Statistical theory of a near-forward stimulated Brillouin scattering driven by a spatially and temporally smoothed laser beam

A model predicting the spatial gain of the near-forward stimulated Brillouin scattering excited by a laser beam smoothed by a random phase plate is extended to the temporal smoothing by spectral dispersion and polarization smoothing schemes relevant to high-energy laser facilities. Both smoothing schemes partially stabilize the beam spray amplification by reducing the beamlet correlations. A finite laser bandwidth causes a frequency shift of the ion-acoustic resonance due to internal competition between the amplified scattered waves with different frequencies. Simple analytical estimates of the convective gain are provided for all smoothing schemes. The model predictions are confirmed with three-dimensional paraxial simulations and applied to two recent experiments in the indirect and direct drive geometry. The forward Brillouin scattering may produce a strong beam spraying in the inertial confinement fusion experiments and can be controlled by the laser spectral bandwidth. The model revises the previous estimates of the laser bandwidth effect on the forward Brillouin scattering in plasma and provides a new quantitative evaluation of the mitigation effect. It also predicts an anisotropic beam spray growth depending on the flow orientation and on the temporal smoothing that is used.