一种非轴对称磁绝缘电子鞘层边界的计算方法

魏浩; 孙凤举; 呼义翔; 梁天学; 丛培天; 邱爱慈

doi:10.7498/aps.66.038402

摘要

长距离磁绝缘传输线内电极偏心、感应腔注入电流非均匀分布引起电子鞘层边界偏心等非对称磁绝缘特性.电子鞘层边界是研究非轴对称磁绝缘特性的重要参数.本文提出一种计算非轴对称磁绝缘电子鞘层边界的方法.通过引入角向非均匀分布的模数，将经典一维轴对称Creedon稳态磁绝缘理论推广应用于圆柱坐标系下二维（r，）平面.建立了感应电压叠加器次级非轴对称磁绝缘的二维Creedon物理模型，给出了非轴对称磁绝缘电子鞘层边界的数值计算方法和计算误差.当阴极角向磁场（阴极电流）角向分布满足余弦函数时，电子鞘层边界接近高斯分布.阴极电流角向不均匀程度越大，电子鞘层边界偏心程度越严重，计算误差越大.

关键词:

Abstract

The nonaxisymmetrical magnetic insulation would occur due to the disalignment of inner electrodes in long magnetically insulated transmission lines, or the nonuniform distributions of injected currents in induction cavities of magnetically insulated induction voltage adders (MIVA). The electron sheath profile is a very important parameter to characterize the nonaxisymmetrical magnetic insulation. In the past, the three-dimensional particle in cell simulation was usually used to determine the electron sheath profile, which is extremely time-consuming and inefficient. In this paper, a fast and efficient calculation method is proposed. The classical one-dimensional Creedon theory of the magnetic insulation equilibrium is generalized to a two-dimensional plane of (r, ) via introducing a parameter defined as the azimuthal mode number. Two-dimensional Creedon is developed to model the asymmetric magnetic insulation of the MIVA. Provided the azimuthal distributions of magnetic flux density on the cathode, which is in proportion to the cathode current, the two-dimensional Creedon model is numerically solved. A numerical solution method to calculate the electron sheath profile is proposed, and then the calculation error is also given. As the azimuthal distribution of magnetic flux density on the cathode meets a cosine function, the profile of the electron sheath is approximate to the Gauss function. As the nonuniform portion of cathode current increases, the electron sheath becomes more eccentric, and the calculation error is also much larger.

Keywords:

作者及机构信息

1.
西安交通大学, 电力设备电气绝缘国家重点实验室, 西安 710049;

2.
西北核技术研究所, 强脉冲辐射环境模拟与效应国家重点实验室, 西安 710024

通信作者: 魏浩, weihaoyy@nint.ac.cn;qiuac@cae.cn ; 邱爱慈, weihaoyy@nint.ac.cn;qiuac@cae.cn

基金项目: 国家自然科学基金（批准号：11505138，51577156）资助的课题.

Authors and contacts

1.
State Key Laboratory of Electrical Insulation and Power Equipment, Xi'an Jiaotong University, Xi'an 710049, China;

2.
State Key Laboratory of Intense Pulsed Radiation Simulation and Effect, Northwest Institute of Nuclear Technology, Xi'an 710024, China

Corresponding author: Wei Hao, weihaoyy@nint.ac.cn;qiuac@cae.cn ; Qiu Ai-Ci, weihaoyy@nint.ac.cn;qiuac@cae.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11505138, 51577156).

参考文献

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[7]	Smith I D 2004 Phys. Rev. Spec. Top. Accel. Beams. 7 064801
[8]	Smith I D, Bailey V L, Fockler J, Gustwiller J S, Johnson D L, Maenchen J E, Droemer D W 2000 IEEE Trans. Plasma Sci. 28 1653
[9]	Thomas K, Beech P, Brown S, Buck J, Burscough J, Clough S, Crotch I, Duff Y J, Goes C, Huckle I, Jones A, King A, Stringer B, Threadgold J, Trenaman S, Wheeldon R, Woodroofe M, Carboni V, DaSilva T, Galver B, Glazebrook W, Hanzel K, Pearce J, Pham J, Pomeroy S, Saunders W, Speits D, Warren T, Whitney B, Wilson J 2011 Proceeding of 18th IEEE Pulsed Power Conference Chicago, USA, 19-23 June, 2011 p1042
[10]	Wei H, Sun F J, Liang T X, Yin J H, Dang T F, Zeng J T, Cong P T, Qiu A C 2014 Rev. Sci. Instrum. 85 083506
[11]	Wei H, Sun F J, Liang T X, Guo J M, Qiu A C, Cong P T, Yin J H, Hu Y X, Jiang X F, Wang Z G, Dang T F 2015 IEEE Trans. Plasma Sci. 43 3359
[12]	Mendel C W, Rosentha S E 1995 Phys. Plasmas 2 1332
[13]	Creedon J M 1975 J. Appl. Phys. 46 2946
[14]	Mendel C W 1979 J. Appl. Phys. 50 3830
[15]	Lawconnell R I, Neri J 1990 Phys. Fluids B 2 629
[16]	Ottinger P F, Schumer J W 2006 Phys. Plasmas 13 063109
[17]	Stygar W A, Wagoner T C, Ives H C, Corcoran P A, Cuneo M E, Douglas J W, Gilliland T L, Mazarakis M G, Ramirez J J, Seamen J F, Seidel D B, Spielman R B 2006 Phys. Rev. Spec. Top. Accel. Beams. 9 090401
[18]	Liu L Q, Liu D G, Wang X Q, Zou W K, Yang C 2012 Acta Phys. Sin. 61 162901 (in Chinese)[刘腊群, 刘大刚, 王学琼, 邹文康, 杨超2012 61 162901]
[19]	Liu L Q, Liu D G, Wang X Q, Yang C, Xia M Z, Peng K 2012 Acta Phys. Sin. 61 162902 (in Chinese)[刘腊群, 刘大刚, 王学琼, 杨超, 夏蒙重, 彭凯2012 61 162902]
[20]	Dai W, Zhu X Z, Liu LQ, Zou W K, Guo F, Liu D G 2015 Modern Electron. Tech. 38 144 (in Chinese)[戴巍, 朱旭智, 刘腊群, 邹文康, 郭帆, 刘大刚2015现代电子技术38 144]
[21]	Zou W K, Chen L, Liu D G, Zhang L, Liu L Q, Zhou L J, Wang M, Wei B, Guo F, Wang X Q, Dai Y M, Xie W P, Deng J J 2012 Phys. Rev. Spec. Top. Accel. Beams 15 110401
[22]	Johnson D L, Smith I D, Corcoran P, Bailey V, Maenchen J, Rovang D, Molina I, Hahn K, Lucero R, Kincy M, Kitterman D, Oliver B, Welch D, Rose D, Goldsack T J, Phillips M A, Sinclair M A, Thomas K J 2002 Proceeding of 14th IEEE High Power Particle Beams Conference Albuquerque, USA, 23-28 June, 2002 p123
[23]	Oliver B V, Genoni T C 2003 Proceeding of 14th IEEE Pulsed Power Conference Dallas, USA, June 15-18, 2003 p395
[24]	Bruner N, Mostrom C, Rose D V, Welch D R, Bailey V, Johnson D L, Oliver B V 2007 Proceeding of 16th IEEE Pulsed Power Conference Albuquerque, USA, June 17-22, 2007 p807
[25]	Qian B L, Liu Y G, Li C L, Liu C B 2000 IEEE Trans. Plasma Sci. 28 760
[26]	Fuks M I, Schamiloglu E 2014 Phys. Plasmas 21 053102
[27]	Bluhm H (translated by Jiang W H, Zhang C) 2008 Pulsed Power Systems:Principles and Application (Beijing:Tsinghua University Press) pp128-135(in Chinese)[布鲁姆H著(江伟华, 张弛译) 2008脉冲功率系统的原理与应用(北京:清华大学出版社)第128-135页]
[28]	Wang M Y 1978 Appl. Phys. Lett. 33 284
[29]	Ma X K 2000 Theory and Application of Electromagnetic Field (Xi'an:Xian Jiaotong University Press) pp206-216(in Chinese)[马西奎2000电磁场理论及应用(西安:西安交通大学出版社)第206–216页]
[30]	Xue D Y Chen Y Q 2011 Technology and Application of System Simulation Based on MATLAB and Simulink (Beijing:Tsinghua University Press) pp108-110(in Chinese)[薛定宇, 陈阳泉2011基于MATLAB/Simulink的系统仿真技术与应用(北京:清华大学出版社)第108-110页]

施引文献

[1]	Stygar W A, Corcoran P A, Ives H C, Spielman R B, Douglas J W, Whitney B A, Mostrom M A, Wagoner T C, Speas C S, Gilliland T L, Allshouse G A, Clark R E, Donovan G L, Hughes T P, Humphreys D R, Jaramillo D M, Johnson M F, Kellogg J W, Leeper R J, Long F W, Martin T H, Mulville T D, Pelock M D, Peyton B P, Poukey J W, Ramirez J J, Reynolds P G, Seamen J F, Seidel D B, Seth A P, Sharpe A W, Shoup R W, Smith J W, Vandevalde D M, Wavrik R W 2009 Phys. Rev. Spec. Top. Accel. Beams. 12 120401
[2]	Stygar W A, Awe T J, Bailey J E, Bennett N L, E W Breden, Campbell E M, Clark R E, Cooper R A, Cuneo M E, Ennis J B, Fehl D L, Genoni T C, Gomez M R, Greiser G W, Gruner F R, Herrmann M C, Hutsel B T, Jennings C A, Jobe D O, Jones B M, M C Jones, Jones P A, Knapp P F, Lash J S, LeChien K R, Leckbee J J, Leeper R J, Lewis S A, Long F W, Lucero D J, Madrid E A, Martin M R, Matzen M K, Mazarakis M G, McBride R D, McKee G R, Miller C L, Moore J K, Mostrom C B, Mulville T D, Peterson K J, Porter J L, Reisman D B, Rochau G A, Rochau G E, Rose D V, Rovang D C, Savage M E, Sceiford M E, Schmit P F, Schneider R F, Schwarz J, Sefkow A B, Sinars D B, Slutz S A, Spielman R B, Stoltzfus B S, Thoma C, Vesey R A, Wakeland P E, Welch D R, Wisher M L, Woodworth J R 2015 Phys. Rev. Spec. Top. Accel. Beams. 18 110401
[3]	Zou W K, Wang M, Chen L, Zhou L J, Guo F, Xie W P, Deng J J 2013 High Power and Laser and Particle Beams 25 2487 (in Chinese)[邹文康, 王勐, 陈林, 周良骥, 郭帆, 谢卫平, 邓建军2013强激光与粒子束25 2487]
[4]	Pate R C, Patterson J C, Dowdican M C, Ramirez J J, Hasti D E, Tolk K M, Poukey J W, Schneider L X, Rosenthal S E, Sanford T W, Alexander J A, Heath C E 1987 Proceeding of 6th IEEE Pulsed Power Conference Arlington, USA, 22-26 June, 1987 p478
[5]	Johnson D, Bailey V, Altes R, Corcoran P, Smith I, Cordova S, Hahn K, Maenchen J, Molina I, Portillo S, Puetz E, Sceiford M, Valde D V, Rose D, Oliver B, Welch D, Droemer D 2005 Proceeding of 15h IEEE Pulsed Power Conference Monterey, USA, 13-17 June, 2005 p314
[6]	Allen R J, Commisso R J, Cooperstein G, Ottinger P F, Schumer J W 2011 Proceeding of 18th IEEE Pulsed Power Conference Chicago, USA, 19-23 June, 2011 p1036
[7]	Smith I D 2004 Phys. Rev. Spec. Top. Accel. Beams. 7 064801
[8]	Smith I D, Bailey V L, Fockler J, Gustwiller J S, Johnson D L, Maenchen J E, Droemer D W 2000 IEEE Trans. Plasma Sci. 28 1653
[9]	Thomas K, Beech P, Brown S, Buck J, Burscough J, Clough S, Crotch I, Duff Y J, Goes C, Huckle I, Jones A, King A, Stringer B, Threadgold J, Trenaman S, Wheeldon R, Woodroofe M, Carboni V, DaSilva T, Galver B, Glazebrook W, Hanzel K, Pearce J, Pham J, Pomeroy S, Saunders W, Speits D, Warren T, Whitney B, Wilson J 2011 Proceeding of 18th IEEE Pulsed Power Conference Chicago, USA, 19-23 June, 2011 p1042
[10]	Wei H, Sun F J, Liang T X, Yin J H, Dang T F, Zeng J T, Cong P T, Qiu A C 2014 Rev. Sci. Instrum. 85 083506
[11]	Wei H, Sun F J, Liang T X, Guo J M, Qiu A C, Cong P T, Yin J H, Hu Y X, Jiang X F, Wang Z G, Dang T F 2015 IEEE Trans. Plasma Sci. 43 3359
[12]	Mendel C W, Rosentha S E 1995 Phys. Plasmas 2 1332
[13]	Creedon J M 1975 J. Appl. Phys. 46 2946
[14]	Mendel C W 1979 J. Appl. Phys. 50 3830
[15]	Lawconnell R I, Neri J 1990 Phys. Fluids B 2 629
[16]	Ottinger P F, Schumer J W 2006 Phys. Plasmas 13 063109
[17]	Stygar W A, Wagoner T C, Ives H C, Corcoran P A, Cuneo M E, Douglas J W, Gilliland T L, Mazarakis M G, Ramirez J J, Seamen J F, Seidel D B, Spielman R B 2006 Phys. Rev. Spec. Top. Accel. Beams. 9 090401
[18]	Liu L Q, Liu D G, Wang X Q, Zou W K, Yang C 2012 Acta Phys. Sin. 61 162901 (in Chinese)[刘腊群, 刘大刚, 王学琼, 邹文康, 杨超2012 61 162901]
[19]	Liu L Q, Liu D G, Wang X Q, Yang C, Xia M Z, Peng K 2012 Acta Phys. Sin. 61 162902 (in Chinese)[刘腊群, 刘大刚, 王学琼, 杨超, 夏蒙重, 彭凯2012 61 162902]
[20]	Dai W, Zhu X Z, Liu LQ, Zou W K, Guo F, Liu D G 2015 Modern Electron. Tech. 38 144 (in Chinese)[戴巍, 朱旭智, 刘腊群, 邹文康, 郭帆, 刘大刚2015现代电子技术38 144]
[21]	Zou W K, Chen L, Liu D G, Zhang L, Liu L Q, Zhou L J, Wang M, Wei B, Guo F, Wang X Q, Dai Y M, Xie W P, Deng J J 2012 Phys. Rev. Spec. Top. Accel. Beams 15 110401
[22]	Johnson D L, Smith I D, Corcoran P, Bailey V, Maenchen J, Rovang D, Molina I, Hahn K, Lucero R, Kincy M, Kitterman D, Oliver B, Welch D, Rose D, Goldsack T J, Phillips M A, Sinclair M A, Thomas K J 2002 Proceeding of 14th IEEE High Power Particle Beams Conference Albuquerque, USA, 23-28 June, 2002 p123
[23]	Oliver B V, Genoni T C 2003 Proceeding of 14th IEEE Pulsed Power Conference Dallas, USA, June 15-18, 2003 p395
[24]	Bruner N, Mostrom C, Rose D V, Welch D R, Bailey V, Johnson D L, Oliver B V 2007 Proceeding of 16th IEEE Pulsed Power Conference Albuquerque, USA, June 17-22, 2007 p807
[25]	Qian B L, Liu Y G, Li C L, Liu C B 2000 IEEE Trans. Plasma Sci. 28 760
[26]	Fuks M I, Schamiloglu E 2014 Phys. Plasmas 21 053102
[27]	Bluhm H (translated by Jiang W H, Zhang C) 2008 Pulsed Power Systems:Principles and Application (Beijing:Tsinghua University Press) pp128-135(in Chinese)[布鲁姆H著(江伟华, 张弛译) 2008脉冲功率系统的原理与应用(北京:清华大学出版社)第128-135页]
[28]	Wang M Y 1978 Appl. Phys. Lett. 33 284
[29]	Ma X K 2000 Theory and Application of Electromagnetic Field (Xi'an:Xian Jiaotong University Press) pp206-216(in Chinese)[马西奎2000电磁场理论及应用(西安:西安交通大学出版社)第206–216页]
[30]	Xue D Y Chen Y Q 2011 Technology and Application of System Simulation Based on MATLAB and Simulink (Beijing:Tsinghua University Press) pp108-110(in Chinese)[薛定宇, 陈阳泉2011基于MATLAB/Simulink的系统仿真技术与应用(北京:清华大学出版社)第108-110页]

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