| The spatiotemporal evolution of parametric instabilities such as stimulated Raman scattering (SRS) is studied analytically in time and two spatial dimensions. Initial and boundary conditions are chosen to represent the entrance, propagation, and exit of a laser pulse of finite extent convecting through a homogeneous collisional plasma channel with definite boundaries. With negligible lateral channel reflectivity, the growth for most scattering angles is found to be dominated by two-dimensional effects with one-dimensional amplitudes being valid for only a small range of near direct forward and near direct backward scattering angles. Sideward convection alters the spatiotemporal character of the instability and inhibits, but does not suppress the growth. When nontrivial lateral reflections are included the growth is enhanced for most scattering angles so that for large times one-dimensional damped modes are formed in which the convective loss created by the transmission of the Stokes wave through the channel boundaries is equivalent to an overall damping of the Stokes amplitudes within the channel. |
