Kinetic theory of harmonic gyrotron oscillator with slotted resonant structure

A kinetic model is defined for the functions of a gyrotron equipped with a single-cavity oscillator (SCO). The SCO was developed as a slotted interaction mechanism which would enhance cyclotron interaction in a harmonic gyrotron at microwave ranges as the harmonic number increases. A periodic fringe field is produced in the orbits of concentrically circulating electrons. The harmonic content of RF fields encountered by the electrons is thereby enhanced. The model treats the electrons as a distribution function in the six-dimensional spatial and momentum spaces. Solution of the Vlasov equation for the evolution of the distribution function in the presence of RF fields yields the spatial dependence of the beam current ac component. Integration of the product of the ac beam current and the RF electric field over the interaction region defines the power deposited by the beam. Account is taken of the beam- and depletion-deposited energy to define the start-oscillation condition and the threshold beam power. The model is extended to identify optimized operating conditions and the dependence of the threshold beam power on the cavity mode, the harmonic number, the cavity dimensions and the beam voltage. High harmonic operation is demonstrated to be feasible at a low beam voltage and a threshold beam power lower than previously predicted.