\omega _ { c } } \\int _ { \\omega / \\omega _ { c } } ^ { \\infty } K _ { 5 / 3 } ( x ) d x . $$ It is shown in Fig. I.10.4. Unlike cyclotron radiation, emitted by non-relativistic electrons, synchrotron radiation has a broadband spectrum, shifted towards higher photon energies with the cube of the Lorentz factor $\\gamma$ . In the Swiss Light Source, the Lorentz factor $\\gamma$ is approximately 5000. As a result, the critical frequency of the radiation emitted by the dipole magnets is in the exahertz range, corresponding to the $\\mathrm { \\Delta X }$ -ray spectrum. The overall spectrum of synchrotron radiation covers infrared, visible, UV and X-ray wavelengths. While coherent beams in or near the visible spectrum can be conveniently generated by lasers, synchrotrons are widely used in research that requires X-ray photons. We will look at some typical
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1
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NO
| 0
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expert
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What is the primary advantage of synchrotron radiation over traditional X-ray tubes?
|
Synchrotron radiation provides much higher brightness, broader spectral coverage, and superior collimation compared to traditional X-ray tubes.
|
Reasoning
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Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation
|
– Photoelectric absorption: absorption by electrons bound to atoms; – Thomson scattering: elastic scattering, i.e. scattering without energy transfer between the X-ray and a free electron; – Compton scattering: inelastic scattering, where energy is transferred from the X-ray photon to an electron. I.10.5.1 Interaction of X-rays with free electrons Thomson scattering occurs when photons with an energy that is much lower than the binding energy of electrons in atoms interact with free or loosely bound electrons. The incident photons are then scattered elastically, i.e. there is no energy transfer between the X-ray photon and the electron. The photon wavelength is inversely proportional to its energy, thus it remains constant in an elastic process. A collision, however, implies in general a change in direction, thus the momentum $\\vec { k }$ of the photon will change its direction. We can describe Thomson scattering by classical electromagnetism, considering a free electron that encounters an electromagnetic wave. The electron will start oscillating and radiate in all directions except the direction of the oscillation, with an intensity given by $I = I _ { 0 } \\cos ^ { 2 } \\vartheta$ . This re-radiated light has the same frequency as the incident light because the electron’s oscillation frequency is driven by the frequency of the electromagnetic wave, and there’s no energy loss in the system.
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1
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NO
| 0
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expert
|
What is the primary advantage of synchrotron radiation over traditional X-ray tubes?
|
Synchrotron radiation provides much higher brightness, broader spectral coverage, and superior collimation compared to traditional X-ray tubes.
|
Reasoning
|
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.
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1
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NO
| 0
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expert
|
What is the primary advantage of synchrotron radiation over traditional X-ray tubes?
|
Synchrotron radiation provides much higher brightness, broader spectral coverage, and superior collimation compared to traditional X-ray tubes.
|
Reasoning
|
Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation
|
– Vacuum system: as a result of the smaller inner bore of the magnets, the vacuum chamber diameter needs to be reduced to a point where a conventional pumping system becomes difficult to implement. A key enabling technology is the use of a distributed getter pump system, where the entire vacuum chamber is coated with a non-evaporable getter (NEG); – Generation of hard X-rays: the strong field in longitudinal gradient bends, peaking at 4. . . 6 Tesla, results in very hard X-rays, up to a photon energy of $8 0 \\mathrm { k e V }$ ; – Momentum compaction factor: when designing a magnetic lattice that employs LGBs and reverse bends, one can achieve a situation where a higher-energy particle takes a shorter path. This can then result in a negative momentum compaction factor of the ring (like in proton synchrotrons below transition energy). The Paul Scherrer Institut is upgrading its storage ring in the year 2024, making use of the principles outlined in this section [5]. I.10.5 Interaction of $\\mathbf { X }$ -rays with matter In the subsequent sections, we will look at the interaction of X-rays with matter, and the use of X-rays for experiments. To understand the processes that lead to absorption, scattering, and diffraction, we will proceed in three steps, and look at the interaction of $\\mathrm { \\Delta X }$ -rays with:
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1
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NO
| 0
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expert
|
What is the primary advantage of synchrotron radiation over traditional X-ray tubes?
|
Synchrotron radiation provides much higher brightness, broader spectral coverage, and superior collimation compared to traditional X-ray tubes.
|
Reasoning
|
Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation
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The total radiated power depends on the fourth power of the Lorentz factor $\\gamma$ , or for a given particle energy, it is inversely proportional to the fourth power of the mass of this particle. This means that synchrotron radiation, and its effect on the beam, are negligible for all proton accelerators except for the highest-energy one. For electron storage rings, conversely, this radiation dominates power losses of the beam, the evolution of the emittance in the ring, and therefore the beam dynamics of the accelerator. Before we will look at this in detail, we will treat one particular case where the electrons pass through a sinusoidal magnetic field. Such a field, generated by wigglers and undulators2, gives rise to strong radiation in the forward direction, which makes it particularly useful for applications of $\\mathrm { \\Delta } \\mathrm { X }$ -rays. I.10.2.3 Coherent generation of X-rays in undulators Wiggler and undulator magnets are devices that impose a periodic magnetic field on the electron beam. These insertion devices have been specially designed to excite the emission of electromagnetic radiation in particle accelerators. Let us assume a cartesian coordinate system with an electron travelling in $z$ direction. A planar insertion device, with a mangetic field in the vertical direction $y$ , has the following field on axis
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What is the primary advantage of synchrotron radiation over traditional X-ray tubes?
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Synchrotron radiation provides much higher brightness, broader spectral coverage, and superior collimation compared to traditional X-ray tubes.
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Reasoning
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Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation
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applications in Section I.10.6. The total radiated power per particle, obtained by integrating over the spectrum, is $$ P _ { \\gamma } = \\frac { e ^ { 2 } c } { 6 \\pi \\varepsilon _ { 0 } } \\frac { \\beta ^ { 4 } \\gamma ^ { 4 } } { \\rho ^ { 2 } } . $$ The energy lost by a particle on a circular orbit, i.e. in an accelerator consisting only of dipole magnets, is $$ U _ { 0 } = \\frac { e ^ { 2 } \\beta ^ { 4 } \\gamma ^ { 4 } } { 3 \\varepsilon _ { 0 } \\rho } , $$ where we have used $T = 2 \\pi \\rho / c$ , assuming $v \\approx c$ . Of course, real accelerators contain also other types of magnets. The energy lost per turn for a particle in an arbitrary accelerator lattice can be calculated by the following ring integral $$ U _ { 0 } = \\frac { C _ { \\gamma } } { 2 \\pi } E _ { \\mathrm { n o m } } ^ { 4 } \\oint \\frac { 1 } { \\rho ^ { 2 } } d s ,
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expert
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What is the primary advantage of synchrotron radiation over traditional X-ray tubes?
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Synchrotron radiation provides much higher brightness, broader spectral coverage, and superior collimation compared to traditional X-ray tubes.
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Reasoning
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Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation
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The scattering amplitude $I _ { 0 }$ can be calculated from classic electromagnetism. For non-relativistic electrons, it is sufficient to consider the electric component of the incoming wave. The Thomson scattering cross section is equal to $$ \\sigma _ { T } = { \\frac { 8 \\pi } { 3 } } \\left( { \\frac { e ^ { 2 } } { 4 \\pi \\varepsilon _ { 0 } m _ { e } c ^ { 2 } } } \\right) ^ { 2 } = 0 . 6 \\cdot 1 0 ^ { - 2 8 } \\mathrm { { m } } = 0 . 6 \\mathrm { { b a r n } , } $$ independent of the wavelength of the incoming photon. This is in contrast to Compton scattering, where we consider photons with an energy above a few $1 0 \\mathrm { k e V . }$ In this case, we have to consider quantum mechanical effects, and the photon transfers energy and momentum to the electron. The wavelength change of the scattered photon can be determined from the conservation of energy and momentum $$ \\Delta \\lambda = \\frac { h } { m _ { e } c } ( 1 - \\cos { \\vartheta } ) ,
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expert
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What is the primary advantage of synchrotron radiation over traditional X-ray tubes?
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Synchrotron radiation provides much higher brightness, broader spectral coverage, and superior collimation compared to traditional X-ray tubes.
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Reasoning
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Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation
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$$ 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 $n = 2 m - 1 , m \\in \\mathbb { N }$
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expert
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What is the primary advantage of synchrotron radiation over traditional X-ray tubes?
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Synchrotron radiation provides much higher brightness, broader spectral coverage, and superior collimation compared to traditional X-ray tubes.
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Reasoning
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Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation
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I.10.2 Generation of radiation by charged particles An accelerated charge emits electromagnetic radiation. An oscillating charge emits radiation at the oscillation frequency, and a charged particle moving on a circular orbit radiates at the revolution frequency. As soon as the particles approach the speed of light, however, this radiation is shifted towards higher frequencies, and it is concentrated in a forward cone, as shown in Fig. I.10.3. I.10.2.1 Non-relativistic particles moving in a dipole field Let us first look at non-relativistic particles. In a constant magnetic field with magnitude $B$ , a particle with charge $e$ and momentum $p = m v$ will move on a circular orbit with radius $\\rho$ $$ \\rho = \\frac { p } { e B } . $$ This is an accelerated motion, and the particle emits radiation. For non-relativistic particles, this radiation is called cyclotron radiation, and the total emitted power is $$ P = \\sigma _ { t } \\frac { B ^ { 2 } v ^ { 2 } } { \\mu _ { 0 } c } , $$ where $\\sigma _ { t }$ is the Thomson cross section $$ \\sigma _ { t } = \\frac { 8 \\pi } { 3 } \\left( \\frac { e ^ { 2 } } { 4 \\pi \\varepsilon _ { 0 } m c ^ { 2 } } \\right) ^ { 2 } .
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augmentation
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expert
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What is the primary advantage of synchrotron radiation over traditional X-ray tubes?
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Synchrotron radiation provides much higher brightness, broader spectral coverage, and superior collimation compared to traditional X-ray tubes.
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Reasoning
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Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation
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I.10.7.2 Brilliance Estimate the brilliance $\\boldsymbol { B }$ of the sun on its surface, for photons in the visible spectrum. What is the brilliance of the sun on the surface of the Earth? For simplicity, ignore the influence of the Earth’s atmosphere. Table: Caption: Sun Body: <html><body><table><tr><td>Radiated power</td><td>3.828 · 1026</td><td>W</td></tr><tr><td>Surface area</td><td>6.09 ·1012</td><td>km²</td></tr><tr><td>Distance to Earth</td><td>1.496 · 108</td><td>km</td></tr><tr><td>Angular size,seen from Earth</td><td>31.6.. .32.7</td><td>minutes of arc</td></tr><tr><td>Age</td><td>4.6 · 109</td><td>years</td></tr></table></body></html> I.10.7.3 Synchrotron radiation Synchrotron radiation. . . (check all that apply: more than one answer may be correct) a) . . . is used by scientists in numerous disciplines, including semiconductor physics, material science and molecular biology b) . . . can be calculated from Maxwell’s equations, without the need of material constants c) . . . is emitted at much longer wavelengths, as compared to cyclotron radiation d) . . . is emitted uniformly in all directions, when seen in the reference frame of the particle e) . . . is emitted in forward direction in the laboratory frame, and uniformly in all directions, when seen in the reference frame of the electron bunches I.10.7.4 Crab Nebula On July 5, 1054, astronomers observed a new star, which remained visible for about two years, and it was brighter than all stars in the sky (with the exception of the Sun). Indeed, it was a supernova, and the remnants of this explosion, the Crab Nebula, are still visible today. It was discovered in the 1950’s that a significant portion of the light emitted by the Crab Nebula originates from synchrotron radiation (Fig. I.10.17).
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expert
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What is the primary advantage of synchrotron radiation over traditional X-ray tubes?
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Synchrotron radiation provides much higher brightness, broader spectral coverage, and superior collimation compared to traditional X-ray tubes.
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Reasoning
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Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation
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– The Lorentz factor $\\gamma$ , – The magnetic field to bend the beam (assume for simplicity that the ring consists of a uniform dipole field), – The critical energy of the synchrotron radiation, – The energy emitted by each electron through synchrotron radiation in one turn. I.10.7.7 Future Circular Collider: FCC-hh Particle physicists are evaluating the potential of building a future circular collider, which aims at colliding two proton beams with $5 0 0 \\mathrm { m A }$ current each and $1 0 0 \\mathrm { T e V }$ particle energy (FCC-hh). The protons would be circulating in a storage ring with $1 0 0 \\mathrm { k m }$ circumference, guided by superconducting magnets. The dipoles aim at a field of $1 6 \\mathrm { T }$ Calculate: – The Lorentz factor $\\gamma$ , – The critical energy of the synchrotron radiation, – The total power emitted by both beams through synchrotron radiation. I.10.7.8 Simple storage ring Let’s build a very simple synchrotron! Consider a storage ring that is located at the (magnetic) North Pole of the Earth. Assume that the Earth’s magnetic field of $5 0 \\mu \\mathrm { T }$ is used to confine electrons to a circular orbit, and ignore the need for focusing magnets. As a particle source, we will use the electron gun of an old TV, which accelerates the particles with a DC voltage of $2 5 \\mathrm { k V }$ (we will ignore the requirement of an injection system).
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augmentation
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expert
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What is the primary advantage of synchrotron radiation over traditional X-ray tubes?
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Synchrotron radiation provides much higher brightness, broader spectral coverage, and superior collimation compared to traditional X-ray tubes.
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Reasoning
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Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation
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– What range can be reached with the fundamental photon energy? – What brilliance can be reached at the fundamental photon energy? – Is there a significant flux higher harmonics? I.10.7.20 Emittance and energy spread The equilibrium emittance of an electron bunch in a storage ring occurs when factors increasing $\\varepsilon$ are compensated by those reducing $\\varepsilon$ . – Which effect increases the horizontal emittance $\\varepsilon _ { x }$ ? – Which effect decreases the horizontal emittance $\\varepsilon _ { x }$ ? – Which effect increases the vertical emittance $\\varepsilon _ { y }$ ? – Which effect decreases the vertical emittance $\\varepsilon _ { y }$ ? I.10.7.21 Swiss Light Source The Swiss Light Source (SLS) is a storage ring optimized for synchrotron radiation generation, located at PSI in Switzerland. An upgraded lattice has been calculated in view of an upgrade10. Design values for this lattice are given below (the synchrotron radiation integrals have been numerically integrated around the design lattice, including undulators and superbends for radiation generation): Table: Caption: SLS Upgrade Lattice Body: <html><body><table><tr><td>Circumference</td><td>290.4 m</td></tr><tr><td>Electron energy</td><td>2.4 GeV</td></tr><tr><td>Horizontal damping partition jx</td><td>1.71</td></tr><tr><td>Vertical damping partition jy</td><td>1</td></tr><tr><td>Longitudinal damping partition jz</td><td>1.29</td></tr><tr><td>Second synchrotron radiation integral I2</td><td>1.186 m-1</td></tr><tr><td>Fourth synchrotron radiation integral I4</td><td>-0.842 m-1</td></tr></table></body></html>
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augmentation
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expert
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What is the primary advantage of synchrotron radiation over traditional X-ray tubes?
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Synchrotron radiation provides much higher brightness, broader spectral coverage, and superior collimation compared to traditional X-ray tubes.
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Reasoning
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Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation
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How is the situation different when one decreases the gap to keep the photon energy constant? Describe qualitatively the effects on the undulator parameter $K$ and the brilliance $\\boldsymbol { B }$ ! I.10.7.13 Muons Muons are considered as an alternative to electrons for a future circular lepton collider. Argue – Why they might be preferable to electrons? – What could be possible disadvantages? I.10.7.14 Electrons vs. muons Consider an electron storage ring at an energy of $8 0 0 \\mathrm { M e V } .$ , a circulating current of $1 \\mathrm { { A } }$ , and a bending radius of $\\rho = 1 . 7 8 4 \\mathrm { ~ m ~ }$ . Calculate the energy loss of each electron per turn, and the total synchrotron radiation power from all bending magnets. What would the radiation power be if the particles were 800 MeV muons? I.10.7.15 Swiss Light Source 2.0 Calculate how much energy is stored in the electron beam in the SLS-2.0 storage ring, with a circumference of $2 9 0 . 4 \\mathrm { m }$ and an average current of $4 0 0 \\mathrm { m A }$ . The particle energy is $2 . 4 { \\mathrm { G e V } } .$ Assume the RF trips off. Knowing that the momentum acceptance is $\\pm 5 \\%$ , compute how long the beams survives in the ring before hitting the wall.
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expert
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What is the primary advantage of synchrotron radiation over traditional X-ray tubes?
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Synchrotron radiation provides much higher brightness, broader spectral coverage, and superior collimation compared to traditional X-ray tubes.
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Reasoning
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Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation
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$$ I.10.3.4 Quantum excitation Finally, we are ready to look at effects that increase the emittance of the beam. While radiation damping inherently reduces emittance, there exist concurrent processes and phenomena that act in opposition, increasing the emittance. When such effects are integrated into our analysis, these emittance-increasing effects can counterbalance the radiation damping. As a consequence of this dynamic equilibrium between damping and amplifying factors, the beam stabilizes at a non-zero equilibrium emittance. This state represents a balance where the rate of emittance reduction due to radiation damping is compensated by the rate of emittance growth from other processes. Let us first consider the horizontal phase space. An electron emitting an X-ray photon receives an equal and opposite recoil momentum. This quantized emission process is inherently stochastic, leading to fluctuations in the energy of individual electrons. As a consequence of these quantum fluctuations, the momentum change due to the emission of individual photons thus increases the horizontal emittance. The process is further amplified by the dispersion of the lattice. Including the effects of radiation damping and quantum excitation, the emittance in the horizontal plane varies as $$ \\varepsilon _ { x } ( t ) = \\varepsilon _ { x } ( 0 ) \\exp { \\left( - 2 \\frac { t } { \\tau _ { x } } \\right) } + \\varepsilon _ { x } ( \\infty ) \\left[ 1 - \\exp { \\left( - 2 \\frac { t } { \\tau _ { x } } \\right) } \\right]
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augmentation
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expert
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What is the primary advantage of synchrotron radiation over traditional X-ray tubes?
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Synchrotron radiation provides much higher brightness, broader spectral coverage, and superior collimation compared to traditional X-ray tubes.
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Reasoning
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Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation
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$$ Shifting our view to a broader perspective, we now consider the properties of the entire electron bunch. By definition, the emittance is given as the ensemble average of the action. The change in emittance follows thus from the change in action $$ \\begin{array} { r c l } { d \\varepsilon _ { y } } & { = } & { \\langle d J _ { y } \\rangle } \\\\ & { = } & { - \\langle \\alpha _ { y } \\underbrace { \\langle g p _ { y } \\rangle } _ { = - \\alpha _ { y } \\varepsilon _ { y } } + \\beta _ { y } \\underbrace { \\langle p _ { y } ^ { 2 } \\rangle } _ { = \\gamma _ { \\mathrm { t r } } \\varepsilon _ { y } } \\frac { \\partial p _ { \\mathrm { t } } } { \\partial P _ { 0 } } } \\\\ & & { - \\langle - \\alpha _ { y } ^ { 2 } \\varepsilon _ { y } + \\beta _ { y } \\gamma _ { y } \\varepsilon _ { y } \\rangle \\frac { \\partial p _ { \\mathrm { t } } } { \\partial P _ { 0 } } } \\\\ & { = } & { - \\varepsilon _ { y } \\langle \\underbrace { \\delta _ { y } \\gamma _ { y } } _ { \\mathrm { 1 } } - \\alpha _ { y } ^ { 2 } \\rangle \\frac { d p _ { \\mathrm { f } } } { P _ { 0 } } } \\\\ & & { - \\varepsilon _ { y } \\frac { d p _ { \\mathrm { f } } } { D _ { 0 } } , } \\end{array}
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expert
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What is the primary advantage of synchrotron radiation over traditional X-ray tubes?
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Synchrotron radiation provides much higher brightness, broader spectral coverage, and superior collimation compared to traditional X-ray tubes.
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Reasoning
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Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation
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$$ Computing the photon flux $\\dot { N } _ { \\gamma }$ for an undulator is even more elaborate than the calculation for a single dipole, and we just cite the result [2] $$ { \\dot { N } } _ { \\gamma } = 1 . 4 3 \\cdot 1 0 ^ { 1 4 } N I _ { b } Q _ { n } ( K ) , $$ where $$ Q _ { n } ( K ) = \\frac { 1 + K ^ { 2 } / 2 } { n } F _ { n } ( K ) . $$ We denote the harmonic number by $n = 2 m - 1$ with $m \\in \\mathbb { N }$ , the number of periods in the undulator by $N$ , the beam current in A by $I _ { b }$ , the undulator parameter by $K$ , and $F _ { n } ( K )$ is given by $$ \\begin{array} { r c l } { { F _ { n } ( K ) } } & { { = } } & { { \\displaystyle \\frac { n ^ { 2 } K ^ { 2 } } { ( 1 + K ^ { 2 } / 2 ) ^ { 2 } } \\left( J _ { ( n + 1 ) / 2 } ( Y ) - J _ { ( n - 1 ) / 2 } ( Y ) \\right) ^ { 2 } } } \\\\ { { } } & { { } } & { { } } \\\\ { { Y } } & { { = } } & { { \\displaystyle \\frac { n K ^ { 2 } } { 4 ( 1 + K ^ { 2 } / 2 ) } , } } \\end{array}
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Expert
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What is the resolution of the DSCR screens at SwissFEL?
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The resolution, measured as the smallest spot size that can be seen on the screen, is around 14 µm.
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Fact
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[ScreenUpgrade]RevSciInst_94_073301(2023).pdf
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2023 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1063/5.0155444 I. INTRODUCTION Beam profile monitors are one of the primary instruments at accelerator facilities around the world for the characterization of particle beams as they pass through the various elements in the accelerator. Although these screens are simple devices in principle, the details of their implementation have become more and more complicated as the requirements for resolution and accuracy at accelerator facilities have become more sophisticated. The accelerators have become more complex in the kind of beams they deliver and the modes they provide. X-ray free-electron lasers (FELs) are one of these more advanced accelerators that have been developed in the past two decades to provide laser-like $\\mathbf { x }$ -ray pulses. These machines accelerate bunches of electrons of nC or less charge down hundreds of meters or even kilometers of accelerators, through undulators, and generate fs-duration x-ray pulses for use by experimenters.1–7 The screens developed for the characterization of these electron beams have had to be adapted at these facilities, some having to adopt special geometries to direct coherent optical transition radiation (COTR) away from the camera, and with all having their resolution for beam size measurement being a key parameter.8–13 Here, we present a new design of the transverse profile monitors at SwissFEL,7 the x-ray FEL at the Paul Scherrer Institute in Switzerland. The design is based on using high-quality filters and dynamic focusing. The new design results in a significantly better beam size resolution: we improve the resolution from 20 to $1 4 \\mu \\mathrm m$ .
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Expert
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What is the resolution of the DSCR screens at SwissFEL?
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The resolution, measured as the smallest spot size that can be seen on the screen, is around 14 µm.
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Fact
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[ScreenUpgrade]RevSciInst_94_073301(2023).pdf
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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.
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Expert
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What is the resolution of the DSCR screens at SwissFEL?
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The resolution, measured as the smallest spot size that can be seen on the screen, is around 14 µm.
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Fact
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[ScreenUpgrade]RevSciInst_94_073301(2023).pdf
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$$ \\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.
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Expert
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What is the resolution of the DSCR screens at SwissFEL?
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The resolution, measured as the smallest spot size that can be seen on the screen, is around 14 µm.
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Fact
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[ScreenUpgrade]RevSciInst_94_073301(2023).pdf
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$^ { 8 } { \\mathrm { C } } .$ Wiebers, M. Hoz, G. Kube, D. Noelle, G. Priebe, and H.-C. Schroeder, in Proceedings of the 2nd International Beam Instrumentation Conference (IBIC 2013) (JACOW, Oxford, UK, 16-19 September 2013), p. 807. ${ ^ \\circ _ { \\mathrm { H } } } .$ D. T. ChoiKim, M. Chae, J. Hong, S.-J. Park, and C. Kim, in Proceedings of the 4th International Particle Accelerator Conference (IPAC 2013) (JACOW, Shanghai, China, 12-17 May 2013), p. 610. $^ { 1 0 } \\mathrm { R } .$ Ischebeck, E. Prat, V. Thominet, and C. O. Loch, Phys. Rev. Spec. Top.–Accel. Beams 18, 082802 (2015). ${ } ^ { 1 1 } \\mathrm { H }$ . Loos, in Proceedings of the 3rd International Beam Instrumentation Conference (IBIC 2014) (JACOW, Monterey, CA, 14-18 September 2014), p. 475. $^ { 1 2 } \\mathrm { Y }$ . Otake, H. Maesaka, S. Matsubara, S. Inoue, K. Yanagida, H. Ego, C. Kondo, T. Sakurai, T. Matsumoto, and H. Tomizawa, Phys. Rev. Spec. Top.–Accel. Beams 16, 042802 (2013). $^ { 1 3 } \\mathrm { B }$ . Walasek-Hohne, C. Andre, P. Forck, E. Gutlich, G. Kube, P. Lecoq, and A. Reiter, IEEE Trans. Nucl. Sci. 59(5), 2307–2312 (2012).
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Expert
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What is the resolution of the DSCR screens at SwissFEL?
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The resolution, measured as the smallest spot size that can be seen on the screen, is around 14 µm.
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Fact
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[ScreenUpgrade]RevSciInst_94_073301(2023).pdf
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$^ { 1 4 } \\mathrm { M }$ . Castellano and V. A. Verzilov, Phys. Rev. Spec. Top.–Accel. Beams 1, 062801 (1998). $^ { 1 5 } \\mathrm { E }$ . Prat, P. Craievich, P. Dijkstal, S. Di Mitri, E. Ferrari, T. G. Lucas, A. Malyzhenkov, G. Perosa, S. Reiche, and T. Schietinger, Phys. Rev. Accel. Beams 25, 104401 (2022). $^ { 1 6 } \\mathrm { E }$ . Prat, P. Dijkstal, M. Aiba, S. Bettoni, P. Craievich, E. Ferrari, R. Ischebeck, F. Löhl, A. Malyzhenkov, G. L. Orlandi, S. Reiche, and T. Schietinger, Phys. Rev. Lett. 123, 234801 (2019). 17E. Prat, P. Dijkstal, E. Ferrari, A. Malyzhenkov, and S. Reiche, Phys. Rev. Accel. Beams 23, 090701 (2020). $^ { 1 8 } \\mathrm { J }$ . Rossbach and P. Schmuser, in CAS—CERN Accelerator School: 5th General Accelerator Physics Course, edited by S. Turner (CERN, 1994), pp. 17–88. ${ } ^ { 1 9 } \\mathrm { H } .$ . J. Qian, M. Krasilnikov, A. Lueangaramwong, X. K. Li, O. Lishilin, Z. Aboulbanine, G. Adhikari, N. Aftab, P. Boonpornprasert, G. Georgiev, J. Good, M. Gross, C. Koschitzki, R. Niemczyk, A. Oppelt, G. Shu, F. Stephan, G. Vashchenko, and T. Weilbach, Phys. Rev. Accel. Beams 25, 083401 (2022). $^ { 2 0 } \\mathrm { S } .$ . Tomin, I. Zagorodnov, W. Decking, N. Golubeva, and M. Scholz, Phys. Rev. Accel. Beams 24, 064201 (2021).
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What is the role of the Bragg reflector in the radiator design?
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To form a cavity that reflects backward-propagating waves, enhancing directionality and spectral purity of the emitted radiation.
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Reasoning
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hermann-et-al-2022-inverse-designed-narrowband-thz-radiator-for-ultrarelativistic-electrons.pdf
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INTRODUCTION Ions are used in radiotherapy due to their ability to deposit a maximum dose at the end of their range, in a sharp peak called the “Bragg peak”, compared to $\\mathbf { \\nabla } _ { \\mathbf { X } }$ -rays that deposit dose along the entire path [1]. This feature is advantageous as it minimizes the impact on the healthy cells surrounding the tumour. When an ion beam passes through a medium, the beam’s energy is absorbed and causes a transient rise in pressure which results in the emission of an acoustic (pressure) wave that propagates within it [2]. Components of such waves can be detected using ultrasound transducers whose bandwidth is within the frequency range of the acoustic signals produced. The data can be used to form reconstruction components of the dose distribution by using appropriate algorithms. Similarly, when the beam travels through a scintillator, the absorbed energy causes the emission of scintillation light. The luminescence is directly proportional to the energy absorbed, and hence, an appropriate optical system, such as a CMOS camera, can be used to detect and reconstruct the light distribution [3]. If the light yield of the scintillator is known, a calibrated dose distribution can be obtained.
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What is the role of the Bragg reflector in the radiator design?
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To form a cavity that reflects backward-propagating waves, enhancing directionality and spectral purity of the emitted radiation.
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Reasoning
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hermann-et-al-2022-inverse-designed-narrowband-thz-radiator-for-ultrarelativistic-electrons.pdf
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The radiator is installed in a holder with a YAG:Ce screen and the holder uses a 5-axis motorized stage (Newport 8081- UHV) and a 1-axis stage (Thorlabs Z812V). The 5-axis stage is precisely controllable in the X, Y, Z, $\\theta \\mathbf { x }$ and $\\theta$ y directions and is used for tilt with the beam and fine alignment with the camera. The 1-axis stage is installed at the bottom and is used to move the screen and radiator so that they can be used alternately, and to vary the distance between the radiator and beam. The alignment of the electron beam and the radiator is mainly to transfer light to the camera, but as shown in Fig. 5, the non-parallelism of the beam with the wide side of the radiator will affect the beam size measurement. To prepare for this problem, two screens are installed in the holder, but accurate beam size measurement requires a method to scan to the angle with the smallest beam size. DISCUSSION It can be seen from Fig. 1 that the photon emission of ChDR is sensitive to the impact factor, especially in the low energy case. Considering the transverse cross-section of an electron bunch, even within the same bunch, the distance to the radiator can vary by several hundred $\\mu \\mathrm { m }$ , in which case the light intensity observed at the detector is mostly due to electrons generated by the radiator at close range. In general, if the electron bunch has a perfect Gaussian distribution, the beam size will have the same regardless of which layer is measured, so there is no difficulty in measuring the beam size, but it is worth checking whether the same result is obtained in the case where the electron bunch is not perfectly Gaussian.
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NO
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IPAC
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What is the role of the Bragg reflector in the radiator design?
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To form a cavity that reflects backward-propagating waves, enhancing directionality and spectral purity of the emitted radiation.
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Reasoning
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hermann-et-al-2022-inverse-designed-narrowband-thz-radiator-for-ultrarelativistic-electrons.pdf
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Experimentally this asymmetry can be observed with a scintillating crystal detector (see Fig. 1) sensitive to the bremsstrahlung energy spectrum. By measuring the detector energy deposit between reversed states of the electron or target helicity, one computes an experimental asymmetry $A _ { E }$ which is directly proportional to the electron beam spin POLARIMETER The radiator is made of high-purity copper with a $0 . 6 0 \\mathrm { c m } \\cdot$ - thick front face. This thickness was chosen to completely stop an electron beam of $9 . 5 \\mathrm { M e V }$ kinetic energy. The radiator is water-cooled and serves as a beam dump. The radiator is connected to the beam pipe through a ceramic break to allow for beam current measurement. The collimator is $1 4 . 6 \\mathrm { c m }$ long with inner diameter of $0 . 8 0 \\mathrm { c m }$ , outer diameter of $1 0 . 2 \\mathrm { c m }$ , and made of copper. It is used to stop the largeangle scattered photons and allows the forward photons to the center of the magnets, eliminating the photons that may reach the detector without passing through the magnet core.
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NO
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IPAC
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What is the role of the Bragg reflector in the radiator design?
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To form a cavity that reflects backward-propagating waves, enhancing directionality and spectral purity of the emitted radiation.
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Reasoning
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hermann-et-al-2022-inverse-designed-narrowband-thz-radiator-for-ultrarelativistic-electrons.pdf
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Some of the challenges in making this design work are the long image path from the object plane at the target and the image plane at the cameras, thermal expansion of the system due to the proximity to the target, radiation transport challenge through the optical path, and initial alignment. These challenges are augmented by the lack of accessibility in the target vessel and the expected and experienced radiation levels in the target hall resulting in the need for remote manipulation and installation. MECHANICAL DESIGN Optical Design The mechanical design is first anchored to the optical path of the system. shows the optical design; this is comprised of five flat mirrors and a pair of Cassegrain telescopes. The Cassegrain telescopes are comprised of four spherical mirrors. Mirror #1 is made entirely of copper as this is in very close proximity to the target. All the other mirrors, including those of the telescope, are fused silica (quartz) with a silver coating on the reflective face. The purpose of the telescope here is to focus the image and reduce the size of the viewport. Also, as the system requires shielding in the vacuum chamber, this allows the size of the shielding opening to be smaller. As the target image is relayed through the mirrors, the size of the mirrors required is larger and larger; the telescope takes in the diverging image and focuses it at an equal focal distance as the target; hence, the telescope is mid-way in the optical path. Using this telescope allows us to use the same size mirrors for #2 & #5 (4 in) as well as the same mirrors for #3 & #4 (6 in). The resulting clear aperture requirements for the viewport is 2.75 in for which a 3 in viewport is used on a 4.5 in conflat. The telescope spherical mirrors are 7 in $\\& 2 . 9$ in in diameter for the primary and secondary mirrors respectively. These have a spherical surface with radii of $1 6 0 \\mathrm { c m }$ for the primary mirror & $3 2 0 \\mathrm { c m }$ for the secondary mirror. The development of the optical system was designed in part using Zemax software and Monte-Carlo simulations; more details of this design can be found in [1].
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augmentation
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NO
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IPAC
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What is the role of the Bragg reflector in the radiator design?
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To form a cavity that reflects backward-propagating waves, enhancing directionality and spectral purity of the emitted radiation.
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Reasoning
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hermann-et-al-2022-inverse-designed-narrowband-thz-radiator-for-ultrarelativistic-electrons.pdf
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The proposed geometry is designed to be inserted from the inner side of the storage ring. To be able to do so without interfering with the electron beam, the absorber features a cut-out in the shape of Elettra 2.0 vacuum chamber, to maintain continuity along the electron beam path. The absorber insertion from the inner portion allows for better sighting of the alignment fiduciaries, since it makes use of the presence of the pathways on the same side, giving ampler angles of vision to the laser tracker. To protect the downstream vacuum vessel from the incoming synchrotron radiation, the teethed part of the absorber protrudes for $2 \\mathrm { m m }$ in the electron beam portion of the design. The teeth are parallel to the electron beam trajectory after the dipole interaction, in order not to create thin structures next to the point of SPD maximum value, which is the closest to the electron beam. Cooling wise, the design dissipate heat through two cylindrical blind channels, situated below the absorber jaw. Having blind holes allow not to have any brazing in contact with the vacuum, eliminating the risk of a failure and vacuum contamination with the coolant. Reflected Photon Minimization
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augmentation
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NO
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IPAC
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What is the role of the Bragg reflector in the radiator design?
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To form a cavity that reflects backward-propagating waves, enhancing directionality and spectral purity of the emitted radiation.
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Reasoning
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hermann-et-al-2022-inverse-designed-narrowband-thz-radiator-for-ultrarelativistic-electrons.pdf
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Initial thermal simulations were conducted assuming a single circuit flow path that travels through a channel in the air-side inner conductor, circulates inside the inner diameter of the ceramic window, and exits through a separate channel in the air-side inner conductor. This design eliminates braze joints that separate water from vacuum volumes, a highly desirable design goal for accelerator systems. However, the initial simulations highlighted the need to incorporate cooling on the outside surfaces of the waveguides as well as the ceramic because thermal losses in copper on the inner surface of the outer conductor were at least 120 W, leading led to additional heating of the ceramics by $3 0 ^ { \\circ } \\mathrm { C }$ . In response to this problem, the engineering model was updated to include additional cooling lines that are bonded to exterior surfaces during the sub-assembly braze runs. Thanks to the additional five cooling pipes, it was possible to significantly reduce the maximum heating as shown in Figure 5. We have got that the heating of A0497U made of Kyocera ceramics is no more than $0 . 3 ^ { \\circ } \\mathrm { C }$ at an average power of $3 6 0 \\mathrm { k W }$ and no more than ${ 7 ^ { \\circ } } \\mathrm { C }$ for AL300 ceramics.
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augmentation
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NO
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IPAC
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What is the role of the Bragg reflector in the radiator design?
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To form a cavity that reflects backward-propagating waves, enhancing directionality and spectral purity of the emitted radiation.
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Reasoning
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hermann-et-al-2022-inverse-designed-narrowband-thz-radiator-for-ultrarelativistic-electrons.pdf
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MECHANICAL AND THERMAL ASPECTS Figure 6 show the mechanical design for the P2 and P3 dampers. Copper-colored materials represent $\\operatorname { C u C r Z r }$ and the gray ones, stainless steel. The designs were strongly influenced by the employment of $\\mathrm { C u C r Z r }$ , so no brazed joints are necessary. While the rod probe is screwed to the tapered ridge of the P2 damper, the P3 one has the line and probe machined from a single bar. The thermal validation model comprises the Complete model with the detailed feedtroughs. The power density maps for the heat losses were calculated and rescaled in MATLAB [12] from the exported EM fields for each solved eigenmode. For the FM it was considered a dissipated power of $3 0 \\mathrm { k W }$ . For the HOMs, the power was rescaled according to the wake losses of each HOM and then superposed, considering: $5 0 0 \\mathrm { m A }$ average current, no bunch roll-o! in spectrum, HOM frequency shifted to coincide with the nearest revolution harmonic, and uneven fill. For the P2 damper, $2 8 \\mathrm { W }$ heat load is deposited in the surfaces by the fundamental mode and 0.72 W by the HOMs. The former is mainly located at the probe and the latter at the feedthrough. The volumetric losses in the $\\mathrm { S i O } _ { x }$ ceramics $( \\epsilon _ { r } = 3 . 9 \\$ , tan $\\delta = 1 \\times 1 0 ^ { - 3 }$ ) provides a total power $0 . 5 3 \\mathrm { W }$ L1, L4 and L10 contribute with $4 0 . 9 \\%$ , $1 7 . 5 \\%$ and $2 8 . 7 \\%$ of this amount, respectively. The fundamental mode deposition in the ceramics was negligible, $1 0 \\mu \\mathrm { W }$ . The P3 damper faces greater surface losses from both fundamental $( 3 5 . 2 \\mathrm { W } )$ and HOMs (1.6 W) than the P2 one. Although having smaller surface area than the P2 damper, the P3 one is surrounded by stronger FM H-field (see Fig. 2). Also, such damper is tuned to L4, the mode closest to an RF harmonic. The ceramic losses were validated as 1.23 W. L4, L10 and L12 contribute with $8 2 . 7 \\%$ , $4 . 8 \\%$ and $1 0 . 8 \\%$ of this amount, respectively.
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augmentation
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NO
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IPAC
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What is the role of the Bragg reflector in the radiator design?
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To form a cavity that reflects backward-propagating waves, enhancing directionality and spectral purity of the emitted radiation.
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Reasoning
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hermann-et-al-2022-inverse-designed-narrowband-thz-radiator-for-ultrarelativistic-electrons.pdf
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provide an initial estimate of the temperature gradients in the linac [7]. For the steady-state (SS) thermal simulation, water pipes were placed around the linac as a single circuit made of linear thermal fluid elements with a constant temperature of $3 5 ^ { \\circ } \\mathrm { C }$ at the water inlet. The RF surface losses from HFSS were imported, shown at the top of Fig. 4, scaled to an input power or $8 5 0 ~ \\mathrm { W }$ and applied to the faces of the structure that see the RF. At first, an analytical estimate of the heat transfer coefficient (htc) was used for the pipes, as described in [8]. The resulting temperature distribution is shown at the bottom of Fig. 4, where a $1 3 . 8 ^ { \\circ } \\mathrm { C }$ temperature rise is seen between the iris and the inlet water and $\\mathfrak { a } \\approx 4 ^ { \\circ } C$ rise between the hottest iris and the equator. Surface Loss. [Wim^2] 000E 9.0476E+0 8.1429E+0 7.2381E+08 ))))) mperab Tmt 10216 8.861Ma 47.66 46.47 537 41.697 44.089 008 40.503 39.309 38.115Min The individual cells with $\\beta < 1$ were then optimised using the found lengths, with each cell being selected from a different Pareto front. The design required a short, low amplitude first bunching cell, achieved using an asymmetric design. The cells were then combined with a coupler, and then the whole linac was tuned to give the correct frequency and field amplitudes. The final linac design and electric fields are shown in Fig. 3.
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augmentation
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NO
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IPAC
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What is the role of the Bragg reflector in the radiator design?
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To form a cavity that reflects backward-propagating waves, enhancing directionality and spectral purity of the emitted radiation.
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Reasoning
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hermann-et-al-2022-inverse-designed-narrowband-thz-radiator-for-ultrarelativistic-electrons.pdf
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CYBORG is cooled via high thermal conductance braids manufactured by Techapps. We have further designed several cryocooler coupling pieces for maximum versatility as this project is new and details of the design can change through our exploratory commissioning work. In addition, several designs for alternative for cryocooler connections were designed and evaluated. These studies are covered more extensively in an associated proceedings contribution. Black body radiation is shielded from the gun by multi layer insulation (MLI). Fourteen layers of alternating aluminized mylar sheets and thermal insulators are wrapped around the cryocooler, gun, and copper coupler pieces. They are maintained as isotherms with the cold samples they shield. In an attempt to future proof our setup, we considered the necessity of a second cryocooler to also cool an additional (slightly warmer) outer shielding. The idea of this shielding would that it could be placed in the cryostat but not used unless the gun needed extra cooling due to increase RF rep rates in future measurements. Photos of the outer shielding design that was created are shown in Fig. 3. Initial implementation of the colder outer shielding where shown to be superfluous in the case of the simple test load measurements and while cooling pillboxes (as expected). More about the scientific merit of these pillbox experiments is detailed in a companion proceedings contribution. Pragmatically speaking however, the shield was not spaced far enough from the inner shield in the final gun configuration to prevent detrimental heat leaks preventing reaching target low temperatures. As a result, the outer shielding layer will likely not be used in the near term CYBORG experiments.
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augmentation
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NO
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Expert
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What is the role of the Bragg reflector in the radiator design?
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To form a cavity that reflects backward-propagating waves, enhancing directionality and spectral purity of the emitted radiation.
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Reasoning
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hermann-et-al-2022-inverse-designed-narrowband-thz-radiator-for-ultrarelativistic-electrons.pdf
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The second difficulty arises from the long-range evanescent waves of ultrarelativistic electrons. The spectral density of the electric field of a line charge decays with $\\bar { \\exp ( - \\kappa | x | ) }$ , where $\\kappa =$ $2 \\pi / \\beta \\gamma \\lambda$ , with $\\beta \\approx 1$ and $\\gamma \\approx 6 0 0 0$ for $E = 3 . 2$ GeV.34 This means the evanescent waves will reach the boundaries of our simulation cell in the $x$ -direction. Generalized perfectly matched layers $\\left( \\mathrm { P M L s } \\right) ^ { 3 5 }$ are chosen, such that they can absorb both propagating and evanescent waves. A detailed look at Figure 1b reveals that our implementation of generalized PMLs is not fully capable of absorbing evanescent waves. Hence, we make use of symmetry to further reduce the effect of evanescent waves at the boundaries of the simulation cell. Note that the evanescent electric field for $\\beta \\approx 1$ is almost entirely polarized along the transverse direction $x .$ . This means if the simulation cell is mirror symmetric with respect to the electron channel, antiperiodic boundaries can be applied after the PMLs to cancel out the effect of evanescent waves at the boundaries. This turned out to work well for us, although the structure is not mirror symmetric with respect to the electron axis.
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Expert
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What is the role of the Bragg reflector in the radiator design?
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To form a cavity that reflects backward-propagating waves, enhancing directionality and spectral purity of the emitted radiation.
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Reasoning
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hermann-et-al-2022-inverse-designed-narrowband-thz-radiator-for-ultrarelativistic-electrons.pdf
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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.
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NO
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IPAC
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What is the role of the Bragg reflector in the radiator design?
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To form a cavity that reflects backward-propagating waves, enhancing directionality and spectral purity of the emitted radiation.
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Reasoning
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hermann-et-al-2022-inverse-designed-narrowband-thz-radiator-for-ultrarelativistic-electrons.pdf
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Power density distributions on absorber surfaces calculated from SYNRAD simulation were transferred into finite element (FE) model in ANSYS Workbench. In thermal mechanical calculations, spatial heat power density distribution was defined as TABLE using APDL command $\\ast _ { \\mathrm { D I M } }$ for each absorber beam intercepting surface. Due to the large number of faces, the repetitive APDL script generation was performed using a MATLAB program, which also converted the SYNRAD output data into the desired format for the ANSYS software. This approach enabled fast and efficient data transfer from SYNRAD to ANSYS. To minimize the error in heat load mapping, a mesh seed size of $0 . 2 ~ \\mathrm { m m }$ was selected, which was smaller than the SYNRAD mesh size on surfaces with high power density. For the remaining irradiated surfaces, the mesh seed size was $0 . 8 \\mathrm { m m }$ , while the general mesh size of the model was $2 ~ \\mathrm { m m }$ . The finite element model consisted of a total of 3 million nodes and 2 million elements, presented in Fig. 5. In the finite element analysis, stress, thermal deformation and temperature of absorber were calculated and verified against design criteria. The maximal temperature on absorber surface was $2 9 7 ^ { \\circ } \\mathrm { C }$ (shown in Fig. 6) and maximal thermal stress was $1 7 1 \\ \\mathrm { N / m m } ^ { 2 }$ . The maximal cooling water temperature was limited to $1 6 0 ^ { \\circ } \\mathrm { C }$ , below the water boiling temperature at 6 bar.
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NO
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IPAC
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What is the role of the Bragg reflector in the radiator design?
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To form a cavity that reflects backward-propagating waves, enhancing directionality and spectral purity of the emitted radiation.
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Reasoning
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hermann-et-al-2022-inverse-designed-narrowband-thz-radiator-for-ultrarelativistic-electrons.pdf
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Another promising method for the longitudinal alignment is the use of a pulse arrival time chirp [9, 10]. Introducing an arrival time chirp on the order of about 1 ps over a pulse train enables the longitudinal scanning for seeding with a much relaxed tolerance of hundreds of $\\mu \\mathrm { m }$ per mechanical translation of the downstream chamber. Using cryogenic cooling for the diamond Bragg reflectors is a common attempt to improve the cavity’s stability by better distributing the pulsed heat load given by the interaction of the Bragg reflector with the powerful X-ray pulses. Pulsed cryogenic coolers are also planned to be installed for the CBXFEL demonstrator. Our simulations [5] revealed that due to cryogenic cooling, a significant increase of the out coupled pulse energy by about a factor of 30 is expected. Monitoring the significant increase of pulse energy due to cryogenic cooling is another important milestone for the demonstrator project. Nevertheless, due to the high heat load on the $1 0 0 \\mu \\mathrm { m }$ thin crystals, stable operation under saturation is not expected for our current demonstrator project. beforeBraggreflecttion.....noerr. afterBraggreflection noerr. transmitted noerr. 101 10-2 10-5 0.6 70 75808590 95 0 20 40 60 80 numberofroundtrips
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Expert
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What is the role of the Bragg reflector in the radiator design?
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To form a cavity that reflects backward-propagating waves, enhancing directionality and spectral purity of the emitted radiation.
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Reasoning
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hermann-et-al-2022-inverse-designed-narrowband-thz-radiator-for-ultrarelativistic-electrons.pdf
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$$ 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.
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Expert
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What is the role of the Bragg reflector in the radiator design?
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To form a cavity that reflects backward-propagating waves, enhancing directionality and spectral purity of the emitted radiation.
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Reasoning
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hermann-et-al-2022-inverse-designed-narrowband-thz-radiator-for-ultrarelativistic-electrons.pdf
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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.
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Expert
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What is the role of the Bragg reflector in the radiator design?
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To form a cavity that reflects backward-propagating waves, enhancing directionality and spectral purity of the emitted radiation.
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Reasoning
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hermann-et-al-2022-inverse-designed-narrowband-thz-radiator-for-ultrarelativistic-electrons.pdf
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File Name:hermann-et-al-2022-inverse-designed-narrowband-thz-radiator-for-ultrarelativistic-electrons.pdf Inverse-Designed Narrowband THz Radiator for Ultrarelativistic Electrons Benedikt Hermann,# Urs Haeusler,# Gyanendra Yadav, Adrian Kirchner, Thomas Feurer, Carsten Welsch, Peter Hommelhoff, and Rasmus Ischebeck\\* Cite This: ACS Photonics 2022, 9, 1143−1149 ACCESS 山 Metrics & More 国 Article Recommendations ABSTRACT: THz radiation finds various applications in science and technology. Pump−probe experiments at free-electron lasers typically rely on THz radiation generated by optical rectification of ultrafast laser pulses in electro-optic crystals. A compact and cost-efficient alternative is offered by the Smith−Purcell effect: a charged particle beam passes a periodic structure and generates synchronous radiation. Here, we employ the technique of photonic inverse design to optimize a structure for Smith− Purcell radiation at a single wavelength from ultrarelativistic electrons. The resulting design is highly resonant and emits narrowbandly. Experiments with a 3D-printed model for a wavelength of $9 0 0 \\mu \\mathrm { m }$ show coherent enhancement. The versatility of inverse design offers a simple adaption of the structure to other electron energies or radiation wavelengths. This approach could advance beam-based THz generation for a wide range of applications. KEYWORDS: THz generation, Smith−Purcell radiation, inverse design, light−matter interaction, free-electron light sources $\\mathbf { C }$ aopuprlciecs iof ,TiHnzc rdaidniagtiwoinr aerses ofmimntuenriecsat fonr ,n2uelmeecrtrouns acceleration,3−5 and biomedical and material science.6,7 Freeelectron laser (FEL) facilities demand versatile THz sources for pump−probe experiments.8 Intense, broadband THz pulses up to sub-mJ pulse energy have been demonstrated using optical rectification of high-power femtosecond lasers in lithium niobate crystals.9,10 The Smith−Purcell effect11 offers a compact and cost-efficient alternative for the generation of beam-synchronous THz radiation at electron accelerators. This effect describes the emission of electromagnetic waves from a periodic metallic or dielectric structure excited by electrons moving parallel to its surface. The wavelength of Smith− Purcell radiation at an angle $\\theta$ with respect to the electron beam follows:11
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What is the role of the Bragg reflector in the radiator design?
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To form a cavity that reflects backward-propagating waves, enhancing directionality and spectral purity of the emitted radiation.
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Reasoning
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hermann-et-al-2022-inverse-designed-narrowband-thz-radiator-for-ultrarelativistic-electrons.pdf
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ACS PHOTONICS READ Quasi-BIC Modes in All-Dielectric Slotted Nanoantennas for Enhanced $\\mathbf { E r ^ { 3 + } }$ Emission Boris Kalinic, Giovanni Mattei, et al.JANUARY 18, 2023 ACS PHOTONICS READ Get More Suggestions >
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augmentation
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Expert
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What is the role of the Bragg reflector in the radiator design?
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To form a cavity that reflects backward-propagating waves, enhancing directionality and spectral purity of the emitted radiation.
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Reasoning
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hermann-et-al-2022-inverse-designed-narrowband-thz-radiator-for-ultrarelativistic-electrons.pdf
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A typical autocorrelation measurement for a charge of 9.4 pC is depicted in Figure 2b. The shape of the autocorrelation is not perfectly symmetric in amplitude and stage position. The amplitude asymmetry could be a result of a nonlinear detector response (onset of saturation). This is in agreement with the slight deviation of the pulse energy from the quadratic fit (Figure 4). Since the length of only one arm is changed and the radiation might not be perfectly collimated, the position scan of the mirror is not creating a perfectly symmetric autocorrelation signal. AUTHOR INFORMATION Corresponding Author Rasmus Ischebeck − Paul Scherrer Institut, 5232 Villigen, PSI, Switzerland; $\\circledcirc$ orcid.org/0000-0002-5612-5828; Email: rasmus.ischebeck@psi.ch Authors Benedikt Hermann − Paul Scherrer Institut, 5232 Villigen, PSI, Switzerland; Institute of Applied Physics, University of Bern, 3012 Bern, Switzerland; Galatea Laboratory, Ecole Polytechnique Fédérale de Lausanne (EPFL), 2000 Neuchâtel, Switzerland; $\\circledcirc$ orcid.org/0000-0001-9766-3270 Urs Haeusler − Department Physik, Friedrich-AlexanderUniversität Erlangen-Nürnberg (FAU), 91058 Erlangen, Germany; Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, United Kingdom; $\\circledcirc$ orcid.org/0000- 0002-6818-0576 Gyanendra Yadav − Department of Physics, University of Liverpool, Liverpool L69 7ZE, United Kingdom; Cockcroft Institute, Warrington WA4 4AD, United Kingdom Adrian Kirchner − Department Physik, Friedrich-AlexanderUniversität Erlangen-Nürnberg (FAU), 91058 Erlangen, Germany
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augmentation
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NO
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Expert
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What is the role of the Bragg reflector in the radiator design?
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To form a cavity that reflects backward-propagating waves, enhancing directionality and spectral purity of the emitted radiation.
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Reasoning
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hermann-et-al-2022-inverse-designed-narrowband-thz-radiator-for-ultrarelativistic-electrons.pdf
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The objective function $G$ , quantifying the performance of a design $\\phi ,$ is given by the line integral of the Poynting vector $\\begin{array} { r } { { \\bf S } ( x , y ) = \\mathrm { R e } \\left\\{ \\frac { 1 } { 2 } { \\bf E } \\times { \\bf H } ^ { * } \\right\\} } \\end{array}$ in the $x$ -direction along the length of one period, evaluated at a point $x _ { S }$ outside the design region: $$ G ( \\phi ) = \\int _ { 0 } ^ { a } S _ { x } ( x _ { S } , y ) \\mathrm { d } y $$ The optimization problem can then be stated as $$ \\begin{array} { r l } & { \\operatorname* { m a x } _ { \\phi } G ( \\phi ) \\quad \\mathrm { s u b j e c t t o } \\quad \\nabla \\times \\mathbf { E } = - i \\omega \\mu \\mathbf { H } \\quad \\mathrm { a n d } } \\\\ & { \\quad \\nabla \\times \\epsilon ( \\phi ) ^ { - 1 } \\nabla \\times \\mathbf { H } - \\omega ^ { 2 } \\mu \\mathbf { H } = \\nabla \\times \\epsilon ( \\phi ) ^ { - 1 } \\mathbf { J } } \\end{array}
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augmentation
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NO
| 0
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Expert
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What is the role of the Bragg reflector in the radiator design?
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To form a cavity that reflects backward-propagating waves, enhancing directionality and spectral purity of the emitted radiation.
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Reasoning
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hermann-et-al-2022-inverse-designed-narrowband-thz-radiator-for-ultrarelativistic-electrons.pdf
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$$ \\lambda = \\frac { a } { m } \\Biggl ( \\frac { 1 } { \\beta } - \\cos { \\theta } \\Biggr ) $$ where $\\beta$ is the normalized velocity of the electrons, a is the periodicity of the structure, and $m$ is the mode order. Smith‚àí Purcell emission from regular metallic grating surfaces has been observed in numerous experiments, first using $3 0 0 ~ \\mathrm { k e V }$ electrons11 and later also using ultrarelativistic electrons.12,13 If electron pulses shorter than the emitted wavelength are used, the fields from individual electrons add coherently, and the radiated energy scales quadratically with the bunch charge.14 The typically used single-sided gratings emit a broadband spectrum,15 which is dispersed by the Smith‚àíPurcell relation (eq 1). To enhance emission at single frequencies, a concept called orotron uses a metallic mirror above the grating to form a resonator.16,17 Dielectrics can sustain fields 1‚àí2 orders of magnitude larger than metals18 and are therefore an attractive material for strong Smith‚àíPurcell interactions. Inverse design is a computational technique that has been successfully employed to advance integrated photonics.19 Algorithms to discover optical structures fulfilling desired functional characteristics are creating a plethora of novel subwavelength geometries: applications include wavelengthdependent beam splitters19,20 and couplers,21 as well as dielectric laser accelerators.22
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augmentation
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NO
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expert
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What is the structure radius when the gaps are closed
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0.5 mm
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Definition
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Design_of_a_quadripartite_wakefield_structure_for_free_electron_laser_applications.pdf.pdf
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MECHANICAL DESIGN To fully leverage these advantages, the four corrugated plates must be positioned with high precision, making the mechanical design critical for the proposed structure. Consequently, a prototype structure (Fig. 4) featuring $1 \\mathrm { m }$ -long aluminium corrugation plates has been designed for beam test at Dalian Coherent Light Source (DCLS, Fig. 5) [22] to benchmark the simulation results and validate engineering aspects. For manufacturing simplicity, the corrugation has been designed as flat configuration, and each $1 \\mathrm { m }$ -long plate are divided into four $0 . 2 5 \\mathrm { m }$ sections, which are bolted onto a main girder, as illustrated in Fig. 6. To match the realistic beam condition, $p , t$ , and $h$ are respectively designed to be $2 \\mathrm { m m }$ , $1 \\mathrm { m m }$ , and $1 \\mathrm { m m }$ , and the minimal effective gap is set to be $3 . 5 ~ \\mathrm { m m }$ . Alignment of the sections on the same girder will be achieved through precise trimming. Venting slots are incorporated into both the corrugation sections and the main girders to maintain ultra-high vacuum. With two $4 0 0 \\mathrm { L / s }$ ion pumps places at the ends, the vacuum inside the chamber is simulated to be better than $1 { \\times } 1 0 ^ { - 7 } \\ \\mathrm { P a }$ .
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1
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Yes
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expert
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What is the structure radius when the gaps are closed
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0.5 mm
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Definition
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Design_of_a_quadripartite_wakefield_structure_for_free_electron_laser_applications.pdf.pdf
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File Name:Design_of_a_quadripartite_wakefield_structure_for_free_electron_laser_applications.pdf.pdf DESIGN OF A QUADRIPARTITE WAKEFIELD STRUCTURE FOR FREE ELECTRON LASER APPLICATIONS Y. Ji1, C. Lei1, J. Shao1,‚à ó , Y. $\\mathrm { Y u ^ { 1 } }$ , J. Sun2, Zongbin $\\mathrm { L i ^ { \\mathrm { 1 } } }$ , L. $\\mathrm { H e ^ { 1 } }$ , H. Wang1, J. Wei1, W. Wei1, W. Wang1, J. Yang2, W. Zhang2, X. Yang2 1Institute of Advanced Science Facilities, Shenzhen, China 2Dalian Institute of Chemical Physics, Dalian, China Abstract Wakefield structures are broadly employed in free electron laser (FEL) facilities for beam manipulation. Compared with cylindrical geometries, planar structures are typically preferred due to their increased flexibility, allowing for tunable wakefield strength through gap adjustment. However, these planar configurations can induce time-dependent quadrupole wakefields, which require careful compensation in various applications. To address this issue, we propose a novel structure design incorporating four identical corrugated elements which are independently controllable. By adjusting the gaps between orthogonal pairs, the quadrupole wakefield can be either fully compensated to avoid emittance growth or significantly amplified to enhance beam mismatch for slice lasing control. This manuscript presents both the physical and mechanical design of the proposed structure, as well as the planned proof-of-principle experiment.
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1
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Yes
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expert
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What is the structure radius when the gaps are closed
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0.5 mm
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Definition
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Design_of_a_quadripartite_wakefield_structure_for_free_electron_laser_applications.pdf.pdf
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INTRODUCTION Wakefields are induced when a charged bunch traverses a corrugated or dielectric pipe. Structure-based wakefield acceleration represents a promising approach to achieve gradients significantly higher than those attained by conventional techniques [1–3]. Furthermore, wakefield have been demonstrated to be effective tools for beam manipulation in FELs, where the short-range wakefield from the bunch head can alter the longitudinal or transverse momentum of the tail [4–18]. Initially, wakefield structures were employed in FELs as dechirpers to mitigate the linear energy chirp introduced for magnetic bunch compression [4, 5, 7]. Since then, these structures have been adapted for a broader range of applications, such as passive linearization [6, 13], slice lasing control [8, 10–12, 14, 15], and passive deflection [9, 17, 18]. The Shenzhen Superconducting Soft X-Ray Free-Electron Laser $( { \\mathrm { S } } ^ { 3 } { \\mathrm { F E L } } )$ is a newly proposed, high repetition-rate FEL facility featuring multiple undulator lines that lase in the $1 { - } 3 0 ~ \\mathrm { n m }$ range [19]. Wakefield structures are under development to serve as dechirpers and as key components for advanced FEL modes. Their performance is crucial to achieving high lasing quality in $S ^ { 3 } \\mathrm { F E L }$ .
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1
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Yes
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expert
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What is the structure radius when the gaps are closed
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0.5 mm
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Definition
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Design_of_a_quadripartite_wakefield_structure_for_free_electron_laser_applications.pdf.pdf
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Table: Caption: Table 1: Parameters of the Quadripartite Wakefield Structure Body: <html><body><table><tr><td>Parameter</td><td>Value</td><td>Unit</td></tr><tr><td>Corrugation period p</td><td>0.5</td><td>mm</td></tr><tr><td>Corrugation length t</td><td>0.25</td><td>mm</td></tr><tr><td>Corrugation depth h</td><td>0.5</td><td>mm</td></tr><tr><td>Effective horizontal gap gx</td><td>1.4</td><td>mm</td></tr><tr><td>Effective vertical gap gy</td><td>1.4</td><td>mm</td></tr><tr><td>Slot length w</td><td>7</td><td>mm</td></tr><tr><td>Pipe radius a when fully closed</td><td>0.5</td><td>mm</td></tr></table></body></html> ECHO3D [20] and CST wakefield solver [21] have been used to simulate the wakefield of the proposed structure, and their results have been benchmarkded against each other. Figure 2 and 3 illustrate the simulation results for an on-axis charged beam with a Gaussian temporal distribution and an rms bunch length of $1 2 \\mu \\mathrm { m }$ . When $g _ { x } = g _ { y }$ , the quadrupole wakefield is not induced due to the structure symmetry. Furthermore, compared to the planar structure using the same corrugation parameters $p , t$ , and $h$ , the quadripartite structure produces $\\sim 5 0 \\%$ stronger longitudinal wakefield, leading to a shorter required length to mitigate a given energy chirp. Conversely, when $g _ { x }$ is fixed as $1 . 4 \\mathrm { m m }$ and $g _ { y }$ is adjusted, the quadrupole wakefield can be significantly enhanced to either direction, while the variation in the longitudinal wakefield remains moderate.
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4
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Yes
| 1
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expert
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What is the structure radius when the gaps are closed
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0.5 mm
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Definition
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Design_of_a_quadripartite_wakefield_structure_for_free_electron_laser_applications.pdf.pdf
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Each ${ 1 \\mathrm { m } }$ -long plate is controlled by two synchronized high-precision motors. The misalignment between the main girders due to assembly, deforming, and motor position error is required to be less than $5 0 \\mu \\mathrm { m }$ . PLANNED PROOF-OF-PRINCIPLE EXPERIMENT The proof-of-principle experiment is scheduled to be conducted in DCLS where low-emittance electron beam is produced by an S-band 1.6-cell photocathode RF gun and accelerated to $3 0 0 \\mathrm { M e V }$ via six S-band $3 \\mathrm { m }$ -long linacs. The prototype wakefield structure will be installed between the undulator beamline and the downstream diagnostics section. Diagnostics involved in the experiment will include a $1 2 \\mathrm { M V }$ S-band deflecting cavity, a dipole magnet with beam dump, and several beam profile monitors. In alignment with methodologies established in previous studies [5, 23], the longitudinal, dipole, and quadrupole wakefields will be inferred from the longitudinal phase space, beam tail offset, and slice transverse size, respectively. Beam dynamics simulation has been thoroughly conducted to obtain the proper lattice settings for the experiment. CONCLUSION A quadripartite wakefield structure comprising four identical corrugated elements has been proposed for FEL applications. The independently controllable plates enable a flexible configuration to control the longitudinal and quadrupole wakefields. A prototype structure has been designed and is currently under fabrication. The proof-of-principle experiment is scheduled to take place at DCLS in 2025.
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augmentation
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Yes
| 0
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IPAC
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What is the underlying reason for longitudinal damping?
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Electronsthat have a larger energy than the reference particle radiate more, while those that have smaller energy radiate less.
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Reasoning
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Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation
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There is a very good agreement between calculated and measured results, with a maximum difference of $1 7 \\%$ . Differences are likely to be explained by the simplified boundary condition in the models, geometry and wall thickness differences, and material parameters. More complete (and time consuming) models are for the moment not required. Table: Caption: Table 1: LFD and PS values calculated and measured for jacketed (JC) and bare cavity (BC) With the validated DQW JC model and an additional spring for the tuner stiffness, the values of the PS and LFD during operation were computed (Table 2) and compared to the RFD calculated values [3]. Body: <html><body><table><tr><td></td><td>LFD [Hz/MV^2]</td><td>PS [Hz/mbar]</td></tr><tr><td>JCcalculated</td><td>-256</td><td>-215</td></tr><tr><td>BCcalculated</td><td>-418</td><td>-494</td></tr><tr><td>JC measured</td><td>-218</td><td>-244</td></tr><tr><td>BCmeasured</td><td>-358</td><td>-422</td></tr></table></body></html> Table: Caption: Table 2: LFD and PS values calculated operation values for DQW and RFD Body: <html><body><table><tr><td></td><td>LFD [Hz/MV^2]</td><td>PS [Hz/mbar]</td></tr><tr><td>DQW</td><td>-126</td><td>-110</td></tr><tr><td>RFD</td><td>-659</td><td>-244</td></tr></table></body></html> The stiffness of the tuning system of the DQW cavity decreases the jacketed cavity LFD and PS values almost by a factor of two. To further evaluate and possibly optimise the influence of the tuning system stiffness, a parametric study of the tuning system stiffness was performed (Fig. 6). As expected, the absolute values of PS and LFD of the cavity decrease with the stiffness of the tuning system. The decrease is however non-linear. Further increase in the tuner stiffness beyond the current $6 . 9 \\mathrm { k N / m m }$ will not create a sufficient gain against dynamic perturbations.
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augmentation
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NO
| 0
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IPAC
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What is the underlying reason for longitudinal damping?
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Electronsthat have a larger energy than the reference particle radiate more, while those that have smaller energy radiate less.
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Reasoning
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Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation
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The entire geometry was modelled in the electromagnetic simulation code CST [9]. The calculation of the longitudinal impedance was carried out by using the wakefield solver. Figure 3 shows the predicted longitudinal beam impedance of the kicker KFA79 versus frequency up to $1 . 6 \\mathrm { G H z }$ . The impedance increases to $1 . 7 \\mathrm { k } \\Omega$ up to ${ 5 0 0 } \\mathrm { M H z }$ , with a peak of $1 . 8 \\mathrm { k } \\Omega$ around $6 5 0 \\mathrm { M H z }$ , it then generally decreases until the end of the considered range of frequency. The envelope of the impedance curve represents the so-called broadband behavior and it is directly caused by the ferrites. Three resonances, at $1 9 . 7 ~ \\mathrm { M H z }$ , $3 2 . 3 ~ \\mathrm { M H z }$ and $4 5 . 5 ~ \\mathrm { { M H z } }$ , are excited by the beam inside the vacuum tank and between the modules (Fig. 4). Their shunt impedance is in the order of several hundred ohms. These resonances can be critical for the stability of the beam because they could be located in correspondence with the beam spectrum lines and generate induced voltage contributions. Therefore, a complete understanding of their origin was the main focus of investigation. The electric field was calculated from the wakefield simulation by using field monitors at the frequencies of interest. The electric field distribution allowed to identify the location of the critical resonances in the low frequency range. An example of $E$ -field monitor for the impedance peak at $1 9 . 7 \\mathrm { M H z }$ is shown in Fig. 5. The $E$ -field monitors from the three low frequency peaks revealed resonances building up between the side walls of the vacuum tank and the ground plates of the modules at the extremities. A large $E$ -field intensity was also seen between the ground plates of two consecutive modules.
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augmentation
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NO
| 0
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IPAC
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What is the underlying reason for longitudinal damping?
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Electronsthat have a larger energy than the reference particle radiate more, while those that have smaller energy radiate less.
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Reasoning
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Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation
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File Name:MEASUREMENTS_OF_BEAM_CORRELATIONS_INDUCED_VIA_COUPLED.pdf MEASUREMENTS OF BEAM CORRELATIONS INDUCED VIA COUPLED RESONANCE CROSSING IN THE CERN PSB E. Lamb‚àó1, S. Albright, F. Asvesta, H. Bartosik, T. Prebibaj, G. Sterbini, CERN, Meyrin, Switzerland G. Franchetti, GSI Helmholtzzentrum f√ºr Schwerionenforschung GmbH, Darmstadt, Germany M. Seidel1, PSI, Switzerland 1also at EPFL, Lausanne, Switzerland Abstract Beam profile measurements in the LHC and its injector complex show heavy tails in both transverse planes. From standard profile measurements, it is not possible to determine if the underlying phase space distribution is statistically independent. A measurement campaign in the CERN PSB was carried out to introduce cross-plane dependence in bunched beams in controlled conditions, in view of characterizing the LHC operational beam distributions. The results of the measurement campaign demonstrate how heavy tails can be created via coupled resonance excitation of the lattice in the presence of space charge, in accordance with predictions from the fixed line theory. The coupled resonance introduces dependence between the different planes, which persists after the resonance excitation is removed. INTRODUCTION recent theoretical and experimental investigations [3‚Äì6]. The fixed lines are structures visible in the $x$ -ùë¶ Poincar√© sections, resembling Lissajous figures. These curves are correlated in the ùë•-ùë¶ planes, which explains how correlation is built into the distribution when particles are trapped or scattered to higher amplitudes by these structures. When the particles no longer meet the resonant condition, the correlations persist as the Courant-Snyder amplitudes in $x - p _ { x } , y - p _ { y }$ of a given particle are preserved [7].
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augmentation
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NO
| 0
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expert
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What is the underlying reason for longitudinal damping?
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Electronsthat have a larger energy than the reference particle radiate more, while those that have smaller energy radiate less.
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Reasoning
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Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation
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– Vacuum system: as a result of the smaller inner bore of the magnets, the vacuum chamber diameter needs to be reduced to a point where a conventional pumping system becomes difficult to implement. A key enabling technology is the use of a distributed getter pump system, where the entire vacuum chamber is coated with a non-evaporable getter (NEG); – Generation of hard X-rays: the strong field in longitudinal gradient bends, peaking at 4. . . 6 Tesla, results in very hard X-rays, up to a photon energy of $8 0 \\mathrm { k e V }$ ; – Momentum compaction factor: when designing a magnetic lattice that employs LGBs and reverse bends, one can achieve a situation where a higher-energy particle takes a shorter path. This can then result in a negative momentum compaction factor of the ring (like in proton synchrotrons below transition energy). The Paul Scherrer Institut is upgrading its storage ring in the year 2024, making use of the principles outlined in this section [5]. I.10.5 Interaction of $\\mathbf { X }$ -rays with matter In the subsequent sections, we will look at the interaction of X-rays with matter, and the use of X-rays for experiments. To understand the processes that lead to absorption, scattering, and diffraction, we will proceed in three steps, and look at the interaction of $\\mathrm { \\Delta X }$ -rays with:
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1
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NO
| 0
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expert
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What is the underlying reason for longitudinal damping?
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Electronsthat have a larger energy than the reference particle radiate more, while those that have smaller energy radiate less.
|
Reasoning
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Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation
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I.10.7.16 Critical energy For the electron beam of the previous exercise, calculate the critical photon energy $\\varepsilon _ { c }$ that is emitted by the superbends with $B = 6 \\mathrm { \\ : T }$ and draw a sketch of the radiation spectrum. What is the useful photon energy range for experiments, assuming that the spectral intensity should be within $1 \\%$ of the maximum value? I.10.7.17 Critical frequency What do we understand by critical frequency? a) The frequency $\\omega _ { c }$ at which a storage ring becomes unstable b) The frequency of the photons coming from an undulator c) The frequency $\\omega _ { c }$ at which the integrated spectral density of photons with $\\omega < \\omega _ { c }$ is $50 \\%$ of the total energy radiated d) The revolution frequency of the electrons in a synchrotron e) The frequency $\\omega _ { c }$ where the highest spectral density of photos is emitted f) The frequency $\\omega _ { c }$ at which critical components fail I.10.7.18 Undulator radiation Assume an undulator of $1 8 ~ \\mathrm { m m }$ period and $5 . 4 \\mathrm { ~ m ~ }$ length. The pole tip field is $B _ { t } = 1 . 5 \\ : \\mathrm { T } _ { : }$ , and the gap can be varied between 10 and $2 0 \\mathrm { m m }$ .
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1
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NO
| 0
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expert
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What is the underlying reason for longitudinal damping?
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Electronsthat have a larger energy than the reference particle radiate more, while those that have smaller energy radiate less.
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Reasoning
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Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation
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$$ After the emission of a photon, the action of our single electron is $$ \\begin{array} { r c l } { { J _ { y } ^ { \\prime } } } & { { = } } & { { \\displaystyle \\frac { 1 } { 2 } \\gamma _ { y } y ^ { 2 } + \\alpha _ { y } y p _ { y } \\left( 1 - \\frac { d p } { P _ { 0 } } \\right) + \\frac { 1 } { 2 } \\beta _ { y } p _ { y } ^ { 2 } \\left( 1 - \\frac { d p } { P _ { 0 } } \\right) ^ { 2 } } } \\\\ { { } } & { { } } & { { } } \\\\ { { } } & { { = } } & { { \\displaystyle \\frac { 1 } { 2 } \\gamma _ { y } y ^ { 2 } + \\alpha _ { y } y p _ { y } - \\alpha _ { y } y p _ { y } \\frac { d p } { P _ { 0 } } + \\frac { 1 } { 2 } \\beta _ { y } p _ { y } ^ { 2 } - 2 \\cdot \\frac { 1 } { 2 } \\beta _ { y } p _ { y } ^ { 2 } \\frac { d p } { P _ { 0 } } + \\frac { 1 } { 2 } \\beta p _ { y } ^ { 2 } \\left( \\frac { d p } { P _ { 0 } } \\right) ^ { 2 } . } } \\end{array}
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1
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NO
| 0
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expert
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What is the underlying reason for longitudinal damping?
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Electronsthat have a larger energy than the reference particle radiate more, while those that have smaller energy radiate less.
|
Reasoning
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Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation
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$$ For a synchrotron consisting of only dipoles $$ \\oint { \\frac { 1 } { \\rho ^ { 2 } } } d s = { \\frac { 2 \\pi \\rho } { \\rho ^ { 2 } } } = { \\frac { 2 \\pi } { \\rho } } . $$ More generally, we use the second synchrotron radiation integral as defined in Equation I.10.12, and we can write the energy loss per turn as a function of $I _ { 2 }$ $$ U _ { 0 } = \\frac { C _ { \\gamma } } { 2 \\pi } E _ { \\mathrm { n o m } } ^ { 4 } I _ { 2 } . $$ Notice that $I _ { 2 }$ is a property of the lattice (actually, a property of the reference trajectory), and does not depend on the properties of the beam. The emittance evolves as $$ \\varepsilon _ { y } ( t ) = \\varepsilon _ { y } ( 0 ) \\exp \\left( - 2 \\frac { t } { \\tau _ { y } } \\right) . $$ From this, it follows that the emittance decreases exponentially, asymptotically approaching zero. This phenomenon is termed radiation damping. While radiation damping plays a key role in influencing the emittance of the beam in a synchrotron, there exist other factors and effects that counterbalance its influence. These countering mechanisms ensure that the emittance does not perpetually decline due to the sole influence of radiation damping, but that it reaches a non-zero equilibrium value. Before diving into these balancing effects, we turn our attention to the horizontal plane, examining its unique characteristics and dynamics in the context of our ongoing analysis.
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1
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NO
| 0
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expert
|
What is the underlying reason for longitudinal damping?
|
Electronsthat have a larger energy than the reference particle radiate more, while those that have smaller energy radiate less.
|
Reasoning
|
Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation
|
$$ d \\varepsilon _ { y } = - \\varepsilon _ { y } \\frac { U _ { 0 } } { E _ { \\mathrm { { n o m } } } } . $$ Using the revolution period $T _ { 0 }$ $$ \\frac { d \\varepsilon _ { y } } { d t } = - \\varepsilon _ { y } \\frac { U _ { 0 } } { E _ { \\mathrm { n o m } } T _ { 0 } } . $$ The damping time is thus $$ \\tau _ { y } = 2 \\frac { E _ { \\mathrm { { n o m } } } } { U _ { 0 } } T _ { 0 } . $$ We use the (classical) result from Equation I.10.9 for the power radiated by a particle of charge $e$ and energy $E _ { \\mathrm { n o m } }$ . Integrating around the ring, we have the energy loss per turn $$ \\begin{array} { l l l } { { U _ { 0 } } } & { { = } } & { { \\displaystyle \\oint P _ { \\gamma } d t } } \\\\ { { } } & { { = } } & { { \\displaystyle \\oint \\frac { 1 } { c } P _ { \\gamma } d s } } \\\\ { { } } & { { = } } & { { \\displaystyle \\frac { C _ { \\gamma } } { 2 \\pi } E _ { \\mathrm { n o m } } ^ { 4 } \\oint \\frac { 1 } { \\rho ^ { 2 } } d s . } } \\end{array}
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2
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NO
| 0
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expert
|
What is the underlying reason for longitudinal damping?
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Electronsthat have a larger energy than the reference particle radiate more, while those that have smaller energy radiate less.
|
Reasoning
|
Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation
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I.10.6.2 Spectroscopy Spectroscopic methods are used for investigating the electronic structure, chemical composition, and dynamic properties of matter. X-ray absorption spectroscopy (XAS) techniques, including X-ray absorption near edge structure (XANES), Extended X-ray Absorption Fine Structure (EXAFS) and Near Edge X-ray Absorption Fine Structure (NEXAFS), use the sudden change in absorption near edges (Section I.10.5.2) to probe the local atomic structure and electronic states of specific elements within a material (see Fig. I.10.14). Absorption edges, related to the ionization potential of inner-shell electrons in an atom, have a very small dependence on the chemical configuration of the atom in a molecule, as this shifts the energy levels slightly. X-ray fluorescence (XRF) is based on the principle that when a material is irradiated with Xrays, electrons from the inner shells of the atoms in the material can be ejected, leading to the emission of fluorescence $\\mathrm { \\Delta X }$ -rays as electrons from higher energy levels fill these vacancies. The energy of the emitted fluorescence $\\mathrm { \\Delta } X$ -rays is characteristic of each element, thus enabling qualitative and quantitative analysis of the elemental composition of the sample (see Fig. I.10.15). Similarly, X-ray photoelectron spectroscopy (XPS) measures the kinetic energy and the number of electrons that are emitted from the sample upon X-ray irradiation. Since the mean free path of free electrons in solids is only a few molecular layers, this technique enables the study of surface chemistry. Angular-resolved photoelectron spectroscopy (ARPES) allows reconstructing the momentum of the electrons in the solid, which is used to reconstruct the electronic band structure of the material.
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augmentation
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NO
| 0
|
expert
|
What is the underlying reason for longitudinal damping?
|
Electronsthat have a larger energy than the reference particle radiate more, while those that have smaller energy radiate less.
|
Reasoning
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Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation
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$$ Shifting our view to a broader perspective, we now consider the properties of the entire electron bunch. By definition, the emittance is given as the ensemble average of the action. The change in emittance follows thus from the change in action $$ \\begin{array} { r c l } { d \\varepsilon _ { y } } & { = } & { \\langle d J _ { y } \\rangle } \\\\ & { = } & { - \\langle \\alpha _ { y } \\underbrace { \\langle g p _ { y } \\rangle } _ { = - \\alpha _ { y } \\varepsilon _ { y } } + \\beta _ { y } \\underbrace { \\langle p _ { y } ^ { 2 } \\rangle } _ { = \\gamma _ { \\mathrm { t r } } \\varepsilon _ { y } } \\frac { \\partial p _ { \\mathrm { t } } } { \\partial P _ { 0 } } } \\\\ & & { - \\langle - \\alpha _ { y } ^ { 2 } \\varepsilon _ { y } + \\beta _ { y } \\gamma _ { y } \\varepsilon _ { y } \\rangle \\frac { \\partial p _ { \\mathrm { t } } } { \\partial P _ { 0 } } } \\\\ & { = } & { - \\varepsilon _ { y } \\langle \\underbrace { \\delta _ { y } \\gamma _ { y } } _ { \\mathrm { 1 } } - \\alpha _ { y } ^ { 2 } \\rangle \\frac { d p _ { \\mathrm { f } } } { P _ { 0 } } } \\\\ & & { - \\varepsilon _ { y } \\frac { d p _ { \\mathrm { f } } } { D _ { 0 } } , } \\end{array}
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What is the underlying reason for longitudinal damping?
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Electronsthat have a larger energy than the reference particle radiate more, while those that have smaller energy radiate less.
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Reasoning
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Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation
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$$ \\vec { B } ( 0 , 0 , z ) = \\vec { u } _ { y } B _ { 0 } \\sin ( k _ { u } z ) , $$ where $k _ { u } = 2 \\pi / \\lambda _ { u }$ with $\\lambda _ { u }$ the period of the magnetic field, $B _ { 0 }$ is the maximum field and $\\vec { u } _ { y }$ is the unit vector in $y$ direction. Due to the Maxwell equations, the curl and divergence of the static magnetic field vanish in vacuum, $\\vec { \\nabla } \\times \\vec { B } = 0$ and $\\vec { \\nabla } \\cdot \\vec { B } = 0$ . Thus, the field acquires a $z$ component for $y \\ne 0$ $$ \\begin{array} { r c l } { { { \\cal B } _ { x } } } & { { = } } & { { 0 } } \\\\ { { { \\cal B } _ { y } } } & { { = } } & { { { \\cal B } _ { 0 } \\cosh ( k _ { u } y ) \\sin ( k _ { u } z ) } } \\\\ { { { \\cal B } _ { z } } } & { { = } } & { { { \\cal B } _ { 0 } \\sinh ( k _ { u } y ) \\cos ( k _ { u } z ) . } } \\end{array}
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What is the underlying reason for longitudinal damping?
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Electronsthat have a larger energy than the reference particle radiate more, while those that have smaller energy radiate less.
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Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation
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$$ Equation (I.10.16) becomes $$ \\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 }$
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What is the underlying reason for longitudinal damping?
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Electronsthat have a larger energy than the reference particle radiate more, while those that have smaller energy radiate less.
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Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation
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Suggest a way to lower the emittance at the existing machine in order to test the instrumentation. What are some issues with your suggestion? I.10.7.24 Upgrade The SLS 2.0 Upgrade, amongst other things, considers an increase of the electron energy from 2.4 to $2 . 7 \\mathrm { G e V . }$ – What can be the rationale for this change? Assume that the lattice is the same for both energies. – Are there detrimental aspects to an energy increase? I.10.7.25 Neutron star A proton with energy $E _ { p } = 1 0 \\mathrm { T e V }$ moves through the magnetic field of a neutron star with strength $B = 1 0 ^ { 8 } \\mathrm { T }$ . – Calculate the diameter of the proton trajectory and the revolution frequency. – How large is the power emitted by synchrotron radiation? – How much energy does the proton lose per revolution? I.10.7.26 Cosmic electron A cosmic electron with an energy of $1 \\mathrm { G e V }$ enters an interstellar region with a magnetic field of $1 \\ \\mathrm { n T }$ . Calculate: – The radius of curvature, – The critical energy of the emitted synchrotron radiation, – The energy emitted in one turn.
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What is the underlying reason for longitudinal damping?
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Electronsthat have a larger energy than the reference particle radiate more, while those that have smaller energy radiate less.
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Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation
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– The Lorentz factor $\\gamma$ , – The magnetic field to bend the beam (assume for simplicity that the ring consists of a uniform dipole field), – The critical energy of the synchrotron radiation, – The energy emitted by each electron through synchrotron radiation in one turn. I.10.7.7 Future Circular Collider: FCC-hh Particle physicists are evaluating the potential of building a future circular collider, which aims at colliding two proton beams with $5 0 0 \\mathrm { m A }$ current each and $1 0 0 \\mathrm { T e V }$ particle energy (FCC-hh). The protons would be circulating in a storage ring with $1 0 0 \\mathrm { k m }$ circumference, guided by superconducting magnets. The dipoles aim at a field of $1 6 \\mathrm { T }$ Calculate: – The Lorentz factor $\\gamma$ , – The critical energy of the synchrotron radiation, – The total power emitted by both beams through synchrotron radiation. I.10.7.8 Simple storage ring Let’s build a very simple synchrotron! Consider a storage ring that is located at the (magnetic) North Pole of the Earth. Assume that the Earth’s magnetic field of $5 0 \\mu \\mathrm { T }$ is used to confine electrons to a circular orbit, and ignore the need for focusing magnets. As a particle source, we will use the electron gun of an old TV, which accelerates the particles with a DC voltage of $2 5 \\mathrm { k V }$ (we will ignore the requirement of an injection system).
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What is the underlying reason for longitudinal damping?
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Electronsthat have a larger energy than the reference particle radiate more, while those that have smaller energy radiate less.
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Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation
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$$ The difference to Equation I.10.13 is small for $k _ { u } y \\ll 1$ and will be neglected in the following. Helical undulators have a magnetic field on the axis $$ \\begin{array} { r } { \\vec { B } ( z ) = \\vec { u } _ { x } B _ { 0 } \\cos ( k _ { u } z ) - \\vec { u } _ { y } B _ { 0 } \\sin ( k _ { u } z ) . } \\end{array} $$ A rigorous analytic discussion of helical undulators is somewhat easier since the longitudinal component of the electron velocity $v _ { z } = \\beta _ { z } c$ is constant. Planar undulators, however, are much more common in synchrotron radiation facilities, therefore we will continue our discussion using a magnetic field according to Equation I.10.13. The magnetic field exerts a force on the electron $$ m _ { e } \\gamma \\frac { \\mathrm { d } \\vec { v } } { \\mathrm { d } t } = \\vec { F } = - e \\vec { v } \\times \\vec { B }
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What is the underlying reason for longitudinal damping?
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Electronsthat have a larger energy than the reference particle radiate more, while those that have smaller energy radiate less.
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Reasoning
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Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation
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$$ Computing the photon flux $\\dot { N } _ { \\gamma }$ for an undulator is even more elaborate than the calculation for a single dipole, and we just cite the result [2] $$ { \\dot { N } } _ { \\gamma } = 1 . 4 3 \\cdot 1 0 ^ { 1 4 } N I _ { b } Q _ { n } ( K ) , $$ where $$ Q _ { n } ( K ) = \\frac { 1 + K ^ { 2 } / 2 } { n } F _ { n } ( K ) . $$ We denote the harmonic number by $n = 2 m - 1$ with $m \\in \\mathbb { N }$ , the number of periods in the undulator by $N$ , the beam current in A by $I _ { b }$ , the undulator parameter by $K$ , and $F _ { n } ( K )$ is given by $$ \\begin{array} { r c l } { { F _ { n } ( K ) } } & { { = } } & { { \\displaystyle \\frac { n ^ { 2 } K ^ { 2 } } { ( 1 + K ^ { 2 } / 2 ) ^ { 2 } } \\left( J _ { ( n + 1 ) / 2 } ( Y ) - J _ { ( n - 1 ) / 2 } ( Y ) \\right) ^ { 2 } } } \\\\ { { } } & { { } } & { { } } \\\\ { { Y } } & { { = } } & { { \\displaystyle \\frac { n K ^ { 2 } } { 4 ( 1 + K ^ { 2 } / 2 ) } , } } \\end{array}
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What is the underlying reason for longitudinal damping?
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Electronsthat have a larger energy than the reference particle radiate more, while those that have smaller energy radiate less.
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Reasoning
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Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation
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– Longitudinal gradient bends: these are dipole magnets whose magnetic field varies along their length. By providing a variable field strength along the bend, longitudinal gradient bends (LGBs) concentrate the highest magnetic field in the middle, where the dispersion reaches a minimum. This further reduces the horizontal emittance, making diffraction-limited designs possible even for small storage rings; – Reverse bends: these are dipoles that have the opposite magnetic field of the regular dipoles, effectively bending the beam outwards. By carefully configuring the reverse bends, designers can disentangle horizontal focusing from dispersion matching, achieving a net reduction in beam dispersion. Combining MBAs with LGBs and reverse bends, designers can achieve a lower horizontal emittance. For the case of SLS 2.0, the reduction in emittance is a factor 25. The combination of longitudinal gradient bends with reverse bends is shown in Fig. I.10.8. Technical and beam dynamics considerations for diffraction-limited storage rings: – Magnet design: DLSRs require a significantly more complex magnetic lattice compared to conventional storage rings. The magnetic elements in these lattices, including bending magnets, quadrupoles, and sextupoles, are not only more numerous but also often feature higher magnetic field strengths. The quadrupoles and sextupoles are therefore built with a smaller inner bore. Energy-efficient magnet designs employ permanent magnets for the basic lattice and use electromagnets only where tuning is necessary;
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Electronsthat have a larger energy than the reference particle radiate more, while those that have smaller energy radiate less.
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Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation
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$$ where $\\vartheta$ is the angle at which the photon is scattered. I.10.5.2 Scattering of $\\mathbf { X }$ -rays on atoms In the case of photon energies less than a few keV, the wavelength is longer than the size of the atom. The scattering is then coherent, i.e., the phases of the scattered waves from different parts of the electron cloud add up constructively. The electric field amplitude of the scattered wave is then proportional to the total number of electrons in the atom $Z$ , and the scattered intensity is proportional to $Z ^ { 2 }$ . The total cross section is then $$ \\sigma = Z ^ { 2 } \\sigma _ { T } . $$ The $Z ^ { 2 }$ dependence makes the scattering cross section for heavier atoms much larger compared to lighter ones, significantly influencing how $\\mathrm { \\Delta X }$ -rays are used in science and medicine. When we increase the photon energy, the wavelength becomes smaller than the size of the electron cloud of an atom, and decoherence between the scattered waves reduces the scattering cross section. As an approximation, the cross-section drops off as $1 / E _ { \\gamma } ^ { 2 }$ . The precise drop-off can be described by the atomic form factor $f ^ { 0 }$ , which depends on both the scattering angle and the photon wavelength. It can be parametrized as
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Electronsthat have a larger energy than the reference particle radiate more, while those that have smaller energy radiate less.
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Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation
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File Name:Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation.pdf Chapter I.10 Synchrotron radiation Rasmus Ischebeck Paul Scherrer Institut, Villigen, Switzerland Electrons circulating in a storage ring emit synchrotron radiation. The spectrum of this powerful radiation spans from the far infrared to the $\\boldsymbol { \\mathrm { \\Sigma } } _ { \\mathrm { X } }$ -rays. Synchrotron radiation has evolved from being a mere byproduct of particle acceleration to a powerful tool leveraged in diverse scientific and engineering fields. Indeed, synchrotrons are the most brilliant X-ray sources on Earth, and they find use in a wide range of fields in research. In this chapter, we will look at the generation of radiation of charged particles in an accelerator, at the influence of this on the beam dynamics, and on the physics behind applications of synchrotron radiation for research. I.10.1 Introduction It is difficult to overstate the importance of X-rays for medicine, research and industry. Already a few years after their discovery by Wilhelm Conrad Röntgen, their ability to penetrate matter established Xrays as an important diagnostics tool in medicine. Experiments with $\\mathrm { \\Delta X }$ -rays have come a long way since the inception of the first $\\mathrm { \\Delta } X$ -ray tubes. The short wavelength of $\\mathrm { \\Delta X }$ -rays allowed Rosalynd Franklin and Raymond Gosling to take diffraction images that would lead to the discovery of the structure of DNA. Today, X-ray diffraction is an indispensable tool in structural biology and in pharmaceutical research. Industrial applications of X-rays range from cargo inspection to sterilization and crack detection.
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Blumenfeld_et_al._-_2007_-_Energy_doubling_of_42_GeV_electrons_in_a_metre-scale_plasma_wakefield_accelerator.pdf
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The Livingston plot, shown in Figure 1, illustrates how the progress in achieving the energy frontier has been enabled by the history of invention in accelerator science and technology. One can clearly see that over several decades, there has been an exponential growth in the maximum attained energy. But the exponential growth in maximum achieved energy was made possible by the development of different accelerator technologies (for example Electrostatics, Cyclotrons, Linacs, Synchrotrons, Colliders). As often occurs in any technological field, new accelerating technologies often replaced each other once the previous technology had reached its full potential and saturates its evolution curve [1]. In more recent decades, represented by the LHC collider, the exponential energy growth has started slowing down again. This suggests that existing acceleration technologies have reached their maximum potential and further advancements would require the development of new accelerator concepts, possibly based on more compact and cost-effective methods. Promising emerging techniques, such as laser-driven and beam-driven plasma acceleration, have the potential to reestablish the exponential trend in the energy growth depicted by the Livingston plot. Plasma wakefield accelerator relies on a coherent charge density oscillation in a plasma to provide the accelerating force. The plasma oscillation is driven by an externally injected short pulse, which can be either a laser (LWFA [3]) or an electron beam (PWFA [4]), which blows outward the electrons in an ionized gas (plasma), leaving behind a region of positive charge, as shown in Figure 2. Along the axis where the beam propagates, the electric field causes a trailing pulse of electrons injected near the rear of the bubble to feel a very strong forward acceleration. Gradient up to $1 0 0 \\mathrm { ~ G V / m }$ have been observed in several experiments [5]. Difficulties in the plasma scheme arise from the small scales involved (sub-mm transverse diameter), required micrometer tolerances and stability which may cause beam quality degradation with respect to conventional accelerators. But in recent time the plasma generated beam quality has advanced sufficiently to reach the requirements for driving a Free Electron Laser (FEL). There have been several reports of pilot free-electron lasing in plasma-based accelerators: one relying on LWFA by a team in China [6] and one relying on PWFA by the EuPRAXIA team in Frascati [7,8], Italy. Another experiment run by a French and German team has also recently confirmed seeding of the FEL process in a LWFA plasma accelerator [9].
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Blumenfeld_et_al._-_2007_-_Energy_doubling_of_42_GeV_electrons_in_a_metre-scale_plasma_wakefield_accelerator.pdf
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INTRODUCTION In recent years charged particle acceleration using solidstate nanostructured plasmas has attracted attention as a novel method of achieving ultra-high acceleration gradients, beam manipulation and gamma- or $\\mathrm { \\Delta X }$ -ray generation $[ 1 -$ 10]. In this context, PIC simulations have shown that the excitation of carbon nanotube (CNT) or graphene based multi-channel structures using either a driver beam [1,6] or a laser pulse [2,9] might achieve electric wakefield amplitudes in the order of $\\mathrm { T V / m }$ or beyond. In this paper, we specifically investigate laser wakefield acceleration (LWFA) in multi-hollow nanostructured high density plasmas. In this setup, a single, short, high-intensity pulse drives the wakefield. To excite a wakefield, the laser pulse length $L$ must be in the order of the plasma wavelength $\\lambda _ { p }$ (see for example [11]): $L \\simeq \\lambda _ { p } = 2 \\pi / \\omega _ { p } =$ $2 \\pi \\sqrt { m _ { e } \\varepsilon _ { 0 } / ( n _ { e } e ^ { 2 } ) }$ , where $\\omega _ { p }$ is the angular frequency of the plasma, $\\scriptstyle { \\varepsilon _ { 0 } }$ the vacuum permittivity, $e$ the elementary electric charge, $m _ { e }$ the electron rest mass and $n _ { e }$ the plasma density. This ensures that the excitations created by the ponderomotive force are in phase with the pulse group velocity.
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What limits the acceleration of electron in a plasma wakefield accelerator beyond 85 GeV?
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Blumenfeld_et_al._-_2007_-_Energy_doubling_of_42_GeV_electrons_in_a_metre-scale_plasma_wakefield_accelerator.pdf
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INTRODUCTION To perform physics precision studies or discover physics beyond the Standard Model, high-energy colliders such as the existing Large Hadron Collider (LHC), the past Large Electron-Positron (LEP) or the Future Circular Collider (FCC) [1, 2] are desireable. However, limitations such as speed or radio-frequency characteristics create barriers to achieving higher physics goals, with gradient limits typically in the order of $1 0 0 { \\mathrm { M V / m } }$ due to surface breakdown, arcing, cavity damage, or wakefield effects [3, 4]. In the ’80s-’90s, Tajima and Dawson proposed laser wakefield acceleration (LWFA) where laser pulses were used as wakefield drivers [5]. To further overcome the limits of the existing techniques and achieve acceleration gradients on the order of $\\mathrm { T V / m }$ and beyond, alternative methods based on solid-state plasma wakefield were also proposed [6, 7] Taking into account that solid-state structures can have a density of conduction electrons 4-5 orders of magnitude higher compared to gaseous plasma medium [8], preionised solid-state targets might offer a way to create inhomogeneous structured plasmas, able to sustain ultra-high acceleration gradients [9, 10]. CNT array-based nanostructures can create a structured non-homogeneous plasma with a density modulation wavelength of several $\\mu \\mathrm { m }$ which can be tailored to optimize the acceleration gradient and the confinement of particles [11].
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Blumenfeld_et_al._-_2007_-_Energy_doubling_of_42_GeV_electrons_in_a_metre-scale_plasma_wakefield_accelerator.pdf
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INTRODUCTION Solid-state wakefield acceleration using crystals was proposed in the 1980s and 1990s by T. Tajima and others [1–3] as an alternative particle acceleration technique to sustain $\\mathrm { T V } / \\mathrm { m }$ acceleration gradients. Solid-based acceleration media (e.g. nanostructures or crystals) could offer a possible solution to overcome the plasma wave-breaking limit, which increases with the plasma density [4], since the density of conduction band electrons in solids is four or five orders of magnitude higher than in gaseous plasma mediums. However, natural crystals have two main drawbacks: (i) the beam intensity acceptance is significantly limited by the angstromsize channels and (ii) such small size channels are physically vulnerable to high energy interactions. In this context, nanostructures could offer an excellent way to overcome many of the limitations of natural crystals. For instance, CNT-based structures can help to relax the constraints to more realistic regimes with respect to natural crystals. CNTs are large macromolecules that are unique for their size, shape, and physical properties, presenting the following advantages over natural crystals: (i) transverse acceptances of the order of up to $1 0 0 ~ \\mathrm { { n m } }$ [5] (i.e. three orders of magnitude higher than a typical silicon channel); (ii) larger degree of dimensional flexibility and thermo-mechanical strength; (iii) lower dechannelling rate; and (iv) less disruptive effects such as filamentation and collisions. Consequently, CNTs are considered a robust candidate for solid-state wakefield acceleration. Wakefields in crystals or nanostructures can be induced by means of the excitation of surface plasmonic modes [6, 7] (or simply plasmons), which are high-frequency collective oscillations of the conduction electrons, acting like a structured plasma through the crystalline ionic lattice. However, to properly excite wakefields, the driver dimensions need to match the spatial $( \\sim \\mathsf { n m } )$ and time (sub-femtoseconds) scales of the excited plasmonic oscillations. Wakefield driving sources working on these scales are now experimentally realizable. For instance, attosecond X-ray lasers are possible thanks to the pulse compression technique [8] and, in the case of beam-driven wakefields, future facilities such as FACET-II at SLAC [9] might allow access to quasi-solid electron bunches with densities up to $\\sim 1 0 ^ { 3 0 } \\mathrm { m } ^ { - 3 }$ and sub-micrometer bunch length scale.
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Blumenfeld_et_al._-_2007_-_Energy_doubling_of_42_GeV_electrons_in_a_metre-scale_plasma_wakefield_accelerator.pdf
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THE AWAKE EXPERIMENT AWAKE is an R&D experiment at CERN with the aim to develop proton-driven based plasma wakefield acceleration. The wakefields are driven by highly-relativistic ${ \\mathrm { 4 0 0 G e V } }$ , relativistic factor $\\gamma _ { p + } \\sim 4 2 7 )$ and energetic $( > 1 9 \\mathrm { k J } )$ proton bunches, supplied by the CERN Super Proton Synchrotron (SPS). Since these proton bunches are longer than the plasma wavelength $\\lambda _ { p e }$ (where $\\lambda _ { p e } = 2 \\pi c / \\omega _ { p e }$ , with $\\omega _ { p e } = \\sqrt { n _ { p e } e ^ { 2 } / \\epsilon _ { 0 } m _ { e } }$ is the plasma electron frequency, $c$ the speed of light, $m _ { e }$ the electron mass, $e$ the electron charge, $\\epsilon _ { 0 }$ the vacuum permittivity and $n _ { p e }$ the plasma electron density) and less dense than the plasma $\\hat { ( n _ { b } < \\sim 1 0 ^ { - 3 } n _ { p e } }$ where $n _ { b }$ is the bunch density), the proton bunches have to be self-modulated to excite wakefields with $\\mathrm { G V / m }$ amplitudes [1, 2]; this requires $n _ { p e } > 1 0 ^ { 1 4 } \\mathrm { c m } ^ { - 3 }$ (corresponding to $\\lambda _ { p e } < 3 \\mathrm { m m } )$ ). The plasma is created by laser ionisation (pulse length: ${ \\sim } 1 0 0$ fs, energy per pulse: $\\sim 1 0 0 \\mathrm { m J }$ , central wavelength: $8 0 0 \\mathrm { n m }$ ) of rubidium vapour [3, 4]. It is $1 0 \\mathrm { m }$ long, with a radius $> \\sim 1 \\mathrm { m m }$ . Seeded proton bunch selfmodulation and subsequent wakefield growth, as well as the acceleration of externally injected witness electrons was demonstrated in AWAKE Run 1 [5–7].
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What limits the acceleration of electron in a plasma wakefield accelerator beyond 85 GeV?
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Blumenfeld_et_al._-_2007_-_Energy_doubling_of_42_GeV_electrons_in_a_metre-scale_plasma_wakefield_accelerator.pdf
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ACCELERATION TO HIGHER ENERGIES Plasma acceleration at FLASHFoward is limited to maximum acceleration gradients $\\propto \\sqrt { n _ { e } }$ of $1 { - } 2 \\mathrm { G V } \\mathrm { m } ^ { - 1 }$ . The restriction on the plasma density is that both the driver and the trailing bunch, which should carry considerable charge, must fit into the first wakefield period. Stronger bunch compression can, therefore, lead to higher acceleration gradients, although this risks degradation of the bunches from coherent synchrotron radiation effects in the bunch compressors. The bunch length and $n _ { e }$ used at FLASHForward represents a balance between desiring high bunch quality and rapid plasma acceleration. In order to produce high energy gains with simultaneous high overall energy efficiency, it is necessary to use a long plasma cell. The first step towards this was taken by attempting to accelerate many tens of $\\mathsf { p C }$ at $1 \\mathrm { G V } \\mathrm { m } ^ { - 1 }$ in a $1 9 5 \\mathrm { m m }$ -long plasma cell. Figure 2 (a) displays driver and trailing-bunch spectra from this cell, where the scraper position and width were manually altered from the optimised working point from the $5 0 \\mathrm { m m }$ cell. Figure 2 (b) displays a histogram of the measured trailing bunch energy. Trailing bunch acceleration from $1 2 0 8 \\mathrm { M e V }$ to $( 1 4 6 0 \\pm 6 )$ ) MeV was observed—an energy gain of $( 2 5 2 \\pm 6 ) \\mathrm { M e V }$ at $1 . 3 \\mathrm { G V } \\mathrm { m } ^ { - 1 }$ . The energy uncertainty is the standard deviation, which is at the level of $2 . 6 \\%$ . Similar histograms are shown for the charge and full width at half maximum (FWHM) percentage energy spread of the trailing bunches in Fig. 2 (c) and (d), with mean values of $Q = ( 4 0 \\pm 3 ) \\mathrm { p C }$ and $\\sigma _ { E , \\mathrm { F W H M } } = ( 0 . 1 7 \\pm 0 . 0 4 ) \\ : \\%$ , respectively, the latter being measured on a narrowband spectrometer with higher spectral resolution. The average total energy gained by the trailing bunch was $\\Delta W = Q \\Delta E = \\left( 1 0 \\pm 1 \\right) \\mathrm { m J }$ which for the incoming driver with a charge of $2 3 0 \\mathrm { p C }$ and mean electron energy of $1 2 0 0 \\mathrm { M e V }$ corresponds to an overall energy transfer efficiency of $( 3 . 6 \\pm 0 . 3 ) \\%$ .
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Blumenfeld_et_al._-_2007_-_Energy_doubling_of_42_GeV_electrons_in_a_metre-scale_plasma_wakefield_accelerator.pdf
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File Name:PROGRESS_TOWARDS_HIGH-QUALITY,_HIGH-REPETITION-RATE.pdf PROGRESS TOWARDS HIGH-QUALITY, HIGH-REPETITION-RATE PLASMA ACCELERATION AT FLASHForward J. C. Wood∗,1, L. Boulton1, J. Beinortaite˙1,2, J. Björklund Svensson1, G. Boyle1, J. Cowley3, A. Ferran Pousa1, B. Foster1,2, M. J. Garland1, P. González-Caminal1, M. Huck1, H. Jones1, A. Kanekar1, C. A. Lindstrøm,1,4, G. Loisch1, T. Long1, S. M. Mewes1, J. Osterhoff1, F. Peña1, S. Schröder1, M. Thévenet1, S. Wesch1, M. Wing1,2 and R. D’Arcy1,3 1Deutsches Elektronen-Synchrotron DESY, Hamburg, Germany 2University College London, United Kingdom 3 University of Oxford, United Kingdom 4 University of Oslo, Norway Abstract Plasma-wakefield acceleration represents an exciting route towards reducing the footprint of future high-energy electron accelerators by accelerating bunches in fields exceeding ${ \\mathrm { ~ 1 ~ G V / m } }$ . One such technique employs a doublebunch structure where the trailing bunch is accelerated in the field of a high-amplitude plasma-density wake driven by the leading bunch. A future particle collider or photon science facility incorporating plasma accelerators will be required to accelerate up to millions of bunches per second with high energy efficiency while preserving the brightness of the accelerating bunch. This contribution presents the latest progress towards these goals at FLASHForward (DESY). INTRODUCTION Electron-bunch-driven plasma wakefield accelerators (PWFAs) [1, 2] have the potential to greatly extend the energy reach of existing and future electron accelerators in a compact footprint by boosting the energy of bunches in fields $> 1 \\mathrm { G V } \\mathrm { m } ^ { - 1 }$ . A short, relativistic electron bunch of density $n _ { b }$ travelling through an underdense plasma of density $n _ { e } \\ll n _ { b }$ will expel all nearby plasma electrons, driving a fully-cavitated plasma wake that travels at close to the speed of light [3, 4]. The heavier plasma ions barely move over short timescales, providing linear focussing fields that can preserve bunch quality [5], and a strong longitudinal field providing rapid, phase-locked acceleration for a trailing bunch. By shaping the trailing bunch, the wakefield can be loaded to preserve the energy spread of the entire trailing bunch, while simultaneously transferring energy from the driver to the trailing bunch with high efficiency [6, 7].
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Blumenfeld_et_al._-_2007_-_Energy_doubling_of_42_GeV_electrons_in_a_metre-scale_plasma_wakefield_accelerator.pdf
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CONCLUSION [1] T. Behnke et al., “The international linear collider technical design report-volume 1: Executive summary,” 2013. doi:10.48550/arXiv.1306.6327 [2] J. N. Galayda, “The LCLS-II: A High Power Upgrade to the LCLS”, in Proc. IPAC’18, Vancouver, Canada, Apr.-May 2018, pp. 18–23. doi:10.18429/JACoW-IPAC2018-MOYGB2 [3] M. Burns et al., “Dahrt accelerators update and plans for initial operation,” in Proceedings of the 1999 Particle Accelerator Conference (Cat. No.99CH36366), vol. 1, 1999, 617–621. doi:10.1109/PAC.1999.795776 [4] W. Gai et al., “Experimental demonstration of wake-field effects in dielectric structures,” Phys. Rev. Lett., vol. 61, no. 24, p. 2756, 1988. doi:10.1103/PhysRevLett.61.2756. [5] B. O’Shea et al., “Observation of acceleration and deceleration in gigaelectron-volt-per-metre gradient dielectric wakefield accelerators,” Nat. Commun., vol. 7, no. 1, pp. 1–7, 2016. doi:10.1038/ncomms12763 [6] M. Thompson et al., “Breakdown limits on gigavolt-permeter electron-beam-driven wakefields in dielectric structures,” Phys. Rev. Lett., vol. 100, no. 21, p. 214801, 2008. doi:10.1103/PhysRevLett.100.214801 [7] A. Kanareykin, W. Gai, C.-J. Jing, A. L. Kustov, J. G. Power, and P. Schoessow, “Beam Breakup Instabilities in Dielectric Structures”, in Proc. PAC’07, Albuquerque, NM, USA, Jun. 2007, paper FRPMS094, pp. 4300–4302. [8] C. Li, W. Gai, C. Jing, J. G. Power, C. X. Tang, and A. Zholents, “High gradient limits due to single bunch beam breakup in a collinear dielectric wakefield accelerator,” Phys. Rev. ST Accel. Beams, vol. 17, p. 091302, 2014. doi:10.1103/PhysRevSTAB.17.091302
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Blumenfeld_et_al._-_2007_-_Energy_doubling_of_42_GeV_electrons_in_a_metre-scale_plasma_wakefield_accelerator.pdf
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In the first plasma zone $( z ~ \\lesssim ~ 3 0 0 0 ~ \\mu \\mathrm { m } )$ , nitrogen is present, and the laser pulse can get strong $a _ { 0 } > 1 . 5$ , ionizing electrons from the inner shells of nitrogen, which are eventually captured in the wakefield bubble, giving rise to the electron beam. There, the beam emittance is set. It is higher in the laser pulse’s polarization plane due to oscillations of the electric field vector E. Low emittance requires a small field amplitude, whereas, in opposition, high charge necessitates a larger field amplitude. In the second plasma zone $( 3 0 0 0 ~ \\mu \\mathrm { m } \\lesssim ~ z \\lesssim 4 5 0 0 ~ \\mu \\mathrm { m } )$ , only hydrogen is present. There, electrons trapped in the wakefield bubble are significantly focused and accelerated to hundreds of $\\mathrm { \\mathbf { M e V } } .$ . The electric field is determined by the bubble which is generated by ponderomotive forces that depend on the field gradient amplitude squared $| \\nabla { \\bf E } | ^ { 2 }$ . Since the latter present cylindrical symmetry, the ratio $\\epsilon _ { x } / \\epsilon _ { y }$ stays nearly constant, and the Twiss parameters $( \\alpha , \\beta , \\gamma ) _ { x , y }$ are nearly identical in both $x$ and $y$ −directions. Strong focusing forces significantly reduce beam’s transverse size while $\\gamma _ { x , y }$ reads $\\sim 1 0 ^ { 3 } ~ \\mathrm { m } ^ { - 1 }$ . Energy spread usually reduces during acceleration but can increase due to longitudinal wakefield variations along the bunch length. Since high charge results in longer bunch length, there is a competition between high charge and low energy spread.
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Blumenfeld_et_al._-_2007_-_Energy_doubling_of_42_GeV_electrons_in_a_metre-scale_plasma_wakefield_accelerator.pdf
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FLASHForward is a plasma acceleration experiment using high-quality electron bunches from the linac of the FLASH FEL [8], with the goal of developing plasma technologies to match the beam-quality-preserving and highrepetition rate acceleration of radiofrequency accelerators. Notable results include the preservation of transverse emittance during acceleration [5], the preservation of per-mille energy spread [9], and the demonstration that plasma accelerators can recover rapidly enough to support $O \\left( { 1 0 } \\mathbf { M } \\mathbf { H } \\mathbf { z } \\right)$ 1 interbunch repetition rates [10]. Ref. [9] also showed that the instantaneous transfer efficiency, meaning the energy gained by the trailing bunch divided by the energy lost by the driver, was as high as $( 4 2 \\pm 4 ) \\ \\%$ . Further experimental studies showed that $( 5 9 \\pm 3 ) \\ \\%$ of the driver bunch energy can be deposited into the plasma before part of the driver bunch was completely decelerated [11]. These results suggest that a plasma stage with an overall efficiency (trailing bunch energy gain divided by initial driver energy) of tens of percent could be within reach. Recent results from FLASHForward are presented in this paper, working towards this goal. In a useful PWFA, a large trailing bunch charge must be coupled into the wakefield and accelerated with low energy spread. Wakefield acceleration can be affected by many input parameters, therefore, Bayesian optimisation routines have been employed to control the acceleration process. This paper reports on optimisation results from a $5 0 \\mathrm { m m }$ plasma cell, followed by a demonstration of acceleration by more than $2 0 0 \\mathrm { M e V }$ in a $1 9 5 \\mathrm { m m }$ plasma. To push the overall efficiency higher in our setup, a $5 0 0 \\mathrm { m m }$ discharge plasma source was developed and its characterisation is described.
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Blumenfeld_et_al._-_2007_-_Energy_doubling_of_42_GeV_electrons_in_a_metre-scale_plasma_wakefield_accelerator.pdf
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File Name:ION-ION_COLLISIONS_IN_PLASMA_WAKEFIELD_ACCELERATORS.pdf ION-ION COLLISIONS IN PLASMA WAKEFIELD ACCELERATORS M.Yadav‚àó, K. Letko, J.B. Rosenzweig University of California, Los Angeles, California, USA Abstract The plasma wakefield accelerator, with acceleration gradients ranging from $\\mathrm { G e V / m }$ to $\\mathrm { T e V } / \\mathrm { m }$ , holds promise for propelling particles to high energies in linear colliders. This results in exceptionally bright beams characterized by intense ion-derived focusing, leading to the collapse of plasma ions. Our study extends prior research focused on electron acceleration by investigating ion-ion collisions, studying different collision models and emphasizing the near-equilibrium state post-ion collapse using the OSIRIS Particle -in-cell (PIC) code. Notably, our findings reveal that parametric excitations arising from plasma non-uniformity have an insignificant impact on phase space diffusion, a crucial insight for optimizing linear colliders. INTRODUCTION Plasma wakefield acceleration (PWFA) employs waves in a plasma medium chosen to naturally avoid breakdown issues. These waves are excited by an intense drive beam to accelerate a trailing beam. PWFAs have already demonstrated acceleration gradients exceeding $5 0 \\mathrm { G e V / m }$ . To explore the suitability of the PWFA for linear collider applications, proposals [1, 2] have been put forward that analyze the use of an afterburner at the end of a conventional linear collider injector, with the goal of doubling the beam energy [3].
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Blumenfeld_et_al._-_2007_-_Energy_doubling_of_42_GeV_electrons_in_a_metre-scale_plasma_wakefield_accelerator.pdf
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LASER-PLASMA ACCELERATOR Recent demonstrations of ${ \\sim } 1 \\mu \\mathrm { C }$ electron acceleration from kilo-joule laser OMEGA EP [2] and stable generation of ${ \\sim } 2 . 2 \\mathrm { p C }$ electron acceleration at $2 . 5 \\mathrm { H z }$ with $1 7 0 \\mathrm { m J }$ Ti-Sapphire laser [3] in the MeV range indicate promise of MeV range laser wakefield accelerators for application in various fields. We consider employing the supersonic gas jet target [4] used in both experiments [2, 3] along with ARCO Hybrid Ti-Saphh laser from Amplitude [5] or Quark 30/45 from THALES [6] to drive a laser plasma accelerator with mean electron energy of $2 0 \\mathrm { M e V }$ , total charge of $1 2 \\mathrm { - } 2 2 \\mathrm { p C }$ and geometric emittance $< 3 3 \\mu \\mathrm { m }$ mrad and beam divergence of less than $5 ^ { \\circ }$ . Following similar approach to Ref. [7], we estimate the desired laser and gas-target parameters for laser wakefield acceleration [8] and the corresponding anticipated plasma and electron beam parameters in Table 1. We note that $\\leq 1 \\%$ of the electron beam charge with energy spread $\\leq 1 0 ^ { - 3 }$ transmits through the collimator (Fig. 1) to be accelerated in the cryomodules.
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Blumenfeld_et_al._-_2007_-_Energy_doubling_of_42_GeV_electrons_in_a_metre-scale_plasma_wakefield_accelerator.pdf
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It has been demonstrated that PWFA can be optimized with large datasets of accelerator measurements [3], which suggests that a search for an optimum could be automated [4]. At laser-driven plasma wakefield accelerators, Bayesian optimization was already applied successfully [5–7]. The objective of this work is to examine how simulations using a computational model of the FACET-II beamline could serve as a guide for experimental efforts at increasing the energy gain of PWFA while maintaining or reducing transverse emittance growth, a figure of merit for beam quality. A start-to-end model of the beamline was developed and used in a numerical optimization schema to determine the final focusing quadrupole magnet strengths which would best optimize these two beam characteristics. During the PWFA process, the energy gain is calculated by quantifying the difference between the mean energy of the particle beam at the beginning and end of the plasma process. The mean energy gain divided by the length of the plasma $( L _ { \\mathrm { p l a s m a } } )$ , gives the acceleration gradient, or the amount of energy the particles gained on average per meter of travel: INTRODUCTION A relatively new method of providing high accelerating gradients for charged particles in the Accelerator Physics community is known as Plasma Wakefield Acceleration (PWFA). This technique, which uses strong electromagnetic fields generated in plasma, has demonstrated accelerating gradients of over $1 0 \\mathrm { G e V / m }$ [1] which is orders of magnitude larger than traditional radiofrequency (RF) technology. The wake field, excited by a drive electron beam transfers energy to the witness electron beam trailing in the back of the wake. One of the challenges in the development of PWFA is that the plasma wake not only provides strong longitudinal fields which accelerate charged particles but it also makes strong transverse fields that can lead to deterioration of beam quality. The ability to sustain good beam quality and high accelerating gradients is a vital concern that we hope to address.
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Blumenfeld_et_al._-_2007_-_Energy_doubling_of_42_GeV_electrons_in_a_metre-scale_plasma_wakefield_accelerator.pdf
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Current experimental and theoretical research on PWFAs has focused on the nonlinear blowout regime due to its favorable properties for acceleration and focusing. In the blowout regime, the electron beam density is much greater than the ambient plasma electron density, and the collective fields of the beam eject the plasma electrons from the region near the beam axis. This creates a bubble of negligible electron density [4]. Furthermore, in this scenario, an electromagnetic wave is trapped inside of this bubble that provides acceleration in uniform phase fronts, as in standard relativistic electron accelerators. Further, in this scenario the plasma ions left behind, if undisturbed, provide a uniformly charged column that yields strong, linear (emittance-preserving) focusing. In this way, one may achieve high quality, low energy spread acceleration without emittance growth due to geometric aberrations. However, the stationary ion assumption does not hold in the proposed PWFA afterburner case [5]. In this case the plasma ions fall toward the center of the beam. The degree of ion motion can be quantified by a dimensionless parameter known as the phase advance $$ \\Delta \\phi = 2 \\pi \\sigma _ { z } \\sqrt { \\frac { r _ { e } Z _ { i } n _ { b , 0 } m _ { e } } { m _ { i } } }
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Blumenfeld_et_al._-_2007_-_Energy_doubling_of_42_GeV_electrons_in_a_metre-scale_plasma_wakefield_accelerator.pdf
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File Name:Blumenfeld_et_al._-_2007_-_Energy_doubling_of_42_GeV_electrons_in_a_metre-scale_plasma_wakefield_accelerator.pdf Energy doubling of 42 GeV electrons in a metre-scale plasma wakefield accelerator Ian Blumenfeld1, Christopher E. Clayton2, Franz-Josef Decker1, Mark J. Hogan1, Chengkun Huang2, Rasmus Ischebeck1, Richard Iverson1, Chandrashekhar Joshi2, Thomas Katsouleas3, Neil Kirby1, Wei Lu2, Kenneth A. Marsh2, Warren B. Mori2, Patric Muggli3, Erdem ${ \\mathsf { O } } z ^ { 3 }$ , Robert H. Siemann1, Dieter Walz1 & Miaomiao Zhou2 The energy frontier of particle physics is several trillion electron volts, but colliders capable of reaching this regime (such as the Large Hadron Collider and the International Linear Collider) are costly and time-consuming to build; it is therefore important to explore new methods of accelerating particles to high energies. Plasma-based accelerators are particularly attractive because they are capable of producing accelerating fields that are orders of magnitude larger than those used in conventional colliders1–3. In these accelerators, a drive beam (either laser or particle) produces a plasma wave (wakefield) that accelerates charged particles4–11. The ultimate utility of plasma accelerators will depend on sustaining ultrahigh accelerating fields over a substantial length to achieve a significant energy gain. Here we show that an energy gain of more than $4 2 \\mathbf { G e V }$ is achieved in a plasma wakefield accelerator of ${ \\bf 8 5 c m }$ length, driven by a $4 2 \\mathbf { G e V }$ electron beam at the Stanford Linear Accelerator Center (SLAC). The results are in excellent agreement with the predictions of three-dimensional particle-in-cell simulations. Most of the beam electrons lose energy to the plasma wave, but some electrons in the back of the same beam pulse are accelerated with a field of ${ \\sim } 5 2 \\mathrm { G V } \\mathrm { m } ^ { - 1 }$ . This effectively doubles their energy, producing the energy gain of the 3-km-long SLAC accelerator in less than a metre for a small fraction of the electrons in the injected bunch. This is an important step towards demonstrating the viability of plasma accelerators for high-energy physics applications.
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Blumenfeld_et_al._-_2007_-_Energy_doubling_of_42_GeV_electrons_in_a_metre-scale_plasma_wakefield_accelerator.pdf
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In a plasma wakefield accelerator large-amplitude electric fields result from space-charge waves excited by the passage of an ultrarelativistic electron beam through a plasma12. A fully ionized plasma can be formed in a neutral vapour when the radial electric field of the electron beam exceeds the field ionization threshold13. The ionization occurs in a narrow region in the front of the beam. This ionization front produces a plasma that has a radius much larger than the beam itself. If the beam density exceeds the plasma density, the plasma electrons are expelled from the volume of the electron pulse, leaving a column of more massive ions behind14. Subsequently, the expelled plasma electrons are pulled back (by the ions) to the beam axis behind the pulse, overshoot, and set up a space-charge oscillation or wake. The longitudinal field of this wake varies continuously along the pulse, decelerating its core but accelerating the particles in the back. The ion column also provides a focusing force15 that guides the beam over many diffraction lengths, allowing an efficient transfer of the beam energy to the wake. This force also causes the transverse size of the beam to oscillate as it propagates through the plasma—the socalled betatron oscillations (see Supplementary Movie 1).
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Blumenfeld_et_al._-_2007_-_Energy_doubling_of_42_GeV_electrons_in_a_metre-scale_plasma_wakefield_accelerator.pdf
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The images have been corrected at the level of a few per cent for the nonuniform collection efficiency of the optics. Pixel-to-pixel variations in the CCD offset and a common mode have been subtracted; the signal from X-rays that hit the CCD directly has been eliminated. Simulations. The simulations were done using the quasi-static, three-dimensional, particle-in-cell code called QuickPIC. The three-dimensional computational grid forms a box xy $z ( 2 4 0 \\mu \\mathrm { m } \\times 2 4 0 \\mu \\mathrm { m } \\times 2 6 0 \\mu \\mathrm { m } )$ in size whose axial coordinate is z-ct. Therefore, the simulation window moves at the speed of light, which is very close to the beam speed in the $z$ direction. The number of grid points is $2 5 6 \\times 2 5 6 \\times 5 1 2$ respectively. The beam is initialized so that in vacuum, it would focus $1 5 \\mathrm { c m }$ beyond the start of the lithium vapour with a $1 0 \\mu \\mathrm { m }$ root-mean-square spot size. The longitudinal current profile is extracted from the unique LiTrack simulation that matches the experimentally measured beam spectrum produced by the SLAC accelerator. The resulting current profile approximates a gaussian $( \\sigma _ { z } \\approx 1 5 \\mu \\mathrm { m } )$ with a small tail. We use 8.4 million particles for the beam and $2 . 6 \\times 1 0 ^ { 5 }$ particles for each ‘slice’ of lithium. In the quasi-static approximation, as the entire beam moves through a slice of gas, the lithium ionizes, the resulting plasma evolves transversely and, to account for the axial motion, the charge on each particle is suitably changed. The resulting plasma forces are stored for each slice and are then used to advance the momentum and position of each beam electron. The beam electrons are advanced every $1 . 0 \\mathrm { m m }$ , which is 1/26th of a betatron wavelength for 42 GeV electrons in the flat density region. The simulations were done on the Apple X-serve Dawson Cluster at UCLA.
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Blumenfeld_et_al._-_2007_-_Energy_doubling_of_42_GeV_electrons_in_a_metre-scale_plasma_wakefield_accelerator.pdf
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Thus, the full ionization extends over a radius of more than $1 0 0 \\mu \\mathrm { m }$ and ionization begins far earlier than the peak of the bunch current. Because the ionization region extends over a radius larger than the plasma collisionless skin depth $c / \\omega _ { \\mathrm { p } } ,$ where $\\omega _ { \\mathrm { p } } = ( n _ { \\mathrm { e } } e ^ { 2 } / \\varepsilon _ { 0 } m _ { \\mathrm { e } } ) ^ { 1 / 2 }$ is the plasma angular frequency; $e$ is the charge on the electron, $\\scriptstyle { \\varepsilon _ { 0 } }$ is the permittivity of free space and $m _ { \\mathrm { e } }$ is the mass of the electron), the wake is similar to that in a preformed plasma. Energy measurement. The energy spectrometer consists of a dipole magnet that disperses the electrons vertically according to their momentum $\\boldsymbol { p }$ . The dispersion can be closely approximated by a deflection at the centre of the magnet: $\\theta _ { 1 } = e \\int B \\mathrm { d } L / p$ . Using the measured dispersion, its integrated magnetic flux density #BdL was calculated to be $1 . 2 \\mathrm { T m }$ . In general, all particles in a pulse leave the plasma from a well-defined spot, but with a non-negligible exit angle $\\theta _ { 0 }$ . To discriminate between a vertical exit angle and the deflection by the magnet, the particle distribution is measured at two planes, $8 6 \\mathrm { c m }$ and $1 8 6 \\mathrm { c m }$ downstream of the centre of the dipole (Fig. 1).
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Blumenfeld_et_al._-_2007_-_Energy_doubling_of_42_GeV_electrons_in_a_metre-scale_plasma_wakefield_accelerator.pdf
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The beam has geometric transverse emittances of $\\varepsilon _ { x } = 9 . 5 \\times 1 0 ^ { - 1 0 } \\mathrm { m }$ and $\\varepsilon _ { y } = 1 . 2 \\times 1 0 ^ { - 1 0 } \\mathrm { m }$ . It is focused with a quadrupole doublet to a spot with $1 0 \\mu \\mathrm { m }$ radius at the entrance of the plasma. With this beam energy, bunch length and spot size, the corresponding power density is $3 \\times 1 0 ^ { 2 0 } \\mathrm { W } \\mathrm { c m } ^ { - 2 }$ . Plasma generation. A column of lithium vapour with a density of $2 . 7 \\times 1 0 ^ { 1 7 } \\mathrm { c m } ^ { - 3 }$ is produced in a heat-pipe oven21. The lithium vapour is confined by a helium buffer gas, which is in turn separated from the beam-line vacuum by a $5 0 \\mathrm { - } \\mu \\mathrm { m }$ -thick beryllium window upstream and by a $7 5 \\mathrm { - } \\mu \\mathrm { m }$ -thick beryllium window downstream. Lithium was chosen because of the low ionization potential of its first electron $( 5 . 4 \\mathrm { e V } )$ and the relatively high potential for its two subsequent electrons (76 and $1 2 2 \\mathrm { e V }$ ). In the present experiments the transverse electric field of the ultrashort electron pulses is large enough to field-ionize the first lithium electron over a timescale shorter than the bunch duration. The ADK theory for field ionization22 indicates that full ionization occurs in the volume surrounding the pulse in which the electric field exceeds ${ \\sim } 6 \\mathrm { G V m } ^ { - 1 }$ .
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Blumenfeld_et_al._-_2007_-_Energy_doubling_of_42_GeV_electrons_in_a_metre-scale_plasma_wakefield_accelerator.pdf
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At each of the two planes, the particle distribution is measured by imaging Cherenkov radiation emitted as the electrons pass through a $1 5 \\mathrm { - m m }$ -wide air gap established by two silicon wafers (not shown in Fig. 1), positioned at an angle of $4 5 ^ { \\circ }$ to the beam. The second wafer acts as a mirror and deflects the Cherenkov light into a lens that images the origin of the light onto a cooled charge-coupled device camera (CCD). The electrons pass the silicon almost unperturbed. A system of equations is set up relating the offsets at the two planes to two angles, the exit angle at the plasma $\\theta _ { 0 }$ and the deflection angle in the magnet $\\theta _ { 1 }$ (see Fig. 1). For each feature in the spectrum that can be identified on both screens, for instance scalloping of the beam shown in Fig. 2a, this system of equations has been solved for $\\theta _ { 0 }$ and $\\theta _ { 1 }$ , the latter angle giving the particle energy. The highest-energy feature that can clearly be resolved (see Fig. 2a) is used to determine the energy gain for this event. The uncertainty in the energy measurement is dominated by the uncertainty in the determination of the position of this feature.
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What physical phenomena makes a DLA work?
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reverse the Cherenkov effect and the Smith-Purcell effect
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Beam_Dynamics_in_Dielectric_Laser_Acceleration.pdf
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DIELECTRIC LASER ACCELERATORS Dielectric laser accelerators (DLAs) are optical-scale lithographically-fabricated laser-driven particle accelerators. Typical laser pulse lengths are 0.1 to 1 ps, and the peak surface electric fields of the dielectric materials in the $\\mathrm { G V / m }$ regime, allowing a potential length reduction of 1 or 2 orders of magnitude compared with conventional accelerators. Power sources for DLA-based accelerators are lasers, whose required pulse energies are in the mJ range, while repetition rates can be 10s of MHz [7]. An important point relating to dark sector searches is that laser- and beam-driven plasma accelerators (denoted by LWA and PWFA, respectively) feature characteristic bunch charges of order $1 \\mathrm { n C }$ at about $1 5 \\mathrm { k H z }$ repetition rate, whereas DLAs have much lower bunch charges of order 1 fC (or a few 1000 electrons per bunch) at a much higher repetition rate. This di!erence is clearly evident from Table 1, which was assembled for the European Strategy’s Accelerator R&D Roadmap [5]. For all three types of accelerators, the e"ciency of converting wall-plug power to beam power is forecast to exceed $1 0 \\%$ In view of their high repetition rate and low bunch charge, however, the DLAs are a particularly appealing option for indirect DM searches, where individual incident electron tagging and characterization is a key asset.
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