  We develop the statistical theory of the stimulated Brillouin backscatter
(BSBS) instability of a spatially and temporally partially incoherent laser
beam for laser fusion relevant plasma. We find a new regime of BSBS which has a
much larger threshold than the classical threshold of a coherent beam in
long-scale-length laser fusion plasma. Instability is collective because it
does not depend on the dynamics of isolated speckles of laser intensity, but
rather depends on averaged beam intensity. We identify convective and absolute
instability regimes. Well above the incoherent threshold the coherent
instability growth rate is recovered. The threshold of convective instability
is inside the typical parameter region of National Ignition Facility (NIF)
designs although current NIF bandwidth is not large enough to insure dominance
of collective instability and suggests lower instability threshold due to
speckle contribution. In contrast, we estimate that the bandwidth of
KrF-laser-based fusion systems would be large enough.
