Statistical and coherence properties of radiation from x-ray free-electron lasers

We describe the statistical and coherence properties of radiation from x-ray free-electron lasers (XFEL). It is shown that the XFEL radiation before saturation is described with Gaussian statistics. Particularly important is the case of the optimized XFEL studied in detail. Applying similarity techniques to the results of numerical simulations allowed us to find universal scaling relations for the main characteristics of an XFEL operating in the saturation regime: efficiency, coherence time and degree of transverse coherence. We find that with an appropriate normalization of these quantities, they are functions of only the ratio of the geometrical emittance of the electron beam to the radiation wavelength. Statistical and coherence properties of the higher harmonics of the radiation are highlighted as well.