ANALYSIS OF FREE ELECTRON LASER SMALL-SIGNAL GAIN FOR GAUSSIAN BEAMS

A three-dimensional gain expression is presented and analysed for a Gaussian optical beam in small signal case. An asymptotic gain formula is given for a broader electron beam in cross section compared to the optical beam. When electron beam transverse dimension is smaller than the beam waist of the Gaussian mode, an analytic approximate formula is given and the results are in good agreement with numerical simulations.