Resonant frequencies in an electromagnetic eccentric spherical cavity

Authors:
John D. Kanellopoulos and John G. Fikioris

Journal:
Quart. Appl. Math. **37** (1979), 51-66

MSC:
Primary 78A50; Secondary 45E99

DOI:
https://doi.org/10.1090/qam/530668

MathSciNet review:
530668

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The interior boundary-value electromagnetic (vector) problem in the region between two perfectly conducting spheres of radii , and distance between their centers is considered. Surface singular integral equations are used to formulate the problem. Use of spherical vector wave functions and related addition theorems reduces the solution of the integral equations to the problem of solving an infinite set of linear equations. Their determinant is evaluated in powers of to a few terms. It is then specialized to the axially symmetric case and set equal to zero. This yields closed-form expressions for the coefficients in the resulting relations for the natural frequencies of the cavity. Numerical results, comparisons and possible generalizations are also included.

**[1]**J. D. Kanellopoulos and J. G. Fikioris,*Acoustic resonant frequencies in an eccentric spherical cavity*, J. Acoust. Soc. Am.**64**, 286-297 (1978)**[2]**C. Müller,*Foundations of the mathematical theory of electromagnetic waves*, Springer-Verlag. Berlin (English translation). 1969 MR**0253638****[3]**H. Hönl, A. W. Maue and K. Westpfahl,*Theory of diffraction*, Handbuch der Physik**25/1**, pp. 218-573. Springer-Verlag, Berlin, 1961**[4]**J. Van Bladel,*Electromagnetic fields*, McGraw-Hill Book Co., New York, N. Y., 1964**[5]**O. D. Kellogg,*Foundations of potential theory*, Dover Publ., New York, N. Y., 1953**[6]**O. R. Cruzan,*Translational addition theorems for spherical vector wave functions*, Quart. Appl. Math.**20**, 33-40 (1962) MR**0132851****[7]**P. M. Morse and H. Feshbach,*Methods of theoretical physics*, McGraw-Hill Book Co., New York. N. Y., 1953 MR**0059774****[8]**J. A. Stratton,*Electromagnetic theory*, McGraw-Hill Book Co., New York, N. Y., 1941**[9]**H. Y. Yee and N. F. Audeh,*Cutoff frequencies of eccentric waveguides*, IEEE Trans, on MTT**14**, 487-493 (1966)

Retrieve articles in *Quarterly of Applied Mathematics*
with MSC:
78A50,
45E99

Retrieve articles in all journals with MSC: 78A50, 45E99

Additional Information

DOI:
https://doi.org/10.1090/qam/530668

Article copyright:
© Copyright 1979
American Mathematical Society