Mode interaction through amplitudes and phases in a two-mode gyrotron oscillator

An analysis is made of temporal evolution of electromagnetic modes in a two-mode gyrotron oscillator characterized by phase and amplitude interaction through the terms linear in the oscillator power. The problem is solved in the context of amplitudes and phases which vary slowly compared with the period of oscillation. Specific reference is made to competition between TE_11q modes in a closed cavity gyrotron. Qualitative features which are found include phase locking, beat frequencies, periodic pulling, and mode excitation. This work has applicability when the frequency separation between the modes is on the order of the frequency bandwidth of each mode, or the modes are equally spaced in frequency. Gyrotrons of this type include those with low-quality-factor modes or degenerate modes. Phase interaction in the case of equally spaced cavity modes is of importance in analyzing mode-locking phenomena