The interest in relativistic beam-plasma instabilities has been greatly rejuvenated over the past two decades by novel concepts in laboratory and space plasmas. Recent advances in this long-standing field are here reviewed from both theoretical and numerical points of view. The primary focus is on the two-dimensional spectrum of unstable electromagnetic waves growing within relativistic, unmagnetized, and uniform electron beam-plasma systems. Although the goal is to provide a unified picture of all instability classes at play, emphasis is put on the potentially dominant waves propagating obliquely to the beam direction, which have received little attention over the years. First, the basic derivation of the general dielectric function of a kinetic relativistic plasma is recalled. Next, an overview of two-dimensional unstable spectra associated with various beam-plasma distribution functions is given. Both cold-fluid and kinetic linear theory results are reported, the latter being based on waterbag and Maxwell-Jüttner model distributions. The main properties of the competing modes ͑developing parallel, transverse, and oblique to the beam͒ are given, and their respective region of dominance in the system parameter space is explained. Later sections address particle-in-cell numerical simulations and the nonlinear evolution of multidimensional beam-plasma systems. The elementary structures generated by the various instability classes are first discussed in the case of reduced-geometry systems. Validation of linear theory is then illustrated in detail for large-scale systems, as is the multistaged character of the nonlinear phase. Finally, a collection of closely related beam-plasma problems involving additional physical effects is presented, and worthwhile directions of future research are outlined.

The paraxial propagation of a relativistic electron beam in a solid target is examined, within a three-dimensional model of particles interacting with the target electron return current via a diffusive electromagnetic field. Simulations of a modulated beam show amplification of the modulation seed, with growth rates comparing reasonably well with the linear analysis of the model. Scenarios of beam fragmentation are observed and discussed in more realistic conditions, when beam collisions on both target ions and electrons and the resulting solid heating and ionization are taken into account.

The nonlinear electronic susceptibility induced by an electrostatic wave slowly varying in space and time, which is the key parameter for the kinetic modeling of stimulated Raman scattering (SRS), is derived analytically. When calculating the real part of the susceptibility, by making the adiabatic approximation, account is taken of the amplitude dependence of the wave frequency. Then, the “loss of resonance” of a plasma wave is found to occur at much larger amplitudes than has been predicted by Rose and Russel [H. A. Rose and D. A. Russell, Phys. Plasmas 11, 4784 (2001)] using the constant-frequency approximation. The imaginary part of the susceptibility, from which is deduced the Landau damping rate of the plasma wave, is derived using two different approaches (perturbative or not) depending on the wave amplitude. It is shown to be a nonlocal function of the wave amplitude, which underlines the importance of interspeckle interactions in SRS.

The stability analysis of an electron-beam-plasma system is of critical relevance in many areas of physics. Surprisingly, decades of extensive investigation have not yet resulted in a realistic unified picture of the multidimensional unstable spectrum within a fully relativistic and kinetic framework. All attempts made so far in this direction were indeed restricted to simplistic distribution functions and/or did not aim at a complete mapping of the beam-plasma parameter space. The present Letter comprehensively tackles this problem by implementing an exact linear model. Three kinds of modes compete in the linear phase, which can be classified according to the direction of their wave number with respect to the beam. We determine their respective domain of preponderance in a three-dimensional parameter space and support our results with multidimensional particle-in-cell simulations.

Collisionless shocks are ubiquitous in astrophysics and in the lab. Recent numerical simulations and experiments have shown how they can arise from the encounter of two collisionless plasma shells. When the shells interpenetrate, the overlapping region turns unstable, triggering the shock formation. As a first step towards a microscopic understanding of the process, we analyze here in detail the initial instability phase. On the one hand, 2D relativistic PIC simulations are performed where two symmetric initially cold pair plasmas collide. On the other hand, the instabilities at work are analyzed, as well as the field at saturation and the seed field which gets amplified. For mildly relativistic motions and onward, Weibel modes govern the linear phase. We derive an expression for the duration of the linear phase in good agreement with the simulations. This saturation time constitutes indeed a lower-bound for the shock formation time.

The evolution of laser-generated MeV, MA electron beams propagating through conductors and insulators has been studied by comparing measurement and modeling of the distribution of MeV protons that are sheath accelerated by the propagated electrons. We find that electron flow through metals is uniform and can be laser imprinted, whereas propagation through insulators induces spatial disruption of the fast electrons. Agreement is found with material dependent modeling.

International audienceThe interaction of short and intense laser pulses with plasmas or solids is a very efficient source of high-energy ions. This paper reports the detailed study, with particle-in-cell simulations, of the interaction of such a laser pulse with thin, dense targets, and the resulting proton acceleration. Depending on the laser intensity and pulse duration, the most energetic protons are found to come from the front, the core, or the back of the target. The main accelerating mechanisms discussed in this paper are plasma expansion acceleration, where proton acceleration is driven by the hot electron population, and shock acceleration, originating from the laser ponderomotive potential imposed at the front target surface. Three main regimes of proton acceleration are defined and the parameters for which each regime is dominant are obtained. For irradiances close to 10^20 W/cm^2, the highest proton energies are obtained from thin foils efficiently heated by relativistic transparency. At larger intensities, a complex interplay between collisionless shock acceleration and plasma expansion acceleration is evidenced

Following a recent Letter by Bret [Phys. Rev. Lett. 100, 205008 (2008)], we present a detailed report of the entire unstable k spectrum of a relativistic collisionless beam-plasma system within a fully kinetic framework. In contrast to a number of previously published studies, our linear analysis makes use of smooth momentum distribution functions of the Maxwell-Jüttner form. The three competing classes of instabilities, namely, two-stream, filamentation, and oblique modes, are dealt with in a unified manner, no approximation being made regarding the beam-plasma densities, temperatures, and drift energies. We investigate the hierarchy between the competing modes, paying particular attention to the relatively poorly known quasielectrostatic oblique modes in the regime where they govern the system. The properties of the fastest growing oblique modes are examined in terms of the system parameters and compared to those of the dominant two-stream and filamentation modes.