Influence of guiding magnetic field on emission of stimulated photons in   generators utilizing periodic slow-wave structures
  Effect of guiding magnetic field on evolution of stimulated emission is considered. It is shown that the transverse dynamics of electrons contributes to generation process and that contribution decreases with the magnetic field grows. The equation of generation for stimulated radiation of electron beam passing over periodic medium in magnetic field of arbitrary value is derived. The critical value of guiding field for which the transverse dynamics of electron don't contribute to emission is determined. It is shown, that transverse dynamics of electron modifies the boundary conditions. It follows from the derived generation equation that transverse dynamics yields to ~25% increase of the increment magnitude in high gain regime. In the limit of small signal the generation gain twice increases when transverse dynamics evolves. Obtained results are valid for every FEL system, which use the mechanism of waves slowing in the slow-wave structures for generation. 
Vladimir G. Baryshevsky, Konstantin G. Batrakov