Effect of cross-focusing of two q-Gaussian laser beams on excitation of electron plasma wave in collisional plasma

This paper presents theoretical investigation of the effect of cross-focusing of two q-Gaussian laser beams on excitation of electron plasma wave (EPW) in an underdense plasma where collisional nonlinearity is operative. The EPW is generated on account of beating of the two laser beams of slightly different frequencies ω1 and ω2. Starting from Maxwell's equations, the coupled differential equations governing the evolution of spot size of the two laser beams with distance of propagation have been derived with the help of moment theory approach in Wentzel-Kramers-Brillouin (W.K.B.) approximation. The collisional nonlinearity depends not only on the intensity of first laser beam but also on that of second laser beam. Therefore, the dynamics of one laser beam affects that of other and hence, cross-focusing of the two laser beams takes place. Due to nonuniform intensity distribution of the laser beams, the background electron concentration is modified. The amplitude of EPW, that depends on the background electron concentration, is thus nonlinearly coupled with the laser beams. The effects of collisional nonlinearity and cross-focusing of the laser beams on excitation of EPW have been incorporated. Numerical simulations have been carried out to investigate the effect of laser and plasma parameters on cross-focusing of the two laser beams and further its effect on EPW excitation.