We investigate the statistical properties (e.g., shot-to-shot power fluctuations) of the radiation from a high-gain free-electron laser (FEL) operating in the nonlinear regime. We consider the case of an FEL amplifier reaching saturation whose shot-to-shot fluctuations in input radiation power follow a gamma distribution. We analyze the corresponding output power fluctuations at and beyond first saturation, including beam energy spread effects, and find that there are well-characterized values of undulator length for which the fluctuation level reaches a minimum.

This book contains the Proceedings of the 24th International Free Electron Laser Conference and the 9th Free Electron Laser Users Workshop, which were held on September 9-13, 2002 at Argonne National Laboratory. Part I has been reprinted from Nucl. Instr. and Meth. A 507 (2003), Nos. 1-2.

The development of coherent radiation in high-gain free electron lasers, either from initial noise or from low-power input radiation, is analyzed in terms of three-dimensional Maxwell-Klimontovich equations. Exponential growth and saturation, transverse radiation profiles, transverse coherence and spectral features are discussed. Two possible systems of high-gain free electron lasers, one based on a storage ring and by-pass, another based on a linac and damping rings, are considered for the generation of 400 A radiation.

We study the saturated state of an untapered free electron laser in the Compton regime, arising after exponential amplification of an initial low level of radiation by an initially monoenergetic, unbunched electron beam. The saturated state of the FEL is described by oscillations about an equilibrium state. Using the two invariants of the motion, and certain assumptions motivated by computer simulations, we provide approximate analytic descriptions of the radiation field and electron distribution in the saturation regime. We first consider a one-dimensional approximation, and later extend our approach to treat an electron beam of finite radial extent. Of note is a result on the radiated power in the case of an electron beam with small radius.