Abstract

In most previous studies of the quantum-mechanical description of spontaneous emission in Compton-regime free-electron lasers, the equations of motion derived from the theory have been solved to the lowest order of perturbation theory, Hence, the results are appropriate for situations in which the probability that an electron changes its state by emitting a photon while transiting the wiggler is small. For long wigglers, this probability need not remain snail, and this paper presents a non-perturbative solution of the quantum equations appropriate to this case. Results are derived for the spectrum of spontaneously-emitted light and for the small- signal gain. In both cases, our expressions for short wigglers reduce to previously derived (from quantum mechanics and classical electrodynamics) formulae for the spontaneous spectrum and the gain, while, for long wigglers, our results show important modifications of the previous results.

© 1984 Optical Society of America