Dispersion Curve of the Helically Corrugated Waveguide Based on Helicoidal Coordinate Transform

This article presents the dispersion curve study of the helically corrugated waveguide (HCW) using the 2-D finite element method (FEM) method based on the helicoidal coordinate transform. Calculation of the dispersion curve is 60 times faster compared with 3-D FEM simulation while maintaining similar accuracy. The 2-D method was used to investigate the relative error between it and a 1-D analytical method based on perturbation theory. Over a narrow parametric range, the 1-D method has a similar dispersion (within a relative error of 3%) in comparison to the 2-D/3-D methods but the error greatly increased when the parameter space was expanded. Correction factors were determined to greatly enhance the 1-D method accuracy over the wider parametric range. Assisted by the improved 1-D method, it allows identifying the desired operating mode automatically within the multiple eigenvalues from the 2-D simulation results. Therefore, it can be integrated into an optimization routine to explore the applications of the HCWs at wider parameter ranges.

I. Introduction

Helically corrugated waveguide (HCW) that contains both axial and azimuthal periodicities attracts significant interest in applications such as gyro-devices [1]–[4], microwave undulators [5], microwave pulse compressors [6], [7], and arbitrary mode converters [8], due to its unique dispersion characteristics. By varying the geometric parameters, different dispersion curves can be generated to satisfy the requirements of different applications. For example, a dispersion curve with a constant group velocity at small axial wavenumbers over a large frequency band is desired for broadband amplification in gyrotron traveling wave amplifiers (gyro-TWAs) [9]–[11]. While in microwave pulse compressors, dispersion curves with large differences in the group velocities and low ohmic loss at a wide frequency band are preferred to achieve a high compression ratio [12], [13].