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

摘要

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