Evolution of spontaneous and coherent radiation in the free-electron-laser oscillator

An analysis of the free-electron-laser (FEL) oscillator startup problem in the linear regime is presented. The model is spatially one dimensional, though many important three-dimensional effects are included heuristically. The electron beam consists of pulses of arbitrary shape separated by approximately twice the radiation transit time. The small gain per pass approximation is employed in deriving an energy rate equation, which describes the evolution of the radiation pulses within the resonator. The wiggler field is assumed to occupy a portion of the finite Q resonator. In the energy rate equation, the spontaneous (incoherent) radiation term is represented by a source matrix, while the stimulated (coherent) radiation term is represented by a gain matrix. The effect of small variations in the mirror separation are investigated in the context of laser lethargy. Our analysis suggests possible methods which could substantially shorten the startup times in FEL oscillators. Finally, our results are compared with the FEL oscillator experiments performed at Stanford University.