We discuss a phenomenological one-dimensional, self-consistent, multimode (longitudinal) theory for a free-electron-laser oscillator. A strong fundamental mode and a weak sideband mode are followed through many passes in the optical cavity as the energy of the electron beam decreases monotonically. The time evolution of the laser power exhibits oscillations produced by the sequential growth to saturation and subsequent decay of longitudinal modes evenly distributed in frequency.
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Gallardo et al. (1986) studied this question.
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