Simple Technique for Determining Length of Biconical Cavity’s Evanescent Zones

This paper presents a simple technique for finding the length of evanescent zones near the ends of the biconical cavity, where sample insertion openings can be made without significantly affecting the resonance frequencies or the field structure. The technique combines the overlapping domain decomposition method with the collocation method. The interior of the cavity is divided into two overlapping regions, on the boundaries of which collocation points are specified. In each region, the electric field is represented as an eigenfunction expansion. A homogeneous system of linear equations in the expansion coefficients is derived from the equality of the electric fields in both regions at the collocation points. The expansion coefficients are determined as an eigenvector of the system matrix associated with its zero eigenvalue. Using the found expansion coefficients, the distribution of the electric field normalized to the maximum electric field in the cavity is calculated to give the length of evanescent zones, which are defined as regions where the electric field does not exceed a specified small fraction of the maximum electric field in the cavity. Because as few as four pairs of collocation points were proved to be sufficient, the computational effort of the proposed technique is relatively moderate, thus allowing it to be used in the development of instruments based on open-ended biconical cavities.