Spectrum, temporal structure, and fluctuations in a high-gain free-electron laser starting from noise

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, ${\mathit{scrl}}_{\mathit{b}}$ is much longer thatn the cooperation length, ${\mathit{scrl}}_{\mathit{c}}$, or of the order of a few ${\mathit{scrl}}_{\mathit{c}}$. The field evolution is dominated by slippage effects in both cases, and shows the presence of superradiant spikes.