We expand on the material that was published in the previous Proceedings of the CERN Accelerator School on Plasma Wakefield Acceleration. The material focused on Plasma Wakefield Acceleration in the short, narrow bunch regime. After a brief introduction, we describe Plasma Wakefield Acceleration driven by a bunch train. We then attempt to give simple and intuitive descriptions of bunch self-modulation, occurring when the bunch is long, and of current filamentation, occurring when the bunch is wide. Self-modulation is a means to use existing bunches carrying large amounts of energy to drive plasma wakefields. Current filamentation instability imposes a limitation on how wide a particle bunch can be before transverse break-up may disrupt the wakefields generation and the acceleration process. As in the previous material, we show sample experimental results that demonstrate that much of the physics at play has been observed experimentally.
Wakefield particle acceleration in hollow plasma channels is under extensive study nowadays. Here we consider an externally magnetized plasma layer (external magnetic field of arbitrary magnitude is along the structure axis) and investigate wakefields generated by a point charge passing along the layer axis.
A novel effect of fast heating and charging a finite-radius plasma is discovered in the context of plasma wakefield acceleration. As the plasma wave breaks, the most of its energy is transferred to plasma electrons which create strong charge-separation electric field and azimuthal magnetic field around the plasma. The slowly varying field structure is preserved for hundreds of wakefield periods and contains (together with hot electrons) up to 80% of the initial wakefield energy.
Plasma Wakefield Accelerators promise huge acceleration gradients that are three orders of magnitude greater than today's conventional radio frequency (RF) accelerators. These novel accelerators show also the potential of diminishing the size of the future accelerators nearly by the same factor. This review gives brief explanations and the working principles of the Plasma Wakefield Accelerators and shows the recent developments of the field. The current challenges are given and the potential future use of the Plasma Wakefield Accelerators are discussed.
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…
A train of short charged particle bunches can efficiently drive a strong plasma wakefield over a long propagation distance only if all bunches reside in focusing and decelerating phases of the wakefield. This is shown possible with equidistant bunch trains, but requires the bunch charge to increase along the train and the plasma frequency to be higher than the bunch repetition frequency.
The self-modulation instability is a key effect that makes possible the usage of nowadays proton beams as drivers for plasma wakefield acceleration. Development of the instability in uniform plasmas and in plasmas with a small density up-step is numerically studied with the focus at nonlinear stages of beam evolution. The step parameters providing the strongest established wakefield are found, and the mechanism of stable bunch train formation is identified.
Though wakefield acceleration in crystal channels has been previously proposed, x-ray wakefield acceleration has only recently become a realistic possibility since the invention of the single-cycled optical laser compression technique. We investigate the acceleration due to a wakefield induced by a coherent, ultrashort x-ray pulse guided by a nanoscale channel inside a solid material. By two-dimensional particle in- cell computer simulations, we show that an acceleration gradient of TeV/cm is attainable. This is about 3 orders of magnitude stronger than that of the conventional plasma-based wa…
In the past decades, beam-driven plasma wakefield acceleration (PWFA) experiments have seen remarkable progress by using high-energy particle beams such as electron, positron and proton beams to drive wakes in neutral gas or pre-ionized plasma. This review highlights a few recent experiments in the world to compare experiment parameters and results.
Nonlinear effects responsible for elongation of the plasma wave period are numerically studied with the emphasis on two-dimensionality of the wave. The limitation on the wakefield amplitude imposed by detuning of the wave and the driver is found.
We study experimentally the longitudinal and transverse wakefields driven by a highly relativistic proton bunch during self-modulation in plasma. We show that the wakefields' growth and amplitude increase with increasing seed amplitude as well as with the proton bunch charge in the plasma. We study transverse wakefields using the maximum radius of the proton bunch distribution measured on a screen downstream from the plasma. We study longitudinal wakefields by externally injecting electrons and measuring their final energy. Measurements agree with trends predicted by theory and numerical simul…
We generalize the temporally encoded spectral shifting (TESS) analysis for measuring plasma wakefields using spectral interferometry to dissimilar probe pulses of arbitrary spectral profile and to measuring nonlinear wakefields. We demonstrate that the Gaussian approximation used up until now results in a substantial miscalculation of the wakefield amplitude, by a factor of up to two. A method to accurately measure higher amplitude quasilinear and nonlinear wakefields is suggested, using an extension to the TESS procedure, and we place some limits on its accuracy in these regimes. These extens…
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.
Effects of plasma inhomogeneity on self-modulating proton bunches and accelerated electrons were studied numerically. The main effect is the change of the wakefield wavelength which results in phase shifts and loss of accelerated particles. This effect imposes severe constraints on density uniformity in plasma wakefield accelerators driven by long particle bunches. The transverse two stream instability that transforms the long bunch into a train of micro-bunches is less sensitive to density inhomogeneity than are the accelerated particles. The bunch freely passes through increased density regi…
The energy gain in laser wakefield acceleration (LWFA) is ultimately limited by dephasing, occurring when accelerated electrons outrun the accelerating phase of the wakefield. We apply quasi-phasematching, enabled by axially modulated plasma channels, to overcome this limitation. By matching the modulation period to the dephasing length, a relativistic electron can undergo energy gain over several dephasing lengths. Theory and simulations are presented showing that at a weakly relativistic laser intensity, ~10^17 W/cm2, and millijoule level pulse energies, quasi-phasematched LWFA results in en…
A scheme of laser wakefield acceleration, when a relatively rare and long bunch of non-relativistic or weakly-relativistic electrons is initially in front of the laser pulse, is suggested and considered. The motion of test electrons is studied both in the one-dimensional case (1D wakefield) and in the three-dimensional laser wakefield excited in a plasma channel. It is shown that the bunch is trapped, effectively compressed both in longitudinal and transverse directions and accelerated to ultra-relativistic energies in the region of first accelerating maximum of the wakefield. The accelerated …
A unified model of electron penetration into linear plasma wakefields is formulated and studied. The optimum angle for side injection of electrons is found. At smaller angles, all electrons are reflected radially. At larger angles, electrons enter the wakefield with superfluous transverse momentum that is unfavorable for trapping. Separation of incident electrons into penetrated and reflected fractions occur in the outer region of the wakefield at some "reflection" radius that depends on the electron energy.
A linear theory of a wakefield excitation in a plasma-dielectric accelerating structure by a drive electron bunch in the case of an off-axis bunch injection has been constructed. The structure under investigation is a round dielectric-loaded metal waveguide with a channel for the charged particles, filled with homogeneous cold plasma. Derived theory was used to investigate numerically the spatial distribution of the bunch-excited wakefield components, which act on both the drive and witness bunches.
We present a new concept for a plasma wakefield accelerator driven by magnetowaves (MPWA). This concept was originally proposed as a viable mechanism for the "cosmic accelerator" that would accelerate cosmic particles to ultra high energies in the astrophysical setting. Unlike the more familiar Plasma Wakefield Accelerator (PWFA) and the Laser Wakefield Accelerator (LWFA) where the drivers, the charged-particle beam and the laser, are independently existing entities, MPWA invokes the high-frequency and high-speed whistler mode as the driver, which is a medium wave that cannot exist outside of …
Seeded Self-modulation (SSM) has been demonstrated to transform a long proton bunch into many equidistant micro-bunches (e.g., the AWAKE case), which then resonantly excite strong wakefields. However, the wakefields in a uniform plasma suffer from a quick amplitude drop after reaching the peak. This is caused by a significant decrease of the wake phase velocity during self-modulation. A large number of protons slip out of focusing and decelerating regions and get lost, and thus cannot contribute to the wakefield growth. Previously suggested solutions incorporate a sharp or a linear plasma long…
A laser pulse guided in a curved plasma channel can excite wakefields that steer electrons along an arched trajectory. As the electrons are accelerated along the curved channel, they emit synchrotron radiation. We present simple analytical models and simulations examining laser pulse guiding, wakefield generation, electron steering, and synchrotron emission in curved plasma channels. For experimentally realizable parameters, a ~2 GeV electron emits 0.1 photons per cm with an average photon energy of multiple keV.
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 …
Plasma wakefield acceleration in the blowout regime is particularly promising for high-energy acceleration of electron beams because of its potential to simultaneously provide large acceleration gradients and high energy transfer efficiency while maintaining excellent beam quality. However, no equivalent regime for positron acceleration in plasma wakes has been discovered to-date. We show that after a short propagation distance, an asymmetric electron beam drives a stable wakefield in a hollow plasma channel that can be both accelerating and focusing for a positron beam. A high charge positron…
A new regime of proton-driven plasma wakefield acceleration is discovered, in which the plasma nonlinearity increases the phase velocity of the excited wave compared to that of the protons. If the beam charge is much larger than minimally necessary to excite a nonlinear wave, there is sufficient freedom in choosing the longitudinal plasma density profile to make the wave speed close to the speed of light. This allows electrons or positrons to be accelerated to about 200 GeV with a 400 GeV proton driver.
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…
Self-Adaptive Stabilization and Quality Boost for Electron Beams from All-Optical Plasma Wakefield Accelerators
University of Strathclyde（思克莱德大学）；Ludwig-Maximilians-Universität München（慕尼黑大学）；Heinrich Heine University Düsseldorf（杜塞尔多夫大学）；Cockcroft Institute（科克克罗夫特研究所）；Forschungszentrum Jülich（于利希研究中心）；École Polytechnique（巴黎综合理工学院）；Helmholtz-Zentrum Dresden–Rossendorf（德累斯顿罗森多夫亥姆霍兹中心）；Deutsches Elektronen-Synchrotron DESY（德国电子同步加速器）
Hollow plasma has been introduced into the proton-driven plasma wakefield accelerators to overcome the issue of beam quality degradation caused by the nonlinear transverse wakefields varying in radius and time in uniform plasma. It has been demonstrated in simulations that the electrons can be accelerated to energy frontier with well-preserved beam quality in a long hollow plasma channel. However, this scheme imposes tight requirements on the beam-channel alignment. Otherwise asymmetric transverse wakefields along the axis are induced, which could distort the driving bunch and deteriorate the …
Plasma wakefield acceleration studies currently rely considerably on simulating this effect numerically using highly specialized software. Exorbitant computational difficulty of the problem requires simplifying models and methods,limiting such software applicability. Quasistatic approximation, for example, utilizes a plasma model that does not include trapping plasma electrons by the wakefield. This article presents a method that reuses a quasistatic plasma-beam solver to calculate parameters of wakefield-trapped plasma electrons.
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…
Ultra-relativistic hollow electron beams can drive plasma wakefields ($\sim$ GV/m) suitable for positron acceleration. Stable propagation of hollow electron beams for long distances in plasmas is required to accelerate positrons to high energies by these plasma wakefields. In this work, we show by quasi-static kinetic simulations using the code WAKE that an ultra-relativistic azimuthally-symmetric hollow electron beam propagates in a plasma by developing fish-bone like structure and shifting its bulk, differentially along its length (rear part fastest), towards its axis due to the decrease in …
The multi-stage technique for laser driven acceleration of electrons become a critical part of full-optical, jitter-free accelerators. Use of several independent laser drivers and shorter length plasma targets allows the stable and reproducible acceleration of electron bunches (or beam) in the GeV energies with lower energy spreads. At the same time the charge coupling, necessary for efficient acceleration in the consecutive acceleration stage(s), depends collectively on the parameters of the injected electron beam, the booster stage, and the non-linear transverse dynamics of the electron beam…
We demonstrate experimentally the resonant excitation of plasma waves by trains of laser pulses. We also take an important first step to achieving an energy recovery plasma accelerator by showing that unused wakefield energy can be removed by an out-of-resonance trailing laser pulse. The measured laser wakefields are found to be in excellent agreement with analytical and numerical models of wakefield excitation in the linear regime. Our results indicate a promising direction for achieving highly controlled, GeV-scale laser-plasma accelerators operating at multi-kilohertz repetition rates. This…
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 …
In the design of laser plasma electron injectors for multi-stage laser driven wakefield accelerators, the control of plasma density is a key element to stabilize the acceleration process. A cell with variable parameters is used to confine the gas and tailor the density profile. The gas filling process was characterized both experimentally and by fluid simulations. Results show a good agreement between experiments and simulations. Simulations were also used to study the effect of each of the gas cell parameters on the density distribution and show the possibility to finely control the density p…
The excitation of wakefields by a triangular temporal profile laser pulse with an abrupt fall in a step density profile plasma channel is investigated analytically and an exact solution is obtained. The excitation is more efficient for t~tp, where t is the rise time of the pulse and tp is the plasma period, though it is still significant for t~20 tp. The wake potential in the former case is 1.7 times the ponderomotive potential, whereas it falls to 1.4 times the ponderomotive potential for the latter.
We study the long-term evolution (LTE) of plasma wakefields over multiple plasma-electron periods and few plasma-ion periods, much less than a recombination time. The evolution and relaxation of such a wakefield-perturbed plasma over these timescales has important implications for the upper limits of repetition-rates in plasma colliders. Intense fields in relativistic lasers (or intense beams) create plasma wakefields (modes around ωpe) by transferring energy to the plasma electrons. Charged-particle beams in the right phase may be accelerated with acceleration/focusing gradients of tens of Ge…
Heavy ion driven plasma wakefield acceleration with drift-like phase-shift acceleration scheme
Institute of Modern physics, Chinese Academy of Sciences（中国科学院近代物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）；University of Manchester（曼彻斯特大学）；Cockcroft Institute（科克沃尔研究所）
In the frame of laser-driven wakefield acceleration, the main characteristics oflaser propagation and plasma wave excitation are described, with an emphasis onthe role of propagation distance for electron acceleration. To optimizeinteraction length and maximize energy gain, operation at low plasma density isthe most promising regime for achieving ultra-relativistic energies. Among thepossible methods of extending propagation length at low plasma density, laserguiding by grazing incidence reflection at the wall of dielectric capillarytubes has several assets. The properties of laser guiding and…
The spatio-temporal structure of the bulk wakefields excited by a relativistic electron bunch in plasma of semiconductors and semimetals is studied. It is shown that these wakefield consists of the field of longitudinal plasmons and Cherenkov electromagnetic radiation, which is a set of eigen electromagnetic waves of the semiconductor or semimetal waveguide. A branch of the surface plasmons appears in a waveguide with an axial vacuum channel. The process of wake excitation of the surface plasmons by the relativistic electron bunch is also investigated. The intensity of the excited wake surface…
There is a new effect that can limit the lifetime of a weakly nonlinear wakefield in a radially bounded plasma. If the drive beam is narrow, some of the plasma electrons fall out of the collective motion and leave the plasma radially, forming a negatively charged halo around it. These electrons repeatedly return to the plasma under the action of the charge separation field, interact with the plasma wave and cause its damping. The lowest-energy halo electrons take the energy from the wave more efficiently, because their trajectories are bent by the plasma wave towards the regions of the stronge…
The goal of this paper is to examine experimental progress in laser wakefield acceleration over the past decade (2004-2014), and to use trends in the data to understand some of the important physical processes. By examining a set of over 50 experiments, various trends concerning the relationship between plasma density, accelerator length, laser power and the final electron beam en- ergy are revealed. The data suggest that current experiments are limited by dephasing and that current experiments typically require some pulse evolution to reach the trapping threshold.
The plasma wakefield amplitudes which could be achieved via the modulation of a long proton bunch are investigated. We find that in the limit of long bunches compared to the plasma wavelength, the strength of the accelerating fields is directly proportional to the number of particles in the drive bunch and inversely proportional to the square of the transverse bunch size. The scaling laws were tested and verified in detailed simulations using parameters of existing proton accelerators, and large electric fields were achieved, reaching 1 GV/m for LHC bunches. Energy gains for test electrons bey…
We study electron acceleration in a plasma wakefield under the influence of the radiation-reaction force caused by the transverse betatron oscillations of the electron in the wakefield. Both the classical and the strong quantum-electrodynamic (QED) limits of the radiation reaction are considered. For the constant accelerating force, we show that the amplitude of the oscillations of the QED parameter $χ$ in the radiation-dominated regime reaches the equilibrium value determined only by the magnitude of the accelerating field, while the averaged over betatron oscillations radiation reaction forc…
Using a periodic electron beam bunch train to resonantly excite plasma wakefields in the quasi-nonlinear (QNL) regime has distinct advantages over employing a single, higher charge bunch. Resonant excitation in the QNL regime can produce plasma electron blowout using very low emittance beams with a small charge per pulse: the local density perturbation is extremely nonlinear, achieving total rarefaction, yet the resonant response of the plasma electrons at the plasma frequency is preserved. Such a pulse train, with inter-bunch spacing equal to the plasma period, can be produced via inverse fre…
We measure the emission of energetic electrons from the interaction between ultrashort laser pulses and a solid density plasma in the relativistic regime. We detect an electron beam that only appears with few-cycle pulses (< 10 fs) and large plasma scale lengths ($L > λ_0$). Numerical simulations, in agreement with the experiments, reveal that these electrons are accelerated by a laser wakefield. Plasma waves are indeed resonantly excited by the few-cycle laser pulses in the near-critical-density region of the plasma. Electrons are then injected by ionization into the plasma waves and accelera…
A Gaussian laser pulse with a square profile in time propagating in a parabolic plasma channel, exerts a ponderomotive force on electrons that drives a large amplitude electrostatic wake potential phi. An analytic solution for phi is possible when a characteristic relation is fulfilled. For pulse duration tau ~ 9 tau_p / 4, where tau_p is the plasma period, the plasma wake potential on the axis is twice the ponderomotive potential phi_0.
In the cavitation regime of plasma-based accelerators, a population of high-energy electrons tailing the driver can undergo betatron motion. The motion results in X-ray emission, but the brilliance and photon energy are limited by the electrons' initial transverse coordinate. To overcome this, we exploit parametrically unstable betatron motion in a cavitated, axially modulated plasma. Theory and simulations are presented showing that the unstable oscillations increase both the total X-ray energy and average photon energy.
The electric field in laser-driven plasma wakefield acceleration is orders of magnitude higher than conventional radio-frequency cavities, but the energy gain is limited by dephasing between the ultra-relativistic electron bunch and the wakefield, which travels at the laser group velocity. We present a way to overcome this limit within a single plasma stage. The amplitude of the wakefield behind a train of laser pulses can be controlled in-flight by modulating the density profile. This creates a succession of resonant laser-plasma accelerator sections and non-resonant drift sections, within wh…
