Analysis of statistical correlations and intensity spiking in the self-amplified spontaneous-emission free-electron laser

The narrow band chaotic output of the self- amplified spontaneous- emission free- electron laser exhibits intensity spikes. In the linear regime before saturation, we use an approach developed by Rice to determine probability distributions for the peak values of intensity in both the time and frequency domains. We also find the average number of spikes per unit time or frequency. In addition, we derive joint probabilities for the intensity in the output pulse to have values I-1 and I2 at times t(1) and t(2), and for the spectral intensity to have values (I) over tilde (1) and (I) over tilde (2) at frequencies omega(1) and omega(2).