Statistical properties of radiation from SASE FEL driven by short electron bunches

We analyze statistical properties of the radiation from a SASE FEL driven by short electron bunches. In the linear regime the radiation from a SASE FEL is a Gaussian random process. When approaching saturation point, statistical properties of the radiation change drastically on a scale of one field gain length. Particular attention is devoted to the analysis of fluctuations of total energy in the radiation pulse and after a narrow-band monochromator. It was found that fluctuations at saturation are significantly suppressed when electron pulse length becomes comparable with cooperation length.