Stimulated Raman and induced Compton scattering of an intense photon spectrum in an isotropic plasma

The nonlinear kinetics of an intense, incoherent, high-frequency (${\omega }_t\gg {\omega }_p$), isotropic photon spectrum of wide spectral width ($\delta \omega \gg {\Delta }_{\mathrm{Doppler}}\omega \gg {\omega }_p$) propagating through a rarefied isotropic plasma is examined when induced Raman and Compton effects are both included. In the presence of weak plasma turbulence, $\frac{W}{n_e\mathrm{kT}}\gtrsim \left(\frac{{\omega }_t}{{\omega }_p}\right)\left(\frac{{k_t}^3}{n_e}\right)$, Kompaneet's differential equation must be replaced by a new nonlinear kinetic equation of the Burger type which accounts for the linear Raman diffusion and for the nonlinear induced Compton scattering.