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The sheet beam extended interaction klystron is an important kind of millimeter-wave and sub-millimeter-wave vacuum electron device, which has extensive applications such as in high resolution radar, imaging system, satellite communication and precision guided missiles. Compared with conventional pencil beam klystron, the sheet beam extended interaction klystron, in which a thin rectangular sheet beam is used, can generate higher power by obtaining higher current and reducing space-charge-effect of electron beam. Kinematical theory and space charge wave theory are extensively used to analyze the bunching process of electrons. Kinematical theory is precise when electron beam is especially small because the influence of space charge effect is ignored, while space charge wave theory is accurate when the modulation of electron beam is small since it is based on the premise of small amplitude. Electron flow oscillatory theory is a compromise between kinematical theory and space charge wave theory, which adapts to the bigger modulation of electron beam than space charge wave theory, while it is inaccurate in the case of big bunching parameter. Based on electron flow oscillatory theory under the small signal condition, the influence of electron beam on standing wave electric field of 2π mode in a three-gap cavity is analyzed, and the expressions of beam loading conductance and beam loading susceptance in a three-gap cavity are obtained. The influences of plasma frequency, transit angle of single gap and transit angle of drift on the interaction of beam and wave in a three-gap cavity are discussed. The results show that space-charge-effect of beam is unbeneficial to the interaction between beam and wave, otherwise beam loading conductance and beam loading susceptance fluctuate with the increasing of transit angle of single gap and transit angle of drift. A W-band sheet beam extended interaction klystron is designed by theoretical analysis and 3D PIC software. The output power of 5773 W at 94.47 GHz is obtained with an efficiency of 8.46%, a gain of 37.6 dB and a 3 dB bandwith of about 140 MHz, when beam voltage is 19.5 kV, current is 3.5 A and focus magnetic field is 0.85 T. This research is important for the engineering of the W-band sheet beam extended interaction klystron amplifier.
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Keywords:
- W-band /
- sheet beam extended interaction klystron /
- electron flow oscillatory theory /
- beam-wave interaction
[1] Chen S Y, Ruan C J, Yong W, Zhang C Q, Zhao D, Yang X D, Wang S Z 2014 IEEE Trans. Plasma Sci. 42 91
Google Scholar
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Wu Y, Xu Z, Zhou L, Li W J, Tang C X 2012 Acta Phys. Sin. 61 224101
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Ruan C J, Wang S Z 2010 Vacuum Electronics 6 12
Google Scholar
[8] Burtsev A A, Danilushkin A V 2014 Tech. Phys. Lett. 44 793
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Google Scholar
[10] Pasour J, Wright E, Nguyen K T, Balkcum A, Wood F N, Myers R E, Levush B 2014 IEEE Trans. Electron Dev. 61 1630
Google Scholar
[11] Shin Y M, Wang J X, Barnett L R, Luhmann N C 2011 IEEE Trans. Electron Dev. 58 251
Google Scholar
[12] Gamzina D, Barnett L R, Ravani B, Luhmann N C 2017 IEEE Trans. Electron Dev. 64 2675
Google Scholar
[13] Wang J X, Li X X, Rui L S, Liu Z, Liu G, Jiang W, Wu Z W, Hu Y L, Luo Y 2019 IEEE International Vacuum Electronics Conference Busan, South Korea, April 29–May 1, 2019 p324
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Google Scholar
[15] 刘振帮, 赵欲聪, 黄华, 金晓, 雷禄容 2015 物理学报 64 108404
Google Scholar
Liu Z B, Zhao Y C, Huang H, Jin X, Lei L R 2015 Acta Phys. Sin. 64 108404
Google Scholar
[16] Zhao Y C, Li S F, Huang H, Liu Z B, Wang Z L, Dan Z Y, Li X Y, Wei Y Y, Gong Y B 2015 IEEE Trans. Plasma Sci. 43 1862
Google Scholar
[17] 范植开, 刘庆想, 刘锡三, 周传民, 胡海膺 1999 强激光与粒子束 11 633
Fan Z K, Liu Q X, Liu X S, Zhou C M, Hu H Y 1999 High Power Laser and Particle Beams 11 633
[18] Lemke R W, Clark M C, Marder B M 1994 J. Appl. Phys. 75 5423
[19] 范植开, 刘庆想, 刘锡三, 何琥, 周传民 1999 强激光与粒子束 11 482
Fan Z K, Liu Q X, Liu X S, He H, Zhou C M 1999 High Power Laser and Particle Beams 11 482
[20] Marcum J 1946 J. Appl. Phys. 17 4
Google Scholar
[21] Marder B M, Clark M C, Bacon L D, Hoffman J M, Lemke R W, Coleman P D 1992 IEEE Trans. Plasma Sci. 20 312
Google Scholar
[22] Carlsten B E, Haynes W B 1996 IEEE Trans. Plasma Sci. 24 1249
Google Scholar
[23] 范植开 1999 博士学位论文 (北京: 中国工程物理研究院)
Fan Z K 1999 Ph. D. Dissertation (Beijing: China Academy of Engineering Physics) (in Chinese)
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Zeng Z J, Hu L L, Ma Q S, Jiang Y, Chen H B 2019 Acta Phys. Sin. 68 084101
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[30] 贝克著 (王以德 译) 1965 空间电荷波与慢电磁波 (北京: 科学出版社) 第100—150页
Beck A H (translated by Wang Y D) 1965 Space-Charge Waves and Slow Electromagnetic Waves (Beijing: Science Press) pp100–150 (in Chinese)
[31] 谢家麟, 赵永翔 1966 速调管群聚理论 (北京: 科学出版社) 第33—177页
Xie J L, Zhao Y X 1966 Bunching Theory of Klystron (Beijing: Science Press) pp33–177 (in Chinese)
[32] 哈依柯夫 著 (黄高年 译) 1980 速调管放大器 (北京: 国防工业出版社) 第99—105页
Eckertova L (translated by Hang G N) 1980 Клиотронные усилители (Beijing: National Defense Industry Press) pp99–105 (in Chinese)
[33] 曾造金 2014 硕士学位论文 (成都: 电子科技大学)
Zeng Z J 2014 M. S. Thesis (Chengdu: University of Electronic Science and Technology of China) (in Chinese)
[34] 丁耀根 2008 大功率速调管的理论与计算模拟 (北京: 国防工业出版社) 第53—66页
Ding Y G 2008 Theory and Computer Simulation of High Power Klystron (Beijing: National Defense Industry Press) pp53–66 (in Chinese)
[35] 吴洋, 许州, 谢鸿全, 李正红, 马乔生 2015 物理学报 64 084102
Google Scholar
Wu Y, Xu Z, Xie H Q, Li Z H, Ma Q S 2015 Acta Phys. Sin. 64 084102
Google Scholar
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图 1 三间隙谐振腔2π模场示意图
Figure 1. Simplified E-field of 2π mode in three-gap cavity.
图 2 归一化电子负载电导Geff3/G0与βeL的关系
Figure 2. Geff3/G0 versus βeL of three-gap cavity.
图 3 归一化电子负载电导Geff3/G0与βeL的关系
Figure 3. Geff3/G0 versus βeL of three-gap cavity.
图 4 归一化电子负载电导Geff3/G0与渡越角βed的关系
Figure 4. Geff3/G0 versus βed of three-gap cavity.
图 5 归一化电子负载电纳Beff3/G0与βeL的关系
Figure 5. Beff3/G0 versus βeL of three-gap cavity.
图 6 归一化电子负载电纳Beff3/G0与βeL的关系
Figure 6. Beff3/G0 versus βeL of three-gap cavity.
图 7 归一化电子负载电纳Beff3/G0与渡越角βed的关系
Figure 7. Beff3/G0 versus βed of three-gap cavity.
图 8 两种理论计算的Gb/G0与βeL的关系
Figure 8. Gb/G0 versus βeL of three-gap cavity.
图 9 两种理论计算的Bb/G0与βeL的关系
Figure 9. Bb/G0 versus βeL of three-gap cavity.
图 10 带状注扩展互作用速调管高频结构仿真模型
Figure 10. model of the sheet beam extended interaction klystron.
图 11 归一化电子负载电导Geff3/G0与间隙直流渡越角βed和相邻间隙中心之间的直流渡越角βeL的关系
Figure 11. Geff3/G0 versus βed and βeL of three-gap cavity.
图 12 归一化缩减等离子体频率与工作电压的关系
Figure 12. Fp versus U of three-gap cavity.
图 13 电子负载电导与工作电压的关系
Figure 13. Gb versus U of three-gap cavity.
图 14 各模式Ez沿轴向的分布 (a)输入腔; (b)中间腔1; (c)中间腔2; (d)输出腔
Figure 14. Ez versus axial distance of each mode: (a) Input cavity; (b) middle cavity 1; (c) middle cavity 2; (d) output cavity.
图 15 各间隙中心Ez沿y轴的分布 (a)输入腔; (b)中间腔1; (c)中间腔2; (d)输出腔
Figure 15. Ez versus y axial of each mode: (a) Input cavity; (b) middle cavity 1; (c) middle cavity 2; (d) output cavity.
图 16 各间隙中心Ez沿x轴的分布 (a)输入腔; (b)中间腔1; (c)中间腔2; (d)输出腔
Figure 16. Ez versus x axial of each mode: (a) Input cavity; (b) middle cavity 1; (c) middle cavity 2; (d) output cavity.
图 17 各模式Qt与电压U的关系 (a)输入腔; (b)中间腔1; (c)中间腔2; (d)输出腔
Figure 17. Qt versus U of each mode: (a) Input cavity; (b) middle cavity 1; (c) middle cavity 2; (d) output cavity.
图 18 带状注速调管高频结构y-z剖面图及电子轨迹
Figure 18. y-z section plane of the extended interaction cavity and particle trajectories.
图 19 带状注速调管高频结构x-z剖面图及电子轨迹
Figure 19. x-z section plane of the extended interaction cavity and particle trajectories.
图 20 瞬时输入功率波形
Figure 20. Waveform of input microwave.
图 21 前三腔调制电流基频分量沿轴向的分布
Figure 21. Fundamental modulated current amplitude versus axial distance.
图 22 输出腔入口处调制电流波形
Figure 22. Waveform of current at the entry of output cavity.
图 23 电子能量分布随轴向距离的变化
Figure 23. Kinetic energy distribution vs. axial distance.
图 24 瞬时输出功率波形
Figure 24. Instantaneous waveform of output microwave.
图 25 输出功率频谱
Figure 25. Spectrum of output microwave.
图 26 输出功率和电子效率与输入微波频率的关系
Figure 26. Output power and efficiency versus input microwave frequency.
图 27 输出功率和电子效率与输入微波功率的关系
Figure 27. Output power and efficiency versus input microwave power.
表 1 W波段带状注扩展互作用速调管高频结构参数
Table 1. Structural parameters of W-band sheet beam extended interaction klystron amplifier.
谐振腔 纵向工作模式 谐振频率/GHz 固有品质因数Q0 外观品质因数Qext 起始位置/mm 输入腔 2π模 94.52 562 627 0 中间腔1 2π模 94.56 555 ∞ 3.04 中间腔2 2π模 94.56 555 ∞ 6.08 输出腔 2π模 94.52 562 627 9.22 
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[1] Chen S Y, Ruan C J, Yong W, Zhang C Q, Zhao D, Yang X D, Wang S Z 2014 IEEE Trans. Plasma Sci. 42 91
Google Scholar
[2] Chang Z W, Meng L, Yin Y, Wang B, Li H L, Rauf A, Ullah S, Bi L J, Peng R B 2018 IEEE Trans. Electron Dev. 65 1179
Google Scholar
[3] 吴洋, 许州, 周霖, 李文君, 唐传祥 2012 物理学报 61 224101
Google Scholar
Wu Y, Xu Z, Zhou L, Li W J, Tang C X 2012 Acta Phys. Sin. 61 224101
Google Scholar
[4] Grigor’ev A D, Muchkaev V Y 2018 J. Commun. Technol. Electron. 63 577
Google Scholar
[5] Li R J, Ruan C J, Zhang H F, Fahad A K, Shan S Y, He Y B 2019 J. Infrared Millim. Terahertz Waves 40 5
[6] Ma T L, Zhao D, Zhang Z C, Xiang Y D, Wang W L 2014 IEEE Trans. Plasma Sci. 47 1762
[7] 阮存军, 王树忠 2010 真空电子技术 6 12
Google Scholar
Ruan C J, Wang S Z 2010 Vacuum Electronics 6 12
Google Scholar
[8] Burtsev A A, Danilushkin A V 2014 Tech. Phys. Lett. 44 793
[9] Pasour J, Nguyen K, Wright E, Balkcum A, Atkinson J, Cusick M, Levush B 2011 IEEE Trans. Electron Dev. 58 1792
Google Scholar
[10] Pasour J, Wright E, Nguyen K T, Balkcum A, Wood F N, Myers R E, Levush B 2014 IEEE Trans. Electron Dev. 61 1630
Google Scholar
[11] Shin Y M, Wang J X, Barnett L R, Luhmann N C 2011 IEEE Trans. Electron Dev. 58 251
Google Scholar
[12] Gamzina D, Barnett L R, Ravani B, Luhmann N C 2017 IEEE Trans. Electron Dev. 64 2675
Google Scholar
[13] Wang J X, Li X X, Rui L S, Liu Z, Liu G, Jiang W, Wu Z W, Hu Y L, Luo Y 2019 IEEE International Vacuum Electronics Conference Busan, South Korea, April 29–May 1, 2019 p324
[14] Wilks S, Katsouleas T, Dawson J M, Chen P, Su J J 1987 IEEE Trans. Plasma Sci. 15 210
Google Scholar
[15] 刘振帮, 赵欲聪, 黄华, 金晓, 雷禄容 2015 物理学报 64 108404
Google Scholar
Liu Z B, Zhao Y C, Huang H, Jin X, Lei L R 2015 Acta Phys. Sin. 64 108404
Google Scholar
[16] Zhao Y C, Li S F, Huang H, Liu Z B, Wang Z L, Dan Z Y, Li X Y, Wei Y Y, Gong Y B 2015 IEEE Trans. Plasma Sci. 43 1862
Google Scholar
[17] 范植开, 刘庆想, 刘锡三, 周传民, 胡海膺 1999 强激光与粒子束 11 633
Fan Z K, Liu Q X, Liu X S, Zhou C M, Hu H Y 1999 High Power Laser and Particle Beams 11 633
[18] Lemke R W, Clark M C, Marder B M 1994 J. Appl. Phys. 75 5423
[19] 范植开, 刘庆想, 刘锡三, 何琥, 周传民 1999 强激光与粒子束 11 482
Fan Z K, Liu Q X, Liu X S, He H, Zhou C M 1999 High Power Laser and Particle Beams 11 482
[20] Marcum J 1946 J. Appl. Phys. 17 4
Google Scholar
[21] Marder B M, Clark M C, Bacon L D, Hoffman J M, Lemke R W, Coleman P D 1992 IEEE Trans. Plasma Sci. 20 312
Google Scholar
[22] Carlsten B E, Haynes W B 1996 IEEE Trans. Plasma Sci. 24 1249
Google Scholar
[23] 范植开 1999 博士学位论文 (北京: 中国工程物理研究院)
Fan Z K 1999 Ph. D. Dissertation (Beijing: China Academy of Engineering Physics) (in Chinese)
[24] 曾造金, 胡林林, 马乔生, 蒋艺, 陈洪斌 2019 物理学报 68 084101
Google Scholar
Zeng Z J, Hu L L, Ma Q S, Jiang Y, Chen H B 2019 Acta Phys. Sin. 68 084101
Google Scholar
[25] Webster D L 1939 J. Appl. Phys. 10 501
Google Scholar
[26] Webster D L 1942 J. Appl. Phys. 13 786
Google Scholar
[27] Webster D L 1939 J. Appl. Phys. 10 864
Google Scholar
[28] Ramot S 1939 Proceedings of the I.R.E. Washington, USA, April 28–28, 1939 p757
[29] Ramot S 1939 Phys. Rev. 56 276
Google Scholar
[30] 贝克著 (王以德 译) 1965 空间电荷波与慢电磁波 (北京: 科学出版社) 第100—150页
Beck A H (translated by Wang Y D) 1965 Space-Charge Waves and Slow Electromagnetic Waves (Beijing: Science Press) pp100–150 (in Chinese)
[31] 谢家麟, 赵永翔 1966 速调管群聚理论 (北京: 科学出版社) 第33—177页
Xie J L, Zhao Y X 1966 Bunching Theory of Klystron (Beijing: Science Press) pp33–177 (in Chinese)
[32] 哈依柯夫 著 (黄高年 译) 1980 速调管放大器 (北京: 国防工业出版社) 第99—105页
Eckertova L (translated by Hang G N) 1980 Клиотронные усилители (Beijing: National Defense Industry Press) pp99–105 (in Chinese)
[33] 曾造金 2014 硕士学位论文 (成都: 电子科技大学)
Zeng Z J 2014 M. S. Thesis (Chengdu: University of Electronic Science and Technology of China) (in Chinese)
[34] 丁耀根 2008 大功率速调管的理论与计算模拟 (北京: 国防工业出版社) 第53—66页
Ding Y G 2008 Theory and Computer Simulation of High Power Klystron (Beijing: National Defense Industry Press) pp53–66 (in Chinese)
[35] 吴洋, 许州, 谢鸿全, 李正红, 马乔生 2015 物理学报 64 084102
Google Scholar
Wu Y, Xu Z, Xie H Q, Li Z H, Ma Q S 2015 Acta Phys. Sin. 64 084102
Google Scholar
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