Wave profile modification in the free electron laser with and without a waveguide

The modification of the transverse wave profile by the free electron laser (FEL) interaction in the collective Raman regime is considered. The gain is calculated and the transverse wave profile is found by solving for the eigenvalues and the actual eigenmodes of the system. When a waveguide is employed, a strong FEL interaction is shown to couple various vacuum waveguide modes, as was demonstrated by A. Bhattacharjee et al. (1988). When no waveguide or cavity is present, a coupling parameter which measures the strength of the interaction is identified. Expressions are derived for the gain for large and small values of the coupling parameter, corresponding to a strong optical guiding and large diffraction, respectively. Comparing the present results for the Raman regime with previous results for the strong pump regime, it is shown that the gain scales differently in each case, depending on both the regime of operation and on the beam geometry. The linear analysis is valid when the signal is small, and is useful mainly when the gain is high prior to saturation