Beyond the random phase approximation: Stimulated Brillouin backscatter for finite laser coherence times

We develop a statistical theory of stimulated Brillouin backscatter (BSBS) of a spatially and temporally partially incoherent laser beam for laser fusion relevant plasma. We find a new collective regime of BSBS (CBSBS) with intensity threshold controlled by diffraction, an insensitive function of the laser coherence time, $T_c$, once light travel time during $T_c$ exceeds a laser speckle length. The BSBS spatial gain rate is approximately the sum of that due to CBSBS, and a part which is independent of diffraction and varies linearly with $T_c$. We find that the bandwidth of KrF-laser-based fusion systems would be large enough to allow additional suppression of BSBS.