CLOSED-FORM EIGENFREQUENCIES IN PROLATE SPHEROIDAL CONDUCTING CAVITY

摘要

In this paper, an efficient approach is proposed to analyse the interior boundary value problem in a spheroidal cavity with perfectly conducting wall. Since the vector wave equations are not fully separable in spheroidal coordinates, it becomes necessary to double-check validity of the vector wave functions employed in analysis of the vector boundary problems. In this paper, a closed-form solution has been obtained for the eigenfrequencies f_(nso) based on TE and TM cases. From a series of numerical solutions for these eigenfrequencies, it is observed that the f_(nso) varies with the coordinates of the parameter ξ in the form of f_(nso) (ξ) = f_(ns)(o) [1 + g~((1)) / ξ~2 + g~((2)) / ξ~4 + g~((3)) / ξ~6 + ...]. By means of least squares fitting technique, the values of the coefficients, g~((1)), g~((2), g~((3), ... , are determined numerically. It provides analytical results, and fast computations, of the eigenfrequencies and the results are valid although ξ is large (e.g., ξ ? 100).