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

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.