  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.
