Theory of nonlinear mode interaction at higher harmonics in a gyrotron

The undesired excitation of modes at the fundamental frequency presents a major problem for stable operation of harmonic gyrotrons and can preclude one from reaching the most efficient operating regime, as has been verified experimentally. A study of nonlinear dynamics of mode interaction at the cyclotron harmonics in a gyrotron oscillator is presented here. A multifrequency, time-dependent nonlinear theory is used to carry out numerical simulations. The simulations are used to understand various types of mode interactions and to optimize the cavity design and the operating parameters.; The simulation study presented here can be divided into three parts. The first part involves analyzing the stability of single mode equilibrium at the fundamental frequency when perturbed by a parasitic mode at the fundamental. The regions of parameter space in which a preexisting large-amplitude (operating) mode is able to suppress competing satellites are determined for cases in which the coupling coefficients and cavity quality factors are different for each mode. A general design guideline is established in terms of a normalized interaction length parameter {dollar}mu{dollar}. For {dollar}mu < 15{dollar} the maximum efficiency operating point is stable to mode competition. The effect of the quality of the electron beam on the efficiency is also investigated.; The second part involves a study of nonlinear dynamics of two-mode interaction between the modes at second harmonic and fundamental frequencies. The accessibility of a stable, efficient equilibrium at the second harmonic is analyzed in the presence of the parasitic mode at the fundamental for two start-up scenarios. When the electrode voltages rise very fast as compared to the cavity fill time, the mode at the fundamental can be helpful in the excitation of the second harmonic for a certain range of operating parameters. When the voltages rise on the cavity fill time scale, the mode competition between the first and second harmonics is more severe.; In the third part, the theoretical formulation is further extended to carry out numerical studies of interactions between three modes that are parametrically coupled together. The presence of modes at the fundamental and second harmonic can lead to parametric excitation of the mode at the third harmonic. This phenomenon can be used to access the stable, efficient operating regime of the third harmonic. Two practical designs of 94 and 210 GHz gyrotrons are presented as examples.; The study presented here demonstrates the feasibility of stable, efficient operation of a gyrotron at cyclotron harmonics.