Laser pulse modulation instabilities in plasma channels

In this paper the modulational instability associated with propagation of intense laser pulses in a partially stripped, preformed plasma channel is analyzed. In general, modulation instabilities are caused by the interplay between (anomalous) group velocity dispersion and self-phase modulation. The analysis is based on a systematic approach that includes finite-perturbation-length effects, nonlinearities, group velocity dispersion, and transverse effects. To properly include the radial variation of both the laser field and plasma channel, the source-dependent expansion method for analyzing the wave equation is employed. Matched equilibria for a laser beam propagating in a plasma channel are obtained and analyzed. Modulation of a uniform (matched) laser beam equilibrium in a plasma channel leads to a coupled pair of differential equations for the perturbed spot size and laser field amplitude. A general dispersion relation is derived and solved. Surface plots of the spatial growth rate as a function of laser beam power and the modulation wave number are presented.