Abstract
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.
Highlights
Gyrotron is an important high power and high frequency microwave source
We focus on the spatial harmonics method (SHM) method, it can achieve satisfactory accuracy by using some high order spatial harmonics that brought by the corrugations
We calculate the eigenvalue curves χ(c) of the TM modes with azimuthal index m = 8 in the region of χ ∈ (0,25)
Summary
Gyrotron is an important high power and high frequency microwave source. Since it has lots of special properties in the field of high efficiency and big power capability, it has become popular and been applied in a lot of cooperation projects in the world,[1,2,3,4] such as Electron Cyclotron Resonance Heating (ECRH) system,[5,6] plasma diagnostics, secure communication and medicine.[7]. In order to enhance the mode selectivity, the method that introduces the corrugations on the smooth outer wall is proposed.[18] The additional outer corrugations could evoke more spatial harmonics that would cause more modes to be coupled in the cavity, so the eigenvalue spectrum will be rearranged again by using the outer corrugations. This method will help us to research the distribution of the eigenvalues again.
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