In this article, the time-dependent multimode competition equations, the dependence of the starting current on the static magnetic field, and the current ratio of a coaxial cavity gyrotron with multiple electron beams are investigated according to the linear and nonlinear theories. By numerical calculation, the mode competition of a 170-GHz coaxial cavity gyrotron is studied when it has one, two, and three electron beams. Researches demonstrate that under the given magnetic field $B$ , electron beam voltage $U$ , and pitch factor ${\alpha }$ , a gyrotron with different electron beam numbers has different startup scenarios, which show that the gyrotron with three electron beams has potential in the selection of mode, the depression of mode competition, and the increase of output power. Results find that the coaxial cavity gyrotron with three electron beams can operate steadily in the ${\text {TE}_{38,18-}}$ mode at 170.39 GHz and it has an output power of 5.02 MW and a beam–wave interaction efficiency of 35.42% when $B=6.82\text{T}$ , $U=88$ kV, $\alpha =1.3$ , $I=158$ A and the three electron beams locate at 11.14, 12.93, and 14.32 mm. Three electron beams in the gyrotron have different beam–wave interaction efficiencies, and the closer the electron beam is to the inner conductor, the higher its beam–wave interaction efficiency is.

中文翻译：

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具有多电子束的同轴腔回旋管的多模竞争仿真

本文根据线性和非线性理论研究了时间相关的多模竞争方程、启动电流对静磁场的依赖性以及多电子束同轴腔回旋管的电流比。通过数值计算，研究了170GHz同轴腔回旋管具有一、二、三束电子束时的模式竞争。研究表明，在给定磁场下 $B$ , 电子束电压 $U$ , 和音调因数 ${\alpha }$ ，不同电子束数的回旋管具有不同的启动场景，说明三束电子束的回旋管在模式选择、模式竞争抑制、输出功率提升等方面具有潜力。结果发现，三束电子束同轴腔回旋管可以稳定运行。 ${\text {TE}_{38,18-}}$ 模式在 170.39 GHz 时，它具有 5.02 MW 的输出功率和 35.42% 的波束相互作用效率。 $B=6.82\text{T}$ , $U=88$ 千伏， $\alpha =1.3$ , $I=158$ A 和三个电子束位于 11.14、12.93 和 14.32 mm。回旋管中的三束电子束具有不同的束波相互作用效率，电子束离内导体越近，其束波相互作用效率越高。