Collective parametric instabilities of many overlapping laser beams with finite bandwidth

Abstract

A class of collective three‐wave parametric instabilities resulting from the overlap of N, phase‐independent, converging laser beams, each with finite frequency bandwidth and modest spatial incoherence is considered. A statistical analysis is employed based on the random phase approximation (RPA) to derive the thresholds, growth rates, and spatial gain coefficients for these instabilities. When the laser beams are symmetrically distributed in a converging conical array it is argued that collective parametric instabilities can be excited in which one of the daughter waves propagates along the symmetry axis of the cone and is coupled equally to all the pump beams and to the other daughter waves that lie in another cone determined by the matching conditions. For a sufficiently large number of beams the collective modes have lower thresholds than the single‐beam instabilities. The collective thresholds are greater than or equal to the incoherent thresholds for a single beam containing N times the single‐beam power. To be effective the spatial extent of the beam overlap region must be long enough to allow significant convective amplification or absolute instability. A potentially dangerous collective instability, resulting from stimulated Raman scattering (SRS), has a common electron plasma wave along the axis of symmetry and has a low threshold for coherent beams. This common plasma wave may be detrimental to laser fusion as a potential source of hot electrons. Sufficient bandwidth and angular divergence of the beams can suppress this instability relative to a more benign collective mode where the scattered light is the common mode along the symmetry axis.