Abstract:
Beam-plasma instabilities are a key physical process in many astrophysical phenomena. Within the fireball model of Gamma ray bursts, they first mediate a relativistic collisionless shock before they produce upstream the turbulence needed for the Fermi acceleration process. While non-relativistic systems are usually governed by flow-aligned unstable modes, relativistic ones are likely to be dominated by normally or even obliquely propagating waves. After reviewing the basis of the theory, results related to the relativistic kinetic regime of the poorly-known oblique unstable modes will be presented. Relevant systems besides the well-known electron beam-plasma interaction are presented, and it is shown how the concept of modes hierarchy yields a criterion to assess the proton to electron mass ratio in Particle in cell simulations.

Abstract:
We present a particle-in-cell simulation of the generation of a collisionless turbulent shock in a dense plasma driven by an ultra-high-intensity laser pulse. From the linear analysis, we highlight the crucial role of the laser-heated and return-current electrons in triggering a strong Weibel-like instability, giving rise to a magnetic turbulence able to isotropize the target ions.

Abstract:
Besides being one of the most fundamental basic issues of plasma physics, the stability analysis of an electron beam-plasma system is of critical relevance in many areas of physics. Surprisingly, decades of extensive investigation had 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 paper comprehensively tackles this problem by implementing an exact linear model. We show that three kinds of modes compete in the linear phase, which can be classified according to the direction of their wavenumber with respect to the beam. We then determine their respective domain of preponderance in a three-dimensional parameter space. All these results are supported by multidimensional particle-in-cell simulations.

Abstract:
We present a novel laser based ion acceleration scheme, where a petawatt circularly polarized laser pulse is shot on an ultra-thin (nano-scale) double-layer target. Our scheme allows the production of high-quality light ion beams with both energy and angular dispersion controllable by the target properties. We show that extraction of all electrons from the target by radiation pressure can lead to a very effective two step acceleration process for light ions if the target is designed correctly. Relativistic protons should be obtainable with pulse powers of a few petawatt. Careful analytical modeling yields estimates for characteristic beam parameters and requirements on the laser pulse quality, in excellent agreement with one and two-dimensional Particle-in Cell simulations.

Abstract:
We present an exact calculation of the power spectrum of the electromagnetic fluctuations in a relativistic equilibrium plasma described by Maxwell-J\"uttner distribution functions. We consider the cases of wave vectors parallel or normal to the plasma mean velocity. The relative contributions of the subluminal and supraluminal fluctuations are evaluated. Analytical expressions of the spatial fluctuation spectra are derived in each case. These theoretical results are compared to particle-in-cell simulations, showing a good reproduction of the subluminal fluctuation spectra.

Abstract:
The physics of instabilities in the precursor of relativistic collisionless shocks is of broad importance in high energy astrophysics, because these instabilities build up the shock, control the particle acceleration process and generate the magnetic fields in which the accelerated particles radiate. Two crucial parameters control the micro-physics of these shocks: the magnetization of the ambient medium and the Lorentz factor of the shock front; as of today, much of this parameter space remains to be explored. In the present paper, we report on a new instability upstream of electron-positron relativistic shocks and we argue that this instability shapes the micro-physics at moderate magnetization levels and/or large Lorentz factors. This instability is seeded by the electric current carried by the accelerated particles in the shock precursor as they gyrate around the background magnetic field. The compensation current induced in the background plasma leads to an unstable configuration, with the appearance of charge neutral filaments carrying a current of the same polarity, oriented along the perpendicular current. This ``current-driven filamentation'' instability grows faster than any other instability studied so far upstream of relativistic shocks, with a growth rate comparable to the plasma frequency. Furthermore, the compensation of the current is associated with a slow-down of the ambient plasma as it penetrates the shock precursor (as viewed in the shock rest frame). This slow-down of the plasma implies that the ``current driven filamentation'' instability can grow for any value of the shock Lorentz factor, provided the magnetization \sigma <~ 10^{-2}. We argue that this instability explains the results of recent particle-in-cell simulations in the mildly magnetized regime.

Abstract:
The production of ion beams from the interaction of a circularly polarized laser pulse with a nanometric double-layer target is discussed in the regime where all electrons are expelled from the target by laser radiation pressure. Quasi-monochromatic, well-collimated ion beams are observed in two-dimensional particle-in-cell simulations. The ion beam properties are derived from a simple analytical model, and the possibility to control those properties by using a laser-pulse with sharp-rising edge is discussed. Potential application to hadron-therapy is finally considered.

Abstract:
We present a predictive model of the nonlinear phase of the Weibel instability induced by two symmetric, counter-streaming ion beams in the non-relativistic regime. This self-consistent model combines the quasilinear kinetic theory of Davidson et al. [Phys. Fluids 15, 317 (1972)] with a simple description of current filament coalescence. It allows us to follow the evolution of the ion parameters up to a stage close to complete isotropization, and is thus of prime interest to understand the dynamics of collisionless shock formation. Its predictions are supported by 2-D and 3-D particle-in-cell simulations of the ion Weibel instability. The derived approximate analytical solutions reveal the various dependencies of the ion relaxation to isotropy. In particular, it is found that the influence of the electron screening can affect the results of simulations using an unphysical electron mass.

Abstract:
In this paper, we derive coupled envelope equations modeling the growth of stimulated Raman scattering (SRS) in a multi-dimensional geometry, and accounting for nonlinear kinetic effects. In particular, our envelope equations allow for the nonlinear reduction of the Landau damping rate, whose decrease with the plasma wave amplitude depends on the rate of side-loss. Account is also made of the variations in the extent of the plasma wave packet entailed by the collisionless dissipation due to trapping. The dephasing between the electron plasma wave (EPW) and the laser drive, as well as the self-focussing of the plasma wave, both induced by the EPW nonlinear frequency shift, are also included in our envelope equations. These equations are solved in a multi-dimensional geometry using our code dubbed BRAMA, whose predictions regarding the evolution of Raman reflectivity as a function of the laser intensity are compared against previously published PIC results, thus illustrating the ability of BRAMA simulations to provide the correct laser threshold intensity for SRS, as well as the right order of magnitude of Raman reflectivity above threshold.

Abstract:
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.