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Method of optimizing secondary impedances for magnetically-insulated induction voltage adders with impedance under-matched loads

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

Wei Hao, Sun Feng-Ju, Hu Yi-Xiang, Qiu Ai-Ci
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  • The magnetically-insulated induction voltage adder (MIVA) is a pulsed-power accelerator widely used in the X-ray flash radiography and -ray radiation simulation. The operating impedance of magnetically-insulated transmission line (MITL) on the secondary side of MIVA will produce significant influence on the power coupling between the pulsed-power driving source and the terminal load. Therefore, optimizing the secondary impedance of MIVA to maximize the electrical-power or radiated output of load is critical for the design of MIVA facility. According to whether the MITL operating impedance is smaller than the load impedance, MIVAs can be divided into two different types, i.e., the impedance-matched case and impedance undermatched case. For the impedance-matched MIVA, because the MITL of MIVA operates at the minimal current point or self-limited flow, the output of MIVA just depends on the MITL operating impedance and is independent of load. Correspondingly, the circuit analysis is relatively easy. However, for MIVA with impedance undermatched load, the analysis method is more complicated. Based on the classical Creedon theory of the magnetic insulation equilibrium and the sheath electron re-trapping theory, a circuit method is established for MIVA with impedance under-matched load. The analysis process consists of two steps. Firstly, the working point of the forward magnetic insulation wave is solved by the minimal current theory on the assumption that the MIVA is terminated by impedance-matched load. Then, the actual operating point after the re-trapping wave has passed is solved, in which the characteristic impedance of the re-trapping wave is treated as a vacuum impedance. And the relationship between the output parameters of MIVA, e.g., the output voltage, the cathode and anode current, and the electrical power, and the undermatched extent of load is obtained numerically. Based on the analysis method, a method to optimize the secondary impedance of MIVA with ten-stage cavities stacked in series to drive X-ray radiographic diodes is developed. This optimization method aims at maximizing the radiated X-ray dose rate of the diode loads on the assumption that only the cathode current is available for the X-ray radiographic diode. The optimization secondary impedance, Zop*, varying with the scaling factor, , is achieved, where is the power exponent between the dose rate and the diode voltage (Ḋ Ud). is usually determined by the diode type, geometrical structure, and operating characteristics. It is found that the optimization secondary impedance Zop* decays exponentially with the increase of value , i.e., the increase of the diode-voltage-dependent degree of the radiated X-ray dose rate. And the larger the load impedance, the larger the value of Zop* is. The circuit analysis method and the impedance optimization method developed in this paper are specially useful for the applications of MIVA in the flash radiographic fields.
      Corresponding author: Wei Hao, weihao@nint.ac.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11505138, 51577156).
    [1]

    Smith I D 2004 Phys. Rev. Spec. Top. Accel. Beams 7 064801

    [2]

    Smith I D, Bailey V L, Fockler J, Gustwiller J S, Johnson D L, Maenchen J E, Droemer D W 2000 IEEE Trans. on Plasma Sci. 28 1653

    [3]

    Oliver B V 2008 Proceeding of 17th IEEE High Power Particle Beams Conference Xi' an, Shaanxi, China, July 7-11, 2008 p1

    [4]

    Thomas K 2014 IEEE Pulsed Power Symposium Loughborough, UK, March 18-20, 2014, pp1-29

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    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, IL, June 19-23, 2011 p1042

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    Guo F, Zou W K, Gong B Y, Jiang J H, Chen L, Wang M, Xie W P 2017 Phys. Rev. Accel. Beams 20 020401

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    Wei H, Sun F J, Qiu A C, Zeng J T, Liang T X, Yin J H, Hu Y X 2014 IEEE Trans. Plasma Sci. 42 3057

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    Sun F J, Qiu A C, Yang H L, Zeng J T, Gai T Y, Liang T X, Yin J H, Sun J F, Cong P T, Huang J J, Su Z F, Gao Y, Liu Z G, Jiang X F, Li J Y, Zhang Z, Song G Z, Pei M J, Niu S L 2010 High Power and Laser and Particle Beams 22 936 (in Chinese)[孙凤举, 邱爱慈, 杨海亮, 曾江涛, 盖同阳, 梁天学, 尹佳辉, 孙剑锋, 丛培天, 黄建军, 苏兆锋, 高屹, 刘志刚, 姜晓锋, 李静雅, 张众, 宋顾周, 裴明敬, 牛胜利2010强激光与粒子束22 936]

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    Zhang T K, Han D, Wu Y C, Yan Y H, Zhao Z Q, Gu Y Q 2016 Acta Phys. Sin. 65 045203 (in Chinese)[张天奎, 韩丹, 吴玉迟, 闫永宏, 赵宗清, 谷渝秋2016物理学报65 045203]

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    Wei H, Sun F J, Hu Y X, Liang T X, Cong P T, Qiu A C 2017 Acta Phys. Sin. 66 038402 (in Chinese)[魏浩, 孙凤举, 呼义翔, 梁天学, 丛培天, 邱爱慈2017物理学报66 038402]

    [11]

    Zhou J, Zhang P F, Yang H L, Sun J, Sun J F, Su Z F, Liu W D 2012 Acta Phys. Sin. 61 245203 (in Chinese)[周军, 张鹏飞, 杨海亮, 孙江, 孙剑峰, 苏兆锋, 刘万东2012物理学报61 245203]

    [12]

    Bailey V, Corcoran P, Carboni V, Smith I, Johnson D L, Oliver B, Thomas K, Swierkosz M 2005 Proceeding of 15th IEEE Pulsed Power Conference Monterey, CA, USA, June 13-15, 2005 p322

    [13]

    Bailey V L, Johnson D L, Corcoran P, Smith I, Maenchen J E, Molina I, Hahn K, Rovang D, Portillo S, Oliver B V, Rose D, Welsh D, Droemer D, Guy T 2003 Proceeding of 14th IEEE International Pulsed Power Conference Dallas, Texas, USA, June 15-18, 2003 p399

    [14]

    Ottinger P, Schumer J, Hinshelwood D, Allen R J 2008 IEEE Trans. Plasma Sci. 36 2708

    [15]

    Ottinger P, Schumer J 2006 Phys. Plasma 13 063109

    [16]

    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, Virginia, 1987 pp478-481

    [17]

    Guo F, Zou W K, Chen L 2014 High Power and Laser and Particle Beams 26 045010(in Chinese)[郭帆, 邹文康, 陈林2014强激光与粒子束26 045010]

    [18]

    Liu X S 2005 High Pulsed Power Technologh (Beijing:National Defense Industry Press) pp128-262(in Chinese)[刘锡三2005高功率脉冲技(北京:国防工业出版社)第128262页].

    [19]

    Zou W K, Deng J J, Song S Y 2007 High Power and Laser and Particle Beams 19 992(in Chinese)[邹文康, 邓建军, 宋盛义2007强激光与粒子束19 992]

    [20]

    Bailey V L, Corcoran P, Johnson D L, Smith I, Oliver B, Maenchen J 2007 Proceeding of 16th IEEE Pulsed Power Conference Albuquerque, New Mexico, USA, June 17-22, 2007 p1268

    [21]

    Bailey V L, Corcoran P, Johnson D L, Smith I D, Maenchen J E, Rahn K D, Molina I, Rovang D C, Portillo S, Puetz E A, Oliver B V, Rose D V, Welch D R, Droemer D W, Guy T 2004 Proceeding of 14th IEEE high Power Beams Conference Dallas, Texas, USA, 2004 p247

    [22]

    Hahn K, B V Oliver, Cordova S R, Leckbee J, Molina I, Johnston M, Webb T, Bruner N, Welch D R, Portillo S, ZiskaD, Crotch I, Threadgold J 2009 Proceeding of 17th IEEE Pulsed Power Conference Washington, DC, USA, June 28-July 2, 2009 p34

    [23]

    Hahn K, Maenchen J, Cordova S, Molina I, Portillo S, Rovang D, Rose D, Oliver B, Welch D, Bailey V, Johnson D L, Schamiloglu E 2003 Proceeding of 14th IEEE Pulsed Power Conference Dallas, Texas, USA, June 15-18, 2003 p871

    [24]

    Portillo S, Hahn K, Maenchen J, Molina I, Cordova S, Johnson D L, Rose D, Oliver B, Welch D 2003 Proceeding of 14th IEEE Pulsed Power Conference Dallas, Texas, USA, June 15-18, 2003 p879

    [25]

    Hu Y X, Sun F J, Zeng J T, Cong P T 2015 Modern Appl. Phys. 6 191 (in Chinese)[呼义翔, 孙凤举, 曾江涛, 丛培天2015现代应用物理6 191]

    [26]

    Wei H 2017 Ph. D. Dissertation (Xi' an:Xi' an Jiaotong University) (in Chinese)[魏浩2017博士学位论文(西安:西安交通大学)]

    [27]

    Creedon J M 1975 J. Appl. Phys. 46 2946

  • [1]

    Smith I D 2004 Phys. Rev. Spec. Top. Accel. Beams 7 064801

    [2]

    Smith I D, Bailey V L, Fockler J, Gustwiller J S, Johnson D L, Maenchen J E, Droemer D W 2000 IEEE Trans. on Plasma Sci. 28 1653

    [3]

    Oliver B V 2008 Proceeding of 17th IEEE High Power Particle Beams Conference Xi' an, Shaanxi, China, July 7-11, 2008 p1

    [4]

    Thomas K 2014 IEEE Pulsed Power Symposium Loughborough, UK, March 18-20, 2014, pp1-29

    [5]

    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, IL, June 19-23, 2011 p1042

    [6]

    Guo F, Zou W K, Gong B Y, Jiang J H, Chen L, Wang M, Xie W P 2017 Phys. Rev. Accel. Beams 20 020401

    [7]

    Wei H, Sun F J, Qiu A C, Zeng J T, Liang T X, Yin J H, Hu Y X 2014 IEEE Trans. Plasma Sci. 42 3057

    [8]

    Sun F J, Qiu A C, Yang H L, Zeng J T, Gai T Y, Liang T X, Yin J H, Sun J F, Cong P T, Huang J J, Su Z F, Gao Y, Liu Z G, Jiang X F, Li J Y, Zhang Z, Song G Z, Pei M J, Niu S L 2010 High Power and Laser and Particle Beams 22 936 (in Chinese)[孙凤举, 邱爱慈, 杨海亮, 曾江涛, 盖同阳, 梁天学, 尹佳辉, 孙剑锋, 丛培天, 黄建军, 苏兆锋, 高屹, 刘志刚, 姜晓锋, 李静雅, 张众, 宋顾周, 裴明敬, 牛胜利2010强激光与粒子束22 936]

    [9]

    Zhang T K, Han D, Wu Y C, Yan Y H, Zhao Z Q, Gu Y Q 2016 Acta Phys. Sin. 65 045203 (in Chinese)[张天奎, 韩丹, 吴玉迟, 闫永宏, 赵宗清, 谷渝秋2016物理学报65 045203]

    [10]

    Wei H, Sun F J, Hu Y X, Liang T X, Cong P T, Qiu A C 2017 Acta Phys. Sin. 66 038402 (in Chinese)[魏浩, 孙凤举, 呼义翔, 梁天学, 丛培天, 邱爱慈2017物理学报66 038402]

    [11]

    Zhou J, Zhang P F, Yang H L, Sun J, Sun J F, Su Z F, Liu W D 2012 Acta Phys. Sin. 61 245203 (in Chinese)[周军, 张鹏飞, 杨海亮, 孙江, 孙剑峰, 苏兆锋, 刘万东2012物理学报61 245203]

    [12]

    Bailey V, Corcoran P, Carboni V, Smith I, Johnson D L, Oliver B, Thomas K, Swierkosz M 2005 Proceeding of 15th IEEE Pulsed Power Conference Monterey, CA, USA, June 13-15, 2005 p322

    [13]

    Bailey V L, Johnson D L, Corcoran P, Smith I, Maenchen J E, Molina I, Hahn K, Rovang D, Portillo S, Oliver B V, Rose D, Welsh D, Droemer D, Guy T 2003 Proceeding of 14th IEEE International Pulsed Power Conference Dallas, Texas, USA, June 15-18, 2003 p399

    [14]

    Ottinger P, Schumer J, Hinshelwood D, Allen R J 2008 IEEE Trans. Plasma Sci. 36 2708

    [15]

    Ottinger P, Schumer J 2006 Phys. Plasma 13 063109

    [16]

    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, Virginia, 1987 pp478-481

    [17]

    Guo F, Zou W K, Chen L 2014 High Power and Laser and Particle Beams 26 045010(in Chinese)[郭帆, 邹文康, 陈林2014强激光与粒子束26 045010]

    [18]

    Liu X S 2005 High Pulsed Power Technologh (Beijing:National Defense Industry Press) pp128-262(in Chinese)[刘锡三2005高功率脉冲技(北京:国防工业出版社)第128262页].

    [19]

    Zou W K, Deng J J, Song S Y 2007 High Power and Laser and Particle Beams 19 992(in Chinese)[邹文康, 邓建军, 宋盛义2007强激光与粒子束19 992]

    [20]

    Bailey V L, Corcoran P, Johnson D L, Smith I, Oliver B, Maenchen J 2007 Proceeding of 16th IEEE Pulsed Power Conference Albuquerque, New Mexico, USA, June 17-22, 2007 p1268

    [21]

    Bailey V L, Corcoran P, Johnson D L, Smith I D, Maenchen J E, Rahn K D, Molina I, Rovang D C, Portillo S, Puetz E A, Oliver B V, Rose D V, Welch D R, Droemer D W, Guy T 2004 Proceeding of 14th IEEE high Power Beams Conference Dallas, Texas, USA, 2004 p247

    [22]

    Hahn K, B V Oliver, Cordova S R, Leckbee J, Molina I, Johnston M, Webb T, Bruner N, Welch D R, Portillo S, ZiskaD, Crotch I, Threadgold J 2009 Proceeding of 17th IEEE Pulsed Power Conference Washington, DC, USA, June 28-July 2, 2009 p34

    [23]

    Hahn K, Maenchen J, Cordova S, Molina I, Portillo S, Rovang D, Rose D, Oliver B, Welch D, Bailey V, Johnson D L, Schamiloglu E 2003 Proceeding of 14th IEEE Pulsed Power Conference Dallas, Texas, USA, June 15-18, 2003 p871

    [24]

    Portillo S, Hahn K, Maenchen J, Molina I, Cordova S, Johnson D L, Rose D, Oliver B, Welch D 2003 Proceeding of 14th IEEE Pulsed Power Conference Dallas, Texas, USA, June 15-18, 2003 p879

    [25]

    Hu Y X, Sun F J, Zeng J T, Cong P T 2015 Modern Appl. Phys. 6 191 (in Chinese)[呼义翔, 孙凤举, 曾江涛, 丛培天2015现代应用物理6 191]

    [26]

    Wei H 2017 Ph. D. Dissertation (Xi' an:Xi' an Jiaotong University) (in Chinese)[魏浩2017博士学位论文(西安:西安交通大学)]

    [27]

    Creedon J M 1975 J. Appl. Phys. 46 2946

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  • Received Date:  10 March 2017
  • Accepted Date:  03 July 2017
  • Published Online:  05 October 2017

Method of optimizing secondary impedances for magnetically-insulated induction voltage adders with impedance under-matched loads

    Corresponding author: Wei Hao, weihao@nint.ac.cn
  • 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
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant Nos. 11505138, 51577156).

Abstract: The magnetically-insulated induction voltage adder (MIVA) is a pulsed-power accelerator widely used in the X-ray flash radiography and -ray radiation simulation. The operating impedance of magnetically-insulated transmission line (MITL) on the secondary side of MIVA will produce significant influence on the power coupling between the pulsed-power driving source and the terminal load. Therefore, optimizing the secondary impedance of MIVA to maximize the electrical-power or radiated output of load is critical for the design of MIVA facility. According to whether the MITL operating impedance is smaller than the load impedance, MIVAs can be divided into two different types, i.e., the impedance-matched case and impedance undermatched case. For the impedance-matched MIVA, because the MITL of MIVA operates at the minimal current point or self-limited flow, the output of MIVA just depends on the MITL operating impedance and is independent of load. Correspondingly, the circuit analysis is relatively easy. However, for MIVA with impedance undermatched load, the analysis method is more complicated. Based on the classical Creedon theory of the magnetic insulation equilibrium and the sheath electron re-trapping theory, a circuit method is established for MIVA with impedance under-matched load. The analysis process consists of two steps. Firstly, the working point of the forward magnetic insulation wave is solved by the minimal current theory on the assumption that the MIVA is terminated by impedance-matched load. Then, the actual operating point after the re-trapping wave has passed is solved, in which the characteristic impedance of the re-trapping wave is treated as a vacuum impedance. And the relationship between the output parameters of MIVA, e.g., the output voltage, the cathode and anode current, and the electrical power, and the undermatched extent of load is obtained numerically. Based on the analysis method, a method to optimize the secondary impedance of MIVA with ten-stage cavities stacked in series to drive X-ray radiographic diodes is developed. This optimization method aims at maximizing the radiated X-ray dose rate of the diode loads on the assumption that only the cathode current is available for the X-ray radiographic diode. The optimization secondary impedance, Zop*, varying with the scaling factor, , is achieved, where is the power exponent between the dose rate and the diode voltage (Ḋ Ud). is usually determined by the diode type, geometrical structure, and operating characteristics. It is found that the optimization secondary impedance Zop* decays exponentially with the increase of value , i.e., the increase of the diode-voltage-dependent degree of the radiated X-ray dose rate. And the larger the load impedance, the larger the value of Zop* is. The circuit analysis method and the impedance optimization method developed in this paper are specially useful for the applications of MIVA in the flash radiographic fields.

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