A study of linewidth, noise and fluctuations in a FEL operating in SASE

We study the evolution of the FEL radiation intensity and spectrum starting from noise in the electron beam longitudinal distribution. Due to the slippage both the time and frequency structure of the emitted radiation pulse show a very different behavior when the bunch length is much longer than or of the order of the cooperation length lc. The occurrence of superradiant spikes is discussed. We present analytical and numerical results.