Stimulated Raman scattering of nonlinear space‐charge and transverse magnetic waves with a longitudinal wiggler

A formulation is given for the parametric coupling of nonlinear space‐charge waves with transverse magnetic (TM) waveguide modes through a longitudinal wiggler field. The model is based upon the simplifying assumption of thin electron beam geometry, which requires only one‐dimensional dynamics of the space‐charge waves, and is an exact formulation in the limit of infinitesimally thin beams. A reduced model, obtained through the application of standard time‐averaging techniques, leads to an analytic expression for the parametric growth rate as a function of beam parameters, pump strength, and wave mismatch. A numerical code is developed and used to solve the unapproximated model equations, and comparisons are made with the analytic theory. Agreement is good in the domain of applicability of the theory. It is also found numerically that nonlinear steepening and associated slowing of the space‐charge waves—aspects usually neglected in ponderomotive theories—have important consequences on the evolution of the instability in the strongly nonlinear regime.