The local–global analysis of the stimulated Brillouin scattering in the regime of nonlinear sound waves

The effect of ion sound wave (ISW) nonlinearities on the stimulated Brillouin scattering (SBS) in long plasmas is investigated within the framework of the Korteweg–de Vries–Maxwell equations. The nonlinear evolution of the driven ISW results in the localization of the ion density on a scale shorter than the wavelength (λs) of the resonant ISW satisfying SBS three-wave matching conditions. Since the transverse wave amplitudes vary on a much longer scale, a local–global modeling of SBS is proposed in which this scale separation is exploited. The local part of the procedure includes a solution to the damped KdV equation with periodic boundary conditions and driven by a constant amplitude ponderomotive force. In the global part of the analysis approximate solutions for the transverse waves in long plasmas are constructed using the results from the local part. Particle-in-cell simulations have been performed in order to investigate the importance of kinetic effects for the local model. Numerical results obtained from the solutions to the KdV–Maxwell equations are well approximated by the local–global modeling. They are also compared with the results of a harmonic decomposition approximation.