Resonance frequencies of cavities with sinusoidally rippled cross sections

The cylindrical waveguide with azimuthally periodic corrugations described by a sinusoidal function is investigated. Relevant to magnetron and harmonic gyrotron interactions, a TE-mode dispersion equation linking the transverse eigenvalue and corrugation parameters is derived upon expansion of the field quantities in terms of space harmonics. Theory is compared with experiment by measuring on 4- and 8-period cross section cavities the resonance frequencies of all the normal modes, in close agreement with the values anticipated by calculation.