Theory of Linear and Nonlinear Gain in a Gyroamplifier Using a Confocal Waveguide

Alexander V. Soane, Michael A. Shapiro, Jacob C. Stephens, Richard J. Temkin

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


The linear and nonlinear theory of a gyroamplifier using a confocal waveguide is presented. A quasi-optical approach to describing the modes of a confocal waveguide is derived. Both the equations of motion and the mode excitation equation are derived in detail. The confocal waveguide circuit has the advantage of reducing mode competition, but the lack of azimuthal symmetry presents challenges in calculating the gain. In the linear regime, the gain calculated using the exact form factor for the confocal waveguide agrees with an azimuthally averaged form factor. A beamlet code, including velocity spread effects, has been written to calculate the linear and nonlinear (saturated) gain. It has been successfully benchmarked against the MAGY code for azimuthally symmetric cases. For the confocal waveguide, the beamlet code shows that the saturated gain is reduced when compared with results obtained using an azimuthally averaged form factor. The beamlet code derived here extends the capabilities of nonlinear gyroamplifier theory to configurations that lack azimuthal symmetry.

Original languageEnglish
Article number8014466
Pages (from-to)2438-2449
Number of pages12
JournalIEEE Transactions on Plasma Science
Issue number9
StatePublished - Sep 2017


  • Gyrotrons
  • Microwave amplifiers
  • Millimeter wave circuits
  • Waveguides


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