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The phenomenon of stimulated Raman scattering (SRS) of elliptical  q -Gaussian laser beams interacting nonlinearly with underdense plasmas has been investigated theoretically. Using variational theory semi analytical solutions of the coupled nonlinear wave equations for the three waves (pump, EPW and scattered) have been obtained under W.K.B approximation technique. The equations so obtained have been solved numerically to envision the effects of laser as well as plasma parameters on the dynamics of pump beam and further its effect on the power of scattered wave. It has been observed that power of the scattered wave is significantly affected by the self focusing effect of pump beam.

Stimulated Raman scattering of self focused elliptical q -Gaussian laser beam in plasma with axial temperture ramp: effect of ponderomotive force