Dispersion curve of the helically corrugated waveguide based on helicoidal coordinate transform

Liang Zhang, Jack Easton, Craig R. Donaldson, Colin G. Whyte, Adrian W. Cross

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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.
Original languageEnglish
Pages (from-to)3427 - 3432
Number of pages6
JournalIEEE Transactions on Electron Devices
Issue number6
Early online date9 May 2022
Publication statusPublished - Jun 2022


  • helically corrugated waveguide
  • gyrotron travelling-wave amplifier
  • dispersion curve
  • heliocidal coordinate transform
  • finite element method


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