Sideband growth rates for differentiable and discontinuous distribution functions.

This article addresses the stability of a nonlinear electron plasma wave (EPW) against the growth of longitudinal sidebands. The electron distribution function consistent with the EPW is assumed to only depend on the dynamical action. Consequently, the EPW is either stationary (a so-called Berstein-Greene-Kruskal mode) or varies very slowly in space and time (a so-called adiabatic wave).

Erratum: Global change in action due to trapping: How to derive it whatever the rate of variation of the dynamics [Phys. Rev. E 91, 042915 (2015)].

This corrects the article DOI: 10.1103/PhysRevE.91.

Global change in action due to trapping: How to derive it whatever the rate of variation of the dynamics.

In this paper, we investigate the motion of a set of charged particles acted upon by a growing electrostatic wave in the limit when the initial wave amplitude is vanishingly small and when all the particles have the same initial action, I(0). We show, both theoretically and numerically, that when all the particles have been trapped in the wave potential, the distribution in action exhibits a very sharp peak about the smallest action. Moreover, as the wave keeps growing, the most probable action tends toward a constant, I(f), which we estimate theoretically.

Stability of nonlinear Vlasov-Poisson equilibria through spectral deformation and Fourier-Hermite expansion.

We study the stability of spatially periodic, nonlinear Vlasov-Poisson equilibria as an eigenproblem in a Fourier-Hermite basis (in the space and velocity variables, respectively) of finite dimension, N. When the advection term in the Vlasov equation is dominant, the convergence with N of the eigenvalues is rather slow, limiting the applicability of the method. We use the method of spectral deformation introduced by Crawford and Hislop [Ann.

Self-organization and threshold of stimulated Raman scattering.

We derive, both theoretically and using an envelope code, threshold intensities for stimulated Raman scattering, which compare well with results from Vlasov simulations. To do so, we account for the nonlinear decrease of Landau damping and for the detuning induced by both the nonlinear wave number shift δk{p} and the frequency shift δω{p} of the plasma wave. In particular, we show that the effect of δk{p} may cancel out that of δω{p}, but only in that plasma region where the laser intensity decreases along the direction of propagation of the scattered wave.

Nonlinear Landau damping rate of a driven plasma wave.

In this Letter, we discuss the concept of the nonlinear Landau damping rate, nu, of a driven electron plasma wave, and provide a very simple, practical formula for nu, which agrees very well with results inferred from Vlasov simulations of stimulated Raman scattering. nu actually is more complicated an operator than a plain damping rate, and it may only be seen as such because it assumes almost constant values before abruptly dropping to 0. The decrease of nu to 0 is moreover shown to occur later when the wave amplitude varies in the direction transverse to its propagation.