Propagation Characteristics of Confocal Waveguides Based on Spheroidal Functions for a ${W}$ -Band Gyro-TWT

The propagation characteristics of a confocal waveguide are related to the radial spheroidal function, which is extremely complicated. A quadratic polynomial fitting (QPF) expression derived from numerical results by interpolation was successfully applied to the development of confocal gyrotrons. However, the QPF expression is valid only for a moderate spheroidal parameter. As a result, it cannot work well for confocal gyrotron travelling-wave tube (gyro-TWT) applications since the Fresnel parameter may be small for stable operations. For the first time, an efficient algorithm is developed to accurately calculate the spheroidal functions. Based on it, the MATLAB code with high accuracy and efficiency is developed to analyze the propagation characteristics of confocal waveguide. The calculated results and the QPF results are compared for different mirror apertures, and then demonstrated by high frequency structure simulator (HFSS). The calculated results show good agreement with the HFSS results for different mirror apertures while the QPF solution agrees with the HFSS results only for large apertures. The code is valid for arbitrary mirror apertures for both the confocal gyrotron and gyro-TWT applications.