Nonlinear saturation of stimulated Raman scattering in a collisional homogeneous plasma

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Abstract
Using multiple timescale analysis, the nonlinear saturation of the stimulated Raman scattering instability is examined in a collisional homogeneous plasma. This purely temporal problem, with a ubiquitous driver and arbitrary damping for each wave, is solved for incident pump amplitudes exceeding threshold by the factor m (where m can be much larger than unity). New expressions are obtained for the saturated amplitude of each wave, and it is demonstrated that the nonlinear frequency shift vanishes. The reflection coefficient is (Ω2/Ω1)3[(m−1)/m2], where Ω1 and Ω2 are the frequencies of the incident and scattered electromagnetic waves. This is to be compared with a previous calculation with only one wave damped in which the reflection coefficient is Ω2/Ω1. A result which includes the effect of mismatch is also given. In addition, it is shown that the complete time dependence can be obtained in the threshold regime (m−1≪1).