Langmuir wave filamentation in the kinetic regime. I. Filamentation   instability of Bernstein-Greene-Kruskal modes in multidimensional Vlasov   simulations
  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. 
Denis A. Silantyev, Pavel M. Lushnikov and Harvey A. Rose
physics.plasm-ph nlin.PS