Buildup of oscillations in two-mode gyrotron

Power gyrotrons with evolution of the interaction space are considered for generating stable single-mode oscillations under conditions favoring self-excitation of several modes. Interaction of two modes, occurring in small resonator cavities, can be treated as a suppression of the mode with a smaller initial increment than that with a larger initial increment and as a nonlinear excitation of the second mode after excitation of the first mode acting as a primer. The attendant transient processes in a two-mode gyrotron are described by a self-consistent system of equations including a short equation of motion for electrons in an external magnetic field and in the field of two modes as well as equation of mode excitation, the same equation for both modes. These equations are supplemented with an integral expression for mode excitation by an electron beam. Numerical analysis of this system for two modes having Gaussian longitudinal profiles and resonating at the fundamental gyrofrequency or at its multiple confirm that both mechanisms stabilize single-mode oscillation under efficiency-optimum conditions and also that stable two-mode oscillation is possible.