Instability and dynamics of two nonlinearly coupled laser beams in a plasma

The nonlinear interaction between two laser beams in a plasma is investigated in the weakly nonlinear and relativistic regime. The evolution of the laser beams is governed by two nonlinear Schrödinger equations that are coupled with the slow plasma density response. A nonlinear dispersion relation is derived and used to study the growth rates of the Raman forward and backward scatteringinstabilities as well of the Brillouin and self-focusing/modulational instabilities. The nonlinear evolution of the instabilities is investigated by means of direct simulations of the time-dependent system of nonlinear equations