Eigenmodes for electromagnetic waves propagating in a toroidal cavity

• Published in: IEEE transactions on plasma science Vol. 18; no. 1; pp. 78 - 85
• Main Authors: Janaki, M.S., Dasgupta, B.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01-02-1990; Institute of Electrical and Electronics Engineers
• Subjects: 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; 700108 > Fusion Energy > Plasma Research > Wave Phenomena; ANNULAR SPACE; BOUNDARY CONDITIONS; CAVITY RESONATORS; CLOSED CONFIGURATIONS; Conductivity; CONFIGURATION; Electromagnetic coupling; Electromagnetic fields; Electromagnetic heating; Electromagnetic propagation; ELECTROMAGNETIC PULSES; ELECTROMAGNETIC RADIATION; Electromagnetic scattering; ELECTRONIC EQUIPMENT; Exact sciences and technology; Fundamental areas of phenomenology (including applications); HARMONICS; HELMHOLTZ INSTABILITY; INSTABILITY; MAGNETIC FIELD CONFIGURATIONS; Maxwell equations; Microwave propagation; Optics; OSCILLATIONS; Partial differential equations; Physics; PLASMA; PLASMA INSTABILITY; PLASMA MACROINSTABILITIES; PULSES; RADIATIONS; RESONATORS; SPACE 700107 > Fusion Energy > Plasma Research > Instabilities; TOROIDAL CONFIGURATION; Wave optics; WAVE PROPAGATION; Wave propagation in random media; Wave propagation; Cavity; Toroidal mode; Electromagnetic wave; Eigenmode
• ISSN: 0093-3813; 1939-9375
• DOI: 10.1109/27.45509

A solution has been attempted by means of the Helmholtz equation for an electromagnetic wave propagating in an empty torus in a system of toroidal coordinates. The electromagnetic fields are expressed in terms of the Hertz vector to obtain a scalar Helmholtz equation. The latter has been solved by making use of an inverse aspect ratio expansion of the solution. Unlike most previous workers, the authors have obtained their solutions in terms of hypergeometric functions whose static limit is the toroidal harmonics. The cylindrical solutions in terms of Bessel functions can also be recovered by taking the appropriate large aspect ratio limit. The eigenmodes, with arbitrary toroidal and poloidal mode numbers, have been obtained by applying the boundary conditions on the metallic walls of infinite conductivity, and they cannot be distinguished as TE or TM modes. Eigenfrequencies for various toroidal and poloidal mode numbers are plotted against the inverse aspect ratio. First-order approximations to the fields in the toroidal cavity have also been derived.< >