Abstract
The mode competition in a long-pulse free-electron laser operating in a high-gain Compton regime is analyzed. Due to the strong crossed saturation, a dominant mode is able to suppress competing modes, leading to single-mode operation. This is explicitly shown by a stability analysis of the system of coupled integrodifferential equations describing the evolution of two competing modes, of which only one survives at saturation. In the course of the study the radiation field evolution in the small-signal regime is treated in a unified manner for low and high gain.
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