Instability versus equilibrium propagation of a laser beam in plasma.

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 nonequilibrium (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.