Three-dimensional theory of free electron lasers with an axial guide field

The collective interaction in a free electron laser with a combined helical wiggler and uniform axial guide field is presented in the low-gain regime. The wiggler model we employ is fully self-consistent and includes all transverse inhomogeneities. The analysis is performed for a free electron laser (FEL) amplifier in which the radial dependence of the radiation is treated using both the TE and TM waveguide modes. Substantial discrepancies are found to exist between the results for the realizable and ideal wigglers, and a selection rule relating the TE
ln
and TM
ln
modes with resonant amplification at the
l
th harmonic of the FEL Doppler upshift.