We study the time structure, the frequency composition, and the shot to shot fluctuations of the radiation emitted by a free-electron laser starting from shot noise in the electron beam longitudinal distribution, taking into account slippage and finite bunch length effects. We find a very different behavior when the bunch length, scrlb is much longer thatn the cooperation length, scrlc, or of the order of a few scrlc. The field evolution is dominated by slippage effects in both cases, and shows the presence of superradiant spikes.
Bonifacio, R., De Salvo, L., Pierini, P., Piovella, N., & Pellegrini, C. (1994). Spectrum, temporal structure, and fluctuations in a high-gain free-electron laser starting from noise. Physical Review Letters, 73(1), 70–73. https://doi.org/10.1103/PhysRevLett.73.70