Closed-form eigenfrequencies in prolate spheroidal conducting cavity

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 f/sub ns0/ based on TE and TM cases. From a series of numerical solutions for these eigenfrequencies, it is observed that the f/sub ns0/ varies with the parameter /spl xi/ among the spheroidal coordinates (/spl eta/, /spl xi/, /spl phi/) in the form of f/sub ns0/(/spl xi/) =f/sub ns/(0)[1+g/sup (1)///spl xi//sup 2/+g/sup (2)///spl xi//sup 4/+g/sup (3)///spl xi//sup 6/+/spl middot//spl middot//spl middot/]. By means of the least squares fitting technique, the values of the coefficients, g/sup (1)/, g/sup (2)/, g/sup (3)/, ..., are determined numerically. It provides analytical results and fast computations of the eigenfrequencies, and the results are valid if /spl xi/ is large (e.g., /spl xi//spl ges/100).