A method to calculate the electron sheath profile of the nonaxisymmetrical magnetic insulation

Wei Hao; Sun Feng-Ju; Hu Yi-Xiang; Liang Tian-Xue; Cong Pei-Tian; Qiu Ai-Ci

doi:10.7498/aps.66.038402

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:

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).

References

[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物理学报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物理学报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]

Cited By

[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物理学报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物理学报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]

[1]	Chen Long, Tan Cong-Qi, Cui Zuo-Jun, Duan Ping, An Yu-Hao, Chen Jun-Yu, Zhou Li-Na. Multi-ion magnetized sheath properties with non-extensive electron distribution. Acta Physica Sinica, 2024, 73(5): 055201. doi: 10.7498/aps.73.20231452
[2]	Gong Zhen-Zhou, Wei Hao, Fan Si-Yuan, Hong Ya-Ping, Wu Han-Yu, Qiu Ai-Ci. Analysis of electron flow current in vacuum magnetically-insulated-transmission-line sheath for 15-MA Z-pinch driver. Acta Physica Sinica, 2023, 72(3): 035204. doi: 10.7498/aps.72.20221901
[3]	Zou Xiu, Liu Hui-Ping, Zhang Xiao-Nan, Qiu Ming-Hui. Structure of collisional magnetized plasma sheath with non-extensive distribution of electrons. Acta Physica Sinica, 2021, 70(1): 015201. doi: 10.7498/aps.70.20200794
[4]	Chen Long, Sun Shao-Juan, Jiang Bo-Rui, Duan Ping, An Yu-Hao, Yang Ye-Hui. Characteristics of non-Maxwellian magnetized sheath with secondary electron emission. Acta Physica Sinica, 2021, 70(24): 245201. doi: 10.7498/aps.70.20211061
[5]	Zhao Xiao-Yun, Zhang Bing-Kai, Wang Chun-Xiao, Tang Yi-Jia. Effects of q-nonextensive distribution of electrons on secondary electron emission in plasma sheath. Acta Physica Sinica, 2019, 68(18): 185204. doi: 10.7498/aps.68.20190225
[6]	Wei Hao, Sun Feng-Ju, Hu Yi-Xiang, Qiu Ai-Ci. Method of optimizing secondary impedances for magnetically-insulated induction voltage adders with impedance under-matched loads. Acta Physica Sinica, 2017, 66(20): 208401. doi: 10.7498/aps.66.208401
[7]	Qing Shao-Wei, Li Mei, Li Meng-Jie, Zhou Rui, Wang Lei. Effect of wall secondary electron distribution function on the characteristics of stable sheath near a dielectric wall. Acta Physica Sinica, 2016, 65(3): 035202. doi: 10.7498/aps.65.035202
[8]	Chen Yu, Chen Jia-Lin, Zha Guo-Qiao, Zhou Shi-Ping. Tunneling conductance spectrum of graphene ferromagnet-insulator-superconductor junctions. Acta Physica Sinica, 2014, 63(17): 177402. doi: 10.7498/aps.63.177402
[9]	Duan Ping, Cao An-Ning, Shen Hong-Juan, Zhou Xin-Wei, Qin Hai-Juan, Liu Jin-Yuan, Qing Shao-Wei. Effect of electron temperature on the characteristics of plasma sheath in Hall thruster. Acta Physica Sinica, 2013, 62(20): 205205. doi: 10.7498/aps.62.205205
[10]	Chen Dai-Bing, Zhang Yun-Jian, Zhang Bei-Zheng, Wang Dong, Qin Fen, Wen Jie, Jin Xiao, Wu Yong, Yu Ai-Ming. Relation analysis between cathode ablation and voltage for a magnetically insulated transmission line oscillator. Acta Physica Sinica, 2013, 62(1): 012901. doi: 10.7498/aps.62.012901
[11]	Wu Xin-Yi, Ma Jun, Xie Zhen-Bo. Effect of inhomogeneous distribution of ion channels on collective electric activities of neurons in a ring network. Acta Physica Sinica, 2013, 62(24): 240507. doi: 10.7498/aps.62.240507
[12]	Zhang Yu-Jie, Zhang Wan-Rong, Jin Dong-Yue, Chen Liang, Fu Qiang, Guo Zhen-Jie, Xing Guang-Hui, Lu Zhi-Yi. Effects of Ge profile on thermal characteristics of SiGe heterojunction bipolar transistor with non-uniform doping profile in base region. Acta Physica Sinica, 2013, 62(3): 034401. doi: 10.7498/aps.62.034401
[13]	Zeng Lun-Wu, Song Run-Xia. Inducing magnetic monopole in conductor and topological insulator by point charge. Acta Physica Sinica, 2012, 61(11): 117302. doi: 10.7498/aps.61.117302
[14]	Chen Dai-Bing, Wang Dong, Qin Fen, Wen Jie, Jin Xiao, An Hai-Shi, Zhang Xin-Kai. Relation analysis between starting voltage and input voltage for a magneticaly insulated linear oscillator. Acta Physica Sinica, 2012, 61(1): 012901. doi: 10.7498/aps.61.012901
[15]	Qing Shao-Wei, Ding Yong-Jie, Duan Ping, Wang Xiao-Gang, Yu Da-Ren. Effect of electron temperature anisotropy on BN dielectric wall sheath characteristics in Hall thrusters. Acta Physica Sinica, 2011, 60(2): 025204. doi: 10.7498/aps.60.025204
[16]	Li Xiao-Wei. The dc Josephson current in superconductor-ferromagnet/insulator/spin-triplet p-wave superconductor junctions. Acta Physica Sinica, 2006, 55(12): 6637-6642. doi: 10.7498/aps.55.6637
[17]	Hao Jian-Hong, Ding Wu, Dong Zhi-Wei. Moltipactor discharge in a magnetically insulated transmission line oscillator. Acta Physica Sinica, 2006, 55(9): 4789-4794. doi: 10.7498/aps.55.4789
[18]	LI FANG-YU, LUO JUN, TANG MENG-XI. EFFECT OF GRAVITATIONAL WAVES ON PHONON IN AXISYMMETRIC NON-UNIFORM ELASTIC MEDIUM. Acta Physica Sinica, 1994, 43(8): 1217-1225. doi: 10.7498/aps.43.1217
[19]	. . Acta Physica Sinica, 1965, 21(1): 231-234. doi: 10.7498/aps.21.231
[20]	. . Acta Physica Sinica, 1962, 18(4): 224-226. doi: 10.7498/aps.18.224

Catalog

Vol. 66, Issue 3 - 2017-02-05

Metrics

Abstract views: 4765
PDF Downloads: 139
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板