Free-electron lasers: Amplification, multiphoton transitions, saturation, and geometry

A review of the literature and the main ideas on free-electron lasers (FEL's) is presented. Various approaches to describe the physical processes in FEL's are discussed. With the aid of a general quantum-mechanical description, the probabilities of multiphoton transitions in FEL's are found. Typically, the number of photons that are absorbed or emitted in FEL's is large even in a very weak field. Nevertheless, over a wide range of parameters the gain coefficient in the FEL coincides with that derived in the weak-field approximation. At the strong-field limit, an analytical expression for the saturated gain is found using either a quantum-mechanical or classical approach. The possibility of optimizing the gain in the Compton laser is discussed; this optimization is connected with use of a noncolinear scattering scheme for electron beams with a rather large energy spread.