Three-wave parametric-decay instability with arbitrary dissipation in homogeneous plasmas

Abstract

The theory of the nonlinear decay of a steady incident pump wave into two oppositely propagating modes in a bounded homogeneous region is extended to include arbitrary dissipation on each wave. A new representation of the coupled mode equations shows that, in addition to the usual coupling nonlinearity, two transverse-wave-damping-induced nonlinearities appear, leading to enhanced saturation. A threshold analysis yields general absolute and convective instability criteria extending earlier results of Kroll, and of Porkolab and Chang. The steady-state boundary value problem is solved to obtain the eigenvalue of the stimulated backscattering problem, the anomalous reflectivity, or the convective amplification of a noise source. Good agreement is found between the results of analytical and numerical integrations.