Transient setting of relativistic ponderomotive nonlinearity and filamentation of ultra-short laser pulses in plasmas

We study the setting up of relativistic ponderomotive nonlinearity when the laser frequency is much larger than the electron plasma frequency (viz. under dense plasma far away from critical density region). Brandi et al. [1] have studied the relativistic ponderomotive nonlinearity when the laser frequency is more than the electron plasma frequency (but near the electron plasma frequency only). Therefore, their approach cannot be applied to the present case. Using the two fluid approach, the nonlinear dynamics of the plasma oscillations under the combined effects of relativistic mass variation and ponderomotive force of laser beam has been derived. We present the numerical simulation for the coupled system of equations governing the dynamics of laser and plasma oscillations in a collisionless plasma, when the coupling arises through relativistic ponderomotive non-linearity.