Laurent Gremillet

Multidimensional electron beam-plasma instabilities in the relativistic regime

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–Juttner model distributions. The main properties of the competing modes (developing parallel, transverse, and oblique to the beam) 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.

Proton acceleration mechanisms in high-intensity laser interaction with thin foils

The 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.

Exact Relativistic Kinetic Theory of an Electron-Beam-Plasma System: Hierarchy of the Competing Modes in the System-Parameter Space

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 shock formation, spontaneous electromagnetic fluctuations and streaming instabilities

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 Particle-In-Cell 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.

Nonlinear plasma response to a slowly varying electrostatic wave, and application to stimulated Raman scattering

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.

Theory of fast electron transport for fast ignition

Fast ignition (FI) inertial confinement fusion is a variant of inertial fusion in which DT fuel is first compressed to high density and then ignited by a relativistic electron beam generated by a fast (<20?ps) ultra-intense laser pulse, which is usually brought in to the dense plasma via the inclusion of a re-entrant cone. The transport of this beam from the cone apex into the dense fuel is a critical part of this scheme, as it can strongly influence the overall energetics. Here we review progress in the theory and numerical simulation of fast electron transport in the context of FI. Important aspects of the basic plasma physics, descriptions of the numerical methods used, a review of ignition-scale simulations, and a survey of schemes for controlling the propagation of fast electrons are included. Considerable progress has taken place in this area, but the development of a robust, high-gain FI ?point design? is still an ongoing challenge.

Linear and nonlinear development of oblique beam-plasma instabilities in the relativistic kinetic regime

Collisionless beam-plasma instabilities are expected to play a crucial role during the early phase of the relativistic electron transport in the Fast Ignition scheme. This Letter presents a theoretical study of these instabilities in a two-dimensional geometry, highlighting the role of unstable modes propagating obliquely to the beam direction. The main features identified through a linearized analysis in a very general kinetic framework are examined by means of a particle-in-cell simulation. Good agreement between the two approaches is observed in the linear phase. Beam trapping is found to account for the nonlinear wave saturation.

Improved modeling of relativistic collisions and collisional ionization in particle-in-cell codes

An improved Monte Carlo collisional scheme modeling both elastic and inelastic interactions has been implemented into the particle-in-cell code CALDER [E. Lefebvre et al., Nucl. Fusion 43, 629 (2003)]. Based on the technique proposed by Nanbu and Yonemura [J. Comput. Phys. 145, 639 (1998)] allowing to handle arbitrarily weighted macro-particles, this binary collision scheme uses a more compact and accurate relativistic formulation than the algorithm recently worked out by Sentoku and Kemp [J. Comput. Phys. 227, 6846 (2008)]. Our scheme is validated through several test cases, demonstrating, in particular, its capability of modeling the electrical resistivity and stopping power of a solid-density plasma over a broad parameter range. A relativistic collisional ionization scheme is developed within the same framework, and tested in several physical scenarios. Finally, our scheme is applied in a set of integrated particle-in-cell simulations of laser-driven fast electron transport.

Channeling dynamics of relativistic-intensity laser pulses

Two-dimensional particle-in-cell simulations were performed to study the channeling in long (>500μm) underdense plasmas of long duration (>10 ps), relativistic-intensity (I=1018-20 W/cm2) laser pulses. We describe five different types of channeling behaviors, and the corresponding ranges of plasmas and laser parameters are given. In all of these cases, self-corrective mechanisms come into play, which help straighten the channel provided that the laser pulse is long enough to push the plasma ahead. High-quality channels are observed when ξ=(nnc(1+a02/2)-0.5)1.22πW0λa0<0.2, where nc is the critical density, a0 is the vacuum vector potential, W0 is the waist of the laser pulse, and λ is its wavelength. We also define a method to measure the channeling velocity without ambiguity, and we establish scaling laws. It is then possible to use them to predict the channel front position in an inhomogeneous plasma, such as the coronal plasma of a fast ignition target, and to deduce the energy needed to reach the criti...

Nonlinear group velocity of an electron plasma wave

The nonlinear group velocity of an electron plasma wave is investigated numerically using a Vlasov code, and is found to assume values which agree very well with those predicted by a recently published theory [D. Benisti et al., Phys. Rev. Lett. 103, 155002 (2009)], which we further detail here. In particular we show that, once Landau damping has been substantially reduced due to trapping, the group velocity of an electron plasma wave is not the derivative of its frequency with respect to its wave number. This result is moreover discussed physically, together with its implications in the saturation of stimulated Raman scattering.