Storage-Ring FEL longitudinal dynamics

We study the modifications induced on the longitudinal dynamical behaviour of an e-beam circulating in a Storage-Ring (S.R.) and undergoing a FEL interaction. We discuss the low gain amplifier case and, using the Fokker-Planck equation, evaluate the effect of the FEL interaction on the longitudinal damping time, which is shown to be a function of the detuning parameter and of the intensity itself. We develop a self-consistent model of the S.R. FEL dynamics capable of including saturation, induced energy spread and damping time modifications. The model is shown to be particularly useful to investigate the system evolution and the interplay between the various features causing the saturation of the device.