In the present work, excitation of nonlinear ion acoustic wave (IAW) in collisionless plasma by laser beam having null intensity at the center is examined considering relativistic nonlinearity. The differential equation for beam-width parameter is determined considering relativistic nonlinearity using the paraxial and Wentzel–Kramers–Brillouin approximations by the parabolic equation method. The propagation features of the IAW are found to be modified due to the nonlinearity present in the system. The hollow Gaussian beam (HGB) gets nonlinearly coupled with the seed IAW, results in excitation of nonlinear IAW. The interaction of nonlinear IAW with pump beam demonstrated stimulated Brillouin scattering (SBS) of HGB. It is found that the power of IAW and power of SBS is affected with the order of HGB. The power of IAW and backscattered power of SBS is determined analytically and numerically for various orders of HGB. It is found that the power of IAW and the backscattering is diminished for higher order of HGB.

Brillouin backward scattering is investigated in the interaction of linearly polarized short laser pulse with a homogenous underdense transversely magnetized plasma by taking into account the relativistic and nonlinearity effects up to third order. The plasma is embedded in a uniform magnetic field perpendicular to both of propagation direction and electric vector of the radiation field. Temporal growth rate of instability is calculated by using of the nonlinear wave equation. Results are significantly different in comparison with lower order computations. The growth rate of Brillouin backward instability shows a decrease due to the presence of external magnetic field, while relativistic and higher order nonlinearities due to the external magnetic field, give rise the Brillouin backward scattering instability.

Recent particle-in-cell simulations of the stimulated Brillouin backscattering (SBBS) of electromagnetic radiation have shown that even at sub-relativistic intensities (Iλ2 = 1016 Wμm2/cm2) non-drifting solitary waves, “solitons” for short, are easily produced, and remain almost unchanged all along the simulation time, typically for several thousands of optical cycles. They appear in the form of stable local concentrations of electromagnetic radiation trapped inside quasi-neutral density holes. The plasma density inhomogeneity associated with their presence disrupts the resonant SBBS amplification. The cavitation process is accompanied by strong electron and ion heating. The physical characteristics of such solitons are discussed and they are compared with the theoretical predictions of an analytical model for localized solution of the Maxwell equations in warm plasma.