Statistical correlations and intensity spiking in the SASE FEL

In the linear regime before saturation, we describe the statistical correlations in the narrow band chaotic output of the self-amplified spontaneous emission free-electron laser. At a fixed position along the undulator axis, we derive joint probability distributions for the intensity in the output pulse to have values I1 and I2 at times t1 and t2, and for the spectral intensity to have values Ĩ1 and Ĩ2 at frequencies ω1 and ω2. Probability distributions for the peak values of intensity in the time and frequency domains are also determined.