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从电子束一维稳态传输的电势非线性Poisson方程出发，推导了圆柱波导内实心束和环形束空间极限电流与电子入射电势的依赖关系，给出了数值求解方法和解的特征，分析比较了数值计算与现有解析公式及粒子模拟的结果.考虑电子的横向运动，对数值方法进行了二维修正，计算结果与粒子模拟结果具有很好的一致性.说明利用数值方法计算电子电势非线性微分方程能够得到更精确的电子束在圆柱波导内的空间极限电流；另外，对其他形状的波导，尤其是难以得到解析式的情况，根据实际几何结构设置边界条件，数值方法可以方便地给出束流传输特性，对设计新型结构的高功率微波器件提供理论指导.The space-charge-limited currents of both solid electron beam and annular electron beam in cylindrical waveguide are derived from the nonlinear Poisson equation for potential in the region of electron beams. Corrections for the transverse motion of electrons are made to the solution, which bring more consistent with the results from PIC simulations. Though numerical computation, it is showed that electrons located along the axis and by outer radius of solid and annular electron beams respectively and electrons standing near to the outside of the beam has larger axial velocity than these inside. This approach is available for analyzing the characteristics of electron beam transporting in high power microwave generator with other configuration waveguide.
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Keywords:
- relativistic electron beam /
- cylindrical waveguide /
- space-charge-limited current /
- electron beam transportation
[1] ［1］Miller R M 1982 An Introduction to the Physics of Intense Charge Particle Beams(New York: Plenum) p91
[2] ［2］Breizman B, Ryutov D D 1974 Nucl. Fusion 14 873
[3] ［3］Bogdankevich L S, Rukhadze A A 1971 Sov. Phys. Usp. 14 163
[4] ［4］Zeng Z Z, Liu G Z, Shao H 2002 Plasma Sci. Technol. 4 1093
[5] ［5］Sotnikov G V, Yatsenko T Y 2002 Tech. Phys. 47 535
[6] ［6］Song S Y, Qiu X, Wang W D, Lin Q W, Sun C W 2005 High Pow Part. Beams 17 441 (in Chinese) ［宋盛义、仇旭、王文斗、林其文、孙承纬 2005强激光与粒子束17 441］
[7] ［7］Belomyttsev S Y 2003 Tech. Phys. Lett. 29 666
[8] ［8］Li J Q, Mo Y L 2007 Chin. Phys. 16 2716
[9] ［9］Li Y D, He F, Liu C L 2005 High Power Laser Part. Beams 17 913 (in Chinese) ［李永东、何锋、刘纯亮 2005强激光与粒子束 17 913］
[10] ］Liu G Z, Shao H 2003 Chin. Phys. 12 204
[11] ］Shao H, Liu G Z, Song Z M, Huang W H, Hu Y M, Ning H 2001 High Power Laser Part. Beams 13 631 (in Chinese)［邵浩、刘国治、宋志敏、黄文华、胡咏梅、宁辉 2001 强激光与粒子束 13 631］
[12] ］Xiao R Z, Liu G Z, Chen C H 2008 Chin. Phys. B 17 3807
[13] ］Fan Y W, Zhong H H, Li Z Q, Shu T, Yang H W, Yang J H 2008 Chin. Phys. B 17 1804
[14] ］Sloan M L, Thompson J R 1977 Austin Research Associates Report I-ARA-77-U-54
[15] ］Chen Y, Mankowski J, Walter J, Kristiansen M 2007 IEEE Trans. Dielectr. Electr. Insul. 14 1037
[16] ］Mattias E, Tomas H, Anders L, Cecilia M, Sten N 2008 IEEE Trans. Plasma Sci. 36 638
[17] ］Genoni T C, Proctor W A 1978 IEEE International Conference on Plasma Science 18—22 Sept 1978 Montreal p94
[18] ］Tarakanov V P 2004 User’s Manual for Code KARAT (Virginia: Berkeley Research Associate)
[19] ］Li Z Q, Shu T, Zhong H H, Fan Y W, Yang J H, Xu L R, Zhao Y S 2009 High Power Laser Part. Beams 21 421 (in Chinese) ［李志强、舒挺、钟辉煌、樊玉伟、杨建华、许流荣、赵延宋 2009强激光与粒子束21 421］
[20] ］Luo X, Liao C, Meng F B, Zhang Y J, Wang X D 2007 High Power Laser Part. Beams 19 92 (in Chinese) ［罗雄、廖成、孟凡宝、张云俭、王晓东 2007 强激光与粒子束 19 92］
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[1] ［1］Miller R M 1982 An Introduction to the Physics of Intense Charge Particle Beams(New York: Plenum) p91
[2] ［2］Breizman B, Ryutov D D 1974 Nucl. Fusion 14 873
[3] ［3］Bogdankevich L S, Rukhadze A A 1971 Sov. Phys. Usp. 14 163
[4] ［4］Zeng Z Z, Liu G Z, Shao H 2002 Plasma Sci. Technol. 4 1093
[5] ［5］Sotnikov G V, Yatsenko T Y 2002 Tech. Phys. 47 535
[6] ［6］Song S Y, Qiu X, Wang W D, Lin Q W, Sun C W 2005 High Pow Part. Beams 17 441 (in Chinese) ［宋盛义、仇旭、王文斗、林其文、孙承纬 2005强激光与粒子束17 441］
[7] ［7］Belomyttsev S Y 2003 Tech. Phys. Lett. 29 666
[8] ［8］Li J Q, Mo Y L 2007 Chin. Phys. 16 2716
[9] ［9］Li Y D, He F, Liu C L 2005 High Power Laser Part. Beams 17 913 (in Chinese) ［李永东、何锋、刘纯亮 2005强激光与粒子束 17 913］
[10] ］Liu G Z, Shao H 2003 Chin. Phys. 12 204
[11] ］Shao H, Liu G Z, Song Z M, Huang W H, Hu Y M, Ning H 2001 High Power Laser Part. Beams 13 631 (in Chinese)［邵浩、刘国治、宋志敏、黄文华、胡咏梅、宁辉 2001 强激光与粒子束 13 631］
[12] ］Xiao R Z, Liu G Z, Chen C H 2008 Chin. Phys. B 17 3807
[13] ］Fan Y W, Zhong H H, Li Z Q, Shu T, Yang H W, Yang J H 2008 Chin. Phys. B 17 1804
[14] ］Sloan M L, Thompson J R 1977 Austin Research Associates Report I-ARA-77-U-54
[15] ］Chen Y, Mankowski J, Walter J, Kristiansen M 2007 IEEE Trans. Dielectr. Electr. Insul. 14 1037
[16] ］Mattias E, Tomas H, Anders L, Cecilia M, Sten N 2008 IEEE Trans. Plasma Sci. 36 638
[17] ］Genoni T C, Proctor W A 1978 IEEE International Conference on Plasma Science 18—22 Sept 1978 Montreal p94
[18] ］Tarakanov V P 2004 User’s Manual for Code KARAT (Virginia: Berkeley Research Associate)
[19] ］Li Z Q, Shu T, Zhong H H, Fan Y W, Yang J H, Xu L R, Zhao Y S 2009 High Power Laser Part. Beams 21 421 (in Chinese) ［李志强、舒挺、钟辉煌、樊玉伟、杨建华、许流荣、赵延宋 2009强激光与粒子束21 421］
[20] ］Luo X, Liao C, Meng F B, Zhang Y J, Wang X D 2007 High Power Laser Part. Beams 19 92 (in Chinese) ［罗雄、廖成、孟凡宝、张云俭、王晓东 2007 强激光与粒子束 19 92］
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