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string | Question
string | Answer
string | Question_type
string | Referenced_file(s)
string | chunk_text
string | expert_annotation
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expert
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According to the beam requirements for a typical DLA, is an electron source with 5 mm emittance suitable?
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No, the aperture is sub-400nm
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reasoning
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Beam_Dynamics_in_Dielectric_Laser_Acceleration.pdf
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In fact, with a full control over amplitude and phase seen by the particles the question becomes how to best optimize the drive pulse. At this purpose, it is envisioned adopting machine learning algorithms to optimize the 2D mask which gets applied to the laser drive pulse by the liquid crystal modulator [48]. 5 DLA Undulator Similar to a conventional magnetic undulator, a DLA undulator needs to provide an oscillatory deflection force as well as transversal confinement to achieve stable beam transport and scalable radiation emission. On the long run, a DLA based radiation source would use beams provided by a DLA accelerator. However, closer perspectives to experiments favor using advanced RF accelerators which can also provide single digit femtosecond bunches at high brightness. The ARES accelerator [49] at SINBAD/DESY provides such beam parameters suitable to be injected into DLA undulators. Thus, we adapt our design study on the $1 0 7 \\mathrm { M e V }$ electron beam of ARES. 5.1 Tilted Grating Design Figure 10 shows one cell of a tilted DLA structure composed of two opposing silica $\\epsilon _ { \\mathrm { r } } = 2 . 0 6 8 1 \\$ ) diffraction gratings for the laser wavelength $\\lambda = 2 \\pi / k = 2 \\mu \\mathrm { m }$ . The laser excites a grating-periodic electromagnetic field with $k _ { \\mathrm { z } } = 2 \\pi / \\lambda _ { \\mathrm { g } }$ which imposes a deflection force [17] on the electrons. Our investigation considers two different concepts for the application of tilted DLA gratings as undulators. First, the concept introduced in refs. [17, 18] which uses a phase-synchronous DLA structure fulfilling the Wideroe condition Eq. (1.1) (see ref. [9] for an analysis of the dynamics therein). Second, a concept similar to microwave [50], terahertz [51] or laser [52] driven undulators which uses a non-synchronous DLA structure that does not fulfill Eq. (1.1).
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4
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Yes
| 1
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expert
|
According to the beam requirements for a typical DLA, is an electron source with 5 mm emittance suitable?
|
No, the aperture is sub-400nm
|
reasoning
|
Beam_Dynamics_in_Dielectric_Laser_Acceleration.pdf
|
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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4
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Yes
| 1
|
expert
|
According to the beam requirements for a typical DLA, is an electron source with 5 mm emittance suitable?
|
No, the aperture is sub-400nm
|
reasoning
|
Beam_Dynamics_in_Dielectric_Laser_Acceleration.pdf
|
4.2 Soft tuning of DLA parameters 11 5 DLA Undulator 13 5.1 Tilted Grating Design 13 5.2 Analytical Model for the Non-Synchronous Undulator 14 5.3 Simulation of the Beam Dynamics in Tilted Gratings 16 6 Conclusion 18 1 Introduction The combination of periodic dielectric structures and coherent light allows to reverse the Cherenkov effect and the Smith-Purcell effect [1] in order to attain acceleration of electrons. It was proposed already in 1962 [2, 3], shortly after the invention of the laser. The use of dielectric gratings in conjunction with laser light sources has been named Dielectric Laser Acceleration (DLA) after it became a viable approach to accelerate electrons with record gradients. These record gradients are enabled especially by modern ultrashort-pulsed laser systems, mostly in the infrared spectrum, and by nanofabrication techniques for the high damage threshold dielectric materials, as adopted from the semiconductor industry. Due to these high technical demands, the experimental demonstration of electron acceleration in DLA came only in 2013, more than 50 years later than the original proposal [4, 5]. These promising results of gradients, generating only energy spread so far, lead to the funding of the ACHIP collaboration [6], in order to achieve an accelerator attaining MeV energy gain. A summary of DLA research as it stood in 2014 is given in [7].
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1
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Yes
| 0
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expert
|
According to the beam requirements for a typical DLA, is an electron source with 5 mm emittance suitable?
|
No, the aperture is sub-400nm
|
reasoning
|
Beam_Dynamics_in_Dielectric_Laser_Acceleration.pdf
|
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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5
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Yes
| 1
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expert
|
According to the beam requirements for a typical DLA, is an electron source with 5 mm emittance suitable?
|
No, the aperture is sub-400nm
|
reasoning
|
Beam_Dynamics_in_Dielectric_Laser_Acceleration.pdf
|
$$ where $m _ { 0 } c ^ { 2 } / q = 5 1 1 \\mathrm { \\ k V }$ is the rest energy equivalent and $\\phi$ is the phase within one DLA cell. Analyzing the solutions of the equation for transverse motion into a slowly varying secular component and a fast oscillation, we can rewrite for the slow drift motion $$ { \\frac { \\partial y ^ { \\prime } } { \\partial z } } = { \\frac { q E _ { 0 } } { m _ { 0 } c ^ { 2 } } } { \\frac { k y } { \\gamma ^ { 3 } \\beta ^ { 2 } } } \\cos \\phi - \\left[ { \\frac { E _ { 1 } } { m _ { 0 } c ^ { 2 } } } { \\frac { k } { \\gamma \\beta } } ( 1 - \\beta \\beta _ { 1 } ) \\right] ^ { 2 } { \\frac { y } { 2 \\delta _ { k } ^ { 2 } } } $$ and noting that the coefficient second term is negative for all phases, retrieve the ponderomotive focusing effect [42]. The main drawback of the ponderomotive focusing scheme (compared to the APF scheme discussed above) is the significant need for power in the non-resonant harmonic $E _ { 1 }$ to compensate the strong resonant defocusing, so that the laser is not efficiently used to accelerate the particles (i.e. $E _ { 0 }$ is relatively small). Interestingly, in 2D APF focusing schemes the focusing term scales with the energy as $1 / \\gamma ^ { 3 }$ , here it scales as $1 / \\gamma ^ { 2 }$ and for the 3D APF scheme it scales as $1 / \\gamma$ [15], which eventually dominates over the resonant defocusing scaling as $1 / \\gamma ^ { 3 }$ . Thus, spatial harmonic focusing provides a matched (average) beta function proportional to the beam energy, perfectly compensating the adiabatic geometric emittance decrease to provide a constant spot size along the accelerator.
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1
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Yes
| 0
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expert
|
According to the beam requirements for a typical DLA, is an electron source with 5 mm emittance suitable?
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No, the aperture is sub-400nm
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reasoning
|
Beam_Dynamics_in_Dielectric_Laser_Acceleration.pdf
|
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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5
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Yes
| 1
|
expert
|
According to the beam requirements for a typical DLA, is an electron source with 5 mm emittance suitable?
|
No, the aperture is sub-400nm
|
reasoning
|
Beam_Dynamics_in_Dielectric_Laser_Acceleration.pdf
|
Key to the high gradients in DLA is the synchronization of optical near fields to relativistic electrons, expressed by the Wideroe condition $$ \\lambda _ { g } = m \\beta \\lambda $$ where $\\lambda _ { g }$ is the grating period, $\\lambda$ is the laser wavelength, and $\\beta = \\nu / c$ is the the electron velocity in units of the speed of light. The integer number $m$ represents the spatial harmonic number at which the acceleration takes place. The zeroth harmonic is excluded by means of the Lawson-Woodward theorem [7] as it represents just a plane wave; the first harmonic $( m = 1 )$ is most suitable for acceleration, as it usually has the highest amplitude. Phase synchronous acceleration (fulfilling Eq. 1.1) at the first harmonic can be characterized by the synchronous Fourier coefficient $$ e _ { 1 } ( x , y ) = \\frac { 1 } { \\lambda _ { g } } \\int _ { \\lambda _ { g } } E _ { z } ( x , y , z ) e ^ { 2 \\pi i z / \\lambda _ { g } } \\mathrm { d } z
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augmentation
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Yes
| 0
|
expert
|
According to the beam requirements for a typical DLA, is an electron source with 5 mm emittance suitable?
|
No, the aperture is sub-400nm
|
reasoning
|
Beam_Dynamics_in_Dielectric_Laser_Acceleration.pdf
|
$$ \\lambda _ { \\mathrm { { p } } } = \\frac { \\lambda _ { \\mathrm { { u } } } } { 2 { \\gamma _ { 0 } } ^ { 2 } } \\left( 1 + \\frac { { K _ { \\mathrm { { z } } } } ^ { 2 } } { 2 } \\right) \\approx 9 ~ \\mathrm { { n m } , } $$ 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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augmentation
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Yes
| 0
|
expert
|
According to the beam requirements for a typical DLA, is an electron source with 5 mm emittance suitable?
|
No, the aperture is sub-400nm
|
reasoning
|
Beam_Dynamics_in_Dielectric_Laser_Acceleration.pdf
|
4.2 Soft tuning of DLA parameters The original plan proposed to hard-wire spatial harmonics into the structure to obtain the ponderomotive focusing effect. In practice, one can also simply modulate the drive laser phase, effectively introducing spatial harmonics into a generic, strictly periodic grating, see Fig. 8. This is due to the low Q-factor of the structures used for DLA, so that the fields in the electron beam channel are actually faithful reproductions of the illuminating laser pulses. Therefore, dynamically controlling phase and amplitude of the drive laser actually offers an interesting alternative to soften the tight tolerance requirements on structure fabrication and enable tuning of the accelerator characteristics without the need to modify/manufacture delicate and expensive dielectric structures [43]. While it is likely that in the future phase and amplitude control of the drive pulses will be implemented using on-chip laser manipulation [44, 45], the first exploratory research can be carried out using free space coupling combining pulse front tilt illumination with modern technologies readily available for nearly arbitrary shaping of laser fields in the transverse plane. Pulse front tilt can be easily coupled with standard methods for spatial light manipulation such as digital micromirror devices or liquid crystal masks [46]. Exploiting the 2D nature of these devices, they can be used to apply not only arbitrary phase, but also arbitrary amplitude masks to the transverse profile of the laser which gets converted by the pulse front tilt illumination into temporal modulation seen by the electrons. As masks can be changed essentially online, at very high repetition rates (up to KHz), such system will allow to fine tune the DLA output beam parameters online, with direct guidance from beam diagnostics. In the experimental phase this will also allow testing of various beam dynamics control approaches, including alternate phase focusing, ponderomotive focusing or anything else in between. A new code has been developed to self-consistently calculate the interaction of relativistic particles with different phase velocities spatial harmonics [47] (see Fig. 9).
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augmentation
|
Yes
| 0
|
expert
|
According to the beam requirements for a typical DLA, is an electron source with 5 mm emittance suitable?
|
No, the aperture is sub-400nm
|
reasoning
|
Beam_Dynamics_in_Dielectric_Laser_Acceleration.pdf
|
$$ where $E _ { z }$ is the longitudinal component of the electric field at the laser center frequency in the channel. Often, $E _ { z }$ is normalized to the amplitude of the incident laser field. The transverse dependence of $\\boldsymbol { e } _ { 1 }$ allows also to calculate the the transverse kicks by means of the Panofsky-Wenzel theorem [8, 9]. The laser systems used in current experiments are mostly $8 0 0 \\mathrm { n m }$ Ti:Sapphire amplifiers providing femtosecond pulses; either directly or followed by an Optical Parametric Amplifier (OPA) to transform into longer infrared wavelengths. Other systems based on $1 0 0 0 \\mathrm { n m }$ sources are also available. Moreover, with modern Holmium / Thulium doped fiber systems, $2 \\mu \\mathrm { m }$ pulses can also be obtained directly. Generally, there is a quest for longer wavelength, as this eases the nanophotonic structure fabrication precision requirement. Working with ultrashort pulses in the femotsecond realm is paramount in DLA, in order obtain high electric fields at low pulse energy. The pulse energy divided by the transverse size defines the fluence, and the acceleration structure material choice is predominantly made by the counteracting figures of merit of high damage threshold fluence and high refractive index, both at given laser wavelength.
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augmentation
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Yes
| 0
|
expert
|
According to the beam requirements for a typical DLA, is an electron source with 5 mm emittance suitable?
|
No, the aperture is sub-400nm
|
reasoning
|
Beam_Dynamics_in_Dielectric_Laser_Acceleration.pdf
|
$$ The first term recovers the tracking equation of DLATrack6D (see ref. [9]). The correction terms contribute less than $1 \\%$ for the investigated structures. Figure 14 a) compares tracking results for the particle at the beam center of a synchronous and a non-synchronous DLA undulator. In the synchronous undulator the phase jumps by $\\Delta \\varphi _ { 0 } = \\pi$ due to a $\\lambda _ { g } / 2$ drift section after each ${ \\lambda _ { \\mathrm { u } } } / { 2 }$ such that deflection force acting on the particle always switches between its maximum and minimum value. Hence, the reference particle’s momentum $x ^ { \\prime }$ changes linearly between two segments. The subsequent triangular trajectory introduces contributions of higher harmonics into the radiation. Furthermore, the accumulation of deflections leads to a deviation from the reference trajectory for $z \\ge 1 0 \\mathrm { m m }$ and the accumulated extra distance travelled by the reference particle leads to dephasing, which damps the momentum oscillation. In the non-synchronous DLA undulator the particle trajectory follows a harmonic motion. A smooth phase shift of $\\Delta \\varphi _ { \\mathrm { 0 } } = 2 \\pi \\lambda _ { \\mathrm { z } } / \\lambda _ { \\mathrm { u } }$ per DLA cell generates a harmonically oscillating deflection which is approximately $30 \\%$ smaller compared to the synchronous DLA. A tapering of the deflection strength introduced towards $z = 0$ and $z = 1 6 . 4 \\mathrm { m m }$ ensures a smooth transition at the ends of the non-synchronous DLA undulator.
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augmentation
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Yes
| 0
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expert
|
According to the beam requirements for a typical DLA, is an electron source with 5 mm emittance suitable?
|
No, the aperture is sub-400nm
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reasoning
|
Beam_Dynamics_in_Dielectric_Laser_Acceleration.pdf
|
k _ { x } ^ { 2 } + k _ { y } ^ { 2 } = - \\frac { \\omega ^ { 2 } } { \\beta ^ { 2 } \\gamma ^ { 2 } c ^ { 2 } } , $$ where $\\omega = 2 \\pi c / \\lambda$ is the laser angular frequency and $\\beta , \\gamma$ are the relativistic velocity and mass factors. Note that the longitudinal field Eq. 3.1 suffices to describe the entire threedimensional kick on a particle in the DLA cell, since the transverse kick can be calculated by the Panofsky-Wenzel theorem [9]. The horizontal propagation constant $k _ { y }$ is always purely imaginary, that is an inherent consequence of DLA being a nearfield acceleration scheme. The vertical propagation constant $k _ { x }$ can however be either purely imaginary or purely real. If $k _ { x }$ is purely imaginary (as $k _ { y }$ ), we call the focusing scheme ’in-phase’, since both transverse directions are simultaneously focused, while the longitudinal direction is defocused, and vice versa. Oppositely, if $k _ { x }$ is real valued, the vertical direction $\\mathbf { \\tau } ( \\mathbf { x } )$ focuses simultaneously with the longitudinal direction, exactly when the horizontal direction (y) is defocusing and vice versa; the scheme is thus called ’counter-phase’.
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augmentation
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Yes
| 0
|
expert
|
According to the beam requirements for a typical DLA, is an electron source with 5 mm emittance suitable?
|
No, the aperture is sub-400nm
|
reasoning
|
Beam_Dynamics_in_Dielectric_Laser_Acceleration.pdf
|
$$ \\\\mathbf { a } \\\\left( x , y , z , c t \\\\right) = a _ { \\\\mathrm { z } } \\\\cosh \\\\left( k _ { \\\\mathrm { y } } y \\\\right) \\\\sin \\\\left( k c t - k _ { \\\\mathrm { z } } z + k _ { \\\\mathrm { x } } x \\\\right) \\\\mathbf { e } _ { \\\\mathrm { z } } $$ with the reciprocal grating vectors of the tilted DLA cell $k _ { \\\\mathrm { z } }$ and $k _ { \\\\mathrm { x } } ~ = ~ k _ { \\\\mathrm { z } } \\\\tan \\\\alpha$ (see ref. [9]), ${ k _ { \\\\mathrm { y } } } \\\\equiv \\\\sqrt { \\\\left| { k ^ { 2 } - { k _ { \\\\mathrm { x } } } ^ { 2 } - { k _ { \\\\mathrm { z } } } ^ { 2 } } \\\\right| } ,$ , and the dimensionless amplitude defined as $$ { a } _ { \\\\mathrm { z } } \\\\equiv \\\\frac { q \\\\left| \\\\boldsymbol { e } _ { 1 } \\\\left( \\\\alpha \\\\right) \\\\right| / k } { m _ { 0 } c ^ { 2 } } \\\\mathrm { ~ . ~ }
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augmentation
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Yes
| 0
|
expert
|
According to the beam requirements for a typical DLA, is an electron source with 5 mm emittance suitable?
|
No, the aperture is sub-400nm
|
reasoning
|
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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augmentation
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Yes
| 0
|
expert
|
According to the beam requirements for a typical DLA, is an electron source with 5 mm emittance suitable?
|
No, the aperture is sub-400nm
|
reasoning
|
Beam_Dynamics_in_Dielectric_Laser_Acceleration.pdf
|
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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augmentation
|
Yes
| 0
|
expert
|
According to the beam requirements for a typical DLA, is an electron source with 5 mm emittance suitable?
|
No, the aperture is sub-400nm
|
reasoning
|
Beam_Dynamics_in_Dielectric_Laser_Acceleration.pdf
|
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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augmentation
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Yes
| 0
|
expert
|
According to the beam requirements for a typical DLA, is an electron source with 5 mm emittance suitable?
|
No, the aperture is sub-400nm
|
reasoning
|
Beam_Dynamics_in_Dielectric_Laser_Acceleration.pdf
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Logan Su, Rahul Trivedi, Yu Miao, Olav Solgaard, Robert L Byer, and Jelena Vuckovic. On-chip integrated laser-driven particle accelerator. Science, 367(January):79–83, 2020. [46] D. Cesar, J. Maxson, P. Musumeci, X. Shen, R. J. England, and K. P. Wootton. Optical design for increased interaction length in a high gradient dielectric laser accelerator. Nuclear Instruments and Methods in Physics Research, Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 909(January):252–256, 2018. [47] A. Ody, S. Crisp, P. Musumeci, D. Cesar, and R. J. England. SHarD: A beam dynamics simulation code for dielectric laser accelerators based on spatial harmonic field expansion. Nuclear Instruments and Methods in Physics Research, Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 1013(April):165635, 2021. ISSN 01689002. doi: 10.1016/j.nima.2021.165635. URL https://doi.org/10.1016/j.nima.2021.165635. [48] Auralee Edelen, Nicole Neveu, Matthias Frey, Yannick Huber, Christopher Mayes, and Andreas Adelmann. Machine learning for orders of magnitude speedup in multiobjective optimization of particle accelerator systems. Physical Review Accelerators and Beams, 23(4):44601, 2020. ISSN 24699888. doi: 10.1103/PhysRevAccelBeams.23.044601. URL https://doi.org/10.1103/PhysRevAccelBeams.23.044601. [49] Huseyin Cankaya, Frank Mayet, Willi Kuropka, Christoph Mahnke, Caterina Vidoli, Luca Genovese, Francois Lemery, Florian Burkart, Sebastian Schulz, Thorsten Lamb, Mikheil Titberidze, Jost Müller, Ralph Aßmann, Ingmar Hartl, and Franz X. Kärtner. Temporal and spatial challenges for electron acceleration inside dielectric laser accelerators in the relativistic regime. Optics InfoBase Conference Papers, 1, 2021. doi: 10.1364/cleo $\\{ \\backslash _ { - } \\}$ si.2021.sth1c.1.
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augmentation
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Yes
| 0
|
expert
|
According to the beam requirements for a typical DLA, is an electron source with 5 mm emittance suitable?
|
No, the aperture is sub-400nm
|
reasoning
|
Beam_Dynamics_in_Dielectric_Laser_Acceleration.pdf
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$$ K _ { \\mathrm { z } } = a _ { \\mathrm { z } } { \\frac { k _ { \\mathrm { x } } } { k _ { \\mathrm { u } } } } = { \\frac { q } { m _ { 0 } c ^ { 2 } } } { \\frac { k _ { \\mathrm { z } } } { k k _ { \\mathrm { u } } } } \\left| e _ { 1 } \\left( \\alpha \\right) \\right| \\tan \\alpha \\ . $$ Figure $1 3 \\mathrm { a }$ ) shows the dependency of the undulator parameter $K _ { \\mathrm { z } }$ on the grating tilt angle $\\alpha$ and the undulator wavelength $\\lambda _ { \\mathrm { u } }$ in a vertically symmetric opposing silica grating structure. For this purpose the synchronous harmonic $\\boldsymbol { e } _ { 1 }$ at the center of the structure was determined as function of the tilt angle. The undulator parameter $K _ { \\mathrm { z } }$ shows a local maximum at an tilt angle of $\\alpha \\approx 2 5$ degrees. Furthermore, $K _ { \\mathrm { z } }$ increases linearly with the undulator wavelength $\\lambda _ { \\mathrm { u } }$ . We investigate a design using $\\lambda _ { \\mathrm { u } } = 4 0 0 \\lambda _ { \\mathrm { z } }$ which corresponds to an effective undulator parameter of $K _ { \\mathrm { z } } \\approx 0 . 0 4 5$ . In Fig. 13 b) the detuning with respect to the synchronous operation $k - \\beta k _ { \\mathrm { z } }$ determines the transversal oscillation amplitude $\\hat { x }$ and the energy of the generated photons $E _ { \\mathrm { p } }$ . For $0 . 2 5 \\%$ deviation from synchronicity, the silica DLA undulator induces a $\\hat { x } \\approx 3 0 \\mathrm { n m }$ electron beam oscillation and a wavelength of [55]
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augmentation
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Yes
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expert
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According to the beam requirements for a typical DLA, is an electron source with 5 mm emittance suitable?
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No, the aperture is sub-400nm
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reasoning
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Beam_Dynamics_in_Dielectric_Laser_Acceleration.pdf
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Different types of DLA structures (single cells) are described in Fig. 2 for low energy (subrelativistic) and in Fig. 6 for high energy (relativistic). The usual materials are silicon or fused silica $( \\\\mathrm { S i O } _ { 2 } )$ , which can be nanofabricated by established techniques from the semiconductor industry. The vertical confinement problem can be solved by using a two-material wafer with high refractive index contrast as shown in Fig. 2 (e). This gives rise to the threedimensional APF for DLA scheme [15] which finally makes DLA fully length scalable. From Maxwell’s equations and the phase synchronicity condition Eq. 1.1 one can derive the synchronous longitudinal field as $$ e _ { 1 } ( x , y ) = e _ { 1 0 } \\\\cosh ( i k _ { x } x ) \\\\cosh ( i k _ { y } y ) , $$ where $e _ { 1 0 }$ is usually referred to as the structure constant. It needs to be determined for each structure individually (by numerical techniques) and takes values between 0.05 and 1.2 in practical cases. The propagation constants fulfill the dispersion relation $$
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augmentation
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Yes
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expert
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According to the beam requirements for a typical DLA, is an electron source with 5 mm emittance suitable?
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No, the aperture is sub-400nm
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reasoning
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Beam_Dynamics_in_Dielectric_Laser_Acceleration.pdf
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6 Conclusion For the study of beam dynamics in DLA, computer simulations will remain essential. With combined numerical and experimental approaches, the challenges of higher initial brightness and brightness preservation along the beamline can be tackled. The electron sources available from electron microscopy technology are feasible for experiments, however cost and size puts a major constraint on them. The upcoming immersion lens nanotip sources offer a suitable alternative. Their performance does not reach the one of the commercial microscopes yet, but one can expect significant improvements in the near future. This will enable low energy DLA experiments with high energy gain and full six-dimensional confinement soon. Full confinement is a requirement for high energy gain at low injection energies, since the low energy electrons are highly dynamical. Recent APF DLA experiments showed that (as theoretically expected) the so-called invariant dimension is in fact not invariant for the mostly used silicon pillar structures. The consequences are energy spread and emittance increase, eventually leading to beam losses. A way to overcome this is to turn towards a 3D APF scheme, which can be implemented on commercial SOI wafers. The 3D scheme has also advantages at high energy, since it avoids the focusing constants going to zero in the ultrarelativistic limit. Only the square-sum goes to zero and thus a counterphase scheme is possible with high individual focusing constants. Using a single high damage threshold material for these structures leads however to fabrication challenges.
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augmentation
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Yes
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Expert
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At what signal voltage is the gas detector pulse energy signal no longer in the linear range?
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If the peak of the signal is higher than about 0.8 Volts.
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Fact
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[FELFastPulseEnergy]_JSR_30(2023).pdf
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Another component of the gas detector system developed by DESY and used at various facilities, including SwissFEL, is the huge aperture open multiplier (HAMP), which is a large multiplier used for single-shot relative flux measurements that are not an absolute evaluation of the pulse energy. The response of this device to the ions generated from the photoionization depends on the potential that they are operated under, and the energy and charge of the photoionized ions that are impacting the HAMP surface. Furthermore, this response changes with time, as the multiplier coating slowly depletes over years of use. It is theoretically possible to evaluate the absolute single-shot pulse energy from the HAMP measurements if one can characterize the multiplier for every gas type and pressure, photon energy and voltage setting, year after year. Furthermore, the multiplier itself must be set with a voltage that has the signal generated by the ion impact to be in the linear regime. A constant monitoring of the signal amplitude must be implemented that feeds back on the multiplier voltage to ensure the operation of this device in a reliable manner. It was developed to deal with hard X-rays and lower fluxes which are encountered at most hard $\\mathbf { X }$ -ray FEL facilities.
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2
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Yes
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Expert
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At what signal voltage is the gas detector pulse energy signal no longer in the linear range?
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If the peak of the signal is higher than about 0.8 Volts.
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Fact
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[FELFastPulseEnergy]_JSR_30(2023).pdf
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The HAMPs, in contrast, need characterization to evaluate their range of linearity under an applied gain voltage. This voltage needs to be regulated through an overwatch program so that the HAMP detector signals remain linear, while also being high enough to provide a good signal-to-noise ratio on its analog-to-digital converter (ADC). An example of the ion signal on the ADC from the HAMP is presented by Sorokin et al. (2019). Since the response of the HAMP multiplier also changes with the photon energy, pulse energy and gas type, the most appropriate metric to observe in order to ensure linearity is the signal from the HAMP itself, or its maximum absolute peak height. The commissioning of the HAMP at SwissFEL used the fact that we have two such devices, one oriented along the vertical axis and another along the horizontal axis, and kept the settings of the horizontal (HAMP-X) constant and in the linear range, and changed the gain voltage on the vertical (HAMP-Y) to observe which peak heights are in the linear range. Further consultations with the team at DESY who built the devices concluded that the detector is linear between the maximum peak voltage of $1 \\mathrm { m V }$ and $1 0 \\mathrm { m V }$ , which translates to $1 0 \\mathrm { m V }$ and $1 0 0 \\mathrm { m V }$ on the ADC due to a $2 0 \\mathrm { d B }$ pre-amplifier between the HAMP and the 16-bit Ioxos ADC card used at the Aramis branch of SwissFEL. As shown in Fig. 1, the linear response also extends beyond this range and only begins to be non-linear once the peak value of the signal reaches around $0 . 9 \\mathrm { V } .$ . The ADC maximum input voltage restricts the maximum signal strength to $1 \\mathrm { V }$ resulting in the flat line once this value is reached.
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5
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Yes
| 1
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Expert
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At what signal voltage is the gas detector pulse energy signal no longer in the linear range?
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If the peak of the signal is higher than about 0.8 Volts.
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Fact
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[FELFastPulseEnergy]_JSR_30(2023).pdf
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File Name:[FELFastPulseEnergy]_JSR_30(2023).pdf Online absolute calibration of fast FEL pulse energy measurements Received 29 November 2022 Accepted 7 February 2023 Edited by Y. Amemiya, University of Tokyo, Japan Keywords: free-electron lasers; FELs; shot-to-shot absolute flux measurements. Pavle Juranic´,\\* Arturo Alarcon and Rasmus Ischebeck Paul Scherrer Institut, Forschungsstrasse 111, Villigen 5232, Switzerland. \\*Correspondence e-mail: [email protected] One of the challenges facing modern free-electron laser (FEL) facilities is the accurate pulse-to-pulse online measurement of the absolute flux of the X-ray pulses, for use by both machine operators for optimization and users of the photon beam to better understand their data. This manuscript presents a methodology that combines existing slow-measurement methods currently used in gas detectors across the world and fast uncalibrated signals from multipliers, meant for relative flux pulse-to-pulse measurements, which create a shot-to-shot absolute flux measurement through the use of sensor-based conditional triggers and algorithms at SwissFEL. 1. Introduction The need for an absolute online measurement of photon flux at $\\mathrm { \\Delta X }$ -ray free-electron lasers (FELs) has been apparent since the inception of these new large-scale devices. The photon pulse energy is one of the main measures of the effectiveness of the FEL setup, and is used for, among other things, gain curve measurements of the undulators, sorting of data to find non-linear effects in experiments and judging the effectiveness of different machine setups. This measurement of the pulse energy has been pioneered by the diagnostics group at the Free Electron Laser in Hamburg (FLASH) at the Deutsches Elektronen Synchrotron (DESY) and the X-ray gas monitor detector (XGMD) developed there (Sorokin et al., 2019). Use of this technology as an online measurement has spread to other FELs, with similar devices now existing at facilities such as LCLS, SACLA, FERMI, European XFEL and SwissFEL (Sorokin et al., 2019; Tiedtke et al., 2014; Zangrando et al., 2009; Gru¨ nert et al., 2019; Owada et al., 2018; Tono et al., 2013). The accuracy of the XGMD system has been confirmed several times at various facilities with measurements against a radiative bolometer using both soft and hard X-rays (Tiedtke et al., 2014; Kato et al., 2012; Juranic et al., 2019). The XGMD mainly measures the flux on a long time scale, evaluating the total current on a copper plate from the ions that have been photoionized and then drawn to the plate by a strong electric field. The hardware and robustness of the device ensures the accuracy of the measurement, but it delivers data on a long time scale, typically giving an average current in roughly 10 to $3 0 { \\mathrm { ~ s . } }$ The XGMD has the option to measure the electron current on the plates opposite the ions and extract a shot-toshot evaluation that can be calibrated to the pulse energy, but this feature requires a very high photon flux or a large crosssection for sufficient signal, with the latter available only for soft X-rays. The XGMD is an excellent tool to evaluate the average pulse energy, but it cannot provide a single-shot evaluation of the pulse energy for hard $\\mathbf { X }$ -rays and low fluxes.
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4
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Yes
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Expert
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At what signal voltage is the gas detector pulse energy signal no longer in the linear range?
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If the peak of the signal is higher than about 0.8 Volts.
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Fact
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[FELFastPulseEnergy]_JSR_30(2023).pdf
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If the repetition rate of the FEL changes, the rolling buffer size is recalculated to accommodate the larger number of points in the chosen time period, and the buffer itself is reset. However, the constant $C$ remains unchanged unless the photon energy or the HAMP gain voltage change. The data buffer and single-shot pulse energy evaluation process is restarted when the FEL changes its photon energy or the HAMP gain voltage changes by more than $1 0 \\mathrm { V } ,$ , since both of these alter the ratio between the XGMD and HAMP readings. Once the rolling buffer is full, an algorithm checks the data within the rolling buffer and checks whether the data are within the stability criteria set to evaluate the ratio. In the case of SwissFEL, these stability criteria are based on the HAMP and XGMD data, with the most commonly used stability criteria being that the XGMD readings should have a peak-to-peak variance of less than $5 \\%$ of the average pulse energy over the length of the rolling buffer. These criteria ensure that the conversion constant between the XGMD and HAMP readings is taken when the beam is in a stable mode, and gives an accurate evaluation of the conversion constant $C$ . If the beam is not on, the rolling buffer is not full, or the beam stability is not within the set parameters, $C$ is not updated, and the constant that existed up to that point is used. As long as the HAMP voltage or the photon energy does not change, $C$ is constant for the calculations, as the HAMP response relative to the XGMD signal does not change. If there is no constant, no fast absolute pulse energy is displayed until the constant can be evaluated. If the beam is on, the rolling buffer is full and the beam is within the stability criteria, the calibration constant $C$ updates with every pulse according to the process described above. The flowchart in Fig. 2 illustrates the dataprocessing flow.
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2
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Yes
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Expert
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At what signal voltage is the gas detector pulse energy signal no longer in the linear range?
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If the peak of the signal is higher than about 0.8 Volts.
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Fact
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[FELFastPulseEnergy]_JSR_30(2023).pdf
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The method and algorithm described here have been shown to work at SwissFEL with its repetition rate of up to $1 0 0 \\mathrm { H z }$ . The optimization of the algorithm to process the data has been shown to be $1 0 0 \\%$ reliable even at the maximum $1 0 0 \\mathrm { H z }$ repetition rate, has no skipped points and matches perfectly with other beam-synchronous measurements. Other facilities with larger repetition rates may have more difficulty in finding the time necessary between the pulses to execute full evaluations to provide a real-time single-shot pulse energy measurement. However, the algorithm can also be used to assign pulse energies to data after the fact, though some of the features such as fast online optimization and quick gain curve acquisition would be lost. 4. Conclusions The development of the absolute fast pulse energy measurement is a step forward in creating a system that can be more responsive to lasing efficiency and fluctuations. Most gasbased pulse energy detectors currently offer a choice between a fast uncalibrated signal or a slow calibrated signal to investigate and optimize machine performance, both of which have downsides. A slow calibrated signal leads to a slow correction response, whereas a fast uncalibrated signal only works while the pulse energy or photon energy are within parameters that enable full functionality of the fast signals, like the HAMPs. The absolute fast pulse energy measurement ensures a fast response to both large and small changes, and would be significantly faster than the slow calibrated signal.
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4
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Yes
| 1
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Expert
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At what signal voltage is the gas detector pulse energy signal no longer in the linear range?
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If the peak of the signal is higher than about 0.8 Volts.
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Fact
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[FELFastPulseEnergy]_JSR_30(2023).pdf
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This manuscript describes the developments in hardware characterization, feedback and monitoring programs, and processing algorithms that allow the photon pulse energy monitor (PBIG) at SwissFEL to deliver absolute pulse energy evaluations on a shot-to-shot basis (Juranic´ et al., 2018). The PBIG is the renamed DESY-developed and constructed pulse energy monitor, and the methods proposed here can be adapted to any similar device at FELs around the world. 2. Measurement setup 2.1. Detector reliability The precursor to effective data processing and evaluation of pulse-resolved pulse energy is the reliability of the input data for this evaluation. The XGMD slow absolute energy measurement must be calibrated against another device, and the fast HAMP measurement has to be operating so it can react linearly to the incoming pulse energies, and hence the data collected for eventual algorithmic processing are not dominated by noise or empty measurements. The XMGD average pulse energy measurements are linear and were calibrated in previous work (Juranic et al., 2019). The copper plate from which the current is measured by a Keithley 6514 calibrated multimeter has a quantum efficiency of 1, and the multimeter has a linear measurement range for current measurements that spans more than ten orders of magnitude. This device provides the calibrated long-scale average signal that will be used to evaluate the shot-to-shot pulse energy from the HAMPs.
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augmentation
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Yes
| 0
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Expert
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At what signal voltage is the gas detector pulse energy signal no longer in the linear range?
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If the peak of the signal is higher than about 0.8 Volts.
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Fact
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[FELFastPulseEnergy]_JSR_30(2023).pdf
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2.2. Algorithm for data-processing The core of the data processing and evaluation of the absolute pulse energy on a shot-to-shot basis is the evaluation of the ratio between the slow signals and the fast signals. The slow absolute evaluation from the XGMD has an integration time of about $1 0 { \\mathrm { ~ s } } .$ , updated every second as the Keithley multimeter updates its readout. The fast signal reads out the relative pulse energy from the integral of the ion peaks at the repetition rate of SwissFEL, up to $1 0 0 \\mathrm { H z }$ . To be able to compare these two evaluations with each other directly on a pulse-by-pulse basis, we first create a rolling buffer of pulseresolved measurements that is as long as or longer than the XGMD evaluation integration time. The rolling buffer always maintains the same number of elements, adding a new element with each new processed FEL pulse, while dropping the oldest element in the buffer. The rolling buffer is updated at the repetition rate of the FEL, and is used to continuously evaluate the conversion constant $C _ { i }$ so that $$ C _ { i } \\ = \\ I _ { \\mathrm { X G M D } } / I _ { \\mathrm { H A M P } } ,
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augmentation
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Yes
| 0
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Expert
|
At what signal voltage is the gas detector pulse energy signal no longer in the linear range?
|
If the peak of the signal is higher than about 0.8 Volts.
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Fact
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[FELFastPulseEnergy]_JSR_30(2023).pdf
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$$ where $I _ { \\mathrm { X G M D } }$ and ${ \\cal I } _ { \\mathrm { H A M P } }$ are the evaluations of the XGMD and HAMP signal data in the buffer, respectively. This constant is then used in further evaluations. A weighted average algorithm is used to evaluate the current conversion constant so that $$ C = W C _ { i } + \\left( 1 - W \\right) C _ { i - 1 } , $$ where $W$ is the weighting factor, equal to the period of the FEL divided by the chosen buffer length time constant, and $C _ { i - 1 }$ is the previous conversion constant. A 10 s time constant and $1 0 0 \\mathrm { H z }$ repetition rate would yield a weighting factor of 0.001. The role of this weighting factor and the data buffer is to ensure that the conversion constant between the XGMD and HAMP readouts is not affected by single-shot losses of pulse energies and remains stable unless the relationship between the two devices is altered due to a change in photon energy or multiplier voltage gain. The FEL radiation can vary significantly on a shot-to-shot basis owing to the stochastic nature of the self-amplified spontaneous emission (SASE), so such a large buffer is necessary to establish a suitable conversion constant between the two devices. The last step of the data processing is to evaluate the single pulse energy, which is equal to C IHAMP .
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augmentation
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Yes
| 0
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Expert
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At what signal voltage is the gas detector pulse energy signal no longer in the linear range?
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If the peak of the signal is higher than about 0.8 Volts.
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Fact
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[FELFastPulseEnergy]_JSR_30(2023).pdf
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3. Results and discussion The resulting evaluation of the absolute single-shot pulse energy matches both the absolute numbers measured by the XGMDs, and shows the shot-to-shot fluctuations of their amplitudes, as seen in Fig. 3. The fast measurement comparison was made under conditions that kept the HAMP gain voltage constant, at a constant photon energy. The ratio between the two HAMPs comes from the different detector responses. The signal yields vary between different HAMPs due to the artisanal quality of their manufacturing and coating procedure, in this case by about $3 0 \\%$ . The standard deviation from the mean ratio of the signals from HAMP-Y versus HAMP-X was about $1 . 4 \\%$ , which is also the relative measurement accuracy of the single-shot measurement. Additionally, the fast algorithm can react quickly to sudden drops in pulse energy, showing the sudden stop and return to lasing almost instantaneously, while the slow signal takes significant time to ramp back up, as shown in Fig. 4. This allows users who need to stop and restart their measurements to resume reliable data collection more quickly, and the operators can immediately see how well the FEL is lasing after some kind of a temporary failure, without waiting for up to $3 0 { \\mathrm { ~ s . } }$ The fast signal can also be employed for faster acquisitions of gain curve scans of the undulators (Milton et al., 2001) and quicker optimization algorithms for machine performance owing to a faster monitoring parameter as the main input (Kirschner et al., 2022).
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augmentation
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Yes
| 0
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Expert
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At what signal voltage is the gas detector pulse energy signal no longer in the linear range?
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If the peak of the signal is higher than about 0.8 Volts.
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Fact
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[FELFastPulseEnergy]_JSR_30(2023).pdf
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Though the setup described is fast, an even better setup would be one where the evaluation of the pulse energy would depend completely on values measured from the HAMPs, their gain voltage and a photon energy. This is theoretically possible, but would require a long-term project to gather sufficient data to correlate these parameters to the absolutely measured pulse energy on a shot-to-shot basis, and a setup that ensures every data point measured is valid. The scheme described in this manuscript creates such a system. The data gathered by the fast pulse energy measurement are currently evaluated using a comparison against the slow pulse energy measurement. However, with enough time and data points, one could use this data to create a machinelearning algorithm that would enable the evaluation of the pulse energy directly, without having to compare the HAMP values with the slow calibrated XGMD signals. In that respect, the effort described here is the first step to eventually create a wholly calibrated fast pulse energy measurement for all possible beam parameters. Acknowledgements The authors would like to thank Florian Lo¨ hl, Nicole Hiller and Sven Reiche for fruitful discussions about the imple mentation and execution of the fast pulse energy measurement, as well as Antonios Foskolos and Mariia Zykova for their help with the measurements.
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augmentation
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Yes
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expert
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Describe the SHINE dechirper
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Flat, corrugated, metallic plates separated by an adjustable gap
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Summary
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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] $$ \\begin{array} { c } { { f _ { \\mathrm { { q } } } ^ { - 1 } ( s ) = k _ { \\mathrm { { q } } } ^ { 2 } ( s ) L = \ \\frac { \\pi ^ { 3 } } { 2 5 6 a ^ { 4 } } Z _ { 0 } c \\left( \ \\frac { e Q L } { E l } \\right) s ^ { 2 } , } } \\\\ { { f _ { \\mathrm { { d } } } ^ { - 1 } ( s ) = k _ { \\mathrm { { d } } } ^ { 2 } ( s ) L = \ \\frac { \\pi ^ { 3 } } { 1 2 8 a ^ { 4 } } Z _ { 0 } c \\left( \ \\frac { e Q L } { E l } \\right) s ^ { 2 } . } } \\end{array}
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1
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Yes
| 0
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expert
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Describe the SHINE dechirper
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Flat, corrugated, metallic plates separated by an adjustable gap
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Summary
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Beam_performance_of_the_SHINE_dechirper.pdf
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The $\\beta$ functions for both models are plotted in Fig. 9. In [28], the emittance growth caused by the quadrupole wakefield is fully compensated only if $\\beta _ { x } = \\beta _ { y }$ . In practice, however, the beta functions always fluctuate, and the beam suffers from the residual quadrupole wakefield. For a period FODO cell, the difference between the maximum and minimum $\\beta$ values is given by Eq. (18) [29], where $K$ and $L$ denote the quadrupole strength and length separately, and $l$ the length for each separated dechirper (5 and $2 . 5 \\mathrm { ~ m ~ }$ for the two- and four-dechirpers, respectively). $$ \\beta _ { \\mathrm { m a x } } - \\beta _ { \\mathrm { m i n } } = { 4 l } / { \\sqrt { 6 4 - K ^ { 2 } L ^ { 2 } l ^ { 2 } } } . $$ Figure 11 compares the $\\beta$ functions for two- and fourdechirpers by scanning the magnet strength $K$ and the magnet length $L$ . The minimum differences are $2 . 5 0 \\mathrm { ~ m ~ }$ and 1.25 for the two- and four-dechirpers, respectively. This implies a better compensation of the quadrupole wakefieldinduced emittance growth in the four-dechirper schemes. In practical engineering applications, four-dechirpers are considered appropriate to simplify the system.
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1
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Yes
| 0
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expert
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Describe the SHINE dechirper
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Flat, corrugated, metallic plates separated by an adjustable gap
|
Summary
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Beam_performance_of_the_SHINE_dechirper.pdf
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$$ 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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1
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Yes
| 0
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expert
|
Describe the SHINE dechirper
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Flat, corrugated, metallic plates separated by an adjustable gap
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Summary
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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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1
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Yes
| 0
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expert
|
Describe the SHINE dechirper
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Flat, corrugated, metallic plates separated by an adjustable gap
|
Summary
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Beam_performance_of_the_SHINE_dechirper.pdf
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The effect of a high group velocity in the radiation pulse also merits discussion. At the end of the structure length, the pulse length can be expressed [1] as $l _ { \\mathrm { p } } = 2 h t L / a p$ . For the structural parameters of SHINE, we have $l _ { \\mathrm { p } } = 5 \\mathrm { m }$ which is much longer than the actual bunch length of the particle. This effect does not have to be taken. During RF acceleration and beam transportation, the electron beam traveling from the VHF gun to the linac is affected by several beam-dynamic processes. These include the space-charge effect in the injector, the wakefield effect from SC structures, coherent synchrotron radiation (CSR) and non-linear effects during bunch compression [23]. Non-linearities in both the accelerating fields and the longitudinal dispersion can distort the longitudinal phase space. The typical final double-horn current distribution after the SHINE linac is shown in Fig. 4. The particles are concentrated within the first $2 0 ~ { \\mu \\mathrm { m } }$ with a linear energy spread. The wakefield for the actual simulated bunch distribution is shown in Fig. 5. Compared with the Gaussian and rectangular bunch distributions, as the head-tail wakefield effect of the beam, the double-horn bunch distribution distorts the expected chirp from the Gaussian bunch. The high peak current at the head of the beam complicates the situation further. The maximal chirp generated at different positions is also related to the feature in the bunch distribution. The particles in the double-horn bunch descend steeply over $1 5 ~ { \\mu \\mathrm { m } }$ , but the particles in the Gaussian and rectangular bunches hold a gender distribution. Nevertheless, the chirp induced by the double-horn beam distribution in less than $5 \\%$ differences in the maximal chirp and shows great correspondence on the tail. This proves that the analytical method is also perfectly suitable for the actual bunch in SHINE.
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1
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Yes
| 0
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expert
|
Describe the SHINE dechirper
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Flat, corrugated, metallic plates separated by an adjustable gap
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Summary
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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] $$ \\begin{array} { r l } & { w _ { y \\mathrm { d } } \\approx \\displaystyle \\frac { Z _ { 0 } \\mathrm { c } \\pi ^ { 3 } } { 6 4 a ^ { 4 } } { \\mathit { s } } _ { 0 \\mathrm { d } } \\bigg [ 1 - \\big ( 1 + \\sqrt { { s } / { s } _ { 0 \\mathrm { d } } } \\big ) e ^ { \\sqrt { { s } / { s } _ { 0 \\mathrm { d } } } } \\bigg ] , } \\\\ & { w _ { y \\mathrm { q } } \\approx \\displaystyle \\frac { Z _ { 0 } \\mathrm { c } \\pi ^ { 3 } } { 6 4 a ^ { 4 } } { \\mathit { s } } _ { 0 \\mathrm { q } } \\bigg [ 1 - \\big ( 1 + \\sqrt { { s } / { s } _ { 0 \\mathrm { q } } } \\big ) e ^ { \\sqrt { { s } / { s } _ { 0 \\mathrm { q } } } } \\bigg ] , } \\\\ & { { \\mathit { s } } _ { 0 \\mathrm { d } } = s _ { 0 \\mathrm { r } } \\bigg ( \\displaystyle \\frac { 1 5 } { 1 4 } \\bigg ) ^ { 2 } , { \\mathit { s } } _ { 0 \\mathrm { q } } = s _ { 0 \\mathrm { r } } \\bigg ( \\displaystyle \\frac { 1 5 } { 1 6 } \\bigg ) ^ { 2 } . } \\end{array}
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augmentation
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Yes
| 0
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expert
|
Describe the SHINE dechirper
|
Flat, corrugated, metallic plates separated by an adjustable gap
|
Summary
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Beam_performance_of_the_SHINE_dechirper.pdf
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We next simply consider the quadrupole wake, where the beam is on-axis $( \\mathrm { y } _ { \\mathrm { c } } = 0 )$ . The transfer matrices for the focusing and defocusing quadrupole are given in Eq. (16), where $L$ is the length of the corrugated structure [25]. $$ \\begin{array} { r } { \\boldsymbol { R } _ { \\mathrm { f } } = \\left[ \\begin{array} { c c } { \\cos k _ { \\mathrm { q } } L } & { \\frac { \\sin k _ { \\mathrm { q } } L } { k _ { \\mathrm { q } } } } \\\\ { - k _ { \\mathrm { q } } \\sin k _ { \\mathrm { q } } L } & { \\cos k _ { \\mathrm { q } } L } \\end{array} \\right] , \\boldsymbol { R } _ { \\mathrm { d } } = \\left[ \\begin{array} { c c } { \\cosh k _ { \\mathrm { q } } L } & { \\frac { \\sin k _ { \\mathrm { q } } L } { k _ { \\mathrm { q } } } } \\\\ { k _ { \\mathrm { q } } \\sinh k _ { \\mathrm { q } } L } & { \\cosh k _ { \\mathrm { q } } L } \\end{array} \\right] . } \\end{array}
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augmentation
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Yes
| 0
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IPAC
|
Explain the Earnshaw’s theorem
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At least two focusing directions have to be alternating.
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definition
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Alternating-Phase_Focusing_for_Dielectric-Laser_Acceleration.pdf
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$$ where $$ F \\left( \\xi \\right) = \\int _ { - \\infty } ^ { \\xi } A ^ { \\prime } { } ^ { 2 } ( \\xi ^ { \\prime } ) d \\xi ^ { \\prime } , $$ $$ G \\left( \\xi \\right) = \\int _ { - \\infty } ^ { \\xi } A ( \\xi ^ { \\prime } ) A ^ { \\prime 2 } ( \\xi ^ { \\prime } ) d \\xi ^ { \\prime } , $$ $$ H \\left( \\xi \\right) = 1 + \\frac { 2 } { 3 } r _ { e } \\hat { \\beta } _ { 0 } ^ { \\lambda } k _ { \\lambda } F \\left( \\xi \\right) , $$ $$ \\begin{array} { l } { { \\displaystyle I \\left( \\xi \\right) = A ( \\xi ) + \\frac { 2 } { 3 } r _ { e } \\hat { \\beta } _ { 0 } ^ { \\lambda } k _ { \\lambda } A ^ { \\prime } ( \\xi ) } } \\\\ { { \\displaystyle ~ + \\frac { 2 } { 3 } r _ { e } \\hat { \\beta } _ { 0 } ^ { \\lambda } k _ { \\lambda } \\left( A ( \\xi ) F \\left( \\xi \\right) - G \\left( \\xi \\right) \\right) , } } \\end{array}
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augmentation
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NO
| 0
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IPAC
|
Explain the Earnshaw’s theorem
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At least two focusing directions have to be alternating.
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definition
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Alternating-Phase_Focusing_for_Dielectric-Laser_Acceleration.pdf
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\\begin{array} { c l c r } { \\bar { x } , \\bar { y } = x , y } \\\\ { \\bar { p } _ { x , y } = \\displaystyle \\frac { P _ { x , y } } { \\bar { P } _ { s } } = \\displaystyle \\frac { p _ { x , y } P _ { s } } { \\bar { P } _ { s } } = \\displaystyle \\frac { p _ { x , y } } { 1 + \\delta } , } \\\\ { \\bar { p } _ { t } = \\displaystyle \\frac { E - \\bar { E } _ { s } } { c \\bar { P } _ { s } } = 0 , } \\end{array} $$ Finally, we redefine $E _ { i } , R _ { i j } , T _ { i j k }$ as a function of $\\bar { E } _ { i } , \\bar { R } _ { i j } , \\bar { T } _ { i j k }$ :
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augmentation
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NO
| 0
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IPAC
|
Explain the Earnshaw’s theorem
|
At least two focusing directions have to be alternating.
|
definition
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Alternating-Phase_Focusing_for_Dielectric-Laser_Acceleration.pdf
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$$ \\epsilon _ { x } = C _ { q } \\gamma ^ { 2 } \\frac { I _ { 5 } } { I _ { 2 } - I _ { 4 } } $$ with ùëíùëÑ $C _ { q } = { \\frac { 5 5 } { 3 2 { \\sqrt { 3 } } } } { \\frac { \\hbar } { m c } } \\approx 3 . 8 3 2 \\times 1 0 ^ { - 1 3 } \\mathrm { { m } }$ and $$ \\left\\{ \\begin{array} { l l } { \\displaystyle I _ { 2 } = \\oint \\frac { 1 } { \\rho ^ { 2 } } \\mathrm { d } s } & { \\displaystyle I _ { 3 } = \\oint \\frac { 1 } { | \\rho ^ { 3 } | } \\mathrm { d } s } \\\\ { \\displaystyle I _ { 4 } = \\oint \\frac { \\eta _ { x } } { \\rho } ( \\frac { 1 } { \\rho ^ { 2 } } + 2 k _ { 1 } ) \\mathrm { d } s } & { \\displaystyle I _ { 5 } = \\oint \\frac { \\mathcal { H } _ { x } } { | \\rho ^ { 3 } | } \\mathrm { d } s } \\\\ { \\displaystyle \\mathcal { H } _ { x } = \\gamma _ { x } \\eta _ { x } ^ { 2 } + 2 \\alpha _ { x } \\eta _ { x } \\eta _ { x } ^ { \\prime } + \\beta _ { x } \\eta _ { ~ x } ^ { \\prime 2 } } \\end{array} \\right.
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augmentation
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NO
| 0
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IPAC
|
Explain the Earnshaw’s theorem
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At least two focusing directions have to be alternating.
|
definition
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Alternating-Phase_Focusing_for_Dielectric-Laser_Acceleration.pdf
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$$ where the dependency on $\\widehat { \\tau }$ of $Q _ { s } ( \\widehat { \\tau } )$ has been introduced. The rightmost integral is given by $$ \\begin{array} { r l } & { \\frac { 1 } { | \\alpha _ { x y } | } \\displaystyle \\int _ { 0 } ^ { \\infty } d J _ { y } f _ { y } ( J _ { y } ) \\delta \\left( J _ { y } - \\frac { \\pm Q _ { F _ { 0 } } \\pm \\alpha _ { x } J _ { x } + p Q _ { s } - \\tilde { \\omega } } { \\mp \\alpha _ { x y } } \\right) } \\\\ & { = \\left\\{ \\frac { 1 } { | \\alpha _ { x y } | \\epsilon _ { y } } e ^ { \\frac { \\pm Q _ { F _ { 0 } } \\pm \\alpha _ { x } J _ { x } + p Q _ { s } - \\tilde { \\omega } } { \\pm \\alpha _ { x y } \\epsilon _ { y } } } \\quad \\mathrm { i f } \\frac { \\pm Q _ { F _ { 0 } } \\pm \\alpha _ { x } J _ { x } + p Q _ { s } - \\tilde { \\omega } } { \\mp \\alpha _ { x y } } > 0 , \\right. } \\\\ & { \\quad \\left. \\mathrm { o t h e r w i s e } . \\right. } \\end{array}
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augmentation
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NO
| 0
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IPAC
|
Explain the Earnshaw’s theorem
|
At least two focusing directions have to be alternating.
|
definition
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Alternating-Phase_Focusing_for_Dielectric-Laser_Acceleration.pdf
|
$$ where $\\mathcal { K } _ { m }$ consists of homogeneous polynomials in $p$ and $q$ of $( m + 2 )$ degree $$ \\begin{array} { r l } & { \\mathcal { K } _ { 0 } = C _ { 2 , 0 } p ^ { 2 } + C _ { 1 , 1 } p q + C _ { 0 , 2 } q ^ { 2 } , } \\\\ & { \\mathcal { K } _ { 1 } = C _ { 3 , 0 } p ^ { 3 } + C _ { 2 , 1 } p ^ { 2 } q + C _ { 1 , 2 } p q ^ { 2 } + C _ { 0 , 3 } q ^ { 3 } , } \\\\ & { \\cdots , } \\end{array} $$ and $C _ { i , j }$ are coefficients to be determined to satisfy Eq. (2). The reader can check that, in the first two orders of this perturbation theory, a general result is provided $$ \\begin{array} { r l r } & { } & { \\mathcal { K } ^ { ( 2 ) } [ p , q ] = \\mathcal { K } _ { 0 } [ p , q ] - \\varepsilon \\frac { b } { a + 1 } ( p ^ { 2 } q + p q ^ { 2 } ) + } \\\\ & { } & { \\qquad + \\varepsilon ^ { 2 } \\left( \\left[ \\frac { b ^ { 2 } } { a ( a + 1 ) } - \\frac { c } { a } \\right] p ^ { 2 } q ^ { 2 } + C \\mathcal { K } _ { 0 } ^ { 2 } [ p , q ] \\right) } \\end{array}
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augmentation
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NO
| 0
|
IPAC
|
Explain the Earnshaw’s theorem
|
At least two focusing directions have to be alternating.
|
definition
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Alternating-Phase_Focusing_for_Dielectric-Laser_Acceleration.pdf
|
$$ From Eqs. (3) and (4), it can be further observed that if $\\gamma \\sigma _ { z }$ is extremely large (i.e., $\\gamma \\sigma _ { z } \\infty ,$ ), the term ${ E } _ { s z }$ goes to zero, and Eq. (1) reduces to $$ \\begin{array} { c } { { \\phi \\approx \\displaystyle \\frac { 1 } { 4 \\pi \\varepsilon _ { 0 } } \\frac { N e } { ( 8 \\pi ) ^ { 1 / 2 } } \\frac { 1 } { \\sigma _ { z } } \\exp \\left( \\frac { z ^ { 2 } } { 2 \\sigma _ { z } ^ { 2 } } \\right) \\times } } \\\\ { { \\displaystyle \\int _ { 0 } ^ { \\infty } \\frac { \\exp \\left( - \\frac { x ^ { 2 } } { 2 ( \\sigma _ { x } ^ { 2 } + q ) } - \\frac { y ^ { 2 } } { 2 ( \\sigma _ { y } ^ { 2 } + q ) } \\right) } { ( \\sigma _ { x } ^ { 2 } + q ) ^ { 1 / 2 } ( \\sigma _ { y } ^ { 2 } + q ) ^ { 1 / 2 } } d q = : \\phi ^ { \\mathrm { 2 D } } . } } \\end{array}
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augmentation
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NO
| 0
|
IPAC
|
Explain the Earnshaw’s theorem
|
At least two focusing directions have to be alternating.
|
definition
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Alternating-Phase_Focusing_for_Dielectric-Laser_Acceleration.pdf
|
$$ where the factors $E _ { 1 }$ and $E _ { 2 }$ are given by: $$ \\begin{array} { c } { { E _ { 1 } = \\displaystyle \\frac { H _ { e } } { a } c o s ( \\theta ) - \\displaystyle \\frac { K _ { a n } } { M _ { s a t } \\mu _ { 0 } a } s i n ^ { 2 } ( \\psi - \\theta ) } } \\\\ { { E _ { 2 } = \\displaystyle \\ \\frac { H _ { e } } { a } c o s ( \\theta ) - \\displaystyle \\frac { K _ { a n } } { M _ { s a t } \\mu _ { 0 } a } s i n ^ { 2 } ( \\psi + \\theta ) } } \\end{array} $$ for average anisotropy energy density $K _ { a n }$ ùëé and an angle between $H _ { e }$ and the anisotropy easy-axis $\\psi$ ùúì. Lacking any known analytical form, the derivative of $M _ { a n } ^ { a n i s o }$ with respect to the field is taken by finite difference [7]:
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augmentation
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NO
| 0
|
IPAC
|
Explain the Earnshaw’s theorem
|
At least two focusing directions have to be alternating.
|
definition
|
Alternating-Phase_Focusing_for_Dielectric-Laser_Acceleration.pdf
|
For a charged particle moving at a constant high $\\beta$ velocity, or being accelerated along its predominant $\\beta$ vector component, the magnetic and acceleration-dependent terms for an observer on-axis with $\\beta$ (i.e. in the direction of $\\mathbf { n }$ ) go to zero, and the electric field reduces as $$ \\begin{array} { l } { \\displaystyle \\mathbf { E } _ { n } = e \\left[ \\frac { \\mathbf { n } - \\boldsymbol { \\beta } } { \\boldsymbol { \\gamma } ^ { 2 } ( 1 - \\boldsymbol { \\beta } \\cdot \\mathbf { n } ) ^ { 3 } R ^ { 2 } } \\right] } \\\\ { \\displaystyle \\quad = e \\left[ \\frac { ( 1 - \\boldsymbol { \\beta } _ { n } ) \\mathbf { n } } { \\boldsymbol { \\gamma } ^ { 2 } ( 1 - \\boldsymbol { \\beta } _ { n } ) ^ { 3 } R ^ { 2 } } \\right] } \\\\ { \\displaystyle \\quad \\approx e \\left[ \\frac { ( 1 - \\boldsymbol { \\beta } ^ { 2 } ) } { ( 1 - \\boldsymbol { \\beta } ) ^ { 2 } R ^ { 2 } } \\right] \\mathbf { n } } \\end{array}
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augmentation
|
NO
| 0
|
IPAC
|
Explain the Earnshaw’s theorem
|
At least two focusing directions have to be alternating.
|
definition
|
Alternating-Phase_Focusing_for_Dielectric-Laser_Acceleration.pdf
|
$$ where we have split the transformed phase space coordinates $$ u _ { k } = \\mathcal { M } _ { k } ( x ) $$ into orthogonal axes $u _ { k _ { \\parallel } } \\in \\mathbb { R } ^ { M }$ and $u _ { k _ { \\perp } } \\in \\mathbb { R } ^ { N - M }$ . In the absence of many views, various distributions may fit the data. To select a single distribution from the feasible set, we maximize a convex functional $H [ \\rho ( x ) ]$ subject to the measurement constraints in Eq. (1). By requiring the constrained maximum of $H$ to be unique, invariant with respect to coordinate transformation, subset-independent, and system-independent [1], we arrive at the Shannon entropy: $$ H [ \\rho ( x ) , \\rho _ { \\ast } ( x ) ] = - \\int \\rho ( x ) \\log \\Bigg ( \\frac { \\rho ( x ) } { \\rho _ { \\ast } ( x ) } \\Bigg ) d x , $$ where prior $\\rho _ { * } ( x )$ encodes our knowledge in the absence of data. $H [ \\rho ( x ) , \\rho _ { \\ast } ( x ) ] \\leq 0$ , reaching its maximum when $\\rho ( x ) = \\rho _ { * } ( x )$ .
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augmentation
|
NO
| 0
|
IPAC
|
Explain the Earnshaw’s theorem
|
At least two focusing directions have to be alternating.
|
definition
|
Alternating-Phase_Focusing_for_Dielectric-Laser_Acceleration.pdf
|
$$ where $E _ { z 0 } ( z ) \\equiv E _ { z } ( z , r = 0 )$ and similarly for $B _ { z 0 }$ . Then $$ \\frac { 2 } { r } F _ { \\perp } + F _ { z } ^ { \\prime } = - \\frac { \\beta _ { z } ^ { \\prime } } { \\beta _ { z } } \\frac { E _ { z 0 } } { \\beta _ { z } c } . $$ We can clean up the expression for $\\widetilde { \\kappa }$ by expressing $\\beta _ { z } ^ { \\prime } / \\beta _ { z }$ in terms of $E _ { z 0 }$ . Assuming $\\beta _ { z }$ is much larger than $\\beta _ { x }$ and $\\beta _ { y }$ , $$ \\frac { \\beta _ { z } ^ { \\prime } } { \\beta _ { z } } \\approx \\frac { 1 } { \\gamma ^ { 2 } } \\frac { E _ { z 0 } / \\beta _ { z } c } { [ B \\rho ] } .
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augmentation
|
NO
| 0
|
IPAC
|
Explain the Earnshaw’s theorem
|
At least two focusing directions have to be alternating.
|
definition
|
Alternating-Phase_Focusing_for_Dielectric-Laser_Acceleration.pdf
|
$$ where $q _ { 1 } = \\sqrt { q ^ { 2 } + \\hat { \\nu } k ^ { 2 } }$ and $n = 2$ in region $I I$ and $n = 3$ in region $I I I$ , and in region $I V$ $$ \\left( \\begin{array} { c c } { { \\bar { E } _ { z } } } & { { \\bar { H } _ { z } } } \\\\ { { \\tilde { E } _ { x } } } & { { \\tilde { H } _ { x } } } \\end{array} \\right) = \\left( \\begin{array} { c c } { { E _ { 4 } } } & { { i E _ { 4 } } } \\\\ { { A _ { 4 } + q E _ { 4 } } } & { { - B _ { 4 } + i q E _ { 4 } } } \\end{array} \\right) e ^ { - q y } , $$ where $E _ { 4 } = - \\alpha ( A _ { 4 } + i B _ { 4 } )$ and we have imposed that the field components in region $I V$ vanish at infinity.
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augmentation
|
NO
| 0
|
expert
|
Explain the Earnshaw’s theorem
|
At least two focusing directions have to be alternating.
|
definition
|
Alternating-Phase_Focusing_for_Dielectric-Laser_Acceleration.pdf
|
File Name:Alternating-Phase_Focusing_for_Dielectric-Laser_Acceleration.pdf Alternating-Phase Focusing for Dielectric-Laser Acceleration Uwe Niedermayer,1,\\* Thilo Egenolf,1 Oliver Boine-Frankenheim,1,3 and Peter Hommelhoff2 1Technische Universität Darmstadt, Schlossgartenstrasse 8, D-64289 Darmstadt, Germany $^ 2$ Department Physik, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Staudtstrasse 1, D-91058 Erlangen, Germany 3GSI Helmholtzzentrum für Schwerionenforschung GmbH, Planckstrasse 1, D-64291 Darmstadt, Germany (Received 13 June 2018; published 20 November 2018) The concept of dielectric-laser acceleration provides the highest gradients among breakdown-limited (nonplasma) particle accelerators. However, stable beam transport and staging have not been shown experimentally yet. We present a scheme that confines the beam longitudinally and in one transverse direction. Confinement in the other direction is obtained by a single conventional quadrupole magnet. Within the small aperture of $4 2 0 \\mathrm { n m }$ we find the matched distributions, which allow an optimized injection into pure transport, bunching, and accelerating structures. The combination of these resembles the photonics analogue of the radio frequency quadrupole, but since our setup is entirely two dimensional, it can be manufactured on a microchip by lithographic techniques. This is a crucial step towards relativistic electrons in the MeV range from low-cost, handheld devices and connects the two fields of attosecond physics and accelerator physics. DOI: 10.1103/PhysRevLett.121.214801 Since dielectric-laser acceleration (DLA) of electrons was proposed in 1962 [1,2], the development of photonic nanostructures and the control of ultrashort laser pulses has advanced significantly (see Ref. [3] for an overview). Phase synchronous acceleration was experimentally demonstrated first in 2013 [4,5]. Damage threshold limited record gradients, more than an order of magnitude higher than in conventional accelerators, were achieved meanwhile for both relativistic [6] and low-energy electrons [7]. These gradients, so far, express themselves only in the generation of energy spread, not as a coherent acceleration. Moreover, the interaction length is limited to the Rayleigh length, after which the electron beam defocuses and hits the small (submicrometer) aperture. During synchronous acceleration, there are additional defocusing forces which cannot be overcome by magnetic focusing only [8] since equivalent magnetic focusing gradients would have to be in the MT/m range [9].
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4
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NO
| 1
|
IPAC
|
Explain the Earnshaw’s theorem
|
At least two focusing directions have to be alternating.
|
definition
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Alternating-Phase_Focusing_for_Dielectric-Laser_Acceleration.pdf
|
$$ \\phi _ { i + 2 } = - \\frac { 1 } { 1 + h x } \\left( \\partial _ { x } \\left( ( 1 + h x ) \\partial _ { x } \\phi _ { i } \\right) + \\partial _ { s } \\left( \\frac { 1 } { 1 + h x } \\partial _ { s } \\phi _ { i } \\right) \\right) . $$ From this recurrence relation, only two initial functions can be independently chosen. These two functions, $\\phi _ { 0 }$ and $\\phi _ { 1 }$ , can be expanded in $x$ as follows, $$ \\begin{array} { l } { \\displaystyle \\phi _ { 0 } ( \\boldsymbol { x } , \\boldsymbol { s } ) = - a _ { 0 } ( \\boldsymbol { s } ) - \\sum _ { n = 1 } ^ { \\infty } a _ { n } ( \\boldsymbol { s } ) \\frac { \\boldsymbol { x } ^ { n } } { n ! } } \\\\ { \\displaystyle \\phi _ { 1 } ( \\boldsymbol { x } , \\boldsymbol { s } ) = - \\sum _ { n = 1 } ^ { \\infty } b _ { n } ( \\boldsymbol { s } ) \\frac { \\boldsymbol { x } ^ { n - 1 } } { ( n - 1 ) ! } } \\end{array}
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1
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NO
| 0
|
expert
|
Explain the Earnshaw’s theorem
|
At least two focusing directions have to be alternating.
|
definition
|
Alternating-Phase_Focusing_for_Dielectric-Laser_Acceleration.pdf
|
Earnshaw’s theorem dictates that constant focusing cannot be achieved in all three spatial directions simultaneously [29]. Thus, at least two focusing directions have to be alternating. In conventional Alvarez linacs or in synchrotrons constant focusing is applied in the longitudinal direction and alternating quadrupole lattices provide transverse confinement [30]. In our APF scheme, we apply the alternation to the disjoint focusing phase ranges of the longitudinal plane and the noninvariant transverse plane $( y )$ . Jumping the reference particle by means of a fractional cell drift between the orange circles in Fig. 2 provides stable transport at constant energy, and between the red dots we additionally obtain acceleration. The strong acceleration defocusing in $y$ is compensated by acceleration focusing at the longitudinally unstable phase. In the invariant $x$ direction a single conventional quadrupole magnet [9] suffices to confine the beam to an area in the center of the structure height, where the laser fields are homogeneous, i.e., do not depend on $x$ . We find the fixed points of the motion by setting $\\nabla V = 0$ as $s _ { f 1 } = \\varphi _ { s } \\lambda _ { g } / 2 \\pi$ and $s _ { f 2 } = - \\lambda _ { g } / 2 \\pi [ \\varphi _ { s } + 2 \\arg ( e _ { 1 } ) ]$ and define $\\Delta s _ { 1 } = s - s _ { f 1 }$ and $\\Delta s _ { 2 } = s - s _ { f 2 }$ . Note that in the longitudinal plane for $\\arg ( e _ { 1 } ) = 0$ the fixed point $s _ { f 1 }$ is elliptic and $s _ { f 2 }$ is hyperbolic, and vice versa in the transverse plane. Expanding $V$ to second order and omitting constant terms shows the APF principle:
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5
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NO
| 1
|
expert
|
Explain the Earnshaw’s theorem
|
At least two focusing directions have to be alternating.
|
definition
|
Alternating-Phase_Focusing_for_Dielectric-Laser_Acceleration.pdf
|
In this Letter we solve this outstanding problem with a laser-based scheme which allows transport and acceleration of electrons in dielectric nanostructures over arbitrary lengths. It is applicable to changing DLA period lengths, which is required to accelerate subrelativistic electrons. Moreover, we find the maximum tolerable emittances and beam envelopes in DLA beam channels. Another substantial advancement of our scheme is ballistic bunching of subrelativistic electrons down to attosecond duration, while the beam remains transversely confined. Thus, our scheme makes DLA scalable, which paves the way for a low-cost accelerator on a microchip, providing electrons in the MeV range from a small-scale, potentially handheld device. Our scheme uses only one spatial harmonic, namely, the synchronous one, but its magnitude and phase change along the DLA grating. This is interpreted as a time dependent focusing potential. A focusing concept using nonsynchronous spatial harmonics of traveling waves was presented by Naranjo et al. [10]. They derived stability due to retracting ponderomotive forces from the nonsynchronous spatial harmonics, while the synchronous one serves for acceleration. Our description is in the comoving real space, as compared to Naranjo’s description in the spatial frequency domain. This supports changes of all grating-related quantities, while the Courant-Snyder (CS) theory [11] from conventional accelerator physics is still applicable. Stable beam confinement is achieved by alternating-phase focusing (APF), which had already been developed in the 1950s for ion acceleration [12–14]. However, the later developed radio frequency quadrupole (RFQ) cavities turned out to have better performance, especially for high current beams. Thus, APF was rejected in favor of the RFQ and was only rarely implemented [14]. In the 1980s APF was also proposed for grating-based linacs [15–18], but these three-dimensional designs are hardly feasible at optical wavelengths. Since 3D structures such as RFQs or rotated gratings are not feasible for lithographic fabrication on a microchip, we present an entirely two-dimensional APF scheme in this Letter, enabling stable and almost lossless electron transport in high-gradient DLA.
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1
|
NO
| 0
|
expert
|
Explain the Earnshaw’s theorem
|
At least two focusing directions have to be alternating.
|
definition
|
Alternating-Phase_Focusing_for_Dielectric-Laser_Acceleration.pdf
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$$ \\begin{array} { l } { { V ( x , y , s = s _ { f 1 } + \\Delta s ) = - V ( x , y , s = s _ { f 2 } + \\Delta s ) } } \\\\ { { \\displaystyle ~ = \\frac { q | e _ { 1 } | \\lambda _ { g } } { 2 \\pi } \\left[ \\frac { 1 } { 2 } \\left( \\frac { \\omega y } { \\beta \\gamma c } \\right) ^ { 2 } - \\frac { 1 } { 2 } \\left( \\frac { 2 \\pi } { \\lambda _ { g } } \\Delta s \\right) ^ { 2 } \\right] \\sin ( \\varphi _ { 0 } ) } ; } \\end{array} $$ i.e., switching between $s _ { f 1 }$ and $s _ { f 2 }$ with $\\Delta s = \\Delta s _ { 1 } = \\Delta s _ { 2 }$ flips the sign of the potential. Only the nonaccelerating case $( \\varphi _ { 0 } = \\pi / 2 )$ provides two interchangeable buckets, whereas a $\\pi$ -shifted version of the accelerating bucket will be decelerating and unstable due to a mismatch with the ramp. Hill’s equations of the linearized motion are found from Eqs. (1) and (5) as
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Explain the Earnshaw’s theorem
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At least two focusing directions have to be alternating.
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definition
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Alternating-Phase_Focusing_for_Dielectric-Laser_Acceleration.pdf
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$$ L ^ { f } = \\sum _ { n = 1 } ^ { p } \\lambda _ { g } ^ { ( n ) } , \\qquad L ^ { d } = \\sum _ { n = p + 1 } ^ { 2 p } \\lambda _ { g } ^ { ( n ) } , $$ $$ l ^ { f } = ( 2 \\pi - \\varphi _ { s } ^ { ( p ) } ) \\lambda _ { g } ^ { ( p ) } / \\pi , ~ l ^ { d } = ( \\pi - \\varphi _ { s } ^ { ( 2 p ) } ) \\lambda _ { g } ^ { ( 2 p ) } / \\pi . $$ The solution to Eq. (6) is found by applying the CS formalism [11] to the channel of thick focusing $( F )$ and defocusing $( D )$ elements. We start with a nonaccelerating transport structure, i.e., $\\varphi _ { 0 } = \\pi / 2$ , where the lattice cells are strictly periodic. In a long lattice cell $( p \\gg 1 )$ we can neglect the drift sections and represent it as [9]
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Explain the Earnshaw’s theorem
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At least two focusing directions have to be alternating.
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definition
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Alternating-Phase_Focusing_for_Dielectric-Laser_Acceleration.pdf
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$$ \\varepsilon ( y , y ^ { \\prime } ) = \\hat { \\gamma } y ^ { 2 } + 2 \\hat { \\alpha } y y ^ { \\prime } + \\hat { \\beta } y ^ { \\prime 2 } , $$ $$ \\varepsilon _ { L } ( \\Delta s , \\Delta s ^ { \\prime } ) = \\hat { \\gamma } _ { L } \\Delta s ^ { 2 } + 2 \\hat { \\alpha } _ { L } \\Delta s \\Delta s ^ { \\prime } + \\hat { \\beta } _ { L } \\Delta s ^ { \\prime 2 } , $$ where $\\Delta s ^ { \\prime } = \\Delta W / ( m _ { e } \\gamma ^ { 3 } \\beta ^ { 2 } c ^ { 2 } )$ , and we introduce longitudinal CS functions as a half lattice cell shift of the transverse ones, $\\eta _ { L } ( z ) = \\eta ( z - L / 2 )$ . An accelerating lattice can be attained by taking the initial values from the eigenvalue solution and successively multiplying the segment maps as $\\eta _ { N } = \\mathbf { T } _ { N } . . . \\mathbf { T } _ { 1 } \\eta _ { e }$ to it. In nonperiodic lattices the longitudinal CS functions have to be calculated individually with the same procedure. If the change in length from one period to another is small, the $\\hat { \\boldsymbol { \\beta } }$ function can be approximated by the eigenvalue solution in each cell, which is, however, discontinuous at the boundaries. The line of increasing minimum of $\\hat { \\beta } _ { \\mathrm { m a x } }$ in Fig. 4 is followed only approximately. The increase is counteracted by adiabatic emittance damping due to momentum conservation. Altogether the beam envelope can be written as [30]
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augmentation
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expert
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Explain the Earnshaw’s theorem
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At least two focusing directions have to be alternating.
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definition
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Alternating-Phase_Focusing_for_Dielectric-Laser_Acceleration.pdf
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\\*[email protected] [1] K. Shimoda, Appl. Opt. 1, 33 (1962). [2] A. Lohmann, IBM Technical Note 5, 169, 1962. [3] R. J. England et al., Rev. Mod. Phys. 86, 1337 (2014). [4] E. A. Peralta, K. Soong, R. J. England, E. R. Colby, Z. Wu, B. Montazeri, C. McGuinness, J. McNeur, K. J. Leedle, D. Walz, E. B. Sozer, B. Cowan, B. Schwartz, G. Travish, and R. L. Byer, Nature (London) 503, 91 (2013). [5] J. Breuer and P. Hommelhoff, Phys. Rev. Lett. 111, 134803 (2013). [6] K. P. Wootton, Z. Wu, B. M. Cowan, A. Hanuka, I. V. Makasyuk, E. A. Peralta, K. Soong, R. L. Byer, and R. J. England, Opt. Lett. 41, 2696 (2016). [7] K. J. Leedle, A. Ceballos, H. Deng, O. Solgaard, R. F. Pease, R. L. Byer, and J. S. Harris, Opt. Lett. 40, 4344 (2015). [8] A. Ody, P. Musumeci, J. Maxson, D. Cesar, R. J. England, and K. P. Wootton, Nucl. Instrum. Methods Phys. Res., Sect. A 865, 75 (2017). [9] See Supplemental Material at http://link.aps.org/ supplemental/10.1103/PhysRevLett.121.214801 for mathematical/technical details and movies. [10] B. Naranjo, A. Valloni, S. Putterman, and J. B. Rosenzweig, Phys. Rev. Lett. 109, 164803 (2012). [11] E. Courant and H. Snyder, Ann. Phys. (N.Y.) 3, 1 (1958).
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augmentation
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NO
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expert
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Explain the Earnshaw’s theorem
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At least two focusing directions have to be alternating.
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definition
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Alternating-Phase_Focusing_for_Dielectric-Laser_Acceleration.pdf
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$$ a ( z ) = \\sqrt { \\hat { \\beta } ( z ) \\frac { \\varepsilon _ { 0 } \\beta _ { 0 } \\gamma _ { 0 } } { \\beta ( z ) \\gamma ( z ) } } , $$ where the 0 indices denote initial values. Acceleration from $8 3 \\mathrm { k e V }$ to $1 \\mathrm { M e V }$ at $\\varphi _ { 0 } = 4 \\pi / 3$ , with an average gradient of $1 8 7 ~ \\mathrm { M e V / m }$ and $5 0 0 ~ \\mathrm { M V / m }$ incident laser field strength from both sides, is shown to be well confined within the physical aperture of $\\pm 0 . 2 1 \\ \\mu \\mathrm { m }$ in Fig. 5. The analytical and numerical results coincide for infinitesimally low emittance. At small but achievable emittances [31,32], we obtain $56 \\%$ transmission for $\\varepsilon _ { 0 } = 1 0 0 \\mathrm { p m }$ (see the video in the Supplemental Material [9]), and $9 3 \\%$ for $\\varepsilon _ { 0 } = 2 5 ~ \\mathrm { p m }$ . The phase space density at top energy is plotted in Fig. 6, where $\\Phi _ { P }$ and $\\Delta W$ are the longitudinal coordinates in the comoving (Galilean) laboratory frame. As in Fig. 3, the initial particle positions in Fig. 6 (left panel) are arranged on a Cartesian grid, and only the ones that make it to $1 \\mathrm { M e V }$ are drawn in red. The blue ellipse corresponds to an initially matched bunch adjusted to the area of the surviving particles. Note that this size is slightly reduced at finite transverse emittance; thus, we choose $\\sigma _ { z } = 1 0 ~ \\mathrm { n m }$ . Below this bunch length the transmission depends only on the initial transverse emittance, i.e., is fully scalable.
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IPAC
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For a given transverse beam offset, would a higher of lower plasma density be preferred to reduce the transverse dielectric wakes?
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A higher plasma density screens wakes more effectively
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Reasoning
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Experimental_Observation_of_Space-Charge_Field_Screening.pdf
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One approach for addressing the issue posed by SBBU is through the introduction of an external magnetic lattice to correct for deviations in the beam trajectory due to wakefield effects. This approach is limited however in it’s maximum allowable accelerating gradient due to the fact that longitudinal wakefields scale with $a ^ { - 2 }$ while the transverse fields cale with $a ^ { - 3 }$ where $a$ is the half vacuum-gap as seen in Fig. 1 [8]. Another approach is to abandon the historical cylindrical dielectric structure and use a planar-symmetric design instead. It has been shown that using such a structure, in the limit of an infinitely wide beam of fixed charge density, that the net transverse wakefields vanish [9]. Outside of that limit, in the finite-charge case, the transverse and longitudinal wakefields scale with the beam width, $\\sigma _ { x }$ , as $\\sigma _ { x } ^ { - 3 }$ and $\\sigma _ { x } ^ { - 1 }$ respectively. This implies that there should exist a beam width such that the transverse wakefields are weak enough to allow the beam to propagate through the entire structure but the longitudinal wakefields are still strong enough to be of interest [10]. While the primary dipole deflecting fields are indeed suppressed, secondary quadrupole-like fields persist which can severely distort the tail of the beam and again, eventually lead to SBBU [11].
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IPAC
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For a given transverse beam offset, would a higher of lower plasma density be preferred to reduce the transverse dielectric wakes?
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A higher plasma density screens wakes more effectively
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Reasoning
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Experimental_Observation_of_Space-Charge_Field_Screening.pdf
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$$ SIMULATIONS RESULTS Simulations are performed using QuickPIC [8], a 3-D quasi-static PIC code, with the simulation parameters specified in Table ??. The ellipticities were calculated from the transverse cross section of the blowout cavity by taking the gradient of the density above a specific threshold, which is typically at the edge of the ion column. This transverse cross section and corresponding fit is illustrated in Fig. 1. The ellipticities were calculated at di!erent longitudinal positions with a separation of $0 . 1 \\ k _ { p } ^ { - 1 }$ . This method of fitting works well when the blowout sheath is distinct, as it allows us to make the uniform ion column approximation. We do this for di!erent beam densities and the results at initialization along with the corresponding analytical fits (To keep the linear charge density constant, we scale down the beam density by a factor of 2) are shown in Figure 2. CONCLUSION The simulations agree well with the formula derived using the simplified theory, especially at high beam densities. Table: Caption: Table 1: SIMULATION PARAMETERS TUPA: Tuesday Poster Session: TUPA Body: <html><body><table><tr><td>Parameter</td><td>Value</td><td>Unit</td></tr><tr><td>Beam density, nb</td><td>20</td><td>no</td></tr><tr><td></td><td></td><td></td></tr><tr><td>Energy,Eb</td><td>501</td><td></td></tr><tr><td>Ox,Oy</td><td>0.25,0.025</td><td></td></tr><tr><td>Ex，,Ey</td><td>200,2</td><td>μm-rad</td></tr><tr><td>Plasma density, no</td><td>7 ×1013</td><td>cm-3</td></tr></table></body></html> Improvements can be made by considering the sheath distribution of the plasma electrons and their velocities. Understanding the plasma blowout structure, will allow us to understand the fields to determine the matching conditions and dynamics of the particle beams inside the plasma column [9]. An experiment is being planned at AWA to determine the basic features of the flat beam driven PWFA [10]. An argon based capillary discharge plasma source which has a multi decade range of densities is being developed at UCLA for this experiment [11]. We are planning to use betatron diagnostics [12] to investigate the characteristics of the created wakefields.
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IPAC
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For a given transverse beam offset, would a higher of lower plasma density be preferred to reduce the transverse dielectric wakes?
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A higher plasma density screens wakes more effectively
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Reasoning
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Experimental_Observation_of_Space-Charge_Field_Screening.pdf
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This beam, with $\\sigma _ { z } = 9 5 \\mu \\mathrm { m }$ , is numerically injected into a $n _ { 0 } = 1 0 ^ { 1 3 } \\mathrm { c m } ^ { - 3 }$ plasma, yielding the condition with $k _ { p } \\sigma _ { z } \\simeq$ 2. The head of the beam is decelerated while the tail is accelerated, thus producing the desired distribution as shown in the phase space plot in Fig. 7. The ion focusing in this case is very strong, resulting in a matched transverse beam size of $\\sigma _ { x } \\simeq 5 \\mu \\mathrm { m }$ . This beta-matching is obtained by using a strong, adjustable permanent magnet quadrupole triplet. The matching process is completed by utilizing the up-ramp of the plasma density that increases the focusing strength. At the LAPD, introduction of a highly magnetized plasma yields yet another variable that can give a very strong effect on the system’s long-term behavior. The initiation of the interaction is shown in Fig 8, which shows, in the very short term, plasma wavelength-scale response to the beam’s wake excitation. Most critically, we show the differences between the unmagnetized and the highly-magnetized cases. In the magnetized $( 0 . 9 \\mathrm { T } )$ scenario, one avoids nearly completely the density spikes at the end of the blowout bubble. Efforts are currently underway to finalize the beam transport system to the LAPD.
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IPAC
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For a given transverse beam offset, would a higher of lower plasma density be preferred to reduce the transverse dielectric wakes?
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A higher plasma density screens wakes more effectively
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Reasoning
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Experimental_Observation_of_Space-Charge_Field_Screening.pdf
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BEAM TRANSPORT An electric discharge-based capillary plasma source is being built at UCLA [5]. The $8 \\mathrm { c m }$ long capillary is created by boring a $4 \\mathrm { m m }$ wide opening inside a macor structure with a single channel gas supply tube. The plasma density inside this capillary has been measured to be in the $1 0 ^ { 1 4 } ~ \\mathrm { c m } ^ { - 3 }$ range [6]. A flat beam plasma wakefield acceleration experiment has been proposed at the Argonne Wakefield Accelerator (AWA) using a flat beam with asymmetric transverse emittances and spot sizes [7, 8]. This beam produces an asymmetric wakefield structure that creates different focusing forces in the transverse planes [9, 10]. Our beam transport analysis begins with understanding the matching requirements for the elliptical beam within this plasma. These requirements are influenced by the ellipticity of the plasma blowout structure produced by the driver [1, 2], and the matched beta functions can be calculated using the following relation: Table: Caption: Table 1: Beam Parameters Body: <html><body><table><tr><td>Parameter</td><td>Value</td><td>Unit</td></tr><tr><td>Energy,Eb</td><td>58</td><td>MeV</td></tr><tr><td>En,x,En,y</td><td>188.6, 1.64</td><td>μm-rad</td></tr><tr><td>βo,x, βo.y</td><td>2.078, 8.089</td><td>m</td></tr><tr><td>ao,x, ao,y</td><td>-0.309,-5.634</td><td></td></tr><tr><td>Plasma density, no</td><td>2 ×1014</td><td>cm-3</td></tr><tr><td>Plasma length, L</td><td>8</td><td>cm</td></tr><tr><td>Plasma ramp,σp</td><td>0.5</td><td>cm</td></tr></table></body></html> Table: Caption: Body: <html><body><table><tr><td></td><td>x (vacuum)</td><td>y (vacuum)</td><td></td></tr><tr><td></td><td>x(αp:2)</td><td>y(ap:2)</td><td>Plasma profile (a.u.)</td></tr><tr><td></td><td>x (αp:1)</td><td>·</td><td>y(αp:1)</td></tr></table></body></html>
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IPAC
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For a given transverse beam offset, would a higher of lower plasma density be preferred to reduce the transverse dielectric wakes?
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A higher plasma density screens wakes more effectively
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Reasoning
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Experimental_Observation_of_Space-Charge_Field_Screening.pdf
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$$ \\sigma ^ { * 2 } = \\epsilon \\beta ^ { * } ( 1 + \\xi ^ { 2 } \\delta _ { p } ^ { 2 } ) , $$ where $\\epsilon$ is the beam emittance, $\\beta ^ { * }$ is the beta-function at the IP, $\\delta _ { p }$ is the relative momentum spread of the beam and $\\xi$ is the chromaticity at the IP. SYNCHROTRON RADIATION IN THE COLLIMATION SYSTEM Scaling of the Bending Angles To minimize the radiation generated in the Collimation system, the bending angles of the dipoles must be reduced as much as possible which will lead to a reduction in dispersion. A decrease in dispersion will lead to a reduction in the spoiler gap [10] and, as mentioned above, to a high wakefield e!ects especially the transverse wakefields can lead to a significant emittance dilution. The kick due to the wakefield e!ect is proportional to $$ < \\Delta y ^ { \\prime } > \\propto \\frac { L _ { s p o i l e r } } { \\gamma \\sqrt { \\sigma _ { z } \\sigma } Z _ { 0 } g ^ { 3 } } ,
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augmentation
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IPAC
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For a given transverse beam offset, would a higher of lower plasma density be preferred to reduce the transverse dielectric wakes?
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A higher plasma density screens wakes more effectively
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Reasoning
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Experimental_Observation_of_Space-Charge_Field_Screening.pdf
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The physical solution of the quadratic equation is: $$ \\begin{array} { c } { { D _ { x } = \\displaystyle \\frac { ( S + 5 \\sqrt { \\epsilon _ { i n j } \\beta _ { x } } ) \\Delta } { \\Delta ^ { 2 } - 2 5 \\delta _ { c i r } ^ { 2 } } + } } \\\\ { { \\displaystyle \\frac { 5 \\sqrt { \\epsilon _ { c i r } \\beta _ { x } ( \\Delta ^ { 2 } - 2 5 \\delta _ { c i r } ^ { 2 } ) + ( S + 5 \\sqrt { \\epsilon _ { i n j } \\beta _ { x } } ) ^ { 2 } \\delta _ { c i r } ^ { 2 } } } { \\Delta ^ { 2 } - 2 5 \\delta _ { c i r } ^ { 2 } } } } \\end{array} $$ In Z mode, the beam equilibrium horizontal emittances for the collider and booster rings are $0 . 7 1 \\mathrm { n m }$ and $0 . 2 6 \\mathrm { n m }$ , respectively [7]. Considering an energy offset of the injected beam of $1 \\%$ , we represent the relationship between $\\beta _ { x }$ and $D _ { x }$ for various septa blade thicknesses in Fig. 1. This figure shows a monotonic relationship where a larger $\\beta _ { x }$ leads to a larger beam size, necessitating increased dispersion to enhance the separation between the injected and circulating beams at the injection points, while maintaining the constraints of Eq. 1.
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IPAC
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For a given transverse beam offset, would a higher of lower plasma density be preferred to reduce the transverse dielectric wakes?
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A higher plasma density screens wakes more effectively
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Reasoning
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Experimental_Observation_of_Space-Charge_Field_Screening.pdf
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$$ 2 \\pi f \\Delta \\tau \\ll 1 , $$ where $f$ is the characteristic frequency of the wake, and $\\Delta \\tau$ is the distance between the rings. For the PETRA wake, dom inated by the resistive wall e!ects, a choice of $n _ { r } = 9$ works reasonably well. Figure 2 shows the radial discretization. NUMERICAL SIMULATION To assess the e!ect of gaps in filling patterns on beam dynamics we have conducted a series of parameter scans, varying the lengths of the gaps while keeping the bunch charge constant. The gaps varied in length from 0 (no gap) to 20 bunches every 24 bunches with 4 ns spacing (Fig. 3). The simulation included e!ects of transverse feedback and chromaticity. The numerical setup included 21 azimuthal, 9 radial head-tail modes, and up to 1920 coupled-bunch modes. $$ \\underbrace \\begin{array} { c } { { 2 4 \\cdot N \\mathrm { b u n c h e s } } } \\\\ { { \\underbrace { \\begin{array} { r l } { \\mathbf { \\sigma } } \\end{array} } \\cdots \\textbf { \\sigma } \\mathbf { 0 } \\qquad \\begin{array} { r l } { { ^ { N \\mathrm { e m p t y } } } } \\\\ { { \\cdots } \\mathbf { \\sigma } \\mathrm { ~ \\mathscr { O } ~ e ~ } \\mathbf { 0 } \\cdots \\mathbf { \\sigma } } \\end{array} } } \\end{array}
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IPAC
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For a given transverse beam offset, would a higher of lower plasma density be preferred to reduce the transverse dielectric wakes?
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A higher plasma density screens wakes more effectively
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Reasoning
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Experimental_Observation_of_Space-Charge_Field_Screening.pdf
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Table: Caption: Table 1: Beam Parameters at the Exit of the S-band Injector. Body: <html><body><table><tr><td>Injector exit parameters</td><td>Witness</td><td>Driver</td></tr><tr><td>Charge (pC)</td><td>30</td><td>200</td></tr><tr><td>Rms spot size (μm)</td><td>118</td><td>127</td></tr><tr><td>Rms length (fs)</td><td>17</td><td>207</td></tr><tr><td>Emittance (μm)</td><td>0.55</td><td>1.5</td></tr><tr><td>Mean energy (MeV)</td><td>124</td><td>126</td></tr><tr><td>Energy spread (%)</td><td>0.18</td><td>0.55</td></tr><tr><td>Bunch separation (ps)</td><td>0.5</td><td></td></tr></table></body></html> Benchmark with ELEGANT As a preliminary step, we start by establishing the validity of our models by a benchmark with previous simulations performed with ELEGANT [14, 15]. Figure 1 shows a comparison of the rms transverse envelope within the first X-band linac stage $( \\lesssim 3 5 0 \\mathrm { M e V } )$ . In this simple example, the beam propagates on axis and is not subjected to wakefield e!ects. The transverse optics system consists of alternating gradient quadrupoles located in the drift spaces among consecutive sections. It can be noticed that, due to the high charge ratio, the dynamics are mainly dominated by the driver beam and that the agreement with ELEGANT is excellent. Short-range Wakes in RF Linacs Short-range wakefields in periodic accelerating structures have been studied extensively by use of di!raction theory [16–18] and well known formulas for the wake-function of short bunches can be found in [19]. Such models show that small cell irises induce intense wakefields whose e!ect is particularly relevant for high frequency linacs such as those in the X-band stage. The main concern is represented by the transverse dipole wakes since their strength scales as $ { a ^ { - 3 } }$ $\\mathbf { \\chi } _ { a }$ being the iris radius) and they cause emittance dilution due to the correlation between the planes [20]. Here we use MILES to investigate the emittance growth in presence of alignment errors. In Fig. 2 we consider the 8 accelerating sections in the first stage of the X-band linac at EuPRAXIA and we assume that they are a!ected by $\\pm 5 0 \\mu \\mathrm { m }$ o!sets with alternate sign. It can be noticed that, as the beam travels o!- axis exciting dipole wakefields, the overall emittance grows. However, the witness is only slightly a!ected by this process $( \\sim - 9 \\%$ variation) because, due to the short dimensions, the intra-beam correlation e!ect remains moderate.
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NO
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IPAC
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For a given transverse beam offset, would a higher of lower plasma density be preferred to reduce the transverse dielectric wakes?
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A higher plasma density screens wakes more effectively
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Reasoning
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Experimental_Observation_of_Space-Charge_Field_Screening.pdf
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Table: Caption: Table 1: Comparison of Beam Dynamics for Three Different Input Distributions after Optimisation Body: <html><body><table><tr><td rowspan="2">Parameter</td><td colspan="3">Distributions</td></tr><tr><td>A</td><td>B</td><td>C</td></tr><tr><td>Emittance,εx (mm mrad)</td><td>6.19</td><td>5.21</td><td>5.00</td></tr><tr><td>Avg. Slice emittnce,εslice (mm mrad)</td><td>5.91</td><td>4.73</td><td>4.39</td></tr><tr><td>RMS bunch length, σs (mm)</td><td>2.12</td><td>2.58</td><td>2.84</td></tr><tr><td>RMS transverse beam size,σx(mm)</td><td>0.47</td><td>0.70</td><td>1.01</td></tr><tr><td>Uncorrelated energy spread,dE(keV)</td><td>4.47</td><td>3.62</td><td>2.96</td></tr></table></body></html> To further investigate the suitability of the final solution (scenario C) the statistical parameters of the whole injector are shown in Fig. 3. As mentioned previously, it is also important that the emittance be as minimal as possible, with this being approximately defined by the value of average slice emittance. In all three scenarios, there is some level of disparity between slices, with a difference of 0.3, 0.5, and 0.6 (mm mrad), respectively for each scenario. This difference in slices can be clearly seen in the transverse phase space presented in Fig. 4. Both phase spaces are separated into six slices, in transverse phase space it is clearly represented how the emittance is different along the length of the bunch. The ‘M’-shape which appears in longitudinal phase space is discussed in Ref. [9]. In the work referenced, this shape is reduced by adding in higher order harmonic cavities. However, here we have shown that it may be possible to also achieve some reduction by optimising the laser input parameters.
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IPAC
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For a given transverse beam offset, would a higher of lower plasma density be preferred to reduce the transverse dielectric wakes?
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A higher plasma density screens wakes more effectively
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Reasoning
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Experimental_Observation_of_Space-Charge_Field_Screening.pdf
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In the following simulation study, we will first evaluate the effect of horizontal impedance (dipole $^ +$ detuning) and then will take into account the vertical one. EFFECT OF HORIZONTAL IMPEDANCE The horizontal beam-beam cross-wake function has been given in Eq. (12) of Ref. [14], $$ W _ { x } ^ { ( - ) } ( z ) = - \\frac { N ^ { ( + ) } r _ { e } } { \\gamma ^ { ( - ) } \\bar { \\sigma } _ { x } ^ { 2 } } \\left\\{ 1 - \\frac { \\sqrt { \\pi } \\theta _ { p } z } { 2 \\bar { \\sigma } _ { z } } \\mathrm { I m } \\left[ w \\left( \\frac { \\theta _ { p } z } { 2 \\sigma _ { z } } \\right) \\right] \\right\\} , $$ where where $N ^ { ( + ) }$ is the number of particles of the $e ^ { + }$ bunch, classical radius of the electron, $\\gamma ^ { ( - ) }$ is the relativistic energy of the $\\bar { \\sigma } _ { x } ^ { 2 } = ( \\sigma _ { x } ^ { ( + ) 2 } + \\sigma _ { x } ^ { \\top - ) 2 } ) / 2$ $e ^ { - }$ bunch, $r _ { e }$ is the $\\theta _ { p } = \\theta _ { c } \\sigma _ { z } / \\bar { \\sigma } _ { x }$ is the Piwinski angle and $w$ is the complex error function. The corresponding cross impedance is obtained by the Fourier transform of the wake force,
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augmentation
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IPAC
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For a given transverse beam offset, would a higher of lower plasma density be preferred to reduce the transverse dielectric wakes?
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A higher plasma density screens wakes more effectively
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Reasoning
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Experimental_Observation_of_Space-Charge_Field_Screening.pdf
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$$ \\begin{array} { r } { \\beta _ { x } = \\sqrt { ( 1 + \\alpha _ { p } ^ { 2 } ) \\gamma } k _ { p } ^ { - 1 } } \\\\ { \\beta _ { y } = \\sqrt { \\displaystyle \\frac { ( 1 + \\alpha _ { p } ^ { 2 } ) \\gamma } { \\alpha _ { p } ^ { 2 } } } k _ { p } ^ { - 1 } , } \\end{array} $$ where, $\\gamma$ is the Lorentz factor, $\\boldsymbol { \\alpha } _ { p }$ is the ellipticity of the blowout structure, $k _ { p } ^ { - 1 } = \\sqrt { m _ { e } \\epsilon _ { 0 } c ^ { 2 } / n _ { 0 } e ^ { 2 } }$ is the plasma skin depth, $n _ { 0 }$ is the nominal plasma density, $m _ { e }$ is the electron mass and $e$ is the electron charge. The blowout ellipticity created by the flat beam driver depends on the beam density, $n _ { b }$ , and the beam ellipticity, $\\scriptstyle \\alpha _ { b }$ . We can use these asymmetric beta functions as the starting point for our beam transport by estimating the blowout ellipticity, $\\alpha _ { p }$ , based on the beam parameters inside the plasma (here we assume $\\begin{array} { r } { { \\alpha _ { p } } = 2 } \\end{array}$ and a plasma density $n _ { 0 } = 2 \\times 1 0 ^ { 1 4 } ~ \\mathrm { c m } ^ { - 3 } ,$ ). Additionally, we assume a ramped Gaussian profile of the form of ùëõ0ùëí(‚àíùëß2/ùúé2ùëù) at the ends of the plasma with $\\sigma _ { p } = 0 . 5 ~ \\mathrm { c m }$ , and match the beam to this profile [11]. Matching the beam to the focusing plasma forces ensures near-equilibrium propagation and emittance preservation, whereas the propagation of a mismatched beam is characterized by beam envelope oscillations [12].The beta function and spot size evolution of the beam envelope has been shown in Fig. 1. The vacuum and $\\alpha _ { p } = 1$ evolution is also depicted in the figure, which illustrates scenarios without plasma focusing fields and with axisymmetric focusing fields, respectively.
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For a given transverse beam offset, would a higher of lower plasma density be preferred to reduce the transverse dielectric wakes?
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A higher plasma density screens wakes more effectively
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Reasoning
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Experimental_Observation_of_Space-Charge_Field_Screening.pdf
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Table: Caption: Table 1: Beam and DLW Parameters for DWA Experiments Body: <html><body><table><tr><td>Parameter</td><td></td></tr><tr><td>Beam Momentum</td><td>35.5MeV/c</td></tr><tr><td>Total Charge</td><td>85-100 pC</td></tr><tr><td>Normalised Emittance</td><td>~5 mm mrad</td></tr><tr><td>RMSBeamSizeatDLW</td><td>~100 μm</td></tr><tr><td>DLWPlate Separation</td><td>4.0 mm</td></tr><tr><td>Dielectric Thickness</td><td>0.2 mm</td></tr><tr><td>Dielectric Permitivity</td><td>3.75 (Quartz)</td></tr></table></body></html> RECONSTRUCTION RESULTS $$ O f f - C r e s t P h a s e = - 6 ^ { \\circ } $$ Reconstruction measurements were conducted at a range of offsets, with consistent profiles as shown in Fig. 3. The minimisation of the variation function at each offset (Fig. 4) gives a measurement of the RMS bunch length for each offset. The average of each RMS bunch length measurement is $2 9 5 \\pm 2 0$ fs, in agreement with the simulated value of 303 fs. Using the results of multiple offsets significantly increases the resolution; using the resolution equation given in [12] the resolution with an offset of $1 4 8 0 \\mu \\mathrm { m }$ is ${ \\sim } 1 7 0$ fs at the tail of the bunch. The profile shape also agrees with the simulated profile. To test the validity of the final reconstructed profile, this profile is forward propagated to the screen as shown in Fig. 5, showing agreement with the measured transverse profile. It can therefore be determined that the profiles are consistent with simulations and reconstructions demonstrated an approximately Gaussian profile with ${ \\sim } 3 0 0$ fs RMS bunch length. The agreement of the results at each offsets support the use of a scan of different offsets to improve the resolution of streaker measurements.
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For a given transverse beam offset, would a higher of lower plasma density be preferred to reduce the transverse dielectric wakes?
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A higher plasma density screens wakes more effectively
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Reasoning
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Experimental_Observation_of_Space-Charge_Field_Screening.pdf
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In the misaligned case [Fig. 2(b)], on the contrary, the centroid is clearly deflected, with increasing displacement along the bunch. Figure 2(d) shows that the centroid position and the running sum follow the same trend along the bunch. This confirms the expectation that the amplitude of the transverse wakefields (and therefore of the transverse deflection) at any time $t$ along the bunch depends on the amount of charge ahead of it, in agreement with the formulation of $W _ { \\perp } ( t )$ . The amplitude of the transverse wakefields $W _ { \\perp }$ reaches a maximum at the back of the bunch. We calculate the average wakefield potential experienced by the particles in the last slice of the bunch $( t \\sim 6 . 7 ~ \\mathrm { p s } )$ as $\\bar { W } _ { \\perp } = x ( t ) E / e d L \\sim 0 . 4 ~ \\mathrm { M V / m }$ . We also note that, in both cases, the transverse size slightly increases along the bunch. This is due to the fact that the dielectric wakefields also have a quadrupolar (defocusing) component, growing in amplitude along the bunch.
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For a given transverse beam offset, would a higher of lower plasma density be preferred to reduce the transverse dielectric wakes?
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A higher plasma density screens wakes more effectively
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Reasoning
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Experimental_Observation_of_Space-Charge_Field_Screening.pdf
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Two DLW geometries are under active consideration, circular/cylindrical and planar/slab DLWs. Strong transverse fields are excited off-axis in both geometries, leading to beam breakup instability induced by small initial offsets [4]. A method for compensating this instability is required before applications of DWA can be realised. One proposed method is to line a circular DWA with a quadrupole wiggler, BNS damping, continuously compensating any offset and returning the beam to the DLW axis [4, 5]. This method can only be applied to a circular DWA structure. BNS damping also leads to an oscillating RMS transverse beam size through the circular DWA. The effect of a non-radially symmetric beam in a circular DWA has not been investigated. Evidence of transverse fields excited on-axis in circular DWA structures has been experimentally demonstrated, but the source of these fields has not been fully explained [6, 7]. In these proceedings, the field excited by non-radially symmetric beams have been calculated. Higher-order fields have been shown to be excited and a potential new source of beam instability demonstrated. Table: Caption: Table 1: Beam, Mesh, and Circular DLW Parameters for Field Calculations Body: <html><body><table><tr><td>Parameter</td><td></td></tr><tr><td>Charge Longitudinal Momentum RMS Bunch Length, Ot Longitudinal Profile Shape RMS Beam Width, Ox,y</td><td>250 pC 250 MeV/c 200 fs Gaussian 50 μm</td></tr><tr><td>Longitudinal Mesh Density, Cells per Ot Transverse Mesh Density, Cells per Ox,y</td><td>5 3</td></tr><tr><td>DLW Vacuum Radius, a Dielectric Thickness,δ Dielectric Permittivity</td><td>500 μm 200 μm</td></tr></table></body></html>
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For a given transverse beam offset, would a higher of lower plasma density be preferred to reduce the transverse dielectric wakes?
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A higher plasma density screens wakes more effectively
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Reasoning
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Experimental_Observation_of_Space-Charge_Field_Screening.pdf
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$$ \\begin{array} { r } { \\left[ ( 1 + \\nu _ { z } ) \\vec { W } _ { \\perp } - \\nu _ { z } \\vec { E } _ { i \\perp } + ( 1 - \\nu _ { z } ) \\vec { E _ { b \\perp } } \\right] \\Big | _ { \\partial \\Omega } = 0 , } \\end{array} $$ where $\\vec { \\pmb { W } } _ { \\perp }$ is the transverse plasma wake field and $\\vec { E } _ { i \\perp }$ and $\\vec { E } _ { b \\perp }$ are the transverse electric fields for ion column and the driver beam, respectively. The velocities of plasma electrons can be approximated by assuming that the return current sheath extends to one plasma skin depth, $k _ { p } ^ { - 1 }$ . Consequently, the longitudinal velocity, $\\nu _ { z }$ , is given by $\\nu _ { z } = \\lambda _ { b } / ( \\pi ( a _ { p } + 1 ) ( b _ { p } + 1 ) )$ , where $\\lambda _ { b }$ is the beam charge per unit length.
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expert
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For a given transverse beam offset, would a higher of lower plasma density be preferred to reduce the transverse dielectric wakes?
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A higher plasma density screens wakes more effectively
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Reasoning
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Experimental_Observation_of_Space-Charge_Field_Screening.pdf
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Figure 4 shows the position of the centroid at $t = 3 . 6$ ps (a), 4.1 ps (b), and 4.6 ps (c) behind the front of the bunch as a function of $n _ { P E }$ , for three misalignment distances (see Legend). The displacement, which is due to the effect of the dielectric wakefields, decreases when increasing $n _ { P E }$ because the amplitude of the space-charge field reaching the dielectric surface is progressively more screened by plasma. The trend is in good agreement with the typical exponential decay expected from plasma screening. The solid lines show the result of the fit for each dataset, where the distance from the bunch to the dielectric surface is considered as a free parameter. For $X = 0 . 3 7 5 ~ \\mathrm { m m }$ (black points), full screening (i.e., centroid position in agreement with the aligned case with no plasma) occurs for $n _ { P E } > 0 . 7 \\times 1 0 ^ { 1 6 } ~ \\mathrm { c m } ^ { - 3 }$ (black dashed vertical line), corresponding to $\\delta < 0 . 0 6 3 ~ \\mathrm { m m }$ , that is ${ \\sim } 1 0$ times shorter than the distance between the bunch and capillary surface $R _ { c } - X = 0 . 6 2 5 ~ \\mathrm { m m }$ . For smaller misalignments, screening occurs at lower $n _ { P E }$ : for $R _ { c } - X = 0 . 7 5 0 \\mathrm { m m }$ , $n _ { P E } > 0 . 5 \\times 1 0 ^ { 1 6 } \\mathrm { c m } ^ { - 3 }$ $\\mathrm { \\delta \\delta < 0 . 0 7 5 m m }$ , red points and dashed vertical line); and for $R _ { c } - X = 0 . 8 7 5 \\mathrm { m m }$ , $n _ { P E } > 0 . 2 4 \\times 1 0 ^ { 1 6 } \\mathrm { c m } ^ { - 3 }$ $\\delta < 0 . 1 0 9 \\mathrm { m m }$ , blue points and dashed vertical line). As expected from the screening process, $\\delta$ must be much shorter than the distance between the bunch and dielectric surface to obtain full screening. We also note that the ratio $( R _ { c } - X ) / \\delta$ at full screening increases when the misalignment increases. This is likely due to the finite transverse size of the bunch, as some particles are closer to the dielectric material than those at the bunch center.
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For a given transverse beam offset, would a higher of lower plasma density be preferred to reduce the transverse dielectric wakes?
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A higher plasma density screens wakes more effectively
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Reasoning
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Experimental_Observation_of_Space-Charge_Field_Screening.pdf
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Thus, when a bunch travels with transverse offset $( x , y )$ , parallel to its axis, it drives transverse dipolar wakefields along the bunch described by [16]: $\\begin{array} { r } { W _ { \\perp } ( t ) = w ( x , y ) \\int _ { 0 } ^ { t } n _ { b } ( t ) d t } \\end{array}$ , where the bunch front is at $t = 0$ . The amplitude of the wakefields follows the same trend as the running integral of the bunch charge: particles in the back of the bunch are deflected more strongly than those in the front. The polarity of $W _ { \\perp }$ is such that the trailing particles are pulled further toward the dielectric material [19]. Dielectric capillaries are common tools for generating plasmas in plasma wakefield accelerators (PWFA), as they enable gas injection in a high-vacuum environment [20]. The plasma is generated by ionizing the gas injected in the capillary with a high-voltage discharge applied between electrodes at each end [21], or with an ionization field such as a high-intensity laser pulse [22] or a relativistic charged particle bunch [23]. Capillaries are also employed because they allow shaping the transverse and longitudinal profiles of the plasma density [24], and locally injecting different gas species for various injection schemes [25].
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For a given transverse beam offset, would a higher of lower plasma density be preferred to reduce the transverse dielectric wakes?
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A higher plasma density screens wakes more effectively
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Reasoning
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Experimental_Observation_of_Space-Charge_Field_Screening.pdf
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The dielectric capillary has radius $R _ { c } = 1 ~ \\mathrm { m m }$ and length $L = 1 0 ~ \\mathrm { c m }$ . The plasma is generated by a discharge pulse ${ \\sim } 4 5 5$ A peak current) flowing through the capillary after the introduction of hydrogen gas ${ \\sim } 1 0$ mbar) through a high-speed solenoid valve. The capillary is installed in a vacuum chamber connected to the linac with a windowless, three-stage differential pumping system. The latter ensures that $1 0 ^ { - 8 }$ mbar is maintained in the linac, while flowing the gas, and to preserve the quality of the electron bunch. By varying the delay between the bunch arrival time and the peak of the discharge pulse we vary $n _ { P E }$ , due to recombination of the plasma. We measure the average $n _ { P E }$ with the Stark broadening technique [32] between 0.65 and $2 . 6 5 ~ \\mu \\mathrm { s }$ after the peak of the discharge pulse, and we extrapolate the values of $n _ { P E }$ (with ${ \\sim } 1 0 \\%$ uncertainty) at the delays used in the experiment (between 5.60 and $1 0 . 1 0 ~ \\mu \\mathrm { s } ^ { \\prime }$ ) by fitting the measured values with an exponential decay function [33]. The plasma electron density is essentially constant along the capillary (see Supplemental Material [34]), but nonuniformities are present at the two extremes because the gas flow expands in the vacuum chamber. However, as no capillary material is present, there is also no dielectric wakefield effect along the entrance and exit ramps. Thus, in the following we neglect these nonuniformities.
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For a given transverse beam offset, would a higher of lower plasma density be preferred to reduce the transverse dielectric wakes?
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A higher plasma density screens wakes more effectively
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Reasoning
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Experimental_Observation_of_Space-Charge_Field_Screening.pdf
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\\*Contact author: [email protected] [1] F. F. Chen, Introduction to Plasma Physics and Controlled Fusion (Springer International Publishing, New York, 2016). [2] F. Otsuka, T. Hada, S. Shinohara, and T. Tanikawa, Penetration of a radio frequency electromagnetic field into a magnetized plasma: One-dimensional pic simulation studies, Earth Planets Space 67, 85 (2015). [3] S. Shinohara and K. P. Shamrai, Effect of electrostatic waves on a rf field penetration into highly collisional helicon plasmas, Thin Solid Films 407, 215 (2002). [4] T. Shoji, Description of radio-frequency plugging and heating in terms of plasma impedance, J. Phys. Soc. Jpn. 49, 327 (1980). [5] D. A. Whelan and R. L. Stenzel, Electromagnetic-wave excitation in a large laboratory beam-plasma system, Phys. Rev. Lett. 47, 95 (1981). [6] P. Chen, J. M. Dawson, R. W. Huff, and T. Katsouleas, Acceleration of electrons by the interaction of a bunched electron beam with a plasma, Phys. Rev. Lett. 54, 693 (1985). [7] R. Keinigs and M. E. Jones, Two-dimensional dynamics of the plasma wakefield accelerator, Phys. Fluids 30, 252 (1987). [8] J. D. Jackson, Classical Electrodynamics (John Wiley & Sons, New York, 1962). [9] K. L. Bane, P. B. Wilson, and T. Weiland, Wake fields and wake field acceleration, AIP Conf. Proc. 127, 875 (1985).
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How do bound states in the continuum (BICs) enhance Smith-Purcell radiation?
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BICs offer high-Q resonances embedded in the radiation continuum, creating large modal overlaps and enabling emission rates to diverge when phase-matched with electron trajectories.
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Reasoning
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Maximal_spontaneous_photon_emission_and_energy_loss_from_free_electrons.pdf
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File Name:SCATTERED_SPECTRA_FROM_INVERSE_COMPTON_SOURCES.pdf SCATTERED SPECTRA FROM INVERSE COMPTON SOURCESOPERATING AT HIGH LASER FIELDS ANDHIGH ELECTRON ENERGIES B. Terzi!‚Üí, E. Breen, P. Rogers, R. Shahan, E. Johnson, G. A. Kra"t1 Old Dominion University, Norfolk, Virginia, USA G. Wilson, Regent University, Virginia Beach, Virginia, USA 1 also at Thomas Je"erson National Accelerator Facility, Newport News, Virginia, USA Abstract As inverse Compton X-ray and gamma-ray sources become more prevalent, to understand their performance in a precise way it becomes important to be able to compute the distribution of scattered photons precisely. An ideal model would: (1) include the full Compton e"ect frequency relations between incident and scattered photons, (2) allow the field strength to be large enough that nonlinear e"ects are captured, and (3) incorporate the e"ects of electron beam emittance. Various authors have considered various pieces of this problem, but until now no analytical or numerical procedure is known to us that captures these three e"ects simultaneously. Here we present a model for spectrum calculations that does simultaneously cover these aspects. The model is compared to a published full quantum mechanical calculation and found to agree for a case where both full Compton e"ect and nonlinear field strength are present. We use this model to investigate chirping prescriptions to mitigate ponderomotive broadening.
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How do bound states in the continuum (BICs) enhance Smith-Purcell radiation?
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BICs offer high-Q resonances embedded in the radiation continuum, creating large modal overlaps and enabling emission rates to diverge when phase-matched with electron trajectories.
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Reasoning
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Maximal_spontaneous_photon_emission_and_energy_loss_from_free_electrons.pdf
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Table: Caption: Table 1: RMS emittances for an $1 8 \\mathrm { G e V }$ ESR lattice with fractional tunes $( \\boldsymbol { Q _ { x } } , \\boldsymbol { Q _ { y } } , \\boldsymbol { Q _ { s } } ) = ( 0 . 1 2 , 0 . 1 0 , 0 . 0 5 )$ . Body: <html><body><table><tr><td></td><td>Ea,RMs [nm]</td><td>E b,RMs [nm]</td></tr><tr><td>Analytical</td><td>27.7</td><td>~0</td></tr><tr><td>1st Order Map Tracking</td><td>27.7</td><td>~0</td></tr><tr><td>2nd Order Map Tracking</td><td>31.4</td><td>2.4</td></tr><tr><td>3rd Order Map Tracking</td><td>28.9</td><td>10.6</td></tr><tr><td>Bmad Tracking</td><td>28.7</td><td>12.3</td></tr><tr><td>PTC Tracking</td><td>28.8</td><td>12.3</td></tr></table></body></html> Figure 2 shows the vertical core emittances as a function of the number of particles included in the core. For the tracking that includes the most nonlinear effects (Bmad, PTC and $3 ^ { \\mathrm { r d } }$ order map tracking) $\\epsilon _ { b }$ is about $5 \\mathrm { n m }$ which is significantly larger than the linear radiation-integral prediction. It should 14 -Analytical Bmad Tracking (AllNonlinear) 12 \\*Bmad Tracking W/lst Order Rotator Quads ‚òÖBmad Tracking w/ 2nd Order Rotator Quads 10 Bmad Trackingw/3rd OrderRotator Quads ÁõÆ 8 G 6 2 (\\*xrx_x_xx1vx_xxxxxepeeeeexxgx_X√ó√ó 20 40 60 80 100 $\\%$ Particles Included in Core be noted that for $2 ^ { \\mathrm { n d } }$ order tracking the distribution remains Gaussian (the core emittance is constant regardless of cutoff percent). However, $\\epsilon _ { b } \\approx 2 \\ : \\mathrm { n m }$ in this case. This strongly suggests that there is some nonlinear effect present that blows up the beam vertically even in the core.
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How do bound states in the continuum (BICs) enhance Smith-Purcell radiation?
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BICs offer high-Q resonances embedded in the radiation continuum, creating large modal overlaps and enabling emission rates to diverge when phase-matched with electron trajectories.
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Reasoning
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Maximal_spontaneous_photon_emission_and_energy_loss_from_free_electrons.pdf
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The first of the coupled equations describes the change of energy due to a longitudinal electric field caused by a gradient of the charge distribution. The second equation can be rewritten as $d z _ { i } / d s = \\eta _ { i } / \\gamma ^ { 2 }$ meaning that relativistic particles with an energy offset change their longitudinal position due to a velocity mismatch. Figure 3 shows an example of the squared bunching factor $| b _ { 1 0 } | ^ { 2 }$ as function of $R _ { 5 6 }$ and drift length for a moderate peak current of $7 0 0 \\mathrm { A }$ (before density modulation). Along the $R _ { 5 6 }$ axis, the first maximum occurs for optimum density modulation. The Ǡth maximum results from a modulation with two density maxima which are $( n - 1 ) \\lambda _ { \\mathrm { L } } / 1 0$ apart as illustrated by Fig. 4 for $n \\leq 3$ . The bunching factor decreases strongly over a drift length of $2 0 \\mathrm { m }$ , but the LSC-induced reduction is different for each maximum, causing their relative height to change. Furthermore, the maxima are slightly shifted to lower $R _ { 5 6 }$ with increasing drift length because the LSC effect causes additional longitudinal dispersion.
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How do bound states in the continuum (BICs) enhance Smith-Purcell radiation?
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BICs offer high-Q resonances embedded in the radiation continuum, creating large modal overlaps and enabling emission rates to diverge when phase-matched with electron trajectories.
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Reasoning
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Maximal_spontaneous_photon_emission_and_energy_loss_from_free_electrons.pdf
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Example of radiation spectra from CR and CB can be observed in Fig. 1. This experiment was conducted at the Mainzer Mikrotron (MAMI), where a beam of electrons of $6 0 0 \\mathrm { M e V }$ impinges on a $0 . 3 1 \\mathrm { m m }$ thick diamond crystal along the (110) plane at various angles. Directly at angle $0 \\mu \\mathrm { r a d }$ , the channeling condition is respected, showcasing a peak at low energy. At increasing angles, the peak position shifts towards harder photon’s energies. Indeed the periodicity of particle’s motion under CB depends on the incidence angle, $\\theta$ , as $d / \\theta$ , where $d$ is the interplanar distance. At larger $\\theta$ , the period is smaller, thereby leading to harder photon energies, but lower intensities. CB is currently used in different facilities to generate linearly polarized hard gamma-rays [5]. On the other hand, even if CR is more intense than CB in the $\\mathbf { M e V }$ region and may found application in, for instance, medical physics [6], its utilization for applications is still absent. Bent Crystals Bent crystals have attracted considerable attention for their beam deflection properties, which are critical in applications such as beam collimation and extraction in current and future colliders [7]. Recent research has expanded to include the study of radiation emissions from $e ^ { + }$ and $e ^ { - }$ in these settings [8]. In bent crystals, a unique phenomenon known as volume reflection (VR) occurs. VR involves the reflection of a particle’s trajectory off the bent crystal planes when the incidence angle slightly exceeds the Lindhard angle [9]. This process affects particles that are not channeled, termed over-barrier particles, and is notably immune to dechanneling. Consequently, VR provides higher deflection efficiency than channeling, although the deflection angles are similar to those observed in $\\theta _ { c }$ . However, VR’s efficiency is often moderated by volume capture (VC), a process where overbarrier particles become trapped in a channeling state due to incoherent scattering with lattice atoms at points near the crystal’s reflective surface.
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How do bound states in the continuum (BICs) enhance Smith-Purcell radiation?
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BICs offer high-Q resonances embedded in the radiation continuum, creating large modal overlaps and enabling emission rates to diverge when phase-matched with electron trajectories.
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Reasoning
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Maximal_spontaneous_photon_emission_and_energy_loss_from_free_electrons.pdf
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As an example from [18], Fig. 3 the simulation of the radiation emission probability by a $1 0 \\mathrm { G e V }$ positron beam with $3 0 \\mu \\mathrm { r a d }$ of divergence on silicon CU with $\\lambda _ { u } = 3 3 4 \\mu \\mathrm { m }$ , amplitude $A = 1 . 2 8 \\mathrm { n m }$ and strength parameter $k = 0 . 4 6$ . The amplitude A surpasses the interplanar spacing d, aligning with the requirements for a feasible CU in regimes of large amplitude and period [14]. The spectrum in Fig. 3 shows a pronounced peak at approximately $1 . 5 \\mathrm { M e V }$ , markedly higher—over twentyfold—than the radiation from an equivalent amorphous silicon sample within the $0 . 5 \\mathrm { M e V }$ to $2 \\mathrm { M e V }$ range. All this kind of $\\mathbf { \\boldsymbol { X } }$ and $\\gamma$ -ray sources based on oriented crystals should be compared to the others already existing in the literature. The most promising of which is ICS, where an intense laser beam of visible or near-infrared photons is scattered off an electron beam with typically a few hundred MeV energy. Crystal-based sources offer cost advantages, as they do not necessitate powerful, short-pulse laser systems.
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How do bound states in the continuum (BICs) enhance Smith-Purcell radiation?
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BICs offer high-Q resonances embedded in the radiation continuum, creating large modal overlaps and enabling emission rates to diverge when phase-matched with electron trajectories.
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Reasoning
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Maximal_spontaneous_photon_emission_and_energy_loss_from_free_electrons.pdf
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Table: Caption: Table 1: STAR Parameters Body: <html><body><table><tr><td colspan="2">Electron beam parameters</td></tr><tr><td>Energy (MeV) Bunch charge (pC)</td><td>140 500</td></tr><tr><td>Energy spread (rms, %)</td><td>0.24</td></tr><tr><td>E n,x,y (mm mrad)</td><td>1.32</td></tr><tr><td>ge,x,y(μm)</td><td>18</td></tr><tr><td></td><td>0.66</td></tr><tr><td>Bunch length (rms,mm)</td><td></td></tr><tr><td>Laser pulse parameters</td><td>5</td></tr><tr><td>Interaction angle (deg) Pulse Energy (J)</td><td>0.5</td></tr><tr><td>Wave length (nm)</td><td>1030</td></tr><tr><td></td><td></td></tr><tr><td>σl,x,y(μm)</td><td>10</td></tr><tr><td>Pulse length (rms, ps)</td><td>1</td></tr></table></body></html> THEORETICAL APPROACH In the field of Compton backscattering (CBS) or inverse Compton scattering (ICS), the spectrum of scattered photons depends on various parameters of the initial electron bunch and laser pulse. The spectral bandwidth can be approximated by the scaling laws shown in Equation 1, $$ \\frac { \\delta E _ { p h } } { E _ { p h } } = \\sqrt { \\left( \\frac { \\sigma _ { \\theta } } { E _ { \\theta } } + \\frac { \\sigma _ { \\varepsilon } } { E _ { \\varepsilon } } \\right) ^ { 2 } + \\left( \\frac { \\sigma _ { L } } { E _ { L } } \\right) ^ { 2 } + \\left( \\frac { \\sigma _ { \\gamma } } { E _ { \\gamma } } \\right) ^ { 2 } } $$ where each term represents a corresponding contribution by kinematics of scattering $\\left( { \\frac { \\sigma _ { \\theta } } { E _ { \\theta } } } \\right)$ , emittance $\\left( \\frac { \\sigma _ { \\varepsilon } } { E _ { \\varepsilon } } \\right)$ , laser bandwidth $\\left( { \\frac { \\sigma _ { L } } { E _ { L } } } \\right)$ and energy spread of electrons $\\left( \\frac { \\sigma _ { \\gamma } } { E _ { \\gamma } } \\right)$ A more detailed discussion of this formula can be found in the works [8, 9].
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How do bound states in the continuum (BICs) enhance Smith-Purcell radiation?
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BICs offer high-Q resonances embedded in the radiation continuum, creating large modal overlaps and enabling emission rates to diverge when phase-matched with electron trajectories.
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Reasoning
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Maximal_spontaneous_photon_emission_and_energy_loss_from_free_electrons.pdf
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$$ where $\\omega _ { c }$ is the critical frequency defined at half power spectrum, $E _ { 0 }$ is the particle energy, $\\gamma$ is the relativistic factor, $\\boldsymbol { a }$ is the fine structure constant and $r _ { e }$ is the electron’s classical radius. For $\\Upsilon \\gg 1$ , the photon spectrum is given by the SokolovTernov formula, which truncates the photon energy at $E _ { \\gamma } =$ $E _ { 0 }$ as opposed to the classical formula which extends infinitely [11] (Fig. 2a). $$ \\frac { d N _ { \\gamma } } { d \\bar { x } } = \\frac { \\alpha } { \\sqrt { 3 } \\pi \\gamma ^ { 2 } } \\left[ \\frac { \\hbar \\omega } { E } \\frac { \\hbar \\omega } { E - \\hbar \\omega } K _ { 2 / 3 } ( \\bar { x } ) + \\int _ { \\bar { x } } ^ { \\infty } K _ { 5 / 3 } ( x ^ { \\prime } ) d x ^ { \\prime } \\right] $$ where $\\bar { x } = \\omega / \\omega _ { c } \\cdot E _ { 0 } / ( E _ { 0 } - \\hbar \\omega ) \\propto 1 / \\Upsilon$ is the modified frequency ratio, and $K _ { i }$ is the modified Bessel function of order $i$ .
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IPAC
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How do bound states in the continuum (BICs) enhance Smith-Purcell radiation?
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BICs offer high-Q resonances embedded in the radiation continuum, creating large modal overlaps and enabling emission rates to diverge when phase-matched with electron trajectories.
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Reasoning
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Maximal_spontaneous_photon_emission_and_energy_loss_from_free_electrons.pdf
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Turning on the effect of ideal Siberian snakes fixes the closed-orbit spin tune at $\\nu _ { 0 } ~ = ~ 1 / 2$ , which prevents the crossing of any 1st-order intrinsic resonances. Nevertheless, higher-order intrinsic resonances can be crossed by large-amplitude particles for which the spin tune deviates from _x0012__x0010__x0013_ [5]. Polarization tends to be reduced in two energy regions during the ramps of RHIC. These are energy regions where strong $1 ^ { \\mathrm { s t } }$ -order resonances would be crossed without Siberian snakes. Upon focusing around the vicinity of the second strongest of these regions and increasing the vertical emittance, we find strong dips in the equilibrium polarization of the ISF. As seen in Fig. 2, associated with these dips are spin tune jumps whose size determines twice the resonance strength (at that orbital amplitude). While in other regions the ADST is a smooth function of energy, here several jumps can be observed, showing that nonlinear depolarizing resonances are crossed, even though the closed orbit spin tune $\\boldsymbol { \\nu } _ { 0 }$ remains _x0012__x0010__x0013_ at all times. Resonance conditions are indicated by horizontal lines, and it is evident that the spin tune jumps symmetrically across resonance lines.
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1
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NO
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Expert
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How do bound states in the continuum (BICs) enhance Smith-Purcell radiation?
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BICs offer high-Q resonances embedded in the radiation continuum, creating large modal overlaps and enabling emission rates to diverge when phase-matched with electron trajectories.
|
Reasoning
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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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NO
| 0
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Expert
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How do bound states in the continuum (BICs) enhance Smith-Purcell radiation?
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BICs offer high-Q resonances embedded in the radiation continuum, creating large modal overlaps and enabling emission rates to diverge when phase-matched with electron trajectories.
|
Reasoning
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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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4
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NO
| 1
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Expert
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How do bound states in the continuum (BICs) enhance Smith-Purcell radiation?
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BICs offer high-Q resonances embedded in the radiation continuum, creating large modal overlaps and enabling emission rates to diverge when phase-matched with electron trajectories.
|
Reasoning
|
Maximal_spontaneous_photon_emission_and_energy_loss_from_free_electrons.pdf
|
Finally, we turn our attention to an ostensible peculiarity of the limits: equation (4) evidently diverges for lossless materials $( \\mathrm { I m } \\chi \\to 0 ) \\dot { { \\frac { . } { . } } }$ ), seemingly providing little insight. On the contrary, this divergence suggests the existence of a mechanism capable of strongly enhancing Smith–Purcell radiation. Indeed, by exploiting high-Q resonances near bound states in the continuum (BICs)13 in photonic crystal slabs, we find that Smith–Purcell radiation can be enhanced by orders of magnitude, when specific frequency-, phaseand polarization-matching conditions are met. A 1D silicon $\\left( \\chi = 1 1 . 2 5 \\right)$ -on-insulator $\\mathrm { \\ S i O } _ { 2 } ,$ $\\chi = 1 . 0 7 \\$ ) grating interacting with a sheet electron beam illustrates the core conceptual idea most clearly. The transverse electric (TE) $( E _ { x } , H _ { y } , E _ { z } )$ band structure (lowest two bands labelled $\\mathrm { T E } _ { 0 }$ and $\\mathrm { T E } _ { 1 . } ^ { \\cdot }$ ), matched polarization for a sheet electron beam (supplementary equation S41b)), is depicted in Fig. 4b along the $\\Gamma { \\mathrm { - } } \\mathrm { X }$ direction. Folded electron wavevectors, $k _ { \\nu } = \\omega / \\nu ,$ are overlaid for two distinct velocities (blue and green). Strong electron–photon interactions are possible when the electron and photon dispersions intersect: for instance, $k _ { \\nu }$ and the $\\mathrm { T E } _ { 0 }$ band intersect (grey circles) below the air light cone (light yellow shading). However, these intersections are largely impractical: the $\\mathrm { T E } _ { 0 }$ band is evanescent in the air region, precluding free-space radiation. Still, analogous ideas, employing similar partially guided modes, such as spoof plasmons33, have been explored for generating electron-enabled guided waves34,35.
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1
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NO
| 0
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Expert
|
How do bound states in the continuum (BICs) enhance Smith-Purcell radiation?
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BICs offer high-Q resonances embedded in the radiation continuum, creating large modal overlaps and enabling emission rates to diverge when phase-matched with electron trajectories.
|
Reasoning
|
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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4
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NO
| 1
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IPAC
|
How do bound states in the continuum (BICs) enhance Smith-Purcell radiation?
|
BICs offer high-Q resonances embedded in the radiation continuum, creating large modal overlaps and enabling emission rates to diverge when phase-matched with electron trajectories.
|
Reasoning
|
Maximal_spontaneous_photon_emission_and_energy_loss_from_free_electrons.pdf
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For ELI-NP parameters (Table 1), the e#cacy of FM is evaluated as a function of $a _ { 0 }$ . The results in Fig. 6 show close to perfect recovery of the peak spectral density at $a _ { 0 } = 1$ . CONCLUSION Accurate computation of scattered spectra from ICS operating in the nonlinear Compton regime requires properly accounting for nonlinearities due to both the electron recoil and the high laser field strength (Fig. 5). The e"ects are non-additive, and cannot be simply obtained from codes addressing these nonlinearities individually. We have confirmed that the interference peaks associated with ponderomotive broadening tend to be washed out when the full emittance and energy spread of the beam are included in the calculation (Fig. 4). As before [1, 6], we find that even in the nonlinear Compton regime, chirping of the laser pulse significantly improves the spectral property of the emitted radiation. ACKNOWLEDGMENTS This work is authored by Je"erson Science Associates, LLC under U.S. Department of Energy (DOE) Contract No. DE-AC05-06OR23177. The U.S. Government retains a nonexclusive, paid-up, irrevocable, world-wide license to publish or reproduce this manuscript for U.S. Government purposes. We acknowledge the support by the US National Science Foundation, through CAREER Grant No. 1847771 and Research Experience for Undergraduates at Old Dominion University Grant No. 1950141.
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1
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NO
| 0
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Expert
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How do bound states in the continuum (BICs) enhance Smith-Purcell radiation?
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BICs offer high-Q resonances embedded in the radiation continuum, creating large modal overlaps and enabling emission rates to diverge when phase-matched with electron trajectories.
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Reasoning
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Maximal_spontaneous_photon_emission_and_energy_loss_from_free_electrons.pdf
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Author contributions Y.Y., O.D.M., I.K. and M.S. conceived the project. Y.Y. developed the analytical models and numerical calculations. A.M. prepared the sample under study. Y.Y., A.M., C.R.-C., S.E.K. and I.K. performed the experiment. Y.Y., T.C. and O.D.M. analysed the asymptotics and bulk loss of the limit. S.G.J., J.D.J., O.D.M., I.K. and M.S. supervised the project. Y.Y. wrote the manuscript with input from all authors. Competing interests The authors declare no competing interests. Additional information Supplementary information is available for this paper at https://doi.org/10.1038/ s41567-018-0180-2. Reprints and permissions information is available at www.nature.com/reprints. Correspondence and requests for materials should be addressed to Y.Y. or O.D.M. or I.K. Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Methods Fourier transform convention. Throughout the paper, we adopt the following Fourier transform conventions $$ f ( \\omega ) \\triangleq \\int f ( t ) \\mathrm { e } ^ { i \\omega t } \\mathrm { d } t , f ( t ) \\triangleq \\frac { 1 } { 2 \\pi } \\int f ( \\omega ) \\mathrm { e } ^ { - i \\omega t } \\mathrm { d } \\omega $$ $$
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augmentation
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NO
| 0
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Expert
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How do bound states in the continuum (BICs) enhance Smith-Purcell radiation?
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BICs offer high-Q resonances embedded in the radiation continuum, creating large modal overlaps and enabling emission rates to diverge when phase-matched with electron trajectories.
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Reasoning
|
Maximal_spontaneous_photon_emission_and_energy_loss_from_free_electrons.pdf
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The Smith–Purcell effect epitomizes the potential of free-electron radiation. Consider an electron at velocity $\\beta = \\nu / c$ traversing a structure with periodicity $a$ ; it generates far-field radiation at wavelength $\\lambda$ and polar angle $\\theta$ , dictated by2 $$ \\lambda = \\frac { a } { m } \\left( \\frac { 1 } { \\beta } - \\mathrm { c o s } \\theta \\right) $$ where $m$ is the integer diffraction order. The absence of a minimum velocity in equation (1) offers prospects for threshold-free and spectrally tunable light sources, spanning from microwave and terahertz14–16, across visible17–19, and towards $\\bar { \\mathrm { X - r a y } } ^ { 2 0 }$ frequencies. In stark contrast to the simple momentum-conservation determination of wavelength and angle, there is no unified yet simple analytical equation for the radiation intensity. Previous theories offer explicit solutions only under strong assumptions (for example, assuming perfect conductors or employing effective medium descriptions) or for simple, symmetric geometries21–23. Consequently, heavily numerical strategies are often an unavoidable resort24,25. In general, the inherent complexity of the interactions between electrons and photonic media have prevented a more general understanding of how pronounced spontaneous electron radiation can ultimately be for arbitrary structures, and consequently, how to design the maximum enhancement for free-electron light-emitting devices.
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augmentation
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NO
| 0
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Expert
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How do bound states in the continuum (BICs) enhance Smith-Purcell radiation?
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BICs offer high-Q resonances embedded in the radiation continuum, creating large modal overlaps and enabling emission rates to diverge when phase-matched with electron trajectories.
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Reasoning
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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 ) $$ The function ${ \\mathcal { G } } ( { \\boldsymbol { \\beta } } , k d )$ is an azimuthal integral (see Supplementary Section 3) over the Meijer G-function $G _ { 1 , 3 } ^ { 3 , 0 }$ (ref. $^ { 3 2 } )$ that arises in the radial integration of the modified Bessel functions $K _ { n }$ . We emphasize that equation (6) is a specific case of equation (4) for grating structures without any approximations and thus can be readily generalized to multi-material scenarios (see Supplementary equation (37)).
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augmentation
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NO
| 0
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Expert
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How do bound states in the continuum (BICs) enhance Smith-Purcell radiation?
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BICs offer high-Q resonances embedded in the radiation continuum, creating large modal overlaps and enabling emission rates to diverge when phase-matched with electron trajectories.
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Reasoning
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Maximal_spontaneous_photon_emission_and_energy_loss_from_free_electrons.pdf
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$$ written in cylindrical coordinates $( x , \\rho , \\psi )$ ; here, $K _ { n }$ is the modified Bessel function of the second kind, $k _ { \\nu } = \\omega / \\nu$ and $k _ { \\rho } = \\sqrt { k _ { \\nu } ^ { 2 } - k ^ { 2 } } =$ k/βγ $\\scriptstyle ( k = \\omega / c$ , free-space wavevector; $\\gamma = 1 / \\sqrt { 1 - \\beta ^ { 2 } }$ , Lorentz factor). Hence, the photon emission and energy loss of free electrons can be treated as a scattering problem: the electromagnetic fields $\\mathbf { F } _ { \\mathrm { i n c } } { = } ( \\mathbf { E } _ { \\mathrm { i n c } } , \\ Z _ { 0 } \\mathbf { H } _ { \\mathrm { i n c } } ) ^ { \\mathrm { T } }$ (for free-space impedance $Z _ { 0 } ^ { \\mathrm { ~ \\tiny ~ { ~ \\chi ~ } ~ } }$ are incident on a photonic medium with material susceptibility $\\overline { { \\overline { { \\chi } } } }$ (a $6 { \\times } 6$ tensor for a general medium), causing both absorption and far-field scattering—that is, photon emission—that together comprise electron energy loss (Fig. 1a).
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augmentation
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NO
| 0
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Expert
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How do bound states in the continuum (BICs) enhance Smith-Purcell radiation?
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BICs offer high-Q resonances embedded in the radiation continuum, creating large modal overlaps and enabling emission rates to diverge when phase-matched with electron trajectories.
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Reasoning
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Maximal_spontaneous_photon_emission_and_energy_loss_from_free_electrons.pdf
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g ( \\mathbf { k } ) \\triangleq \\int f ( \\mathbf { r } ) \\mathrm { e } ^ { - i \\mathbf { k } \\cdot \\mathbf { r } } \\mathrm { d } \\mathbf { r } , g ( \\mathbf { r } ) \\triangleq \\frac { 1 } { \\left( 2 \\pi \\right) ^ { 3 } } \\int g ( \\mathbf { k } ) \\mathrm { e } ^ { i \\mathbf { k } \\cdot \\mathbf { r } } \\mathrm { d } \\mathbf { k } $$ Numerical methods. The photonic band structure in Fig. 4b is calculated via the eigenfrequency calculation in COMSOL Multiphysics. Numerical radiation intensities (Figs. 1d,e, 2b,c, 3d and 4d–f) are obtained via the frequency-domain calculation in the radiofrequency module in COMSOL Multiphysics. A surface (for 3D problems) or line (for 2D problems) integral on the Poynting vector is calculated to extract the radiation intensity at each frequency. Experimental set-up and sample fabrication. Our experimental set-up comprises a conventional SEM with the sample mounted perpendicular to the stage. A microscope objective was placed on the SEM stage to collect and image the light emission from the surface. The collected light was then sent through a series of
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augmentation
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NO
| 0
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Expert
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How do bound states in the continuum (BICs) enhance Smith-Purcell radiation?
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BICs offer high-Q resonances embedded in the radiation continuum, creating large modal overlaps and enabling emission rates to diverge when phase-matched with electron trajectories.
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Reasoning
|
Maximal_spontaneous_photon_emission_and_energy_loss_from_free_electrons.pdf
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The grating limit (equation (6)) exhibits the same asymptotics as equations (5a) and (5b), thereby reinforcing the optimal-velocity predictions of Fig. 1c. The $( \\beta , k \\dot { d } )$ dependence of $\\mathcal { G }$ (see Fig. 2a) shows that slow (fast) electrons maximize Smith–Purcell radiation in the small (large) separation regime. We verify the limit predictions by comparison with numerical simulations: at small separations (Fig. 2b), radiation and energy loss peak at velocity $\\beta \\approx 0 . 1 5$ , consistent with the limit maximum; at large separations (Fig. 2c), both the limit and the numerical results grow monotonically with $\\beta$ . The derived upper limit also applies to Cherenkov and transition radiation, as well as bulk loss in electron energy-loss spectroscopy. For these scenarios where electrons enter material bulk, a subtlety arises for the field divergence along the electron’s trajectory $( \\rho = 0$ in equation (2)) within a potentially lossy medium. This divergence, however, can be regularized by introducing natural, system-specific momentum cutoffs26, which then directly permits the application of our theory (see Supplementary Section 6). Meanwhile, there exist additional competing interaction processes (for example, electrons colliding with individual atoms). However, they typically occur at much smaller length scales.
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augmentation
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NO
| 0
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Expert
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How do bound states in the continuum (BICs) enhance Smith-Purcell radiation?
|
BICs offer high-Q resonances embedded in the radiation continuum, creating large modal overlaps and enabling emission rates to diverge when phase-matched with electron trajectories.
|
Reasoning
|
Maximal_spontaneous_photon_emission_and_energy_loss_from_free_electrons.pdf
|
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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augmentation
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NO
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expert
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How does Carilli’s interferometric method measure beam size?
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By analyzing fringe visibilities from synchrotron light passing through a non-redundant aperture mask and fitting them to a Gaussian source model.
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Reasoning
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Carilli_2024.pdf
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The derived coherences, ie. visibility fractional amplitudes (relative to the zero spacing) corrected for the voltage gains, are show in Figure 10, for both 3-hole and 5-hole data, and listed in Table II. Gain fitting is not possible with 3-hole data since the problem becomes under-constrained, so the three hole coherences were derived assuming the 5-hole gains for illumination correction. The coherences are remarkably stable, to less than a percent. The 3-hole coherences are a few percent higher than the 5-hole data for matching baselines. This difference may relate to the assumed gains and possible different mask illumination for that particular experiment. Indeed, the fact that for one baseline on the 3-hole data some of the coherences are slightly larger than unity (which is unphysical), suggests the assumed gains may not be quite correct. A general point is that all the coherences are high, $\\geq 6 5 \\%$ , indicating that the source is only margninally resolved spatially. Columns 6 and 7 in Table II list the coherences derived after summing the 30 images taken over the 30 seconds of the time series before deriving the coherences. These data are plotted in Figure 11. If no centering at all is performed (column 6), the image wander and structural changes due to phase fluctuations across the field leads to decoherence up to $3 5 \\%$ . If image centering is performed based on the centering of the Airy disk before summing the images, the coherences increase, but remain lower than the average from each individual frame by 5% or so. Centering on the Airy disk, corresponds effectively to a ’tip-tilt’ correction, meaning correcting for a uniform phase gradient across the mask (the lowest order term in the phase screen). Decoherence is even seen when comparing 1 ms to $3 \\mathrm { m s }$ averaging (see Section V D).
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2
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Yes
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expert
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How does Carilli’s interferometric method measure beam size?
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By analyzing fringe visibilities from synchrotron light passing through a non-redundant aperture mask and fitting them to a Gaussian source model.
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Reasoning
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Carilli_2024.pdf
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dominated by a phenomenon such as CCD read noise. Figure 26 shows a plot of the mean coherences and rms of the coherences over the 30 record time series assuming no bias, and subtracting a bias of 3.7 counts per pixel. The coherences are systematically lower by about 2% with no bias subtracted, and the rms values are unchanged. Figure 27 shows a plot of the closure phases over the 30 record time series assuming no bias, and subtracting a bias of 3.7 counts per pixel. The closure phases and scatter are effectively unchanged. Overall, bias subtraction has a measurable, but not major, effect on the results of the interferometric measurements. Fortunately, the bias is directly measurable on the images, and hence we do not feel the bias is a significant source of uncertainty in our source size estimates. VI. DECOHERENCE DUE TO REDUNDANCY We demonstrate the decoherence caused by redundantly sampled visibilities using the 6-hole data. Recall that the 6-hole data has an outer square of holes, leading to two redundant baselines: the horizontal and vertical 16 mm baselines, corresponding to [0-1 + 2-5] and [0-2 + 1-5]. In the Fourier domain, these redundant baselines sample the same spatial frequency. With no phase fluctuations, these two fringes will add in phase and roughly double the visibility amplitude (modulo the gain factors). But if there is a phase difference between the two fringes, then fringe contrast, or visibility coherence, will be lower (see Figure 31).
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2
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Yes
| 0
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expert
|
How does Carilli’s interferometric method measure beam size?
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By analyzing fringe visibilities from synchrotron light passing through a non-redundant aperture mask and fitting them to a Gaussian source model.
|
Reasoning
|
Carilli_2024.pdf
|
Note that the target source size is $\\leq 6 0 \\mu m$ , which at a distance of $\\mathrm { 1 5 . 0 5 m }$ implies an angular size of $\\leq 0 . 8 4 \\$ . For comparison, the angular interferometric fringe spacing of our longest baseline in the mask of $2 2 . 6 \\mathrm { m m }$ at $5 4 0 ~ \\mathrm { n m }$ wavelength is 5”. This maximum baseline in the mask is dictated by the illumination pattern on the mask (Figure 1). Hence, for all of our measurements, the source is only marginally resolved, even on the longer baselines. However, the signal to noise is extremely high, with millions of photons in each measurement, thereby allowing size measurements on partially resolving baselines. We consider masks with 2, 3, 5, and 6 holes. The 2-hole experiment employs a $1 6 \\mathrm { m m }$ hole separation, and the mask is rotated by $4 5 ^ { o }$ and $9 0 ^ { o }$ sequentially to obtain two dimensional information, as per Torino & Irison (2016). The 3-hole mask experiment employs apertures Ap0, Ap1, and Ap2. The 5-hole experiment used all of the apertures except Ap5 (see Figure 2).
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4
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Yes
| 1
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expert
|
How does Carilli’s interferometric method measure beam size?
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By analyzing fringe visibilities from synchrotron light passing through a non-redundant aperture mask and fitting them to a Gaussian source model.
|
Reasoning
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Carilli_2024.pdf
|
Notice that, for the 6-hole mask Figure 8, the u,v data points corresponding to the vertical and horizontal 16mm baseline have roughly twice the visibility amplitude as neighboring points (and relative to the 5-hole mask). This is because these are now redundantly sampled, meaning the 16mm horizontal baseline now includes photons from 0-1 and 2-5, and 16mm vertical baseline includes 0-2 and 1-5. C. Self-calibration The self-calibration and source size fitting is described in more detail in Nikolic et al. (2024). For completeness, we summarize the gain fitting procedure and equations herein, since it is relevant to the results presented below. For computational and mathematical convenience (see Nikolic et al. 2024), the coherence is modelled as a twodimensional Gaussian function parametrised in terms of the overall width $( \\sigma )$ and the distortion in the ‘ $+ \\mathbf { \\nabla } ^ { \\prime } \\left( \\eta \\right)$ and ‘X’ $( \\rho )$ directions. Dispersion in e.g., the $u$ direction is $\\sigma / \\sqrt { 1 + \\eta }$ while in the $v$ direction it is $\\sigma / { \\sqrt { 1 - \\eta } }$ , which shows that values $\\eta$ or $\\rho$ close to $1$ indicate that one of the directions is poorly constrained.
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End of preview. Expand
in Data Studio
Accel-IR Benchmark: A Gold Standard for Particle Accelerator Physics
This repository contains the Accel-IR Benchmark, a domain-specific Information Retrieval (IR) dataset for particle accelerator physics. It was developed as part of the Master's Thesis "From Dataset to Optimization: A Benchmarking Framework for Information Retrieval in the Particle Accelerator Domain" by Qing Dai (University of Zurich, 2025), in collaboration with the Paul Scherrer Institute (PSI).
Dataset Configurations
This benchmark is available in two configurations. You can load specific versions based on your evaluation needs:
| Configuration | Rows | Description | Use Case |
|---|---|---|---|
expert_core |
390 | Purely expert-annotated pairs. Labeled by 7 domain experts (PhDs/Researchers) from PSI. | Precise evaluation against human ground truth. |
augmented |
1,357 | The expert_core + curated hard negatives. The negatives were generated using a expert-validated automatic annotation pipeline. |
Realistic IR evaluation with many more negatives than positives. |
Dataset Structure
Data Fields
Each row in the dataset represents a query-document pair with the following columns:
Source: The referenced paper or an IPAC publication, source of the chunks.Question: The domain-specific scientific question.Answer: Answer to the question.Question_type: The category of the question, simulating diverse information needs:Fact: Specific details or parameters.Definition: Explanations of concepts/terms.Reasoning: Logic behind phenomena or mechanisms.Summary: Key points or conclusions.
Referenced_file(s): Referenced papers for the questions, provided by experts.chunk_text: The text passage retrieved from domain-expert-referenced papers or IPAC conference papers.expert_annotation(Core only): The raw relevance score given by domain experts on a 5-point Likert scale:1: Irrelevant2: Partially Irrelevant3: Hard to Decide (Excluded from Core)4: Partially Relevant5: Relevant
specific to paper: Indicates if the question is "Context-Dependent" (answerable only by the referenced paper) or "General" (answerable by broader domain knowledge).Label: The binary ground truth used for evaluation metrics (nDCG/MAP).1(Relevant): Derived from expert scores 4 & 5.0(Irrelevant): Derived from expert scores 1 & 2, or pipeline hard negatives.
Creation Methodology
Expert Core:
- Created by 7 domain experts from the Electron Beam Instrumentation Group at PSI.
- Experts reviewed query-chunk pairs and annotated them on a 1-5 scale using a custom interface.
- Pairs labeled as "3 - Not Sure" were removed to ensure no ambiguity.
Augmentation (Hard Negatives):
- To simulate realistic retrieval scenarios where negatives far outnumber positives, the core dataset was augmented.
- Hard Negatives were generated using an expert-validated automatic annotation pipeline.
Usage
You can load the datasets using the Hugging Face datasets library.
Load the Expert Core (390 pairs)
from datasets import load_dataset
# Load the pure expert-annotated subset
ds_core = load_dataset("qdai/Accel-IR", "expert_core", split="test")
print(ds_core[0])
Citation
If you use this dataset, please cite:
Qing Dai, "From Dataset to Optimization: A Benchmarking Framework for Information Retrieval in the Particle Accelerator Domain", Master's Thesis, University of Zurich, 2025.
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