A mode matching technique for modeling and simulation of a gyrotron oscillator

The mode matching technique (MMT) is used to compute the electromagnetic fields, stored energy, quality (Q) factors, input admittances and resonant frequencies in an electron beam driven gyorotron cavity in the steady state. The MMT is used here because fields in and near the aperture must be computed accurately, and because the eigenmode decomposition is advantageous for the inclusion of the electron beam. Electromagnetic fields and the electron beam momentum equations are solved self-consistently. The MMT is based on matching the cavity and waveguide eigenmodes across the aperture. The complete set of modes including the irrotational modes required to expand the cavity magnetic field are used. External and Ohmic quality factors which are determined in a qualitative way in much of gyrotron literature are computed accurately here. The MMT is numerically implemented for cavities of rectangular and circular cylindrical cross-section. Coupling between transverse and axial modes through Ohmic and external losses is demonstrated. The electron beam motion equations are solved in the steady state using a fourth order Runge-Kutta method with Gill's constants and the power transfer from the beam to the cavity fields is computed. A Newton-Raphson root search method is used to compute the amplitudes and frequencies of various cavity eigenmodes. Results from the MMT are benchmarked against a time dependent method in cavities with Ohmic and external losses. The MMT is used to determine the resonant frequencies and Q factors of tapered cavities which are important in gyrotron research. Results are benchmarked in the cases of various cavities used in experiments at Navy Research Labs, MIT, and University of Maryland. The frequency spectrum of a tapered gyrotron cavity is computed and benchmarked against the experimental measurement done at MIT.