Stimulated Brillouin scattering reflectivity in the case of a spatially smoothed laser beam interacting with an inhomogeneous plasma

The stimulated Brillouin scattering (SBS) instability is investigated theoretically in the case of a spatially smoothed laser beam interacting with an inhomogeneous plasma in the regime of strong ion acoustic damping. The domain of parameters being considered corresponds to most of the present day experiments carried out with nanosecond laser pulses interacting with preformed plasmas: the characteristic length for convective amplification is assumed to be much shorter than the longitudinal correlation length of the laser field. The SBS reflectivity of one individual hot spot is analytically computed taking into account thermal noise emission and pump depletion within the hot spot. The SBS reflectivity of the whole beam is then obtained by summing up the individual hot spot reflectivities in accordance with their statistical distribution.