Electromagnetic resonances in toroidal cavities

Electromagnetic resonances in a toroidal cavity are studied both theoretically and experimentally. In the theory the dispersion relation is obtained solving Maxwell's equation in the cavity using perturbation theory, as in the literature, but with a different expansion which keeps the singularity for unit aspect ratio. The results are obtained in zeroth order, including toroidal effects, in terms of hypergeometric functions for which the values of the eigenfrequencies can be calculated. In the experiment the eigenfrequencies are measured in a toroidal cavity with aspect ratio 1.25 (R0 = 0.125 m and r0 = 0.100 m). The results, although they do not consider a detailed comparison of modes, show an overall disagreement with theoretically calculated values of the paper and of the literature, varying from a few per cent to 100%. (author). 10 refs, 2 figs, 1 tab