Numerical stimulations of startup and statistical properties of SASE FEL

Mathematical model based on spontaneous emission and shotnoise of SASE FEL is introduced. A detailed study of startup and statistical properties of the radiation from a SASE FEL operating has been performed by means of the modified 1D timedependent FEL code. It is shown that the width of the radiation spectrum becomes at first narrow then broad. After several gain lengths the spectrum transforms into that of the high gain FEL amplifier. The statistical properties of the radiation have been proved that finitetime integrals of the instantaneous power follow a gamma distribution.