Stimulated scattering of electromagnetic waves by a relativistic electron beam in a three-dimensional geometry

The properties of stimulated coherent scattering of an electromagnetic wave by a relativistic electron beam were studied in the framework of a three-wave approximation for a noncollinear geometry, when the incident and the scattered waves can propagate at arbitrary angles relative to the electron beam direction. The dispersion equation was obtained, making it possible to investigate the modes of collective (Raman) and single-particle (Compton) scattering from a unified viewpoint and to include the effect of an external longitudinal magnetic field on the electron motion in the field of a combination wave. Formulas were obtained for the amplitude increments of the scattered and the combination waves for those scattering modes, which can be used to make estimates when selecting the optimal scheme of a free-electron laser with a noncollinear scattering geometry.