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Statistical analysis of a self-seeded x-ray free-electron laser in the presence of the microbunching instability

Self-seeding is one of the most promising methods to improve the longitudinal coherence and spectral purity of free-electron lasers (FELs). Measurements of the multishot-averaged, soft x-ray self-seeding spectrum at the Linac Coherent Light Source (LCLS) FEL often have a pedestal-like distribution around the seeded wavelength. In this paper, a theoretical model based on the mechanism of spectral sideband generation is developed to explain the statistical behavior of the seed and pedestal. The model is in good agreement with statistical analysis of numerical FEL simulations and experimental measurements that show that pedestal fluctuations reflect the level of long-wavelength microbunching structures in the beam, and are driven by fluctuations of the seed.