Self-organization and threshold of stimulated Raman scattering

We derive, both theoretically and using an envelope code, threshold intensities for stimulated Raman scattering, which compare well with results from Vlasov simulations. To do so, we account for the nonlinear decrease of Landau damping and for the detuning induced by both the nonlinear wave number shift δk{p} and the frequency shift δω{p} of the plasma wave. In particular, we show that the effect of δk{p} may cancel out that of δω{p}, but only in that plasma region where the laser intensity decreases along the direction of propagation of the scattered wave. Elsewhere, δk{p} enhances the detuning effect of δω{p}.