Modulation and nonlinear evolution of multi-dimensional Langmuir wave envelopes in a relativistic plasma

TL;DR

This paper investigates how relativistic effects influence the modulational instability and evolution of Langmuir wave packets in a 2D unmagnetized plasma, deriving a DS-like model and analyzing wave collapse and stabilization.

Contribution

It derives a coupled DS-like equation for 2D Langmuir waves in relativistic plasmas and analyzes the effects of relativistic flow on instability and wave collapse.

Findings

Relativistic effects enhance the instability of LW envelopes in the kθ plane.

Growth rate of MI increases with electron thermal velocity and modulation angle.

Relativistic flow can cause wave collapse, which can be halted by thermal pressure or flow relaxation.

Abstract

The modulational instability (MI) and the evolution of weakly nonlinear two-dimensional (2D) Langmuir wave (LW) packets are studied in an unmagnetized collisionless plasma with weakly relativistic electron flow. By using a 2D self-consistent relativistic fluid model and employing the standard multiple-scale technique, a coupled set of Davey-Stewartson (DS)-like equations is derived which governs the slow modulation and the evolution of LW packets in relativistic plasmas. It is found that the relativistic effects favor the instability of LW envelopes in the k{\theta} plane, where k is the wave number and {\theta} the angle of modulation. It is also found that as the electron thermal velocity or {\theta} increases, the growth rate of MI increases with cutoffs at higher wave numbers of modulation. Furthermore, in the nonlinear evolution of the DS-like equations, it is seen that with an effect of the relativistic flow, a Gaussian wave beam collapses in a finite time, and the collapse can be arrested when the effect of the thermal pressure or the relativistic flow is slightly relaxed. The present results may be useful to the MI and the formation of localized LW envelopes in cosmic plasmas with a relativistic flow of electrons.