Laser hot spots and the breakdown of linear instability theory with application to stimulated Brillouin scattering

Convective instabilities in the strongly damped regime are shown to exhibit essential nonlinear behavior due to laser hot spots when the average laser intensity left-angle I right-angle approaches a critical threshold value Ic. The onset of this nonlinear regime is formally signaled by the divergence of the average convective amplification left-angle A right-angle as left-angle I right-angle →Ic. An independent hot spot model of random phase plate optics predicts that left-angle A right-angle ∼1/(Ic-left-angle I right-angle)2. A saturated hot spot model of nonlinear stimulated Brillouin scattering (SBS) predicts a rapid turn on and saturation of SBS reflectivity with laser intensity and optic f number