Abstract
The nonlinear mode interaction in FELs is studied in an analytic perturbative framework both for low as well as high gain regimes. The mode coupling depends on the saturation terms which mainly arise from third order perturbation. Both self- and crossed saturation are obtained and the ratio crossed/self characterizes the strength of the mode coupling. The mode competition is analyzed by studying the two mode problem. Mathematically, this entails a stability analysis of a system of two coupled integro-differential equations. In FELs the crossed saturation is twice as strong as the self-saturation. As a consequence of the strong crossed saturation, a dominant mode is able to suppress other competing modes and the result is single mode operation.
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