Stimulated Raman scattering in a lossy magnetized relativistic electron beam

A general, systematic theoretical study is given for stimulated Raman scattering from a relativistic electron beam with the inclusion of collision and mismatch losses. Shown to be internally consistent, a set of coupled amplitude transport equations is derived for the three-wave interaction among the transverse electromagnetic pump wave, the longitudinal slow space-charge wave, and the transverse (either electromagnetic or electrokinetic) signal wave. The wave instability, amplitude thresholds, and growth rates are examined in the parametric case. In the laboratory frame, the nature of the instability is shown to be strictly convective. The velocity of the convective instability is determined. The nonlinear problem is treated analytically and numerically. Comparisons are made for various magnetostatic field strengths. Important for free-electron laser design, exact analytical expressions for the spatial and temporal periods of the signal wave are determined in the no-loss case. Three-wave coupling where the idler wave is a transverse electrokinetic wave is analyzed. No such coupling is shown to exist.