  We obtain, for the first time, an analytic theory of the forward stimulated
Brillouin scattering instability of a spatially and temporally incoherent laser
beam, that controls the transition between statistical equilibrium and
non-equilibrium (unstable) self-focusing regimes of beam propagation. The
stability boundary may be used as a comprehensive guide for inertial
confinement fusion designs. Well into the stable regime, an analytic expression
for the angular diffusion coefficient is obtained, which provides an essential
correction to a geometric optic approximation for beam propagation.
