Self-consistent non-stationary theory of the gyrotron

For a long time, the gyrotron theory was developed assuming that the transit time of electrons through the interaction space is much shorter than the cavity fill time. Correspondingly, it was assumed that during this transit time, the amplitude of microwave oscillations remains constant. A recent interest to such additional effects as the after-cavity interaction between electrons and the outgoing wave in the output waveguide had stimulated some studies of the beam-wave interaction processes over much longer distances than a regular part of the waveguide which serves as a cavity in gyrotrons. Correspondingly, it turned out that the gyrotron theory free from the assumption about constant amplitude of microwave oscillations during the electron transit time should be developed. The present paper contains some results obtained in the framework of such theory. The main attention is paid to modification of the boundary between the regions of oscillations with constant amplitude and automodulation in the plane of normalized parameters characterizing the external magnetic field and the beam current. It is shown that the theory free from the assumption about the frozen wave amplitude during the electron transit time predicts some widening of the region of automodulation.