Absorption and stimulated radiation of quanta of an external inhomogeneous electromagnetic field of free electrons

The possibilities of absorption or stimulated radiation of quanta of an electromagnetic field by a free electron resulting from the inhomogeneity of the spatial distribution of the intensity or the limited duration of the pulse are investigated. The probabilities of multiphoton processes are determined, and the nonrelativistic and relativistic limiting cases are discussed. It is shown, in particular, that during the propagation of a beam of relativistic electrons at a small angle to the direction of the propagation of the laser beam, a very significant energy broadening of the beam may arise, which depends on the intensity of the field and is due to its inhomogeneity or to the short duration of the pulse.