Nonlinear interaction of a Gaussian intense laser beam with plasma: Relativistic modulational instability

Abstract

The nonlinear interaction of a circularly polarized Gaussian intense laser pulse in a collisionless cold plasma with immobile ions is analyzed. The laser beam is assumed to have a nonuniform intensity distribution (along its wave front) in a plane transverse to the direction of propagation. To properly include the nonuniformity of the laser field, the wave equation is integrated over the transversal distribution. In this way, the mean transversal effects are taken into account. In this frame of work the relativistic modulational instability (RMI) of a long pulse is analyzed. A general dispersion relation is derived and solved. Plots of the temporal growth rate as a function of the laser beam power and the modulation wave number are presented and compared with the case when a uniform intensity distribution along the laser wave front is assumed. It is found that the nonuniformity of the laser beam has a significant effect on the characteristics of RMI. It is shown as a conclusion that the effect of transverse distribution in the growth rate reduction, in comparison with the case when it was neglected, becomes more significant for shorter wavelength of the RMI and stronger pump waves.