Modulation and filamentation instability of ultrarelativistic electromagnetic waves in electron-positron-ion plasma

Abstract

In this study, we have analytically investigated the effects of nonlinear Landau damping on the temporal growth rate of modulation and filamentation instabilities. Here, the nonlocal nonlinear Landau damping phenomena is appearing due to the nonlinear interaction between ultrarelativistic electromagnetic (UREM) wave (having wave vector normal to the beam) and electron-positron-ion plasma. We found that the ultrarelativistic ponderomotive force is linear, while usually it is nonlinear in relativistic case. We construct three dimensional kinetic nonlinear Schrödinger equation for a slowly varying spatio and temporal amplitude of UREM waves. The equations are then Fourier analyzed to obtain dispersion relation, which admit both modulation and filamentation instabilities. It is shown that nonlinear Landau damping is the main source of modulation instability, for a particular condition taking into account later one the maximum growth rate of modulation instability obtained as a function of amplitude of UREM waves and is displayed graphically. Further, it is shown that for an oscillating density profile, plane wave of uniform intensity becomes unstable and gets filamented. Growth rate of stationary state filament is found to be a function of amplitude of UREM waves and is emphasized that the maximum value of growth rate of filamentation instability is further increased in the presence of nonlinear Landau damping term. Finally, the growth rate of non stationary state filamentation instability is calculated and is shown that the characteristic growth length increases both with perpendicular wave vector and the amplitude of UREM waves.