| Development of higher frequency gyrotron and peniotron devices involves harmonic operation. The Magnetron-Wall Waveguide (MWWG) has electromagnetic field content suitable for these devices. The circuit has been referred to as a “slotted resonant structure,” “cusptron,” “ridged waveguide,” and “rising sun” circuit. A model capable of accurately predicting the full TE and TM waveguide mode spectrum with the concomitant electromagnetic fields and energy for all modes is needed. The model commonly used cannot predict the complete mode spectrum, or accurately describe many modes it does predict.; The mode matching method employed uses two infinite Fourier-Bessel series to satisfy all boundary conditions of the central (circular) waveguide region and the outer (annular sector) slots. The series are truncated for numerical evaluation. The complete spectrum for the lowest 10 (TE and TM) modes of a two-vane circuit (having unequal slot and vane sizes) was calculated using the theoretical model, measured using a physical model, correlated and optimized using statistical analysis, and verified self-consistently using TM modes. The experimental cavity transmission, frequency measurement, and statistical mode correlation processes were verified using rectangular waveguide.; The method provides the complete accurate MWWG field, energy, and mode spectrum for a fixed frequency band, providing necessary precautions are employed during the process. Results are compared with those of others who have used trigonometric series expansion, difference equation, finite element, and mode matching methods. The commonly used (constant tangential electric field at the slot) model is most accurate for pi modes and less accurate for all others. Its accuracy deteriorates for higher-order (non-pi) modes. The commonly used (incomplete) model is shown mathematically to be a subset of the (complete, accurate) model developed here. A number of previously used methods were found lacking in some aspects. The methods developed are extensible, to describe previously untreated hybrid modes of multi-dielectric filled MWWG horn antennas. Complete accurate mode content, suitable for harmonic devices and other applications, is obtained using this model. Mode cutoff constant agreement (theoretical vs. measured) better than 0.1% was obtained. The method is accurate to the limits of physical waveguide measurement, providing enough terms are used. |
