Nonlinear theory of the stimulated scattering of waveguide modes by a relativistic electron beam focused by a longitudinal magnetic field - Basic equations

The paper obtains a self-consistent system of equations describing the stimulated scattering of E and H waves by a tubular relativistic electron beam focused by a longitudinal magnetic field. It is considered that this field suppresses transverse drift due to the inhomogeneities of these waves without freezing the electron oscillations in the signal and pump fields. It is shown that, at a sufficiently large value of the focusing field where the averaged motion of the electrons is one-dimensional, these equations coincide with an accuracy to constant coefficients with equations describing the scattering of plane homogeneous TEM waves by a homogenenous unbounded electron beam. The intrinsic field of a bunched electron beam moving in a circular waveguide is analyzed.