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In this paper, a transmission line circuit model of a magnetically insulated transmission line(MITL) system is developed for a 15-MA Z-pinch driver. The current loss characteristics of multi-level MITL and the ion emission due to the expansion of anode and cathode plasma in the post hole vacuum convolute(PHC) and inner-MITL region are analyzed. The spatiotemporal distribution of current loss of the outer-MITL and ion current of the PHC and inner-MITL of the 15 MA driver are obtained. The results show that the first electron emission happens at the end of constant-impedance MITL and the beginning of constant-gap MITL, and the end of constant-gap MITL firstly achieves fully magnetic insulation. Electron emission occurs at the start of load current and its duration is about 30 ns, which is short for a single pulse and has little effect on the rising edge nor peak value of the load current. The waveform of the electron flow varying with time resembles a saddle shape, whose amplitude first goes up, then comes down, and increases again. The electron flow current decreases from upstream to downstream in constant-gap MITL in space. The starting time of the loss current of the PHC is synchronized with the gap closing time. The loss current amplitude increases rapidly, reaching 4 MA at the peak load current time and 6.5 MA in the end. In the inner-MITL region, the main positive ion species are protons and oxygen 2+. At the beginning, the ion loss current of protons is larger than that of oxygen 2+, and then the protons are quickly magnetically insulated due to the small charge-to-mass ratio. The ion loss current of the inner-MITL region mainly increases after the peak load current time, and its peak value is 2.1 MA. Given the input conditions, the stack is going to deliver current of about 18 MA, the hold voltage is about 2.3 MV, and the peak load current is about 13.5 MA.
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Keywords:
- magnetically insulated transmission line /
- TL-code /
- electron sheath current /
- ion current
[1] Stygar W A, Corcoran P A, Ives H C, Spieman 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, Smith J W, Van De Valde D M, Wavrik R W 2009 Phys. Rev. ST Accel. Beams 12 120401
Google Scholar
[2] Hutsel B T, Corcoran P A, Cuneo M E, Gomez M R, Hess M H, Hinshelwood D D, Jennings C A, Laity G R, Lamppa D C, McBride R D, Moore J K, Myers A, Rose D V, Slutz S A, Stygar W A, Waisman E M, Welch D R, Whitney B A 2018 Phys. Rev. Accel. Beams 21 030401
Google Scholar
[3] Spielman R B, Froula D H, Brent G, Campbell E M, Reisman D B, Savage M E, Shoup Ⅲ M J, Stygar W A, Wisher M L 2017 Matter Radiat. Extremes 5 204
Google Scholar
[4] Spielman R B, Reisman D B 2019 Matter Radiat. Extremes 4 027402
Google Scholar
[5] 宋盛义, 王文斗, 曹文彬, 林其文, 冯晓晖, 孙承纬 2004 强激光与粒子束 16 800
Song S Y, Wang W D, Cao W B, Lin Q W, Feng X H, Sun C W 2004 High Power Laser and Partical Beams 16 800
[6] Hu Y X, Qiu A C, Wang L P, Huang T, Cong P T, Zhang X J, Li Y, Zeng Z Z, Sun T P, Lei T S, Wu H Y, Guo N, Han J J 2011 Plasma Sci. Technol 13 631
Google Scholar
[7] Zou W K, Guo F, Chen L, Song S Y, Wang M, Xie W P, Deng J J 2014 Phys. Rev. ST Accel. Beams 17 110401
Google Scholar
[8] 邹文康, 郭 帆, 王贵林, 陈 林, 卫 兵, 宋盛义 2015 高电压技术 41 1844
Zou W K, Guo F, Wang G L, Chen L, Wei B, Song S Y 2015 High Volat. Engineer. 41 1844
[9] 薛 创, 丁宁, 孙顺凯, 肖德龙, 张杨, 黄俊, 宁成, 束小建 2014 物理学报 63 125207
Google Scholar
Xue C, Ding N, Sun S K, Xiao D L, Zhang Y, Huang J, Ning C, Su X J 2014 Acta Phys. Sin. 63 125207
Google Scholar
[10] 薛创, 丁宁, 张杨, 肖德龙, 孙顺凯, 宁成, 束小建 2016 强激光与粒子束 28 015014
Google Scholar
Xue C, Ding N, Zhang Y, Xiao D L, Sun S K, Ning C, Su X J 2016 High power laser and Partical Beams 28 015014
Google Scholar
[11] 毛重阳, 薛创, 肖德龙, 丁宁 2020 强激光与粒子束 32 025004
Mao C Y, Xue C, Xiao D L, Ding N 2020 High power laser and Partical Beams 32 025004 (in Chinese)
[12] VanDevender J P, Stinnett R W, Anderson R J 1981 Appl. Phys. Lett. 38 229
Google Scholar
[13] Stinnett R W, Stanley T 1982 J. Appl. Phys. 53 3819
Google Scholar
[14] Stinnett R W, Palmer M, Spielman R B 1983 IEEE Trans. Plasma Sci. 11 216
Google Scholar
[15] Presura R, Bauer B S, Esaulov A, Fuelling S, Ivanov V, Le Galloudec N, Makhin V, Siemon R E, Sotnikov V I, Wirtz R, Astanovitskiy A, Batie S, Faretto H, Le Galloudec B, Oxner A, Angelova M, Laca P, Guzzetta S, Keely S, Rogowski S 2003 IEEE Pulsed power conference, Dallas, Texas, June 15–18, 2003 p859
[16] Ivanov V V, Laca P J, Bauer B S, Presura R, Sotnikov V I, Astanovitskiy A L, Galloudec B L, Glassman J, Wirtz R A 2004 IEEE Trans. Plasma Sci. 32 1843
Google Scholar
[17] Bakshaev Y L, Bartov A V, Blinov P I, Chernenko A S, Dan’ko S A, Kalinin Y G, Kingsep A S, Korolev V D, Mizhiritskii V I, Smirnov V P, Shashkov A Y, Sasorov A Y, Tkachenko S I 2007 Plasma Phys. Rep. 33 259
Google Scholar
[18] Rose D V, Welch D R, Hughes T P, Clark R E 2008 Phys. Rev. ST Accel. Beams 11 060401
Google Scholar
[19] Madrid E A, Rose D V, Welch D R, Clark R E, Mostrom C B, Stygar W A, Cuneo M E, Gomez M R, Hughes T P, Pointon T D, Seidel D B 2013 Phys. Rev. ST Accel. Beams 16 120401
Google Scholar
[20] Rose D V, Madrid E A, Welch D R, Clark R E, Mostrom C B, Stygar W A, Cuneo M E 2015 Phys. Rev. ST Accel. Beams 18 030402
Google Scholar
[21] Gomez M R, Gilgenbach R M, Cuneo M E, Jennings C A, McBride R D, Waisman E M, Hutsel B T, Stygar W A, Rose D V, Maron Y 2017 Phys. Rev. Accel. Beams 20 010401
Google Scholar
[22] Waisman E M, Desjarlais M P, Cuneo M E 2019 Phys. Rev. Accel. Beams 22 030402
Google Scholar
[23] Jennings C A, Chittenden J P, Cuneo M E, Stygar W A, Ampleford D J, Waisman E M, Jones M, Savage M E, LeChien K R, Wagoner T C 2010 IEEE Trans. Plasma Sci. 38 529
Google Scholar
[24] Bennett N, Welch D R, Jenning C A, Yu E, Hess M H, Hutsel B T, Laity G, Moore J K, Rose D V, Peterson K, Cuneo M E 2019 Phys. Rev. Accel. Beams 22 120401
Google Scholar
[25] Rose D V, Waisman E M, Desjarlais M P, Cuneo M E, Hutsel B T, Welch D R, Bennett N, Laity G R 2020 Phys. Rev. Accel. Beams 23 080401
Google Scholar
[26] Bennett N, Welch D R, Laity G, Rose D V, Cuneo M E 2021 Phys. Rev. Accel. Beams 24 060401
Google Scholar
[27] Samokhin A A 2010 Plasma Phys. Rep. 36 149
Google Scholar
[28] Ottinger P F, Schumer J W, Allen R J, Commisso R J 2003 IEEE Pulsed power conference, Dallas, Texas, June 15–18, 2003 p849
[29] Stygar W A, Wagoner T C, Ives H C, Corcoran P A, Cuneo M E, Douglas J W, Gilliland T L, Mazarakis M G, Ramiriez J J, Seamen J F, Seidel D B, Spielman R B 2006 Phys. Rev. ST Accel. Beams 9 090401
Google Scholar
[30] Pointon T D, Savage M E 2005 IEEE Pulsed Power Conference, Monterey, California, June 13–17, 2005 p151
[31] Stygar W A, Rosenthal S E, Ives H C, Wagoner T C, Allshouse G O, Androlewicz K E, Donovan G L, Fehl D L, Frese M H, Gilliland T L, Johnson M F, Mills J A, Reisman D B, Reynolds P G, Speas C S, Spielman R B, Struve K W, Toor A, Waisman E M 2008 Phys. Rev. ST Accel. Beams 11 120401
Google Scholar
[32] Stygar W A, Awe T J, Bailey J E, Bennett N L, Breden E W, 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, Jones M C, 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. ST Accel. Beams 18 110401
Google Scholar
[33] Cuneo M E 1999 IEEE Trans. Dielectrics Electrical Insul. 6 469
Google Scholar
[34] Bloomberg H W, Lampe M, Colombant D G 1980 J. Appl. Phys. 51 5277
[35] 邹文康, 陈林, 周良骥, 王勐, 杨礼兵, 谢卫平, 邓建军 2011 物理学报 60 115204
Google Scholar
Zou W K, Chen L, Zhou L J, Wang M, Yang L B, Xie W P, Deng J J 2011 Acta Phys. Sin. 60 115204
Google Scholar
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图 1 15 MA装置中心汇流区示意图
Figure 1. Cross-sectional view of the central converge region of the 15 MA driver.
图 2 15 MA装置4层MITL电气和结构参数随半径变化规律 (a) 真空电感(包括绝缘堆和外MITL); (b) 真空阻抗; (c) 间隙距离
Figure 2. The outer-MITL parameters of the 15 MA driver: (a) The vacuum inductance (including the stack and MITL); (b) the vacuum impedance; (c) the gap distance.
图 3 15 MA装置MITL电路模型
Figure 3. TL-code model of the MITL system of the 15 MA driver.
图 4 15 MA装置绝缘堆参数 (a) 绝缘堆电流; (b) 绝缘堆电压
Figure 4. The stack parameters of the 15 MA driver: (a) The stack current; (b) the stack voltage.
图 5 D层MITL不同传输线单元电参数 (a) 阳极电压; (b) 电场强度; (c) 空间电荷流损失
Figure 5. The MITL parameters of several elements within the D Level: (a) Line voltage; (b) electric field; (c) electron-loss current.
图 6 鞘层电子流对比(负载聚爆时刻约355 ns) (a) D层MITL恒间隙各段; (b) 4层MITL恒间隙末端及4层之和
Figure 6. The comparison of the electron flow current in each element (the Z-pinch stagnation approximately equal to 355 ns): (a) Each element of the constant-gap MITL segment of the D-level; (b) the end of the four level constant-gap MITL and the sum of the flow current.
图 7 汇流柱电参数 (a)等效损失电阻; (b) 汇流柱电压及损失电流对比
Figure 7. Electrical parameters of the PHC: (a) The loss resistance; (b) comparison of the voltage and the loss current of the PHC.
图 8 内MITL电流损失
Figure 8. The current loss in the inner-MITL region.
图 9 中心汇流区典型位置电流损失对比
Figure 9. Comparison of the loss current in the typical locations of the central converge region.
图 10 中心汇流区典型位置电流对比
Figure 10. Comparison of the current in the typical locations of the central converge region.
表 1 电路模型输入参数
Table 1. The input parameters of the circuit model.
物理量 符号 单位 数值 阴极表面电子发射阈值[1] Et kV/cm 240 调制空间电荷流前沿的电场强度[27] E2 kV/cm 300 外MITL等离子体运动速率[1] vocp cm/μs 2.5 PHC等离子体运动速率[23] vp cm/μs 21 内MITL等离子体运动速率[2] vi cm/μs 3.7 鞘层电子流再俘获系数[2] krt — 0.074 PHC放电通道面积[23] Ap cm2 15 内MITL电极面积 Ai cm2 100 PHC放电通道电阻率[23] η Ω·m 0.035 PHC初始间隙距离[1] dpi cm 1.14 内MITL初始间隙距离 dii cm 0.6 有无空间电荷增强效应的
离子运动速度之比[2]kvi — 1.3 进入内MITL并在间隙积累的
鞘层电子流比例[2]fen, im — 0.02 
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[1] Stygar W A, Corcoran P A, Ives H C, Spieman 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, Smith J W, Van De Valde D M, Wavrik R W 2009 Phys. Rev. ST Accel. Beams 12 120401
Google Scholar
[2] Hutsel B T, Corcoran P A, Cuneo M E, Gomez M R, Hess M H, Hinshelwood D D, Jennings C A, Laity G R, Lamppa D C, McBride R D, Moore J K, Myers A, Rose D V, Slutz S A, Stygar W A, Waisman E M, Welch D R, Whitney B A 2018 Phys. Rev. Accel. Beams 21 030401
Google Scholar
[3] Spielman R B, Froula D H, Brent G, Campbell E M, Reisman D B, Savage M E, Shoup Ⅲ M J, Stygar W A, Wisher M L 2017 Matter Radiat. Extremes 5 204
Google Scholar
[4] Spielman R B, Reisman D B 2019 Matter Radiat. Extremes 4 027402
Google Scholar
[5] 宋盛义, 王文斗, 曹文彬, 林其文, 冯晓晖, 孙承纬 2004 强激光与粒子束 16 800
Song S Y, Wang W D, Cao W B, Lin Q W, Feng X H, Sun C W 2004 High Power Laser and Partical Beams 16 800
[6] Hu Y X, Qiu A C, Wang L P, Huang T, Cong P T, Zhang X J, Li Y, Zeng Z Z, Sun T P, Lei T S, Wu H Y, Guo N, Han J J 2011 Plasma Sci. Technol 13 631
Google Scholar
[7] Zou W K, Guo F, Chen L, Song S Y, Wang M, Xie W P, Deng J J 2014 Phys. Rev. ST Accel. Beams 17 110401
Google Scholar
[8] 邹文康, 郭 帆, 王贵林, 陈 林, 卫 兵, 宋盛义 2015 高电压技术 41 1844
Zou W K, Guo F, Wang G L, Chen L, Wei B, Song S Y 2015 High Volat. Engineer. 41 1844
[9] 薛 创, 丁宁, 孙顺凯, 肖德龙, 张杨, 黄俊, 宁成, 束小建 2014 物理学报 63 125207
Google Scholar
Xue C, Ding N, Sun S K, Xiao D L, Zhang Y, Huang J, Ning C, Su X J 2014 Acta Phys. Sin. 63 125207
Google Scholar
[10] 薛创, 丁宁, 张杨, 肖德龙, 孙顺凯, 宁成, 束小建 2016 强激光与粒子束 28 015014
Google Scholar
Xue C, Ding N, Zhang Y, Xiao D L, Sun S K, Ning C, Su X J 2016 High power laser and Partical Beams 28 015014
Google Scholar
[11] 毛重阳, 薛创, 肖德龙, 丁宁 2020 强激光与粒子束 32 025004
Mao C Y, Xue C, Xiao D L, Ding N 2020 High power laser and Partical Beams 32 025004 (in Chinese)
[12] VanDevender J P, Stinnett R W, Anderson R J 1981 Appl. Phys. Lett. 38 229
Google Scholar
[13] Stinnett R W, Stanley T 1982 J. Appl. Phys. 53 3819
Google Scholar
[14] Stinnett R W, Palmer M, Spielman R B 1983 IEEE Trans. Plasma Sci. 11 216
Google Scholar
[15] Presura R, Bauer B S, Esaulov A, Fuelling S, Ivanov V, Le Galloudec N, Makhin V, Siemon R E, Sotnikov V I, Wirtz R, Astanovitskiy A, Batie S, Faretto H, Le Galloudec B, Oxner A, Angelova M, Laca P, Guzzetta S, Keely S, Rogowski S 2003 IEEE Pulsed power conference, Dallas, Texas, June 15–18, 2003 p859
[16] Ivanov V V, Laca P J, Bauer B S, Presura R, Sotnikov V I, Astanovitskiy A L, Galloudec B L, Glassman J, Wirtz R A 2004 IEEE Trans. Plasma Sci. 32 1843
Google Scholar
[17] Bakshaev Y L, Bartov A V, Blinov P I, Chernenko A S, Dan’ko S A, Kalinin Y G, Kingsep A S, Korolev V D, Mizhiritskii V I, Smirnov V P, Shashkov A Y, Sasorov A Y, Tkachenko S I 2007 Plasma Phys. Rep. 33 259
Google Scholar
[18] Rose D V, Welch D R, Hughes T P, Clark R E 2008 Phys. Rev. ST Accel. Beams 11 060401
Google Scholar
[19] Madrid E A, Rose D V, Welch D R, Clark R E, Mostrom C B, Stygar W A, Cuneo M E, Gomez M R, Hughes T P, Pointon T D, Seidel D B 2013 Phys. Rev. ST Accel. Beams 16 120401
Google Scholar
[20] Rose D V, Madrid E A, Welch D R, Clark R E, Mostrom C B, Stygar W A, Cuneo M E 2015 Phys. Rev. ST Accel. Beams 18 030402
Google Scholar
[21] Gomez M R, Gilgenbach R M, Cuneo M E, Jennings C A, McBride R D, Waisman E M, Hutsel B T, Stygar W A, Rose D V, Maron Y 2017 Phys. Rev. Accel. Beams 20 010401
Google Scholar
[22] Waisman E M, Desjarlais M P, Cuneo M E 2019 Phys. Rev. Accel. Beams 22 030402
Google Scholar
[23] Jennings C A, Chittenden J P, Cuneo M E, Stygar W A, Ampleford D J, Waisman E M, Jones M, Savage M E, LeChien K R, Wagoner T C 2010 IEEE Trans. Plasma Sci. 38 529
Google Scholar
[24] Bennett N, Welch D R, Jenning C A, Yu E, Hess M H, Hutsel B T, Laity G, Moore J K, Rose D V, Peterson K, Cuneo M E 2019 Phys. Rev. Accel. Beams 22 120401
Google Scholar
[25] Rose D V, Waisman E M, Desjarlais M P, Cuneo M E, Hutsel B T, Welch D R, Bennett N, Laity G R 2020 Phys. Rev. Accel. Beams 23 080401
Google Scholar
[26] Bennett N, Welch D R, Laity G, Rose D V, Cuneo M E 2021 Phys. Rev. Accel. Beams 24 060401
Google Scholar
[27] Samokhin A A 2010 Plasma Phys. Rep. 36 149
Google Scholar
[28] Ottinger P F, Schumer J W, Allen R J, Commisso R J 2003 IEEE Pulsed power conference, Dallas, Texas, June 15–18, 2003 p849
[29] Stygar W A, Wagoner T C, Ives H C, Corcoran P A, Cuneo M E, Douglas J W, Gilliland T L, Mazarakis M G, Ramiriez J J, Seamen J F, Seidel D B, Spielman R B 2006 Phys. Rev. ST Accel. Beams 9 090401
Google Scholar
[30] Pointon T D, Savage M E 2005 IEEE Pulsed Power Conference, Monterey, California, June 13–17, 2005 p151
[31] Stygar W A, Rosenthal S E, Ives H C, Wagoner T C, Allshouse G O, Androlewicz K E, Donovan G L, Fehl D L, Frese M H, Gilliland T L, Johnson M F, Mills J A, Reisman D B, Reynolds P G, Speas C S, Spielman R B, Struve K W, Toor A, Waisman E M 2008 Phys. Rev. ST Accel. Beams 11 120401
Google Scholar
[32] Stygar W A, Awe T J, Bailey J E, Bennett N L, Breden E W, 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, Jones M C, 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. ST Accel. Beams 18 110401
Google Scholar
[33] Cuneo M E 1999 IEEE Trans. Dielectrics Electrical Insul. 6 469
Google Scholar
[34] Bloomberg H W, Lampe M, Colombant D G 1980 J. Appl. Phys. 51 5277
[35] 邹文康, 陈林, 周良骥, 王勐, 杨礼兵, 谢卫平, 邓建军 2011 物理学报 60 115204
Google Scholar
Zou W K, Chen L, Zhou L J, Wang M, Yang L B, Xie W P, Deng J J 2011 Acta Phys. Sin. 60 115204
Google Scholar
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