Closed-form eigenfrequencies in prolate spheroidal conducting cavity

Abstract

In this paper, an efficient approach is proposed to analyze 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 fns0 based on TE and TM cases. From a series of numerical solutions for these eigenfrequencies, it is observed that the fns0 varies with the parameter ξ among the spheroidal coordinates (η, ξ, φ) in the form of fns0 (ξ) = fns(0) [1 + g(1)/ξ2 + g(2)/ξ4 + g(3)/ξ6 + ⋯]. By means of the 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 if ξ is large (e.g., ξ ≥ 100).