Theory of electron cyclotron maser interactions in a cavity at the harmonic frequencies

A theory of the cyclotron maser interactions between an annular electron beam and the standing electromagnetic wave in a cavity structure is formulated on the basis of the relativistic Vlasov equation and the Maxwell equations. Detailed analytical expressions for the beam-wave coupling coefficient, beam energy gain, and threshold beam power have been derived for the fundamental and higher cyclotron harmonics. Physical interpretations of these results and comparison with cyclotron maser interactions in a waveguide structure will be presented. Methods of parameter optimization and their applications to experiments will be illustrated through numerical examples.