STATISTICAL PROPERTIES OF LASER HOT-SPOTS PRODUCED BY A RANDOM PHASE PLATE

A quantitative theory of laser hot spots, which control plasma instabilities in real laser-plasma interactions, is presented in the case of random phase plate (RPP) optics. It is shown that the probability density of intense hot spots with intensity I, P(hot)(I), is given by P(hot)(I) approximately (I/I0(2))exp (-I/I0) where I0 is the average intensity, and that the detailed amplitude and phase variation of the laser field in the vicinity of an intense hot spot is uniquely specified by the optics and is deterministic. These hot spots may be the source of below threshold stimulated Raman scattering (SRS) and its variation with I0 is shown to be super exponential. A brief preview of a quantitative nonlinear theory of hot-spot-induced laser filamentation is presented.