| Summary: | Here we present a detailed study on eigenvalues for TM modes. In order to achieve enough accuracy, the spatial harmonics method (SHM) is used to derive the eigenfunction of TM modes in the coaxial cavity with both inner and outer corrugations. After that, the equations can be numerically solved with some constraints. Meanwhile, the influences of the variations of the corrugation parameters on the eigenvalues of TM modes are analyzed carefully, which is helpful for us to learn the distribution rule of the TM modes. In addition, the differences and similarities between TM and TE modes are studied comprehensively to select the suitable mode in the coaxial cavity. The numerical results are presented in this paper, the comparisons are also made with the published results.
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