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expert | Who first observed synchrotron radiation and when? | It was first observed on April 24, 1947, by Herb Pollock, Robert Langmuir, Frank Elder, and Anatole Gurewitsch at General Electric¬Ç√Ñ√¥s Research Lab in Schenectady, New York. | Fact | Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation | ‚Äì 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; ‚Äì 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: ‚Äì 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; | augmentation | NO | 0 |
IPAC | Why are very accurate measurements of beam size required for dielectric laser accelerators? | To ensure that the beam size fits into the small structure aperture | Reasoning | Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf | INTRODUCTION Accurate beam size measurements are of utmost importance for current and future particle accelerators. The transverse dimensions of the particle beams directly impact the luminosity in particle colliders [1] and determine the quality of the emitted X-rays in synchrotron light sources [2]. Moreover, measurements of the transverse beam sizes in combination with knowledge of the machine optics functions allow accelerator scientists to infer the beam emittance, a fundamental parameter to quantify the performances of particle accelerators [3]. The analysis of the emitted Synchrotron Radiation (SR) is perhaps the most convenient method to measure the beam size in light sources [4]. In this context, beam size measurement techniques can be grouped into either direct imaging or interferometry, of which the X-ray pinhole camera and the double-slit scheme are paradigmatic examples [5, 6]. In direct imaging techniques, light from an aperture forms a magnified image of the source. The two-dimensional (2D) beam profile is available, but di!raction e!ects pose serious challenges for the detection of small beam sizes [4]. Interferometry represents an interesting option to overcome such challenges, since in this case resolution is ultimately limited by the radiation wavelength. In interferometric techniques, light from di!erent apertures is combined to form interference patterns, and the beam size is retrieved from the visibility of the interference fringes [7]. However, most techniques are restricted to one-dimensional (1D) measurements and typically employed with visible light [4]. | augmentation | NO | 0 |
IPAC | Why are very accurate measurements of beam size required for dielectric laser accelerators? | To ensure that the beam size fits into the small structure aperture | Reasoning | Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf | MEASUREMENT ERRORS The accuracy of beam size measurements is a!ected by various factors, such as CCD noise, beam jitter, and beamline vibrations. The resulting errors, denoted by $\\Delta \\sigma$ , are related to the errors in visibility measurements, $\\Delta \\lvert \\gamma \\rvert$ , by the formula $$ \\Delta \\sigma = - \\frac { 1 } { \\sqrt { 8 } } \\frac { \\lambda L } { \\pi D } \\frac { 1 } { | \\gamma | \\sqrt { \\ln \\frac { 1 } { | \\gamma | } } } \\Delta | \\gamma | . $$ Assuming a visibility measurement error of 0.01, Fig. 2 shows the beam size measurement error as a function of beam size for di!erent acceptance angles of two slits. Achieving an accuracy of $0 . 2 \\mu \\mathrm { m }$ for a beam size of around $1 0 \\mu \\mathrm { m }$ requires an acceptance angle of approximately 6 mrad. Ideally, two diagnostic beamlines at di!erent source points are needed to measure both beam emittance and energy spread independently. These two source points should have di!erent dominant beam size contributions from either Betatron oscillation or dispersion functions. Due to cost and space constraints, a single diagnostic beamline will be built based on dipole 7, sharing the similar front-end vacuum system design as the IR user beamline. The energy spread will be measured independently with a extracted beam at the Storagre-Ring-to-Accumulator (STA) transferline with less than $5 \\%$ resolution. | augmentation | NO | 0 |
IPAC | Why are very accurate measurements of beam size required for dielectric laser accelerators? | To ensure that the beam size fits into the small structure aperture | Reasoning | Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf | INTRODUCTION Particle accelerators have revolutionized our understanding of the universe and enabled numerous technological advancements. However, conventional accelerators have limitations such as high cost and large size. This has led the accelerator scientific community to look up for smaller and cheaper alternatives with equal or even increased performance compared with their mainstream peers. One promising device for such an ambitious goal is the Dielectric Laser-driven Accelerator (DLA). The latest years advancements in the fields of laser technology and the latest achievements in the design of dielectric Photonic-Crystal devices have been driving a growing interest in DLAs microstructures [1]. Thanks to the low ohmic-losses and the higher breakdown thresholds of the dielectrics with respect to the conventional metallic RF Linear Accelerators, the DLAs show a significant improvement of the acceleration gradient (in the $\\mathrm { G V / m }$ regime), leading also to scaled size devices and thus to orders of magnitude costs reduction with respect to the RF metallic accelerating structures [2]. For these reasons, several periodic structures have been proposed for laser-driven acceleration: photonic bandgap (PBG) fibers [3], side-coupled non-co-linear structures [4], 3D woodpile geometries [5], metamaterials-based optical dielectric accelerators [6]. Several PhC can be employed in order to obtain waveguide–or cavity–based accelerating structures. The wide range of potential applications [7] for these compact devices make them a significant instrument for futures technologies and experiments. | augmentation | NO | 0 |
IPAC | Why are very accurate measurements of beam size required for dielectric laser accelerators? | To ensure that the beam size fits into the small structure aperture | Reasoning | Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf | Table: Caption: Table 2: Parameters of the beam used to test the alternating gradient dielectric structure as measured at the entrance to the structure by a three-screen measurement. Body: <html><body><table><tr><td>Charge (Q) Energy (U) RMS beam size (σ)</td><td>X</td><td>1 nC 61MeV 0.61 mm</td></tr><tr><td>Emittance (ε)</td><td>Y X Y</td><td>0.55 mm 50 μm Rad 39 μm Rad</td></tr><tr><td>β</td><td>X Y</td><td>0.908 m 0.93 m</td></tr><tr><td>a</td><td>X Y</td><td>1.327Rad 1.216 Rad</td></tr></table></body></html> EXPERIMENT To test the alternating dielectric structure configuration experimentally we constructed an apparatus as seen in Fig. 2 which gave us total transverse control over the structure positioning. The parameters for the dielctric structure are available in Table 1 although it should be noted that the first and last segments of dielectric are half-length to eliminate secular drift. The slab motion is controlled via motorized linear actuators to allow for real-time adjustments of the structure configuration while running. Slab alignment is provided by precision rods that are referenced to the vacuum flange faces and then trimmed to provide parallelism between opposing dielectric faces. Once the structure was assembled we installed it in the location indicated in Fig. 3 and aligned it to the nominal beam axis with a simple He-Ne laser checking the angular orientation of the structure with the diffraction pattern as the laser passed through the fully closed slab arrays. Final dielectric positioning was done by observing the effect of the structure on the beam. | augmentation | NO | 0 |
IPAC | Why are very accurate measurements of beam size required for dielectric laser accelerators? | To ensure that the beam size fits into the small structure aperture | Reasoning | Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf | File Name:DIAGNOSTICS_BEAMLINE_DEVELOPMENT_FOR_ALS-U#U2192.pdf DIAGNOSTICS BEAMLINE DEVELOPMENT FOR ALS-U C. Sun†, S.D. Santis, L. Kistulentz, K. Mccombs and H. Muratagic Lawrence Berkeley National Laboratory, Berkeley, CA 94706, USA Abstract INTERFEROMETER TECHNIQUES The Advanced Light Source (ALS) at Lawrence Berkeley National Laboratory is currently undergoing an upgrade known as ALS-U. As part of this upgrade, the existing TripleBend Achromat (TBA) storage ring lattice is being replaced with a Multi-Bend Achromat (MBA) lattice, which allows for the tight focusing of electron beams to approximately $1 0 \\mu \\mathrm { m }$ , reaching the di!raction limit in the soft $\\mathbf { \\boldsymbol { x } }$ -ray region. However, accurately measuring the beam size in such a tightly focused beam presents a challenge. This paper presents a diagnostics beamline design for ALS-U that utilizes a 2-slit interferometer technique to achieve a sub-micron resolution for beam size measurement. The impact of beam jitter, optics vibration as well as the incoherent depth-of-field e!ect on the measurement are also discussed. INTRODUCTION The Advanced Light Source Upgrade (ALS-U) project, currently underway at Lawrence Berkeley National Laboratory, aims to provide $\\mathbf { \\boldsymbol { x } }$ -ray beams that are at least 100 times brighter than those produced by the existing ALS facility [1]. This upgrade involves replacing the existing Triple Bend Achromat storage ring lattice with a new compact MultiBend Achromat lattice capable of tightly focusing electron beams down to approximately $1 0 \\mu \\mathrm { m }$ in both the horizontal and vertical directions. However, accurately measuring the size of such a small beam is a challenging task, and many synchrotron light source facilities have developed techniques to measure beam size with a high degree of accuracy. Among these techniques, the use of an interferometer with visible light from synchrotron radiation is a powerful and simple method for resolving small beam sizes. | augmentation | NO | 0 |
IPAC | Why are very accurate measurements of beam size required for dielectric laser accelerators? | To ensure that the beam size fits into the small structure aperture | Reasoning | Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf | PERTURBED BEAMS The stability of plasma-based accelerators against transverse misalignments and asymmetries of the drive beam is crucial for their applicability. Even small centroid change of the drive beam centroid can couple coherently to the plasma wake grow, and ultimately lead to emittance degradation or beam loss for a trailing witness beam. High-intensity laser pulses or high-density particle bunches to drive a plasma wake. Blowout regime where the driver expels plasma electrons as shown in Fig. 1, leaving an ion cavity with focusing fields. This emphasizes the importance of drive beam stability in plasma accelerators for practical applications. Figure 2 and Fig. 3 shows the banana beam profiles at $0 \\mathrm { c m }$ , $1 1 . 9 \\mathrm { c m }$ and $1 4 . 9 \\mathrm { c m }$ in the plasma for two different centroid changes. The plasma profile chosen was a semiGaussian ramp with up-ramp $_ { 0 - 1 0 \\mathrm { c m } }$ , $1 0 { - } 2 0 ~ \\mathrm { c m }$ uniform ramp and $2 0 { - } 3 0 \\mathrm { c m }$ downramp. Beam perturbations can often interfere with measurements, reflecting altered distributions in electron beams that add dimensions of increased error to experimental analysis. In plasma lengths exceeding $2 0 \\mathrm { c m }$ , however, there is a self-correcting phenomenon that forces the electron beam to become denser as it passes through the plasma. This allows for beams to be analyzed at a higher quality and with greater certainty, particularly when machine learning can be incorporated into assessing the optimal location of analysis [17, 18]. | augmentation | NO | 0 |
IPAC | Why are very accurate measurements of beam size required for dielectric laser accelerators? | To ensure that the beam size fits into the small structure aperture | Reasoning | Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf | File Name:STUDY_ON_TRANSVERSE_BEAM_SIZE_MEASUREMENT_USING.pdf STUDY ON TRANSVERSE BEAM SIZE MEASUREMENT USING CHERENKOV DIFFRACTION RADIATION IN LOW-ENERGY ELECTRON ACCELERATOR W. Song, G. Yun, Pohang University of Science and Technology, Pohang, Korea D. Song, D. Kim, S. Jang, I. Nam, J. Huang, T. Ha, G. Hahn∗ Pohang Accelerator Laboratory, Pohang, Korea Abstract Cherenkov Diffraction Radiation (ChDR), which is emitted when relativistic charged particles pass around dielectric materials, has recently been presented as non-invasive beam diagnostics in various studies. We intend to measure transverse beam size using ChDR in electron Linear Accelerator for Basic science (e-LABs), a $1 0 0 \\mathrm { M e V }$ electron experimental accelerator at the Pohang Accelerator Laboratory (PAL). The electron energy of e-LABs is low, so the intensity of photons generated by ChDR is absolutely small. Therefore, a cumulative dielectric radiator with a length of $1 5 7 ~ \\mathrm { m m }$ was designed to increase the photons incident on the detector. This contribution shows the characteristics of ChDR simulated numerically at low energies. Furthermore, we present an experimental configuration for measuring transverse beam size with some considerations. INTRODUCTION Due to the characteristic that ChDR has non-invasive properties despite emitting a strong signal, previous studies have shown promise as a good diagnostic device, such as measuring transverse beam profile [1–3], bunch length [4], and beam position [5]. In particular, the beam profile measurement used ChDR emitted from high-energy particles above GeV, so it was possible to obtain enough light in the visible region and make precise measurements. The beam profile monitor needs to measure the size not only in the full energy range, but also at lower energies, but it is difficult to measure accurately because the amount of photons emitted decreases rapidly when the energy of the beam is low. Therefore, in this study, we analyze the characteristics of ChDR produced by low-energy particles and introduce the experimental plan and its fundamental design studies using a test linac generating electron beams below $1 0 0 \\mathrm { M e V }$ . | augmentation | NO | 0 |
IPAC | Why are very accurate measurements of beam size required for dielectric laser accelerators? | To ensure that the beam size fits into the small structure aperture | Reasoning | Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf | Laser RF HV RF RF ALPHA -THz Undulator corrector Longit. YPM 三 DO Y Solenoid Spectomter Quadrupoles FC YAG THz FEL YAG BETA-Advanced Accelerator Concepts For stable operation and achieving the design parameters of the machine, it is necessary to have an appropriate beam diagnostic system. AREAL Linac diagnostic tasks include measuring beam transverse size, charge, emittance, beam energy and energy spread. To implement these measurements, a magnetic spectrometer is used to measure the energy and energy spread, a YAG station to measure the beam profile, and a Faraday cup station to measure the beam charge [4], [5]. In addition to these parameters, the beam transverse emittance can be measured in the gun section using a quadrupole magnet using the quadrupole scanning method. Unlike some traditional emittance measurement methods that involve intercepting the beam, the quadrupole scan technique is non-destructive, allowing for continuous beam monitoring without perturbing its properties. Quadrupole scans offer high sensitivity to changes in beam parameters, making them suitable for characterizing beams with low emittance and high brightness, typical of laserdriven accelerators. The quadrupole scan technique is versatile and can be adapted to different beam energies and pulse durations, making it suitable for a wide range of AREAL Linac configurations. | augmentation | NO | 0 |
expert | Why are very accurate measurements of beam size required for dielectric laser accelerators? | To ensure that the beam size fits into the small structure aperture | Reasoning | Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf | In the last step of each iteration, a small random value is added to each coordinate according to the Gaussian kernel defined in Eq. (2). This smoothes the distribution on the scale of $\\rho$ . For the reconstruction of the measurement presented in Sec. IV, $\\rho _ { x , y }$ was set to $8 0 \\ \\mathrm { n m }$ . The iterative algorithm is terminated by a criterion based on the relative change of the average of the difference $\\Delta _ { z , \\theta } ^ { i }$ (further details in Appendix B). The measurement range along $z$ ideally covers the waist and the spacing between measurements is reduced close to the waist, since the phase advance is the largest here. Since the algorithm does not where $P _ { z , \\theta } ^ { m }$ and $P _ { z , \\theta } ^ { r }$ are the measured and reconstructed projections for the current iteration at position $z$ and angle $\\theta$ . The difference between both profiles quantifies over- and underdense regions in the projection. Then, $\\Delta _ { z , \\theta } ( \\xi )$ is interpolated back to the particle coordinates along the wire scan direction, yielding $\\Delta _ { z , \\theta } ^ { i }$ for the ith particle. Afterwards, we calculate the average over all measured $z$ and $\\theta$ : | 2 | NO | 0 |
IPAC | Why are very accurate measurements of beam size required for dielectric laser accelerators? | To ensure that the beam size fits into the small structure aperture | Reasoning | Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf | $$ D _ { \\mathrm { b e a m } } = 2 f \\mathrm { N A } \\Leftrightarrow f = \\frac { D _ { \\mathrm { b e a m } } } { 2 \\mathrm { N A } } $$ gives the (ray optics approximate) optimal focal length $f$ of the collimator. Here, a Thorlabs F950FC-A collimator with $f = 9 . 9 \\mathrm { { m m } }$ and an entrance aperture of $D _ { \\mathrm { c o l l } } = 1 1 \\mathrm { m m }$ is used. Its geometry does not match Eq. 5 and the fixed distance between the lens doublet and the optical fiber does not allow focusing. This requires additional optical elements to collimate the divergent beam from the synchrotron first. EXPERIMENTAL SETUP Before mounting the setup in the booster enclosure, tests at the more accessible $2 . 5 \\mathrm { G e V }$ KARA beamline for visible light diagnostics are performed. Due to the divergent nature of the beam, focusing mirrors and lenses are necessary to reduce the beam waist diameter. Because etendue in the optical phase space is conserved in a lens system[6], only a compromise between small beam size and low divergence angle can be achieved. With cylinder lenses, the ratio of the beam waist sizes in the horizontal and vertical planes is brought to about unity at the fiber collimator, see Fig. 4 and note the almost round Gaussian fit. | 2 | NO | 0 |
IPAC | Why are very accurate measurements of beam size required for dielectric laser accelerators? | To ensure that the beam size fits into the small structure aperture | Reasoning | Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf | One approach for addressing the issue posed by SBBU is through the introduction of an external magnetic lattice to correct for deviations in the beam trajectory due to wakefield effects. This approach is limited however in it’s maximum allowable accelerating gradient due to the fact that longitudinal wakefields scale with $a ^ { - 2 }$ while the transverse fields cale with $a ^ { - 3 }$ where $a$ is the half vacuum-gap as seen in Fig. 1 [8]. Another approach is to abandon the historical cylindrical dielectric structure and use a planar-symmetric design instead. It has been shown that using such a structure, in the limit of an infinitely wide beam of fixed charge density, that the net transverse wakefields vanish [9]. Outside of that limit, in the finite-charge case, the transverse and longitudinal wakefields scale with the beam width, $\\sigma _ { x }$ , as $\\sigma _ { x } ^ { - 3 }$ and $\\sigma _ { x } ^ { - 1 }$ respectively. This implies that there should exist a beam width such that the transverse wakefields are weak enough to allow the beam to propagate through the entire structure but the longitudinal wakefields are still strong enough to be of interest [10]. While the primary dipole deflecting fields are indeed suppressed, secondary quadrupole-like fields persist which can severely distort the tail of the beam and again, eventually lead to SBBU [11]. | 1 | NO | 0 |
expert | Why are very accurate measurements of beam size required for dielectric laser accelerators? | To ensure that the beam size fits into the small structure aperture | Reasoning | Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf | V. DISCUSSION The reconstructed phase space represents the average distribution of many shots, since shot-to-shot fluctuations in the density cannot be characterized with multishot measurements like wire scans. Errors induced by total bunch charge fluctuations and position jitter of the electron beam could be corrected for by evaluating beam-synchronous BPM data. Since the BPMs in the Athos branch were still uncalibrated, their precision was insufficient to correct orbit jitter in our measurement. This issue is considered further in Appendix A. The expected waist is located at the center of the chamber $z = 0 \\mathrm { c m } )$ , whereas the reconstructed waist is found $6 . 2 \\mathrm { c m }$ downstream. In addition, the $\\beta$ -function at the waist $( \\beta ^ { * } )$ was measured to be around $3 . 6 \\ \\mathrm { c m }$ in both planes, which is in disagreement with the design optics $( \\beta _ { x } ^ { * } = 1 ~ \\mathrm { c m }$ , $\\beta _ { y } ^ { * } = 1 . 8 ~ \\mathrm { c m } ,$ ). This indicates that the beam is mismatched at the chamber entrance and improving the matching of the electron beam to the focusing lattice could provide even smaller (submicrometer) beams in the ACHIP chamber. | 1 | NO | 0 |
IPAC | Why are very accurate measurements of beam size required for dielectric laser accelerators? | To ensure that the beam size fits into the small structure aperture | Reasoning | Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf | The typical length for a $1 \\mathrm { M e V }$ DLA injector would be around $1 \\mathrm { c m }$ with an energy gradient of $5 0 0 \\mathrm { M e V } / \\mathrm { m }$ . The guiding concept of alternating phase focusing (APF) for a DLA requires that the laser phase in the structure be regularly flipped — through the design of the structure — so as to alternate between focusing and defocusing in each plane [24]. Figure 3 illustrates the operating parameter range for a periodic APF accelerator cell. The three-dimensional APF allows scalability to longer and multiple staged DLA structures. Phase jumps can be combined with tapering [23]. The physical interaction of the DLA electromagnetic field and the particle beam can be simulated by the code DLAtrack6D [27], which efficiently models the 3D APF [28], and can be used for any periodic structure [29]. This code applies one wake kick per DLA cell. However, challenges exist associated with electron tracking on a femtosecond time scale, since tiny electron bunches and huge fields can render the tracking simulations prohibitively slow. A possible solution consists in adopting a “moving window” tracker which provides (1) multiple static or frequency domain fields; (2) a clustered particle vector (direct particle-particle spacecharge interaction) and (3) statistics as in a many-shot experiment. Predictions from the “FemtoTrack” code with space charge [30] were compared with beam measurements at the Stanford “glassbox” experiment [25]. DLA structures for Stanford are designed for 70 and $1 0 0 \\mathrm { M e V / m }$ peak gradients (35 and $5 0 \\mathrm { M e V / m }$ average), which enables sub-relativistic acceleration with high gain. Currently, at PSI, a single structure with $2 \\mu \\mathrm m$ period is being optimised using a genetic algorithm [31]. An energy gradient of $2 . 1 4 \\ : \\mathrm { G e V / m }$ is assumed in the simulations. Passing through a $7 \\mathrm { m m }$ long structure consisting of 3500 cells, in simulations, a $1 \\mathrm { G e V }$ beam is accelerated by $1 4 ~ \\mathrm { M e V }$ with a final rms relative energy spread of less than $2 \\times 1 0 ^ { - 5 }$ [31]. This structure was optimized not only for low energy spread, but also for high survival rate, achieving $1 0 0 \\%$ transmission after the optimisation. A single-electron source similar to those used in electron microscopes is considered, with a repetition rate of $3 \\mathrm { G H z }$ ; the expected normalized beam emittance of $1 0 \\mathrm { p m }$ is suitable for the $4 0 0 \\mathrm { n m }$ aperture, even taking into account the field non-uniformity. | 5 | NO | 1 |
expert | Why are very accurate measurements of beam size required for dielectric laser accelerators? | To ensure that the beam size fits into the small structure aperture | Reasoning | Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf | 2. Amplitude errors Jitter to the BLM signal is introduced by read-out noise of the PMT $( < 1 \\% )$ , charge fluctuations of the machine and halo-particles scattering at other elements of the accelerator. The charge measured by the BPMs fluctuated by $1 . 3 \\%$ (rms) during the measurement. The signal-to-noise ratio (SNR) of the measurements varies from 25 to 45 depending on the respective projected beam size. We define the SNR as: $s _ { \\mathrm { m a x } } / \\sigma _ { \\mathrm { n o i s e } }$ , where $s _ { \\mathrm { m a x } }$ is the maximum of the signal and $\\sigma _ { \\mathrm { n o i s e } }$ refers to the standard deviation of the background. 3. Uncertainty of the reconstruction Due to the error sources mentioned above the measured projections are not fully compatible with each other, i.e., the reconstructed distribution cannot match to all measured data points. The error of the reconstructed phase space density and the derived quantities is estimated by a procedure similar to the main reconstruction algorithm. The reconstructed distribution is now taken as input. Instead of averaging over all projections, the iteration is performed for each projection individually. Hence, a set of $n _ { z } \\times n _ { \\theta }$ distributions is generated, in which each distribution matches best to one measured projection. All derived quantities, such as the emittance or $\\beta$ -function, are computed for each distribution and the error is taken as the standard deviation of this set. | augmentation | NO | 0 |
expert | Why are very accurate measurements of beam size required for dielectric laser accelerators? | To ensure that the beam size fits into the small structure aperture | Reasoning | Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf | D. Beam loss monitor Electrons scatter off the atomic nuclei of the metallic wire and a particle shower containing mainly x-rays, electrons and positrons is generated. The intensity of the secondary particle shower depends on the electron density integrated along the wire and is measured with a downstream beam loss monitor (BLM). The BLM consists of a scintillating fiber wrapped around the beam pipe. The fiber is connected to a photomultiplier tube (PMT). The signal of the PMT is read-out beam synchronously in a shot-by-shot manner. To avoid saturation of the PMT, the gain voltage needs to be set appropriately. SwissFEL is equipped with a series of BLMs, which are normally used to detect unwanted beam losses and are connected to an interlock system. For the purpose of wire scan measurements, individual BLMs can be excluded from the machine protection system. Details about the BLMs at SwissFEL can be found in [18]. For the wire scan measurement reported here, a BLM located $1 0 \\mathrm { ~ m ~ }$ downstream of the interaction with the wire was used. III. TRANSVERSE PHASE SPACE RECONSTRUCTION ALGORITHM Inferring a density distribution from a series of projection measurements is a problem arising in many scientific and medical imaging applications. Standard tomographic reconstruction techniques, e.g., filtered back projection or algebraic reconstruction technique [19] use an intensity on a grid to represent the density to be reconstructed. The complexity of these algorithms scales as $O ( n ^ { d } )$ , where $n$ is the number of pixels per dimension and $d$ is the number of dimensions of the reconstructed density. Typically, for real space density reconstruction, $d$ is 2 (slice reconstruction) or 3 (volume reconstruction). In the case of transverse phase space tomography $d$ equals 4 $( x , x ^ { \\prime } , y , y ^ { \\prime } )$ , leading to very long reconstruction times. | augmentation | NO | 0 |
expert | Why are very accurate measurements of beam size required for dielectric laser accelerators? | To ensure that the beam size fits into the small structure aperture | Reasoning | Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf | The ensemble of particles is iteratively optimized so that their projections match with the set of measured projections. The algorithm starts from a homogeneous particle distribution. One iteration consists of the following operations. (i) Transport $T ( z )$ (ii) Rotation $R ( \\theta )$ (iii) Histogram of the transported and rotated coordinates (iv) Convolution with wire profile (v) Interpolation to measured wire positions (vi) Comparison of reconstruction and measurement (vii) Redistribution of particles In the case of ultrarelativistic electrons transverse space charge effects can be neglected since they scale as $\\mathcal { O } ( \\gamma ^ { - 2 } )$ and hence $T ( z )$ becomes the ballistic transport matrix: $$ T ( z ) = { \\left( \\begin{array} { l l } { 1 } & { z } \\\\ { 0 } & { 1 } \\end{array} \\right) } $$ for $( x , x ^ { \\prime } )$ and $\\left( { y , y ^ { \\prime } } \\right)$ . The rotation matrix is then applied to $( x , y )$ : $$ R ( \\theta ) = { \\binom { \\cos \\theta } { - \\sin \\theta } } \\quad \\sin \\theta { \\Big ) } . | augmentation | NO | 0 |
expert | Why are very accurate measurements of beam size required for dielectric laser accelerators? | To ensure that the beam size fits into the small structure aperture | Reasoning | Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf | assume a specific shape (e.g., Gaussian) of the distribution, asymmetries, double-peaks, or halos of the distribution can be reconstructed (an example is shown in Appendix C). Properties of the transverse phase space including, transverse emittance in both planes, astigmatism and Twiss parameters can be calculated from the reconstructed distribution. To obtain the full 4D emittance, cross-plane information, such as correlations in $x - y ^ { \\prime }$ or $x ^ { \\prime } - y$ need to be assessed. For this purpose, the phase advance has to be scanned independently in both planes. This can be achieved with a multiple quadrupole scan as explained for instance in [20,21] but is not achieved by measuring beam projections along a waist, as the phase advance in both planes is correlated. The presented phase space reconstruction algorithm could also be adapted to use two-dimensional profile measurements from a screen at different phase advances to characterize the four-dimensional transverse phase space. The python-code related to the described tomographic reconstruction technique is made available on github [22]. A. Reconstruction of a simulated measurement To verify the reconstruction algorithm, we generate a test distribution and calculate a set of wire scan projections (nine projections along different angles at seven locations along the waist). The algorithm then reconstructs the distribution based on these simulated projections. For this test, we choose a Gaussian beam distribution with Twiss parameters $\\beta _ { x } ^ { * } = 2 . 0 ~ \\mathrm { c m }$ , $\\beta _ { y } ^ { * } = 3 . 0 ~ \\mathrm { c m }$ and a transverse emittance of 200 nm rad in both planes. An astigmatism of $- 1 \\ \\mathrm { c m }$ (longitudinal displacement of the horizontal waist) is artificially introduced. Moreover, noise is added to the simulated wire scan profiles to obtain a signal-to-noise ratio similar to the experimental data show in Sec. IV. The Gaussian kernel size for the reconstruction $\\rho _ { x , y }$ [see Eq. (2)] is $8 0 \\mathrm { n m }$ , which is around one order of magnitude smaller than the beam size in this test. Figure 4 compares the original and reconstructed transverse phase space at $z = 0$ cm. Good agreement ( $\\text{‰}$ error) is achieved for the emittances and astigmatism, which is manifested as a tilt in the $x - x ^ { \\prime }$ plane. For this numerical experiment, the algorithm terminates according to the criterion described in Appendix B after around 100 iterations. The run-time on a single-core of a standard personal computer is around two minutes. Parallelizing the computation on several cores would reduce the computation time by few orders of magnitude. | augmentation | NO | 0 |
expert | Why are very accurate measurements of beam size required for dielectric laser accelerators? | To ensure that the beam size fits into the small structure aperture | Reasoning | Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf | APPENDIX C: RECONSTRUCTION OF NON-GAUSSIAN BEAMS Our particle based tomographic reconstruction algorithm does not assume any specific shape for the density profile. Therefore, asymmetric density variations, such as tails of a localized core can be reconstructed. To demonstrate this capability of our tomographic technique, we show here a measurement of a non-Gaussian beam shape and compare the result to a 2D Gaussian fit. This measurement was performed with different machine settings than the measurement presented in Sec. IV. The electron bunch carried a charge of around $1 0 ~ \\mathrm { p C }$ . The transverse beam profile was characterized with nine wire scans at different angles at one z position. Therefore we can only reconstruct the twodimensional $( x , y )$ beam profile. The measurement and the tomographic reconstruction are shown in Fig. 8. For comparison, we add the result of a single two-dimensional Gaussian fit to all nine measured projections (Fig. 9). The core and tails observed in the measurement are well represented by the tomographic reconstruction, whereas the Gaussian fit overestimates the core region by trying to approximate the tails. [1] E. Esarey, C. Schroeder, and W. Leemans, Physics of laser-driven plasma-based electron accelerators, Rev. Mod. Phys. 81, 1229 (2009). | augmentation | NO | 0 |
expert | Why are very accurate measurements of beam size required for dielectric laser accelerators? | To ensure that the beam size fits into the small structure aperture | Reasoning | Hermann_et_al._-_2021_-_Electron_beam_transverse_phase_space_tomography_using_nanofabricated_wire_scanners_with_submicromete.pdf | ACKNOWLEDGMENTS We would like to express our gratitude to the SwissFEL operations crew, the PSI expert groups, and the entire ACHIP collaboration for their support with these experiments. We would like to thank Thomas Schietinger for careful proofreading of the manuscript. This research is supported by the Gordon and Betty Moore Foundation through Grant No. GBMF4744 (ACHIP) to Stanford University. APPENDIX A: ERROR ESTIMATION 1. Position errors The uncertainty of the position of the wire scanner with respect to the electron beam is affected by the readout precision of the hexapod $( < 1 ~ \\mathrm { n m } )$ , vibrational motion of the hexapod $\\phantom { + } < 1 0 ~ \\mathrm { { n m } } )$ and position jitter of the electron beam, which at SwissFEL is typically a few-percent of the beam size. The orbit of the electron beam is measured with BPMs along the accelerator. Unfortunately, the BPMs along the Athos branch of SwissFEL have not been calibrated (the measurement took place during the commissioning phase of Athos). Nevertheless, we tried correcting the orbit shot-by-shot based on five BPMs and the magnetic lattice around the interaction point. However, it does not reduce the measured beam emittance, as their position reading is not precise enough to correct orbit jitter at the wire scanner location correctly. Therefore, we do not include corrections to the wire positions based on BPMs. The reconstructed beam phase space represents the average distribution for many shots including orbit fluctuations. After the calibration of the BPMs in Athos we plan to characterize the effect of orbit jitter to wire scan measurements in detail. | augmentation | NO | 0 |
IPAC | Why do diffraction-limited storage rings use such a small vacuum chamber? | This is to accomodate the smaller inner bore of the magnets. | Reasoning | Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation | Increasing the brightness and coherence will also have a direct impact on the achievable temporal resolution for exploiting processes in real time of material fabrication and functioning. All spectroscopic, ‚Äòclassical‚Äô diffraction and scattering methods with gain from the brightness, whereas in the case of e.g. XPCS, the major gain will derive from the coherence, since the time resolution - proportional to the square of the coherent flux ‚Äì will be limited only by the electron bunch length $( \\sim 5 0$ ps FWHM including the effect of the bunch lengthening from the 3HC) at $4 0 0 ~ \\mathrm { \\ m A }$ intensity. It should also be noted that although the 21st century has seen major developments in the area of high-harmonic generation (HHG) and $\\mathrm { \\Delta X }$ -ray free-electron laser (XFEL) sources, DLSRs remain indispensable. This derives not only from capacity considerations - i.e., the limited number of beamlines that HHG and XFEL sources can serve as compared to DLSRs - but also from quality considerations. Using diffraction-limited storage rings is not only complementary, but also absolutely necessary because of the significantly higher repetition rate $( > 1 0 0 ~ \\mathrm { \\ M H z } )$ available at DLSRs as compared to the present HHG and FELs, together with the higher stability in intensity, wavelength and bandpass from pulse to pulse. The high average flux distributed over many electron bunches is highly beneficial for photon- and coherence-hungry techniques allowing a better handling of undesired effects in experiments due to a high ionization rate, for example space-charge problems in electron detection and radiationinduced sample damage, problems that cannot be overcome using the full power of FEL pulses. | augmentation | NO | 0 |
IPAC | Why do diffraction-limited storage rings use such a small vacuum chamber? | This is to accomodate the smaller inner bore of the magnets. | Reasoning | Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation | 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 | augmentation | NO | 0 |
expert | Why do diffraction-limited storage rings use such a small vacuum chamber? | This is to accomodate the smaller inner bore of the magnets. | Reasoning | Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation | The natural energy spread $\\Delta E / E$ is given by $$ \\frac { \\Delta E } { E } = \\sqrt { \\frac { C _ { q } \\gamma ^ { 2 } } { 2 j _ { z } \\langle \\rho \\rangle } } , $$ where $\\langle \\rho \\rangle$ is the average radius of curvature in the storage ring. Finally, in the vertical phase space of accelerators, the dynamics are somewhat different than in the horizontal or longitudinal phase spaces. This is primarily because of typically negligible dispersion in the vertical plane, and because this phase space is typically not coupled to the other dimensions. This means that, under normal conditions, variations in the energy of a particle do not significantly affect its vertical position. However, that does not exempt the vertical phase space from the effects of quantum excitation. Three effects remain that counterbalance radiation damping even in the vertical plane: ‚Äì A (small) vertical component of the emitted photon, ‚Äì Intra-beam scattering, ‚Äì A remnant coupling between the horizontal and vertical plane. In most accelerators, the last point usually dominates, despite a careful set-up of the accelerator lattice that avoids coupling terms. It is worth noting that quantum effects determine macroscopic effects such as the beam size in a synchrotron. In fact, the value of Planck‚Äôs constant $\\hbar$ has just the right magnitude to make practical the construction of large electron synchrotrons [3]. | 1 | NO | 0 |
expert | Why do diffraction-limited storage rings use such a small vacuum chamber? | This is to accomodate the smaller inner bore of the magnets. | Reasoning | Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation | $$ for any natural number $n$ . $$ A B = B C = { \\frac { d } { \\sin \\vartheta } } $$ and $$ \\ A C = { \\frac { 2 d } { \\tan \\vartheta } } , $$ from which follows $$ A C ^ { \\prime } = A C \\cos \\vartheta = { \\frac { 2 d } { \\tan \\vartheta } } \\cos \\vartheta = { \\frac { 2 d } { \\sin \\vartheta } } \\cos ^ { 2 } \\vartheta , $$ and we conclude $$ \\begin{array} { r c l } { { n \\lambda } } & { { = } } & { { \\displaystyle \\frac { 2 d } { \\sin \\vartheta } - \\frac { 2 d } { \\tan \\vartheta } \\cos \\vartheta = \\displaystyle \\frac { 2 d } { \\sin \\vartheta } \\big ( 1 - \\cos ^ { 2 } \\vartheta \\big ) = \\displaystyle \\frac { 2 d } { \\sin \\vartheta } \\sin ^ { 2 } \\vartheta } } \\\\ { { } } & { { = } } & { { \\displaystyle 2 d \\sin \\vartheta , } } \\end{array} | 1 | NO | 0 |
IPAC | Why do diffraction-limited storage rings use such a small vacuum chamber? | This is to accomodate the smaller inner bore of the magnets. | Reasoning | Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation | With the same RF cavity of the present HLS storage ring, the momentum aperture of DDBA-H6BA lattice is tracked, -3-2-10123Momentum aperture [%] WHLWLH WVVWVV 0 8 16 24 32 40 48 56 64 s [m] as shown in Fig. 6. The MA at straight sections are about $3 \\% { \\sim } 4 \\%$ and larger than $1 . 5 \\%$ at the dispersion bump. With the same condition in the IBS e!ect calculation, the Touschek lifetimes of this new storage ring are about $3 . 3 \\mathrm { h }$ and $4 . 1 \\mathrm { h }$ for $5 \\%$ and $1 0 \\%$ transverse coupling, respectively. CONCLUSION In this paper, we proposed a DDBA-H6BA lattice and applied it to the design of the potential upgrade of HLS storage ring. Compared to the present HLS storage ring designed with DBA lattice, the natural emittance is significantly reduced from $3 6 . 4 \\ \\mathrm { n m }$ rad to $1 . 8 \\mathrm { n m }$ rad at the cost of two short straight sections. Due to the low emittance and beta functions, the synchrotron radiation brightness can be enhanced by more than one order of magnitude. Benefiting from the optimization of nonlinear dynamics indicators and the $- I$ transformation approximatively achieved between sextupoles, the DA and MA are large enough which promise a reasonable injection e"ciency and lifetime. | 2 | NO | 0 |
expert | Why do diffraction-limited storage rings use such a small vacuum chamber? | This is to accomodate the smaller inner bore of the magnets. | Reasoning | Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation | $$ \\begin{array} { r c l } { { \\displaystyle \\sigma _ { r } } } & { { = } } & { { \\displaystyle \\frac { 1 } { 4 \\pi } \\sqrt { \\lambda L } } } \\\\ { { \\displaystyle \\sigma _ { r ^ { \\prime } } } } & { { = } } & { { \\displaystyle \\sqrt { \\frac { \\lambda } { L } } . } } \\end{array} $$ This diffraction limit is symmetric in $x$ and $y$ . The effective source size is $$ \\begin{array} { r c l } { \\sigma _ { ( x , y ) , \\mathrm { e f f } } } & { = } & { \\sqrt { \\sigma _ { ( x , y ) } ^ { 2 } + \\sigma _ { r } ^ { 2 } } } \\end{array} $$ $$ \\begin{array} { r c l } { \\sigma _ { ( x ^ { \\prime } , y ^ { \\prime } ) , \\mathrm { e f f } } } & { = } & { \\sqrt { \\sigma _ { ( x ^ { \\prime } , y ^ { \\prime } ) } ^ { 2 } + \\sigma _ { r ^ { \\prime } } ^ { 2 } } . } \\end{array} | 1 | NO | 0 |
IPAC | Why do diffraction-limited storage rings use such a small vacuum chamber? | This is to accomodate the smaller inner bore of the magnets. | Reasoning | Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation | $1 0 0 \\mu \\mathrm { m } / 1 0 0 \\mu \\mathrm { m } / 2 0 0 \\mu \\mathrm { m }$ , roll angle misalignments should be better than $2 0 0 \\mu \\mathrm { r a d }$ . INSTABILITY ANALYSIS Instabilities induced by beam collective effects are dominant limitation of average current in storage rings, especially for the case of low energy like LUTF ${ 5 0 0 } \\mathrm { M e V }$ ring. For a purpose of potential higher current, the vacuum pipe is designed to octagon with copper (the left of Fig. 5). The flanges, bellows, valves are all shielded type. And all transitions are also required to have a taper smaller than 0.2 for small geometrical impedance. In the current design, the preliminary obtained total longitudinal geometrical impedance is given in the right of Fig. 5. The effective impedance $\\left| { \\frac { Z } { n } } \\right| _ { \\mathrm { e f f } } = 0 . 2 8 \\Omega$ . For the total resistive wall (RW) impedance, two kinds of pipes are assumed: two elliptical pipes, representing two IDs and each with a (semi-major axis, semi-minor axis, length) of (30, 5.5, 6000) mm and the other octagonal parts. Based on impedance, the threshold current of various instabilities can be estimated. Here, we start from CSR instability first. | 1 | NO | 0 |
expert | Why do diffraction-limited storage rings use such a small vacuum chamber? | This is to accomodate the smaller inner bore of the magnets. | Reasoning | Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation | How would you measure this radiation? I.10.7.27 Superconducting undulators What is the advantage of using undulators made with superconducting coils, in comparison to permanentmagnet arrays? What are drawbacks? I.10.7.28 In-vacuum undulators What are the advantages of using in-vacuum undulators? What are possible difficulties? I.10.7.29 Instrumentation How would you measure the vertical emittance in a storage ring? I.10.7.30 Top-up operation What are the advantages of top-up operation? What difficulties have to be overcome to establish top-up in a storage ring? (give one advantage and one difficulty for 1P.; give one more advantage and one more difficulty for $\\begin{array} { r } { 1 \\mathrm { P } . \\star . } \\end{array}$ .) I.10.7.31 Fundamental limits The SLS 2.0, a diffraction limited storage ring, aims for an electron energy of $2 . 4 \\mathrm { G e V }$ and an emittance of $1 2 6 \\mathrm { p m }$ . How far is this away from the de Broglie emittance, i.e. the minimum emittance given by the uncertainty principle? I.10.7.32 Applications Why are synchrotrons important for science? I.10.7.33 Applications What applications for industry are there to synchrotrons? I.10.7.34 Orbit correction Which devices are used to measure and correct the orbit inside a synchrotron? | augmentation | NO | 0 |
expert | Why do diffraction-limited storage rings use such a small vacuum chamber? | This is to accomodate the smaller inner bore of the magnets. | Reasoning | Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation | $$ where $J$ is the Bessel function of the first kind. As $K$ increases, the higher harmonics play a more signicificant role, but the fundamental harmonic always has the highest flux. I.10.3 Effects of the emission of radiation on beam dynamics In this section, we will delve deeper into the interplay between the radiation emission and the ensuing dynamics of the beam. The treatment closely follows the book by Wolski [4]. First, we will explore the energy transfer that occurs when an electron emits a photon. Following this, we will make a coordinate transformation to the more beneficial action and angle variables, providing a clearer perspective on the underlying mechanisms. We will then proceed to compute the ensemble average to calculate the implications on the emittance of the beam. A noteworthy observation will emerge from our analysis: the emittance decreases exponentially, plateauing at a limit dictated by the fundamental principles of quantum mechanics. This revelation underscores the intricate ties between quantum mechanics and relativistic beam dynamics, shedding light on the broader consequences of radiation emission in storage rings. In the following sections, we will make use of Hamiltonian mechanics. Those not familiar with this matter are invited to watch two introductory videos: "Hamiltonian formalism $1 ^ { \\dag 6 }$ and "Hamiltonian formalism 2"7. | augmentation | NO | 0 |
expert | Why do diffraction-limited storage rings use such a small vacuum chamber? | This is to accomodate the smaller inner bore of the magnets. | Reasoning | Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation | d) . . . requires the rotation of the sample around three orthogonal axes I.10.7.52 Undulator radiation Derive the formula for the fundamental wavelength of undulator radiation emitted at a small angle $\\theta$ : $$ \\lambda = \\frac { \\lambda _ { u } } { 2 \\gamma ^ { 2 } } \\left( 1 + \\frac { K ^ { 2 } } { 2 } + \\gamma ^ { 2 } \\theta ^ { 2 } \\right) $$ from the condition of constructive interference of the radiation emitted by consecutive undulator periods! I.10.7.53 Binding energies In which atom are the core electrons most strongly bound to the nucleus? a) Neon b) Copper c) Lithium d) Osmium e) Helium $f$ ) Iron g) Sodium $h$ ) Gold What about the valence electrons? I.10.7.54 Electron and X-Ray diffraction In comparison to diffractive imaging using electrons, X-ray diffraction. . $a$ ). . . has the advantage that the sample does not need to be in vacuum b). . . gives a stronger diffraction signal for all crystal sizes $c$ ). . . generates the same signal for all atoms in the crystal What are the consequences for the optimum sample thickness for electron diffraction in comparison to X-ray diffraction? | augmentation | NO | 0 |
expert | Why do diffraction-limited storage rings use such a small vacuum chamber? | This is to accomodate the smaller inner bore of the magnets. | Reasoning | Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation | I.10.7.55 Practical applications of synchrotron radiation The Italian Light Source Elettra is a 3rd generation synchrotron source with $2 5 9 \\mathrm { m }$ circumference, and can operate at beam energies of either $2 . 0 \\mathrm { G e V }$ or $2 . 4 \\mathrm { G e V } ,$ with beam currents of $3 1 0 \\mathrm { m A }$ and $1 6 0 \\mathrm { m A }$ , respectively. The Machine Director is feeling thirsty, and would like to use Elettra to make a splendid espresso. By assuming that all radiation emitted as SR from the dipole magnets can be converted into heat, calculate how much time is needed for the $2 . 0 \\mathrm { G e V }$ beam to heat up the espresso water from $2 0 ^ { \\circ } \\mathrm { C }$ to $8 8 ^ { \\circ } \\mathrm { C }$ . One espresso is $3 0 \\mathrm { m L }$ . The radius of curvature in the dipoles is $5 . 5 \\mathrm { m }$ . Neglect potential insertion devices! Hint: the specific heat capacity of water is $\\begin{array} { r } { c _ { w } = 4 . 1 8 6 \\frac { \\mathrm { ~ J ~ } } { \\mathrm { g K } } } \\end{array}$ | augmentation | NO | 0 |
expert | Why do diffraction-limited storage rings use such a small vacuum chamber? | This is to accomodate the smaller inner bore of the magnets. | Reasoning | Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation | File Name:Ischebeck_-_2024_-_I.10_‚Äî_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 R√∂ntgen, 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. | augmentation | NO | 0 |
expert | Why do diffraction-limited storage rings use such a small vacuum chamber? | This is to accomodate the smaller inner bore of the magnets. | Reasoning | Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation | $$ The change in action is thus $$ \\begin{array} { l l l } { { d J _ { y } } } & { { = } } & { { J _ { y } ^ { \\prime } - J _ { y } } } \\\\ { { } } & { { } } & { { } } \\\\ { { } } & { { \\approx } } & { { \\displaystyle - \\alpha _ { y } y p _ { y } \\frac { d p } { P _ { 0 } } - \\beta _ { y } p _ { y } ^ { 2 } \\frac { d p } { P _ { 0 } } } } \\\\ { { } } & { { } } & { { } } \\\\ { { } } & { { = } } & { { \\displaystyle - \\left( \\alpha _ { y } y p _ { y } + \\beta _ { y } p _ { y } ^ { 2 } \\right) \\frac { d p } { P _ { 0 } } . } } \\end{array} | augmentation | NO | 0 |
expert | Why do diffraction-limited storage rings use such a small vacuum chamber? | This is to accomodate the smaller inner bore of the magnets. | 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 | augmentation | NO | 0 |
expert | Why do diffraction-limited storage rings use such a small vacuum chamber? | This is to accomodate the smaller inner bore of the magnets. | Reasoning | Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation | The term diffraction-limited refers to a system, typically in optics or imaging, where the resolution or image detail is primarily restricted by the fundamental diffraction of light rather than by imperfections or aberrations in the source, or in imaging components. In such a system, the performance reaches the theoretical physical limit dictated by the wave nature of the radiation. Achieving diffraction-limited performance means maximizing image sharpness and detail by minimizing all other sources of distortion or blurring to the extent that diffraction becomes the overriding factor in limiting resolution. The horizontal emittance, conversely, is typically an order of magnitude larger. The X-ray beams are thus not diffraction-limited in this dimension. Diffraction-limited storage rings (DLSRs) overcome these constraints by minimizing the horizontal emittance to a level such that horizontal and vertical beam sizes in the undulators are similar. The diffraction limit of the X-ray beam thus becomes the defining factor for the source size, which leads to beams that are transversely fully coherent. This increased coherence translates into improved resolution and contrast in experimental techniques like X-ray imaging and scattering. The implications of achieving diffraction-limited performance are profound. The significantly improved coherence of the X-ray beams allow scientists to use the full beam for diffraction experiments, opening doors to previously intractable scientific questions. We will now see how this is achieved, and discuss briefly the challenges for design, construction and operation. | augmentation | NO | 0 |
expert | Why do diffraction-limited storage rings use such a small vacuum chamber? | This is to accomodate the smaller inner bore of the magnets. | Reasoning | Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation | $$ 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 | augmentation | NO | 0 |
expert | Why do diffraction-limited storage rings use such a small vacuum chamber? | This is to accomodate the smaller inner bore of the magnets. | Reasoning | Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation | ‚Äì Photoelectric absorption: absorption by electrons bound to atoms; ‚Äì Thomson scattering: elastic scattering, i.e. scattering without energy transfer between the X-ray and a free electron; ‚Äì 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‚Äôs oscillation frequency is driven by the frequency of the electromagnetic wave, and there‚Äôs no energy loss in the system. | augmentation | NO | 0 |
expert | Why do diffraction-limited storage rings use such a small vacuum chamber? | This is to accomodate the smaller inner bore of the magnets. | Reasoning | Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation | I.10.6.3 Tomographic imaging and ptychography Tomography is a powerful imaging technique that reconstructs a three-dimensional object from its twodimensional projections. It is used widely in medicine, where it allows a detailed view of our skeleton. Synchrotron radiation sources, with their brilliant and monochromatic beams, allow reducing the exposure time to less than a millisecond while achieving micrometer resolution. This makes the technique useful for research in fields ranging from materials science to biology (see Fig. I.10.16). The process involves rotating the sample through a range of angles relative to the X-ray beam, while collecting a series of two-dimensional absorption images. The three-dimensional distribution is reconstructed from the two-dimensional images. The monochromatic and coherent X-ray beams from a synchrotron allow recording phase contrast images, which can capture finer details of biological samples than the usual absorption contrast images. In ptychography, a coherent X-ray beam is scanned across the sample in overlapping patterns, and the diffraction pattern from each area is recorded. These overlapping diffractions provide redundant information. The reconstruction algorithms used in ptychography are able to retrieve both the amplitude and phase information from the scattered wavefronts, leading to highly detailed images with nanometer resolution. Ptychography is particularly advantageous for studying materials with fine structural details and can be applied to a wide range of materials, including biological specimens, nanomaterials, and integrated electronic circuits (see e.g. https://youtu.be/GvyTiK9CNO0). | augmentation | NO | 0 |
expert | Why do diffraction-limited storage rings use such a small vacuum chamber? | This is to accomodate the smaller inner bore of the magnets. | Reasoning | Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation | $$ where $\\vartheta$ is the angle at which the photon is scattered. I.10.5.2 Scattering of $\\mathbf { X }$ -rays on atoms In the case of photon energies less than a few keV, the wavelength is longer than the size of the atom. The scattering is then coherent, i.e., the phases of the scattered waves from different parts of the electron cloud add up constructively. The electric field amplitude of the scattered wave is then proportional to the total number of electrons in the atom $Z$ , and the scattered intensity is proportional to $Z ^ { 2 }$ . The total cross section is then $$ \\sigma = Z ^ { 2 } \\sigma _ { T } . $$ The $Z ^ { 2 }$ dependence makes the scattering cross section for heavier atoms much larger compared to lighter ones, significantly influencing how $\\mathrm { \\Delta X }$ -rays are used in science and medicine. When we increase the photon energy, the wavelength becomes smaller than the size of the electron cloud of an atom, and decoherence between the scattered waves reduces the scattering cross section. As an approximation, the cross-section drops off as $1 / E _ { \\gamma } ^ { 2 }$ . The precise drop-off can be described by the atomic form factor $f ^ { 0 }$ , which depends on both the scattering angle and the photon wavelength. It can be parametrized as | augmentation | NO | 0 |
expert | Why do diffraction-limited storage rings use such a small vacuum chamber? | This is to accomodate the smaller inner bore of the magnets. | Reasoning | Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation | $$ where $E _ { \\mathrm { n o m } }$ is the nominal beam energy and $$ C _ { \\gamma } = \\frac { e ^ { 2 } } { 3 \\varepsilon _ { 0 } ( m _ { e } c ^ { 2 } ) ^ { 4 } } . $$ We define the following integral as the second synchrotron radiation integral $$ I _ { 2 } : = \\oint \\frac { 1 } { \\rho ^ { 2 } } d s . $$ From the energy lost per turn $U _ { 0 }$ and the critical photon energy $E _ { c }$ , we can calculate an average number of photons to be approximately $$ \\langle n _ { \\gamma } \\rangle \\approx \\frac { 1 6 \\pi } { 9 } \\alpha _ { \\mathrm { f i n e } } \\gamma , $$ where $\\alpha _ { \\mathrm { f i n e } } \\approx 1 / 1 3 7$ is the fine structure constant. This is a relatively small number; we will therefore have to consider the quantum nature of the radiation, and we will see later how this quantum nature ultimately defines the beam emittance in an electron storage ring. | augmentation | NO | 0 |
IPAC | Why do slower (non-relativistic) electrons produce stronger radiation at subwavelength separations? | Because in the near field (??d ? 1), slower electrons generate stronger near-field amplitudes, leading to enhanced spontaneous emission despite increased evanescence. | Reasoning | Maximal_spontaneous_photon_emission_and_energy_loss_from_free_electrons.pdf | $$ Pulsed-beam profiles were computed for several longitudinal coordinates and are presented in Fig. 1. PARTICLE FLIGHT Non-relativistic Results The influence of electric fields with spatio-temporal profiles described in Eq. 3 on free charged particle flight is calculated by finite-difference time-domain simulations. The results presented here assume electron rest mass and charge because relativistic electric field strengths appear to be accessible with the state-of-the-art or may be shortly. However, these results are equivalent to proton- or ion-based simulations with field strength scaled by the charge-to-mass ratio of the particles. In all calculations, the magnetic field is set to zero for simplicity. For non-relativistic particle motion, this can be justified because the electric field strengths dominate the particle motion. In the relativistic case, however, the magnetic field plays a significant role, and so the calculations more properly represent the fields of counter-propagation of two pulsed beams at the plane $z = 0$ (as in [2]), where the interference of the electric fields is perfectly constructive, leaving its form unchanged, and the interference of the magnetic fields is perfectly destructive. Particle location and momentum are tracked throughout the trajectory for particles at rest at several transverse displacements. The transverse and longitudinal size of the pulsed beam followed from the characteristic frequency $f _ { 0 } = 0 . 3 \\mathrm { T H z }$ and Rayleigh length $z _ { R } = 3 0 \\mathrm { m m }$ . The order of the spectrum, $n = 2$ , was selected as it represents the case of a single emitter with a second-order nonlinear polarizability. Two field strengths were considered. In the first case, $| E _ { 0 } | =$ $1 \\mathrm { M V / m }$ the particle motion remained non-relativistic, while in the second case $| E _ { 0 } | = 3 0 \\mathrm { G V / m }$ relativistic effects were apparent. Each simulation is contrasted with the equivalent simulation using SVEA $E ( t ) = R e ( e ^ { i f _ { 0 } ^ { \\prime } t } e ^ { - ( t / \\tau ) ^ { 2 } - ( \\bar { r / \\sigma } ) ^ { 2 } } )$ . In each case, odd (sine-like) and even (cosine-like) pulses were considered. | augmentation | NO | 0 |
IPAC | Why do slower (non-relativistic) electrons produce stronger radiation at subwavelength separations? | Because in the near field (??d ? 1), slower electrons generate stronger near-field amplitudes, leading to enhanced spontaneous emission despite increased evanescence. | Reasoning | Maximal_spontaneous_photon_emission_and_energy_loss_from_free_electrons.pdf | INTRODUCTION At the Fermilab Integrable Optics Test Accelerator (IOTA) [1], an experimental program was initiated to study the classical and quantum properties of undulator radiation from electron bunches and from individual electrons [2]. We are addressing the following scientific questions: What are the properties of radiation from single electrons? Can one directly observe the classical or quantum nature of undulator radiation? Synchrotron-radiation sources have had an immense impact on many scientific fields. The same is true for sources of well-defined quantum states of radiation [3, 4]. Are there new ways to generate quantum states of light? Are there novel applications of the experimental techniques of quantum optics in accelerator physics and beam diagnostics? Radiation from single electrons has been studied in the past [5–7]. Recently, for instance, the techniques of quantum optics were applied to the study of radiation in a tandem undulator [8] and a free-electron laser [9]. In this paper, we present a new, precise interferometric study of undulator radiation from single electrons. Classical electrodynamics explains a wide range of phenomena: reflection and refraction, interference, diffraction, synchrotron radiation, etc. In quantum optics [10–16], the electromagnetic field is quantized, with boson properties. This theory is necessary to explain spontaneous emission, the Lamb shift and the Hong-Ou-Mandel effect [17], for instance. Physical systems are described by different quantum states of radiation. Classical waves, such as those generated by dipole antennas or lasers, are represented by Glauber coherent states, defined as eigenstates of the annihilation operator. Radiation from individual atoms, parametric downconversion or quantum dots, on the other hand, corresponds to Fock number states (eigenstates of the number operator). The properties of thermal or chaotic sources of light, such as light bulbs, black bodies or stars, are represented by incoherent mixtures of states via the density-matrix formalism. Experimentally, states can be identified by observing the statistics of photocounts, such as intensity fluctuations or arrival-time distributions. With multiple photodetectors, one can also study coincidence rates. For instance, Hong, Ou and Mandel observed that when radiation is in a 2-photon number state, coincidences are suppressed. When the energy of the radiation $( { \\sim } \\mathrm { e V } )$ is small compared to the energy of the radiating particle (150-MeV electrons), radiation is expected to be in a coherent state, behaving like a classical wave even when it is emitted by a single electron. | augmentation | NO | 0 |
IPAC | Why do slower (non-relativistic) electrons produce stronger radiation at subwavelength separations? | Because in the near field (??d ? 1), slower electrons generate stronger near-field amplitudes, leading to enhanced spontaneous emission despite increased evanescence. | Reasoning | Maximal_spontaneous_photon_emission_and_energy_loss_from_free_electrons.pdf | Table: Caption: Table 2: Photon Production Parameters Body: <html><body><table><tr><td>Parameter</td><td>Value</td></tr><tr><td>Number of ions per bunch [20]</td><td>0.90 ×108</td></tr><tr><td>Fraction of excited particles</td><td>14.1%</td></tr><tr><td>Number of emitted photons per bunch</td><td>1.27× 107</td></tr><tr><td>Laser wavelength</td><td>1.2 eV (1031 nm)</td></tr><tr><td>Ion excitation energy hωo</td><td>231eV</td></tr><tr><td>Maximum emitted photon energy</td><td>44keV</td></tr></table></body></html> $$ \\omega ^ { \\prime } = ( 1 + \\beta \\cos \\theta ) \\gamma _ { L } \\omega \\approx 2 \\gamma _ { L } \\omega , $$ CONCLUSION where $\\omega ^ { \\prime }$ is the photon frequency in the ion-rest frame, $\\theta$ is the photon-ion angle, $\\gamma _ { L }$ the Lorentz factor, $\\omega$ is the frequency in the lab frame, and the small angle approximation was used. The Eq. (1) shows that the photon frequency in the ion-rest frame $\\omega ^ { \\prime }$ is $2 \\gamma _ { L }$ times larger than the frequency $\\omega$ in the lab frame. The Lorentz transformation also affects the angular spread of the photons that are emitted by the excited ions. In the comoving frame of the ion, the emission is equally probable in every direction. However, in the lab frame, the photons will be emitted with angular spread $\\theta _ { e } \\sim 1 / \\gamma _ { L }$ , which means that the small angle approximation can also be applied to the Doppler frequency shift of the emitted photons. To determine the energy of the photons after spontaneous emission, the Doppler shift is applied to the excitation energy of the ion, which will give another factor of $2 \\gamma _ { L }$ . Consequently, the energy of the emitted photon is enhanced by a factor $4 \\gamma _ { L } ^ { 2 }$ compared to the photons produced by the laser. For example, this factor would be $\\approx 1 0 ^ { 8 }$ for LHC beams [19]. | augmentation | NO | 0 |
IPAC | Why do slower (non-relativistic) electrons produce stronger radiation at subwavelength separations? | Because in the near field (??d ? 1), slower electrons generate stronger near-field amplitudes, leading to enhanced spontaneous emission despite increased evanescence. | Reasoning | Maximal_spontaneous_photon_emission_and_energy_loss_from_free_electrons.pdf | (Ex) [V/m] 0.5 0 三三三 × -0.5 0 500 1000 (Ez)[mV/m] 0.5 4 0 2 0 0 × -2 -0.5 0 500 1000 Z-Z。[nm] R(Ex) [V/m] R(Eγ) [V/m] 1 0. 8 0.。 @ C y -0.5 -0.5 -0.5 0 0.5 -0.5 0 0.5 R(Bx） [nT] R(Bγ) [nT] 0.5 @ 0.5 5 0 0 o y -0.5 -0.5 I -0.5 0 0.5 -0.5 0 0.5 x [mm] x [mm] (E,)[mV/m] (Bz)[T] 0.5 0.5 ol L 1 0 0 y -0.5 -0.5 1 -0.5 0 0.5 -0.5 0 0.5 x [mm] × [mm] A careful study of the images in Fig. 6 shows that the longitudinal wavelength is slightly higher than the original optical wavelength. This phenomenon, described for example here[8], is related to the fact that the phase velocity of the wave $\\nu _ { f }$ is higher than the speed of light in vacuum $c$ by the relation $$ \\nu _ { f } = c / \\cos ( \\theta ) , $$ where $\\cos ( \\theta )$ is given by the ratio of the longitudinal component of the wavevector $k _ { T }$ to the wave vector $k$ . The angle $\\theta$ decreases with distance for both the SLB and HSLB. | augmentation | NO | 0 |
IPAC | Why do slower (non-relativistic) electrons produce stronger radiation at subwavelength separations? | Because in the near field (??d ? 1), slower electrons generate stronger near-field amplitudes, leading to enhanced spontaneous emission despite increased evanescence. | Reasoning | Maximal_spontaneous_photon_emission_and_energy_loss_from_free_electrons.pdf | $$ where $\\omega _ { c }$ is the critical frequency defined at half power spectrum, $E _ { 0 }$ is the particle energy, $\\gamma$ is the relativistic factor, $\\boldsymbol { a }$ is the fine structure constant and $r _ { e }$ is the electron’s classical radius. For $\\Upsilon \\gg 1$ , the photon spectrum is given by the SokolovTernov formula, which truncates the photon energy at $E _ { \\gamma } =$ $E _ { 0 }$ as opposed to the classical formula which extends infinitely [11] (Fig. 2a). $$ \\frac { d N _ { \\gamma } } { d \\bar { x } } = \\frac { \\alpha } { \\sqrt { 3 } \\pi \\gamma ^ { 2 } } \\left[ \\frac { \\hbar \\omega } { E } \\frac { \\hbar \\omega } { E - \\hbar \\omega } K _ { 2 / 3 } ( \\bar { x } ) + \\int _ { \\bar { x } } ^ { \\infty } K _ { 5 / 3 } ( x ^ { \\prime } ) d x ^ { \\prime } \\right] $$ where $\\bar { x } = \\omega / \\omega _ { c } \\cdot E _ { 0 } / ( E _ { 0 } - \\hbar \\omega ) \\propto 1 / \\Upsilon$ is the modified frequency ratio, and $K _ { i }$ is the modified Bessel function of order $i$ . | augmentation | NO | 0 |
IPAC | Why do slower (non-relativistic) electrons produce stronger radiation at subwavelength separations? | Because in the near field (??d ? 1), slower electrons generate stronger near-field amplitudes, leading to enhanced spontaneous emission despite increased evanescence. | Reasoning | Maximal_spontaneous_photon_emission_and_energy_loss_from_free_electrons.pdf | COMPTON BACKSCATTERING Compton backscattering occurs when a photon with energy $E _ { L }$ hits a relativistically moving electron with energy $E _ { e }$ and is scattered back. Energy is transferred from the electron to the photon. The recoil factor $X = ( 4 E _ { e } E _ { L } ) / ( m _ { e } c ^ { 2 } ) ^ { 2 }$ [15] indicates how strong the energy loss and thus the influence on the electrons is. The energy of the scattered photons $E _ { L } ^ { \\prime }$ can be calculated by [16] $$ E _ { L } ^ { \\prime } = \\frac { ( 1 - \\beta \\cos ( \\theta _ { i } ) ) E _ { L } } { ( 1 - \\beta \\cos ( \\theta _ { s } ) ) + ( 1 - \\cos ( \\theta _ { r } ) ) \\frac { E _ { L } } { E _ { e } } } $$ for electrons with $\\beta = \\nu / c , \\theta _ { i }$ the angle between the incident photons and electrons, $\\theta _ { s }$ the scattering angle of the scattered photons and the electron beam axis and $\\theta _ { r } = \\theta _ { i } - \\theta _ { s }$ the reflecting angle between incident and scattered photons. From Eq. (1) it can be concluded that the desired photon energy can be achieved by adjusting both the original electron and photon energy. However, this can also be achieved in a small range by an angle-dependent positioning of the target or detector to the beam axis of the scattered photons, a variation of $\\theta _ { r }$ . The highest photon energy can be achieved by a head-on collision $\\theta _ { i } = 1 8 0 ^ { \\circ }$ , see Eq. (1). Looking at the detection angel of $\\theta _ { r } = 0 ^ { \\circ }$ , Eq. (1) simplifies to | augmentation | NO | 0 |
IPAC | Why do slower (non-relativistic) electrons produce stronger radiation at subwavelength separations? | Because in the near field (??d ? 1), slower electrons generate stronger near-field amplitudes, leading to enhanced spontaneous emission despite increased evanescence. | Reasoning | Maximal_spontaneous_photon_emission_and_energy_loss_from_free_electrons.pdf | File Name:NUMERICAL_SIMULATIONS_OF_RADIATION_REACTION_USING.pdf NUMERICAL SIMULATIONS OF RADIATION REACTION USING LORENTZ-ABRAHAM-DIRAC FORMALISM ∗ P. Rogers1, E. Breen1, R. Shahan1, G. Wilson2, E. Johnson1, B. Terzić1, G. Krafft1,3 1Department of Physics, Old Dominion University, Norfolk, Virginia, USA 2Department of Mathematics, Regent University, Virginia Beach, Virginia, USA 3Thomas Jefferson National Accelerator Facility, Newport News, VA, USA Abstract An accelerating charged particle emits electromagnetic radiation. The motion of the particle is further damped via self-interaction with its own radiation. For relativistic particles, the subsequent motion is described via a correction to the Lorentz force, known as the Lorentz-Abraham-Dirac force. The aim of this research is to use the Lorentz-AbrahamDirac force to computationally simulate the radiation damping that occurs during nonlinear inverse Compton scattering (NLICS). We build on our previous work and the computer program, SENSE [1] [2], which simulates single-emission inverse Compton scattering to incorporate the effect of multiple emissions, thereby modeling radiation reaction. INTRODUCTION The program SENSE [1] [2] was developed to accurately simulate the classical scattering of a photon off of an electron in the linear and non-linear Thomson and Compton regimes. However, in the non-linear regimes the effect of the radiation reaction can become significant. This is clearly the case in the Compton regime where electron recoil is non-negligible due to the expected number of emitted photons being greater than unity, i.e. when $n _ { \\gamma } > 1$ [1]. In particular, the Lorentz force only accurately describes the motion of the electron when $( 8 \\pi \\gamma _ { 0 } r _ { e } a _ { 0 } ^ { 2 } \\sigma ) / ( 3 \\lambda _ { 0 } ) \\ll 1$ [3]. Here, $\\gamma _ { 0 }$ is the initial relativistic factor, $r _ { e }$ is the classical electron radius, $a _ { 0 } =$ $A _ { 0 } / ( m _ { e } c )$ is the normalized field strength parameter, $\\sigma$ is the length of the pulse, and $\\lambda _ { 0 }$ is the wavelength in the lab frame. | augmentation | NO | 0 |
IPAC | Why do slower (non-relativistic) electrons produce stronger radiation at subwavelength separations? | Because in the near field (??d ? 1), slower electrons generate stronger near-field amplitudes, leading to enhanced spontaneous emission despite increased evanescence. | Reasoning | Maximal_spontaneous_photon_emission_and_energy_loss_from_free_electrons.pdf | $$ Intuitively, at very short time, we would expect the fields generated by a given particle to look like free-space radiation, allowing us to further break up $\\mathbf { E } _ { c }$ into $$ \\mathbf { E } _ { c } ( \\mathbf { r } , t ) = \\mathbf { E } _ { 0 } ( \\mathbf { r } , t ) + \\mathbf { E } _ { \\mathrm { q i } } ( \\mathbf { r } , t ) , $$ where $\\mathbf { E } _ { 0 } ( \\mathbf { r } , t )$ is the field generated by a point particle at position $\\mathbf { r } ^ { \\prime }$ and moving with velocity $\\mathbf { v } ( t _ { R } )$ , where $t _ { R } ~ =$ $| \\mathbf { r } - \\mathbf { r } ^ { \\prime } | / c$ is the so-called ’retarded’ time. This field is simply the standard Lienerd-Wiechert potential. The second term, ${ \\bf E } _ { \\mathrm { q i } }$ in Eq. (3) are the contributions due to the first few wall reflections where the evanescent modes still contribute. | augmentation | NO | 0 |
IPAC | Why do slower (non-relativistic) electrons produce stronger radiation at subwavelength separations? | Because in the near field (??d ? 1), slower electrons generate stronger near-field amplitudes, leading to enhanced spontaneous emission despite increased evanescence. | Reasoning | Maximal_spontaneous_photon_emission_and_energy_loss_from_free_electrons.pdf | We adopt notation and analytical electron scattering factors from Kirkland [1] henceforth. THEORY The incident wavefunction of the electron is approximated by a plane wave propagating along the optical axis in ùëß‚àídirection given by $$ \\psi _ { 0 } ( z ) = \\exp \\left( i 2 \\pi k _ { z } z \\right) , $$ where the wavenumber of the electron is related to its deBroglie wavelength by [1] $$ k _ { z } = { \\frac { 1 } { \\lambda } } = { \\frac { \\sqrt { e V ( 2 m c ^ { 2 } + e V ) } } { h c } } . $$ $e$ is the electron charge magnitude, $m$ is electron mass, $c$ is speed of light, $h$ is Planck‚Äôs constant, and $V$ is the accelerating voltage giving rise to electron‚Äôs kinetic energy $e V$ . Equation (2) is easily obtained by equating total energy in particle representation to that in wave representation [1]. Since we are interested in calculating the effects of thin samples in transmitted electrons, the total electron energy in the sample becomes $E = m c ^ { 2 } + e V + e V _ { a }$ , where $\\boldsymbol { V } _ { a }$ is the sample‚Äôs potential. The new wavenumber is given by | augmentation | NO | 0 |
IPAC | Why do slower (non-relativistic) electrons produce stronger radiation at subwavelength separations? | Because in the near field (??d ? 1), slower electrons generate stronger near-field amplitudes, leading to enhanced spontaneous emission despite increased evanescence. | Reasoning | Maximal_spontaneous_photon_emission_and_energy_loss_from_free_electrons.pdf | Table: Caption: Table 2: X-ray Output Properties Body: <html><body><table><tr><td>Parameter</td><td>Analytical</td><td>MITHRA</td><td>Unit</td></tr><tr><td>Max Power</td><td>16.8</td><td>13.7</td><td>MW</td></tr><tr><td>Photon Energy</td><td>1.04</td><td>1.04</td><td>keV</td></tr><tr><td>Gain Length</td><td>137</td><td>220</td><td>μm</td></tr><tr><td>Source Size (rms)</td><td>0.1</td><td>0.2</td><td>μm</td></tr><tr><td>Opening Angle</td><td>0.9</td><td>1.5</td><td>mrad</td></tr><tr><td>Pulse Length</td><td>0.6</td><td>0.5</td><td>fs</td></tr><tr><td>M²</td><td>1.0</td><td>1.8</td><td></td></tr></table></body></html> a) Radiated Power 20 Head-on Static 10 Overtaking 0 0 1 2 3 Interaction (mm) b) Head-on Static Overtaking 2.5 2.5 1 2.5 0 U 0 0 -2.5 0 -2.5 0 -2.5 0 -2.502.5 -2.502.5 -2.502.5 x(mm) x(mm) x(mm) c) HRadiated Spectrum Static Overtaking 0 1.0 1.02 1.04 1.06 Photon Energy (keV) a) Radiated Power 30 57.437 57.837 15 58.237 0 0 1 2 3 Interaction (mm) b) = γ = γ = 2.5 2.5 1 2.5 Ol 0 0 -2.5 0 -2.5 0 -2.5 0 -2.502.5 -2.502.5 -2.502.5 x(mm) x(mm) x(mm) c) 5Radiated Spectrum 57.837 58.237 0 1.0 1.02 1.04 1.06 Photon Energy (keV) [10] which has an $\\mathbf { M } ^ { 2 } = 2$ , at some time frames throughout the simulation. Figure 4 compares simulations of the head-on, static, and overtaking geometries with the same effective undulator period of $7 . 8 \\mu \\mathrm { m }$ . Table 1 includes the electron beam parameters for these cases. For all three cases the radiated power immediately grows exponentially, and the spectrum has one peak with a bandwidth of about $1 \\%$ , which is the inverse of the number of microbunches. We found the best performance in the overtaking case and a better match to the static and head-on case when the electron bunch was nanobunched to a wavelength of $1 . 2 2 \\mathrm { n m }$ instead of $1 . 2 4 \\ : \\mathrm { n m }$ . This also results in the bunch emitting immediately after entering the undulator in the overtaking case. After tuning, the radiated power agrees reasonably well for all 3 cases with the same electron beam and effective undulator parameters. The electromagnetic fields used for head-on and overtaking geometries propagate at light speed in a physically realistic simulation. | augmentation | NO | 0 |
IPAC | Why do slower (non-relativistic) electrons produce stronger radiation at subwavelength separations? | Because in the near field (??d ? 1), slower electrons generate stronger near-field amplitudes, leading to enhanced spontaneous emission despite increased evanescence. | Reasoning | Maximal_spontaneous_photon_emission_and_energy_loss_from_free_electrons.pdf | $$ where $m _ { 0 }$ denotes the rest mass of the electron, $\\beta$ the ratio of the electron velocity and light velocity $c$ , and $\\theta _ { \\gamma }$ the angle of the scattered gamma-ray photon. In the case of a head-on collision, $\\phi = \\pi$ Eq. (1) can be simplified to $$ E _ { \\gamma } = \\frac { ( 1 + \\beta ) E _ { p } } { 1 - \\beta \\cos \\theta _ { \\gamma } + ( E _ { p } / m _ { 0 } c ^ { 2 } ) \\sqrt { 1 - \\beta ^ { 2 } } ( 1 + \\cos \\theta _ { \\gamma } ) } . $$ The maximum scattered photon energy, which can be observed in the backward direction of the incident photon, namely at $\\theta _ { \\gamma } \\ = \\ 0$ , is given by $E _ { \\gamma } = 4 \\gamma ^ { 2 } E _ { p }$ with $\\gamma$ the Lorentz factor, $\\gamma ~ = ~ \\sqrt { 1 - \\beta ^ { 2 } }$ , and $E _ { p }$ the energy of the primary laser photon. As revealed by this equation, the energy of the backward scattered photons is estimated to be $4 \\gamma ^ { 2 }$ times higher than the energy of the initial laser photons. For LHeC, in the case of a $\\mathrm { C O } _ { 2 }$ laser with laser photon energy | augmentation | NO | 0 |
IPAC | Why do slower (non-relativistic) electrons produce stronger radiation at subwavelength separations? | Because in the near field (??d ? 1), slower electrons generate stronger near-field amplitudes, leading to enhanced spontaneous emission despite increased evanescence. | Reasoning | Maximal_spontaneous_photon_emission_and_energy_loss_from_free_electrons.pdf | BETATRON RADIATION We will consider the betatron radiation of an ultrarelativistic electron that propagates in a plasma column, namely ion channel [2]. The plasma column is a cylindrical region free of electron, which is a good approximation of the bubble regime [3]. In much the same way as the accelerating forces in a plasma accelerator are greater than those in a conventional accelerator, so are the focussing forces also many orders of magnitude greater, these transverse, rerstoring forces (Eq. (1)) are created by the radial displacement and longitudinal motion of the plasma wave electrons. $$ F _ { r e s } = - m \\omega _ { p } ^ { 2 } r / 2 $$ Where $\\omega _ { p } = \\sqrt { e ^ { 2 } n _ { e } / m _ { e } \\epsilon _ { 0 } }$ is the plasma frequency. In these fields, the electrons wiggle with a betatron frequency $\\omega _ { \\beta } = $ $\\omega _ { p } / \\sqrt { 2 \\gamma }$ and wavelength given by $\\lambda _ { \\beta } = \\sqrt { 2 \\gamma } \\lambda _ { p } . 4$ 1 | augmentation | NO | 0 |
Expert | Why do slower (non-relativistic) electrons produce stronger radiation at subwavelength separations? | Because in the near field (??d ? 1), slower electrons generate stronger near-field amplitudes, leading to enhanced spontaneous emission despite increased evanescence. | Reasoning | Maximal_spontaneous_photon_emission_and_energy_loss_from_free_electrons.pdf | To overcome this deficiency, we theoretically propose a new mechanism for enhanced Smith–Purcell radiation: coupling of electrons with $\\mathrm { B I C } s ^ { 1 3 }$ . The latter have the extreme quality factors of guided modes but are, crucially, embedded in the radiation continuum, guaranteeing any resulting Smith–Purcell radiation into the far field. By choosing appropriate velocities $\\beta = a / m \\lambda$ ( $m$ being any integer; $\\lambda$ being the BIC wavelength) such that the electron line (blue or green) intersects the $\\mathrm { T E } _ { 1 }$ mode at the BIC (red square in Fig. 4b), the strong enhancements of a guided mode can be achieved in tandem with the radiative coupling of a continuum resonance. In Fig. 4c, the incident fields of electrons and the field profile of the BIC indicate their large modal overlaps. The BIC field profile shows complete confinement without radiation, unlike conventional multipolar radiation modes (see Supplementary Fig. 9). The Q values of the resonances are also provided near a symmetry-protected $\\mathrm { B I C ^ { 1 3 } }$ at the $\\Gamma$ point. Figure 4d,e demonstrates the velocity tunability of BIC-enhanced radiation—as the phase matching approaches the BIC, a divergent radiation rate is achieved. | 4 | NO | 1 |
Expert | Why do slower (non-relativistic) electrons produce stronger radiation at subwavelength separations? | Because in the near field (??d ? 1), slower electrons generate stronger near-field amplitudes, leading to enhanced spontaneous emission despite increased evanescence. | Reasoning | Maximal_spontaneous_photon_emission_and_energy_loss_from_free_electrons.pdf | Finally, we turn our attention to an ostensible peculiarity of the limits: equation (4) evidently diverges for lossless materials $( \\mathrm { I m } \\chi \\to 0 ) \\dot { { \\frac { . } { . } } }$ ), seemingly providing little insight. On the contrary, this divergence suggests the existence of a mechanism capable of strongly enhancing Smith–Purcell radiation. Indeed, by exploiting high-Q resonances near bound states in the continuum (BICs)13 in photonic crystal slabs, we find that Smith–Purcell radiation can be enhanced by orders of magnitude, when specific frequency-, phaseand polarization-matching conditions are met. A 1D silicon $\\left( \\chi = 1 1 . 2 5 \\right)$ -on-insulator $\\mathrm { \\ S i O } _ { 2 } ,$ $\\chi = 1 . 0 7 \\$ ) grating interacting with a sheet electron beam illustrates the core conceptual idea most clearly. The transverse electric (TE) $( E _ { x } , H _ { y } , E _ { z } )$ band structure (lowest two bands labelled $\\mathrm { T E } _ { 0 }$ and $\\mathrm { T E } _ { 1 . } ^ { \\cdot }$ ), matched polarization for a sheet electron beam (supplementary equation S41b)), is depicted in Fig. 4b along the $\\Gamma { \\mathrm { - } } \\mathrm { X }$ direction. Folded electron wavevectors, $k _ { \\nu } = \\omega / \\nu ,$ are overlaid for two distinct velocities (blue and green). Strong electron–photon interactions are possible when the electron and photon dispersions intersect: for instance, $k _ { \\nu }$ and the $\\mathrm { T E } _ { 0 }$ band intersect (grey circles) below the air light cone (light yellow shading). However, these intersections are largely impractical: the $\\mathrm { T E } _ { 0 }$ band is evanescent in the air region, precluding free-space radiation. Still, analogous ideas, employing similar partially guided modes, such as spoof plasmons33, have been explored for generating electron-enabled guided waves34,35. | 4 | NO | 1 |
IPAC | Why do slower (non-relativistic) electrons produce stronger radiation at subwavelength separations? | Because in the near field (??d ? 1), slower electrons generate stronger near-field amplitudes, leading to enhanced spontaneous emission despite increased evanescence. | Reasoning | Maximal_spontaneous_photon_emission_and_energy_loss_from_free_electrons.pdf | The first of the coupled equations describes the change of energy due to a longitudinal electric field caused by a gradient of the charge distribution. The second equation can be rewritten as $d z _ { i } / d s = \\eta _ { i } / \\gamma ^ { 2 }$ meaning that relativistic particles with an energy offset change their longitudinal position due to a velocity mismatch. Figure 3 shows an example of the squared bunching factor $| b _ { 1 0 } | ^ { 2 }$ as function of $R _ { 5 6 }$ and drift length for a moderate peak current of $7 0 0 \\mathrm { A }$ (before density modulation). Along the $R _ { 5 6 }$ axis, the first maximum occurs for optimum density modulation. The Ǡth maximum results from a modulation with two density maxima which are $( n - 1 ) \\lambda _ { \\mathrm { L } } / 1 0$ apart as illustrated by Fig. 4 for $n \\leq 3$ . The bunching factor decreases strongly over a drift length of $2 0 \\mathrm { m }$ , but the LSC-induced reduction is different for each maximum, causing their relative height to change. Furthermore, the maxima are slightly shifted to lower $R _ { 5 6 }$ with increasing drift length because the LSC effect causes additional longitudinal dispersion. | 1 | NO | 0 |
Expert | Why do slower (non-relativistic) electrons produce stronger radiation at subwavelength separations? | Because in the near field (??d ? 1), slower electrons generate stronger near-field amplitudes, leading to enhanced spontaneous emission despite increased evanescence. | Reasoning | Maximal_spontaneous_photon_emission_and_energy_loss_from_free_electrons.pdf | $$ written in cylindrical coordinates $( x , \\rho , \\psi )$ ; here, $K _ { n }$ is the modified Bessel function of the second kind, $k _ { \\nu } = \\omega / \\nu$ and $k _ { \\rho } = \\sqrt { k _ { \\nu } ^ { 2 } - k ^ { 2 } } =$ k/βγ $\\scriptstyle ( k = \\omega / c$ , free-space wavevector; $\\gamma = 1 / \\sqrt { 1 - \\beta ^ { 2 } }$ , Lorentz factor). Hence, the photon emission and energy loss of free electrons can be treated as a scattering problem: the electromagnetic fields $\\mathbf { F } _ { \\mathrm { i n c } } { = } ( \\mathbf { E } _ { \\mathrm { i n c } } , \\ Z _ { 0 } \\mathbf { H } _ { \\mathrm { i n c } } ) ^ { \\mathrm { T } }$ (for free-space impedance $Z _ { 0 } ^ { \\mathrm { ~ \\tiny ~ { ~ \\chi ~ } ~ } }$ are incident on a photonic medium with material susceptibility $\\overline { { \\overline { { \\chi } } } }$ (a $6 { \\times } 6$ tensor for a general medium), causing both absorption and far-field scattering—that is, photon emission—that together comprise electron energy loss (Fig. 1a). | 1 | NO | 0 |
Expert | Why do slower (non-relativistic) electrons produce stronger radiation at subwavelength separations? | Because in the near field (??d ? 1), slower electrons generate stronger near-field amplitudes, leading to enhanced spontaneous emission despite increased evanescence. | Reasoning | Maximal_spontaneous_photon_emission_and_energy_loss_from_free_electrons.pdf | As recently shown in refs 27–29, for a generic electromagnetic scattering problem, passivity—the condition that polarization currents do no net work—constrains the maximum optical response from a given incident field. Consider three power quantities derived from $\\mathbf { F } _ { \\mathrm { i n c } }$ and the total field F within the scatterer volume $V !$ the total power lost by the electron, $P _ { \\mathrm { l o s s } } = - ( 1 / 2 ) \\mathrm { R e } \\int _ { \\mathrm { V } } \\mathbf { J } ^ { * } \\cdot \\mathbf { E d } V = ( \\epsilon _ { 0 } \\omega / 2 ) \\mathrm { I m } \\hat { \\int _ { V } } \\mathbf { F } _ { \\mathrm { ~ i n c } } ^ { \\dagger } \\overline { { \\chi } } \\mathbf { F d } V ,$ the power absorbed by the medium, $P _ { \\mathrm { { a b s } } } \\mathrm { { = } } \\left( \\epsilon _ { 0 } \\omega / 2 \\right) \\mathrm { I m } \\stackrel { \\cdot } { \\int } _ { V } \\mathbf { F } ^ { \\dagger } \\overline { { \\chi } } \\mathbf { F } \\mathrm { { d } } V ,$ and their difference, the power radiated to the far field, $P _ { \\mathrm { r a d } } { = } P _ { \\mathrm { l o s s } } { - } P _ { \\mathrm { a b s } }$ . Treating $\\mathbf { F }$ as an independent variable, the total loss $P _ { \\mathrm { l o s s } }$ is a linear function of $\\mathbf { F }$ , whereas the fraction that is dissipated is a quadratic function of F. Passivity requires non-negative radiated power, represented by the inequality $P _ { \\mathrm { a b s } } { < } P _ { \\mathrm { l o s s } } ,$ which in this framework is therefore a convex constraint on any response function. Constrained maximization (see Supplementary Section 1) of the energy-loss and photon-emission power quantities, $P _ { \\mathrm { l o s s } }$ and $P _ { \\mathrm { r a d } } ,$ directly yields the limits | augmentation | NO | 0 |
Expert | Why do slower (non-relativistic) electrons produce stronger radiation at subwavelength separations? | Because in the near field (??d ? 1), slower electrons generate stronger near-field amplitudes, leading to enhanced spontaneous emission despite increased evanescence. | Reasoning | Maximal_spontaneous_photon_emission_and_energy_loss_from_free_electrons.pdf | Author contributions Y.Y., O.D.M., I.K. and M.S. conceived the project. Y.Y. developed the analytical models and numerical calculations. A.M. prepared the sample under study. Y.Y., A.M., C.R.-C., S.E.K. and I.K. performed the experiment. Y.Y., T.C. and O.D.M. analysed the asymptotics and bulk loss of the limit. S.G.J., J.D.J., O.D.M., I.K. and M.S. supervised the project. Y.Y. wrote the manuscript with input from all authors. Competing interests The authors declare no competing interests. Additional information Supplementary information is available for this paper at https://doi.org/10.1038/ s41567-018-0180-2. Reprints and permissions information is available at www.nature.com/reprints. Correspondence and requests for materials should be addressed to Y.Y. or O.D.M. or I.K. Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Methods Fourier transform convention. Throughout the paper, we adopt the following Fourier transform conventions $$ f ( \\omega ) \\triangleq \\int f ( t ) \\mathrm { e } ^ { i \\omega t } \\mathrm { d } t , f ( t ) \\triangleq \\frac { 1 } { 2 \\pi } \\int f ( \\omega ) \\mathrm { e } ^ { - i \\omega t } \\mathrm { d } \\omega $$ $$ | augmentation | NO | 0 |
IPAC | Why do synchrotrons not use protons? | Because the radiation power is inversely proportional to the fourth power of particle mass, making radiation effects negligible. | Reasoning | Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation | INTRODUCTION Synchrotron radiation (SR) sources based on electron storage rings are among the primary tools in materials research, physics, chemistry, and biology to study the structure of matter on the atomic scale [1]. However, phase transitions, chemical reactions as well as changes of molecular conformation, electronic or magnetic structure take place on the sub-picosecond scale which cannot be resolved by conventional synchrotron radiation pulses which are constrained to tens of picoseconds by the longitudinal beam dynamics in a storage ring. The femtosecond regime has been accessed by lasers at near-visible wavelengths and with high-harmonic generation, and more recently by high-gain free-electron lasers (FELs) in the extreme ultraviolet and X-ray regime [2]. While X-ray FELs serve one user at a time with the repetition rate of a linear accelerator and their number is worldwide still below ten, there are about 50 SR sources supplying multiple beamlines simultaneously with laser modulator radiator CHG chicane WW EEHG -1 0 z/ z/2 laser modulator laser modulator radiator chicane chicane 8 Ôºö 0.5 before after 0.5 ÂáØ E Ê≠£0.5 -0.5 -0.5 modulation 0 z/2L 0 z/2 0 stable and tunable radiation at a rate of up to ${ 5 0 0 } \\mathrm { M H z }$ . It is therefore worthwhile to consider possibilities of extending SR sources towards shorter pulse duration. | augmentation | NO | 0 |
IPAC | Why do synchrotrons not use protons? | Because the radiation power is inversely proportional to the fourth power of particle mass, making radiation effects negligible. | Reasoning | Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation | $$ \\Delta W _ { s } = q E _ { z } T l \\cos \\phi = q T V \\cos ( \\phi ) , $$ where $q$ , and $T$ are the particle charge, and transit time factor of the design particles, respectively. Much more details are available in text or handy USPAS lecture notes [10]. The SLAC, Fermilab, and LANSCE (LANL) accelerators are the successors to this technique in a larger space. However, there are many small-size C-band, S-band, and X-band RF accelerators around with much shorter lengths and very high energy gradient [11, 12]. Some of these are used for radiotherapy and security applications ( $7 0 0 \\mathrm { R } / \\mathrm { m } )$ [13, 14]. Betatron A betatron [15‚Äì20] is a circular electron accelerator based on Faraday‚Äôs law. Figure 4(a) shows an electric conductive coil, that is driven by a $5 0 { \\mathrm { - } } 6 0 \\operatorname { H z }$ pulse voltage, is embedded to magnetic materials to generate magnetic flux $( \\phi )$ . A change of flux $( \\partial \\phi / \\partial t )$ produces an electric field $( E )$ . If electrons are injected into a nearby orbit within a torodial vacuum chamber, injecting electrons causes the field to influence and accelerate them azimuthally, while the vertical magnetic field density $( B )$ focuses them in a circular motion. | augmentation | NO | 0 |
expert | Why do synchrotrons not use protons? | Because the radiation power is inversely proportional to the fourth power of particle mass, making radiation effects negligible. | Reasoning | Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation | $$ and $$ \\vec { A } ( \\vec { x } , t ) = \\frac { 1 } { 4 \\pi \\varepsilon _ { 0 } C ^ { 2 } } \\int d ^ { 3 } \\vec { x } ^ { \\prime } \\int d t ^ { \\prime } \\frac { \\vec { j } ( \\vec { x } ^ { \\prime } , t ) } { | \\vec { x } - \\vec { x } ^ { \\prime } | } \\delta \\left( t ^ { \\prime } + \\frac { \\vec { x } - \\vec { x } ^ { \\prime } } { c } - t \\right) . $$ Solving the wave equation in this most general sense is quite elaborate. The derivation can be found in Jackson [1], Chapter 6. Here, we just cite the result: the intensity of the radiation per solid angle $d \\Omega$ and per frequency interval $d \\omega$ is given by $$ \\frac { d ^ { 3 } I } { d \\Omega d \\omega } = \\frac { e ^ { 2 } } { 1 6 \\pi ^ { 3 } \\varepsilon _ { 0 } c } \\left( \\frac { 2 \\omega \\rho } { 3 c \\gamma ^ { 2 } } \\right) ^ { 2 } \\left( 1 + \\gamma ^ { 2 } \\vartheta ^ { 2 } \\right) ^ { 2 } \\left[ K _ { 2 / 3 } ^ { 2 } ( \\xi ) + \\frac { \\gamma ^ { 2 } \\vartheta ^ { 2 } } { 1 + \\gamma ^ { 2 } \\vartheta ^ { 2 } } K _ { 1 / 3 } ^ { 2 } ( \\xi ) \\right] , | 4 | NO | 1 |
expert | Why do synchrotrons not use protons? | Because the radiation power is inversely proportional to the fourth power of particle mass, making radiation effects negligible. | Reasoning | Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation | $$ When deriving the equations for the beam dynamics in the horizontal phase space, we need to consider: ‚Äì Change in momentum: the emission of radiation leads to a recoil of the electron. This change in momentum is the same that we considered in the vertical phase space; ‚Äì Dispersion: the emission of radiation results in a change in the energy deviation, denoted as $\\delta$ . This deviation brings about subsequent changes in the horizontal coordinate $x$ and its associated momentum $p _ { x }$ . When we explored the beam dynamics in the vertical phase space, we ignored the second factor, as we assumed that the vertical dispersion is zero. This assumption streamlined the analysis, but it can certainly not be made in the horizontal dimension. While the details of the interplay between the emission of synchrotron radiation and the damping of the emittance are unique to each plane, the outcomes are similar. The horizontal emittance decays exponentially $$ \\frac { d \\varepsilon _ { x } } { d t } = - \\frac { 2 } { \\tau _ { x } } \\varepsilon _ { x } $$ $$ \\Rightarrow \\varepsilon _ { x } ( t ) = \\varepsilon _ { x } ( 0 ) \\exp \\left( - 2 \\frac { t } { \\tau _ { x } } \\right) | 1 | NO | 0 |
expert | Why do synchrotrons not use protons? | Because the radiation power is inversely proportional to the fourth power of particle mass, making radiation effects negligible. | 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 | 1 | NO | 0 |
expert | Why do synchrotrons not use protons? | Because the radiation power is inversely proportional to the fourth power of particle mass, making radiation effects negligible. | Reasoning | Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation | ‚Äì Free electrons, ‚Äì Electrons bound to an atom, ‚Äì Crystals. The interaction of X-rays with matter is determined by the cross-section, which is itself proportional to the square of the so-called Thomson radius. The Thomson radius, in turn, is inversely proportional to the mass of the charged particle. Consequently, considering the substantial mass difference between protons and electrons, the interaction with protons can be ignored. Furthermore, neutrons, which have the same mass as protons but lack electric charge, so do not interact with electromagnetic radiation, such as $\\mathrm { \\Delta } X$ -rays. They can thus be entirely ignored. The attenuation of $\\mathrm { \\Delta X }$ -rays in matter can be described by Beer‚Äôs Law $$ I ( z ) = I _ { 0 } \\exp ( - \\mu z ) , $$ where $\\mu$ is the attenuation coefficient. One commonly normalizes to the density $\\rho$ , and defines the mass attenuation coefficient as $\\mu / \\rho$ . Values for attenuation coefficient can be found in the $\\mathrm { \\Delta } X$ -ray data booklet [6] or at https://henke.lbl.gov/optical_constants/atten2.html. The relevant processes that contribute to the X-ray cross section are shown in Fig. I.10.9. Nuclear processes are only relevant for gamma rays, i.e. at photon energies far higher than what can be achieved by presently available synchrotrons. Pair production can occur only for photon energies above twice the electron rest energy, $2 \\times 5 1 1 \\mathrm { k e V } .$ The only processes relevant in synchrotrons are: | 1 | NO | 0 |
expert | Why do synchrotrons not use protons? | Because the radiation power is inversely proportional to the fourth power of particle mass, making radiation effects negligible. | Reasoning | Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation | $$ and the equilibrium value, also called the natural horizontal emittance is $$ \\varepsilon _ { x } ( \\infty ) = C _ { q } \\gamma ^ { 2 } \\frac { I _ { 5 } } { j _ { x } I _ { 2 } } , $$ where the fifth synchrotron radiation integral $I _ { 5 }$ is defined in Equation I.10.35, and the electron quantum constant $C _ { q }$ is $$ C _ { q } = \\frac { 5 5 } { 3 2 \\sqrt { 3 } } \\frac { \\hbar } { m _ { e } c } \\approx 3 . 8 3 2 \\cdot 1 0 ^ { - 1 3 } \\mathrm { m } . $$ (The factor $\\frac { 5 5 } { 3 2 { \\sqrt { 3 } } }$ comes from the calculation of the emission spectrum of synchrotron radiation, integrating over all photon energies and angles). A similar effect occurs in the longitudinal phase space. An electron emitting an X-ray photon loses a small, but significant fraction of its energy. This induces an energy spread among the electrons in the bunches. This energy spread, in tandem with the action of dispersion in the accelerator, results in an increase in the longitudinal phase space distribution, thereby increasing the longitudinal emittance of the beam. Quantum excitation thus acts as a natural counterpart to radiation damping. | 1 | NO | 0 |
expert | Why do synchrotrons not use protons? | Because the radiation power is inversely proportional to the fourth power of particle mass, making radiation effects negligible. | Reasoning | Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation | 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 . }$ ‚Äì What can be the rationale for this change? Assume that the lattice is the same for both energies. ‚Äì 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 }$ . ‚Äì Calculate the diameter of the proton trajectory and the revolution frequency. ‚Äì How large is the power emitted by synchrotron radiation? ‚Äì 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: ‚Äì The radius of curvature, ‚Äì The critical energy of the emitted synchrotron radiation, ‚Äì The energy emitted in one turn. | 1 | NO | 0 |
expert | Why do synchrotrons not use protons? | Because the radiation power is inversely proportional to the fourth power of particle mass, making radiation effects negligible. | Reasoning | Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation | File Name:Ischebeck_-_2024_-_I.10_‚Äî_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 R√∂ntgen, 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. | augmentation | NO | 0 |
expert | Why do synchrotrons not use protons? | Because the radiation power is inversely proportional to the fourth power of particle mass, making radiation effects negligible. | Reasoning | Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation | $$ \\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} | augmentation | NO | 0 |
expert | Why do synchrotrons not use protons? | Because the radiation power is inversely proportional to the fourth power of particle mass, making radiation effects negligible. | Reasoning | Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation | The size of an atom is on the order of $1 \\ \\mathring { \\mathrm { A } } = 1 0 ^ { - 1 0 } \\ \\mathrm { m }$ , while the pixels of an X-ray detector are around $1 0 0 ~ { \\mu \\mathrm { m } }$ in size. A magnification of $1 0 ^ { 6 }$ would thus be required, and it turns out that no X-ray lens can provide this9. Unlike lenses for visible light, where glasses of different index of refraction and different dispersion can be combined to compensate lens errors, this is not possible for X-rays. Scientist use thus diffractive imaging, where a computer is used to reconstruct the distribution of atoms in the molecule from the diffraction pattern. When a crystal is placed in a coherent X-ray beam, constructive interference occurs if the Bragg condition (Equation I.10.48) for the incoming and outgoing rays is fulfilled for any given crystal plane. The resulting diffraction pattern appears as a series of spots or fringes, commonly captured on a detector. As an example, the diffraction pattern of a complex biomolecule is shown in Fig. I.10.13. The crystal is then rotated to change the incoming angle, to allow for diffraction from other crystal planes to be recorded. Note that the detector records the number of photons, i.e., the intensity of the diffracted wave, but all phase information is lost. | augmentation | NO | 0 |
expert | Why do synchrotrons not use protons? | Because the radiation power is inversely proportional to the fourth power of particle mass, making radiation effects negligible. | Reasoning | Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation | $$ \\begin{array} { r c l } { { \\displaystyle \\sigma _ { r } } } & { { = } } & { { \\displaystyle \\frac { 1 } { 4 \\pi } \\sqrt { \\lambda L } } } \\\\ { { \\displaystyle \\sigma _ { r ^ { \\prime } } } } & { { = } } & { { \\displaystyle \\sqrt { \\frac { \\lambda } { L } } . } } \\end{array} $$ This diffraction limit is symmetric in $x$ and $y$ . The effective source size is $$ \\begin{array} { r c l } { \\sigma _ { ( x , y ) , \\mathrm { e f f } } } & { = } & { \\sqrt { \\sigma _ { ( x , y ) } ^ { 2 } + \\sigma _ { r } ^ { 2 } } } \\end{array} $$ $$ \\begin{array} { r c l } { \\sigma _ { ( x ^ { \\prime } , y ^ { \\prime } ) , \\mathrm { e f f } } } & { = } & { \\sqrt { \\sigma _ { ( x ^ { \\prime } , y ^ { \\prime } ) } ^ { 2 } + \\sigma _ { r ^ { \\prime } } ^ { 2 } } . } \\end{array} | augmentation | NO | 0 |
expert | Why do synchrotrons not use protons? | Because the radiation power is inversely proportional to the fourth power of particle mass, making radiation effects negligible. | Reasoning | Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation | $$ 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} | augmentation | NO | 0 |
expert | Why do synchrotrons not use protons? | Because the radiation power is inversely proportional to the fourth power of particle mass, making radiation effects negligible. | Reasoning | Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation | I.10.6.3 Tomographic imaging and ptychography Tomography is a powerful imaging technique that reconstructs a three-dimensional object from its twodimensional projections. It is used widely in medicine, where it allows a detailed view of our skeleton. Synchrotron radiation sources, with their brilliant and monochromatic beams, allow reducing the exposure time to less than a millisecond while achieving micrometer resolution. This makes the technique useful for research in fields ranging from materials science to biology (see Fig. I.10.16). The process involves rotating the sample through a range of angles relative to the X-ray beam, while collecting a series of two-dimensional absorption images. The three-dimensional distribution is reconstructed from the two-dimensional images. The monochromatic and coherent X-ray beams from a synchrotron allow recording phase contrast images, which can capture finer details of biological samples than the usual absorption contrast images. In ptychography, a coherent X-ray beam is scanned across the sample in overlapping patterns, and the diffraction pattern from each area is recorded. These overlapping diffractions provide redundant information. The reconstruction algorithms used in ptychography are able to retrieve both the amplitude and phase information from the scattered wavefronts, leading to highly detailed images with nanometer resolution. Ptychography is particularly advantageous for studying materials with fine structural details and can be applied to a wide range of materials, including biological specimens, nanomaterials, and integrated electronic circuits (see e.g. https://youtu.be/GvyTiK9CNO0). | augmentation | NO | 0 |
expert | Why do synchrotrons not use protons? | Because the radiation power is inversely proportional to the fourth power of particle mass, making radiation effects negligible. | Reasoning | Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation | ‚Äì Photoelectric absorption: absorption by electrons bound to atoms; ‚Äì Thomson scattering: elastic scattering, i.e. scattering without energy transfer between the X-ray and a free electron; ‚Äì 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‚Äôs oscillation frequency is driven by the frequency of the electromagnetic wave, and there‚Äôs no energy loss in the system. | augmentation | NO | 0 |
expert | Why do synchrotrons not use protons? | Because the radiation power is inversely proportional to the fourth power of particle mass, making radiation effects negligible. | Reasoning | Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation | How would you measure this radiation? I.10.7.27 Superconducting undulators What is the advantage of using undulators made with superconducting coils, in comparison to permanentmagnet arrays? What are drawbacks? I.10.7.28 In-vacuum undulators What are the advantages of using in-vacuum undulators? What are possible difficulties? I.10.7.29 Instrumentation How would you measure the vertical emittance in a storage ring? I.10.7.30 Top-up operation What are the advantages of top-up operation? What difficulties have to be overcome to establish top-up in a storage ring? (give one advantage and one difficulty for 1P.; give one more advantage and one more difficulty for $\\begin{array} { r } { 1 \\mathrm { P } . \\star . } \\end{array}$ .) I.10.7.31 Fundamental limits The SLS 2.0, a diffraction limited storage ring, aims for an electron energy of $2 . 4 \\mathrm { G e V }$ and an emittance of $1 2 6 \\mathrm { p m }$ . How far is this away from the de Broglie emittance, i.e. the minimum emittance given by the uncertainty principle? I.10.7.32 Applications Why are synchrotrons important for science? I.10.7.33 Applications What applications for industry are there to synchrotrons? I.10.7.34 Orbit correction Which devices are used to measure and correct the orbit inside a synchrotron? | augmentation | NO | 0 |
expert | Why do synchrotrons not use protons? | Because the radiation power is inversely proportional to the fourth power of particle mass, making radiation effects negligible. | Reasoning | Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation | Two important aspects: ‚Äì The photon energy is proportional to the square of the energy of the electrons; ‚Äì The photon energy decreases with higher magnetic field.4 We are looking at spontaneous radiation, thus the total energy loss of the electrons is proportional to the distance travelled. Consequently, the total intensity of the radiation grows proportionally to the distance travelled. The width of the radiation cone for the fundamental wavelength decreases inversely proportional to the distance, therefore the central intensity grows as the square of the undulator length. The radiation is linearly polarized in $x$ direction. Undulators thus make use of the coherent enhancement of the radiation of each electron individually, which leads to a substantial increase in brillance (Equation I.10.1). This coherence occurs at specific wavelengths, which can be tuned by adjusting the strength of the magnetic field5, and occurs in a very narrow angle around the forward direction. Free electron lasers achieve an additional coherent enhancement from multiple electrons in each microbunch, which results in another supercalifragilisticexpialidocious enhancement in the peak brilliance. To compute the brillance of the radiation from an undulator, one first has to determine the flux $\\dot { N } _ { \\gamma }$ and the effective source size $\\boldsymbol { \\sigma } _ { ( x , y ) \\mathrm { e f f } }$ and divergence $\\sigma _ { ( x ^ { \\prime } , y ^ { \\prime } ) , \\mathrm { e f f } }$ . These are given by the electron beam size $\\sigma _ { ( x , y ) }$ and divergence $\\sigma _ { ( x ^ { \\prime } , y ^ { \\prime } ) }$ , and the diffraction limit for the radiation. Electron beam size and divergence can be calculated from the Twiss parameters $\\beta$ and $\\gamma$ , and the emittance $\\varepsilon$ of the beam. The diffraction limits for the radiation $\\sigma _ { r }$ and $\\sigma _ { r ^ { \\prime } }$ can be calculated, considering the length of the source (which is equal to the undulator length) $L$ | augmentation | NO | 0 |
expert | Why do synchrotrons not use protons? | Because the radiation power is inversely proportional to the fourth power of particle mass, making radiation effects negligible. | Reasoning | Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation | $$ The radiation is emitted in all directions except in the direction of acceleration (see Fig. I.10.3 A). The frequency of the emitted radiation is exactly the revolution frequency $$ f = { \\frac { v } { 2 \\pi \\rho } } . $$ I.10.2.2 Relativistic particles moving in a dipole field For relativistic particles, this radiation is Lorentz-boosted in the forward direction (see Fig. I.10.3 B). The relativistic Doppler shift results in significantly shorter wavelengths, corresponding to higher photon energies. Furthermore, the radiation seen by an observer in the plane of revolution is pulsed, peaking every time that the particle passes by. The properties of this so-called synchrotron radiation can be calculated directly from Maxwell‚Äôs equations, without the need for material constants. For a particle that follows a trajectory $\\vec { x } = \\vec { r } ( t )$ , the charge density and the current distribution are given by $$ \\rho ( \\vec { x } , t ) = e \\delta ^ { ( 3 ) } ( \\vec { x } - \\vec { r } ( t ) ) \\quad \\mathrm { a n d } \\quad \\vec { j } ( \\vec { x } , t ) = e \\vec { v } ( t ) \\delta ^ { ( 3 ) } ( \\vec { x } - \\vec { r } ( t ) ) , | augmentation | NO | 0 |
expert | Why do synchrotrons not use protons? | Because the radiation power is inversely proportional to the fourth power of particle mass, making radiation effects negligible. | Reasoning | Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation | One thus receives a series of two-dimensional diffraction patterns. The intensities of the diffracted spots relate to the absolute square of the Fourier transform of the electron density, and their positions correspond to the inverse of the spacing between planes of atoms in the crystal, as described by Bragg‚Äôs law. However, directly computing the electron density from the diffraction pattern is not straightforward due to the phase problem: the detector records only the intensity of the diffracted waves, losing information about their phases. In essence, we only measure the amplitude of the Fourier transform, not its phase, yet both are necessary for accurate reconstruction. Various methods, such as using a known similar structure as a model (molecular replacement) or adding heavy atoms to the crystal (multiple isomorphous replacement), help in estimating these phases. Once the phases are estimated and combined with the intensities, the inverse Fourier transform is used to compute the electron density. The peaks in this electron density map correspond to the locations of the atoms in the crystal. By interpreting this map, scientists can determine the precise arrangement of atoms and thus the molecular structure of the sample. Machine learning (ML) is emerging as a powerful tool in various stages of structure determination from $\\mathrm { \\Delta } X$ -ray crystallography data. | augmentation | NO | 0 |
expert | Why do synchrotrons not use protons? | Because the radiation power is inversely proportional to the fourth power of particle mass, making radiation effects negligible. | Reasoning | Ischebeck_-_2024_-_I.10_—_Synchrotron_radiation | ‚Äì Auger electrons: similarly to fluorescence, this effect starts with the ionization or excitation of an inner-shell electron due to the interaction with the X-ray photon. This leaves a vacancy in the inner shell, which is then filled with an outer-shell electron. However, instead of releasing the excess energy as a photon, the energy is transferred non-radiatively to another outer-shell electron. This transfer of energy gives the second electron enough energy to be ejected from the atom, resulting in the emission of what is known as an Auger electron. These processes are summarized in Fig. I.10.10. Inelastic processes always lead to an energy deposition in the material, often leading to radiation damage, which limits the exposure time in many X-ray experiments. I.10.5.3 Crystal diffraction Imagine many atoms, arranged in a regular lattice, illuminated by a coherent $\\mathrm { \\Delta X }$ -ray source. The elastic scattering on the electron clouds of these atoms will add constructively if all individual waves are in phase. This situation is shown in Fig. I.10.11. Considering a distance $d$ between the crystal planes, and referring to the notation in this figure, we get constructive interference when $$ ( A B + B C ) - ( A C ^ { \\prime } ) = n \\lambda | augmentation | NO | 0 |
IPAC | Why does alternating the structure geometry reduce unwanted effects? | Quadrupole wakes induced in horizontal structure are compensated by vertical structrure downstream | Reasoning | Beam_performance_of_the_SHINE_dechirper.pdf | SUMMARY A detailed experimental study of the transverse dynamics in a variable gap planar DWA structure and for a cylindrical DWA structure has been performed. The results were used to validate the in-house developed, scalable, lightweight code DiWaCAT. The suppression of deflecting dipole wakefields, and consequently suppression of BBU, was observed through increasing the ellipticity of the beam in the planar structure. However, on-axis quadrupole-like wakefields were found to disrupt the beam phase space and increase the projected emittance, with this effect increasing with beam ellipticity. The consequences of this on-axis field were studied in an exploratory study for a ‘practical future’ facility with $1 \\mathrm { G e V }$ $1 0 \\mathrm { n C }$ beam presented in [5]. In summary, these forces act to reduce the horizontal transverse size of the beam, and push charge towards the centre of the structure, where $F _ { y }$ is higher. This leads to substantial losses whether the beam is generated on-axis or with an initial offset. On-axis transverse forces were observed in the cylindrical structure and were comparatively less than the planar structure (when controlled for variation in $\\langle E _ { z } \\rangle$ ). However, their presence suggests that a change of structure geometry will not substantially increase the beam propagation distance, or efficiency, of a future DWA facility. Transverse dynamics, beam stability, and efficiency will be the subject of future study at the FEBE beamline at CLARA [9]. | augmentation | NO | 0 |
IPAC | Why does alternating the structure geometry reduce unwanted effects? | Quadrupole wakes induced in horizontal structure are compensated by vertical structrure downstream | Reasoning | Beam_performance_of_the_SHINE_dechirper.pdf | Power inW[Magnitude 450 400 -0.2\\*sin(t/10) 350 0.6\\*sin(t/10) 300 250 W 200 150 100 50 0.5 1 1.5 2 2.5 3 3.5 4 Time/ns Figure 8 depicts the power loss for three selected period lengths of asymmetric error while keeping the amplitude constant. The modulation of the losses corresponds to the period of the asymmetric error. The difference in loss amplitude is not nearly as pronounced, as in case of a change in error amplitude. Power in W [Magnitude] 210 205 0.2\\*sin(t/3.4) 200 195 190 0.2\\*sin(t/10) WO W185 180 175 170 165 160 0 0.5 1 1.5 2.5 3 3.5 4 Time/ns CONCLUSION AND OUTLOOK Figure 9 shows the maximum losses as a function of asymmetric error period length. There is an increase in maximum losses indicating a resonant effect corresponding to a period of around $3 0 \\mathrm { m m }$ . There needs to be some caution, however when ascribing a resonance to a certain period length in this case. When simulating structures with curved surfaces, there is a resolution limit in the meshing. Some mesh cells cannot be reasonably aligned with the curved conducting surfaces. CST then fills these cells with a perfect electric conductor (PEC), effectively altering the simulated geometry. The peak in Fig. 9 might be an artefact of the meshing resolution. Further simulations are planned to investigate the impact specific meshing has on the observed effect. Please note, that the geometry of the asymmetric error is similar to a concept referred to an image charge undulator (ICU) by Y. Zhang et al. [4]. A concept that puts a sinusoidal conducting structure very close to a flat electron beam and uses the generated wake field as an undulator field for subsequent bunches. The difference to our simulations is the beam trajectory. In our case of asymmetric errors the ICU-structure is located next to the beam trajectory while in the ICU case the beam trajectory goes directly through the sinusoidal structure. So their findings cannot be directly applied to our case. | augmentation | NO | 0 |
IPAC | Why does alternating the structure geometry reduce unwanted effects? | Quadrupole wakes induced in horizontal structure are compensated by vertical structrure downstream | Reasoning | Beam_performance_of_the_SHINE_dechirper.pdf | Structure Layout, Advantages and Drawbacks RF power source can be connected to the feedback waveguide in several different ways: via a directional coupler, or either one, two or more RF power couplers. The one- and two-coupler schemes were examined in detail in [7]. Figure 1 illustrates the two-coupler scheme. A 15-cell cavity operating in a $\\pi / 2$ mode is coupled to a rectangular waveguide at both ends, thus creating a resonant ring. An adjustable matcher with reflection coefficient $\\Gamma$ is used to compensate reflection from the TW section. The scattering matrix formalism was used for the system analysis. For this purpose, the structure is sub-divided into several sections, each characterized by its own scattering matrix. The sections’ boundaries are indicated with dashed lines in the figure, vectors $a _ { n }$ and $b _ { n }$ represent the incident and reflected waves. 10000000000000 a b a b a b 'a6 a a c input 1 input 2 The TW structure provides the following benefits with respect to the conventional standing wave SRF cavity [8]: 1. Higher transit time factor $( T \\sim 1 )$ and higher acceleration gradient for the same peak surface RF magnetic field. For an ideal structure with small aperture $T ( \\varphi ) \\sim \\sin ( \\varphi / 2 ) / ( \\varphi / 2 )$ , where $\\varphi$ is the RF phase advance per cell. Then the acceleration gradient increase compared to the standing wave structure operating in the $\\pi$ mode is | augmentation | NO | 0 |
IPAC | Why does alternating the structure geometry reduce unwanted effects? | Quadrupole wakes induced in horizontal structure are compensated by vertical structrure downstream | Reasoning | Beam_performance_of_the_SHINE_dechirper.pdf | • Even though the length of all straight sections is identical, the height of the peaks are lower at the beginning of the cell than towards the end of the cell. The main reason is additional divergence created by the large momentum spread and $D ^ { \\prime }$ and to a lesser extent due to the betatron oscillations in both planes. $D ^ { \\prime }$ and the Twiss gamma functions become small towards the end of the half cell leading to larger radiation peaks. • The dipolar magnetic field of combined function magnets is lower than the one of pure dipoles leading to slightly increased radiation levels. This is clearly visible, e.g., for the D quadrupole at $s = 0 \\mathrm { m }$ corresponding to $\\vartheta _ { H } = 0$ and the $\\mathrm { ~ F ~ }$ quadrupole at $s \\approx 1 5 \\mathrm { m }$ corresponding to $\\vartheta _ { H } \\approx 9$ mrad. The variations of dose from different positions along the quadrupoles is caused by variations of the beam divergence. Obvious mitigation measures are to minimize the length of straight sections in regions outside the long straight section housing the experiments and to install the device deep underground leading to large values of $L _ { s }$ . Careful lattice design avoiding straight sections without horizontal beam divergence due to $D ^ { \\prime }$ may allow the radiation dose peaks from the arcs to be mitigated. | augmentation | NO | 0 |
IPAC | Why does alternating the structure geometry reduce unwanted effects? | Quadrupole wakes induced in horizontal structure are compensated by vertical structrure downstream | Reasoning | Beam_performance_of_the_SHINE_dechirper.pdf | Table: Caption: Table 1: Comparison of the different cf and sf lattice variants for the most important non-linear parameters. Body: <html><body><table><tr><td>Type</td><td>Circ. in m</td><td>Angle in ° UC, DSC</td><td>Main bend length in m</td><td>ε (UC,DSC) in pm · rad</td><td>Natural chromaticity</td><td>Sext. strength ∑(k2 ·L)²</td><td>TSWM, dp in % for dQx,y = 0.1</td></tr><tr><td>cfcf</td><td>327m</td><td>4.25,2.75</td><td>1.0</td><td>95 (98,78)</td><td>-86,-45</td><td>292e3</td><td>2.0, 3.9</td></tr><tr><td>cfsf</td><td>333 m</td><td>4.25,2.75</td><td>1.0</td><td>99 (99,97)</td><td>-82,-60</td><td>325e3</td><td>2.1, 2.8</td></tr><tr><td>sfcf</td><td>346m</td><td>4.00, 3.25</td><td>1.0</td><td>98 (99,95)</td><td>-94, -39</td><td>110e3</td><td>2.3,3.9</td></tr><tr><td>sfsf</td><td>358 m</td><td>4.375, 2.5</td><td>1.1</td><td>99 (101,81)</td><td>-79,-47</td><td>76e3</td><td>5.0, 3.4</td></tr><tr><td>sfsf4Q</td><td>366 m</td><td>4.375, 2.5</td><td>1.1</td><td>99 (101,80)</td><td>-86,-35</td><td>69e3</td><td>3.8,4.3</td></tr></table></body></html> The TSWA is shown in Figs. 4 and 5 for the different lattices in the middle of a straight with $\\beta _ { x , y } \\approx ( 3 { \\mathrm { m } } , 3 { \\mathrm { m } } )$ . The cfcf-lattice gives the best results with amplitudes of $4 \\mathrm { m m }$ to $5 \\mathrm { m m }$ . The worst case is the sfcf lattice with amplitudes of $1 . 5 \\mathrm { m m }$ to $2 . 5 \\mathrm { m m }$ , whereas the other three cfsf, sfsf, sfsf4Q range at $2 \\mathrm { m m }$ to $3 . 5 \\mathrm { m m }$ . So far no measures have been introduced to the lattices to optimize the TSWA behavior. The aperture, given by the beam pipe diameter, is at $9 \\mathrm { m m }$ , and so the aperture in the straight with $\\beta _ { x , y } \\approx 3 { \\mathrm { m } }$ is $5 \\mathrm { m m }$ to $6 \\mathrm { m m }$ in the horizontal plane and $3 . 5 \\mathrm { m m }$ to $5 . 5 \\mathrm { m m }$ in the vertical plane. First tests [4, 9] showed that an improvement is possible by splitting up the chromatic sextupole families or introducing geometric/harmonic sextupoles or octupoles and we are aiming to improve the TSWA to match the geometric acceptance. | augmentation | NO | 0 |
IPAC | Why does alternating the structure geometry reduce unwanted effects? | Quadrupole wakes induced in horizontal structure are compensated by vertical structrure downstream | Reasoning | Beam_performance_of_the_SHINE_dechirper.pdf | Two DLW geometries are under active consideration, circular/cylindrical and planar/slab DLWs. Strong transverse fields are excited off-axis in both geometries, leading to beam breakup instability induced by small initial offsets [4]. A method for compensating this instability is required before applications of DWA can be realised. One proposed method is to line a circular DWA with a quadrupole wiggler, BNS damping, continuously compensating any offset and returning the beam to the DLW axis [4, 5]. This method can only be applied to a circular DWA structure. BNS damping also leads to an oscillating RMS transverse beam size through the circular DWA. The effect of a non-radially symmetric beam in a circular DWA has not been investigated. Evidence of transverse fields excited on-axis in circular DWA structures has been experimentally demonstrated, but the source of these fields has not been fully explained [6, 7]. In these proceedings, the field excited by non-radially symmetric beams have been calculated. Higher-order fields have been shown to be excited and a potential new source of beam instability demonstrated. Table: Caption: Table 1: Beam, Mesh, and Circular DLW Parameters for Field Calculations Body: <html><body><table><tr><td>Parameter</td><td></td></tr><tr><td>Charge Longitudinal Momentum RMS Bunch Length, Ot Longitudinal Profile Shape RMS Beam Width, Ox,y</td><td>250 pC 250 MeV/c 200 fs Gaussian 50 μm</td></tr><tr><td>Longitudinal Mesh Density, Cells per Ot Transverse Mesh Density, Cells per Ox,y</td><td>5 3</td></tr><tr><td>DLW Vacuum Radius, a Dielectric Thickness,δ Dielectric Permittivity</td><td>500 μm 200 μm</td></tr></table></body></html> | augmentation | NO | 0 |
IPAC | Why does alternating the structure geometry reduce unwanted effects? | Quadrupole wakes induced in horizontal structure are compensated by vertical structrure downstream | Reasoning | Beam_performance_of_the_SHINE_dechirper.pdf | An alternative approach to reduce RF losses goes through shortening $L _ { c u t }$ . In compensation for the rise of the resonant frequency, the transverse size of the cavity is required to be bigger, thus allowing more space for higher VV V (but shorter) undercuts. The three ending cells of a much wider cavity, $D _ { \\nu } { = } 1 0 5 . 6$ and $D _ { h } { = } 1 3 1 . 4 \\ \\mathrm { m m }$ in vertical and horizontal directions, have been modeled and simulated in CST (see Fig. 6). The undercut length has been reduced to $L _ { c u t } { = } 3 0 . 5 ~ \\mathrm { m m }$ , with an angle of $\\theta _ { c u t } = 3 0 ^ { \\circ }$ . Results show an enhancement of the shunt impedance to $2 6 3 \\ : \\mathrm { M } \\Omega / \\mathrm { m }$ despite having about a $20 \\%$ larger cavity. Suppressing the arc of the second stem as we previously described enhances the shunt impedance even more to $2 8 5 \\ : \\mathrm { M } \\Omega / \\mathrm { m }$ . | augmentation | NO | 0 |
IPAC | Why does alternating the structure geometry reduce unwanted effects? | Quadrupole wakes induced in horizontal structure are compensated by vertical structrure downstream | Reasoning | Beam_performance_of_the_SHINE_dechirper.pdf | $$ where $\\theta _ { i }$ is the accumulated deflecting angle after ùëóth bending magnet, and $\\Delta { y } _ { i } ^ { ' }$ is the change of vertical closed orbit angle between two adjacent dipoles. The function $\\Delta y ^ { ' } ( \\theta )$ can be expanded into a Fourier series [11, 12] $$ \\Delta y ^ { ' } ( \\theta ) = \\sum _ { k = 1 } ^ { \\infty } ( a _ { k } \\cos k \\theta + b _ { k } \\sin k \\theta ) , $$ where $$ \\begin{array} { c } { \ { a _ { k } = \\frac { 1 } { N } \\sum \\Delta y _ { i } ^ { ' } ( \\theta _ { i } ) _ { \\mathrm { s i n } k \\theta _ { i } } ^ { \\mathrm { c o s } k \\theta _ { i } } . } } \\end{array} $$ The $k \\mathrm { s }$ which are adjacent to $\\boldsymbol { a } \\gamma$ make the biggest contributions to the sum. For this demonstration, Fourier coe!cients of $k = 1 0 3$ and $k = 1 0 4$ are minimized using four closed bumps optimized at $4 5 . 8 2 \\mathrm { G e V }$ . Figure 3 shows the polarization curves for first-order $\\tau _ { d e l }$ before and after applying bumps set at $4 5 . 8 2 \\mathrm { G e V }$ . The $( \\delta \\hat { n } _ { 0 } ) _ { \\mathrm { r m s } }$ is decreased from 2.28 mrad to 0.90 mrad at $4 5 . 8 2 \\mathrm { G e V }$ , with the polarization being elevated from $1 0 . 6 8 \\%$ to $8 9 . 6 5 \\%$ with the weakening of the first-order parent synchrotron resonance. The firstorder synchrotron resonance near $k = 1 0 3$ is also weakened so that the polarization near both 103 and 104 is improved using this scheme. This weakening of the first-order resonances would also weaken the highly-depolarizing synchrotron sidebands. | 1 | NO | 0 |
expert | Why does alternating the structure geometry reduce unwanted effects? | Quadrupole wakes induced in horizontal structure are compensated by vertical structrure downstream | Reasoning | Beam_performance_of_the_SHINE_dechirper.pdf | Table: Caption: Table 1 Beam parameters upon exiting the SHINE linac Body: <html><body><table><tr><td>Parameter</td><td>Value</td></tr><tr><td>Energy,E (GeV)</td><td>8</td></tr><tr><td>Charge per bunch, Q (PC)</td><td>100</td></tr><tr><td>Beam current,I (kA)</td><td>1.5</td></tr><tr><td>Bunch length (RMS),σ(μm)</td><td>10</td></tr><tr><td>βx (m)</td><td>60.22</td></tr><tr><td>βy (m)</td><td>43.6</td></tr><tr><td>αx</td><td>1.257</td></tr><tr><td>αy</td><td>1.264</td></tr><tr><td>Enx (mm·mrad)</td><td>0.29</td></tr><tr><td>Eny (mm·mrad)</td><td>0.29</td></tr></table></body></html> 3 Longitudinal Wakefield effect Round pipes and rectangular plates are usually adopted as dechirpers. Round pipes perform better on the longitudinal wakefield by a factor of $1 6 / \\pi ^ { 2 }$ relative to a rectangular plate of comparable dimensions. However, SHINE uses a rectangular plate nonetheless, as its gap can be adjusted by changing the two plates. The corrugated structure is made of aluminum with small periodic sags and crests, with the parameters defined in Fig. 2. The surface impedance of a pipe with small, periodic corrugations has been described in detail [16–18]. The high-frequency longitudinal impedance for the dechirper can be determined by starting from the general impedance expression. Taking $q$ as the conjugate variable in the Fourier transform, we have $$ Z _ { 1 } ( k ) = \\frac { 2 \\zeta } { c } \\int _ { - \\infty } ^ { \\infty } \\mathrm { d } q q \\mathrm { c s c h } ^ { 3 } ( 2 q a ) f ( q ) e ^ { - i q x } , | 1 | NO | 0 |
IPAC | Why does alternating the structure geometry reduce unwanted effects? | Quadrupole wakes induced in horizontal structure are compensated by vertical structrure downstream | Reasoning | Beam_performance_of_the_SHINE_dechirper.pdf | Figure 5 shows the resulting electric field profiles on the $z$ -axis along the first two cells at di!erent cell $\\# 0$ dimensions. Shorter gaps imply greater peaks of gradient, thus greater surface fields, although smaller than in regular cells where fields are more critical (Kilpatrick’s limit). It is also worth mentioning that a shorter gap produces a smaller dipole kick and requires a smaller angle of correction between opposite drift tube faces. EFFICIENCY IMPROVEMENTS Conventional IH-DTL structures assemble the stems over equally-long girders on the top and bottom of the cavity, and undercuts are machined on them. In our model of Fig. 1, the end of the second stem makes a last elliptical arc to imitate the geometry of conventional girders. However, such arc does not play any role neither in the capacitance between drift tubes nor the auto-inductance of the cavity. For this reason, we have proposed to remove the last arc and finish the stem in a vertical wall as depicted in Fig. 6. This modification requires a slight increment of $2 \\mathrm { m m }$ on the undercut length $L _ { c u t }$ to retune the eigenmode frequency to ${ 7 5 0 } \\mathrm { M H z }$ Additional refinement on the dipole electric field correction must be made due to the new alteration of the opposing stems asymmetry. The overall e"ciency performance, in this case, is improved from a shunt impedance of 236 to $2 4 8 \\ : \\mathrm { M } \\Omega / \\mathrm { m }$ Such modification in the geometry of both ends of the cavity entails savings of $4 8 0 \\mathrm { W }$ peak power. | 1 | NO | 0 |
IPAC | Why does alternating the structure geometry reduce unwanted effects? | Quadrupole wakes induced in horizontal structure are compensated by vertical structrure downstream | Reasoning | Beam_performance_of_the_SHINE_dechirper.pdf | $$ B _ { e f f } ^ { 2 } \\equiv \\sum _ { n = 0 } \\frac { B _ { 2 n + 1 } ^ { 2 } } { ( 2 n + 1 ) ^ { 2 } } $$ In order to find a maximal effective magnetic induction, the width, height and length of the main blocks in the periodic part are varied. The end structure is not changed during this step. This geometry is represented in Undumag which subsequently performs the magnetic relaxation process of the ferromagnetic poles and then calculates the effective magnetic induction. The parameter space is initially scanned crudely followed by employment of a multivariate gradient descent algorithm to find a local minimum of the metric (in this case the inverse of $B _ { e f f } )$ . The result is a geometry with an effective magnetic induction of $B _ { e f f } = 1 . 1 5 \\mathrm { T }$ . End Field Configuration The end field needs to be configured such that the field integrals $~ - i _ { k } , k ~ = ~ 1 , 2 -$ lie close to zero which results in deflection and displacement of the beam close to zero. This behavior should ideally persist for all gaps. | 1 | NO | 0 |
expert | Why does alternating the structure geometry reduce unwanted effects? | Quadrupole wakes induced in horizontal structure are compensated by vertical structrure downstream | Reasoning | Beam_performance_of_the_SHINE_dechirper.pdf | File Name:Beam_performance_of_the_SHINE_dechirper.pdf Beam performance of the SHINE dechirper You-Wei $\\mathbf { G o n g } ^ { 1 , 2 } ( \\mathbb { D } )$ • Meng Zhang3 • Wei-Jie $\\mathbf { F a n } ^ { 1 , 2 } ( \\mathbb { D } )$ • Duan $\\mathbf { G } \\mathbf { u } ^ { 3 } \\boldsymbol { \\oplus }$ Ming-Hua Zhao1 Received: 14 August 2020 / Revised: 11 January 2021 / Accepted: 13 January 2021 / Published online: 17 March 2021 $\\circledcirc$ China Science Publishing & Media Ltd. (Science Press), Shanghai Institute of Applied Physics, the Chinese Academy of Sciences, Chinese Nuclear Society 2021 Abstract A corrugated structure is built and tested on many FEL facilities, providing a ‘dechirper’ mechanism for eliminating energy spread upstream of the undulator section of X-ray FELs. The wakefield effects are here studied for the beam dechirper at the Shanghai high repetition rate XFEL and extreme light facility (SHINE), and compared with analytical calculations. When properly optimized, the energy spread is well compensated. The transverse wakefield effects are also studied, including the dipole and quadrupole effects. By using two orthogonal dechirpers, we confirm the feasibility of restraining the emittance growth caused by the quadrupole wakefield. A more efficient method is thus proposed involving another pair of orthogonal dechirpers. | 1 | NO | 0 |
IPAC | Why does alternating the structure geometry reduce unwanted effects? | Quadrupole wakes induced in horizontal structure are compensated by vertical structrure downstream | Reasoning | Beam_performance_of_the_SHINE_dechirper.pdf | The installation of an additional corrugated structure cannot suppress the instability completely because the geometric impedance is increased. To reduce or completely avoid the creation of longitudinal substructures, the impact of reducing the impedance in the frequency range around $f _ { \\mathrm { s u b } }$ needs to be first examined in simulation studies. Based on that, it might be possible to reduce the geometric impedances in the relevant frequency range, allowing higher bunch charges in high-brilliance light sources. ACKNOWLEDGEMENTS This work is supported by the DFG project 431704792 in the ANR-DFG collaboration project ULTRASYNC. S. Maier acknowledges the support by the Doctoral School "Karlsruhe School of Elementary and Astroparticle Physics: Science and Technology“ (KSETA). | 2 | NO | 0 |
expert | Why does alternating the structure geometry reduce unwanted effects? | Quadrupole wakes induced in horizontal structure are compensated by vertical structrure downstream | Reasoning | Beam_performance_of_the_SHINE_dechirper.pdf | $$ where $k _ { \\mathrm { q } } ( s )$ is the effective quadrupole strength, which changes with $s$ within the bunch length $l$ . For the case where the beam is near the axis, a short uniformly distributed bunch was deduced in Ref. [25] to calculate the emittance growth after passing through the dechirper. As mentioned above, Eq. (9) is substituted into Eq. (50) of Ref. [25] to completely eliminate $2 0 \\mathrm { M e V }$ from the invariant: $$ \\begin{array} { r } { \\left( \\frac { \\epsilon _ { y } } { \\epsilon _ { y 0 } } \\right) = \\left[ 1 + \\left( \\frac { 1 0 ^ { 7 } \\pi ^ { 2 } l \\beta _ { y } } { 6 \\sqrt { 5 } a ^ { 2 } E } \\right) ^ { 2 } \\left( 1 + \\frac { 4 y _ { \\mathrm { c } } ^ { 2 } } { \\sigma _ { y } ^ { 2 } } \\right) \\right] ^ { 1 / 2 } . } \\end{array} $$ Based on the SHINE parameters, Fig. 7 shows the growth in emittance for different beam offsets. The value of $y _ { \\mathrm { c } }$ is proven to be a significant factor for determining the projected emittance. When the beam is near the axis and the gap $\\mathrm { ~ a ~ } \\geqslant \\mathrm { ~ 1 ~ m m ~ }$ , the effect on the growth in emittance induced by the dipole wakefield is tolerable. Hence, as a point of technique in beamline operation, maintaining the beam on-axis is an effective way to restrain emittance growth. | augmentation | NO | 0 |
expert | Why does alternating the structure geometry reduce unwanted effects? | Quadrupole wakes induced in horizontal structure are compensated by vertical structrure downstream | Reasoning | Beam_performance_of_the_SHINE_dechirper.pdf | Keywords Corrugated structure $\\mathbf { \\nabla } \\cdot \\mathbf { \\varepsilon }$ Energy spread $\\cdot$ Wakefield $\\mathbf { \\nabla } \\cdot \\mathbf { \\varepsilon }$ Shanghai high repetition rate XFEL and extreme light facility 1 Introduction Eliminating residual energy chirps is essential for optimizing the beam brightness in the undulator of a free electron laser (FEL). There are currently two traditional ways to eliminate chirps in superconducting linear accelerator (linac)-driven X-ray FEL facilities. One involves exploiting the resistive-wall wakefield induced by the beam pipe. The other option, which involves running the beam ‘off-crest,’ is inefficient and costly, especially for ultrashort bunches in FEL facilities [1]. Recently, corrugated metallic structures have attracted much interest within the accelerator community, as they use a wakefield to remove linear energy chirps passively before the beam enters the undulator. The idea of using a corrugated structure as a dechirper in an X-ray FEL was first proposed by Karl and Gennady [1]. Several such structures, XFELs [2], PALXFEL [3], pint-sized facility [4, 5], LCLS [6] and SwissFEL [7] have been built and tested. The feasibility of employing a corrugated structure to precisely control the beam phase space has been demonstrated in various applications. It has also been utilized as a longitudinal beam phase-space linearizer for bunch compression [8, 9], to linearize energy profiles for FEL lasing [10], and as a passive deflector for longitudinal phase-space reconstruction [11]. Meanwhile, many other novel applications of light sources have also been proposed in recent years. Bettoni et al. verified the possibility of using them to generate a two-color beam [12]. A new role for generating fresh-slice multi-color generations in FELs was demonstrated in LCLS [13]. The generation of terahertz waves was also proposed recently [14]. | augmentation | NO | 0 |
expert | Why does alternating the structure geometry reduce unwanted effects? | Quadrupole wakes induced in horizontal structure are compensated by vertical structrure downstream | Reasoning | Beam_performance_of_the_SHINE_dechirper.pdf | We next simply consider the quadrupole wake, where the beam is on-axis $( \\mathrm { y } _ { \\mathrm { c } } = 0 )$ . The transfer matrices for the focusing and defocusing quadrupole are given in Eq. (16), where $L$ is the length of the corrugated structure [25]. $$ \\begin{array} { r } { \\boldsymbol { R } _ { \\mathrm { f } } = \\left[ \\begin{array} { c c } { \\cos k _ { \\mathrm { q } } L } & { \\frac { \\sin k _ { \\mathrm { q } } L } { k _ { \\mathrm { q } } } } \\\\ { - k _ { \\mathrm { q } } \\sin k _ { \\mathrm { q } } L } & { \\cos k _ { \\mathrm { q } } L } \\end{array} \\right] , \\boldsymbol { R } _ { \\mathrm { d } } = \\left[ \\begin{array} { c c } { \\cosh k _ { \\mathrm { q } } L } & { \\frac { \\sin k _ { \\mathrm { q } } L } { k _ { \\mathrm { q } } } } \\\\ { k _ { \\mathrm { q } } \\sinh k _ { \\mathrm { q } } L } & { \\cosh k _ { \\mathrm { q } } L } \\end{array} \\right] . } \\end{array} | augmentation | NO | 0 |
expert | Why does alternating the structure geometry reduce unwanted effects? | Quadrupole wakes induced in horizontal structure are compensated by vertical structrure downstream | Reasoning | Beam_performance_of_the_SHINE_dechirper.pdf | The SHINE linac beam specifications are listed in Table 1. After two stages of bunch compressors, the bunch length is shortened to $1 0 ~ { \\mu \\mathrm { m } }$ , with a time-dependent energy chirp of approximately $0 . 2 5 \\%$ $( 2 0 \\mathrm { M e V } )$ at the exit of the SHINE linac. Compared with normal conducting RF structures, the wakefield generated by the L-band superconducting structure is relatively weak because of its large aperture [15]. Therefore, it is impossible to compensate the correlated energy spread of the beam by adopting the longitudinal wakefield of the accelerating module, which becomes a key design feature of superconducting linacdriven FELs. In the case of the SHINE linac, the electron bunch length is less than $1 0 ~ { \\mu \\mathrm { m } }$ after passing through the second bunch compressor. Therefore, the beam energy spread cannot be effectively compensated by chirping the RF phase of the main linac. The SHINE linac adopts the corrugated structure (Fig. 2) to dechirp the energy spread. This is achieved by deliberately selecting the structural parameters so as to control the wavelength and strength of the field, as verified by beam experiments on many FEL facilities. | augmentation | NO | 0 |
expert | Why does alternating the structure geometry reduce unwanted effects? | Quadrupole wakes induced in horizontal structure are compensated by vertical structrure downstream | Reasoning | Beam_performance_of_the_SHINE_dechirper.pdf | As previously mentioned, $t / p = 0 . 5$ was adopted. The longitudinal wakefields corresponding to different widths are shown in the middle subplot of Fig. 3. The longitudinal wakefield appears to increase with $w$ , but settles at a maximum value when $w = 1 5 \\mathrm { m m }$ . For our calculation, setting $a = 1 \\mathrm { m m }$ and $w = 1 5 \\mathrm { m m }$ yields a sufficiently large ratio $w / a = 1 5$ . The scenarios in Eq. (1) and ECHO2D can all be regarded as flat geometries. The main parameters chosen for SHINE are summarized in Table 2. Assuming that the beam goes through an actual periodic structure, the beam entering the finite-length pipe still displays a transient response, characterized by the catch-up distance $z = a ^ { 2 } / 2 \\sigma _ { z }$ . Based on the parameters in Table 2, the catch-up distance in SHINE is $5 0 ~ \\mathrm { c m }$ , which is small compared to the structure length, suggesting that the transient response of the structure can be ignored. Table: Caption: Table 2 Corrugated structural parameters for SHINE Body: <html><body><table><tr><td>Parameter</td><td>Value</td></tr><tr><td>Half-gap, a (mm)</td><td>1.0</td></tr><tr><td>Period,p (mm)</td><td>0.5</td></tr><tr><td>Depth,h (mm)</td><td>0.5</td></tr><tr><td>Longitudinal gap,t (mm)</td><td>0.25</td></tr><tr><td>Width,w (mm)</td><td>15.0</td></tr><tr><td>Plate length,L (m)</td><td>10.0</td></tr></table></body></html> | augmentation | NO | 0 |
expert | Why does alternating the structure geometry reduce unwanted effects? | Quadrupole wakes induced in horizontal structure are compensated by vertical structrure downstream | Reasoning | Beam_performance_of_the_SHINE_dechirper.pdf | $$ where $f ( q ) = n / d$ , and with $$ \\begin{array} { l } { n = q [ \\cosh [ q ( 2 a - y - y _ { 0 } ) ] - 2 \\cosh [ q ( y - y _ { 0 } ) ] } \\\\ { \\qquad + \\cosh [ q ( 2 a + y + y _ { 0 } ) ] ] } \\\\ { \\qquad - i k \\zeta [ \\sinh [ q ( 2 a - y - y _ { 0 } ) ] + \\sinh [ q ( 2 a + y + y _ { 0 } ) ] ] , } \\end{array} $$ $$ d = [ q \\mathrm { s e c h } ( q a ) - i k \\zeta \\mathrm { c s c h } ( q a ) ] [ q \\mathrm { c s c h } ( q a ) - i k \\zeta \\mathrm { s e c h } ( q a ) ] . $$ We use $( x _ { 0 } , \\ y _ { 0 } )$ and $( x , y )$ to represent the driving and testing particles, respectively. In Eq. (1), the surface impedance is written as $\\zeta$ , which is related to the wavenumber $k$ . In Ref. [18], the impedance at large $k$ is expanded, keeping terms to leading order $1 / k$ and to the next order $1 / k ^ { 3 / 2 }$ . Then, we compare this equation to the round case for a disk-loaded structure in a round geometry, with the same expression in parameters as rectangular plates. The longitudinal impedances at large $q$ for the round and rectangular plates are given by [18–21] | augmentation | NO | 0 |
expert | Why does alternating the structure geometry reduce unwanted effects? | Quadrupole wakes induced in horizontal structure are compensated by vertical structrure downstream | Reasoning | Beam_performance_of_the_SHINE_dechirper.pdf | $$ After calculating the inverse Fourier transformation, the distance s between the test and driving particles yields the longitudinal wake at the origin of $s = 0 ^ { + }$ , according to $w _ { \\mathrm { l } } \\sim e ^ { \\sqrt { s / s _ { 0 1 } } }$ . The relationship between the longitudinal point wake and the distance about the test charge behind the driving charge is expressed as Eq. (8) [19]. $$ w _ { 1 } ( s ) = - \\frac { \\pi Z _ { 0 } c } { 1 6 a ^ { 2 } } e ^ { - \\sqrt { s / s _ { 0 1 } } } . $$ The wakefield of the short bunch is obtained by convoluting the wake with the bunch shape $\\lambda ( s )$ . For a pencil beam, the original wake $w _ { 0 }$ on the axis becomes [19] $$ w _ { 0 } = \\frac { \\pi Z _ { 0 } c } { 1 6 a ^ { 2 } } . $$ Equation (8) shows that the required dechirper length $L$ is determined by the half-gap for a given dechirper strength. The half-gap $a = 1 \\mathrm { m m }$ was chosen as the baseline for the following reasons. On the one hand, it ensures that a sufficiently large proportion of the beam is included in the clear region for beam propagation, an essential requirement for controlling beam loss in a superconducting linac. On the other hands, the aperture size is constrained by the transverse emittance dilution effect, which is discussed in the following section. In [26], it is assumed that the corrugation dimensions are no greater than the gap size, i.e., $t , p \\leq a$ . This ensures that the structure is ‘steeply corrugated,’ such that short-range wakes can be neglected. | augmentation | NO | 0 |
IPAC | Why does the inverse-designed grating exhibit higher efficiency than a conventional rectangular grating? | Because the photonic inverse design tailors the dielectric distribution to maximize directional emission and resonant coupling for the target wavelength. | Reasoning | haeusler-et-al-2022-boosting-the-efficiency-of-smith-purcell-radiators-using-nanophotonic-inverse-design.pdf | Beam Properties Impact Another possible way for emittance degradation compensation is to control beam properties by introducing inverse modulation upstream of the arc to counteract with the CSR e"ect in the arc. This method is similar with the traditional one that typically utilizes DBA pairs with $\\pi$ betatron phase advance separated to compensate the CSR emittance dilution. here we try to manipulate beam properties in the way the first DBA (with phase advance of $\\pi$ upstream of the second one) does. Phase advance in the arc lattice shown in Fig. 1 is close to $3 \\pi$ for both $\\mathbf { \\boldsymbol { x } }$ and y planes, so if we use the output beam as shown in Fig. 2 (c) and (d), the projected emittance growth modulation introduced by CSR e"ect by the arc lattice may compensate the initial emittance. With this new input beam one may expect emittance compensation with keeping the designed dispersion-free optics. Figure 4 shows the case with input beam taken from Fig. 2 (c) and (d) and with inversed slice energy as in Fig. 2 (b). The projected emittance does decrease as shown in Fig. 4 (a), which has values around $\\epsilon _ { x } \\approx 1 . 3 \\epsilon _ { x 0 }$ , less than the input beam, and $\\epsilon _ { \\mathrm { y } } \\approx 1 . 1 \\epsilon _ { \\mathrm { y 0 } }$ at the arc exit. Figure 4 (b) shows that with an inversed slice energy distribution one can get the output beam with nearly flattened beam longitudinal phase space. This additional energy modulation is possible due to the fact that we use the designed dispersion-free optics here, where no extra emittance growth will be introduced by the energy modulation other than the CSR e"ect. Slice centroid deviation and divergence shown in Fig. 4 (c) and (d) is much less than those in Fig. 2, and here with proper magnetic corrector kick the lasing window may be as large as twice of the output beam in Fig. 2. | augmentation | NO | 0 |
IPAC | Why does the inverse-designed grating exhibit higher efficiency than a conventional rectangular grating? | Because the photonic inverse design tailors the dielectric distribution to maximize directional emission and resonant coupling for the target wavelength. | Reasoning | haeusler-et-al-2022-boosting-the-efficiency-of-smith-purcell-radiators-using-nanophotonic-inverse-design.pdf | $$ \\begin{array} { l } { \\displaystyle { \\lambda = \\frac { \\lambda _ { u } } { 2 \\gamma ^ { 2 } h } ( 1 + \\frac { K ^ { 2 } } { 2 } ) } } \\\\ { \\displaystyle { \\approx \\frac { \\lambda _ { u } } { 2 \\gamma _ { 0 } ^ { 2 } h } \\left( 1 + \\frac { K _ { 0 } ^ { 2 } } { 2 } \\right) \\left( 1 + \\frac { 2 K _ { 0 } ^ { 2 } } { 2 + K _ { 0 } ^ { 2 } } \\alpha y - 2 \\eta \\right) } } \\end{array} $$ During the scan, we find the vertical transverse gradient $\\alpha$ should be allowed to deviate from $\\scriptstyle { \\alpha _ { 0 } }$ (where $\\begin{array} { r } { \\alpha _ { 0 } \\hat { D } = \\frac { 2 + K _ { 0 } ^ { 2 } } { K _ { 0 } ^ { 2 } } , } \\end{array}$ If $\\begin{array} { r } { \\alpha D = \\frac { 2 + K _ { 0 } ^ { 2 } } { K _ { 0 } ^ { 2 } } } \\end{array}$ i.e., if $\\boldsymbol { a } = \\boldsymbol { a } _ { 0 }$ , then the gain reduction due to large energy spread is mitigated. Actually, we find the optimized $\\alpha$ close but larger than $\\scriptstyle { a _ { 0 } }$ as shown in Fig. 1g. Thus, due to the relation between energy spread and vertical beam size introduced by the dispersion $D$ , the complete match between gradient $\\alpha$ and dispersion $D$ by $\\begin{array} { r } { \\alpha D = \\frac { \\hat { 2 } + K _ { 0 } ^ { 2 } } { K _ { 0 } ^ { 2 } } } \\end{array}$ does not neccesarily give maximum gain. | augmentation | NO | 0 |
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