Operation of the quasi-optical gyrotron at harmonics of the gyrofrequency

This paper investigates the performance of a quasioptical gyrotron, when the electron beam interacts with the radiation fields at harmonics of the gyrofrequency. The nonlinear equations of motion are obtained in the slow-timescale. The expression for the linear gain is derived and the conditions for excitation are given (frequency threshold, optimal operating point, bean current and resonator quality thresholds). In the nonlinear regime, it is shown that maximum efficiencies comparable to those at the fundemental (50%) are possible, albeit at a prohitively high radiation field amplitude, while realistically feasible field amplitudes can give somewhat smaller, but nevertheless still high efficiencies (15%). Finally, the results are suplemented by empirical scaling laws, useful for experimental designs.