Simple technique for biconical cavity eigenfrequency determination

A number of features of biconical cavities make them attractive for various applications. Expressions for the calculation of the eigenfrequencies of a biconical cavity with large cone angles can be derived using the overlapping domain decomposition method in combination with the collocation method; however, the expressions reported in the literature involve only a single pair of collocation points, thus giving no way to estimate the eigenfrequency determination accuracy. The aim of this paper is to calculate the biconical cavity eigenfrequencies for an arbitrary number of collocation point pairs. An equation in the biconical cavity eigenfrequencies for an azimuthally symmetric transverse electric field at an arbitrary number of collocation point pairs is derived. The equation reduces to two equations, whose solution requires far less computational effort in comparison with the original equation. The solution of one of the two equations are based on modes symmetric about the cavity symmetry plane, and the solutions of the other are based on antisymmetric modes. The calculated eigenfrequencies converge rapidly with increasing number of collocation point pairs, while the use of only one collocation point pair may introduce noticeable error. The proposed technique may be used in the development of components and units on the basis of biconical cavities