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建立了多注电子束在空心圆柱波导中传输的理论模型，定量分析了多注电子束自电磁场力与镜像电磁场力对其角向运动的影响，并推导了考虑镜像束流影响下多注电子束的布里渊磁场.开展了模拟仿真研究，模拟与理论计算结果基本一致.研究发现：当电子束注数较少且靠近波导管壁传输时，镜像电磁场力是影响多注电子束角向漂移的主要因素；随着电子束注数或电子束与波导壁间距的增加，镜像电磁场力迅速减小并趋近于零，此时自电磁场力起主导作用；在一般情况下，漂移角速度的变化百分比只与加速电压有关，与多注电子束的注数、空间位置关系等参数无关.在输出电压约670 kV，电流约7 kA，空心圆柱波导长约100 mm的平台上开展了实验研究，研究发现多注电子束存在明显的畸变，通过进一步的分析认为多注阴极柱的侧面发射是导致电子束畸变的一个主要因素，并且二极管加速区的角向漂移不可忽视.提出并模拟验证了采取倾斜多注阴极柱的方法可提高电子束的引入效率.Multi-beam klystron (MBK) is a promising high power microwave device with the traits of high power, high efficiency, high frequency, etc. For the high power relativistic MBK, the multi-beam rotation around an axis may reduce the transmission efficiency obviously due to the effect of space electromagnetic field. In previous researches, the influence of mirror-image electromagnetic field is ignored, which can play a leading role in some cases. In this study, we present a method by taking into account the mirror-image effect to analyze the angular drift of multi-beam in the hollow cylindrical waveguide. The hollow cylindrical waveguide is a part of relativistic MBK such as input cavity and transition section, which is just behind the diode. In this method, the equation of the multi-beam angular drift is deduced and analyzed quantitatively. Based on the equation, the expression of the angular velocity about the multi-beam in the waveguide is derived, meanwhile the minimum equilibrium magnetic field, called Brillouin magnetic field, is obtained. To verify the effectiveness of the method, numerical simulations are carried out by the three-dimensional (3D) code and the results show good agreement with the theoretical results. The theoretical analysis and simulation results show that the mirror-image electromagnetic field can dominate the multi-beam angular motion in some conditions, especially when the number of the multi-beams and the distance between the conducting wall and the multi-beam are both small. In this case, the mirror-image electromagnetic field can be much higher than the self-induced electromagnetic field. Nevertheless, as the the number of the multi-beams or the distance between the conducting wall and the multi-beam increases, the mirror-image electromagnetic field decreases and approaches to zero rapidly and the self-induced electromagnetic field controls the angular movement. Interestingly, in general cases, it is found that the change rate of the angular speed is not related to the number of multi-beams, nor the radius of waveguide, nor the distance between the multi-beam, nor waveguide, etc, except for the accelerating voltage. In addition, we experimentally investigate the angular drift of the multi-beam at a voltage of about 670 kV, current of about 7 kA and length of waveguide about 100 mm. The experimental results show that the multi-beam distorts obviously, which changes the beam spot shape from circle to ellipse. To solve this problem, we simultaneously investigate the multi-beam emission and transmission in simulation experiment. The analogue results not only reveal that the distortion is mainly caused by the emission of the multi-cathode rods, but also provide a new phenomenon that the angular drift distance in the accelerating gap of the diode is twice as large as that in the cylindrical hollow waveguide due to the low beam speed along the axis and high electrostatic field in the accelerating region. It is also found that the distortion is more evident as the rod radius decreases. Furthermore, we propose an optimization design to improve the relativistic multi-beam system by inclining the multi-cathode rods, which is proved to be effective by simulation. This study could provide theoretical basis for studying the relativistic MBK.
[1] Friedman M, Fernsler R, Slinker S, Hubbard R, Lampe M 1995 Phys. Rev. Lett. 75 1214
[2] Ding Y G 2010 Design, Manufacture and Application of High Power Klystron (Beijing:National Defense Industry Press) pp7-13 (in Chinese)[丁耀根 2010 大功率速调管的制造和应用(北京:国防工业出版社)第7–13 页]
[3] Benford J, Swegle J A 2008 High Power Microwave (2nd Ed.) (Beijing:National Defense Industry Press) pp3-5 (in Chinese)[Benford J, Swegle J A 著 2009 高功率微波(第二版) (中译本) (江伟华, 张弛译)(北京:国防工业出版社) 第3–5 页]
[4] Liu Z B, Zhao Y C, Huang H, Jin X, Lei L R 2015 Acta Phys. Sin. 64 108404 (in Chinese)[刘振帮, 赵欲聪, 黄华, 金晓, 雷禄容 2015 64 108404]
[5] Liu L W, Wei Y Y, Wang S M 2013 Chin. Phys. B 22 108401
[6] Luo J R, Cui J, Zhu M, Guo W 2013 Chin. Phys. B 22 067803
[7] Wang Y, Ding Y G, Liu P K, Xie J X, Zhang R 2005 High Power Laser and Particle Beams 8 1133 (in Chinese)[王勇, 丁耀根, 刘濮鲲, 谢敬新, 张瑞 2005 强激光与粒子束 8 1133]
[8] Khanh T N, Dean E P, David K A, George M 2005 IEEE Trans. Plasma Sci. 33 685
[9] Liu Z B, Jin X, Huang H, Chen H B, Wang G P 2012 Acta Phys. Sin. 61 238402 (in Chinese)[刘振帮, 金晓, 黄华, 陈怀璧, 王淦平 2012 61 238401]
[10] Xie J L, Zhao Y X 1966 Bunching Theory of Klystron (Beijing:Science Press) pp105-107 (in Chinese)[谢家麟, 赵永翔1966 速调管群聚理论(北京:科学出版社) 第105–107 页]
[11] Robert J B, Edl S 2005 High Power Microwave Sources and Technologies (Beijing:Tsinghua University Press) pp282-289 (in Chinese)[Robert J B, Edl S 2005 高功率微波源与技术(中译本) (北京:清华大学出版社) 第282–289 页]
[12] Huang H, Luo X, Lei L R, Luo G Y, Zhang B Z, Jin X, Tan J 2010 Acta Phys. Sin. 59 1907 (in Chinese)[黄华, 罗雄, 雷禄荣, 罗光耀, 张北镇, 金晓, 谭杰 2010 59 1907]
[13] Robert J B, Edl S 2005 High Power Microwave Sources and Technologies (Beijing:Tsinghua University Press) pp78-79 (in Chinese)[Robert J B, Edl S 2005 高功率微波源与技术(中译本) (北京:清华大学出版社) 第77–79 页]
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[1] Friedman M, Fernsler R, Slinker S, Hubbard R, Lampe M 1995 Phys. Rev. Lett. 75 1214
[2] Ding Y G 2010 Design, Manufacture and Application of High Power Klystron (Beijing:National Defense Industry Press) pp7-13 (in Chinese)[丁耀根 2010 大功率速调管的制造和应用(北京:国防工业出版社)第7–13 页]
[3] Benford J, Swegle J A 2008 High Power Microwave (2nd Ed.) (Beijing:National Defense Industry Press) pp3-5 (in Chinese)[Benford J, Swegle J A 著 2009 高功率微波(第二版) (中译本) (江伟华, 张弛译)(北京:国防工业出版社) 第3–5 页]
[4] Liu Z B, Zhao Y C, Huang H, Jin X, Lei L R 2015 Acta Phys. Sin. 64 108404 (in Chinese)[刘振帮, 赵欲聪, 黄华, 金晓, 雷禄容 2015 64 108404]
[5] Liu L W, Wei Y Y, Wang S M 2013 Chin. Phys. B 22 108401
[6] Luo J R, Cui J, Zhu M, Guo W 2013 Chin. Phys. B 22 067803
[7] Wang Y, Ding Y G, Liu P K, Xie J X, Zhang R 2005 High Power Laser and Particle Beams 8 1133 (in Chinese)[王勇, 丁耀根, 刘濮鲲, 谢敬新, 张瑞 2005 强激光与粒子束 8 1133]
[8] Khanh T N, Dean E P, David K A, George M 2005 IEEE Trans. Plasma Sci. 33 685
[9] Liu Z B, Jin X, Huang H, Chen H B, Wang G P 2012 Acta Phys. Sin. 61 238402 (in Chinese)[刘振帮, 金晓, 黄华, 陈怀璧, 王淦平 2012 61 238401]
[10] Xie J L, Zhao Y X 1966 Bunching Theory of Klystron (Beijing:Science Press) pp105-107 (in Chinese)[谢家麟, 赵永翔1966 速调管群聚理论(北京:科学出版社) 第105–107 页]
[11] Robert J B, Edl S 2005 High Power Microwave Sources and Technologies (Beijing:Tsinghua University Press) pp282-289 (in Chinese)[Robert J B, Edl S 2005 高功率微波源与技术(中译本) (北京:清华大学出版社) 第282–289 页]
[12] Huang H, Luo X, Lei L R, Luo G Y, Zhang B Z, Jin X, Tan J 2010 Acta Phys. Sin. 59 1907 (in Chinese)[黄华, 罗雄, 雷禄荣, 罗光耀, 张北镇, 金晓, 谭杰 2010 59 1907]
[13] Robert J B, Edl S 2005 High Power Microwave Sources and Technologies (Beijing:Tsinghua University Press) pp78-79 (in Chinese)[Robert J B, Edl S 2005 高功率微波源与技术(中译本) (北京:清华大学出版社) 第77–79 页]
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