Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



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 $ {R_1}$, $ {R_2}$ and distance $ d$ 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 $ kd = 2\pi d/\lambda $ 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 $ {g_{ns}}$ in the resulting relations $ {\omega _{ns}}\left( {kd} \right) = {\omega _{ns}}\left( 0 \right)\left[ {1 + {g_{ns}}{{\left( {kd} \right)}^2} \\ + \cdot \cdot \cdot } \right]$ for the natural frequencies of the cavity. Numerical results, comparisons and possible generalizations are also included.

References [Enhancements On Off] (What's this?)

  • [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)

Similar Articles

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

American Mathematical Society