Numerical study of X-ray FELS including quantum fluctuation

One of the fundamental limitations towards achieving very short wavelength in a self amplified spontaneous emission free electron laser (SASE FEL) is connected with the energy diffusion in the electron beam due to quantum fluctuations of undulator radiation. Parameters of the LCLS and TESLA X-ray FEL projects are very close to this limit and there exists necessity in upgrading FEL simulation codes for optimization of SASE FEL for operation at a shortest possible wavelength. In this report we describe a one-dimensional FEL simulation code taking into account the effects of incoherent undulator radiation. Using similarity techniques we have calculated universal functions describing degradation of the FEL process due to quantum fluctuations of undulator radiation