A nonlinear beatwave regime of plasma wave excitation is considered. Two beatwave drivers are considered: intensity-modulated laser pulse and density-modulated (microbunched) electron beam. It is shown that a long beatwave pulse can excite strong plasma waves in its wake even when the beatwave frequency is detuned from the electron plasma frequency. The wake is caused by the dynamic bi-stability of the nonlinear plasma wave if the beatwave amplitude exceeds the analytically calculated threshold. In the context of a microbunched beam driven plasma wakefield accelerator, this excitation regime can be applied to developing a femtosecond electron injector.
We present a summary of the beatwave particle acceleration program developed at Ecole Polytechnique. In dedicated experiments, plasma formation, plasma wave generation and saturation, and particle acceleration were successively studied and understood in detail. A maximum energy gain of 1.3 MeV was obtained, which is compatible with an accelerating gradient of 0.7 GV/m.
The near-resonant beatwave excitation of an electron plasma wave (EPW) can be employed for generating the trains of few-femtosecond electromagnetic (EM) pulses in rarefied plasmas. The EPW produces a co-moving index grating that induces a laser phase modulation at the difference frequency. The bandwidth of the phase-modulated laser is proportional to the product of the plasma length, laser wavelength, and amplitude of the electron density perturbation. The laser spectrum is composed of a cascade of red and blue sidebands shifted by integer multiples of the beat frequency. When the beat frequen…
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 …
The interaction of two laser pulses in an underdense plasma has proven to be able to inject electrons in plasma waves, thus providing a stable and tunable source of electrons. Whereas previous works focused on the "beatwave" injection scheme in which two lasers with the same polarization collide in a plasma, this present letter studies the effect of polarization and more specifically the interaction of two colliding cross-polarized laser pulses. It is shown both theoretically and experimentally that electrons can also be pre-accelerated and injected by the stochastic heating occurring at the c…
Recently the interest in relativistic quantum plasma is increasing primarily to understand the fundamentals of the plasma behaviour and its properties. Mathematical models used to investigate these plasma are still need to be matured. Especially, the relativistic quantum electron-ion plasma are modeled using the Klein-Gordon equation and the Dirac equation for relativistic electrons. However, different properties of these plasma are investigated without anti-particles. We note that in order to preserve causality relativistic quantum plasma must contain anti-particles for relativistically dynam…
The stimulated Raman scattering instability in a fully degenerate electron plasma is studied applying relativistic hydrodynamic and Maxwell equations. We demonstrated that the instability develops for weakly as well as strongly relativistic degenerate plasma. It is shown that in the field of strong radiation relativistically degenerate plasma effectively responses as in the case of weak degeneracy.
The existence of standing high frequency electromagnetic (EM) solitons in a fully degenerate overdense electron plasma is studied applying relativistic hydrodynamics and Maxwell equations. The stable soliton solutions are found in both relativistic and nonrelativistic degenerate plasmas.
The existence of soliton-like electromagnetic (EM) distributions in a fully degenerate electron-positron plasma is studied applying relativistic hydrodynamic and Maxwell equations. For circularly polarized wave it is found that the soliton solutions exist both in relativistic as well as nonrelativistic degenerate plasmas. Plasma density in the region of soliton pulse localization is reduced considerably. The possibility of plasma cavitation is also shown.
3D particle-in-cell simulations demonstrate that the enhanced transparency of a relativistically hot plasma is sensitive to how the energy is partitioned between different degrees of freedom. For an anisotropic electron distribution, propagation characteristics, like the critical density, will depend on the polarization of the electromagnetic wave. Despite the onset of the Weibel instability in such plasmas, the anisotropy can persist long enough to affect laser propagation. This plasma can then function as a polarizer or a waveplate to dramatically alter the pulse polarization.
We consider the relativistic ion-acoustic mode in a plasma composed by cold ions and an ultra-degenerate electron gas, described the relativistic Vlasov-Poisson system. A critical examination of popular fluid models for relativistic ion-acoustic waves is provided, comparing kinetic and hydrodynamic results. The kinetic linear dispersion relation is shown to be reproduced by the rigorous relativistic hydrodynamic equations with Chandrasekhar's equation of state.
The collisional coupling of relativistic electrons and non-relativistic ions in hot plasmas has been analysed. It is found that relativistic effects produce a new feature: while the condition T_e<3T_i guarantees a stable collisional coupling between electrons and ions in low-temperature plasmas, relativistic effects shift the upper T_e/T_i boundary of stability to higher values. Moreover, for sufficiently high temperatures, T_{e,i} > 75 keV, collisional decoupling between relativistic electrons and ions becomes impossible.
With the aid of large-scale three-dimensional QED-PIC simulations, we describe a realistic experimental configuration to measure collective effects that couple strong field quantum electrodynamics to plasma kinetics. For two counter propagating lasers interacting with a foil at intensities exceeding $10^{22}$ Wcm$^{-2}$, a binary result occurs; when quantum effects are included, a foil that classically would effectively transmit the laser pulse becomes opaque. This is a dramatic change in plasma behavior, directly as a consequence of the coupling of radiation reaction and pair production to pl…
The influence of motion of ions and electron temperature on nonlinear one-dimensional plasma waves with velocity close to the speed of light in vacuum is investigated. It is shown that although the wavebreaking field weakly depends on mass of ions, the nonlinear relativistic wavelength essentially changes. The nonlinearity leads to the increase of the strong plasma wavelength, while the motion of ions leads to the decrease of the wavelength. Both hydrodynamic approach and kinetic one, based on Vlasov-Poisson equations, are used to investigate the relativistic strong plasma waves in a warm plas…
Relativistic heat transport in electron-two-temperature plasmas with density gradients has been investigated. The Legendre expansion analysis of relativistically modified kinetic equations shows that strong inhibition of heat flux appears in relativistic temperature regimes, suppressing the classical Spitzer-H{ä}rm conduction. The Seebeck coefficient, the Wiedemann-Franz law, and the thermoelectric figure of merit are derived in the relativistic regimes.
In this paper, the effect of finite electron temperature on the space-time evolution and breaking of a large amplitude relativistically intense electron plasma wave has been studied, using a 1-D relativistic Particle-in-Cell (PIC) code. We have found that for phase velocities for which $γ_ϕ\ll 1 + \frac{k_BT_e}{mc^2}$, the wave damps within a few plasma period and essentially follows the relativistic Landau Damping rate predicted by Buti. In the opposite regime (i.e. for $γ_ϕ\gg 1 + \frac{k_BT_e}{mc^2}$) we have observed that waves propagate through the system for a long period of time and in …
The filamentation instability of the electromagnetic (EM) beam in an underdense plasma with high level of degeneracy is examined by means of the momentum equation, continuity equation and Maxwell's equations. It has been demonstrated that the instability develops for weakly as well as strongly relativistic degenerate plasma and arbitrary strong amplitude of EM beams.
One-dimensional steady-state plasma-field structures in overdense plasma are studied assuming that the electron temperature is uniform over plasma bulk and the ions are stationary. It is shown that there may exist solutions for electron distributions with cavitation regions in plasma under the action of ponderomotive force
We consider a recently derived kinetic model for weakly relativistic quantum plasmas. We find that that the effects of spin-orbit interaction and Thomas precession may alter the linear dispersion relation for a magnetized plasma in case of high plasma densities and/or strong magnetic fields. Furthermore, the ponderomotive force induced by an electromagnetic pulse is studied for an unmagnetized plasma. It turns out that for this case the spin-orbit interaction always give a significant contribution to the quantum part of the ponderomotive force.
This paper studies the propagation of intense laser in plasmas in weak relativistic region($0.1<a_0^2<0.5$) using the quasi-periodic approximation. Effective Lorentz factor and density wave effects are calculated in detail. The relativistic correction on stimulated Brillouin instability is investigated in the rest parts. The coupled dispersion relations of Stimulated Brillouin Scattering(SBS) are obtained and investigated numerically.
Creating magnetized relativistic pair plasma in the laboratory would enable the exploration of unique plasma physics relevant to some of the most energetic events in the universe. As a step towards a laboratory pair plasma, we have demonstrated effective confinement of multi-$\mathrm{MeV}$ electrons inside a pulsed-power-driven $13$ $\mathrm{T}$ magnetic mirror field with a mirror ratio of $2.6$. The confinement is diagnosed by measuring the axial and radial losses with magnetic spectrometers. The loss spectra are consistent with $\leq 2.5$ $\mathrm{MeV}$ electrons confined in the mirror for $…
The paper presents a relativistic mechanism that can create a poloidal non-uniformity of a radial electric field on a magnetic surface in a tokamak plasma. This mechanism is associated with a significant current velocity of electrons in plasma for many experimental modes of tokamak operations. It is important that electric fields arise without the traditional separation of charges in plasma. The presented mechanism can explain the previously experimentally measured poloidal non-uniformity of the C+6 carbon ion toroidal rotation velocity in the TORE-SUPRA tokamak plasma
{A simple electrodynamic model is developed to define plasma-field structures in self-consistent ultra-relativistic laser-plasma interactions when the radiation reaction effects come into play. An exact analysis of a circularly polarized laser interacting with plasmas is presented. We define fundamental notations such as nonlinear dielectric permittivity, ponderomotive and dissipative forces acting in a plasma. Plasma-field structures arising during the ultra-relativisitc interactions are also calculated. Based on these solutions we show that about 50% of laser energy can be converted into gam…
On the base of the quantum kinetic equation for density matrix in plasma at the stimulated bremsstrahlung of electrons on ions, the nonlinear absorption rate for high-intensity shortwave radiation in plasma has been obtained within relativistic quantum theory. Both classical Maxwellian and degenerate quantum plasma are considered for x-ray lasers of high intensities. Essentially different dependences of nonlinear absorption rate on polarization of strong laser radiation is stated.
Interaction of an intense electromagnetic (EM) beam with hot relativistic plasma is investigated. It is shown that the thermal pressure brings about a fundamental change in the dynamics - localized, high amplitude, EM field structures, not accessible to a cold (but relativisic) plasma, can now be formed under well- defined conditions. Examples of the trapping of EM beams in self-guiding regimes to form stable 2D solitonic structures in a pure e-p plasma are worked out.
Radiation spectrum of extreme relativistic electrons and a probability of electron-positron pair production by energetic photons in a strong plasma wakefield are derived in the framework of a semiclassical approach. It is shown that that the radiation losses of the relativistic electron in the plasma wakefield scale as $ \propto ε^{2 / 3}$ in the quantum limit when the energy of the radiated photon becomes close to the electron energy, $ε$. The quantum effects will play a key role in future plasma-based accelerators operating at ultrahigh energy of the electrons.
We consider the reflection of relativistically strong radiation from plasma and identify the physical origin of the electrons' tendency to form a thin sheet, which maintains its localisation throughout its motion. Thereby we justify the principle of the relativistic electronic spring (RES) proposed in [A. Gonoskov et al. PRE 84, 046403 (2011)]. Using the RES principle we derive a closed set of differential equations that describe the reflection of radiation with arbitrary variation of polarization and intensity from plasma with arbitrary density profile for arbitrary angle of incidence. PIC si…
We analyze the motion of the plasma critical layer by two different processes in the relativistic-electron laser-plasma interaction regime ($a_0>1$). The differences are highlighted when the critical layer ions are stationary in contrast to when they move with it. Controlling the speed of the plasma critical layer in this regime is essential for creating low-$β$ traveling acceleration structures of sufficient laser-excited potential for laser ion accelerators (LIA). In Relativistically Induced Transparency Acceleration (RITA) scheme the heavy plasma-ions are fixed and only trace-density light-…
The production of weakly relativistic plasma by microwave electric field with circular polarization has been studied. Electron distribution function obtained for this produced plasma and shown that it is non-equilibrium and anisotropic. It is shown that produced plasma accelerated on direction of propagation microwave electric field. The electron velocity on this direction strongly depends on electron origination phase during ionization and microwave electric field phase and it s amplitude. The dielectric tensor obtained for this plasma and the weibel instability studied for it.
A method for the controlled generation of intense high frequency electromagnetic fields by a breaking Langmuir wave (relativistic flying mirrors) in a gradually inhomogeneous plasma is proposed. The wave breaking threshold depends on the local plasma density gradient. Compression, chirping and frequency multiplication of an electromagnetic wave reflected from relativistic mirrors is demonstrated using Particle-In-Cell simulations. Adjusting the shape of the density profile enables control of the reflected light properties.
A self-consistent relativistic two-fluid model is proposed for one-dimensional electron-ion plasma dynamics. A multiple scales perturbation technique is employed, leading to an evolution equation for the wave envelope, in the form of a nonlinear Schrödinger type equation (NLSE). The inclusion of relativistic effects is shown to introduce density-dependent factors, not present in the non-relativistic case - in the conditions for modulational instability. The role of relativistic effects on the linear dispersion laws and on envelope soliton solutions of the NLSE is discussed.
A new quasi-neutral model describing the Weibel instability of a high-current relativistic beam propagating through a resistive plasma is developed. It treats beam electrons as kinetic particles, and ambient plasma as a non-relativistic fluid. For a finite-temperature beam, a new class of negative energy magneto-sound waves is identified, which can possess negative energy. Their growth due to collisional dissipation in the cold return current destabilizes the beam-plasma system even for high beam temperatures. We perform detailed two- and three-dimensional particle-in-cell (PIC) simulations of…
We consider the bremsstrahlung of electrons of fully ionized plasma. Electron energy range extends from a few hundred electron volts before the extreme relativistic energies of several MeV. The results of calculations of effective slow-down rate of a single electron and the power emission from a volume of the plasma with Maxwellian electrons. At relativistic energies, the Born approximation yields highly accurate results. Correction to the Born approximation are considered for low-energy regimes. In the high-energy regimes numerical results are close to extreme relativistic analytic results. T…
Generalising the work of Lenard and Bernstein, we introduce a new, fully relativistic model to describe collisional plasmas. Like the Fokker-Planck operator, this equation represents velocity diffusion and conserves particle number. However, unlike the Fokker-Planck operator it is linear in the distribution function, and so more amenable to a fluid treatment. By taking moments, we derive a new fluid model, and demonstrate the damping effects of collisions on Langmuir waves.
Longitudinal and transverse behavior of magnetic field of relativistic nonlinear three-dimensional plasma wave is investigated. It is shown that the magnetic field of the wave is different from zero and performs higher frequency oscillations compared to the plasma electron frequency. An increase in the nonlinearity leads to strengthening of magnetic field. The oscillations of magnetic field in transverse direction arise, that caused by the phase front curving of nonlinear plasma wave. The numerical results well conform with predictions of the analytical consideration of weakly-nonlinear case.
We develop a method for investigating the relationship between the shape of a 1-particle distribution and non-linear electrostatic oscillations in a collisionless plasma, incorporating transverse thermal motion. A general expression is found for the maximum sustainable electric field, and is evaluated for a particular highly anisotropic distribution.
Creation of angular momentum in a relativistic electron-positron plasma is explored. It is shown that a chain of angular momentum carrying vortices is a robust asymptotic state sustained by the generalized nonlinear Schrodinger equation characteristic to the system. The results may suggest a possible electromagnetic origin of angular momenta when it is applied to the MeV epoch of the early Universe.
The nonlinear propagation of small amplitude ion acoustic solitary wave in relativistic degenerate magneto plasma in presence of ion beam is investigated in detail. The nonlinear equations describing the evolution of solitary wave in presence of relativistic non-degenerate magnetized positive ions and ion beams including magnetized degenerate relativistic electrons are derived in terms of Zakharov-Kuznetsov (Z-K) equation for such plasma systems. The ion beams which are ubiquitous ingredient in such plasma systems, are found to have a decisive role in the propagation of solitary wave in such h…
Strong magnetic fields at plasma-plasma interfaces can be naturally produced in laser-plasma interactions. Using theoretical analysis and fully three-dimensional particle-in-cell simulations, we demonstrate that relativistic topological waves can be generated via Cherenkov and Doppler resonances in the interaction of intense femtosecond laser pulses with near-critical-density plasmas. At the self-magnetized plasma-plasma interface, a new slow-wave branch appears. Its phase velocity is much smaller than the group velocity of the laser pulse and the electron beam velocity. Therefore, the Cherenk…
Magnetic reconnection is a fundamental plasma process associated with conversion of the embedded magnetic field energy into kinetic and thermal plasma energy, via bulk acceleration and Ohmic dissipation. In many high-energy astrophysical events, magnetic reconnection is invoked to explain the non-thermal signatures. However, the processes by which field energy is transferred to the plasma to power the observed emission are still not properly understood. Here, via 3D particle-in-cell simulations of a readily available (TW-mJ-class) laser interacting with a micro-scale plasma slab, we show that …
Singularities in multi-stream flows of relativistic plasmas can efficiently produce coherent high-frequency radiation, as exemplified in the concepts of Relativistic Flying Mirror [S. V. Bulanov, et al., Phys. Rev. Lett. 91, 085001 (2003)] and Burst Intensification by Singularity Emitting Radiation (BISER) [Pirozhkov, et al., Scientific Reports 7, 17968 (2017)]. Direct observation of these singularities is challenging due to their extreme sharpness (tens of nanometers), relativistic velocity, and transient non-local nature. We propose to use ultrafast (a few light cycles) optical probe for ide…
We investigate the propagation of electromagnetic waves in resistive pair plasmas using a onefluid theory derived from the relativistic two-fluid equations. When the resistivity normalized by the electron/positron inertia variable exceeds a critical value, the dispersion relation for electromagnetic waves shows that the group velocity is larger than the light speed in vacuum. However, in such a case, it also is found that the plasma parameter is less than unity: that is, the electron-positron pair medium no longer can be treated as plasma. Thus the simple two-fluid approximation is invalid. Th…
The novel hydrodynamic model of plasmas with the relativistic temperatures consisted of four equations for the material fields: the concentration and the velocity field \emph{and} the average reverse relativistic $γ$ functor and the flux of the reverse relativistic $γ$ functor is applied to study high-frequency part of spectrum of electromagnetic waves propagating perpendicular to the external magnetic field. The thermal effects considered for the temperatures close to the rest energy of electrons considerably change the dispersion equation in compare with the nonrelativistic temperatures. Ana…
Contributions of the current-current and Darwin interactions and weak-relativistic addition to kinetic energy in the quantum hydrodynamic equations are considered. Features of hydrodynamic equations for two-dimensional layer of plasma (two-dimensional electron gas for instance) are described. It is shown that the force fields caused by the Darwin interaction and weak-relativistic addition to kinetic energy are partially reduced. Dispersion of three- and two-dimensional semi-relativistic Langmuir waves is calculated.
The filamentary structures and associated electromagnetic fields of a relativistic electron beam have been studied by three dimensional particle-in-cell (PIC) simulations in the context of Fast Ignition fusion. The simulations explicitly include collisions in return plasma current and distinctly examine the effects of beam temperature and collisions on the growth of filamentary structures generated.
A non-relativistic multi-fluid plasma axisymmetric equilibrium model was developed recently to account for the presence of an energetic electron fluid in addition to thermal electron and ion fluids. The equilibrium formulation of a multi-fluid plasma with relativistic energetic electrons is developed and reported in this paper. Relativistic effects in a fluid model approximation can appear in two ways: due to a large macroscopic fluid velocity comparable to the speed of light and large particle's microscopic random motion which becomes significant if the temperature becomes comparable to or la…
Lorentz invariant scalar functions of the magnetic field are defined in an ideal relativistic plasma. These invariants are advected by the plasma fluid motion and play the role of the {\it potential magnetic field} introduced by R. Hide in Ann. Geophys. 1, 59 (1983) on the line of Ertel's theorem. From these invariants we recover the Cauchy conditions for the magnetic field components in the Eulerian-Lagrangian variable mapping. In addition the adopted procedure allows us to formulate Alfvèn theorem for the conservation of the magnetic flux through a surface comoving with the plasma in a Loren…
Many-particle QED is applied to kinetic theory of radiative processes in many- component plasmas with relativistic electrons and nonrelativistic heavy particles. Within the framework of nonequilibrium Green's function technique, transport and mass-shell equations for fluctuations of the electromagnetic field are obtained. We show that the transverse field correlation functions can be decomposed into sharply peaked (non-Lorentzian) parts that describe resonant (propagating) photons and off-shell parts corresponding to virtual photons in plasmas. Analogous decomposi- tions are found for the long…
Phase mixing of relativistic large amplitude nonlinear plasma wave in presence of a time independent space periodic ion density profile has been investigated. Inhomogeneous ion along with the relativistic variation of electron mass make the characteristic frequency of the wave to acquire a space dependency and thereby it breaks at arbitrarily small amplitude due to phase mixing. An approximate space time dependent solution is obtained in the weakly relativistic limit by Bogoliuboff and Kryloff method of averaging. We find that the change in the ion density perturbation and also the relativisti…
The Alfvenic waves and fast magneto-sound in the relativistically hot plasmas are considered. This study is based on the novel hydrodynamic model of plasmas with the relativistic temperatures consisted of four equations for the material fields: the concentration and the velocity field \emph{and} the average reverse relativistic $γ$ functor and the flux of the reverse relativistic $γ$ functor. Three temperature regimes giving considerably different behavior of the spectrum of Alfvenic waves are found. Four temperature regimes are obtained for the fast magneto-sound. All these regimes show consi…
Relativistic self-focusing and channeling of intense laser pulses have been studied in underdense plasma using 2D PIC simulations, for different laser powers and plasma densities. Analytical solutions for the stationary evacuated channels have been recovered in PIC simulations. It is shown that otherwise stable channels can accelerate electrons due to surface waves on the walls of the channels. Relativistic filaments with finite electron density are unstable to transverse modulations which lead in the nonlinear stage to the break-up of laser pulses into independent filaments. Different regimes…
Tightly focused laser pulses as they diverge or converge in underdense plasma can generate wake waves, having local structures that are spherical waves. Here we report on theoretical study of relativistic spherical wake waves and their properties, including wave breaking. These waves may be suitable as particle injectors or as flying mirrors that both reflect and focus radiation, enabling unique X-ray sources and nonlinear QED phenomena.
In the present analysis we study the self consistent propagation of nonlinear electromagnetic pulses in a one dimensional relativistic electron-ion plasma, from the perspective of nonlinear dynamics. We show how a series of Hamiltonian bifurcations give rise to the electric fields which are of relevance in the subject of particle acceleration. Connections between these bifurcated solutions and results of earlier analysis are made.
The regimes of quasi-mono-energetic electron beam generation were experimentally studied in the sub-relativistic intensity laser plasma interaction. The observed electron acceleration regime is unfolded with two-dimensional-particle-in-cell simulations of laser-wakefield generation in the self-modulation regime.
Trines and Norreys state that a principle aim of their work on warm wave-breaking was ``to create some order in the diverse landscape of warm fluid models and establish which model is most suitable for the study of wave breaking in thermal plasma.'' Unfortunately, we must conclude that they have obfuscated more than they have clarified, and have advanced the waterbag model only by exaggerating or misstating its benefits while mischaracterizing features of alternative warm fluid theories.
