  In this paper, we derive coupled envelope equations modeling the growth of
stimulated Raman scattering (SRS) in a multi-dimensional geometry, and
accounting for nonlinear kinetic effects. In particular, our envelope equations
allow for the nonlinear reduction of the Landau damping rate, whose decrease
with the plasma wave amplitude depends on the rate of side-loss. Account is
also made of the variations in the extent of the plasma wave packet entailed by
the collisionless dissipation due to trapping. The dephasing between the
electron plasma wave (EPW) and the laser drive, as well as the self-focussing
of the plasma wave, both induced by the EPW nonlinear frequency shift, are also
included in our envelope equations. These equations are solved in a
multi-dimensional geometry using our code dubbed BRAMA, whose predictions
regarding the evolution of Raman reflectivity as a function of the laser
intensity are compared against previously published PIC results, thus
illustrating the ability of BRAMA simulations to provide the correct laser
threshold intensity for SRS, as well as the right order of magnitude of Raman
reflectivity above threshold.
