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

We consider nonlinear interactions between two colliding laser beams in an electron plasma, accounting for the relativistic electron mass increase in the laser fields and radiation pressure driven electron-acoustic (EA) perturbations that are supported by hot and cold electrons. By using the hydrodynamic and Maxwell equations, we obtain the relevant equations for nonlinearly coupled laser beams and EA perturbations. The coupled equations are then Fourier analyzed to obtain a nonlinear dispersion relation. The latter is numerically solved to show the existence of new classes of the parametric instabilities in the presence of two colliding laser beams in a two-electron plasma. The dynamics of nonlinearly coupled laser beams in our electron plasma is also investigated. The results should be useful in understanding the nonlinear propagation characteristics of multiple electromagnetic beams in laser-produced plasmas as well as in space plasmas.