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

physics of plasmas

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