Interdependence of parameters of an X-ray FEL

This article presents a dimensionless analysis of a self amplified spontaneous emission (SASE) FEL operating in an X-ray wavelength band. Using similarity techniques we have performed an analysis of the results of numerical simulations and derived simple design formulae for the calculation of the characteristics of the SASE FEL. We have also shown that the growth of the energy spread due to the quantum fluctuations of synchrotron radiation imposes a limit on the minimal achievable value of the wavelength in the X-ray FEL.