The plasma wakefield accelerator may accelerate particles to high energy in a future linear collider with unprecedented acceleration gradients, exceeding the GeV/m range. Beams for this application would have extremely high brightness and, subject to the intense plasma ion-derived focusing, they would achieve densities high enough to induce the plasma ions to collapse into the beam volume. This non-uniform ion density gives rise to strong nonlinear focusing which may lead to deleterious beam emittance growth. The effects of ion collapse and their mitigation has been investigated recently through particle-in-cell simulations, which show that by dynamically matching the beam to the focusing of the collapsed ion distribution, one may avoid serious emittance growth. We extend this work by exploring the near-equilibrium state of the beam-ion system reached after the ions have collapsed, a condition yielding the emittance growth mitigation observed. We show through PIC simulations and analytical theory that in this case a dual electron beam-ion Bennett-type equilibrium distribution is approached. Here, the beam and ion distributions share nearly the same shape, which generates nonlinear transverse electromagnetic fields. We exploit a Bennett-type model to study beam phase space dynamics and emittance growth over time scales much longer than permitted by PIC simulations through use of a 2D symplectic tracking code with Monte Carlo scattering based on Moliere's theory of small angle multiple scattering. We find that while phase space diffusion due to parametric excitations of the beam size due to plasma non-uniformity is negligible, scattering from collapsed ions gives rise to manageable emittance growth in the case of a linear collider. The implications of these results on experiments planned at FACET-II are examined.
The interaction of the witness beam with the surrounding plasma particles and wakefields was studied. The impli- cations of the elastic scattering process on beam emittance and, emittance evolution under the focusing and acceleration provided by plasma wakefields were discussed. Simulations results from GEANT4 are presented in this paper.
In this paper we revisit the calculation of the emittance dilution of charged particle bunches due to collimator wakefield effects in the paraxial approximation. We also compare analytical results with numerical simulations considering the example of a collimator structure installed in the Accelerator Test Facility 2 (ATF2) at KEK
Alternative acceleration technologies are currently under development for cost-effective, robust, compact and efficient solutions. One such technology is plasma wakefield acceleration, driven by either a charged particle or laser beam. However, the potential issues must be studied in detail. In this paper, the emittance growth of the witness beam through elastic scattering from gaseous media is derived. The model is compared with the numerical studies.
Demonstration of ultra-low emittance beams in a kHz laser wakefield accelerator and application to electron diffraction
Laboratoire d’Optique Appliquée (LOA), CNRS, École polytechnique, ENSTA, Institut Polytechnique de Paris（应用光学实验室，法国国家科学研究中心，巴黎综合理工学院，国立高等先进技术学院，巴黎理工学院）；Center for Physical Sciences and Technology（物理与技术中心）；Vytautas Magnus University（维陶塔斯·马格努斯大学）
The initial beam emittance determines the maximum wakefield amplitude that can be reached as a result of beam self-modulation in the plasma. The wakefield excited by the fully self-modulated beam decreases linearly with the increase of the beam emittance. There is a value of initial emittance beyond which the self-modulation does not develop even if the instability is initiated by a strong seed perturbation. The emittance scale at which the wakefield is twice suppressed with respect to the zero-emittance case (the so called critical emittance) is determined by inability of the excited wave to …
The effect of the transverse self-force in a relativistic beam has been studied in the earlier paper of the author [1]. However, the analysis of [1] missed an important observation and has lead to an incorrect estimate of the emittance growth of the beam when it passes through a long bending magnet. Here we correct that analysis. In particular, we conclude that the emittance growth due to the transverse self-force in a long bend is always much smaller than the emittance growth due to the longitudinal coherent synchrotron radiation (CSR) wake.
We investigate beam loading and emittance preservation for a high-charge electron beam being accelerated in quasi-linear plasma wakefields driven by a short proton beam. The structure of the studied wakefields are similar to those of a long, modulated proton beam, such as the AWAKE proton driver. We show that by properly choosing the electron beam parameters and exploiting two well known effects, beam loading of the wakefield and full blow out of plasma electrons by the accelerated beam, the electron beam can gain large amounts of energy with a narrow final energy spread (%-level) and without …
We discovered a novel effect that can cause witness emittance growth in plasma wakefield accelerators. The effect appears in linear or moderately nonlinear plasma waves. The witness experiences a time-varying focusing force and loses quality during the time required for the drive beam to reach transverse equilibrium with the plasma wave. The higher the witness charge, the lower the emittance growth rate because of additional focusing of the witness by its own wakefield. However, the witness head always degrades, and the boundary between degraded and intact parts gradually propagates backward a…
Next-generation plasma-based accelerators can push electron beams to GeV energies within centimetre distances. The plasma, excited by a driver pulse, is indeed able to sustain huge electric fields that can efficiently accelerate a trailing witness bunch, which was experimentally demonstrated on multiple occasions. Thus, the main focus of the current research is being shifted towards achieving a high quality of the beam after the plasma acceleration. In this letter we present beam-driven plasma wakefield acceleration experiment, where initially preformed high-quality witness beam was accelerate…
A framework for integrating transfer matrices with particle-in-cell simulations is developed for TeV staging of plasma wakefield accelerators. Using nonlinear transfer matrices in terms up to ninth order in normalized energy spread $\sqrt{\langleδγ^2\rangle}$ and deriving a compact expression for the chromatic emittance growth in terms of the nonlinear matrix, plasma wakefield accelerating stages simulated using the three-dimensional particle-in-cell framework OSIRIS 4.0 were combined to model acceleration of an electron beam from 10 GeV to 1 TeV in 85 plasma stages of meter scale-length with …
Ionization injection in a plasma wakefield accelerator was investigated experimentally using two lithium plasma sources of different lengths. The ionization of the helium gas, used to confine the lithium, injects electrons in the wake. After acceleration, these injected electrons were observed as a distinct group from the drive beam on the energy spectrometer. They typically have a charge of tens of pC, an energy spread of a few GeV, and a maximum energy of up to 30 GeV. The emittance of this group of electrons can be many times smaller than the initial emittance of the drive beam. The energy …
In the Phase 2 of the AWAKE first experimental run (from May to November 2018), an electron beam was used to probe and test proton-driven wakefield acceleration in a rubidium plasma column. In this work, we analyze the overall charge capture and shot-to-shot reproducibility of the proton-driven plasma wakefield accelerator with various electron bunch injection parameters. The witness electron bunches were produced using an RF-gun equipped with a Cs2Te photocathode illuminated by a tailorable ultrafast deep ultraviolet (UV) laser pulse. The construction of the UV beam optical system enabled app…
An active plasma lens focuses the beam in both the horizontal and vertical planes simultaneously using a magnetic field generated by a discharge current through the plasma. A beam size of 5--10 $μ$m can be achieved within a short distance using a focusing gradient on the order of 100 T/m. The active plasma lens is therefore an attractive element for plasma wakefield acceleration, because an ultra-small size of the witness electron beam is required for injection into the plasma wakefield to minimize emittance growth and to enhance the capturing efficiency. When the drive beam and witness electr…
In its normal mode of operation the Argonne Wakefield Accelerator Facility uses a high charge (10-100 nC), short pulse (3-5 psec) drive bunch to excite high-gradient accelerating fields in various slow-wave structures. To generate this bunch, we designed a 1.5 cell, L-band, rf photocathode gun with an emittance compensating solenoid to give optimal performance at high-charge; it has recently completed commissioning. More recently, we have begun to investigate the possibility of using this gun in a high-brightness, low-charge operating mode, with charge equal to approximately 1 nC, for high-pre…
Ionization injection triggered by short wavelength laser pulses inside a nonlinear wakefield driven by a longer wavelength laser is examined via multi-dimensional particle-in-cell simulations. We find that very bright electron beams can be generated through this two-color scheme in either collinear propagating or transverse colliding geometry. For a fixed laser intensity $I$, lasers with longer/shorter wavelength $λ$ have larger/smaller ponderomotive potential ($\propto I λ^2$). The two color scheme utilizes this property to separate the injection process from the wakefield excitation process.…
Emittance is a beam quality that is vital for many future applications of advanced accelerators, such as compact free-electron lasers and linear colliders. In this paper, we review the challenges of preserving the transverse emittance during acceleration, both inside and outside accelerator stages. Sources of emittance growth range from space charge and instabilities caused by transverse wakefields, which can occur in any advanced accelerator scheme regardless of medium or driver type, to sources more specific to plasma accelerators, such as mismatching, misalignment, ion motion, Coulomb scatt…
In the context of plasma wakefield acceleration beam driven, we exploit a high density charge trailing bunch whose self-fields act by mitigating the energy spread increase via beam loading compensation, together with bunch self-contain operated by the self-consistent transverse field. The work, that will be experimentally tested in the SPARC_LAB test facility, consists of a parametric scan that allows to find optimized parameters in order to preserve the high quality of the trailing bunch over the entire centimeters acceleration length, with a final energy spread increase of 0.1% and an emitta…
The effects on beam dynamics from long-range and short-range wakefields from TESLA-type cavities are considered in regard to a proposed FEL oscillator (FE-LO) operating at 120 nm. This would be driven by the Fermilab Accelerator Science and Technology (FAST) linac at 300 MeV with a 3-MHz micropulse repetition rate. Our wakefield studies showed measurable effects on submacropulse centroid stability and on submicropulse head-tail kicks that can lead to emittance degradation. In the case of the former, we use MINERVA/OPC to simulate the ~100-$μ$m centroid slew effects on the saturated output powe…
Corrugated structures have recently been widely used for manipulating electron beam longitudinal phase space and for producing THz radiation. Here we report on time-resolved measurements of the quadrupole wakefields in planar corrugated structures. It is shown that while the time- dependent quadrupole wakefield produced by a planar corrugated structure causes significant growth in beam transverse emittance, it can be effectively canceled with a second corrugated structure with orthogonal orientation. The strengths of the time-dependent quadrupole wakefields for various corrugated structure gap…
This article introduces an analytical formalism for the calculation of the evolution of beam moments and the transverse emittance for beams which are externally injected into plasma wakefield accelerators. This formalism is then applied to two scenarios with increasing complexity - a single beam slice without energy gain and a single beam slice with energy gain, both propagating at a fixed co-moving position behind the driver. The obtained results are then compared to particle-in-cell (PIC) simulations as well as results obtained using an semi-analytic numerical approach (SANA). We find excell…
In the NLC (Next Linear Collider) small misalignments in each of the individual accelerator structures (or the accelerator cells) will give rise to wakefields which kick the beam from its electrical axis. This wakefield can cause BBU (Beam Break Up) or at the very least it will dilute the emittance of the beam. Several Gaussian detuned structures have been designed and tested [1] at SLAC and in this paper we explore new distributions with possibly better damping properties. The progress of the beam through approximately 5,000 structures is monitored in phase space and results on this are prese…
A new electron injection scheme is proposed in sub-relativistic plasma wakefield accelerators. A transverse laser ionizes a dopant gas and ponderomotively accelerates the released electrons in the direction of wake propagation. This process enables electron trapping in the wakefield even for a wakefield potential below the trapping threshold. We study the scheme theoretically and by means of particle-in-cell simulations to demonstrate high-quality beam formation and acceleration with sub-micrometer normalized emittances and sub-percent uncorrelated energy spreads.
We describe an external electron injection scheme for the AWAKE experiment. We use scattering in two foils, that are necessary as vacuum window and laser beam dump, to decrease the betatron function of the incoming electron beam for injection and matching into plasma wakefields driven by a self-modulated proton bunch. We show that, for a total aluminum foil thickness of $\sim 280\, μ$m, multiple Coulomb scattering increases the beam emittance by a factor of $\sim 10$ and decreases the betatron function by a factor of $\sim 3$. The plasma in the accelerator is created by a ionizing laser pulse,…
Beam-driven plasma wakefield accelerators typically use the external injection scheme to ensure controllable beam quality at injection. However, the externally injected witness bunch may exhibit a non-Gaussian transverse density distribution. Using particle-in-cell simulations, we show that the common beam quality factors, such as the normalized RMS emittance and beam radius, do not strongly depend on the initial transverse shapes of the witness beam. Nonetheless, a beam with a highly-peaked transverse spatial profile can achieve a higher fraction of the total beam charge in the core. The same…
The production of ultra-bright electron bunches using ionization injection triggered by two transversely colliding laser pulses inside a beam-driven plasma wake is examined via three-dimensional (3D) particle-in-cell (PIC) simulations. The relatively low intensity lasers are polarized along the wake axis and overlap with the wake for a very short time. The result is that the residual momentum of the ionized electrons in the transverse plane of the wake is much reduced and the injection is localized along the propagation axis of the wake. This minimizes both the initial 'thermal' emittance and …
Particle acceleration in a quasilinear plasma wake provides access to high acceleration gradients while avoiding self-trapping of the background electrons. However, the plasma response to the externally injected witness bunch leads to a variation of the focussing fields along the bunch length, which can lead to a emittance growth. In order to investigate the impact of this emittance growth on the overall beam quality, we develop a single figure of merit based on a potential high-energy application for the AWAKE experiment at CERN. We show that the development of such a figure of merit naturall…
By means of hollow plasma, multiple proton bunches work well in driving nonlinear plasma wakefields and accelerate electrons to energy frontier with preserved beam quality. However, the acceleration of positrons is different because the accelerating structure is strongly charge dependent. There is a discrepancy between keeping a small normalized emittance and a small energy spread. This results from the conflict that the plasma electrons used to provide focusing to the multiple proton bunches dilute the positron bunch. By loading an extra electron bunch to repel the plasma electrons and meanwh…
Collimator wakefields in the Beam Delivery System (BDS) of future linear colliders, such as the International Linear Collider (ILC) and the Compact Linear Collider (CLIC), can be an important source of emittance growth and beam jitter amplification, consequently degrading the luminosity. Therefore, a better understanding of collimator wakefield effects is essential to optimise the collimation systems of future linear colliders in order to minimise wakefield effects. In the past, measurements of single-bunch collimator wakefields have been carried out at SLAC with the aim of benchmarking theory…
Structure wakefield acceleration (SWFA) is well suited for the linear collider (LC) application due to its natural ability to accelerate positrons and preserve emittance. Under the SWFA roadmap, which was developed in response to Snowmass 2013 recommendations, four principal technologies: drive beam, main beam, wakefield structure, and LC facility design, have been investigated. The two SWFA schemes under development are the collinear wakefield accelerator (CWA), in which the drive and main beam follow the same path through a structure, and the two-beam accelerator (TBA), where the drive and m…
Active plasma lensing is a promising technology for compact focusing of particle beams that has seen a recent surge of interest. While these lenses can provide strong focusing gradients of order kT/m and focusing in both transverse planes, there are limitations from nonlinear aberrations, causing emittance growth in the beams being focused. One cause of such aberrations is beam-driven plasma wakefields, present if the beam density is sufficiently high. We develop simple, but powerful analytic formulas for the effective focusing gradient from these wakefields, and use this to set limits on whic…
The dependence of wakefield amplitude and phase on beam and plasma parameters is studied in the parameter area of interest for self-modulating proton beam-driven plasma wakefield acceleration. The wakefield sensitivity to small parameter variations reveals the expected level of shot-to-shot jitter of experimental results. Of all the parameters, the plasma density stands out, as the wakefield phase is extremely sensitive to this parameter. The study of large variations determines the effects that limit the achievable accelerating field in different parts of the parameter space: nonlinear elonga…
Drive particle beams in linear or weakly nonlinear regimes of the plasma wakefield accelerator quickly reach a radial equilibrium with the wakefield, which is described in detail for the first time. The equilibrium beam state and self-consistent wakefields are obtained by combining analytical relationships, numerical integration, and first-principle simulations. In the equilibrium state, the beam density is strongly peaked near the axis, the beam radius is constant along the beam, and longitudinal variation of the focusing strength is balanced by varying beam emittance. The transverse momentum…
In the laser wakefield accelerator (LWFA) a short intense laser pulse, with a duration of the order of a plasma wave period, excites an unusually strong plasma wake wave (laser wakefield). Recent experiments on laser wakefield acceleration [Nature (London) 431, p.535, p.538, p.541 (2004)] demonstrated generation of ultra-short (with a duration of a few femtoseconds) relativistic electron bunches with relatively low energy spread of the order of a few percent. We have studied the dynamics of such bunches in vacuum and in laser wakefield. The results show strong bunch dynamics already on a few m…
Accelerating particles to high energies in plasma wakefields is considered to be a promising technique with good energy efficiency and high gradient. While important progress has been made in plasma-based electron acceleration, positron acceleration in plasma has been scarcely studied and a fully self-consistent and optimal scenario has not yet been identified. For high energy physics applications where an electron-positron collider would be desired, the ability to accelerate positrons in plasma wakefields is however paramount. Here we show that the preservation of beam quality can be compromi…
Proton-driven plasma wakefield acceleration has been demonstrated in simulations to be capable of accelerating particles to the energy frontier in a single stage, but its potential is hindered by the fact that currently available proton bunches are orders of magnitude longer than the plasma wavelength. Fortunately, proton micro-bunching allows driving plasma waves resonantly. In this paper, we propose using a hollow plasma channel for multiple proton bunch driven plasma wakefield acceleration and demonstrate that it enables the operation in the nonlinear regime and resonant excitation of stron…
We report the development of a multileaf collimator (MLC) for charged particle beams, based on independently actuated tungsten strips which can selectively scatter unwanted particles. The MLC is used in conjunction with an emittance exchange beamline to rapidly generate highly variable longitudinal bunch profiles. The developed MLC consists of 40 independent leaves that are 2 mm wide and can move up to 10 mm, and operates in an ultra high vacuum environment, enabled by novel features such as magnetically coupled actuation. An experiment at the Argonne Wakefield Accelerator, which previously us…
The evolution of beam phase space in ionization-induced injection into plasma wakefields is studied using theory and particle-in-cell (PIC) simulations. The injection process causes special longitudinal and transverse phase mixing leading initially to a rapid emittance growth followed by oscillation, decay, and eventual slow growth to saturation. An analytic theory for this evolution is presented that includes the effects of injection distance (time), acceleration distance, wakefield structure, and nonlinear space charge forces. Formulas for the emittance in the low and high space charge regim…
We propose an innovative beam cooling scheme based on laser driven plasma wakefields to address the challenge of high luminosity generation for a future linear collider. For linear colliders, beam cooling is realised by means of damping rings equipped with wiggler magnets and accelerating cavities. This scheme ensures systematic reduction of phase space volume through synchrotron radiation emission whilst compensating for longitudinal momentum loss via an accelerating cavity. In this paper, the concept of a plasma wiggler and its effective model analogous to a magnetic wiggler are introduced; …
Multi-objective optimization is important for particle accelerators where various competing objectives must be satisfied routinely such as, for example, transverse emittance vs bunch length. We develop and demonstrate an online multi-time scale multi-objective optimization algorithm that performs real time feedback on particle accelerators. We demonstrate the ability to simultaneously minimize the emittance and maintain a reference trajectory of a beam in the electron beamline in CERN's Advanced Proton Driven Plasma Wakefield Acceleration Experiment (AWAKE).
Flat beams -- beams with asymmetric transverse emittances -- have important applications in novel light-source concepts, advanced-acceleration schemes and could possibly alleviate the need for damping rings in lepton colliders. Over the last decade, a flat-beam-generation technique based on the conversion of an angular-momentum-dominated beam was proposed and experimentally tested. In this paper we explore the production of compressed flat beams. We especially investigate and optimize the flat-beam transformation for beams with substantial fractional energy spread. We use as a simulation examp…
A new injection scheme using the interference of two coaxial laser pulses is proposed for generating high quality beams in laser wakefield accelerators. In this scheme, a relatively loosely focused laser pulse drives the plasma wakefield, and a tightly focused laser pulse with similar intensity triggers interference ring pattern which creates onion-like multi sheaths in the plasma wakefield. Due to the wavefront curvature change after the focal position of the tightly focused laser, the innermost sheath of the wakefield expands, which slows down the effective phase velocity of the wakefield an…
We propose to use a frequency doubled pulse colliding with the driving pulse at an acute angle to trigger ionization injection in a laser wakefield accelerator. This scheme effectively reduces the duration that injection occurs, thus high injection quality is obtained. Three-dimensional particle-in-cell simulations show that electron beams with energy of ~500 MeV, charge of ~40 pC, energy spread of ~1% and normalized emittance of a few millimeter milliradian can be produced by ~100 TW laser pulses. By adjusting the angle between the two pulses, the intensity of the trigger pulse and the gas do…
The implications of long-range wakefields on the beam quality are investigated through a detailed beam dynamics study. Injection offsets are considered and the resulting emittance dilution recorded, including systematic sources of error. These simulations have been conducted for damped and detuned structures (DDS) and for waveguide damped structures-both for the CLIC collider.
In AWAKE a self-modulated proton bunch drives wakefields in a plasma. Recent experiments successfully demonstrated many aspects of the self-modulation of the drive bunch as well as acceleration of test electrons. Next experiments will focus on producing a multi-GeV accelerated electron bunch with low emittance and low energy spread. The experiment requires a variety of advanced beam diagnostics to characterize the self-modulated proton bunch at the picosecond time scale. These include optical transition radiation and a streak camera for short and long time scale detailed imaging of self-modula…
In previous work [1] general expressions, valid for arbitrary bunch lengths, were derived for the wakefields of corrugated structures with flat geometry, such as is used in the RadiaBeam/LCLS dechirper. However, the bunch at the end of linac-based X-ray FELs--like the LCLS--is extremely short, and for short bunches the wakes can be considerably simplified. In this work, we first derive analytical approximations to the short-range wakes. These are generalized wakes, in the sense that their validity is not limited to a small neighborhood of the symmetry axis, but rather extends to arbitrary tran…
A near-hollow plasma channel, where the plasma density in the channel is much less than the plasma density in the walls, is proposed to provide independent control over the focusing and accelerating forces in a plasma accelerator. In this geometry the low density in the channel contributes to the focusing forces, while the accelerating fields are determined by the high density in the channel walls. The channel also provides guiding for intense laser pulses used for wakefield excitation. In certain regimes, both electron and positron beams can be accelerated and focused in a nearly symmetric fa…
Beams injected into a linear focusing channel typically have some degree of space-charge nonuniformity. In general, injected particle distributions with systematic charge nonuniformities are not equilibria of the focusing channel and launch a broad spectrum of collective modes. These modes can phase-mix and have nonlinear wave-wave interactions which, at high space-charge intensities, results in a relaxation to a more thermal-like distribution characterized by a uniform density profile. This thermalization can transfer self-field energy from the initial space-charge nonuniformity to the local …
