On the applicability of the traditional perturbation method in the theory of an O-type longtime interaction resonance oscillator

The paper points to the fact that the well-known approximate analytical theory of electron motion in the field of a retarded high-frequency wave is based on the assumption that the parameter of motion nonlinearity is small and appears to have an applicability which is insufficient to describe the electron beam dynamics in the mode of the most efficient energy interchange with the wave. Since the problem of electron motion in the wave field is a component part of the theory of the O-type oscillator with a long-time interaction, fundamental difficulties occur in the analytical description of the oscillator dynamics. It also poses a problem if such a theory is applicable for the description of the oscillator in the mode of a high-efficiency energy exchange between the electron beam and the wave. The present work considers the above issue and leads to a conclusion that such a theory is applicable, however, it does not cover high-efficiency modes.