This work develops a nonlinear and self-consistent framework for the single-mode simulation of TM-mode gyrotrons. Unlike TE modes, a nonlinear TM wave equation is derived by considering the additional axial modulation on the electron beam due to the interaction with the axial electric field. Together with the electrons' equations of motion, particle tracing simulation is conducted to model TM-mode oscillation. For a uniform structure, the electron-beam efficiency of the $\mathrm{T}{\mathrm{M}}_{11}$-mode gyrotron at the $W$ band can achieve 30% over broad parameter space. Its beam-current, beam-voltage, and pitch-factor tuning properties are investigated under different magnetic fields. By optimizing the interaction structure of the proposed gyrotron backward-wave oscillator (gyro-BWO), the maximum interaction efficiency is higher than 30% with a frequency tuning range of more than 6 GHz at the pitch factor of 1.5. The peak efficiency can remain high of 32% at low beam voltage (10 kV) and low magnetic field (32.8 kG), indicating additional operating conditions. These special features may facilitate the development of low-cost and compact gyrotron systems and show great potential in the applications for TM-mode gyro-BWOs.

• Received 19 August 2021
• Revised 20 October 2021
• Accepted 1 December 2021

DOI:https://doi.org/10.1103/PhysRevE.104.065205