The formation of transverse coherence in SASE FELs

This report presents a fully three-dimensional study of the amplification process in the self amplified spontaneous emission (SASE) free electron laser. Investigations are based on the data obtained with the three-dimensional, time-dependent FEL simulation code FAST. Analysis of the data shows that the statistical properties of the radiation can be described with Gaussian statistics. In particular, fluctuations of the instantaneous radiation intensity at one space point follow the negative exponential law, while the finite-time integrals of the radiation intensity (both in space and in time) follow a gamma-distribution. Numerical examples presented in the paper correspond to the 70 nm SASE FEL under construction at the TESLA test facility at DESY.