Ion wake induced mode coupling is investigated experimentally for a horizontal dust chain formed in a complex plasma, verifying results from previous simulation. A double branch of faint spectral lines is detected in the mode spectra which verifies the predicted rule of mode coupling between the vertical z(j=i$\pm$1) modes and the longitudinal mode x(i). Discreet instabilities are observed as the branches of x- and z-modes intersect each other. The mode spectra in the vicinity of the instabilities exhibit enhanced energy density at specific coupled x and z modes, serving as direct evidence that these instabilities are caused by resonance between the coupled modes. The instability-induced melting threshold was found to obey the Lindemann criterion through analysis of the instantaneous relative interparticle distance fluctuation (IDF). The relation between mode spectra and dispersion relations was further studied by multiplying the mode spectra with a transition matrix connecting the bases of normal mode eigenvectors and Fourier series in k space. Typical dispersion relations corresponding to the longitudinal and out-of-plane transverse Dust Lattice Waves (DLWs) are obtained, which also exhibit characteristics unique to finite systems, including discrete bands and strong fluctuations in the energy density.
The concept of a hybrid laser wakefield/direct laser plasma accelerator is proposed. Relativistic electrons undergoing resonant betatron oscillations inside the plasma bubble created by a laser pulse are accelerated by gaining energy directly from the laser pulse and from its plasma wake. The resulting bifurcated phase space of self-injected plasma electrons contains a population that experiences wakefield acceleration beyond the standard one-dimensional limit because of the multi-dimensional nature of its motion that reduces the phase slippage between the electrons and the wake.
The quasi-static code WAKE [P. Mora and T. Antonsen, Phys. Plasmas {\bf 4}, 217(1997)] is upgraded to model the propagation of an ultra-relativistic charged particle beam through a warm background plasma in plasma wakefield acceleration. The upgraded code is benchmarked against the full particle-in-cell code OSIRIS [Hemker et al., Phys. Rev. ST Accel. Beams {\bf 3}, 061301(2000)] and the quasi-static code QuickPIC [Huang et al., J. Comp. Phys. {\bf 217}, 658 (2006)]. The effect of non-zero plasma temperature on the peak accelerating electric field is studied for a two bunch electron beam drive…
In the presence of an external magnetic field, wake fields generated by a short laser pulse can propagate out of the plasma, and thereby provide information about the electron density profile. A method for reconstructing the density profile from a measured wake field spectrum is proposed and a numerical example is given. Finally, we compare our proposal with existing plasma density diagnostic techniques.
We demonstrate a novel approach to the generation of femtosecond electron bunch trains via laser-driven wakefield acceleration. We use two independent high-intensity laser pulses, a drive, and injector, each creating their own plasma wakes. The interaction of the laser pulses and their wakes results in a periodic injection of free electrons in the drive plasma wake via several mechanisms, including ponderomotive drift, wake-wake interference, and pre-acceleration of electrons directly by strong laser fields. Electron trains were generated with up to 4 quasi-monoenergetic bunches, each separate…
We explore the role of the background plasma ion motion in self-modulated plasma wakefield accelerators. We employ J. Dawson's plasma sheet model to derive expressions for the transverse plasma electric field and ponderomotive force in the narrow bunch limit. We use these results to determine the on-set of the ion dynamics, and demonstrate that the ion motion could occur in self-modulated plasma wakefield accelerators. Simulations show the motion of the plasma ions can lead to the early suppression of the self-modulation instability and of the accelerating fields. The background plasma ion mot…
Relativistic wakes produced by intense laser or particle beams propagating through plasmas are being considered as accelerators for next generation of colliders and coherent light sources. Such wakes have been shown to accelerate electrons and positrons to several gigaelectronvolts (GeV), with a few percent energy spread and a high wake-to-beam energy transfer efficiency. However, complete mapping of electric field structure of the wakes has proven elusive. Here we show that a high-energy electron bunch can be used to probe the fields of such light-speed wakes with femtosecond resolution. The …
A stationary wave solution is obtained for the proton driven plasma wake field accelerator (PDPWFA). The wake field excitation by trains of equidistant proton microbunches produced due to self modulational instability has been discussed. Also, considering the necessity of the external magnetic field to control focusing of the beam, studies on the effect of magnetic field on the wake field structures have been done.
Experiments with two-dimensional (2D) plasma crystals are usually carried out in rf plasma sheaths, where the interparticle interactions are modified due to the presence of plasma wakes. The wake-mediated interactions result in the coupling between wave modes in 2D crystals, which can trigger the mode-coupling instability and cause melting. The theory predicts a number of distinct fingerprints to be observed upon the instability onset, such as the emergence of a new hybrid mode, a critical angular dependence, a mixed polarization, and distinct thresholds. In this paper we summarize these key f…
Ion motion in plasma wakefield accelerators can cause temporal increase of the longitudinal electric field shortly before the wave breaks. The increase is caused by re-distribution of the wave energy in transverse direction and may be important for correct interpretation of experimental results and acceleration of high-quality beams.
An interaction of upstream extra particles with a monolayer highly-ordered complex plasma is studied. A principally new abnormal turbulent wake formed behind the supersonic upstream particle is discovered. An anomalous type of the turbulence wake clearly manifests in anomalously low thermal diffusivity and two orders of magnitude larger particle kinetic temperature compared to that of the 'normal' wake (Mach cone) observed by Du et al [Europhys. Lett. 99, 55001 (2012)].
It is found that nonlinear interaction of plasma wakefields driven by counterpropagating laser or particle beams can efficiently generate high-power electromagnetic radiation at the second harmonic of the plasma frequency. Using a simple analytical theory and particle-in-cell simulations, we show that this phenomenon can be attractive for producing high-field ($\sim 10$ MV/cm) narrowband terahertz pulses with the gigawatt power level and millijoule energy content.
Generation of wake fields by a short electromagnetic pulse in a plasma with an inhomogeneous background magnetic field and density profile is considered, and a wave equation is derived. Transmission and reflection coefficients are calculated in a medium with sharp discontinuities. Particular attention is focused on examples where the longitudinal part of the electromagnetic field is amplified for the transmitted wave. Furthermore, it is noted that the wake field can propagate out of the plasma and thereby provide information about the electron density profile. A method for reconstructing the b…
Interaction of external monochromatic, linearly polorized plane EM-wave with nonlinear one-dimensional wake wave, generated by relativistic electron bunch moving in cold plasma, is considered. At definite conditions on parameters of plasma and bunch, nonlinear wake wave can have a pronounced spikes, where plasma electron density has its maximum value and plasma electron velocities are nearing wave breaking limit, i.e. velocity of the rigid driving bunch. Presented calculations show, that external EM-wave, propagating through plasma, normal to the bunch velocity, at such a conditions can be amp…
Motivated by experiments on the generation of streaming plasmas in high energy density facilities, industrial setups, and fundamental dusty plasma research the plasma polarization around a test charge in streaming plasmas is considered. The induced charge density distribution of plasma constituents is discussed for the subsonic, sonic, and supersonic regime. Also, it is shown that the plasma polarization in the vicinity of the test charge shows different scaling in subsonic and supersonic regimes.
Metre-scale plasma wakefield accelerators have imparted energy gain approaching 10 gigaelectronvolts to single nano-Coulomb electron bunches. To reach useful average currents, however, the enormous energy density that the driver deposits into the wake must be removed efficiently between shots. Yet mechanisms by which wakes dissipate their energy into surrounding plasma remain poorly understood. Here, we report ps-time-resolved, grazing-angle optical shadowgraphic measurements and large-scale particle-in-cell simulations of ion channels emerging from broken wakes that electron bunches from the …
The Debye shielding of a charge immersed in a flowing plasma is an old classic problem in plasma physics. It has been given renewed attention in the last two decades in view of experiments with complex plasmas, where charged dust particles are often levitated in a region with strong ion flow. Efforts to describe the shielding of the dust particles in such conditions have been focused on the homogeneous plasma approximation, which ignores the substantial inhomogeneity of the levitation region. We address the role of the plasma inhomogeneity by rigorously calculating the point charge potential i…
It is shown that the wake-mediated interactions between microparticles in a two-dimensional plasma crystal affect the shape of the monolayer, making it non-flat. The equilibrium shape is calculated for various distributions of the particle number density in the monolayer. For typical experimental conditions, the levitation height of particles in the center of the crystal can be noticeably smaller than at the periphery. It is suggested that the effect of wake-induced bending can be utilized in experiments, to deduce important characteristics of the interparticle interaction.
Photon bursts with a wavelength smaller than the plasma inter-particle distance can drive plasma wakes via Compton scattering. We investigate this fundamental process analytically and numerically for different photon frequencies, photon flux, and plasma magnetization. Our results show that Langmuir and extraordinary modes are driven efficiently when the photon energy density lies above a certain threshold. The interaction of photon bursts with magnetized plasmas is of distinguished interest as the generated extraordinary modes can convert into pure electromagnetic waves at the plasma/vacuum bo…
Large-scale particle-in-cell calculations of the plasma wake interactions of two negatively charged grains smaller than the Debye length are carried out using the COPTIC code over a wide range of subsonic plasma flow velocities. In plasmas with temperature ratio $T_e/T_i=100$, it is found that a single grain's oscillatory wake disappears for flow Mach numbers ($M$) less than approximately 0.3, which is the parameter regime where Landau damping is expected to be strong. Neutral collisions suppress potential oscillations above $M=0.3$, but not the trailing attractive potential peak caused by ion…
An improved description for nonlinear plasma wakefields with phase velocities near the speed of light is presented and compared against fully kinetic particle-in-cell simulations. These wakefields are excited by intense particle beams or lasers pushing plasma electrons radially outward, creating an ion bubble surrounded by a sheath of electrons characterized by the source term $S \equiv -\frac{1}{en_p}(ρ-J_z/c)$ where $ρ$ and $J_z$ are the charge and axial current densities. Previously, the sheath source term was described phenomenologically with a positive-definite function, resulting in a po…
A self-consistent nonlinear hydrodynamic theory is presented of the propagation of a long and thin relativistic electron beam, for a typical plasma wake field acceleration configuration in an unmagnetized and overdense plasma. The random component of the trajectories of the beam particles as well as of their velocity spread is modelled by an anisotropic temperature, allowing the beam dynamics to be approximated as a 3-D adiabatic expansion/compression. {It is shown that even in the absence of the {nonlinear plasma wake force}, the localization of the beam in the transverse direction can be ach…
We report here an exact analytical travelling wave solution for nonlinear electron plasma wave excited by an intense ultra-relativistic proton beam. It brings out the underlying physics of longitudinal electric field characteristics of the excited wake wave formed behind the drive beam. The results are further supplemented by a fully relativistic particle in cell (PIC) code OSIRIS in 2D geometry. The plasma and beam parameters in the simulation are chosen in conformity with experimental work and it provides us the anticipated axial and transverse electric field profiles. The investigation is f…
Space-time evolution of relativistic electron beam driven wake-field in a cold, homogeneous plasma, is studied using 1D-fluid simulation techniques. It is observed that the wake wave gradu- ally evolves and eventually breaks, exhibiting sharp spikes in the density profile and sawtooth like features in the electric field profile [1]. It is shown here that the excited wakefield is a longitudi- nal Akhiezer-Polovin mode [2] and its steepening (breaking) can be understood in terms of phase mixing of this mode, which arises because of relativistic mass variation effects. Further the phase mixing ti…
A new method capable of capturing coherent electric field structures propagating at nearly the speed of light in plasma with a time resolution as small as a few femtoseconds is proposed. This method uses a few femtoseconds long relativistic electron bunch to probe the wake produced in a plasma by an intense laser pulse or an ultra-short relativistic charged particle beam. As the probe bunch traverses the wake, its momentum is modulated by the electric field of the wake, leading to a density variation of the probe after free-space propagation. This variation of probe density produces a snapshot…
We study the evolution of nonlinear ion acoustic wave excitations due to a moving charged source in a plasma. Our numerical investigations of the full set of cold fluid equations goes beyond the usual weak nonlinearity approximation and shows the existence of a rich variety of solutions including wakes, precursor solitons and pinned solitons that travel with the source velocity. These solutions represent a large amplitude generalization of solutions obtained in the past for the forced Korteweg deVries equation and can find useful applications in a variety of situations in the laboratory and in…
The radial characteristics of plasma potential and density around an insulating disc obstacle, placed inside a partially magnetized plasma flow created in cylindrical chamber by hot cathode filament are presented. In the absence of obstacle, centrally sharp minima in potential and maxima in plasma density is observed; however when a macroscopic obstacle is introduced in plasma flow, a clear radially off-centred minima in plasma potential is observed having plasma density peaking near the edge of the obstacle. The depth of potential around the obstacle depends on the axial magnetic field streng…
The condition for potential description of the wake waves,generated by flat or cylindrical driving electron bunch in cold plasma is derived. The two-dimensional nonlinear equation for potential valid for small values of that is obtained and solved by the separation of variables. Solutions in the form of cnoidal waves,existing behind the moving bunch at small values of vertical coordinate,are obtained.In particular,at some boundary conditions,corresponding to blow-out regime in the underdense plasma,the solution represents by a solitary nonlinear wave. Approximate solution is also obtained usin…
It is shown that an undesirable curvature of the wave front of two-dimensional nonlinear wake wave excited in uniform plasma by a relativistic charged bunch or laser pulse may be compensated by radial change of the equilibrium plasma density.
A simple 2D model of the bubble formation in a plasma wakefield accelerator is developed and investigated. It is shown that in the case of a flat driver the bubble may consist of two parts that correspond to two different types of the plasma flow: a laminar flow where plasma electron streams do not cross and a two-stream (turbulent) flow. The laminar flow turns out to be robust to the symmetry breaking. Building-of of the developed model we demonstrate that in the case of the laminar flow and non-relativistic plasma electrons the transverse wake field is absent inside the bubble even in the ca…
A non-perturbative method is introduced to measure the particle-particle interaction strengths and in-situ confinement for a vertically aligned dust particle pair in a complex plasma. The intrinsic thermal motion of each particle is tracked, allowing the interaction strengths and confinement in both the vertical and horizontal directions to be determined simultaneously. The method is validated through quantitative agreement with previous measurements of the non-reciprocal interaction strength in the vertical direction, the horizontal ion wake attraction, and the charge reduction and heating of…
The expressions for wake fields, generated in plasma (in the plasma waveguide or unlimited plasma) by relativistic electron bunch, was received and analyzed for the cases of the presence and absence of strong external longitudinal magnetic field. For the both cases the comparative analysis of the dependence of field amplitudes on the parameters of the electron bunch was done.
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.
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…
The nonlinear propagation of a circularly polarized electromagnetic (CPEM) wave in a strongly magnetized electron-positron-ion plasma is investigated. Two coupled equations describing the interaction between a high-frequency CPEM wave and the low-frequency electrostatic wake field are derived. It is found that the generation of the wake fields depends on the presence of the ion species. The wake field generation in turn leads to de-acceleration and frequency down conversion of the electromagnetic pulse.
The effect of nonlinearity on plasma wake wave excited by a relativistic cylindrical charged bunch is investigated. It is shown that owing to the nonlinearity the amplitude of wake wave gets modulated in the longitudinal direction. The nonlinear wavelength in the excited field changes in the transverse direction with the result that the phase front is distored and a turbulence developed. The nonlinear phase front distortion may be compensated by radial change of unperturbed plasma density.
It is demonstrated that the performance of the self-modulated proton driver plasma wakefield accelerator (SM-PDPWA) is strongly affected by the reduced phase velocity of the plasma wave. Using analytical theory and particle-in-cell simulations, we show that the reduction is largest during the linear stage of self-modulation. As the instability nonlinearly saturates, the phase velocity approaches that of the driver. The deleterious effects of the wake's dynamics on the maximum energy gain of accelerated electrons can be avoided using side-injections of electrons, or by controlling the wake's ph…
An electron injector concept for laser-plasma accelerator was developed in ref [1] and [2] ; it relies on the use of counter-propagating ultrashort laser pulses. In [2], the scheme is as follows: the pump laser pulse generates a large amplitude laser wakefield (plasma wave). The counter-propagating injection pulse interferes with the pump laser pulse to generate a beatwave pattern. The ponderomotive force of the beatwave is able to inject plasma electrons into the wakefield. We have studied this injection scheme using 1D Particle in Cell (PIC) simulations. The simulations reveal phenomena and …
Plasma accelerators can sustain very high acceleration gradients. They are promising candidates for future generations of particle accelerators for several scientific, medical and technological applications. Current plasma based acceleration experiments operate in the relativistic regime, where the plasma response is strongly non-linear. We outline some of the key properties of wakefield excitation in these regimes. We outline a multidimensional theory for the excitation of plasma wakefields in connection with current experiments. We then use these results and provide design guidelines for the…
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 …
Three dimensional, particle-in-cell, fully electromagnetic simulations of electron plasma wake field acceleration applicable to solar atmosphere are presented. It is established that injecting driving and trailing electron bunches into solar coronal and chromospheric plasmas, results in electric fields ($-(20-5) \times 10^{6}$ V/m), leading to acceleration of the trailing bunch up to 52 MeV, starting from initial 36 MeV. The results provide one of potentially important mechanisms for the extreme energetic solar flare electrons, invoking plasma wake field acceleration.
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…
The excitation of wake waves by a relativistic homogeneous electron bunch passing through cold magnetized plasma at equilibrium is studied for arbitrary values of the ratio of bunch density to plasma density. The analysis is based on the assumption that the magnetic field is sufficiently strong ($ω_B\gg ω_p$, where $ω_p$ and $ω_B$ are the electron plasma and cyclotron frequences respectively). The periodic and nonperiodic solutions for the momentum of plasma electrons inside and outside the bunch are analyzed. It was shown that the presence of strong external magnetic field may increase the am…
We show that both the maximum energy gain and the accelerated beam quality can be efficiently controlled by the plasma density profile. Choosing a proper density gradient one can uplift the dephasing limitation. When a periodic wake field is exploited, the phase synchronism between the bunch of relativistic particles and the plasma wave can be maintained over extended distances due to the plasma density gradient. Putting electrons into the $n-$th wake period behind the driving laser pulse, the maximum energy gain is increased by the factor $2πn$ over that in the case of uniform plasma. The acc…
Three dimensional particle in cell simulations are used for studying proton driven plasma wake-field acceleration that uses a high-energy proton bunch to drive a plasma wake-field for electron beam acceleration. A new parameter regime was found which generates essentially constant electric field that is three orders magnitudes larger than that of AWAKE design, i.e. of the order of $2 \times 10^{3}$ GV/m. This is achieved in the the extreme blowout regime, when number density of the driving proton bunch exceeds plasma electron number density 100 times.
We discuss the level of natural shot noise in a proton bunch-driven plasma accelerator. The required seeding for the plasma wake field must be larger than the cumulative shot noise. This is the necessary condition for the axial symmetry of the generated wake and the acceleration quality. We develop an analytical theory of the noise field and compare it with multi-dimensional simulations. It appears that the natural noise wake field generated in plasma by the available at CERN super-protons-synchrotron (SPS) bunches is very low, at the level of a few 10 kV/m. This fortunate fact eases the requi…
Self modulated dynamics of a relativistic charged particle beam is reviewed within the context of the theory of plasma wake field excitation. The self-consistent description of the beam dynamics is provided by coupling the Vlasov equation with a Poisson-type equation relating the plasma wake potential to the beam density. An analysis of the beam envelope self-modulation is then carried out and the criteria for the occurrence of the instability are discussed thereby.
A numerical investigation on the spatiotemporal evolution of an electron beam, externally injected in a plasma in the presence of a plasma wake field, is carried out. The latter is driven by an ultra-short relativistic axially-symmetric femtosecond electron bunch. We first derive a novel Poisson-like equation for the wake potential where the driving term is the ultra-short bunch density, taking suitably into account the interplay between the sharpness and high energy of the bunch. Then, we show that a channel is formed longitudinally, through the externally injected beam while experiencing the…
We propose a new and simple strategy for controlled ionization-induced trapping of electrons in a beam-driven plasma accelerator. The presented method directly exploits electric wakefields to ionize electrons from a dopant gas and capture them into a well-defined volume of the accelerating and focusing wake phase, leading to high-quality witness-bunches. This injection principle is explained by example of three-dimensional particle-in-cell (PIC) calculations using the code OSIRIS. In these simulations a high-current-density electron-beam driver excites plasma waves in the blow-out regime insid…
A positron-beam interacting with the plasma electrons drives radial suck-in, in contrast to an electron-beam driven blow-out in the over-dense regime, $n_b>n_0$. In a homogeneous plasma, the electrons are radially sucked-in from all the different radii. The electrons collapsing from different radii do not simultaneously compress on-axis driving weak fields. A hollow-channel allows electrons from its channel-radius to collapse simultaneously exciting coherent fields. We analyze the optimal channel radius. Additionally, the low ion density in the hollow allows a larger region with focusing phase…
The interaction of coherent nonlinear structures (such as sub-cycle solitons, electron vortices and wake Langmuir waves) with a strong wake wave in a collisionless plasma can be exploited in order to produce ultra-short electromagnetic pulses. The electromagnetic field of a coherent nonlinear structure is partially reflected by the electron density modulations of the incident wake wave and a single-cycle high-intensity electromagnetic pulse is formed. Due to the Doppler effect the length of this pulse is much shorter than that of the coherent nonlinear structure. This process is illustrated wi…
The wake behind a large object (such as the moon) moving rapidly through a plasma (such as the solar wind) contains a region of depleted density, into which the plasma expands along the magnetic field, transverse to the flow. It is shown here that (in addition to any ion instability) a bump-on-tail which is unstable appears on the electrons' parallel velocity distribution function because of the convective non-conservation of parallel energy. It arises regardless of any non-thermal features on the external electron velocity distribution. The detailed electron distribution function throughout t…
Numerical simulations of beam-plasma instabilities may produce quantitatively incorrect results because of unrealistically high initial noise from which the instabilities develop. Of particular importance is the wakefield noise, the potential perturbations that have a phase velocity which is equal to the beam velocity. Controlling the noise level in simulations may offer the possibility of extrapolating simulation results to the more realistic low-noise case. We propose a novel method for generating wakefield noise with a controllable amplitude by randomly located charged rods propagating ahea…
In some laboratory and most astrophysical situations plasma wake-field acceleration of electrons is one dimensional, i.e. variation transverse to the beam's motion can be ignored. Thus, one dimensional (1D), particle-in-cell (PIC), fully electromagnetic simulations of electron plasma wake field acceleration are conducted in order to study the differences in electron plasma wake field acceleration in MeV versus GeV and linear versus blowout regimes. First, we show that caution needs to be taken when using fluid simulations, as PIC simulations prove that an approximation for an electron bunch no…
