Scaling function for free-electron-laser gain including alternating-gradient focusing

Abstract

In the exponential regime before saturation, we present a variational calculation of the gain of a free electron laser (FEL), with alternating-gradient focusing used to supplement the natural focusing of the wiggler. The longitudinal velocity modulation due to the quadrupole focusing is properly taken into account and it is found that it does not prevent quadrupole focusing from efficiently increasing the gain. Our analytic calculation agrees with computer simulation to a few percent, and it provides rapid computation facilitating FEL design optimization.