On spectral and temporal coherence of x-ray free-electron laser beams.

A model for the coherence properties of free-electron lasers (FELs) in time and frequency domains is introduced within the framework of classical second-order coherence theory of nonstationary light. An iterative phase-retrieval algorithm is applied to construct an ensemble of field realizations in both domains, based on single-pulse spectra measured at the Linac Coherent Light Source (LCLS) in self-amplified spontaneous emission mode. Such an ensemble describes the specific FEL pulse train in a statistically averaged sense. Two-time and two-frequency correlation functions are constructed, demonstrating that the hard X-ray free-electron laser at LCLS in this case behaves as a quasistationary source with low spectral and temporal coherence. We also show that the Gaussian Schell model provides a good description of this FEL.