Simulation analysis of electron beam performance and beam-wave interaction in megawatt-class gyrotron
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摘要: 在考虑不同电子注性能（速度离散、电子注厚度、空间电荷效应、起振过程、单/双阳极结构）情况下，建立了完善的时域多模自洽非线性注-波互作用模型。以自研的兆瓦级170 GHz、TE25,10模式工作的回旋管为研究对象，系统分析了高频腔结构参数变化、起振电流、单/双阳极电子注电压调制及不同速度和电子注离散下的模式竞争情况。数值模拟研究表明：双阳极调制方式能明显抑制模式竞争，在电子注电压80 kV、电流40 A、磁场6.72 T、横纵速度比1.3的工作条件下，可实现1.35 MW输出功率和42.2%的互作用效率。Abstract:
Background The gyrotron is a relativistic nonlinear device capable of generating high-power electromagnetic radiation in the millimeter-wave and terahertz frequency ranges. In most operating magnetically confined thermonuclear fusion reactors (for electron cyclotron heating and current drive, ECH&CD), high-power gyrotrons serve as the core microwave source devices for their electron cyclotron wave heating and current drive systems. For high-power gyrotrons, the high-frequency cavity must operate in a high-order whispering gallery mode to meet the power capacity requirements. However, high-order mode operation conversely introduces severe mode competition. Electron beam performance is a major factor affecting the mode competition, further limiting their efficient and stable operation, particularly in long-pulse or continuous-wave regimes. Therefore, it is essential to investigate the impact of megawatt-level gyrotron electron beam performance on beam-wave interaction.Purpose The study focuses on a self-developed megawatt-level 170 GHz gyrotron operating at TE25,10 mode, analyzing the structural parameter variations of the high-frequency cavity, the start-oscillation current, and the mode competition in single/dual-anode electron beam modulation.Method This paper comprehensively considers electron beam performance (velocity spread, beam thickness, space charge effects, oscillation startup process, single/dual-anode configuration) and establishes a sophisticated time-domain, multi-mode, multi-frequency self-consistent nonlinear beam-wave interaction model.Results Under operating conditions of 80 kV beam voltage, 40 A beam current, 6.72 T magnetic field, and a velocity ratio of 1.3, the output power reaches 1.35 MW with an interaction efficiency of 42.2%.Conclusion Numerical simulations demonstrate that the dual-anode modulation method significantly suppresses mode competition. The successful demonstration of this device establishes a foundation for further studies on higher power and higher-frequency gyrotron. -
图 1 互作用高频结构及主模的归一化电场幅值分布
Figure 1. Interaction circuit and normalized electric field amplitude distribution of the main mode
图 2 170 GHz、TE25,10模式回旋管高频腔体内主模的相位分布
Figure 2. Phase distribution of the main mode in the high-frequency cavity of a 170 GHz TE25,10 mode gyrotron
图 3 腔体谐振频率和衍射Q值随着入口段倾角变化的关系
Figure 3. Relationship between the resonant frequency of the cavity and diffractive quality factor Qdiff with the variation of the input section inclination angle
图 4 腔体谐振频率和衍射Q值随着出口段倾角变化的关系
Figure 4. Relationship between the resonant frequency of the cavity and diffractive quality factor Qdiff with the variation of the output section inclination angle
图 5 主模TE25,10及其附近主要竞争模式的起振电流随磁场变化情况
Figure 5. Variation of the starting current of the main mode TE25,10 and its neighboring competing modes with the magnetic field
图 6 单阳极和双阳极电子枪结构示意图
Figure 6. Structural diagrams of single-anode and dual-anode electron guns
图 7 不同工作磁场下输出功率与互作用时间关系
Figure 7. Output power varied with interaction time under different magnetic field
图 8 不同模式输出功率与磁场的关系当电压为80 kV，电流为40 A，速度比1.3，
$ {R}_{{\mathrm{g}}} $ = 7.414 mmFigure 8. Relationship between output power and magnetic field when the voltage is 80 kV, current is 40 A,
$ \alpha $ is 1.3,$ {R}_{{\mathrm{g}}} $ = 7.414 mm
图 9 模拟阴极电压与调制极电压在同一时刻达到稳定状态时，电压和调制电压随时间的变化
Figure 9. Simulated cathode voltage and modulation electrode voltage reaching stability simultaneously
图 11 电压和调制电压随时间的变化。
Figure 11. Simulated variation of cathode voltage and modulation electrode voltage
图 12 不同调制状态下，输出功率与互作用时间关系，其中磁场为6.72 T，阴极电压为80 kV，电流为40 A，速度比为1.3，
$ {R}_{{\mathrm{g}}} $ = 7.414 mmFigure 12. Relationship between output power and interaction time under different modulation conditions when magnetic field is 6.72 T, cathode voltage is 80 kV, current is 40 A,
$ \alpha $ is 1.3,$ {R}_{{\mathrm{g}}} $ = 7.414 mm
图 15 电子注电压为76 kV、电流为45 A、磁场为6.71 T、横纵速度比为1.05、速度离散为10%、电子注厚度为
$ \Delta R=3{R}_{{\mathrm{L}}} $ 工作条件下注-波互作用结果Figure 15. Beam-wave interaction results when magnetic field: 6.71 T, cathode voltage: 76 kV, current: 42 A, velocity ratio: 1.05,
$ \delta {{v}}_{\mathrm{t}}=10\mathrm{{\text{%}} } $ ,$ \Delta R=3{R}_{{\mathrm{L}}} $ 
图 14 170 GHz, 兆瓦级回旋管测试结果
Figure 14. Tested results of 170 GHz, megawatt-class gyrotron
表 1 170 GHz TE25,10回旋管高频腔体的相关参数
Table 1. Relevant parameters of 170 GHz TE25,10 gyrotron high-frequency cavity
$ {{R}}_{\rm{in}} $ $ {{R}}_{\rm{m}} $ $ {{R}}_{\rm{out}} $ $ {{L}}_{{1}} $ $ {{L}}_{{2}} $ $ {{R}}_{{1}} $ $ {{R}}_{{2}} $ $ {{R}}_{{3}} $ $ {{R}}_{{4}} $ $ {\theta }/({^{\circ}}) $ $ {\beta }/({^{\circ}}) $ $ {{L}}_{{3}} $ $ {\sigma } $/($ {{\rm{S}}}\cdot {\rm{m}}^{-{1}} $) $ {{Q}}_{\rm{diff}} $ $ {{Q}}_{\rm{ohm}} $ $ {{Q}}_{\rm{t}} $ 9.6$ {\lambda } $ 10.1$ \lambda $ 10.8$ \lambda $ 4.1$ \lambda $ $ 7.7\lambda $ 0 $ 11.3\lambda $ $ 11.3\lambda $ 0 5 3 $ 5.6\lambda $ 1.5$ \times {10}^{7} $ 1630 47725 1576 
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表 2 不同位置倒角半径时，腔体谐振频率
$ \boldsymbol{f} $ 与衍射品质因数$ {\boldsymbol{Q}}_{\boldsymbol{d}\boldsymbol{i}\boldsymbol{f}\boldsymbol{f}} $ Table 2. Resonant frequency f and diffractive quality factor Qdiff at different fillet radius positions
No. $ {{R}}_{{1}}/{\lambda } $ $ {{R}}_{{2}}/{\lambda } $ $ {{R}}_{{3}}/{\lambda } $ $ {{R}}_{{4}}/{\lambda } $ $ {f} $/GHz $ {{Q}}_{\rm{diff}} $ 1 0 0 0 0 169.41937 1681 2 28.3 0 0 0 169.4197 1675.8 2 0 5.7 0 0 169.4202 1668.6 3 0 11.3 0 0 169.4215 1648.6 4 0 17.0 0 0 169.4237 1617.1 5 0 0 10.0 0 169.4197 1670.0 6 0 0 11.3 0 169.4198 1653.7 7 0 0 17.0 0 169.4198 1626.7 8 0 5.7 5.7 0 169.4202 1663.4 9 0 8.5 8.5 0 169.4208 1648.1 10 0 11.3 11.3 0 169.4200 1630.0 11 0 14.2 14.2 0 169.4226 1601.0 12 0 17.0 17.0 0 169.4238 1570.1 13 0 11.3 11.3 11.3 169.4216 1631.7 14 0 11.3 11.3 28.3 169.4217 1646.7 15 11.3 11.3 11.3 28.3 169.4217 1646.7 16 28.3 11.3 11.3 28.3 169.4217 1646.7
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表 3 热腔计算参数
Table 3. Hot cavity calculation parameters
guiding center
radius $ {{R}}_{\rm{g}} $/mmbeam voltage
$ {{U}}_{\rm{b}} $/kVmodulation voltage
$ {{U}}_{\rm{mod}} $/kVvoltage division
ratio $ {\eta } $/%beam current
$ {{I}}_{\rm{b}} $/Amagnetic field
$ {{B}}_{\rm{z}} $/Tpitch factor
α7.414 80 28.5 64 40 6.72 1.3
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表 4 170 GHz TE25,10回旋管实测值与数值模拟值对比
Table 4. Comparison between measured and simulated values of a 170 GHz TE25,10 gyrotron
parameter $ {{U}}_{\rm{b}} $/kV $ {{I}}_{\rm{b}} $/A $ {{B}}_{{0}} $/T $ {\alpha } $ $ \Delta {R} $/mm $ \boldsymbol{\delta }{{v}}_{\rm{t}} $ output power/kW output frequency/GHz measured value 76 45 6.71 1.1 / / 710 169.65 simulated value 76 45 6.71 1.05 0.49 10% 720 169.482
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