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IPAC
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What physical phenomena makes a DLA work?
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reverse the Cherenkov effect and the Smith-Purcell effect
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fact
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Beam_Dynamics_in_Dielectric_Laser_Acceleration.pdf
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File Name:DEMONSTRATION_OF_TRANSVERSE_STABILITY_IN_AN_ALTERNATING.pdf DEMONSTRATION OF TRANSVERSE STABILITY IN AN ALTERNATING SYMMETRY PLANAR DIELECTRIC STRUCTURE∗ W. Lynn†, G. Andonian, N. Majernik, S. O’Tool, J. Rosenzweig, UCLA, Los Angeles, CA, USA S. Doran, SY. Kim, J. Power, E. Wisniewski, Argonne National Laboratory, Lemont, IL P. Piot, Northern Illinois University, DeKalb, IL, USA Abstract Dielectric wakefield acceleration (DWA) is a promising approach to particle acceleration, offering high gradients and compact sizes. However, beam instabilities can limit its effectiveness. In this work, we present the result of a DWA design that uses an alternating structure to counteract quadrupole-mode induced instabilities in the drive beam. We show that this approach is effective at delaying beam breakup, allowing for longer accelerating structures. We have designed and fabricated a new apparatus for positioning the DWA components in our setup. This allows us to precisely and independently control the gap in both transverse dimensions and consequently the strength of the respective destabilizing fields. Our results show that the use of alternating gradient structures in DWA can significantly improve its performance, offering a promising path forward for high-gradient particle acceleration. INTRODUCTION Electron accelerators have a variety of applications, from high energy physics [1] to free electron lasers [2], and even topics as esoteric as nuclear bomb simulations [3]. The impact of electron accelerators on all of these applications, and many more, can be improved by increasing the accelerating gradient of said accelerators, shrinking their footprint and consequently their cost allowing for the proliferation of more machines and improving their accessibility. One method for achieving this increase in accelerating gradient is Dielectric Wakefield Acceleration (DWA) which is a technique where a “driving” bunch of electrons generates an electromagnetic wake by driving a dielectric-lined waveguide. Some distance behind the drive beam, a “witness” bunch interacts with the excited wake and is accelerated [4]. DWA has been shown to generate accelerating gradients up to $1 \\mathrm { G V } / \\mathrm { m }$ which would be a significant improvement over conventional methods [5, 6]. One of the major limitations of DWA techniques is the ability to successfully propagate a beam through a significant length of accelerating structure due to the fact that short-range transverse wakefields can be generated in addition to the longitudinal accelerating field and these transverse fields can deflect and distort the driving beam sufficiently as to cause beam loss as it collides with accelerator components [7]. This phenomenon of selfinduced beam loss is known as Single-bunch Beam Breakup (SBBU).
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augmentation
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NO
| 0
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IPAC
|
What physical phenomena makes a DLA work?
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reverse the Cherenkov effect and the Smith-Purcell effect
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fact
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Beam_Dynamics_in_Dielectric_Laser_Acceleration.pdf
|
For future applications a key property of the DLA will be the length scalability. Two open issues in this regard are (1) the laser synchronization over long distances, and (2) the electron confinement in tiny channels (ca. $4 0 0 \\mathrm { n m }$ aperture). The energy efficiency and repetition rate could be boosted by recirculating the laser pulse through the structure, that is by making the latter part of the laser oscillator [32]. A $2 0 ~ \\mathrm { m }$ long staged dielectric structure with $1 \\mathrm { { G e V / m } }$ energy gradient could deliver single $2 0 \\mathrm { G e V }$ electrons at very high repetition rates [19–21]. $\\mu / \\pi$ PLASMA ACCELERATION Laser- or beam-driven plasma wakefield acceleration (PWA) could be of great interest for non-ultra-relativistic and rapidly decaying particles, like muons and pions. In particular, this scheme could meet the challenging acceleration requirements for a muon collider [33–35]. Another intriguing possibility is low emittance muon sources based on plasma-wakefield accelerators [36] . Plasma acceleration could bring non-relativistic slow particles, such as muons, to relativistic velocities by slowing down the phase velocity of the plasma wake to match the speed of the particles [37, 38]. This can be achieved, for example, by using spatio-temporal laser pulses to slow down the driver [39] by varying the plasma density profile to control the velocity of the wake [37], or by a combination thereof [38]. The muons move at the plasma wave velocity if the phase locking condition [38] $d / d t \\left( m _ { \\mu } c \\beta ( t ) / \\sqrt { 1 + \\beta ^ { 2 } ( t ) } \\right) = e E _ { 0 } \\sqrt { n }$ , is met, where $n$ denotes the electron plasma density normalized to the initial density (so that $n ( 0 ) = 1 { \\bmod { . } }$ ), and $E _ { 0 }$ the longitudinal electric field at the beginning of the acceleration process.
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augmentation
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NO
| 0
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IPAC
|
What physical phenomena makes a DLA work?
|
reverse the Cherenkov effect and the Smith-Purcell effect
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fact
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Beam_Dynamics_in_Dielectric_Laser_Acceleration.pdf
|
DBA LATTICE Linear Optics The designed MLS II lattice consists of 6 identical DBA cells with $8 6 . 4 \\mathrm { ~ m ~ }$ circumference. Each cell contains two homogeneous dipole magnets with a bending radius of 2.27 m according to the critical photon energy of $5 0 0 ~ \\mathrm { e V } .$ . In accordance with the design strategy of MLS [3, 4], a single octupole has been positioned at the center of the DBA cell to adjust the third-order momentum compaction factor $\\scriptstyle a _ { 2 }$ , in addition to the sextupole families that are used to control the second-order term $\\scriptstyle { a _ { 1 } }$ . The linear optics of the DBA cell for the standard mode are shown in Fig. 1. Table: Caption: Table 1: Parameters of DBA Lattice for Standard User Mode Body: <html><body><table><tr><td>Parameter</td><td>Value</td></tr><tr><td>Energy</td><td>800MeV</td></tr><tr><td>Circumference</td><td>86.4 m</td></tr><tr><td>Working point (H/V)</td><td>5.261/4.354</td></tr><tr><td>Natural chromaticities (H/V)</td><td>-7.14/-11.75</td></tr><tr><td>Radiation loss per turn</td><td>15.9 keV</td></tr><tr><td>Damping partition (H/V/L)</td><td>1.023 /1.0 /1.976</td></tr><tr><td>Damping time (H/V/L)</td><td>28.244/28.908/ 14.626 ms</td></tr><tr><td>Natural emittance</td><td>38 nmrad</td></tr><tr><td>Natural energy spread</td><td>4.57 × 10-4</td></tr><tr><td>Momentum compaction</td><td>7.44 × 10-3</td></tr><tr><td>βh,β,@ straight section center</td><td>6.9 /1.4 m</td></tr></table></body></html> Nonlinear Dynamics One DBA cell contains two families of chromatic sextupoles. The momentum acceptance is maximized by adjusting the strength and positions of the two chromatic sextupoles, with the constraint that the linear chromaticities are corrected to $+ 1 . 0$ in both planes. However, it should be noted that the positions of the focusing chromatic sextupoles are located at the center of the DBA cell with large dispersion, while the defocusing chromatic sextupole’s position can be adjusted. The two families of harmonic sextupoles in the straight section are optimized to enlarge the dynamic aperture. The nonlinear dynamics optimization was carried out by using Elegant [5].
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augmentation
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NO
| 0
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IPAC
|
What physical phenomena makes a DLA work?
|
reverse the Cherenkov effect and the Smith-Purcell effect
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fact
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Beam_Dynamics_in_Dielectric_Laser_Acceleration.pdf
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BEAM-DYNAMICS SIMULATIONS The field obtained from the full wave HFSS 3D simulations of the above described woodpile structure have been used as input for the beam-dynamics simulations carried out using ASTRA© beam tracking code. In order to increase the overall energy gain a staging of nine $\\simeq 3 0 { \\mu \\mathrm { m } }$ accelerating structures has been considered to perform the simulations over a total length of $\\simeq 3 0 0 \\mu \\mathrm { m }$ We considered a bunch charge of $1 0 ~ \\mathrm { f c }$ and a normalized transverse emittance $\\epsilon _ { x } = \\epsilon _ { y } = 1 \\ : \\mathrm { n m }$ at the entrance of the woodpile stages: these are typical values required for DLAs working at the considered wavelength [1]. In the preliminary results presented no space-charge effects have been included in the simulations. An energy gain of $1 4 0 \\mathrm { k e V }$ has been obtained as shown in Fig. 2(a), corresponding to an average accelerating gradient of $\\sim 4 7 0 \\ : \\mathrm { M V / m }$ . Because the woodpile defect has a cross section that is not circular (see Fig. 1(a)), there is a break in the cylindrical symmetry, and the radial fields have an azimuthal dependence which results in multipolar field components.
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augmentation
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NO
| 0
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IPAC
|
What physical phenomena makes a DLA work?
|
reverse the Cherenkov effect and the Smith-Purcell effect
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fact
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Beam_Dynamics_in_Dielectric_Laser_Acceleration.pdf
|
In this method of measuring the strength of LD, the polarity of a transverse feedback is reversed to excite a coherent mode in the beam. This creates an antidamper that produces a coupling impedance: $$ Z ( \\omega ) \\propto G e ^ { i \\phi } \\delta ( \\omega ) $$ Where $G$ is the antidamper gain and $\\phi$ is the antidamper phase. The $\\delta ( \\omega )$ shows that the antidamper kicks the bunch as a whole. The coupling impedance in Eq. (2) produces a coherent tune shift: $$ \\Delta \\omega \\propto g e ^ { i \\phi } $$ Where $g$ is the growth rate of the beam’s centeroid position. One can independently change the gain and phase, making the antidamper a source of controlled impedance. Different combinations of phase and gain can be used to observe when the beam becomes unstable. A schematic of a SD can be seen below in Fig. 1. $G$ and $\\phi$ combinations are changed until a growth rate is first observed, where the top-right subfigure of Fig. 1 shows the beam centroid position. The flat blue centroid position corresponds to $G$ and $\\phi$ before growth, where the growing red centroid position corresponds to $G$ and $\\phi$ after growth. The centroid position growth rate is used in Eq. (3) to map onto the complex $\\Delta \\omega$ plane at the red dot on the SD.
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augmentation
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NO
| 0
|
expert
|
What physical phenomena makes a DLA work?
|
reverse the Cherenkov effect and the Smith-Purcell effect
|
fact
|
Beam_Dynamics_in_Dielectric_Laser_Acceleration.pdf
|
$$ k _ { \\mathrm { u } } \\approx \\frac { 1 } { \\beta } k - k _ { \\mathrm { z } } . $$ The analytical model provides design guidelines for the experimental realization of an DLA undulator. In Eq. (5.4) the deviation of $k$ with respect to a synchronous DLA structure determines the undulator wavelength $\\lambda _ { \\mathrm { u } }$ . Hence, altering the laser frequency allows direct adjustments of $\\lambda _ { \\mathrm { u } }$ . Aside from the oscillatory deflection the longitudinal field $a _ { \\mathrm { z } }$ induces a transversal drift motion which depends on the relative phase $$ \\varphi _ { \\mathrm { 0 } } \\equiv k c t _ { \\mathrm { 0 } } + k _ { \\mathrm { z } } \\tan \\alpha x _ { \\mathrm { 0 } } \\ . $$ In exactly the same way as for a magnetostatic undulator this effect might be mitigated by smoothly tapering the deflection field amplitude towards both undulator ends. For an electron in the center of the beam channel the undulator parameter [55] in the analytical model is
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4
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NO
| 1
|
IPAC
|
What physical phenomena makes a DLA work?
|
reverse the Cherenkov effect and the Smith-Purcell effect
|
fact
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Beam_Dynamics_in_Dielectric_Laser_Acceleration.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.
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2
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NO
| 0
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IPAC
|
What physical phenomena makes a DLA work?
|
reverse the Cherenkov effect and the Smith-Purcell effect
|
fact
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Beam_Dynamics_in_Dielectric_Laser_Acceleration.pdf
|
Designing such an experiment based on DLAs, several challenges need to be considered, including: 1. design and optimization of the single cell and the whole structure to achieve GeV energies, 2. high-repetition (GHz) source of single electrons, 3. a high-repetition (GHz) laser, 4. manufacturing the micron-sized structure, 5. longitudinal and transverse alignment of the structures, and 6. the detection process of GHz events (for more information on detection process, see [9]). This paper focuses solely on optimizing the structure with the aim of minimizing particle loss. To design and optimize a DLA structure, we track particles through the structure and optimize its parameters based on survival rate. Our design is based on the work of Uwe Niedermayer et al. [5], who designed the structure for relativistic electrons with an initial energy of $6 \\mathrm { M e V . }$ To perform numerical tracking, we use DLAtrack6D [10], a tracking code specifically developed for dielectric laser accelerators. DLAtrack6D runs e#ciently on an ordinary PC using MATLAB, without requiring a large amount of computing power. CST Studio Suite [11] will be used for the single cell design and simulation of the electric field distribution inside the structure. SIMULATION RESULTS If the DLA structure is periodic along the $z$ -axis, the laser field can be expanded in spatial Fourier series given by
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2
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NO
| 0
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expert
|
What physical phenomena makes a DLA work?
|
reverse the Cherenkov effect and the Smith-Purcell effect
|
fact
|
Beam_Dynamics_in_Dielectric_Laser_Acceleration.pdf
|
By etching the pillars by electron beam lithography and the ’mesa’ by photo lithography, several low energy electron manipulation devices, well known in the accelerator toolbox, were created on a chip. These are ballistic bunchers [33, 34], APF single cells and channels [35, 36], and the first demonstration of low energy spread bunching and coherent acceleration in DLA [37]. Yet all these devices suffer from lack of real length scalability due to a 2D design with insufficient pillar height. Moreover, the coherent acceleration experiment did not attain the energy spread as low as predicted by 2D simulations. The reason for this is the fluctuation of the structure constant $\\boldsymbol { e } _ { 1 }$ as function of the vertical coordinate in conjunction with the beam being unconfined vertically. By building a 3D APF multistage buncher, energy spreads as low as predicted in the 2D simulations have been demonstrated in full 3D simulations, and should thus be achieved in experiments soon. A design and full 3D field and particle simulation of such a multi-stage 3D APF buncher and accelerator is shown in Fig. 5 3.3 High Energy High Gradient Acceleration In order to exploit the unique features of DLA for a high energy accelerator, a high damage threshold material has to be used. A list of such materials is provided in [38]. A particular material which was used to obtain the record gradients the experiments is Fused Silica $( \\mathrm { S i O } _ { 2 } )$ [4, 11, 39]. By bonding two $\\mathrm { S i O } _ { 2 }$ gratings together a symmetric structure is obtained, however, in order to obtain the symmetric fields in the channel also the laser illumination must be symmetric. Theoretically, a Bragg mirror could also be used here, however its fabrication using layers of $\\mathrm { S i O } _ { 2 }$ and vacuum is technically challenging. Moreover, the bonded grating structures are essentially 2D, i.e. the laser spot is smaller than the large aperture dimension. This leads to the small focusing strength as discussed above as $k _ { x } = 0$ and $k _ { y } = i \\omega / ( \\beta \\gamma c ) \\to 0$ for $\\beta \\to 1$ . Strong improvement comes from applying 3D APF in the counter-phase scheme. Structures for this are depicted in Fig. 6. Note that for highly relativistic velocities the in-phase scheme is practically impossible as Eq. 3.1 implies that in this case $e _ { 1 } ( x , y )$ should be constant, and matching with the boundary conditions implies that it must be close to zero. We show an example of casting the counter-phase structures in Fig. 6 (c) and (d) into an accelerator gaining $1 \\mathrm { M e V }$ at $4 \\mathrm { M e V }$ injection energy. The design relies on etching a trench into a $\\mathrm { S i O } _ { 2 }$ slab and leaving out a pillar row with APF phase jumps, see Fig. 7. By direct bonding of two such slabs, 3D APF structures of a single material, as shown in Fig. 6 (c) and (d), are obtained. At a synchronous phase 30 degrees off crest and $5 0 0 ~ \\mathrm { M V / m }$ incident laser field from both sides, about 3000 periods ( $\\mathrm { \\Delta } 6 \\mathrm { m m }$ total length) are required to obtain $1 \\mathrm { M e V }$ energy gain. Figure 7 shows the structure, the electric field, and the betafunctions of a designed lattice containing 7 focusing periods. This structure, or respectively lattice, is not yet optimized. The parameters, including the $8 0 0 \\ \\mathrm { n m }$ aperture, were chosen rather arbitrarily. A preliminary DLAtrack6D simulation shows that an energy gain of $1 \\mathrm { M e V }$ with a throughput of about $70 \\%$ can be obtained with about $0 . 0 8 { \\mathrm { n m } }$ rad normalized emittance and 0.08 fs FWHM bunchlength.
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5
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NO
| 1
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IPAC
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What physical phenomena makes a DLA work?
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reverse the Cherenkov effect and the Smith-Purcell effect
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fact
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Beam_Dynamics_in_Dielectric_Laser_Acceleration.pdf
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Table: Caption: Table 2: Three options for DLA based dark sector searches. Body: <html><body><table><tr><td>DLA scheme</td><td>MDLA</td><td>DADLA</td><td>OEDLA</td></tr><tr><td>eenergy [GeV]</td><td>10</td><td>10</td><td>10</td></tr><tr><td>Gradient [GV/m]</td><td>1</td><td>1</td><td>1</td></tr><tr><td>Act. length [m]</td><td>10</td><td>10</td><td>10</td></tr><tr><td>Rep.rate [GHz]</td><td>0.06</td><td>0.06</td><td>100</td></tr><tr><td>Pulse length [ps]</td><td>0.1</td><td>1</td><td>0.1</td></tr><tr><td>Single e's / pulse</td><td>1</td><td>160</td><td>1</td></tr><tr><td>Av. current [nA]</td><td>0.01</td><td>1.5</td><td>16</td></tr><tr><td>Time sep. [ns]</td><td>17</td><td>17 btw. pulses (7 fs in pulse)</td><td>0.01</td></tr><tr><td>Special features</td><td></td><td>DL defl., segm. det.</td><td>DLA in laser osc.</td></tr><tr><td>e- /yr (2 √ó 107 s)</td><td>6√ó1014</td><td>~1017</td><td>~1018</td></tr><tr><td>Energy/yr [GWh]</td><td>1</td><td>10</td><td>~2</td></tr></table></body></html> OSCILLATOR-ENHANCED DLA (OEDLA) Another promising approach to reaching much higher electron rates is making the DLA structure part of a mmscale laser oscillator [12], as sketched in Fig. 4. Such arrangement could allow for extremely high repetition rates, at the $1 0 0 \\mathrm { G H z }$ level, corresponding to $1 0 \\mathrm { p s }$ time separation, which is close to the time resolution of state-of-the-art detectors. This may achieve $1 0 ^ { 1 8 }$ electrons on target per year, with a time separation of 10 ps, for a total annual laser energy consumption of about 2 GWh (assuming per mil losses in the laser oscillator per cycle). CONCLUSIONS AND OUTLOOK DLAs could deliver single few-GeV electrons at extremely high repetition rates, which are ideally suited for indirect DM searches. Parameters for the three proposed DLA scenarios are compared in Table 2. The next steps include concrete structure design and manufacturing, guided by simulations of wake fields and beam dynamics, as described in the companion paper [9]. In parallel, other topics should be advanced such as the single electron source, and instrumentation for monitoring the electron beam and the electromagnetic field. Suitable $\\mu \\mathrm { J - G H z }$ laser technology will need to be explored. The OEDLA scheme requires couplers feeding the laser beam with transverse electromagnetic fields into, and out of, the DLA structure with a nonzero longitudinal electric field, and also appropriate cooling. Staging and, in particular, the precision alignment of successive DLA stages will be essential for reaching the targeted electron energies around $1 0 \\mathrm { G e V }$ or beyond.
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1
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NO
| 0
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expert
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What physical phenomena makes a DLA work?
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reverse the Cherenkov effect and the Smith-Purcell effect
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fact
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Beam_Dynamics_in_Dielectric_Laser_Acceleration.pdf
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3 Alternating Phase Focusing DLA 3.1 Principle and Nanophotonic Structures The advantage of high gradient in DLA comes with the drawback of non-uniform driving optical nearfields across the beam channel. The electron beam, which usually fills the entire channel, is therefore defocused. The defocusing is resonant, i.e. happening in each cell, and so strong that it cannot be overcome by external quadrupole or solenoid magnets [29]. The nearfields themselves can however be arranged in a way that focusing is obtained in at least one spatial dimension. Introducing phase jumps allows to alternate this direction along the acceleration channel and gives rise to the Alternating Phase Focusing (APF) method [30]. The first proposal of APF for DLA included only a twodimensional scheme (longitudinal and horizontal) and the assumption that the vertical transverse direction can be made invariant. This assumption is hard to hold in practice, since it would require structure dimensions (i.e. pillar heights) that are larger than the laser spot. The laser spot size, however, needs to be large for a sufficiently flat Gaussian top. Moreover, if the vertical dimension is considered invariant, the beam has to be confined by a single external quadrupole magnet [30, 31], which requires perfect alignment with the sub-micron acceleration channel. While these challenges can be assessed with symmetric flat double-grating structures with extremely large aspect ratio (channel height / channel width), it is rather unfeasible with pillar structures where the aspect ratio is limited to about 10-20. For these reasons, the remaining vertical forces render the silicon pillar structures suitable only for limited interaction length.
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4
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NO
| 1
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expert
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What physical phenomena makes a DLA work?
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reverse the Cherenkov effect and the Smith-Purcell effect
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fact
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Beam_Dynamics_in_Dielectric_Laser_Acceleration.pdf
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$$ In general, Eq. (5.1) and Hamilton‚Äôs equations yield six coupled nonlinear differential equations for the phase space coordinates $x , p _ { \\mathrm { x } } , y , p _ { \\mathrm { y } } , c t$ , and $\\gamma$ as a function of the independent variable ùëß. For a DLA undulator with $E _ { 0 } \\sim 1 \\mathrm { G e V } / \\mathrm { m }$ electric field strength, the rest mass of an electron is much larger than its energy modulation across one laser wavelength. Consequently, the amplitude of the dimensionless vector potential, $a _ { \\mathrm { z } } \\approx 6 . 2 e - 4 \\ll 1$ , is small and allows to calculate the solutions of Eq. (5.1) by perturbation. Taking into account the second order terms ${ \\cal O } \\left( \\gamma _ { 0 } \\mathrm { } ^ { - 2 } \\right)$ and the first order terms $O \\left( a _ { \\mathrm { z } } \\right)$ for the $1 0 7 \\mathrm { M e V }$ beam yields analytic approximations for the energy $\\gamma \\left( z \\right)$ and the transverse position $x \\left( z \\right)$ of the electron. Figure 12 compares the approximations with numerically computed solutions of Eq. (5.1). In contrast to a magnetostatic undulator the energy in a DLA undulator oscillates, as can be seen in Fig. 12 a). The analytical approximation for $x \\left( z \\right)$ yields an adequate estimate for the amplitude and periodicity of the transversal particle oscillation in Fig. 12 b). Adding the $O \\left( a _ { \\mathrm { z } } ^ { 2 } \\right)$ terms also reproduces the drift motion, sufficient to provide a good agreement with the numerical solution. A synchronicity deviation as compared to Eq. (1.1) leads to a drift of the drive laser phase with respect to the electron beam. Accordingly, the deflection in $x$ -direction alternates its sign, although the tilt angle remains constant [54]. Thus, the wave number ${ k _ { \\mathrm { u } } } = 2 \\pi / { \\lambda _ { \\mathrm { u } } }$ of the DLA undulator can be determined as
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augmentation
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NO
| 0
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expert
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What physical phenomena makes a DLA work?
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reverse the Cherenkov effect and the Smith-Purcell effect
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fact
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Beam_Dynamics_in_Dielectric_Laser_Acceleration.pdf
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Usually the laser pulses are impinging laterally on the structures, with the polarization in the direction of electron beam propagation. Short pulses thus allow interaction with the electron beam only over a short distance. This lack of length scalability can be overcome by pulse front tilt (PFT), which can be obtained from dispersive optical elements, such as diffraction gratings or prisms [10]. At ultrarelativistic energy, a 45 degree tilted laser pulse can thus interact arbitrary long with an electron, while the interaction with each DLA structure cell can be arbitrary short. The current record gradient of $8 5 0 ~ \\mathrm { M e V / m }$ [11] and record energy gain of $3 1 5 { \\mathrm { ~ k e V } }$ [12] in DLA could be obtained in this way. Generally, the pulse front tilt angle $\\alpha$ must fulfill $$ \\tan \\alpha = { \\frac { 1 } { \\beta } } $$ in order to remain synchronous with the electron [11, 13, 14]. This requires a curved pulse front shape, especially for electron acceleration at low energy, where the speed increment is nonnegligible. A general derivation of the pulse front shape required for a given acceleration ramp design is given in [15], where also pulse length minima are discussed when the curved shape is approximated by linear pieces.
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augmentation
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NO
| 0
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expert
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What physical phenomena makes a DLA work?
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reverse the Cherenkov effect and the Smith-Purcell effect
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fact
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Beam_Dynamics_in_Dielectric_Laser_Acceleration.pdf
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The spatial harmonic focusing scheme is much less efficient than APF, since most of the damage threshold limited laser power goes into focusing rather than into acceleration gradient. However, when equipped with a focusing scheme imprinted on the laser pulse by a liquid crystal phase mask, it can operate on a generic, strictly periodic grating structure. This provides significantly improved experimental flexibility. Moreover, as the scheme intrinsically operates with different phase velocities of electromagnetic waves in the beam channel, it can be easily adapted to travelling wave structures. For a high energy collider, travelling wave structures are definitely required to meet the laser energy efficiency requirement. They can efficiently transfer energy from a co-propagating laser pulse to the electrons, until the laser pulse is depleted. Laterally driven standing wave structures cannot deplete the pulse. In the best case, on can recycle the pulse in an integrated laser cavity [57]. However, significant improvement in energy efficiency as compared to the status quo can be obtained by waveguide driven DLAs, see [44, 45]. More information about the requirements and the feasibility of DLA for a high energy collider can be found in [58]. The on-chip light source is still under theoretical development. Currently we outline a computationally optimized silica grating geometry as well as an analytical description and numerical simulations of the dynamics for electrons passing a soft X-ray radiation DLA undulator. The analytical model provides essential guidelines for the ongoing design process. The concept of a non-synchronous tilted grating structure turns out to be a promising alternative to the synchronous operation mode. The non-synchronous undulator operates without phase jumps in the structure, which relaxes the fabrication requirements and the requirements on the drive laser phase front flatness. Furthermore, variation of the laser wavelength allows direct fine tuning of the undulator period length. Preliminary results indicate that in order to achieve approximately $5 0 \\%$ beam transmission, the geometric emittance must not exceed $\\varepsilon _ { \\mathrm { y } } = 1 0 0 \\mathrm { p m }$ (at $1 0 7 \\mathrm { M e V } .$ ). Optimization of the beam focusing within the DLA undulator structures is outlined for investigations in the near future.
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augmentation
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NO
| 0
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expert
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What physical phenomena makes a DLA work?
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reverse the Cherenkov effect and the Smith-Purcell effect
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fact
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Beam_Dynamics_in_Dielectric_Laser_Acceleration.pdf
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$$ \\lambda _ { \\mathrm { { p } } } = \\frac { \\lambda _ { \\mathrm { { u } } } } { 2 { \\gamma _ { 0 } } ^ { 2 } } \\left( 1 + \\frac { { K _ { \\mathrm { { z } } } } ^ { 2 } } { 2 } \\right) \\approx 9 ~ \\mathrm { { n m } , } $$ corresponding to soft $\\boldsymbol { \\mathrm { X } }$ -rays with $E _ { \\mathrm { p } } = 0 . 1 4 ~ \\mathrm { k e V } .$ . 5.3 Simulation of the Beam Dynamics in Tilted Gratings Using the particle tracking code DLATrack6D [9] we investigate the beam dynamics in both a synchronous as well as a non-synchronous DLA undulator. Each undulator wavelength $\\lambda _ { \\mathrm { u } } = 8 0 0 \\mu \\mathrm { m }$ of the investigated structure consists of 400 tilted DLA cells which are joined along the $z$ -direction. The total length of the undulator is $1 6 . 4 \\mathrm { m m }$ which corresponds to 8200 DLA cells with $\\lambda _ { g } = 2 \\mu \\mathrm { m }$ or $\\approx 2 0$ undulator periods. In order to alternate the deflection for an oscillatory electron motion the relative laser phase needs to shift by $2 \\pi$ in total as the beam passes one undulator wavelength. For that reason, the synchronous DLA undulator design introduces a $\\pi$ phase shift after each $\\lambda _ { \\mathrm { u } } / 2$ . In an experimental setup this can be achieved either by drift sections such as used in the APF scheme or by laser pulse shaping e.g. by a liquid crystal phase mask. In the non-synchronous undulator the drift of the drive laser phase with respect to the electron beam automatically introduces the required shift to modulate the deflection force. Hence, subsequent grating cells automatically induce an oscillatory electron motion.
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expert
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What physical phenomena makes a DLA work?
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reverse the Cherenkov effect and the Smith-Purcell effect
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fact
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Beam_Dynamics_in_Dielectric_Laser_Acceleration.pdf
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Looking towards applications of dielectric laser acceleration, electron diffraction and the generation of light with particular properties are the most catching items, besides the omnipresent goal of creating a TeV collider for elementary particle physics. As such we will look into DLA-type laser driven undulators, which intrinsically are able to exploit the unique properties of DLAtype electron microbunch trains. Morever, the DLA undulators allow creating significatly shorter undulator periods than conventional magnetic undulators, thus reaching the same photon energy at lower electron energy. On the long run, this shall enable us to build table-top lightsources with unprecented parameters [16]. This paper is organized along such a light source beamline and the current efforts undertaken towards achieving it. We start with the ultralow emittance electron sources, which make use of the available technology of electron microscopes, to provide a beam suitable for injection into low energy (sub-relativisitic) DLAs. Then, news from the alternating phase focusing (APF) beam dynamics scheme is presented, especially that the scheme can be implemented in 3D fashion to confine and accelerate the highly dynamical low energy electrons. We also show a higher energy design, as APF can be applied for DLA from the lowest to the highest energies, it only requires individual structures. At high energy, also spatial harmonic focusing can be applied. This scheme gains a lot of flexibility from variable shaping of the laser pulse with a spatial light modulator (SLM) and keeping the acceleration structure fixed and strictly periodic. However, due to the large amount of laser energy required in the non-synchronous harmonics, it is rather inefficient. Last in the chain, a DLA undulator can make use both of synchronous and asynchrounous fields. We outline the ongoing development of tilted DLA grating undulators [17–19] towards first experiments in RF-accelerator facilities which provide the required high brightness ultrashort electron bunches.
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augmentation
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expert
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What physical phenomena makes a DLA work?
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reverse the Cherenkov effect and the Smith-Purcell effect
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fact
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Beam_Dynamics_in_Dielectric_Laser_Acceleration.pdf
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Moving forward, there are possibilities of increasing the acceleration gradients in DC biased electron sources through the use of novel electrode materials and preparation [25, 27] to 20 to 70 $\\mathbf { k V / m m }$ or greater gradients. These higher gradients, combined with the local field enhancement at a nanotip emitter to just short of the field emission threshold, will result in higher brightness and lower emittance beams to be focused by downstream optics. Triggering the cathode with laser pulses matched to its work function also helps minimize the beam energy spread and reduce chromatic aberrations [26]. Beam energy spread is determined by the net effects of space-charge and excess cathode trigger photon energy, and can range from $0 . 6 ~ \\mathrm { e V }$ FWHM for low charge single-photon excitation to over 5 eV FWHM for 100 electrons per shot [21]. This excess energy spread increased the electron bunch duration from a minimum of 200 fs to over 1 ps FWHM at high charge in a TEM [21]. The majority of the space charge induced energy spread occurs within a few microns of the emitter, emphasizing the importance of having a maximum acceleration field at the emitter [28].
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expert
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What physical phenomena makes a DLA work?
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reverse the Cherenkov effect and the Smith-Purcell effect
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fact
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Beam_Dynamics_in_Dielectric_Laser_Acceleration.pdf
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2 Ultra-low Emittance Injector The sub- $4 0 0 \\mathrm { n m }$ wide accelerator channel and field non-uniformity in dielectric laser accelerators place very strict emittance requirements on the electron injector. Typical acceptances in an APF DLA designed for a 2 micron drive laser require a ${ \\sim } 1 0 ~ \\mathrm { n m }$ beam waist radius and 1 mrad beam divergence at $3 0 \\mathrm { k e V }$ to prevent substantial beam loss during acceleration [20]. Generating such a 10 pm-rad beam essentially requires the use of a nanometer scale cathode, most commonly implemented via nanotips of various flavors. A variety of nanotip emitters have demonstrated sufficiently low emittance for DLA applications in a standalone configuration, but an additional challenge is to re-focus the beam coming off a tip into a beam that can be injected into a DLA without ruining the emittance. An additional challenge is that most DLA applications require maximum beam current, so generally injection systems cannot rely on filtering to achieve the required emittance. As such, an ultra-low emittance injector for a DLA requires an ultra-low emittance source and low aberration focusing elements to re-image the tip source into the DLA device at 10’s to $1 0 0 \\mathrm { ^ { \\circ } s }$ of $\\mathrm { k e V }$ energy. Typical RF photoinjectors and flat cathode electron sources cannot produce $< 1 0 0 \\mathrm { n m }$ emittance beams without heavy emittance filtering [21].
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expert
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What physical phenomena makes a DLA work?
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reverse the Cherenkov effect and the Smith-Purcell effect
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fact
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Beam_Dynamics_in_Dielectric_Laser_Acceleration.pdf
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There have been two major approaches to producing injectors of sufficiently high brightness. The first approach uses a nanotip cold field or Schottky emitter in an electron microscope column that has been modified for laser access to the cathode [14, 21, 22]. One can then leverage the decades of development that have been put into transmission electron microscopes with aberration corrected lenses. Such systems are capable of producing beams down to $2 \\mathrm { n m }$ rms with 6 mrad divergence while preserving about $3 \\ \\%$ of the electrons produced at the cathode [23], which meets the ${ \\sim } 1 0$ pm-rad DLA injector requirement for one electron per pulse. Transmission electron microscopes are also available at beam energies up to $3 0 0 \\mathrm { k e V }$ or $\\beta = 0 . 7 8$ , which would reduce the complexity of the sub-relativistic DLA stage compared to a $3 0 \\mathrm { k e V }$ or $\\beta = 0 . 3 3$ injection energy. Moreover, at higher injection energy, the aperture can be chosen wider, which respectively eases the emittance requirement. Laser triggered cold-field emission style TEMs tend to require more frequent flashing of the tip to remove contaminants and have larger photoemission fluctuations than comparable laser triggered Schottky emitter TEMs [21, 23].
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What quantity determines the corrugation sidewall angle?
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Definition
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Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf
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Maintaining the fundamental $\\mathrm { T M } _ { 0 1 }$ and $\\mathrm { H E } _ { 1 1 }$ frequencies within a $\\pm 5$ GHz-bandwidth specified by the design of the output couplers requires dimensional tolerances of roughly $\\pm 1 0 ~ { \\mu \\mathrm { m } } ,$ as shown by Fig. 5. The most sensitive dimension to manufacturing error is the corrugation depth, which must be carefully controlled to produce the desired frequency. Mode conversion due to the straightness of the CWG is not expected to change the acceleration properties over the short length scale between the drive and witness bunch. However, such effects may become relevant in the operation of the output couplers and are a subject of future analysis. Table: Caption: TABLE II. A-STAR key operating parameters. Body: <html><body><table><tr><td colspan="2">Parameter</td></tr><tr><td>a</td><td>1 mm Corrugation minor radius</td></tr><tr><td>d 264 μm</td><td>Corrugation depth</td></tr><tr><td>g 180 μm</td><td>Corrugation vacuum gap</td></tr><tr><td>t 160 μm</td><td>Corrugation tooth width</td></tr><tr><td>80 μm rt.g</td><td>Corrugation corner radius</td></tr><tr><td>P 340 μm</td><td>Corrugation period</td></tr><tr><td>0.06</td><td>Spacing parameter</td></tr><tr><td>L</td><td>50 cm Waveguide module length</td></tr><tr><td>R 5</td><td>Transformer ratio</td></tr><tr><td>|F| 0.382</td><td>Bunch form factor</td></tr><tr><td>q0 10 nC</td><td>Bunch charge</td></tr><tr><td>90 MVm-1 Eacc</td><td>Accelerating gradient</td></tr><tr><td>325 MV m-1 Emax</td><td>Peak surface E field</td></tr><tr><td>610 kA m-1 Hmax</td><td>Peak surface H field</td></tr><tr><td>74°</td><td>Phase advance</td></tr><tr><td>fr 20 kHz</td><td>Repetition rate</td></tr><tr><td>Pdiss 1050 W</td><td>Power dissipation per module</td></tr><tr><td>W 55 W/cm²</td><td>Power density upper bound</td></tr><tr><td>△T 9.5K</td><td>Pulse heating</td></tr></table></body></html>
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Definition
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Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf
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$$ E _ { z , n } ( s \\to \\infty ) = 2 \\kappa _ { n } q _ { 0 } \\mathrm { R e } \\{ e ^ { j k _ { n } s } F ( k _ { n } ) \\} $$ Expanding the real part $$ \\begin{array} { r } { E _ { z , n } ( s \\infty ) = 2 \\kappa _ { n } q _ { 0 } [ \\cos ( k _ { n } s ) \\mathrm { R e } \\{ F ( k _ { n } ) \\} } \\\\ { - \\sin ( k _ { n } s ) \\mathrm { I m } \\{ F ( k _ { n } ) \\} ] . \\qquad } \\end{array} $$ Since we are interested in the maximum value of the longitudinal accelerating field, we define $E _ { \\mathrm { a c c } }$ as the amplitude of $E _ { z , n } \\big ( s \\infty \\big )$ : $$ E _ { \\mathrm { a c c } } = 2 \\kappa q _ { 0 } \\sqrt { \\mathrm { R e } \\{ F ( k _ { n } ) \\} ^ { 2 } + \\mathrm { I m } \\{ F ( k _ { n } ) \\} ^ { 2 } }
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Definition
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Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf
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File Name:Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf Design of a cylindrical corrugated waveguide for a collinear wakefield accelerator A. Siy ,1,2,\\* N. Behdad,1 J. Booske,1 G. Waldschmidt,2 and A. Zholents 2,† 1University of Wisconsin, Madison, Wisconsin 53715, USA 2Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439, USA (Received 30 May 2022; accepted 7 November 2022; published 7 December 2022) We present the design of a cylindrical corrugated waveguide for use in the A-STAR accelerator under development at Argonne National Laboratory. A-STAR is a high gradient, high bunch repetition rate collinear wakefield accelerator that uses a $1 - \\mathrm { m m }$ inner radius corrugated waveguide to produce a $9 0 \\ \\mathrm { M V } \\mathrm { m } ^ { - 1 }$ , 180-GHz accelerating field when driven by a $1 0 \\mathrm { - n C }$ drive bunch. To select a corrugation geometry for A-STAR, we analyze three types of corrugation profiles in the overmoded regime with $a / \\lambda$ ranging from 0.53 to 0.67, where $a$ is the minor radius of the corrugated waveguide and $\\lambda$ is the free-space wavelength. We find that the corrugation geometry that optimizes the accelerator performance is a rounded profile with vertical sidewalls and a corrugation period $p \\ll a$ . Trade-offs between the peak surface fields and thermal loading are presented along with calculations of pulse heating and steady-state power dissipation. In addition to the $\\mathrm { T M } _ { 0 1 }$ accelerating mode, properties of the $\\mathrm { H E M } _ { 1 1 }$ mode and contributions from higher order modes are discussed.
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Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf
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IX. CONCLUSION Through simulation, we have shown how the electromagnetic parameters characterizing the $\\mathrm { T M } _ { 0 1 }$ synchronous mode of a cylindrical CWG used as a slow-wave structure depend on the corrugation period, spacing, sidewall angle, and frequency of the accelerating mode. In analyzing the structures, we found that minimizing the corrugation period plays a key role in reducing the peak electromagnetic fields, thermal loading, and coupling to HOMs. Taking into account electromagnetic and manufacturing considerations, we found the most practical corrugation profile has vertical sidewalls and a corrugation tooth width similar to the width of the vacuum gap. Using the results of our analysis, we have designed a prototype CWG for the A-STAR CWA under development at Argonne National Laboratory. The calculated parameters of A-STAR suggest that a CWA based on a metallic corrugated waveguide is a promising approach to realize a new generation of high repetition rates and compact XFEL light sources. ACKNOWLEDGMENTS This manuscript is based upon work supported by Laboratory Directed Research and Development (LDRD) funding from Argonne National Laboratory (ANL), provided by the Director, Office of Science, of the U.S. Department of Energy under Contract No. DEAC02-06CH11357. Useful discussions with W. Jansma, S. Lee, A. Nassiri, B. Popovic, J. Power, S. Sorsher, K. Suthar, E. Trakhtenberg, and J. Xu of ANL are gratefully acknowledged.
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What quantity determines the corrugation sidewall angle?
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Definition
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Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf
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Comparing the maximum radii and unequal radii rounded corrugation peak fields in Figs. 10 and 11, we note that the two geometry types are identical when the spacing parameter $\\xi = 0$ and the sidewall parameter $\\zeta = 1$ . In both structure types, the minimum $E _ { \\mathrm { m a x } }$ occurs for a negative spacing parameter $\\xi$ , corresponding to a corrugation tooth width wider than the vacuum gap. Increasing the corrugation spacing beyond the minimum point decreases $H _ { \\mathrm { m a x } }$ while increasing $E _ { \\mathrm { m a x } }$ . The sidewall angle determined by $\\zeta$ shifts the plots on the $\\xi$ axis but does not significantly affect the minimum value of the peak fields. While changing the sidewall parameter offers little to no benefit in reducing the peak fields, the practical implications of using values of $\\zeta \\neq 1$ have several disadvantages. For tapered corrugations with $\\zeta < 1$ , the corrugation depth must be greater requiring a thicker vacuum chamber wall and additional manufacturing complexity. Undercut corrugations with $\\zeta > 1$ are also impractical to manufacture for the dimensions of interest in a compact wakefield accelerator. For these reasons, we suggest the maximum radii corrugation with $\\xi$ close to zero as a good candidate for a wakefield accelerator design. Further refinement of the geometry requires experimental determination of where rf breakdown is most likely to occur in order to reduce the peak fields in those regions.
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What quantity determines the corrugation sidewall angle?
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Definition
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Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf
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$$ where $$ x ^ { \\prime } = \\frac { x } { \\hat { a } } , \\qquad y ^ { \\prime } = \\frac { y } { \\hat { a } } , \\qquad z ^ { \\prime } = \\frac { z } { \\hat { a } } , \\qquad \\omega ^ { \\prime } = \\frac { \\omega } { \\hat { a } } . $$ Scaling the fields by $\\hat { a } ^ { - 3 / 2 }$ keeps the stored energy $U ^ { \\prime }$ of the scaled structure same as that of the unscaled structure $U$ , which is seen by integrating the total energy in the fields: $$ \\begin{array} { l } { { \\displaystyle U ^ { \\prime } = \\iiint \\frac { \\epsilon _ { 0 } } { 2 } | \\hat { a } ^ { - 3 / 2 } E ( x ^ { \\prime } , y ^ { \\prime } , z ^ { \\prime } ) | ^ { 2 } } } \\\\ { { \\displaystyle \\quad + \\frac { \\mu _ { 0 } } { 2 } | \\hat { a } ^ { - 3 / 2 } H ( x ^ { \\prime } , y ^ { \\prime } , z ^ { \\prime } ) | ^ { 2 } d x d y d z } } \\\\ { { \\displaystyle = \\iiint \\frac { \\epsilon _ { 0 } } { 2 } | E ( x ^ { \\prime } , y ^ { \\prime } , z ^ { \\prime } ) | ^ { 2 } } } \\\\ { { \\displaystyle \\quad + \\frac { \\mu _ { 0 } } { 2 } | H ( x ^ { \\prime } , y ^ { \\prime } , z ^ { \\prime } ) | ^ { 2 } d x ^ { \\prime } d y ^ { \\prime } d z ^ { \\prime } = U , } } \\end{array}
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Definition
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Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf
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$$ Here we notice the linear scaling of the energy dissipation with the minor radius, $a$ , which helps smaller diameter structures achieve less heating per pulse and thus higher bunch repetition rates. At a gradient of $E _ { \\mathrm { a c c } } = 9 0 ~ \\mathrm { M V } \\mathrm { m } ^ { - 1 }$ , a minor radius of $a = 1 ~ \\mathrm { m m }$ , and a repetition rate of $f _ { r } = 2 0 ~ \\mathrm { k H z }$ , the minimum theoretical thermal power dissipation density on the wall of the corrugated waveguide is roughly $3 6 ~ \\mathrm { W / c m ^ { 2 } }$ . This is well within the cooling capability of single phase cooling systems using water as a working fluid, see for example [27]. In addition to the steady-state thermal load, the transient heating of the corrugation plays an important role in limiting the attainable accelerating gradient. The transient temperature rise due to pulse heating causes degradation of the surface which eventually leads to nucleation sites where electric breakdown may occur [20]. Acceptable transient temperature rise is cited in the literature as $4 0 \\mathrm { K }$ [20], above which the structure begins to incur damage. The transient $\\Delta T$ at the surface is calculated from a Green’s function solution of the thermal diffusion equation in one dimension with Neumann boundary conditions as [20]:
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What quantity determines the corrugation sidewall angle?
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Definition
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Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf
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VI. THERMAL LOADING Thermal loading of the corrugated waveguide places a limit on the maximum repetition rate $f _ { r }$ of the accelerator, where $f _ { r }$ is the number of bunches injected into the structure per second. The thermal loading depends on the electromagnetic properties of the $\\mathrm { T M } _ { 0 1 }$ mode as well as the length of the corrugated waveguide and the conductivity of the wall material. Achieving a high repetition rate requires active cooling of the structure as well as an optimally designed corrugation profile. Here we focus on designing a corrugation that minimizes the steady-state thermal load and transient pulse heating. The thermally induced stresses due to temperature gradients in the wall pose additional design considerations which are discussed further in [26]. Because the group velocity $v _ { g }$ of the electromagnetic wave is less than the electron bunch velocity, the length of the rf pulse behind the bunch grows as it traverses the structure. This causes the thermal energy density deposited in the CWG wall to increase along the direction of propagation. At a distance $z$ from the beginning of the CWG, the field strength of the rf pulse induced by the electron bunch entering at time $t = 0$ is
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Definition
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Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf
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$$ where the integrals are over all space. Applying the normalized fields with $U = 1$ to Eq. (8) for the group velocity shows that group velocity is independent of scaling $$ \\begin{array} { l } { { v _ { g } ^ { \\prime } = \\hat { a } p \\iint \\displaystyle \\frac { 1 } { 2 } \\mathrm { R e } \\big \\{ E ^ { \\prime } ( x , y ) \\times H ^ { \\prime * } ( x , y ) \\big \\} d x d y } } \\\\ { { \\mathrm { ~ } = p \\iint \\displaystyle \\frac { 1 } { 2 } \\mathrm { R e } \\big \\{ E ( x ^ { \\prime } , y ^ { \\prime } ) \\times H ^ { * } ( x ^ { \\prime } , y ^ { \\prime } ) \\big \\} d x ^ { \\prime } d y ^ { \\prime } = v _ { g } . } } \\end{array} $$ Using Eq. (7), the induced voltage $V ^ { \\prime }$ in the scaled structure is $$ V ^ { \\prime } = \\biggr | \\int _ { 0 } ^ { \\hat { a } p } \\hat { a } ^ { - 3 / 2 } E _ { z } ( z ^ { \\prime } ) e ^ { j \\omega _ { c } ^ { \\prime } } d z \\biggr | ,
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What quantity determines the corrugation sidewall angle?
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Definition
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Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf
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$$ Figure 7 shows how the electromagnetic parameters of the maximum radii corrugation depend on the geometry for a CWG with minor radius $a = 1 ~ \\mathrm { m m }$ and electrical conductivity $\\sigma = 4 \\times 1 0 ^ { 7 } ~ \\mathrm { { S m ^ { - 1 } } }$ . The scaling laws derived in Appendix A can be used to project the results to cases with different $a$ and $\\sigma$ . The loss factor $\\kappa$ and group velocity $\\beta _ { g }$ have similar behavior which can be explained in part by the appearance of $( 1 - \\beta _ { g } )$ in the denominator of Eq. (6). This dependence results in a reduction of $\\kappa$ as the corrugation period increases since $\\beta _ { g }$ goes to zero as the phase advance $\\phi$ approaches the $\\pi$ point of the dispersion curve. Structures with shorter corrugation periods, therefore, produce larger group velocities and wake potentials making it desirable to choose the period as short as possible. As the period shrinks, $\\kappa$ approaches a maximum value, which for a single moded steeply corrugated structure with $d \\gtrsim p$ is [18]:
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What quantity determines the corrugation sidewall angle?
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Definition
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Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf
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$$ Making the substitution $u = s - s ^ { \\prime }$ , $$ E _ { z , n } ( s ) = 2 \\kappa _ { n } \\operatorname { R e } \\Biggl \\{ \\int _ { - \\infty } ^ { s } q ( u ) e ^ { j k _ { n } ( s - u ) } d u \\Biggr \\} . $$ Since we are only interested in the fields behind the bunch, we take the limit as $s \\infty$ , noting that the result will be valid outside the bunch where $q ( s ) = 0$ : $$ E _ { z , n } ( s \\to \\infty ) = 2 \\kappa _ { n } \\operatorname { R e } \\left\\{ e ^ { j k _ { n } s } \\int _ { - \\infty } ^ { \\infty } q ( u ) e ^ { - j k _ { n } u } d u \\right\\} . $$ We can now write the field in terms of the previously derived form factor $F ( k _ { n } )$ given in Eq. (B20):
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What quantity determines the corrugation sidewall angle?
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Definition
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Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf
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After determining the minor radius, $a$ , of $1 \\ \\mathrm { m m }$ , the frequency and corresponding aperture ratio of the synchronous $\\mathrm { T M } _ { 0 1 }$ accelerating mode must be chosen. We have shown in Figs. 10 and 12 that the peak surface fields and associated pulse heating increase with aperture ratio while the total power dissipation decreases, as shown by its dependence on the loss factor $\\kappa$ in Eq. (16) and Fig. 7. In addition to these considerations, the frequency must be compatible with the electromagnetic output couplers used to extract rf energy from the structure. An important feature of A-STAR is its ability to measure the trajectory of the bunch in the CWA using the $\\mathrm { H E M } _ { 1 1 }$ mode which is excited when the beam propagates off-axis. Due to mode conversion, the design of the coupler that extracts the $\\mathrm { H E M } _ { 1 1 }$ mode becomes increasingly challenging as the $\\mathrm { H E M } _ { 1 1 }$ wavelength shrinks with respect to the fixed aperture of the waveguide. For the $1 \\mathrm { - m m }$ minor radius cylindrical waveguide, the limiting factor in the $\\mathbf { H E M } _ { 1 1 }$ coupler design was converted to the $\\mathrm { T E } _ { 3 1 }$ mode which has a cutoff frequency of $2 0 0 \\ : \\mathrm { G H z }$ . To address this, the synchronous $\\mathbf { H E M } _ { 1 1 }$ mode was chosen to be $1 0 \\mathrm { G H z }$ below the $\\mathrm { T E } _ { 3 1 }$ cutoff frequency, resulting in a 190-GHz $\\mathrm { H E M } _ { 1 1 }$ mode and 180-GHz $\\mathrm { T M } _ { 0 1 }$ mode with an aperture ratio of $a / \\lambda = 0 . 6 0$ .
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What quantity determines the corrugation sidewall angle?
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Definition
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Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf
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APPENDIX B: BUNCH FORM FACTOR DERIVATION When calculating a bunch’s energy loss to a particular mode of the corrugated waveguide, the shape of the bunch described by the bunch peak current distribution $i ( t )$ is accounted for by scaling the loss factor $\\kappa$ by the Fourier transform ${ \\cal I } ( \\omega _ { n } )$ of the current, where $\\omega _ { n }$ is the angular frequency of the synchronous mode. The form factor $F ( k _ { n } )$ of the bunch is defined as ${ \\cal I } ( \\omega _ { n } ) / q _ { 0 }$ , where $k _ { n }$ is the wave number of the synchronous mode and $q _ { 0 }$ is the total charge of the bunch. Here, time $t$ begins when the head of the bunch passes a fixed observation point in the corrugated waveguide. We begin by considering the kinetic energy lost by an element of charge idt as it moves a distance cdt in an electric field $E _ { z }$ : $$ d ^ { 2 } U _ { \\mathrm { l o s s } } = ( i d t ) ( c d t ) E _ { z } .
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Definition
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Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf
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$$ Here, the electric field $E _ { z }$ is the wakefield left behind by the current in the head of the bunch which has already passed the observation point. The wakefield produced by a current impulse $q _ { 0 } \\delta ( t )$ is the Green’s function $h ( t )$ which is expressed as an expansion over the normal modes of the corrugation unit cell as $$ h ( t ) = \\sum _ { n = 0 } ^ { \\infty } 2 \\kappa _ { n } \\cos { ( \\omega _ { n } t ) } \\theta ( t ) , $$ where $\\theta ( t )$ is the Heaviside theta function $$ \\theta ( t ) = \\left\\{ \\begin{array} { l l } { 0 } & { t < 0 } \\\\ { 1 / 2 } & { t = 0 } \\\\ { 1 } & { t > 0 } \\end{array} \\right. $$ and $\\kappa _ { n }$ is the loss factor given in Eq. (6) in units of $\\mathrm { { V } m ^ { - 1 } C ^ { - 1 } }$ . The fields in the unit cell are time harmonic, oscillating with frequency $\\omega _ { n }$ . Because the structure is approximated to be periodic, the oscillating fields are part of an infinitely long traveling wave that never decays. In terms of the Green’s function $h ( t )$ , the wakefield $E _ { z } ( t )$ due to the total current distribution $i ( t )$ is then constructed with the convolution integral
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What quantity determines the corrugation sidewall angle?
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Definition
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Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf
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$$ \\frac { E _ { \\mathrm { m a x } } ^ { 3 0 } t _ { p } ^ { 5 } } { \\mathrm { B D R } } = \\mathrm { c o n s t . } $$ From a design perspective, reducing the BDR is achieved by reducing the peak surface fields and the pulse length. Calculation of the absolute threshold value of the fields that induce breakdown in sub-THz structures is an active area of research [19,22,23] and reliable models have not yet been developed. The modified Poynting vector introduced in [21] has been used to predict rf breakdown in structures operating up to $3 0 ~ \\mathrm { G H z }$ , but there are limited data for its applicability at higher frequencies. For this reason, the BDR and maximum gradient of the CWA must ultimately be determined experimentally. For the purpose of optimization, we choose the peak surface fields $E _ { \\mathrm { m a x } }$ and $H _ { \\mathrm { m a x } }$ as figures of merit which should be minimized to increase the attainable accelerating gradient. Since some evidence suggests that pulse heating is of fundamental importance to the initiation of rf breakdown in high frequency accelerating structures [24], we give additional weight to the minimization of the peak magnetic surface field. This choice leads to a higher overall thermal efficiency which will be discussed further in Sec. VI.
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Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf
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$$ which can be written as $$ V ^ { \\prime } = \\biggr \\vert \\int _ { 0 } ^ { p } \\hat { a } ^ { - 1 / 2 } E _ { z } ( z ^ { \\prime } ) e ^ { j \\omega _ { c } ^ { z ^ { \\prime } } } d z ^ { \\prime } \\biggr \\vert = \\frac { V } { \\hat { a } ^ { 1 / 2 } } . $$ Since we have normalized the fields with $U = 1 \\mathrm { ~ J ~ }$ and shown that the group velocity $\\beta _ { g }$ is independent of scaling, Equation (6) is used to write the loss factor for the scaled structure as $$ \\kappa ^ { \\prime } = \\frac { V ^ { \\prime 2 } / U } { 4 ( 1 - \\beta _ { g } ) \\hat { a } p } = \\frac { \\kappa } { \\hat { a } ^ { 2 } } . $$ The quality factor $\\boldsymbol { Q }$ of the corrugation unit cell is defined as
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Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf
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$$ W = \\frac { E _ { \\mathrm { a c c } } ^ { 2 } f _ { r } } { 8 \\pi a \\kappa } . $$ Referring to the plot for $\\kappa$ in Fig. 7, the power dissipation density is reduced by minimizing the corrugation period $p$ and maximizing the spacing parameter $\\xi$ . For structures with $p / a \\lesssim 0 . 5$ , the power dissipation density decreases with an increasing aperture ratio. This results in a trade-off between minimizing the peak surface fields and minimizing the thermal loading of the CWG, where choosing a larger aperture ratio (higher $\\mathrm { T M } _ { 0 1 }$ frequency) results in higher peak fields but less thermal power dissipation. Using $\\kappa _ { \\mathrm { m a x } }$ from Eq. (10) in Eq. (16), we obtain the lower bound of the energy dissipation density as $$ \\frac { d Q _ { \\mathrm { d i s s } } ( z \\infty ) } { d S } \\geq \\frac { E _ { \\mathrm { a c c } } ^ { 2 } a } { 4 Z _ { 0 } c } .
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Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf
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VII. HOM CONSIDERATIONS In addition to the fundamental $\\mathrm { T M } _ { 0 1 }$ mode, the wakefield contains contributions from higher order modes (HOMs). Since the HOMs span a range of wavelengths, they may interfere either constructively or destructively with the accelerating mode at the position of the witness bunch leading to a potential reduction in the accelerating gradient. It is desirable to minimize coupling to HOMs to maintain maximum acceleration [12]. Figure 13 shows the wakefield impedance simulated with CST’s wakefield solver for structures with $p / a = 0 . 4$ (left panel) and $p / a = 0 . 7$ (right panel), where the HOMs are seen as additional peaks in the impedance spectrum. Characterization of the HOMs for the maximum radii structures was carried out in CST’s wakefield solver by simulating $2 0 \\mathrm { - m m }$ long corrugated waveguides with minor radius $a = 1$ and an on-axis Gaussian bunch with standard deviation length of $\\sigma _ { s } = 0 . 2 ~ \\mathrm { m m }$ . This bunch length resolves the wake impedance up to $5 0 0 ~ \\mathrm { G H z }$ , capturing a large portion of the HOM spectrum which falls off with frequency. The sum of the loss factors for all modes is calculated as
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Design_of_a_cylindrical_corrugated_waveguide.pdf.pdf
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$$ \\begin{array} { l } { \\displaystyle P ^ { 1 / 2 } ( z , t ) = \\sqrt { \\frac { 2 \\kappa q _ { 0 } ^ { 2 } | F | ^ { 2 } v _ { g } } { 1 - \\beta _ { g } } } e ^ { \\frac { - \\alpha ( v _ { g } t - \\beta _ { g } z ) } { 1 - \\beta _ { g } } } \\cos { \\left[ \\omega \\left( t - \\frac { z } { c } \\right) \\right] } } \\\\ { \\displaystyle \\times \\Pi \\bigg ( \\frac { 2 v _ { g } t - z ( 1 + \\beta _ { g } ) } { 2 z ( 1 - \\beta _ { g } ) } \\bigg ) . } \\end{array} $$ Here the field strength is defined in units of $\\sqrt { \\mathrm { W } }$ for consistency with the units provided by CST simulation, $F$ is the bunch form factor derived in Appendix B, $q _ { 0 }$ is the drive bunch charge, and $\\Pi ( x )$ is the rectangular window function.
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Beam_performance_of_the_SHINE_dechirper.pdf
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Finally, the projected emittance changes for the twoand four-dechirpers were simulated separately in the actual bunch with the working point, as optimized. We also compared both schemes with the ELEGANT code using the actual bunch distribution with the optimized working point. The results are summarized in Table 3. The transverse phase space is shown in Fig. 12. Because of the mismatch in the actual bunch when it goes through either the two- or four-dechirper scheme, the actual bunch hardly maintains the projected emittance as analyzed. The $x$ and $x ^ { \\prime }$ in the Gaussian bunch are almost invariant, but the mismatch in the actual bunch cannot be ignored and must be taken into account. As a result, the actual bunch has a lower emittance in the four-dechirpers scheme. This therefore makes the four-dechirpers a more feasible and efficient scheme for preserving the emittance for SHINE. 5 Brief conclusion and discussion This study systematically investigated the effectiveness of using a corrugated structure as a passive device to remove residual beam chirp in the SHINE project. We simulated the application of the dechirper to the SHINE beam and studied the transverse and longitudinal wakefield effects. A detailed parameter optimization of the corrugated structure was carried out using analytic formulas. It was further verified using the ELEGANT particle-tracking code. Then, we compared the wakefield effects induced by the Gaussian and double-horn beams in SHINE. The results show good consistency and can facilitate further studies. To cancel the quadrupole wakefield effect, a scheme involving two orthogonal dechirpers was adopted. Different combination plans were compared to determine the best suppression of beam-emittance growth. Finally, we proposed a four-dechirper scheme to further improve the performance. The simulation results show that the new scheme is potentially a more effective option for SHINE.
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Beam_performance_of_the_SHINE_dechirper.pdf
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Keywords Corrugated structure $\\mathbf { \\nabla } \\cdot \\mathbf { \\varepsilon }$ Energy spread $\\cdot$ Wakefield $\\mathbf { \\nabla } \\cdot \\mathbf { \\varepsilon }$ Shanghai high repetition rate XFEL and extreme light facility 1 Introduction Eliminating residual energy chirps is essential for optimizing the beam brightness in the undulator of a free electron laser (FEL). There are currently two traditional ways to eliminate chirps in superconducting linear accelerator (linac)-driven X-ray FEL facilities. One involves exploiting the resistive-wall wakefield induced by the beam pipe. The other option, which involves running the beam ‘off-crest,’ is inefficient and costly, especially for ultrashort bunches in FEL facilities [1]. Recently, corrugated metallic structures have attracted much interest within the accelerator community, as they use a wakefield to remove linear energy chirps passively before the beam enters the undulator. The idea of using a corrugated structure as a dechirper in an X-ray FEL was first proposed by Karl and Gennady [1]. Several such structures, XFELs [2], PALXFEL [3], pint-sized facility [4, 5], LCLS [6] and SwissFEL [7] have been built and tested. The feasibility of employing a corrugated structure to precisely control the beam phase space has been demonstrated in various applications. It has also been utilized as a longitudinal beam phase-space linearizer for bunch compression [8, 9], to linearize energy profiles for FEL lasing [10], and as a passive deflector for longitudinal phase-space reconstruction [11]. Meanwhile, many other novel applications of light sources have also been proposed in recent years. Bettoni et al. verified the possibility of using them to generate a two-color beam [12]. A new role for generating fresh-slice multi-color generations in FELs was demonstrated in LCLS [13]. The generation of terahertz waves was also proposed recently [14].
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Beam_performance_of_the_SHINE_dechirper.pdf
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The SHINE linac beam specifications are listed in Table 1. After two stages of bunch compressors, the bunch length is shortened to $1 0 ~ { \\mu \\mathrm { m } }$ , with a time-dependent energy chirp of approximately $0 . 2 5 \\%$ $( 2 0 \\mathrm { M e V } )$ at the exit of the SHINE linac. Compared with normal conducting RF structures, the wakefield generated by the L-band superconducting structure is relatively weak because of its large aperture [15]. Therefore, it is impossible to compensate the correlated energy spread of the beam by adopting the longitudinal wakefield of the accelerating module, which becomes a key design feature of superconducting linacdriven FELs. In the case of the SHINE linac, the electron bunch length is less than $1 0 ~ { \\mu \\mathrm { m } }$ after passing through the second bunch compressor. Therefore, the beam energy spread cannot be effectively compensated by chirping the RF phase of the main linac. The SHINE linac adopts the corrugated structure (Fig. 2) to dechirp the energy spread. This is achieved by deliberately selecting the structural parameters so as to control the wavelength and strength of the field, as verified by beam experiments on many FEL facilities.
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Beam_performance_of_the_SHINE_dechirper.pdf
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The effect of a high group velocity in the radiation pulse also merits discussion. At the end of the structure length, the pulse length can be expressed [1] as $l _ { \\mathrm { p } } = 2 h t L / a p$ . For the structural parameters of SHINE, we have $l _ { \\mathrm { p } } = 5 \\mathrm { m }$ which is much longer than the actual bunch length of the particle. This effect does not have to be taken. During RF acceleration and beam transportation, the electron beam traveling from the VHF gun to the linac is affected by several beam-dynamic processes. These include the space-charge effect in the injector, the wakefield effect from SC structures, coherent synchrotron radiation (CSR) and non-linear effects during bunch compression [23]. Non-linearities in both the accelerating fields and the longitudinal dispersion can distort the longitudinal phase space. The typical final double-horn current distribution after the SHINE linac is shown in Fig. 4. The particles are concentrated within the first $2 0 ~ { \\mu \\mathrm { m } }$ with a linear energy spread. The wakefield for the actual simulated bunch distribution is shown in Fig. 5. Compared with the Gaussian and rectangular bunch distributions, as the head-tail wakefield effect of the beam, the double-horn bunch distribution distorts the expected chirp from the Gaussian bunch. The high peak current at the head of the beam complicates the situation further. The maximal chirp generated at different positions is also related to the feature in the bunch distribution. The particles in the double-horn bunch descend steeply over $1 5 ~ { \\mu \\mathrm { m } }$ , but the particles in the Gaussian and rectangular bunches hold a gender distribution. Nevertheless, the chirp induced by the double-horn beam distribution in less than $5 \\%$ differences in the maximal chirp and shows great correspondence on the tail. This proves that the analytical method is also perfectly suitable for the actual bunch in SHINE.
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Beam_performance_of_the_SHINE_dechirper.pdf
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Table: Caption: Table 1 Beam parameters upon exiting the SHINE linac Body: <html><body><table><tr><td>Parameter</td><td>Value</td></tr><tr><td>Energy,E (GeV)</td><td>8</td></tr><tr><td>Charge per bunch, Q (PC)</td><td>100</td></tr><tr><td>Beam current,I (kA)</td><td>1.5</td></tr><tr><td>Bunch length (RMS),σ(μm)</td><td>10</td></tr><tr><td>βx (m)</td><td>60.22</td></tr><tr><td>βy (m)</td><td>43.6</td></tr><tr><td>αx</td><td>1.257</td></tr><tr><td>αy</td><td>1.264</td></tr><tr><td>Enx (mm·mrad)</td><td>0.29</td></tr><tr><td>Eny (mm·mrad)</td><td>0.29</td></tr></table></body></html> 3 Longitudinal Wakefield effect Round pipes and rectangular plates are usually adopted as dechirpers. Round pipes perform better on the longitudinal wakefield by a factor of $1 6 / \\pi ^ { 2 }$ relative to a rectangular plate of comparable dimensions. However, SHINE uses a rectangular plate nonetheless, as its gap can be adjusted by changing the two plates. The corrugated structure is made of aluminum with small periodic sags and crests, with the parameters defined in Fig. 2. The surface impedance of a pipe with small, periodic corrugations has been described in detail [16–18]. The high-frequency longitudinal impedance for the dechirper can be determined by starting from the general impedance expression. Taking $q$ as the conjugate variable in the Fourier transform, we have $$ Z _ { 1 } ( k ) = \\frac { 2 \\zeta } { c } \\int _ { - \\infty } ^ { \\infty } \\mathrm { d } q q \\mathrm { c s c h } ^ { 3 } ( 2 q a ) f ( q ) e ^ { - i q x } ,
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Beam_performance_of_the_SHINE_dechirper.pdf
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File Name:Beam_performance_of_the_SHINE_dechirper.pdf Beam performance of the SHINE dechirper You-Wei $\\mathbf { G o n g } ^ { 1 , 2 } ( \\mathbb { D } )$ • Meng Zhang3 • Wei-Jie $\\mathbf { F a n } ^ { 1 , 2 } ( \\mathbb { D } )$ • Duan $\\mathbf { G } \\mathbf { u } ^ { 3 } \\boldsymbol { \\oplus }$ Ming-Hua Zhao1 Received: 14 August 2020 / Revised: 11 January 2021 / Accepted: 13 January 2021 / Published online: 17 March 2021 $\\circledcirc$ China Science Publishing & Media Ltd. (Science Press), Shanghai Institute of Applied Physics, the Chinese Academy of Sciences, Chinese Nuclear Society 2021 Abstract A corrugated structure is built and tested on many FEL facilities, providing a ‘dechirper’ mechanism for eliminating energy spread upstream of the undulator section of X-ray FELs. The wakefield effects are here studied for the beam dechirper at the Shanghai high repetition rate XFEL and extreme light facility (SHINE), and compared with analytical calculations. When properly optimized, the energy spread is well compensated. The transverse wakefield effects are also studied, including the dipole and quadrupole effects. By using two orthogonal dechirpers, we confirm the feasibility of restraining the emittance growth caused by the quadrupole wakefield. A more efficient method is thus proposed involving another pair of orthogonal dechirpers.
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Beam_performance_of_the_SHINE_dechirper.pdf
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This paper begins by reviewing the dechirper parameters for a small metallic pipe. The wakefield effects are studied with an ultra-short electron bunch in the Shanghai high repetition rate XFEL and extreme light facility (SHINE). Then, the process in dechirper is studied analytically and verified by numerical simulations. The longitudinal wakefield generated by the corrugated structure was adopted as the dechirper was calculated and simulated for SHINE. The following chapter focuses on the transverse wakefield, discussing emittance dilution effects on different arrangements of two orthogonally oriented dechirpers, mainly for the case of an on-axis beam. We also propose using ‘fourdechirpers’ as a novel approach for controlling the beam emittance dilution effect during dechirping and compare it with the conventional scheme. We then close with a brief conclusion. 2 Background The layout of the SHINE linac and the beam parameters along the beamline are shown in Fig. 1. The electron beam generated by the VHF gun is accelerated to $1 0 0 \\ \\mathrm { M e V }$ before entering the laser heater, to suppress potential subsequent microbunching by increasing the uncorrelated energy spread of the beam. The overall linac system consists of four accelerating sections (L1, L2, L3 and L4) and two bunch compressors (BC1 and BC2). A higher harmonic linearizer (HL), which works in the deceleration phase, is also placed upstream of BC1 for the purpose of linear compression.
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Beam_performance_of_the_SHINE_dechirper.pdf
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$$ where $f ( q ) = n / d$ , and with $$ \\begin{array} { l } { n = q [ \\cosh [ q ( 2 a - y - y _ { 0 } ) ] - 2 \\cosh [ q ( y - y _ { 0 } ) ] } \\\\ { \\qquad + \\cosh [ q ( 2 a + y + y _ { 0 } ) ] ] } \\\\ { \\qquad - i k \\zeta [ \\sinh [ q ( 2 a - y - y _ { 0 } ) ] + \\sinh [ q ( 2 a + y + y _ { 0 } ) ] ] , } \\end{array} $$ $$ d = [ q \\mathrm { s e c h } ( q a ) - i k \\zeta \\mathrm { c s c h } ( q a ) ] [ q \\mathrm { c s c h } ( q a ) - i k \\zeta \\mathrm { s e c h } ( q a ) ] . $$ We use $( x _ { 0 } , \\ y _ { 0 } )$ and $( x , y )$ to represent the driving and testing particles, respectively. In Eq. (1), the surface impedance is written as $\\zeta$ , which is related to the wavenumber $k$ . In Ref. [18], the impedance at large $k$ is expanded, keeping terms to leading order $1 / k$ and to the next order $1 / k ^ { 3 / 2 }$ . Then, we compare this equation to the round case for a disk-loaded structure in a round geometry, with the same expression in parameters as rectangular plates. The longitudinal impedances at large $q$ for the round and rectangular plates are given by [18–21]
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Beam_performance_of_the_SHINE_dechirper.pdf
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According to the middle subplot in Fig. 5, the wakefield generated by the same structural parameters in the corrugated structure depends mainly on the shape of the bunch. As shown in the bottom of Fig. 5, with the longitudinal wakefield by the actual bunch, the energy chirp in the positive slope after L4 in SHINE can be well compensated. We can conclude that the longitudinal wake generated by the corrugated structure over $1 0 \\mathrm { ~ m ~ }$ is adequate and effective at canceling the energy chirp passively. 4 Transverse Wakefield effect For the part of the beam near the axis of plates, $w _ { \\mathrm { y d } }$ and $w _ { y \\mathbf { q } }$ are defined as the transverse quadrupole and dipole wakes, where the driving and test particle coordinates $y _ { 0 }$ and ${ \\boldsymbol { y } } \\ll { \\boldsymbol { a } }$ . For a driving particle at $( x _ { 0 } , \\ y _ { 0 } )$ and a test particle at $( x , y )$ , the transverse wake is given by [24] $$ \\begin{array} { r } { \\begin{array} { r c l } { w _ { y } = y _ { 0 } w _ { y \\mathrm { d } } + y w _ { y \\mathrm { q } } , } \\\\ { w _ { x } = ( x _ { 0 } - x ) w _ { y \\mathrm { q } } . } \\end{array} } \\end{array}
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Beam_performance_of_the_SHINE_dechirper.pdf
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$$ Expanding the surface impedance $\\zeta ~ [ 1 8 ]$ in the first two orders, the short-range vertical dipole and quadrupole wakes near the axis are given by [19] $$ \\begin{array} { r l } & { w _ { y \\mathrm { d } } \\approx \\displaystyle \\frac { Z _ { 0 } \\mathrm { c } \\pi ^ { 3 } } { 6 4 a ^ { 4 } } { \\mathit { s } } _ { 0 \\mathrm { d } } \\bigg [ 1 - \\big ( 1 + \\sqrt { { s } / { s } _ { 0 \\mathrm { d } } } \\big ) e ^ { \\sqrt { { s } / { s } _ { 0 \\mathrm { d } } } } \\bigg ] , } \\\\ & { w _ { y \\mathrm { q } } \\approx \\displaystyle \\frac { Z _ { 0 } \\mathrm { c } \\pi ^ { 3 } } { 6 4 a ^ { 4 } } { \\mathit { s } } _ { 0 \\mathrm { q } } \\bigg [ 1 - \\big ( 1 + \\sqrt { { s } / { s } _ { 0 \\mathrm { q } } } \\big ) e ^ { \\sqrt { { s } / { s } _ { 0 \\mathrm { q } } } } \\bigg ] , } \\\\ & { { \\mathit { s } } _ { 0 \\mathrm { d } } = s _ { 0 \\mathrm { r } } \\bigg ( \\displaystyle \\frac { 1 5 } { 1 4 } \\bigg ) ^ { 2 } , { \\mathit { s } } _ { 0 \\mathrm { q } } = s _ { 0 \\mathrm { r } } \\bigg ( \\displaystyle \\frac { 1 5 } { 1 6 } \\bigg ) ^ { 2 } . } \\end{array}
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Beam_performance_of_the_SHINE_dechirper.pdf
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$$ Figure 6 compares the dipole and quadrupole wakes obtained by convolving with the actual bunch distribution in SHINE and the analytical results verified with the simulated results from the ECHO2D code [22]. Assuming that the beam is close to (and nearly on) the axis, there is good agreement between the numerical and analytical results for the dipole and quadrupole wakes. When the beam is centered off-axis, the emittance growth is generated by the transverse dipole and quadrupole wakefields, leading to a deterioration in the beam brightness. Regardless of whether the beam is at the center, the quadrupole wake focuses in the $x$ -direction and defocuses in the $y -$ direction, increasingly from the head to the tail. This in turn results in an increase in the projected emittance. However, care must be taken that the slice emittance is not affected by the dipole and quadrupole wakes taken by these two orders. For the case of a short uniform bunch near the axis, the quadrupole and dipole inverse focal lengths are given by [25] $$ \\begin{array} { c } { { f _ { \\mathrm { { q } } } ^ { - 1 } ( s ) = k _ { \\mathrm { { q } } } ^ { 2 } ( s ) L = \\displaystyle \\frac { \\pi ^ { 3 } } { 2 5 6 a ^ { 4 } } Z _ { 0 } c \\left( \\displaystyle \\frac { e Q L } { E l } \\right) s ^ { 2 } , } } \\\\ { { f _ { \\mathrm { { d } } } ^ { - 1 } ( s ) = k _ { \\mathrm { { d } } } ^ { 2 } ( s ) L = \\displaystyle \\frac { \\pi ^ { 3 } } { 1 2 8 a ^ { 4 } } Z _ { 0 } c \\left( \\displaystyle \\frac { e Q L } { E l } \\right) s ^ { 2 } . } } \\end{array}
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Beam_performance_of_the_SHINE_dechirper.pdf
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$$ where $k _ { \\mathrm { q } } ( s )$ is the effective quadrupole strength, which changes with $s$ within the bunch length $l$ . For the case where the beam is near the axis, a short uniformly distributed bunch was deduced in Ref. [25] to calculate the emittance growth after passing through the dechirper. As mentioned above, Eq. (9) is substituted into Eq. (50) of Ref. [25] to completely eliminate $2 0 \\mathrm { M e V }$ from the invariant: $$ \\begin{array} { r } { \\left( \\frac { \\epsilon _ { y } } { \\epsilon _ { y 0 } } \\right) = \\left[ 1 + \\left( \\frac { 1 0 ^ { 7 } \\pi ^ { 2 } l \\beta _ { y } } { 6 \\sqrt { 5 } a ^ { 2 } E } \\right) ^ { 2 } \\left( 1 + \\frac { 4 y _ { \\mathrm { c } } ^ { 2 } } { \\sigma _ { y } ^ { 2 } } \\right) \\right] ^ { 1 / 2 } . } \\end{array} $$ Based on the SHINE parameters, Fig. 7 shows the growth in emittance for different beam offsets. The value of $y _ { \\mathrm { c } }$ is proven to be a significant factor for determining the projected emittance. When the beam is near the axis and the gap $\\mathrm { ~ a ~ } \\geqslant \\mathrm { ~ 1 ~ m m ~ }$ , the effect on the growth in emittance induced by the dipole wakefield is tolerable. Hence, as a point of technique in beamline operation, maintaining the beam on-axis is an effective way to restrain emittance growth.
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Beam_performance_of_the_SHINE_dechirper.pdf
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We next simply consider the quadrupole wake, where the beam is on-axis $( \\mathrm { y } _ { \\mathrm { c } } = 0 )$ . The transfer matrices for the focusing and defocusing quadrupole are given in Eq. (16), where $L$ is the length of the corrugated structure [25]. $$ \\begin{array} { r } { \\boldsymbol { R } _ { \\mathrm { f } } = \\left[ \\begin{array} { c c } { \\cos k _ { \\mathrm { q } } L } & { \\frac { \\sin k _ { \\mathrm { q } } L } { k _ { \\mathrm { q } } } } \\\\ { - k _ { \\mathrm { q } } \\sin k _ { \\mathrm { q } } L } & { \\cos k _ { \\mathrm { q } } L } \\end{array} \\right] , \\boldsymbol { R } _ { \\mathrm { d } } = \\left[ \\begin{array} { c c } { \\cosh k _ { \\mathrm { q } } L } & { \\frac { \\sin k _ { \\mathrm { q } } L } { k _ { \\mathrm { q } } } } \\\\ { k _ { \\mathrm { q } } \\sinh k _ { \\mathrm { q } } L } & { \\cosh k _ { \\mathrm { q } } L } \\end{array} \\right] . } \\end{array}
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Beam_performance_of_the_SHINE_dechirper.pdf
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$$ One proposal for effectively preventing the growth in emittance caused by the quadrupole wake was to divide the dechirper into two orthogonal dechirpers [26]. This arrangement mode is explored based on beam-optics optimizations in SHINE. First, the entire $1 0 \\mathrm { ~ m ~ }$ length of the dechirper is required and divided into effectively two-dechirpers with $5 \\mathrm { ~ m ~ }$ intervals. The two sections are oriented orthogonally, one with the plates vertical and the other horizontal. We use $\\mathbf { \\nabla } ^ { \\left. \\mathbf { V } \\right. }$ and $\\mathbf { \\cdot } \\mathbf { H } ^ { \\mathbf { \\cdot } }$ to denote vertical and horizontal plates, respectively. Figure 8 shows the projected emittance growth for four different combinations. The results were verified and compared by simulation using ELEGANT [27]. As expected, while the combinations VV and HH yield a greater projected emittance growth even when the beam is perfectly aligned, the HV and VH combinations preserve the projected emittance effectively after the dechirper section. The different performances are caused by the features in the quadrupole wake. The quadrupole wake holds only one transverse direction in focus, with an equal defocusing strength in the other transverse directions. Therefore, VV and HH degenerate the transverse phase space in one direction, but VH and HV counteract the strength self-consistently.
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Summary
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Beam_performance_of_the_SHINE_dechirper.pdf
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To improve the beam quality in SHINE and maintain the projected emittance, we attempted to divide the dechirper into four sections of uniform length $2 . 5 \\mathrm { ~ m ~ }$ (hereafter named ‘four-dechirpers’). The two-dechirper and four-dechirper layouts are depicted in Fig. 9 based on the FODO design. The blue ellipse represents the bunch on-axis. The transverse direction points perpendicular to the page, while the black arrow under the e-beam defines the longitudinal direction. The corrugated structures are orthogonal, distributed between the quadrupole magnets. One FODO structure is formed in the two-dechirper and two are formed in the four-dechirper. The hypothesis on the beta functions is validated using a thick-lens calculation. The final transfer matrix is thus expressed as a $2 \\times 2$ matrix $M _ { \\mathrm { f } }$ , and the original and final Twiss parameters, given by $( \\alpha _ { 0 } , \\beta _ { 0 } , \\gamma _ { 0 } )$ and $( \\alpha , \\beta , \\gamma )$ , respectively, are related as $\\gamma = ( 1 + \\alpha ^ { 2 } ) / \\beta$ . As shown in Eq. (17) (where $< >$ [ denotes the numerical average obtained by integrating over the bunch length), the quadrupole wake transforms exactly like a magnetic quadrupole for any slice position in $s$ . By computing the transfer matrix with the structural parameters, the average of the final Twiss parameter and the emittance growth can be calculated as
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augmentation
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Yes
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expert
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What t/p ratio was chosen for the SHINE dechirper
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0.5
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Summary
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Beam_performance_of_the_SHINE_dechirper.pdf
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$$ \\epsilon _ { \\mathrm { f } } / \\epsilon _ { 0 } = ( \\langle \\gamma _ { \\mathrm { f } } \\rangle \\langle \\beta _ { \\mathrm { f } } \\rangle - \\langle \\alpha _ { \\mathrm { f } } \\rangle ^ { 2 } ) ^ { 1 / 2 } , $$ where the subscripts f o represent the final (original) situation. Then, the other plane is also suitable. In contrast to the conventional FODO design, we utilized the two- and four-dechirpers, including the quadrupole wake generated in the corrugated structure. This destroys the periodicity in the Twiss parameters and causes the changes in the projected emittance in the final. The projected emittance growth for different magnet lengths $L$ and magnet strengths $K$ of the quadrupole magnets is demonstrated in Fig. 10. However, the minimum projected emittances in the two- and four-dechirpers are $0 . 0 1 7 5 \\%$ and $0 . 0 0 2 3 8 \\%$ , respectively. These values are comparatively small. The projected four-dechirper emittance still performs better. In the case of the symmetric feature in the FODO structure, the conclusion reached for the $x$ -direction does not apply to the $y$ -direction. The optimized working point (red dot) is selected for the quadrupole magnets, where the function $\\beta _ { x }$ is minimal and shows the best performance in terms of the emittance growth. The above calculation confirms the validity of dividing the dechirpers into four.
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augmentation
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Yes
| 0
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expert
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What t/p ratio was chosen for the SHINE dechirper
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0.5
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Summary
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Beam_performance_of_the_SHINE_dechirper.pdf
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The $\\beta$ functions for both models are plotted in Fig. 9. In [28], the emittance growth caused by the quadrupole wakefield is fully compensated only if $\\beta _ { x } = \\beta _ { y }$ . In practice, however, the beta functions always fluctuate, and the beam suffers from the residual quadrupole wakefield. For a period FODO cell, the difference between the maximum and minimum $\\beta$ values is given by Eq. (18) [29], where $K$ and $L$ denote the quadrupole strength and length separately, and $l$ the length for each separated dechirper (5 and $2 . 5 \\mathrm { ~ m ~ }$ for the two- and four-dechirpers, respectively). $$ \\beta _ { \\mathrm { m a x } } - \\beta _ { \\mathrm { m i n } } = { 4 l } / { \\sqrt { 6 4 - K ^ { 2 } L ^ { 2 } l ^ { 2 } } } . $$ Figure 11 compares the $\\beta$ functions for two- and fourdechirpers by scanning the magnet strength $K$ and the magnet length $L$ . The minimum differences are $2 . 5 0 \\mathrm { ~ m ~ }$ and 1.25 for the two- and four-dechirpers, respectively. This implies a better compensation of the quadrupole wakefieldinduced emittance growth in the four-dechirper schemes. In practical engineering applications, four-dechirpers are considered appropriate to simplify the system.
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augmentation
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Yes
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IPAC
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What target wavelength was the inverse-designed Smith-Purcell grating optimized for?
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Approximately 1.4 ?m
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Fact
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haeusler-et-al-2022-boosting-the-efficiency-of-smith-purcell-radiators-using-nanophotonic-inverse-design.pdf
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Though mostly the output power at $R _ { y } = 1 . 4 \\mathrm { m }$ is higher than that of spherical case in far infrared wavelength case, there is an exception region around $1 2 0 \\mu \\mathrm { m }$ . This spectral gap can be explained by the waveguide e!ect that causing a low coupling e"ciency from the hole. The light distribution at the coupling mirror is given in Fig. 4. The intensity distribution at center is lengthening due to the existence of two peaks along vertical direction. To explain the optimum value of $R _ { y } = 1 . 4 \\mathrm { m }$ , we make a simple assumption neglecting the e!ect of diaphragm and coupling hole. Then the light path from waveguide to the reflected mirror and then back to the waveguide port can also be described by a optical matrix. The vertical direction is given as $$ \\begin{array} { r } { T _ { y } = \\binom { 1 } { 0 } l \\binom { 1 } { - 2 / R _ { y } } 1 \\binom { 1 } { 0 } l \\binom { l } { 0 } } \\\\ { = \\binom { 1 - 2 l / R _ { y } } 2 l ( 1 - l / R _ { y } ) } \\\\ { - 2 / R _ { y } 1 - 2 l / R _ { y } } \\end{array}
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augmentation
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NO
| 0
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IPAC
|
What target wavelength was the inverse-designed Smith-Purcell grating optimized for?
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Approximately 1.4 ?m
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Fact
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haeusler-et-al-2022-boosting-the-efficiency-of-smith-purcell-radiators-using-nanophotonic-inverse-design.pdf
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In the dispersion bump section, a large dispersion value is desired to minimize the chromatic sextupole strengths required for chromaticity correction. The phase advance between two dispersion bumps should be matched close to $( 3 \\pi , \\pi )$ to place three pairs of chromatic sextupoles. Therefore, the $- \\boldsymbol { \\mathcal { I } }$ transformation between pairs of sextupoles, cancels the third-order RDTs within a cell. Referring to the layout of the NSLS-II lattice, the minimum lengths required for the entire long straight and short straight are $8 . 4 \\mathrm { m }$ and $5 . 4 \\mathrm { m }$ , respectively. The selection of the optimized solution is based on the lattice figure of merit $F$ , which is a weighted sum of natural emittance, natural chromaticities, momentum compaction, radiation loss per turn, and lengths for long and short straights. The natural emittance and chromaticities are given larger weights when evaluating $F$ , and they are used as optimization objectives when optimizing the lattice section by section. Once the ring is closed, the whole ring optimization will be further carried out. Table: Caption: Table 1: The parameters of the NSLS-II bare lattice and the developed NSLS-IIU CBA lattices comprise 15 standard supercells operating at $3 \\mathrm { G e V }$ and $4 \\mathrm { G e V } .$ . Body: <html><body><table><tr><td>Parameters</td><td colspan="3">Values</td></tr><tr><td></td><td>NSLS-II bare lattice</td><td colspan="2">NSLS-IIU CBA lattice</td></tr><tr><td>Circumference C[m]</td><td>791.958</td><td>791.7679</td><td>791.7252</td></tr><tr><td>Beam energy E[GeV]</td><td>3</td><td>3</td><td>4</td></tr><tr><td>Natural emittance Exo [pm-rad]</td><td>2086</td><td>23.4</td><td>42.5</td></tr><tr><td>Damping partitions (Jx,Jy, Js)</td><td>(1,1,2)</td><td>(2.24, 1, 0.76)</td><td>(2.15,1, 0.85)</td></tr><tr><td>Ring tunes (vx, Vy)</td><td>(33.22,16.26)</td><td>(84.67, 28.87)</td><td>(84.25,29.20)</td></tr><tr><td>Natural chromaticities (§x, §y)</td><td>(-98.5, -40.2)</td><td>(-135, -144)</td><td>(-151, -173)</td></tr><tr><td>Momentum compaction αc</td><td>3.63×10-4</td><td>7.76×10-5</td><td>6.77×10-5</td></tr><tr><td>Energy loss per turn Uo [keV]</td><td>286.4</td><td>196</td><td>656</td></tr><tr><td>Energy spread os [%]</td><td>0.0514</td><td>0.073</td><td>0.093</td></tr><tr><td>(βx, βy) at LS center [m]</td><td>(20.1, 3.4)</td><td>(2.95,2.99)</td><td>(1.63,2.67)</td></tr><tr><td>(βx,βy)at SS center[m]</td><td>(1.8, 1.1)</td><td>(1.87, 1.99)</td><td>(1.43,2.26)</td></tr><tr><td>(βx,max,βy,max)[m]</td><td>(29.99,27.31)</td><td>(13.37,20.82)</td><td>(15.13,26.95)</td></tr><tr><td>(βx,min,βy,min) [m]</td><td>(1.84, 1.17)</td><td>(0.35, 0.84)</td><td>(0.49, 0.70)</td></tr><tr><td>(βx,avg,βy,avg) [m]</td><td>(12.58,13.79)</td><td>(3.99, 7.51)</td><td>(5.05, 8.09)</td></tr><tr><td>Length of Long Straight LLs [m]</td><td>9.3</td><td>8.4</td><td>8.8</td></tr><tr><td>Length of Short Straight Lss [m]</td><td>6.6</td><td>6.1</td><td>6.8</td></tr></table></body></html>
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augmentation
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NO
| 0
|
IPAC
|
What target wavelength was the inverse-designed Smith-Purcell grating optimized for?
|
Approximately 1.4 ?m
|
Fact
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haeusler-et-al-2022-boosting-the-efficiency-of-smith-purcell-radiators-using-nanophotonic-inverse-design.pdf
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The mid-wave infrared generation is summarized in Figs. 3 and 4. Figure 3 (a) shows the effect of the crystal tuning angle on the DFG process. The angular acceptance of the process is narrow, with a measured FWHM of 0.15 degrees. A plausible reason for the lower than expected efficiency lies in the narrow angular acceptance bandwidth. Phase matching theory indicates that a narrow angular acceptance bandwidth is equivalent to a narrow energy acceptance bandwidth. Indeed, the spectrum shown in Fig. 4 indicates a substantial spectral narrowing with respect to the input bandwidth. The $1 2 \\ \\mathrm { n m }$ FWHM shown in the spectrum corresponds to an energy bandwidth of $0 . 7 3 \\mathrm { m e V }$ , while the input beam has an energy bandwidth of roughly $4 . 3 ~ \\mathrm { m e V }$ . This spectral narrowing implies that a substantial portion of the beam is unable to phase match, greatly reducing the conversion efficiency. Additionally, the narrow angular acceptance indicates that angular spread introduced by deviations from perfect collimation would reduce the efficiency as well. To extend this concept past the proof-of-principle phase, several improvements can be made to increase efficiency. First, the most substantial improvement would come in replacing the lithium niobate crystal with a periodically-poled lithium niobate crystal (PPLN). PPLN is a variety of lithium niobate that has ferroelectric domains that alternate direction. This enables quasi-phase matching, greatly extending the angular and energy bandwidths, as well as allowing higher gain by utilizing the largest element of the nonlinear tensor [8]. In this case, the required periodicity would be around $1 2 \\mu \\mathrm { m }$ . Figure 3 (b) shows the scaling of final DFG output energy with input energy. The conversion efficiency is around $4 \\times 1 0 ^ { - 6 }$ , which is on the order of $1 0 ^ { 3 }$ times smaller than expected from SNLO simulations.
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augmentation
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NO
| 0
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IPAC
|
What target wavelength was the inverse-designed Smith-Purcell grating optimized for?
|
Approximately 1.4 ?m
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Fact
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haeusler-et-al-2022-boosting-the-efficiency-of-smith-purcell-radiators-using-nanophotonic-inverse-design.pdf
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Since the optimum dispersion $\\eta _ { o p t }$ is obtained, we next calculate the variation of the effective emittance by using the realistic ID field data shown in Fig. 1. This is done by using the individual ID gap data (Fig. 1, left) not by using their average (Fig. 1, right). The results are shown in Fig. 4 and we see that the variation is indeed suppressed by setting the leaked dispersion to the optimum value of $1 5 . 4 \\mathrm { m m }$ . Storage Ring Lattice Design As mentioned above, we are designing the non-achromat optics whose dispersion value at the straight section $\\eta _ { x \\_ S T }$ is tunable within a certain range (a few mm). One of the key points is the design of the LSS matching section, since the dispersion in LSS must be suppressed to an acceptable level regardless of the $\\eta _ { x \\_ S T }$ value. To avoid degrading the momentum acceptance, the optics matching conditions for off-momentum electrons should also be satisfied at least in an approximate way. In Fig. 5 we show examples of the non-achromat optics with $\\eta _ { x \\_ S T } = 1 2 m m$ (solid curves) and with $\\eta _ { x _ { \\scriptscriptstyle - } S T } = 1 5 m m$ (dashed curves). The two optics can be interchanged by changing the strength of quadrupole magnets. To keep the dynamic stability of the ring even after switching the optics, designing a proper matching cell is very important, and work is currently underway to optimize the linear and nonlinear optics design of this section.
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augmentation
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NO
| 0
|
IPAC
|
What target wavelength was the inverse-designed Smith-Purcell grating optimized for?
|
Approximately 1.4 ?m
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Fact
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haeusler-et-al-2022-boosting-the-efficiency-of-smith-purcell-radiators-using-nanophotonic-inverse-design.pdf
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The design angular acceptance of the HRS is $\\pm 6 0$ mrad, and the full-width slit (2ùëÉ) for a resolving power of 24,000 is $1 0 0 \\mu \\mathrm { m }$ with a given $4 ^ { * } \\mathrm { R M S }$ emittance of $3 \\mu \\mathrm { m }$ and an energy spread $( \\Delta E )$ of $1 \\mathrm { e V }$ for a $6 0 \\mathrm { k e V }$ beam. Figure 3 shows the calculated envelope through the HRS system starting from the magnified object slit to the magnified image slit using the TRANSOPTR code [14, 15]; the beam envelope is calculated for a required magnification of 9 in order to achieve a resolving power of 16,000 with a given $4 ^ { * } \\mathrm { R M S }$ emittance of $3 \\mu \\mathrm { m }$ and a $\\Delta E$ of $1 \\mathrm { e V }$ for a $3 0 \\mathrm { k e V }$ beam. The mass dispersion of the pure HRS is $2 . 4 \\mathrm { m }$ , and thus a resolution of 16,000 requires a full slit size of $1 5 0 \\mu \\mathrm { m }$
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augmentation
|
NO
| 0
|
IPAC
|
What target wavelength was the inverse-designed Smith-Purcell grating optimized for?
|
Approximately 1.4 ?m
|
Fact
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haeusler-et-al-2022-boosting-the-efficiency-of-smith-purcell-radiators-using-nanophotonic-inverse-design.pdf
|
Beamline elements must be carefully placed to avoid interferences with other beamlines and the tunnel walls. The solenoids are particularly challenging due to their considerable width in a tight section of the beamline, but there are many other locations where magnets are very close to either the walls or other beamlines. Much work has been done to eliminate such interferences, primarily by adjusting the geometry of the ESR by means of varying drift lengths and dipole angles, but also modifying other beamlines and considering the use of alternative magnets. Figure 5 shows a representation of the geometry layout of the whole ring. OPTICS Figure 6 shows the matched optics for the $1 8 \\mathrm { G e V }$ lattice with two collision points. Table 1 shows the main lattice parameters at $1 8 \\mathrm { G e V }$ with 1 and $2 \\mathrm { I P s }$ . The two lattices are identical with two full interaction regions; however, for the $1 \\mathrm { I P }$ lattice the $\\beta$ functions are additionally squeezed at IP8. This results in a smaller natural chromaticity for the $1 \\mathrm { I P }$ lattice. Table: Caption: Table 1: ESR Lattice Parameters at $1 8 \\mathrm { G e V }$ with 1 and $2 \\mathrm { I P s }$ Body: <html><body><table><tr><td>Parameter</td><td>1IP</td><td>2 IP</td></tr><tr><td>Arc cell phase adv.</td><td>90°</td><td>90°</td></tr><tr><td>Hor. emit. (nm)</td><td>24</td><td>25</td></tr><tr><td>Energy spread</td><td>0.095%</td><td>0.095%</td></tr><tr><td>β*/β(m)</td><td>0.59 /0.057</td><td>0.59 / 0.057</td></tr><tr><td>Tunes, Qx/Qy</td><td>50.08/44.14</td><td>50.08/44.14</td></tr><tr><td>Nat. chrom., § x/§y</td><td>-92/-92</td><td>-108/ -117</td></tr></table></body></html>
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augmentation
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NO
| 0
|
IPAC
|
What target wavelength was the inverse-designed Smith-Purcell grating optimized for?
|
Approximately 1.4 ?m
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Fact
|
haeusler-et-al-2022-boosting-the-efficiency-of-smith-purcell-radiators-using-nanophotonic-inverse-design.pdf
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To detect the far-field angular pattern of radiation, an Xray-optimized potassium bromide-coated Micro Channel Plate (MCP) assembly of effective diameter $4 0 ~ \\mathrm { \\ m m }$ (PHOTONIS MCP40/12/10/8I60‚à∂1EDRKBR6, P46), having center-to-center spacing of $1 2 \\ \\mu \\mathrm { m }$ nominal and pore size of $1 0 ~ { \\mu \\mathrm { m } }$ nominal, in combination with a phosphor screen and a CMOS camera (Basler Ace acA4112-20um, $4 0 9 6 \\texttt { x } 3 0 0 0$ pixels) has been utilized as a observation screen. MCP plate and Phosphor bias voltage are set to be constant $1 . 7 0 \\mathrm { k V }$ and $5 \\mathrm { k V }$ respectively in this experiment. As a reference, actual aperture of the X-ray shown in the observed X-ray pattern corresponds to an aperture of the filter wheel insertion device having a diameter of $2 0 ~ \\mathrm { m m }$ . EXPERIMENTAL RESULTS So far the set up of Nd:YAG laser ICS has been established as an observation of $8 7 \\mathrm { k e V }$ Hard X-ray ICS through the Au $K$ -edge filtering in the previous experiment BNLATF AE87. Here in this report experimental progress achieved owing to the upgraded multi TW $\\mathrm { C O } _ { 2 }$ laser and newly installed laser optics is presented as a benchmarking of the long wavelength $\\mathrm { C O } _ { 2 }$ laser peak field at Compton I.P.
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augmentation
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NO
| 0
|
IPAC
|
What target wavelength was the inverse-designed Smith-Purcell grating optimized for?
|
Approximately 1.4 ?m
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Fact
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haeusler-et-al-2022-boosting-the-efficiency-of-smith-purcell-radiators-using-nanophotonic-inverse-design.pdf
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Additional studies will investigate the addition of a higherorder RF dechirping cavity at the exit of the gun combined with a same-order decelerating cavity at the sample to mitigate some of these issues. This harmonic cavity can also be used for additional chirp-control in the diffraction line. RESULTS Gun and Decelerating Cavity Only We can estimate the optimum resolution limits using Eq. 1, and normalised emittance and energy-spread values calculated using GPT [7] for a simplified model of the machine, with only gun and dechirping cavity included. The results, excluding the solenoidal lenses and any post-sample transport, for $2 0 0 \\mathrm { f C }$ and $2 0 \\mathrm { p C }$ are shown in Fig. 2 and Fig. 3 respectively. Without the effects of chromatic aberrations from the solenoidal condenser lenses, the optimum working point is at $+ 5 ^ { \\circ } / 5$ ps for the $2 0 0 \\mathrm { f C }$ case and $+ 5 ^ { \\circ } / 1 1$ ps for the $2 0 \\mathrm { p C }$ case. This gives optimal resolution values of $\\mathord { \\sim } 1 \\mathrm { n m }$ at $2 0 0 \\mathrm { f C }$ and ${ \\sim } 1 2 5 \\mathrm { n m }$ at $2 0 \\mathrm { p C }$ , assuming a sample spot-size of $1 0 \\mu \\mathrm { m }$ . Larger spot sizes reduce the calculated resolution, since the beam divergence ( $\\dot { \\mathbf { \\Omega } } \\alpha$ in Eq. 1) at the focus decreases with increasing values of the $\\beta$ -function, but also reduces the electron density and thus can degrade the signal-to-noise ratio at the detector.
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augmentation
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NO
| 0
|
IPAC
|
What target wavelength was the inverse-designed Smith-Purcell grating optimized for?
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Approximately 1.4 ?m
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Fact
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haeusler-et-al-2022-boosting-the-efficiency-of-smith-purcell-radiators-using-nanophotonic-inverse-design.pdf
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Table: Caption: Table 2: Radiator Parameters TUPL: Tuesday Poster Session: TUPL Body: <html><body><table><tr><td></td><td>R1</td><td>R2</td><td>R3</td><td>Unit</td></tr><tr><td>Pulse wavelength</td><td>13.5</td><td>6.75</td><td>4.5</td><td>nm</td></tr><tr><td>Period length</td><td>2</td><td>1.5</td><td>1</td><td>cm</td></tr><tr><td>Period number</td><td>120</td><td>160</td><td>240</td><td>/</td></tr><tr><td>Gap</td><td>7.36</td><td>6.89</td><td>3.54</td><td>mm</td></tr><tr><td>Peak gradient</td><td>0.70</td><td>0.49</td><td>0.74</td><td>T</td></tr><tr><td>K</td><td>1.31</td><td>0.69</td><td>0.69</td><td>/</td></tr></table></body></html> Figures 4 (a) and (b) illustrate the pulse powers and spectra of $1 3 . 5 \\mathrm { n m }$ , $6 . 7 5 \\mathrm { n m }$ and $4 . 5 \\mathrm { n m }$ wavelength radiation, respectively. It is worth noting that the $\\mathbf { \\boldsymbol { x } }$ -axis represents the photon energy relative to the respective central photon energy value in Fig. 4 (b). The simulation results reveal that the $1 3 . 5 \\mathrm { n m }$ radiation has a peak power of approximately $2 . 9 \\mathrm { M W }$ , a pulse duration of $8 . 0 8 \\mu \\mathrm { m }$ (FWHM), and a spectral bandwidth of $0 . 0 8 4 \\%$ (FWHM), 1.14 times the Fourier transform limit. The $6 . 7 5 \\mathrm { n m }$ radiation, on the other hand, has a peak power of approximately $0 . 5 \\mathrm { M W }$ , a pulse duration of $7 . 6 9 \\mu \\mathrm { m }$ (FWHM), and a spectral bandwidth of about $0 . 0 8 8 \\%$ (FWHM), 2.27 times the Fourier transform limit. Finally, the $4 . 5 \\mathrm { n m }$ radiation has a peak power of $0 . 2 2 \\mathrm { M W }$ , a pulse duration of $7 . 9 9 \\mu \\mathrm { m }$ (FWHM), and a spectral bandwidth of about $0 . 0 3 \\%$ (FWHM), 1.23 times the Fourier transform limit.
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augmentation
|
NO
| 0
|
IPAC
|
What target wavelength was the inverse-designed Smith-Purcell grating optimized for?
|
Approximately 1.4 ?m
|
Fact
|
haeusler-et-al-2022-boosting-the-efficiency-of-smith-purcell-radiators-using-nanophotonic-inverse-design.pdf
|
Selection of Operating Point For the operation of hard $\\mathbf { \\boldsymbol { x } }$ -ray self seeding (HXRSS) [9, 10], the SASE2 undulator beamline at European XFEL features two intra-undulator stations combining a magnetic chicane with the possibility to insert and precisely position diamond crystals on the optical axis of the undulator beamline. In this work, we consider using these crystals (thickness $d$ ) in the second HXRSS monochromator as optical high-pass filters and with the pitch angle $\\phi$ the effective material thickness $d _ { \\mathrm { e f f } } = d / \\sin { \\phi }$ can be adjusted to some extent (the smallest possible pitch angle is about $3 0 ^ { \\circ }$ ). From the Lambert-Beer law, $T = \\mathrm { e x p } ( - \\mu d _ { \\mathrm { e f f } } )$ , with $\\mu$ being the attenuation coefficient of the filter material diamond at the photon energy of interest, we see that the $\\mathbf { \\nabla } _ { \\mathbf { X } }$ -ray transmission $T$ of the crystal can thus be adjusted to some extent. The applicability of this filtering scheme requires an optical filter combining significant attenuation at the fundamental with reasonable transmission at the third harmonic. From these requirements and the currently installed diamond crystal $( d = 1 0 5 ~ \\mu \\mathrm { m }$ , density of diamond: $\\rho = 3 . 5 ~ \\mathrm { g } ~ \\mathrm { c m } ^ { - 3 } ,$ ) follows an electron beam energy of $8 . 5 \\mathrm { G e V }$ and a photon energy of $2 . 3 \\mathrm { k e V }$ (corresponding to the SASE2 undulators set to $K = 3 . 5 9$ ). Filter transmission values were computed for the fundamental photon energy of $2 . 3 \\mathrm { k e V }$ and selected pitch angles using data from Ref. [11], the data is compiled in Table 1. For the selected photon energies, the filter element attenuates the fundamental by several orders of magnitude while only mildly attenuating the third harmonic.
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augmentation
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NO
| 0
|
IPAC
|
What target wavelength was the inverse-designed Smith-Purcell grating optimized for?
|
Approximately 1.4 ?m
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Fact
|
haeusler-et-al-2022-boosting-the-efficiency-of-smith-purcell-radiators-using-nanophotonic-inverse-design.pdf
|
EXPERIMENTAL SETUP The layout is shown schematically in Fig. 1. The probe is derived from a regeneratively amplifed Ti:sapphire laser (few ${ \\mu \\mathrm { J } }$ , $8 0 0 \\ \\mathrm { n m }$ , 50 fs) that is synchronised with the $( 3 5 ~ \\mathrm { M e V / c }$ , 1-150 pC, $1 0 ~ \\mathrm { H z }$ ) electron beam [13]. It was chirped to an experimentally verified 8.1 ps by detuning the laser compressor. An adjustable telescope was used to focus the probe to a few $1 0 \\mathrm { s } \\ \\mu \\mathrm { m }$ on the $0 . 5 \\mathrm { m m }$ thick GaP crystal (EO) to allow the probe to be positioned close to the electron beam. A retro-reflection geometry was used to avoid shadowing the Coulomb field. After the EO interaction in the crystal a new pulse with a fraction of a percent of the probe’s intensity was created with an orthogonal polarisation, which co-propogated back with the probe. A quarter-wave plate (٦_x0010__x0015_) was used to compensate for residual birefringence in the EO crystal, followed by a calcite birefringent plate (BRP) which added the required delay between polarisation states. A polariser (POL) was then used to extinguish the probe intensity to a level similar to that of the optically encoded pulse to maximise fringe visibility on a spectrometer (Spec). The SI algorithm is then applied to recover the temporal envelope of the pulse, and thereby the Coulomb field profile. Finding initial overlap between the laser and electron beams was aided by a spare beam pick-up installed near the interaction point, and a fast optical photodiode sampling the probe laser prior to entering the vacuum chamber. The laser was locked to the CLARA RF frequency using a commercial system (Synchrolock, Coherent) and fine scanning was achieved via an optical delay stage. Using GaP with an $8 0 0 \\mathrm { n m }$ probe limited the spectral response of the system due to poor phasematching. ZnTe was originally specified, but the low optical quality of the crystals available (inhomogeneous birefringence and scattering from bubbles) made operating in a retro-reflection geometry and at near extinction of the probe made setting the system up very difficult. The quality of all available GaP crystals was much higher, and with the correct wavelength probe would actually provide a wider bandwidth than ZnTe. The system could be switched back to spectral decoding by removing the birefringent plate, and re-optimising the quarter-wave plate
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augmentation
|
NO
| 0
|
IPAC
|
What target wavelength was the inverse-designed Smith-Purcell grating optimized for?
|
Approximately 1.4 ?m
|
Fact
|
haeusler-et-al-2022-boosting-the-efficiency-of-smith-purcell-radiators-using-nanophotonic-inverse-design.pdf
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To meet the requested performance, in-vacuum undulators (IVU) of $5 ~ \\mathrm { \\ m m }$ aperture will be used. Simulations show that IVUs with $\\mathrm { k } _ { \\mathrm { m a x } } { = } 2$ and $2 0 \\mathrm { m m }$ period at $2 . 4 \\mathrm { G e V }$ will provide the 7th, 9th, 11th and 13th harmonics with the required flux of $1 0 ^ { 1 4 } \\mathrm { p h } / \\mathrm { s } / 0 . 1 \\% \\mathrm { b w }$ on the sample and energy range, while the brilliance is $> 1 0 ^ { 2 1 }$ $\\mathrm { p h } / \\mathrm { s } / \\mathrm { m m } ^ { 2 } / \\mathrm { m r a d } ^ { 2 } / 0 . 1 \\%$ BW (Fig. 6) at $1 0 \\mathrm { k e V } .$ . We intend to reuse some already existing IDs including the super conducting $3 . 5 \\mathrm { T }$ wiggler. Also short IDs i.e. 2 mini wigglers and 3 undulators will be installed in the short straight sections. A prototype of the mini wiggler has been already constructed [29].
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What target wavelength was the inverse-designed Smith-Purcell grating optimized for?
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Approximately 1.4 ?m
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Fact
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haeusler-et-al-2022-boosting-the-efficiency-of-smith-purcell-radiators-using-nanophotonic-inverse-design.pdf
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METHODS The use of an external cavity diode laser as a probe introduces two mechanisms for changing the laser emission center wavelength: injection current modulation (fast) and mechanical cavity adjustments (slow). As shown in Fig. 4, we have implement the Littman-Metcalf design for constructing an external cavity TLDS. In this approach, the collimated (Thorlabs C230TMD-B) first order diffraction mode from a blazed grating $( 1 2 0 0 ~ \\mathrm { g / m m } ~ \\textcircled { \\omega } ~ 5 0 0 ~ \\mathrm { n m }$ , Thorlabs GR25- 1205) is reflected back into the diode (Toptica EYP-RWE0655-00505-2000) forming the laser cavity. Course wavelength selection is achieved with the motorized (Newport Picomotor 8321) position of the mirror. The $0 ^ { \\mathrm { t h } }$ order mode is the output of the laser. The output is sent through an optical isolator (Thorlabs IO-5-670-VLP) and a $4 \\mathrm { x }$ anamorphic prism pair (Edmund Optics 47-274), before being coupled into a single mode fiber with a fiber collimator triplet lens (Thorlabs F280FC-B). The anamorphic prism pair is used to roughly correct the $4 . 5 \\mathrm { x }$ ellipticity of the diode output. The APP increases the coupling efficiency into the single mode fiber. A total coupling efficiency of $3 8 \\%$ is achieved after the single mode fiber, yielding $1 0 \\mathrm { m W }$ of output power.
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IPAC
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What target wavelength was the inverse-designed Smith-Purcell grating optimized for?
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Approximately 1.4 ?m
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Fact
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haeusler-et-al-2022-boosting-the-efficiency-of-smith-purcell-radiators-using-nanophotonic-inverse-design.pdf
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In his simulations, the OAP mirror radius was $R { = } 7 6 . 2$ mm with $\\theta _ { O A } = 6 ^ { \\circ }$ , the central wavelength $\\lambda _ { 0 } = 8 0 0 n m$ , $\\sigma _ { \\lambda } = 3 0$ nm, and the wavelength spectrum in the range between $6 1 8 ~ \\mathrm { n m }$ and $1 , 1 3 0 ~ \\mathrm { n m }$ in increments of $0 . 5 \\mathrm { n m }$ was considered, i.e. using 1,024 iterations in total. $N _ { f }$ was picked at random, and the parent focal length f was calculated using $N _ { f } { = } f / 3 D$ , where $D { = } 4 0$ mm is the FWHM of the laser pulse before focusing. Based on the $\\theta _ { O A }$ and information from Fig. 1, it was possible to obtain the parameters $d$ and $f _ { \\mathrm { A P } }$ , using the identity $t a n ( \\beta ) = c o t ( \\theta _ { O A } )$ . Moreover, the super-Gaussian incident laser pulse was considered. The integration of the real and imaginary parts of the transverse electric field and consequent multiplication by spectral amplitude were performed separately for each wavelength across the chosen spectrum.
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IPAC
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What target wavelength was the inverse-designed Smith-Purcell grating optimized for?
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Approximately 1.4 ?m
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Fact
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haeusler-et-al-2022-boosting-the-efficiency-of-smith-purcell-radiators-using-nanophotonic-inverse-design.pdf
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Alternatively the independent focusing could be achieved by reducing the focusing of the offset quadrupole and then reinstating the bending angle through horizontal-dipole trim coils or coils directly on the vacuum chamber. Table 3 summarises the offset quadrupole properties during commissioning optics and nominal optics. Table: Caption: Table 2: Key Parameters for the Nominal Optics and Commissioning Optics Settings Body: <html><body><table><tr><td></td><td>Nominal</td><td>Comm.</td></tr><tr><td>Energy, (E)</td><td>3 454.8 m</td><td></td></tr><tr><td>Circumference,(C) Harmonic number, (h)</td><td></td><td>758</td></tr><tr><td>Main RF frequency</td><td></td><td>500 MHz</td></tr><tr><td>RF cavity voltage</td><td></td><td>2.3 MV</td></tr><tr><td>Natural chromaticities</td><td>-151.7, -76.3</td><td>-82.7, -67.1</td></tr><tr><td>Chromaticities (§ x, §y)</td><td>0.99, 0.99</td><td>0.06,0.05</td></tr><tr><td>Mom.compaction</td><td>0.056e-3</td><td>0.182e-3</td></tr><tr><td>Hor. emittance (εx)</td><td>50 pm</td><td>213 pm</td></tr><tr><td>Tunes (Qx, Qy)</td><td>70.23,20.81</td><td>53.09,29.60</td></tr><tr><td>Energy spread</td><td></td><td></td></tr><tr><td></td><td>1.11e-3</td><td>4.22e-3</td></tr><tr><td>Bunch length Current</td><td>2.03 mm 400 mA</td><td>13.94 mm</td></tr></table></body></html> Table: Caption: Table 3: Offset quadrupole properties and settings for commissioning optics and for nominal optics for both the original design and the design with the allowance for the further offset during commissioning optics. Body: <html><body><table><tr><td>Optics</td><td>K [m-²]</td><td>Pole-tip radius [mm]</td><td>[T] Bqu</td><td>offset [mm]</td></tr><tr><td>Original design</td><td>11</td><td>12.5</td><td>1.536</td><td>-2.116</td></tr><tr><td>Original design with allowance for comm.optics</td><td>11</td><td>13.1</td><td>1.602</td><td>-2.116</td></tr><tr><td>Commissioning</td><td>8.65</td><td>13.1</td><td>1.293</td><td>-2.690</td></tr></table></body></html> Dynamic Aperture The larger dispersion through the arc during commissioning optics mode of operation, means that the chromaticitycorrecting sextupoles can be weaker, which results in a larger DA as shown in Fig. 2. Typically during commissioning of fourth generation light sources the sextupoles are turned off to begin with [2, 3, 15]. Whilst the sextupoles are needed to increase the DA when a stored beam is established (see Fig. 2), turning off the sextupoles will increase the DA over a limited number of turns (see Fig. 4). Under the commissioning optics settings, the DA remains larger of more turns before the sextupoles are ramped.
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What target wavelength was the inverse-designed Smith-Purcell grating optimized for?
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Approximately 1.4 ?m
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Fact
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haeusler-et-al-2022-boosting-the-efficiency-of-smith-purcell-radiators-using-nanophotonic-inverse-design.pdf
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(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.
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IPAC
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What target wavelength was the inverse-designed Smith-Purcell grating optimized for?
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Approximately 1.4 ?m
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Fact
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haeusler-et-al-2022-boosting-the-efficiency-of-smith-purcell-radiators-using-nanophotonic-inverse-design.pdf
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EXPERIMENTAL SETUP The experimental setup is depicted in Figure 1. We used a mode-locked laser at $1 0 3 0 \\mathrm { - n m }$ center wavelength and ${ \\sim } 3 6 – \\mathrm { M H z }$ pulse repetition rate as the laser source for our experiments. An optical isolator was positioned following the Yb laser to mitigate parasitic backpropagations. The laser output was split into two arms: one short, free-space arm serving as “the reference arm”, and another long, fibercoupled arm including a $7 2 \\mathrm { - m }$ Nested Antiresonant Nodeless Hollow Core Fiber (NAN-HCF, Fig. 1 inset) serving as “the fiber distribution arm”. Control over the power ratio between the reference and the fiber arms was achieved using a half waveplate (HWP) and a polarization beamsplitter cube. In the reference arm, a motorized delay stage (MDL) allowed control over the relative time delay between the pulses. Subsequently, the light was directed to a polarization beam combiner (PBC) for recombination. In the fiber distribution arm, an HWP and a quarter waveplate (QWP) were used to manage the input polarization of the fiber. The 72-m NAN-HCF had an attenuation of $0 . 5 5 \\mathrm { d B / k m }$ at $1 0 3 0 \\mathrm { n m }$ and a core size of $3 2 \\mu \\mathrm { m }$ . It was spliced at both ends with a $2 . 5 – \\mathrm { m }$ standard single mode fiber (SMF) having 2-dB splicing loss. This allowed easy interfacing with fiber-pigtailed collimators and also compensation for the first order dispersion. Following the propagation through the fiber, the pulses were recombined with the reference arm via the PBC.
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Expert
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What target wavelength was the inverse-designed Smith-Purcell grating optimized for?
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Approximately 1.4 ?m
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Fact
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haeusler-et-al-2022-boosting-the-efficiency-of-smith-purcell-radiators-using-nanophotonic-inverse-design.pdf
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Collection Range. The measured Gaussian spectrum from Figure 3a can be explained by the limited numerical aperture of the collection fiber. Smith‚àíPurcell radiation that is emitted in the nonperpendicular direction is offset from the optical axis for collection. This leads to a loss in collection efficiency, which we modeled with the function $\\exp \\{ - 2 r ^ { 2 } / ( { f } \\mathrm { { \\cdot } N A } ) ^ { 2 } \\} ,$ where $r$ is the offset measured at the collimator, $f = 1 2 ~ \\mathrm { m m }$ is the focal length of the collimator, and NA is the numerical aperture of the fiber. We found good agreement with the experimental data for $\\mathrm { N A } = 0 . 1 1$ , which is below the 0.22 stated by the manufacturer and might have been a result of misalignment. ASSOCIATED CONTENT $\\bullet$ Supporting Information The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsphotonics.1c01687. Dependence of radiation on electron beam height within the structure; Determination of effective current; Dependence on beam-grating distance (PDF) 2D time-domain simulation of the inverse design structure (MP4) 2D time-domain simulation of the dual pillar structure with DBR (MP4)
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Expert
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What target wavelength was the inverse-designed Smith-Purcell grating optimized for?
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Approximately 1.4 ?m
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Fact
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haeusler-et-al-2022-boosting-the-efficiency-of-smith-purcell-radiators-using-nanophotonic-inverse-design.pdf
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allows to design the spectrum $( \\omega )$ , spatial distribution $\\mathbf { \\Pi } ( \\mathbf { r } )$ , and polarization (e) of radiation by favoring one kind $| \\mathbf { e } { \\cdot } \\mathbf { E } ( \\mathbf { r } , \\omega ) |$ and penalizing others, $- | \\mathbf { e } ^ { \\prime } { \\boldsymbol { \\cdot } } \\mathbf { E } ( \\mathbf { r } ^ { \\prime } , \\omega ^ { \\prime } ) |$ , with possibly orthogonal polarization $\\mathbf { e ^ { \\prime } }$ . Lifting the periodicity constraint opens the space to complex metasurfaces, which would for example enable designs for focusing or holograms.18,22‚àí27,40 Future efforts could also target the electron dynamics to achieve (self-)bunching and, hence, coherent enhancement of radiation. In that case, the objective function would aim at the field inside the electron channel rather than the far-field emission. This would favor higher quality factors at the cost of lower out-coupling efficiencies. However, direct inclusion of the electron dynamics through an external multiphysics package proves challenging as our inverse design implementation requires differentiability of the objective function with respect to the design parameters. Instead, one may choose to use an analytical expression for the desired electron trajectory or an approximate form for the desired field pattern.
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augmentation
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NO
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IPAC
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What three power quantities (Ploss, Pabs, Prad) are defined in the theoretical framework, and what do they represent?
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Ploss is the total power lost by the electron; Pabs is the power absorbed by the medium; Prad = Ploss - Pabs is the power radiated to the far field.
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Definition
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Maximal_spontaneous_photon_emission_and_energy_loss_from_free_electrons.pdf
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$$ \\begin{array} { l } { \\displaystyle 0 = \\frac { d } { d s } F _ { n } ( z , p _ { z } ; s ) } \\\\ { = \\frac { \\partial F _ { n } } { \\partial s } + \\alpha _ { c } p _ { z } \\frac { \\partial F _ { n } } { \\partial z } + \\left[ \\mathcal { F } ( z ) + \\frac { \\Delta _ { p _ { z } } } { c T _ { 0 } } \\right] \\frac { \\partial F _ { n } } { \\partial p _ { z } } . } \\end{array} $$ Here, $\\alpha _ { c }$ is the momentum compaction, $\\mathcal { F }$ is total rf-force composed of that due to the applied (generator) fields and the collective, long-range wakefields, while $\\Delta _ { p _ { z } } / c T _ { 0 }$ denotes the energy correction $\\Delta _ { p _ { z } }$ given every revolution period $T _ { 0 }$ by the feedback system.
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augmentation
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NO
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IPAC
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What three power quantities (Ploss, Pabs, Prad) are defined in the theoretical framework, and what do they represent?
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Ploss is the total power lost by the electron; Pabs is the power absorbed by the medium; Prad = Ploss - Pabs is the power radiated to the far field.
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Definition
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Maximal_spontaneous_photon_emission_and_energy_loss_from_free_electrons.pdf
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Governing Equation The basic governing equations include the continuity equation, the momentum equation and the energy equation. We apply the k-ε turbulence model [4] and SIMPLEC to solve the velocity and pressure problem. Mass conservation equation (continuity equation) $$ \\frac { \\partial \\rho } { \\partial t } + \\nabla \\cdot \\left( \\rho \\mathbf { u } \\right) = 0 $$ where $\\rho$ is density of fluid (air in the study), $t$ is time and $\\mathbf { u }$ refers to air velocity vector. Momentum conservation equation $$ \\frac { \\hat { \\partial } ( \\rho \\mathbf { u } ) } { \\hat { \\partial } t } + \\nabla \\cdot \\left( \\rho \\mathbf { u } \\mathbf { u } \\right) = - \\nabla p + \\rho \\mathbf { g } + \\nabla \\cdot ( \\mu \\nabla \\mathbf { u } ) - \\nabla \\cdot \\boldsymbol { \\tau } _ { t } $$ where $p$ is pressure, $\\mathbf { g }$ is vector of gravitational acceleration, $\\mu$ is dynamic viscosity of air, and $\\textit { \\textbf { ‰} }$ is divergence of the turbulent stresses which accounts for auxiliary stress due to velocity fluctuations. Energy conservation equation
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augmentation
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NO
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IPAC
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What three power quantities (Ploss, Pabs, Prad) are defined in the theoretical framework, and what do they represent?
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Ploss is the total power lost by the electron; Pabs is the power absorbed by the medium; Prad = Ploss - Pabs is the power radiated to the far field.
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Definition
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Maximal_spontaneous_photon_emission_and_energy_loss_from_free_electrons.pdf
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$$ A = \\frac { \\langle E _ { f } \\rangle - \\langle E _ { i } \\rangle } { L _ { \\mathrm { p l a s m a } } } $$ In the FACET-II portion of the SLAC linear accelerator, bunches of electrons are accelerated using RF cavity acceleration over the course of the one km long beamline before they reach an experimental chamber. This chamber contains a gas jet which can be used to produce a small length of plasma in which tests of PWFA can be performed [2]. The normalized emittance is defined as the area of the beam in the corresponding position-momentum phase space, where $\\mathbf { \\boldsymbol { x } }$ is the position of a particle in the beam and $\\mathbf { x } ^ { \\prime }$ is the angle of its $\\mathbf { \\boldsymbol { x } }$ momentum with respect to its momentum in the $z$ -direction, multiplied by its Lorentz factor, $( \\gamma )$ , to account for the beam’s acceleration [8], $$ \\epsilon _ { n x } = \\gamma \\sqrt { \\langle x ^ { 2 } \\rangle \\langle x ^ { \\prime 2 } \\rangle - \\langle x x ^ { \\prime } \\rangle ^ { 2 } } .
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augmentation
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NO
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IPAC
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What three power quantities (Ploss, Pabs, Prad) are defined in the theoretical framework, and what do they represent?
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Ploss is the total power lost by the electron; Pabs is the power absorbed by the medium; Prad = Ploss - Pabs is the power radiated to the far field.
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Definition
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Maximal_spontaneous_photon_emission_and_energy_loss_from_free_electrons.pdf
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$$ where $\\Phi _ { i } ( \\mathbf { p } )$ denotes the multivariate PC basis corresponding to the PDF used to model the input variations. Once the polynomial coefficients are found by eq. (5), the expectation value and variance can be estimated using $$ \\mathbb { E } \\left[ { f \\left( { \\bf p } \\right) } \\right] = \\tilde { f } _ { 0 } , \\quad \\mathrm { V a r } \\left[ { f \\left( { \\bf p } \\right) } \\right] = \\sum _ { i = 1 } ^ { N } \\big | \\tilde { f } _ { i } \\big | ^ { 2 } . $$ Next, to find the influence of the deformation due to the LF radiation pressure on the merit functions in the meanworst-scenario sense [18, 22], we use the first-order Taylor expansion around the nominal parametric shape $\\Omega \\left( \\mathbf { p } _ { 0 } \\right)$ $$ \\Delta F _ { j } \\left[ \\Omega ( \\mathbf { p } ) \\right] = \\operatorname* { s u p } _ { \\Omega ( \\mathbf { p } ) \\in \\Pi } \\mathbb { E } \\left[ f _ { j } \\left( \\Omega \\left( \\mathbf { p } \\right) \\right) - f _ { j } \\left( \\Omega \\left( \\mathbf { p } _ { 0 } \\right) \\right) \\right] ,
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augmentation
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NO
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IPAC
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What three power quantities (Ploss, Pabs, Prad) are defined in the theoretical framework, and what do they represent?
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Ploss is the total power lost by the electron; Pabs is the power absorbed by the medium; Prad = Ploss - Pabs is the power radiated to the far field.
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Definition
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Maximal_spontaneous_photon_emission_and_energy_loss_from_free_electrons.pdf
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$$ The lowercase letters represent the reflection or transmission coefficients for each port, and the phase of RF power in each cell must be required as shown in Eq. (1), otherwise $\\theta$ is not allowed to be the arbitrary angle. If the power parallel- coupled structure exists, the ideal power transmission is reciprocal and lossless. The constraint holds when $\\theta$ is 0 or $1 8 0 ^ { \\circ }$ [2], and Eq. (1) also holds when $\\theta$ is an arbitrary angle after calculation. Thus, this expression form of scattering matrix can be extended to N-ports structure, which proves that the distributed-coupling structure with arbitrary phase advance is theoretically working. Port①Port5 ↓1 Port② Port④ Port③ WAVEGUIDE STRUCTURE OF POWER DIVIDER Conventional distributed-coupling structures can be split into multiple identical T-junctions, and the distance between each T-structure necessarily equals to one or half of the wavelength in the waveguide, which represent a phase advance of 0 or $1 8 0 ^ { \\circ }$ . Parallel-coupled structures with arbitrary phase shift requires not only changing the distance between T-junctions to the length corresponding to the designed phase advance, but also redesigning the physical structure of Tjunctions to ensure equal power division. We designed the structure using WR90 rectangular waveguide and the phase shift is set to $1 5 0 ^ { \\circ }$ , and the physical structure of the three-port parallel-coupling is demonstrated in Fig. 2.
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augmentation
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NO
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IPAC
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What three power quantities (Ploss, Pabs, Prad) are defined in the theoretical framework, and what do they represent?
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Ploss is the total power lost by the electron; Pabs is the power absorbed by the medium; Prad = Ploss - Pabs is the power radiated to the far field.
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Definition
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Maximal_spontaneous_photon_emission_and_energy_loss_from_free_electrons.pdf
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$$ \\rho ( q , t + \\Delta t ) = \\int \\psi ( q , p , t + \\Delta t ) \\mathrm { d } p . $$ Equation 12 can be expressed in discrete terms utilizing a projection matrix, $\\mathbf { W }$ , as follows: $$ s : = N \\times x + y + 1 , $$ $$ \\rho \\left( x , t + \\Delta t \\right) = \\mathbf { W } \\cdot \\boldsymbol { \\psi } \\left( s , t + \\Delta t \\right) . $$ Subsequently, by substituting Eq. 11 into Eq. 13, the latter can be expressed as: $$ \\rho ( x , t + \\Delta t ) = \\mathbf { W } \\cdot \\mathbf { M } ( \\rho ( t ) ) \\cdot \\psi ( s , t ) . $$ Equation 14 not only correlates a specific phase space with the next bunch profile but also links it to future profiles. With $\\mid m$ bunch profile measurements, the relationship to the initial phase space density is as follows: $$ \\begin{array} { r l r } & { } & { \\mathbf { W } \\cdot \\boldsymbol { \\psi } _ { 1 } = \\bar { \\rho } _ { 1 } } \\\\ & { } & { \\mathbf { W } \\cdot \\mathbf { M } ( \\bar { \\rho } _ { 1 } ) \\cdot \\boldsymbol { \\psi } _ { 1 } = \\bar { \\rho } _ { 2 } } \\\\ & { } & { \\mathbf { W } \\cdot \\mathbf { M } ( \\bar { \\rho } _ { 2 } ) \\cdot \\mathbf { M } ( \\bar { \\rho } _ { 1 } ) \\cdot \\boldsymbol { \\psi } _ { 1 } = \\bar { \\rho } _ { 3 } } \\\\ & { } & { \\vdots } \\\\ & { } & { \\mathbf { W } \\cdot \\mathbf { M } ( \\bar { \\rho } _ { m - 1 } ) \\cdots \\mathbf { M } ( \\bar { \\rho } _ { 1 } ) \\cdot \\boldsymbol { \\psi } _ { 1 } = \\bar { \\rho } _ { m } } \\end{array}
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NO
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IPAC
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What three power quantities (Ploss, Pabs, Prad) are defined in the theoretical framework, and what do they represent?
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Ploss is the total power lost by the electron; Pabs is the power absorbed by the medium; Prad = Ploss - Pabs is the power radiated to the far field.
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Definition
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Maximal_spontaneous_photon_emission_and_energy_loss_from_free_electrons.pdf
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The operator D is calculated by approximating the first and second derivatives of phase space to momentum, as shown in Eq. 7, using the derivatives of the Lagrange polynomials [13]. $$ \\begin{array} { c } { \\displaystyle \\frac { \\partial \\psi } { \\partial t } = \\beta _ { d } \\frac \\partial { \\partial p } ( p \\psi ) + D \\frac { \\partial ^ { 2 } \\psi } { \\partial p ^ { 2 } } , } \\\\ { \\displaystyle \\psi ( q , p , t + \\Delta t ) = \\frac \\partial { \\partial t } \\Delta t + \\psi ( q , p , t ) . } \\end{array} $$ The matrix notation for the presented operators over the phase space is expressed as: $$ \\psi ( s , t + \\Delta t ) = \\mathrm { L } \\cdot \\psi ( s , t ) . $$ The evolution of phase space density is expressed in terms of the matrix operators as follows: $$ \\psi ( s , t + \\Delta t ) = \\mathbf { D } \\cdot \\mathbf { R } _ { \\mathrm { K } } \\cdot \\mathbf { R } _ { \\mathrm { D } } \\cdot \\mathbf { K } ( \\rho ( t ) ) \\cdot \\psi ( s , t ) .
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augmentation
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NO
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IPAC
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What three power quantities (Ploss, Pabs, Prad) are defined in the theoretical framework, and what do they represent?
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Ploss is the total power lost by the electron; Pabs is the power absorbed by the medium; Prad = Ploss - Pabs is the power radiated to the far field.
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Definition
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Maximal_spontaneous_photon_emission_and_energy_loss_from_free_electrons.pdf
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$$ where Rs represents the cavity shunt impedance, $\\mathbf { S } _ { 2 1 }$ is the power ratio of transmitted power to input power of the cavity in decibel, $\\rho$ is the reflection coefficient of the cavity, Vt.LLRF and Pt.LLRF represent the voltage and power measured at the controller input respectively, while $\\mathrm { P _ { t . c a v } }$ denotes the transmitted power of the cavity. The coefficient $\\mathtt { a _ { u } }$ can be obtained from: $$ \\begin{array} { l } { \\displaystyle I _ { G } = S \\cdot V _ { _ { R F , L L R F } } = S \\cdot d \\cdot D A C } \\\\ { \\displaystyle P _ { f } = P _ { _ { R F , L L R F } } \\cdot g _ { 1 } } \\\\ { \\displaystyle a _ { u } = \\sqrt { \\frac { 4 \\beta } { ( 1 + \\beta ) R _ { L } } \\frac { g _ { 1 } } { 5 0 } } \\cdot d } \\end{array}
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augmentation
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What three power quantities (Ploss, Pabs, Prad) are defined in the theoretical framework, and what do they represent?
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Ploss is the total power lost by the electron; Pabs is the power absorbed by the medium; Prad = Ploss - Pabs is the power radiated to the far field.
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Definition
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Maximal_spontaneous_photon_emission_and_energy_loss_from_free_electrons.pdf
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1 Compute Power 1/6 short-range 1/6 long-range ùêø/3 drift 1/3 short-range 1/3 long-range ùêø 3 drift 1/3 short-range 1/3 long-range ùêø/3 drift 1/6 short-range 1/6 long-range Compute Power and/or betatron oscillation (PLACET1 does o!er a full 6D bunch model alternative, but not with an option to compute wakefields). For PLACET3, which o!ers only the 6D model, we opted for an intermediate solution: using a Fast Fourier transform at the site of each wakefield computation, we generate a longitudinal charge mesh and perform the required convolution with the wake function to generate a wakefield potential mesh. This mesh is then interpolated to apply a transverse momentum kick for each macro-particle in our continuous distribution. The most notable di!erence between this model and PLACET1‚Äôa is that, in between wakefield estimations, these macro-particles are allowed to drift longitudinally, altering the charge distribution before the next mesh computation. As an example of the e!ect of a short-range longitudinal wakefield, Fig. 1 presents the tracking results of a DriveBeam bunch through the third-stage CLIC decelerator. In the figure, we can see that a bunch with nominal transverse emittance $( 1 5 0 \\mu \\mathrm { m } )$ is both lengthened by ${ \\sim } 1 . 2 \\%$ and delayed by ${ \\sim } 0 . 1 3 \\mathrm { m m } \\equiv 0 . 4 2 1$ ps as it travels along the decelerator. These results would surpass the requirements established in [4] but can be mitigated by adjusting the initial bunch length for the former and the longitudinal PETS position for the latter. This result is further discussed in [5]. For benchmarking purposes, the tracking of a 0-emittance bunch that su!ers no longitudinal drift driven by betatron oscillations and the results of a PLACET1 simulation is also shown. The two latter results agree as expected.
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augmentation
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IPAC
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What three power quantities (Ploss, Pabs, Prad) are defined in the theoretical framework, and what do they represent?
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Ploss is the total power lost by the electron; Pabs is the power absorbed by the medium; Prad = Ploss - Pabs is the power radiated to the far field.
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Definition
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Maximal_spontaneous_photon_emission_and_energy_loss_from_free_electrons.pdf
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$$ The various parameters here are just constant that are evaluated at each step, the only variables are $x$ and $y$ . When this potential passes through the Lie transform $e ^ { t : p _ { x } ^ { 2 } + p _ { y } ^ { 2 } + H _ { 2 } : } H _ { 2 }$ the part of interest in the result is the sum of powers of sin and cos multiplied by the powers of the momentum. We can examine two therms of the truncated series at the order 3 (for only one $i$ index), the highest order in trigonometric functions: $$ \\beta _ { i } ^ { 2 } t ^ { 2 } \\left( - \\frac { 2 \\beta _ { i } p _ { y } t \\sin \\left( \\beta _ { i } y \\right) } { 3 } - \\frac { \\cos \\left( \\beta _ { i } y \\right) } { 2 } \\right) \\cos \\left( \\beta _ { i } y \\right) \\sin ^ { 2 } \\left( \\alpha _ { i } x \\right) $$ and the highest order in the momenta
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augmentation
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NO
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IPAC
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What three power quantities (Ploss, Pabs, Prad) are defined in the theoretical framework, and what do they represent?
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Ploss is the total power lost by the electron; Pabs is the power absorbed by the medium; Prad = Ploss - Pabs is the power radiated to the far field.
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Definition
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Maximal_spontaneous_photon_emission_and_energy_loss_from_free_electrons.pdf
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$$ For a storage ring collider with bunch spacing $S _ { B }$ ， bunches collide periodically with frequency $f _ { c } = \\beta c / S _ { B }$ and $s _ { 0 } = c t$ ，excluding the dynamical effects, the luminosity is defined as $\\begin{array} { r } { L = P _ { 0 } \\int \\iiint _ { - \\infty } ^ { \\infty } d x d y d s d s _ { 0 } \\rho _ { 1 x } \\rho _ { 1 y } \\rho _ { 1 s } \\rho _ { 2 x } \\rho _ { 2 y } \\rho _ { 2 s } } \\end{array}$ (3) where $\\rho _ { 1 }$ and $\\rho _ { 2 }$ are the time dependent distribution functions of the two beams, $P _ { 0 } = N _ { 1 } N _ { 2 } N _ { b } f _ { c } { \\frac { \\cal K } { c } } , I$ V1 and $N _ { 2 }$ are the bunch intensities,and $N _ { b }$ is the number of colliding bunches, $K$ is the kinematic factor defined as
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augmentation
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Expert
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What three power quantities (Ploss, Pabs, Prad) are defined in the theoretical framework, and what do they represent?
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Ploss is the total power lost by the electron; Pabs is the power absorbed by the medium; Prad = Ploss - Pabs is the power radiated to the far field.
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Definition
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Maximal_spontaneous_photon_emission_and_energy_loss_from_free_electrons.pdf
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We begin our analysis by considering an electron (charge $- e$ ) of constant velocity $\\nu \\hat { \\mathbf { x } }$ traversing a generic scatterer (plasmonic or dielectric, finite or extended) of arbitrary size and material composition, as in Fig. 1a. The free current density of the electron, ${ \\bf \\dot { J } } ( { \\bf r } , t ) = - { \\hat { \\bf x } } e \\nu \\delta ( y ) { \\bf \\ddot { \\delta } } ( z ) \\delta ( x - \\nu t )$ , generates a frequency-dependent $( { \\bf e } ^ { - i \\omega t }$ convention) incident field26 $$ \\mathbf { E } _ { \\mathrm { i n c } } ( \\mathbf { r } , \\omega ) = \\frac { e \\kappa _ { \\rho } \\mathrm { e } ^ { i k _ { \\nu } x } } { 2 \\pi \\omega \\varepsilon _ { 0 } } [ \\hat { \\mathbf { x } } i \\kappa _ { \\rho } K _ { 0 } ( \\kappa _ { \\rho } \\rho ) - \\hat { \\mathbf { \\rho } } \\hat { \\mathbf { e } } k _ { \\nu } K _ { 1 } ( \\kappa _ { \\rho } \\rho ) ]
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1
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NO
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Expert
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What three power quantities (Ploss, Pabs, Prad) are defined in the theoretical framework, and what do they represent?
|
Ploss is the total power lost by the electron; Pabs is the power absorbed by the medium; Prad = Ploss - Pabs is the power radiated to the far field.
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Definition
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Maximal_spontaneous_photon_emission_and_energy_loss_from_free_electrons.pdf
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The limit in equation (4) can be further simplified by removing the shape dependence of $V$ , since the integrand is positive and is thus bounded above by the same integral for any enclosing structure. A scatterer separated from the electron by a minimum distance $d$ can be enclosed within a larger concentric hollow cylinder sector of inner radius $d$ and outer radius $\\infty$ ‚Äã. For such a sector (height $L$ and opening azimuthal angle $\\scriptstyle \\psi \\in ( 0 , 2 \\pi ] )$ , equation (4) can be further simplified, leading to a general closed-form shape-independent limit (see Supplementary Section 2) that highlights the pivotal role of the impact parameter $\\kappa _ { \\rho } d$ : $$ T _ { \\tau } ( \\omega ) \\leq \\frac { \\alpha \\xi _ { \\tau } } { 2 \\pi c } \\frac { | \\chi | ^ { 2 } } { \\mathrm { I m } \\chi } \\frac { L \\psi } { \\beta ^ { 2 } } [ ( \\kappa _ { \\rho } d ) K _ { 0 } ( \\kappa _ { \\rho } d ) K _ { 1 } ( \\kappa _ { \\rho } d ) ]
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1
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IPAC
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What three power quantities (Ploss, Pabs, Prad) are defined in the theoretical framework, and what do they represent?
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Ploss is the total power lost by the electron; Pabs is the power absorbed by the medium; Prad = Ploss - Pabs is the power radiated to the far field.
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Definition
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Maximal_spontaneous_photon_emission_and_energy_loss_from_free_electrons.pdf
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$$ r _ { \\mathrm { e f f } } ( k , t , \\beta ) = r ( k ) \\mathcal { T } ( k , t , \\beta ) ^ { 2 } . $$ At this point, it shall be pointed out that shunt impedance is defined as: $$ R ( k ) = r ( k ) L = \\frac { V _ { \\mathrm { a c c } } ( k ) ^ { 2 } } { P _ { \\mathrm { d i s s } } ( k ) } , $$ with $V _ { \\mathrm { a c c } } = G L$ the accelerating voltage in a cell and $P _ { \\mathrm { d i s s } }$ the dissipated power in the cell. As shown in [3], Eq. (7) holds in the analogy of an accelerating cavity with an RLC circuit, following from the wakefield formalism. For this reason, it shall be stressed that Eq. (6) and Eq. ( 7) assume causality even if Eq. (6) is valid regardless of the velocity of the particles. Therefore, the following calculations are valid for causal but not necessarily ultrarelativistic particles.
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1
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NO
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IPAC
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What three power quantities (Ploss, Pabs, Prad) are defined in the theoretical framework, and what do they represent?
|
Ploss is the total power lost by the electron; Pabs is the power absorbed by the medium; Prad = Ploss - Pabs is the power radiated to the far field.
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Definition
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Maximal_spontaneous_photon_emission_and_energy_loss_from_free_electrons.pdf
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$$ E _ { y } = E _ { o } e ^ { i \\omega t } \\left( c _ { f } e ^ { i \\overline { { n } } \\overline { { e } } _ { \\mathrm { P C } } k x } + c _ { b } e ^ { - i \\bar { n } _ { \\mathrm { P C } } k x } \\right) $$ where $c _ { f }$ and $\\boldsymbol { c } _ { b }$ are the coefficients of the forward and backward travelling waves and $n _ { \\mathrm { P C } }$ is the complex index refraction of the photocathode film. We solve the for coefficients $c _ { f }$ and $\\boldsymbol { c } _ { b }$ by applying boundary conditions for the electric field in the multilayer. We then calculate the net power density flow into the material from the Poynting vector $\\left( S _ { x } \\right) = 1 / 2 E _ { y } \\cdot H _ { z } ^ { * }$ , where $H _ { z } ^ { * }$ is the complex conjugate of the magnetic field in the material which can be derived from $H = ( - 1 / \\mu )$ $\\int { \\nabla X E d t }$ . A quantity for the differential power density can then be defined as $P _ { a } = \\nabla \\cdot \\operatorname { R e } \\left( S _ { x } \\right)$ . The power absorption profile $a ( x )$ in the photocathode film is then equal to the differential power density throughout the film divided by the input power at the surface: $a ( x ) = P _ { a } / P _ { \\mathrm { i n } }$ . Where the input power can be calculated from:
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4
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Expert
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What three power quantities (Ploss, Pabs, Prad) are defined in the theoretical framework, and what do they represent?
|
Ploss is the total power lost by the electron; Pabs is the power absorbed by the medium; Prad = Ploss - Pabs is the power radiated to the far field.
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Definition
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Maximal_spontaneous_photon_emission_and_energy_loss_from_free_electrons.pdf
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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.
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augmentation
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NO
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Expert
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What three power quantities (Ploss, Pabs, Prad) are defined in the theoretical framework, and what do they represent?
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Ploss is the total power lost by the electron; Pabs is the power absorbed by the medium; Prad = Ploss - Pabs is the power radiated to the far field.
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Definition
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Maximal_spontaneous_photon_emission_and_energy_loss_from_free_electrons.pdf
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A surprising feature of the limits in equations (4), (5a) and (5b) is their prediction for optimal electron velocities. As shown in Fig. 1c, when electrons are in the far field of the structure $( \\kappa _ { \\rho } d \\gg 1 )$ , stronger photon emission and energy loss are achieved by faster electrons—a well-known result. On the contrary, if electrons are in the near field $( \\kappa _ { \\rho } d \\ll 1 )$ , slower electrons are optimal. This contrasting behaviour is evident in the asymptotics of equation (5b), where the $1 / \\beta ^ { 2 }$ or $\\mathrm { e } ^ { - 2 \\kappa _ { \\rho } d }$ dependence is dominant at short or large separations. Physically, the optimal velocities are determined by the incident-field properties (equation (2)): slow electrons generate stronger near-field amplitudes although they are more evanescent (Supplementary Section 2). There has been recent interest in using low-energy electrons for Cherenkov10 and Smith–Purcell31 radiation; our prediction that they can be optimal at subwavelength interaction distances underscores the substantial technological potential of non-relativistic free-electron radiation sources. The tightness of the limit (equations (4), (5a) and (5b)) is demonstrated by comparison with full-wave numerical calculations (see Methods) in Fig. 1d,e. Two scenarios are considered: in Fig. 1d, an electron traverses the centre of an annular Au bowtie antenna and undergoes antenna-enabled transition radiation $( \\eta \\approx 0 . 0 7 \\% )$ , while, in Fig. 1e, an electron traverses a Au grating, undergoing Smith–Purcell radiation $( \\eta \\approx 0 . 9 \\% )$ . In both cases, the numerical results closely trail the upper limit at the considered wavelengths, showing that the limits can be approached or even attained with modest effort.
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augmentation
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NO
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Expert
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What three power quantities (Ploss, Pabs, Prad) are defined in the theoretical framework, and what do they represent?
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Ploss is the total power lost by the electron; Pabs is the power absorbed by the medium; Prad = Ploss - Pabs is the power radiated to the far field.
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Definition
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Maximal_spontaneous_photon_emission_and_energy_loss_from_free_electrons.pdf
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The BIC-enhancement mechanism is entirely accordant with our upper limits. Practically, silicon has non-zero loss across the visible and near-infrared wavelengths. For example, for a period of $a = 6 7 6 \\mathrm { n m }$ , the optimally enhanced radiation wavelength is $\\approx 1 { , } 0 5 0 \\mathrm { n m }$ , at which $\\chi _ { \\mathrm { s i } } \\approx 1 1 . 2 5 + 0 . 0 0 1 \\mathrm { i }$ (ref. 36). For an electron– structure separation of $3 0 0 \\mathrm { n m }$ , we theoretically show in Fig. 4f the strong radiation enhancements ${ > } 3$ orders of magnitude) attainable by BIC-enhanced coupling. The upper limit (shaded region; 2D analogue of equation (4); see Supplementary Section 10) attains extremely large values due to the minute material loss $( | \\chi | ^ { 2 } / \\mathrm { I m } \\chi \\approx 1 0 ^ { 5 } )$ ; nevertheless, BIC-enhanced coupling enables the radiation intensity to closely approach this limit at several resonant velocities. In the presence of an absorptive channel, the maximum enhancement occurs at a small offset from the BIC where the $Q$ -matching condition (see Supplementary Section 11) is satisfied (that is, equal absorptive and radiative rates of the resonances).
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augmentation
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NO
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Expert
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What three power quantities (Ploss, Pabs, Prad) are defined in the theoretical framework, and what do they represent?
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Ploss is the total power lost by the electron; Pabs is the power absorbed by the medium; Prad = Ploss - Pabs is the power radiated to the far field.
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Definition
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Maximal_spontaneous_photon_emission_and_energy_loss_from_free_electrons.pdf
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Next, we specialize in the canonical Smith–Purcell set-up illustrated in Fig. 1e inset. This set-up warrants a particularly close study, given its prominent historical and practical role in free-electron radiation. Aside from the shape-independent limit (equations (5a) and (5b)), we can find a sharper limit (in per unit length for periodic structure) specifically for Smith–Purcell radiation using rectangular gratings of filling factor $\\varLambda$ (see Supplementary Section 3) $$ \\frac { \\mathrm { d } { \\varGamma } _ { \\tau } ( \\omega ) } { \\mathrm { d } x } \\leq \\frac { \\alpha \\xi _ { \\tau } } { 2 \\pi c } \\frac { | \\boldsymbol \\chi | ^ { 2 } } { \\mathrm { I m } \\chi } \\varLambda \\mathcal { G } ( \\beta , k d ) $$ The function ${ \\mathcal { G } } ( { \\boldsymbol { \\beta } } , k d )$ is an azimuthal integral (see Supplementary Section 3) over the Meijer G-function $G _ { 1 , 3 } ^ { 3 , 0 }$ (ref. $^ { 3 2 } )$ that arises in the radial integration of the modified Bessel functions $K _ { n }$ . We emphasize that equation (6) is a specific case of equation (4) for grating structures without any approximations and thus can be readily generalized to multi-material scenarios (see Supplementary equation (37)).
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IPAC
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What was the observed bandwidth (FWHM) of the THz radiation?
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Approximately 9%
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Fact
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hermann-et-al-2022-inverse-designed-narrowband-thz-radiator-for-ultrarelativistic-electrons.pdf
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FIRST EXPERIMENTAL RESULTS Variation of the delay between the two seed pulses leads to minima and maxima of the coherently emitted THz signal [20, 21]. At the highest maximum, a dip in the THz signal indicates overlap between the two pulses, because the number of contributing electrons drops, as shown in the example of Fig. 6 (top). The interaction of both pulses with the same electrons also leads to a signal at the radiator wavelength of $2 6 7 \\mathrm { n m }$ observed at beamline BL 4 (Fig. 6, bottom). The peaks near delay 0.5 and 1 ps are believed to result from harmonic generation at an upstream mirror, since they persist when the laser-electron timing is detuned. Measurements around $2 6 7 \\mathrm { n m }$ were repeated under variation of both chicanes leading to similar results. The next odd harmonic would be at $1 3 3 \\mathrm { n m }$ , but the in-vacuum spectrometer was not operable in fall 2022. Measurements at even harmonics of $8 0 0 \\mathrm { n m }$ were not considered because they are also harmonics of the second seed at $4 0 0 \\mathrm { n m }$ . Malfunction of the laser system in January 2023 stopped further investigations.
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IPAC
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What was the observed bandwidth (FWHM) of the THz radiation?
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Approximately 9%
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Fact
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hermann-et-al-2022-inverse-designed-narrowband-thz-radiator-for-ultrarelativistic-electrons.pdf
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The measured frequencies were $1 8 6 . 8 ~ \\mathrm { G H z }$ and 195.8 GHz for the $\\mathrm { T M } _ { 0 1 }$ mode and $\\mathrm { H E } _ { 1 1 }$ mode, respectively, as compared to the design frequencies of $1 8 0 \\mathrm { G H z }$ and $1 9 0 \\mathrm { G H z }$ [4]. These measurements fall within the expected fabrication error margin. Notably, previous measurements reported in [5] produced $1 8 6 \\mathrm { G H z }$ and $1 9 2 \\ : \\mathrm { G H z }$ , respectively. Since the same technology was utilized for the fabrication of the CWG in both experiments, the consistency in discrepancies suggests a potentially systematic error. Indeed, computations reveal that diminishing the corrugation depth by roughly two micrometers elevates the frequency of sub-THz Čerenkov radiation by one gigahertz. It is also worth noting that several small amplitude peaks at the high-frequency end of the spectrum seen in Fig. 5b are likely due to the beam offset at the location of the $\\mathrm { T E } _ { 1 1 }$ coupler [6].
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IPAC
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What was the observed bandwidth (FWHM) of the THz radiation?
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Approximately 9%
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Fact
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hermann-et-al-2022-inverse-designed-narrowband-thz-radiator-for-ultrarelativistic-electrons.pdf
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Experimental Setup For the experimental SRR Compact-TDS setup, a TPF THz generation setup was designed and aligned on a portable module [4] as illustrated in Fig. 2. Here, the input infrared beam wavefront is tilted via a diffraction grating and imaged into the LiN crystal by a $4 { \\cdot } f .$ -telescope system consisting of two cylindrical lenses. After generation, the divergent THz beam is transported achromatically via flat metal mirrors and three THz lenses. Once the THz radiation leaves the module as collimated beam, it then passes a z-cut quartz vacuum window and is finally focused by an off-axis parabolic mirror to the interaction point. Only the last quarter of this beam path of approximately $1 \\mathrm { m }$ length is inside vacuum (Fig. 2c). Facing experimental difficulties (e.g. instabilities of the laser and RF systems) most recent measurement campaigns have not revealed any obvious streaking effects so far [8]. While new simulation studies investigate possible improvements of the system design [9], one other possible reason for the missing streaking observation might be an insufficient THz pulse energy reaching the resonator. Thus, in this contribution the THz transport and environment is studied to increase the resulting streaking strength of the SRR Compact-TDS.
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augmentation
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NO
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IPAC
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What was the observed bandwidth (FWHM) of the THz radiation?
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Approximately 9%
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Fact
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hermann-et-al-2022-inverse-designed-narrowband-thz-radiator-for-ultrarelativistic-electrons.pdf
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Figure 7 shows the THz pulse energy normalized to the first measurement value as well as the relative humidity over time when the filtration system was turned on. It can be noted that after only about 4 hours, the relative humidity in the volume could be decreased by roughly $10 \\%$ resulting in a THz pulse energy gain of about $5 \\%$ . After filtering for $2 4 \\mathrm { h }$ an increase in THz power of nearly $1 5 \\%$ could be observed. CONCLUSION AND OUTLOOK In conclusion, crucial improvements for the THz pulse energy could be realized, which is a critical parameter for achieving single-fs resolution in the SRR Compact-TDS diagnostics experiment at FLUTE. By changing the material and manufacturing UHMWPE THz lenses, as well as enclosing and dehumidifying the THz TPF setup environment, the overall transport loss of THz radiation could be reduced significantly. Based on our measurements, at the SRR interaction point a THz pulse energy of $1 8 8 \\% \\pm 4 0 \\%$ compared to the previous setup can be expected. This results in a factor of the order of two times the streaking strength, which will substantially facilitate the search for streaking in future experiments.
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augmentation
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NO
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IPAC
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What was the observed bandwidth (FWHM) of the THz radiation?
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Approximately 9%
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Fact
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hermann-et-al-2022-inverse-designed-narrowband-thz-radiator-for-ultrarelativistic-electrons.pdf
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File Name:OBSERVATION_OF_COHERENT_TERAHERTZ_BURSTS.pdf OBSERVATION OF COHERENT TERAHERTZ BURSTSDURING LOW-ENERGY OPERATION OF DELTA∗ C. Mai†, B. Büsing, S. Khan, A. Radha Krishnan, W. Salah1, Z. Usfoor,V. Vijayan, Center for Synchrotron Radiation (DELTA), TU Dortmund University, Germany 1on leave from Department of Physics, The Hashemite University, Zarqa, Jordan Abstract The electron storage ring DELTA, which is operated by TU Dortmund University, can be operated at a reduced beam energy down to $4 5 0 \\ \\mathrm { M e V }$ instead of $1 . 5 \\mathrm { \\ G e V . }$ If a single bunch at low energy is stored, the bunch charge threshold for the emission of THz bursts can be exceeded. Using a fast Schottky-barrier detector, coherent synchrotron radiation bursts of THz radiation were detected. Turn-by-turn data of the THz bursting behavior as function of the bunch charge and bursting spectrographs are presented. INTRODUCTION Coherently emitted THz radiation is routinely generated at the short-pulse facility of the $1 . 5 – \\mathrm { G e V }$ electron storage ring DELTA which is operated by the TU Dortmund University. Here, THz diagnostics is used to optimize the interaction of ultrashort laser pulses and a single electron bunch to generate VUV radiation by applying the coherent harmonic generation (CHG) [1] scheme and, more recently, the echoenabled harmonic generation (EEHG) [2, 3] scheme.
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augmentation
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NO
| 0
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IPAC
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What was the observed bandwidth (FWHM) of the THz radiation?
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Approximately 9%
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Fact
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hermann-et-al-2022-inverse-designed-narrowband-thz-radiator-for-ultrarelativistic-electrons.pdf
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BEAM TRANSPORT OPTIMIZATION In order to increase the THz pulse energy coupled into the resonator, the THz beam transport from crystal to the interaction point was improved. Terahertz Optics In the previous design of the TPF module, ZEONEX was chosen as THz lens material, because it exhibits high transmittance and a similar refraction index both in the THz and the visible spectral range. This permits an alignment of the THz beam using a visible alignment laser. However, for a $2 0 \\mathrm { m m }$ thick lens $( f = 7 5 \\mathrm { m m } )$ ) a transmittance of only $8 1 . 8 \\pm$ $1 . 4 \\%$ was measured using our TPF THz source, indicating an absorption coefficient of $\\approx 0 . 1 \\mathrm { c m } ^ { - 1 }$ (see Table 1). Table: Caption: Table 1: Comparison of ZEONEX and UHMWPE for THz optics. The absorption coefficient was derived by a transmittance measurement of $2 0 \\mathrm { m m }$ thick lenses. Body: <html><body><table><tr><td>Material</td><td>Refractive index</td><td>Abs.coeff. (cm-1)</td></tr><tr><td>ZEONEX</td><td>1.53 [10]</td><td>~ 0.1</td></tr><tr><td>UHMWPE</td><td>1.54 ± 0.01[11]</td><td>~ 0.04</td></tr></table></body></html> To increase the transmittance per THz lens we investigated UHMWPE (ultra-high-molecular-weight polyethylene) as an alternative material. Figure 4 shows a THz time-domain spectroscopic measurement [12] of a $1 0 \\mathrm { m m }$ thick planoparallel UHMWPE sample in the time domain and the resulting transmittance over frequency. Since the experiment was conducted in air, the transmission spectrum shows distinct absorption lines caused by water in the air, as well as a somewhat noisy signal for lower frequencies. Nevertheless, it can be confirmed that UHMWPE shows very little transmittance losses for the relevant frequency range of a
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augmentation
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NO
| 0
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IPAC
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What was the observed bandwidth (FWHM) of the THz radiation?
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Approximately 9%
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Fact
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hermann-et-al-2022-inverse-designed-narrowband-thz-radiator-for-ultrarelativistic-electrons.pdf
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NFTHZ has developed a narrow-band THz-FEL capable of tuning its radiation wavelength across a wide range. This instrument relies on a compact electron linear accelerator and utilizes laser pulse shaping technology to generate high-quality electron bunches. The pre-bunched ultrashort electron beam traverses the undulator in a single pass, resulting in the production of coherent spontaneous radiation [3]. Figure 1 illustrates the schematic diagram of the prebunched THz-FEL, while Table 1 provides details of the technical parameters. The online adjustment of the longitudinal spacing of the photocathode-driven laser pulse is facilitated through polarization splitting and combining. Finally, THz radiation with MW-level peak power and a wide-range adjustable central frequency is achieved through microwave phase control (energy adjustment) and matching of the undulator magnetic field intensity. Table: Caption: Table 1: Technical Parameters Body: <html><body><table><tr><td>Technical Parameters</td><td>Values</td></tr><tr><td>Frequency/Wavelength Range</td><td>0.5~5 THz/60~600 μm</td></tr><tr><td>Electron Energy</td><td>10~18MeV</td></tr><tr><td>Maximum Number of Micro Bunches</td><td>16</td></tr><tr><td>Adjustment Range Between Micro Bunches</td><td>0.33~2 ps</td></tr><tr><td>PeakPower ofFEL</td><td>0.1~7MW</td></tr><tr><td>FEL Frequency Range Based on Fundamental Frequency of The Micro Bunches</td><td>0.5~3 THz</td></tr><tr><td>FEL Frequency Range Based on Second Harmonic of The Micro Bunches</td><td>3~5 THz</td></tr></table></body></html> The adjustable range of the spacing of micro-bunches is constrained by certain factors. If the spacing is too long, the overall length of electron beams becomes excessive. Consequently, when accelerated by the microwave field, the intervals between the micro-bunches cease to remain uniform, leading to energy dispersion within the beam. Conversely, if the spacing is too short, the space charge force exerts an effect causing the microbunching structure to become blurred or even disappear [4].
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augmentation
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