EIGENMODES FOR ELECTROMAGNETIC-WAVES PROPAGATING IN A TOROIDAL CAVITY

We have attempted a solution of the Helmholtd equationfor an electromagnetic wave propagating in an empty torus in a system?of toroidal coordinates by expressing the electromagnetic fields in termsof the Herti vector to obtain a scalar Helmholti equation. The latter?has been solved by making use of an inverse-aspect ratio expansion ofthe solution. Unlike most of the previous workers, we have obtained?our solutions in terms of hjpergeometric functions whose static limitare the toroidal harmonics. The cylindrical solutions in terms of Bessel?functions can also be recovered by taking the appropriate large-aspectratio limit. The eigenmode, with arbitrary toroidal and poloidal mode?numbers, have been obtained by applying the boundary conditions onthe metallic walls of infinite conductivity, and they cannot be distinguished?as TE or TM modes. Eigenfrequencies for various toroidal andpoloidal mode numbers are plotted against the inverse aspect ratio.?First-order approximations to the fields in the toroidal cavity have alsobeen derived. © 1990 IEEE