Frequency chirped self-amplified spontaneous-emission free-electron lasers

We present a statistical analysis of the temporal and spectral properties of self- amplified spontaneous emission from an energy- chirped electron beam passing through a long undulator. It is found that the coherence time is independent of the chirp, while the range of spectral coherence is linearly proportional to it. We consider the use of a monochromator to pick out a small temporal slice of the radiation output. For the filtered radiation pulse, we determine the pulse duration, the number of modes, and the energy fluctuation. We apply our analysis to schemes proposed to generate short x- ray pulses at the Linac Coherent Light Source.