Reconstruction of X-Ray Free-Electron Laser Pulse Duration and Energy Chirp from Spectral Intensity Fluctuations

Accurate measurements of the x-ray pulse duration produced by x-ray free-electron lasers (XFELs) typically rely on longitudinal electron beam phase space diagnostics, e.g., an x-band transverse deflecting cavity (XTCAV). An alternative group of methods is based on measurements of radiation statistics and spectral correlations. In this paper, we present a statistical analysis of FEL radiation which extends the previous technique by Lutman et al. [Phys. Rev. ST Accel. Beams 15, 030705 (2012)], including the electron beam energy chirp in the FEL gain model. In doing so, we show that with measurements of the average spectrum and the spectral intensity correlations, one can reconstruct the x-ray pulse length, e-beam chirp, and corresponding spectrometer resolution. We validate our approach with 1D and 3D simulations before moving to an experimental demonstration in which our method finds results similar to those obtained from XTCAV measurements.