Saturation of a high-gain single-pass FEL

We study a perturbation expansion for the solution of the nonlinear one-dimensional FEL equations. We show that in the case of a monochromatic wave, the radiated intensity satisfies a scaling relation that implies, for large distance z traveled along the undulator, a change in initial value of the radiation field corresponds to a translation in z (lethargy). Analytic continuation using Padé approximates yields accurate results for the radiation field early in saturation.