Harmonic decomposition to describe the nonlinear evolution of stimulated Brillouin scattering

An efficient method to describe the nonlinear evolution of stimulated Brillouin scattering (SBS) in long scale-length plasmas is presented in the limit of a fluid description. The method is based on the decomposition of the various functions characterizing the plasma into their long- and short-wavelength components. It makes it possible to describe self-consistently the interplay between the plasma hydrodynamics, stimulated Brillouin scattering, and the generation of harmonics of the excited ion acoustic wave (IAW). This description is benchmarked numerically in one and two spatial dimensions [one dimensional (1D), two dimensional (2D)], by comparing the numerical results obtained along this method with those provided by a numerical code in which the decomposition into separate spatial scales is not made. The decomposition method proves to be very efficient in terms of computing time, especially in 2D, and very reliable, even in the extreme case of undamped ion acoustic waves. A novel picture of the SBS nonlinear behavior arises, in which the IAW harmonics generation gives rise to local defects appearing in the density and velocity hydrodynamics profiles. Consequently, SBS develops in various spatial domains which seem to be decorrelated one from each other, so that the backscattered Brillouin light is the sum of various backscattered waves generated in several independent spatial domains. It follows that the SBS reflectivity is chaotic in time and the resulting time-averaged value is significantly reduced as compared to the case when the IAW harmonics generation and flow modification are ignored. From the results of extensive numerical simulations carried out in 1D and 2D, we are able to infer the SBS reflectivity scaling law as a function of the plasma parameters and laser intensity, in the limit where the kinetic effects are negligible. It appears that this scaling law can be derived in the limit where the IAW harmonics generation is modeled simply by a nonlinear frequency shift