Relativistic Effects on Stimulated Brillouin Scattering of Self-Focused q-Gaussian Laser Beams in Plasmas with Axial Density Ramp

We investigate the phenomenon of stimulated Brillouin scattering (SBS) of q-Gaussian laser beams nonlinearly-interacting with underdense plasmas. When an intense laser beam with frequency omega(0) propagates through plasma, due to relativistic mass nonlinearity of plasma electrons, it gets coupled to a preexisting-ion acoustic wave (IAW) at frequency omega(ia). The nonlinear interaction of pump beam with IAWproduces a back-scattered wave at frequency omega(s) = omega(0)-omega(ia). In view of the variational theory, we obtain semi-analytical solutions of the coupled nonlinear wave equations for the three waves (pump, IAW, and scattered wave) under the Wentzel-Kramers-Brillouin (WKB) approximation. We show that the scattered-wave power is significantly affected by the self-focusing effect of the pump beam.