We introduce a simplified model for the saturation of a self-amplified spontaneous-emission free-electron laser. Within this model, we determine the effect of nonlinearity upon the statistical properties of the output radiation. Comparing our results with the computer simulations of Saldin, Schneidmiller, and Yurkov [The Physics of Free Electron Lasers (Springer-Verlag, Berlin, 2000)], we find that the model provides a good description of the average intensity, field correlation function, and coherence time, but underestimates the intensity fluctuation. Asymmetric spectral broadening phenomena are not included in the model.
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