Linear theory of the collective Raman interaction in a free-electron laser with a planar wiggler and an axial guide field

Abstract

A linear stability analysis of the collective Raman interaction in a free-electron laser with combined planar wiggler and axial guide magnetic fields is presented. The analysis involves a perturbation of the cold-fluid model of the interaction about the single-particle trajectories in the combined external fields, and the complete dispersion equation for a monoenergetic beam is obtained. In contrast to the case of a helical wiggler field in which the interaction excites a right-hand circularly polarized wave, the interaction for a planar wiggler and an axial guide field is with an elliptically polarized wave that contains both the left- and right-hand circular components. However, the results indicate that many facets of the interaction are analogous to those found with helical wiggler. In particular, both the transverse velocity and the growth rate of the instability tend to increase near the resonance at which the Larmor and wiggle periods coincide. In addition, a negative-mass regime is found in which the axial electron velocity increases with decreasing beam energy, which drives the beam space-charge modes unstable.