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

• Published in: IEEE transactions on electron devices Vol. 69; no. 6; pp. 3427 - 3432
• Main Authors: Zhang, Liang, Easton, Jack, Donaldson, Craig R., Whyte, Colin G., Cross, Adrian W.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01-06-2022; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Coordinate transformations; Corrugated waveguides; Dispersion; Dispersion curve; Dispersion curve analysis; Eigenvalues; Eigenvalues and eigenfunctions; Error analysis; Error correction; Finite element analysis; Finite element method; finite element method (FEM); gyrotron traveling-wave amplifier (gyro-TWA); helically corrugated waveguide (HCW); helicoidal coordinate transform; Mathematical analysis; Mathematical models; Microwave theory and techniques; Optimization; Parameters; Perturbation theory; Solid modeling; Transforms
• ISSN: 0018-9383; 1557-9646
• DOI: 10.1109/TED.2022.3170279

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.