Abstract
In this paper, a coaxial gyrotron with outer corrugation is considered. Its multimode electron equation of motion is derived from the Lorentz equation, and its time-dependent amplitude and phase equation for the $\mathrm {TE}_{mn}$ mode is obtained from the wave equation. Using the time-dependent multimode beam–wave interaction equations, the time evolution processes of the time-dependent multimode coaxial cavity gyrotron with outer corrugation are investigated by numerical calculation. Results show that a 170-GHz coaxial gyrotron with outer corrugation can start up and operate stably at the $\mathrm {TE}_{34,19}$ mode and its competing modes are suppressed under different initial field amplitude conditions. By the calculation of the time-dependent multimode and single-mode coaxial gyrotron with outer corrugation, it is found that the output power and the output efficiency of the $\mathrm {TE}_{34,19}$ mode are 1.856 MW and 32.59%, respectively. These studies show the mode competition processes of the coaxial gyrotron with outer corrugation at the beginning start-up stage.
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