Abstract
We develop a perturbation series in powers of the radiation field strength in order to calculate nonlinear corrections to the high-gain, exponential-amplification regime of a single-mode free-electron laser, and thereby to study the onset of saturation in such a device. In such a series, contributions to the optical power gain come only from the odd-order terms. We give an estimate of the radiative power threshold at which nonlinear corrections become comparable to the usual small-signal result.
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