Theory of the longitudinal dynamics of a storage ring FEL

The longitudinal dynamics of an electron beam circulating in a storage ring and undergoing a FEL interaction is discussed with specific reference to the low gain amplifier case. We exploit the Fokker-Planck equation and analyze the multipolar components of the longitudinal electron motion. One of the major achievements of the analysis is relevant to the longitudinal damping time, which is shown to be interaction dependent, i.e. a function of the FEL detuning parameter and laser intensity.