Modulational instability of a laser pulse in a non uniform plasma channel

Abstract

A self-guided Gaussian laser pulse propagating in a non-uniform plasma channel is unstable to a plasma wave perturbation co-moving with the laser with its group velocity. The plasma wave amplitude has a maximum radial profile along the laser propagation axis. As the plasma wave propagates through a non-uniform plasma channel, the plasma wave perturbation causes focusing in the part of the laser that propagates with the electron density trough and defocusing in the part moving with the crest. This yields an axial gradient in the intensity of the laser and produces a ponderomotive force on the electrons. The ponderomotive force drives the plasma wave, which in turn makes the modulational instability grow. The growth rate of the modulational instability becomes larger with the increase in non-uniformity of a shallow plasma channel. In a deep cavitated plasma channel the growth rate of the modulational instability increases with the laser pulse amplitude.