Three-dimensional simulation of the Raman free-electron laser

Abstract

The nonlinear evolution of the free-electron laser amplifier is investigated numerically in the collective Raman regime for a configuration in which a relativistic electron beam propagates through a loss-free cylindrical waveguide in the presence of a helical wiggler and an axial guide magnetic field. A set of coupled nonlinear differential equations is derived that governs the evolution of the TE waveguide modes, the beam space-charge mode, and the trajectories of an ensemble of electrons. Comparison with experiment shows good agreement for cases in which the intersection between the vacuum waveguide mode and the beam resonance line are near ‘‘grazing’’ (i.e., when the intersections are sufficiently close together to result in one broad gain bandwidth). For interactions in which two distinct gain bands occur, the numerical procedure tends to underestimate the beam–plasma frequency and results in a 15%–20% discrepancy with experiment.