Theory of Raman scattering for a short ultrastrong laser pulse in a rarefied plasma

Direct forward and backward Raman scattering in an underdense plasma are considered for relativis- tically strong laser pulses. Dispersion analysis and analytical solutions, taking account of the pulse shape, are presented. It is shown that the Raman instability has an absolute maximum of the growth rate for the laser field amplitude (${\mathit{eE}}_0$/m${\mathrm{\omega }}_0$c)≃1, which corresponds approximately to the power density of ${10}^{18}$ W/${\mathrm{cm}}^2$ for 1 μm wavelength laser radiation. Analytical solutions are obtained for both backward- and forward-scattered light that show the quite different way that the forward and backward scattering affect the global pulse evolution. The forward scattering develops in the whole body of the pulse and affects most considerably the trailing part of the pulse. In contrast with it, the backward scattering can be expected to become saturated aleady in the leading part of the pulse and affects mainly the evolution of the leading pulse edge. The relation of the obtained results and recent three-dimensional studies of the short-pulse evolution are discussed.