G. Laval

Study of stationary plasma thrusters using two-dimensional fully kinetic simulations

Stationary plasma thrusters are devices that use crossed electric and magnetic fields to accelerate ions to high velocities. Ions are created by collisional ionization of a propellant gas with electrons injected from a hollow cathode external to the thruster. A major issue is the electron transport through the magnetic field. It is known to exceed considerably the values predicted by the classical theory. Various 2D models have shown that wall collisions, which have often been invoked as the origin of this anomalous transport, are in fact insufficient. Anomalous turbulent transport has to be added to the model to recover an adequate conductivity. In the present paper the first 2D kinetic model that shows that, indeed, plasma turbulence can explain the observed conductivity is presented. Without any free parameter the model is able to reproduce numerous experimental features. At the end of the paper a preliminary theoretical analysis of the observed instability is provided.

High-frequency electron drift instability in the cross-field configuration of Hall thrusters

A systematic study of a high-frequency electron drift instability is presented. It has very large wave numbers corresponding to wavelengths close to the electron gyroradius. The three-dimensional dispersion relation is derived for a model of a crossed electric and magnetic field configuration existing in the Hall thruster. It is shown that the instability develops in packets of oblique unstable modes perpendicular to the magnetic field. The evolution of the instability is also studied for distorted electron distribution functions obtained in particle-in-cell simulations.

Modulational and Raman instabilities in the relativistic regime

A large amplitude electromagnetic wave propagating in a plasma is known to be subject to severe modulational and Raman instabilities. Previous works were devoted to the weakly relativistic limit and applied mainly to a cold underdense plasma. One extends these works to include the fully relativistic limit for a circularly polarized light for which one derives the dispersion relation in a one‐dimensional plasma. The characteristics of the instabilities are also calculated in the case where the plasma is classically overdense, with 1<(ωp/ω0)2<γ, where ωp is the plasma frequency, ω0 is the laser frequency, and γ is the relativistic factor of an electron in the laser field. Particle‐in‐cell simulations confirm the results of the numerical solutions of the dispersion relation. For (ωp/ω0)2/γ=0.57 the growth rate can be as large as 0.52ω0. The nonlinear stage of the instability results in a strong heating of the electron distribution function. The theory is further extended to the case of an initially hot plasm...

Propagation of ultraintense laser pulses through overdense plasma layers

Due to relativistic effects, a large amplitude electromagnetic wave can propagate in a classically overdense plasma with ω2p≳ω2≳ω2p/γ, where ωp is the plasma frequency, ω the laser frequency, and γ the relativistic factor of an electron in the laser field. Particle‐in‐cell simulations are used to study the interaction of an ultrahigh intensity laser pulse in normal incidence on a one‐dimensional preformed plasma layer. Both electrons and ions dynamics are included. The width of the layer is 10 to 30 μm and the plasma is characterized by (ωp/ω)2=1.5. During the penetration of the electromagnetic wave a large longitudinal electric field is generated. It results in a strong longitudinal heating of electrons which reach relativistic temperatures. This heating further lowers the effective plasma frequency ωp/γ so the layer becomes almost transparent after the plasma crossing by the wave front. Velocity of the wave front, reflection and transmission rates are studied as functions of the incident energy flux, th...

Electron parametric instabilities of ultraintense laser pulses propagating in plasmas of arbitrary density

The dispersion relation for electron parametric instabilities of a circularly polarized laser wave of arbitrary intensity is established without restrictions on the plasma density. It is obtained in an implicit analytical form and solved numerically. The well-known stimulated Raman scattering, relativistic modulational instability, relativistic filamentation instability, and two-plasmon decay are recovered at low intensity. Their behavior in the ultrarelativistic regime is characterized by a wide extent of the unstable region in the wave vector space, with growth rates equal to a fraction of the laser frequency, and a strong harmonic generation. Particle-in-cell simulations confirm these results and show that the instability leads to a very strong heating of the plasma.

Controversies about quasi-linear theory

This paper is devoted to the presentation of various theories describing wave-particle interaction in the case of one-dimensional (1D) turbulence. The results obtained from recent experiments and simulations are compared with the theoretical predictions.

Particle diffusion in stochastic magnetic fields

Particle transport across braided magnetic surfaces is studied by using simple field and collision models. Diffusion along and across field lines is taken into account. A general variational principle is established. It provides a useful guide for numerical computations. In a special case an explicit formula for the diffusion coefficient is obtained. Several diffusion regimes are clearly identified, and their domain of validity is determined. A new form of the diffusion coefficient has to be introduced in the long‐mean‐free‐path regime.

Parametric instabilities due to relativistic electron mass variation

The stability of an electronic plasma in a large-amplitude dipolar field is analyzed. In such a wave the relativistic electron mass variation must be taken into account and in an overdense plasma an instability arises. The corresponding weakly relativistic theory of Tsintsadze [Sov. Phys. JETP 32, 684 (1971)] is extended to the fully relativistic regime. The growth rate of the instability can attain a significant fraction of the dipolar field frequency. The relevance of this instability to the fast ignitor concept is discussed.

Theory and simulation of electronic relativistic parametric instabilities for ultraintense laser pulses propagating in hot plasmas

The dispersion relation for electronic parametric instabilities of a circularly polarized laser wave is solved in the case where the distribution function is supposed to be cold in the transverse direction and to be a linear combination of a cold distribution function and of a Maxwellian in momentum in the longitudinal direction. Only densities below the critical density are considered. It is shown that the longitudinal temperature as expected reduces the growth rate, but that the existence of a hot tail is not sufficient to significantly reduce the instability. It is the bulk of the distribution function that must be heated to efficiently stabilize the system. Another important effect of the heating is to reduce the backscattered component of the instability. An example of a one-dimensional particle simulation performed in the exact conditions of validity of the theory is discussed.

Harmonic generation and departure from quasineutrality in ion sound and Langmuir wave coupling

The validity conditions of the Zakharov equations are reconsidered by investigating the linear stability analysis of a dipolar Langmuir wave. It is shown that the corresponding dispersion relation has a wider range of applicability, W/NT<(kλD)−2, than the usual domain of validity of the Zakharov equations, W/NT<1 (W/NT is the ratio of the Langmuir wave energy to the particle thermal energy, k is the characteristic wave number of the low‐frequency perturbation). This result follows from an exact cancellation between the corrections as a result of the departure from quasineutrality and the contributions from the harmonics of the Langmuir wave. Such a cancellation is interpreted in terms of absence of nonlinear frequency shift caused by a dipolar pump wave in the dispersion relation of the Langmuir waves. The next‐order corrections to the linearized Zakharov equations are computed; the proper renormalization of the low‐frequency part of the dispersion relation is shown to result from the slow time variation ...