Interaction of electrons with the electromagnetic field in free electron lasers

The experimental and theoretical work on free-electron lasers is reviewed. Different amplification schemes and electron scattering mechanisms, the relation between the single-particle scattering of free electrons in high-energy beams and stimulated scattering by collective oscillations in a dense electron-beam plasma (comparatively low-energy) are discussed. Various physical approaches used to describe the processes in freeelectron lasers are discussed. Stimulated multiphoton emission processes in undulators and stimulated Compton scattering processes are examined. The relation between the quantum and classical properties of these phenomena is discussed. The nonlinear behavior of the gain in a free-electron laser under saturation conditions is described. The possibility of optimizing the gain in a Compton laser in a scheme with noncollinear propagation of electrons and electromagnetic waves is discussed.