One-dimensional magneto-hydrodynamics simulation of magnetically driven solid liner implosions on FP-1 facility

Zhang Yang; Dai Zi-Huan; Sun Qi-Zhi; Zhang Zheng-Wei; Sun Hai-Quan; Wang Pei; Ding Ning; Xue Chuang; Wang Guan-Qiong; Shen Zhi-Jun; Li Xiao; Wang Jian-Guo

doi:10.7498/aps.67.20172300

Abstract

As an important cylindrical-convergent drive technology, magnetically driven solid liner implosion has been widely used in the high energy density physics (HEDP) experiments for different researches, such as the properties of condensed matter at an extreme pressure, the hydrodynamic behaviors of imploding systems, and the properties and behaviors of dense plasmas. On the 2.2 MA FP-1 facility (with a rise time of 7 s), implosions of aluminum liners and their impact on target liners are studied experimentally for exploring the applications of instability and ejecta mixing. A one-dimensional Lagrangian codeMADE1D is developed to study liner implosions numerically, which is based on magneto-hydrodynamics model with material strength, wide-range equation of state, Lee-More conductivity, and SCG (Steinberg, Cochran and Guinan) constitutive model. The code is based on the finite difference method. The finite difference equations are written in the covariant form for both Cartesian and cylindrical coordinates which enables the accurate simulation of different load geometries. Numerical results, such as the simulated velocity and radius at inner surface of the liner and target, agree well with the measurements. It shows that FP-1 has the ability to accelerate a 0.5 mm thick aluminum liner with an initial radius of 1.5 mm to a speed of more than 1.1 km/s, and the corresponding velocity of inner surface is more than 1.5 km/s due to the cylindrical convergence effect. In our calculation, most of the liner keeps solid throughout the implosion, though its outer surface is melted due to the Ohmic heating. A cylindrical converging shock about 8-10 GPa can be obtained by setting a target with an initial radius of 8-11 mm inside the liner coaxially. The numerical results show that since the imploding liner is fully magnetized when it impacts the target, the shock and the corresponding reflect release wave run faster than in the unmagnetized target. This means that the target will spall near the liner-target interface, though they are impedance-matched acoustically. The movement of the shocked target can be affected by the pre-filled gas inside. Increasing the gas pressure makes the target lose its velocity quickly, and the rebound radius increases as well. By adjusting the load design and gas pressure appropriately, we can obtain the right implosion process to meet the study requirement.

Keywords:

Authors and contacts

1.
Institute of Applied Physics and Computational Mathematics, Beijing 100088, China;
2.
Institute of Fluid Physics, China Academy of Engineering Physics, Mianyang 621900, China;
3.
Graduate School of China Academy of Engineering Physics, Beijing 100088, China

Corresponding author: Zhang Yang, zhang_yang@iapcm.ac.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11405012, 11675025, 11471048, U1630249), the Science Challenge Project, China (Grant No. JCKY2016212A502), and the Foundation of Laboratory of Computational Physics, China.

References

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[23]	Wu J, Li X, Li M, Li Y, Qiu A 2017 J. Phys. D:Appl. Phys. 50 403002
[24]	Zhao S, Xue C, Zhu X L, Zhang R, Luo H Y, Zou X B, Wang X X, Ning C, Ding N, Shu X J 2013 Chin. Phys. B 22 045205
[25]	Wang G J, Zhao J H, Sun C W, Liu C L, Tan F L, Luo B Q, Zhong T, Cai J T, Zhang X P, Chen X M, Wu G, Shui R J, Xu C, Ma X, Deng S Y, Tao Y H 2015 J. Exp. Mech. 30 252 (in Chinese)[王桂吉, 赵剑衡, 孙承纬, 刘仓理, 谭福利, 罗斌强, 种涛, 蔡进涛, 张旭平, 陈学秒, 吴刚, 税荣杰, 胥超, 马骁, 邓顺义, 陶彦辉 2015 力学实验 30 252]
[26]	Wang G J, Tan F L, Sun C W, Zhao J H, Wang G H, Mo J J, Zhang N, Wang X S, Wu G, Han M 2009 Chinese Journal of High Pressure Physics 4 266 (in Chinese)[王桂吉, 谭福利, 孙承纬, 赵剑衡, 王刚华, 莫建军, 张宁, 汪小松, 吴刚, 韩梅 2009 高压物理学报 4 266]
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[28]	Deng J J, Xie W P, Feng S P, Wang M, Li H T, Song S Y, Xia M H, He A, Tian Q, Gu Y C, Guang Y C, Wei B, Zou W K, Huang X B, Wang L J, Zhang Z H, He Y, Yang L B 2013 IEEE Trans. Plamsa Sci. 41 2580
[29]	Wang G L, Guo S, Shen Z W, Zhang Z H, Liu C L, Li J, Zhang Z W, Jia Y S, Zhao X M, Chen H, Feng S P, Ji C, Xia M H, Wei B, Tian Q, Li Y, Ding Y, Guo F 2014 Acta Phys. Sin. 63 196201 (in Chinese)[王贵林, 郭帅, 沈兆武, 张朝辉, 刘仓理, 李军, 章征伟, 贾月松, 赵小明, 陈宏, 丰树平, 计策, 夏明鹤, 卫兵, 田青, 李勇, 丁瑜, 郭帆 2014 物理学报 63 196201]
[30]	Kan M X, Zhang Z H, Duan S C, Wang G H, Yang L, Xiao B, Wang G L 2015 High Power Laser and Particle Beams 27 125001 (in Chinese)[阚明先, 张朝辉, 段书超, 王刚华, 杨龙, 肖波, 王贵林 2015 强激光与粒子束 27 125001]
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[32]	Zhang Z W, Wei Y, Sun Q Z, Liu W, Zhao X M, Zhang Z H, Wang G L, Guo S, Xie W P 2016 High Power Laser and Particle Beams 28 045017 (in Chinese)[章征伟, 魏懿, 孙奇志, 刘伟, 赵小明, 张朝辉, 王贵林, 郭帅, 谢卫平 2016 强激光与粒子束 28 045017]
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[35]	Steinberg D J, Cochran S G, Guinan M W 1980 J. Appl. Phys. 51 1498
[36]	Lee Y T, More R M 1984 Phys. Fluids 27 1273
[37]	Liu H F, Song H F, Zhang Q L, Zhang G M, Zhao Y H 2016 Matter and Radiation at Extremes 1 123

Cited By

[1]	Sun C W 2007 High Energ. Dens. Phys. 1 41 (in Chinese)[孙承纬 2007 高能量密度物理 1 41]
[2]	Savage M E, Bennett L F, Bliss D E, Clark W T, Coats R S, Elizondo J M, LeChien K R, Harjes H C, Lehr J M, Maenchen J E, McDaniel D H, Pasik M F, Pointon T D, Owen A C, Seidel D B, Smith D L, Stoltzfus B S, Struve K W, Stygar W A, Warne L K, Woodworth J R, Mendel C W, Prestwich K R, Shoup R W, Johnson D L, Corley J P, Hodge K C, Wagoner T C, Wakeland P E 2007 Proceedings of the 2007 IEEE Pulsed Power Conference 1-4 979
[3]	Davis J, Knudson M D, Brown J L 2017 AIP Conference Proceedings 1793 060015
[4]	Lemke R W, Knudson M D, Davis J 2011 Int. J. Impact Eng. 38 480
[5]	Martin M R, Lemke R W, McBride R D, Davis J P, Dolan D H, Knudson M D, Cochrane K R, Sinars D B, Smith I C, Savage M, Stygar W A, Killebrew K, Flicker D G, Herrmann M C 2012 Phys. Plasmas 19 056310
[6]	Lemke R W, Dolan D H, Dalton D G, Brown J L, Tomlinson K, Robertson G R, Knudson M D, Harding E, Mattsson A E, Carpenter J H, Drake R R, Cochrane K, Blue B E, Robinson A C, Mattsson T R 2016 J. Appl. Phys. 119 015904
[7]	Faehl R J, Anderson B G, Clark D A, Ekdahl C A, Goforth J H, Lindemuth I R, Reinovsky R E, Sheehey P T, Peterson T, Tabaka L J, Chernyshev V K, Mokhov V N, Buzin V N, Burenkov O M, Buyko A M, Vakhrushev V V, Garanin S F, Grinevich B E, Ivanova G G, Demidov V A, Dudoladov V I, Zmushko V V, Kuzyaev A I, Kucherov A I, Lovyagin B M, Nizovtsev P N, Petrukhin A A, Pishurov A I, Sofronov V N, Sokolov S S, Solovyev V P, Startsev A I, Yakubov V B, Gubkov E V 2004 IEEE Trans. Plasma Sci. 32 1972
[8]	Bowers R L, Brownell J H, Lee H, McLenithan K D, Scannapieco A J, Shanahan W R 1998 J. Appl. Phys. 83 4146
[9]	Chandler E, Egan P, Winer K, Stokes J, Douglas Fulton R, King N S P, Morgan D V, Obst A W, Oro D W 1997 Lawrence Livermore National Laboratory Report UCRL-JC-127667
[10]	Hammerberg J E, Kyrala G A, Ore D M, Fulton R D, Anderson W E, Obst A W, Oona H, Stokes J 1999 Los Alamos National Laboratory Report LA-UR-99-3378
[11]	Bowman D W, Ballard E O, Barr G, Bennett G A, Cochrane J C, Davis H A, Davis T O, Dorr G, Gribble R F, Griego J R, Hood M, Kimerly H J, Martinez A, MCcuistian T, Miller R B, Ney S, Nielsen K, Pankuch P, Parsons W M, Potter C, Ricketts R, Salazar H R, Scudder D W, Shapiro C, Thompson M C, Trainor R J, Valdez G A, Yonemoto W 1999 IEEE Int. Pulsed Power Conf. 2 933
[12]	Parsons W M, Ballard E O, Barr G W, Bowman D W, Cochrane J C, Davis H A, Elizondo J M, Gribble R F, Griego J R, Hicks R D, Hinckley W B, Hosack K W, Miller R B, Nielsen K E, Parker J V, Rickets R L, Salazar H R, Sanchez P G, Scudder D W, Thompson M C, Trainor R J, Valdez G A, Vigil B N, Waganaar W J, Watt R G, Wysocki F J 1999 IEEE Int. Pulsed Power Conf. 2 976
[13]	Davis H A, Ballard E O, Elizondo J M, Gribble R F, Nielsen K E, Parker J V, Parsons W M 2000 IEEE Trans. Plasma Sci. 28 1405
[14]	Reinovsky R E 2000 IEEE Trans. Plasma Sci. 28 1563
[15]	Rousculp C L, Oro D M, Morris C, Saunders A, Reass W, Griego J R, Turchi P J, Reinovsky R E 2015 Los Alamos Report LA-UR-15-22889
[16]	Rousculp C L, Oro D M, Griego J R, Turchi P J, Reinovsky R E, Bradley J T Ⅲ, Cheng B, Freeman M S, Patten A R 2016 Los Alamos Report LA-UR-16-21901
[17]	Oliphant T A, Witte K H 1987 Los Alamos National Laboratory Report LA-10826
[18]	Keinigs R K, Atchison W L, Faehl R J, Thomas V A, Mclenithan K D, Trainor R J 1999 J. Appl. Phys. 85 7626
[19]	Steinberg D 1996 Lawrence Livermore National Laboratory Report UCRL-MA106439
[20]	Lindemann F A 1911 Phys. Z 11 609
[21]	Qiu A C, Kuai B, Zeng Z Z, Wang W S, Qiu M T, Wang L P, Cong P T, L M 2006 Acta Phys. Sin. 55 5917 (in Chinese)[邱爱慈, 蒯斌, 曾正中, 王文生, 邱孟通, 王亮平, 丛培天, 吕敏 2006 物理学报 55 5917]
[22]	Wu J, Wang L P, Li M, Wu G, Qiu M T, Yang H L, Li X W, Qiu A C 2014 Acta Phys. Sin. 63 035205 (in Chinese)[吴坚, 王亮平, 李沫, 吴刚, 邱孟通, 杨海亮, 李兴文, 邱爱慈 2014 物理学报 63 035205]
[23]	Wu J, Li X, Li M, Li Y, Qiu A 2017 J. Phys. D:Appl. Phys. 50 403002
[24]	Zhao S, Xue C, Zhu X L, Zhang R, Luo H Y, Zou X B, Wang X X, Ning C, Ding N, Shu X J 2013 Chin. Phys. B 22 045205
[25]	Wang G J, Zhao J H, Sun C W, Liu C L, Tan F L, Luo B Q, Zhong T, Cai J T, Zhang X P, Chen X M, Wu G, Shui R J, Xu C, Ma X, Deng S Y, Tao Y H 2015 J. Exp. Mech. 30 252 (in Chinese)[王桂吉, 赵剑衡, 孙承纬, 刘仓理, 谭福利, 罗斌强, 种涛, 蔡进涛, 张旭平, 陈学秒, 吴刚, 税荣杰, 胥超, 马骁, 邓顺义, 陶彦辉 2015 力学实验 30 252]
[26]	Wang G J, Tan F L, Sun C W, Zhao J H, Wang G H, Mo J J, Zhang N, Wang X S, Wu G, Han M 2009 Chinese Journal of High Pressure Physics 4 266 (in Chinese)[王桂吉, 谭福利, 孙承纬, 赵剑衡, 王刚华, 莫建军, 张宁, 汪小松, 吴刚, 韩梅 2009 高压物理学报 4 266]
[27]	Cai J T, Wang G J, Zhao J H, Mo J J, Weng J D, Wu G, Zhao F 2010 Chinese Journal of High Pressure Physics 6 455 (in Chinese)[蔡进涛, 王桂吉, 赵剑衡, 莫建军, 翁继东, 吴刚, 赵峰 2010 高压物理学报 6 455]
[28]	Deng J J, Xie W P, Feng S P, Wang M, Li H T, Song S Y, Xia M H, He A, Tian Q, Gu Y C, Guang Y C, Wei B, Zou W K, Huang X B, Wang L J, Zhang Z H, He Y, Yang L B 2013 IEEE Trans. Plamsa Sci. 41 2580
[29]	Wang G L, Guo S, Shen Z W, Zhang Z H, Liu C L, Li J, Zhang Z W, Jia Y S, Zhao X M, Chen H, Feng S P, Ji C, Xia M H, Wei B, Tian Q, Li Y, Ding Y, Guo F 2014 Acta Phys. Sin. 63 196201 (in Chinese)[王贵林, 郭帅, 沈兆武, 张朝辉, 刘仓理, 李军, 章征伟, 贾月松, 赵小明, 陈宏, 丰树平, 计策, 夏明鹤, 卫兵, 田青, 李勇, 丁瑜, 郭帆 2014 物理学报 63 196201]
[30]	Kan M X, Zhang Z H, Duan S C, Wang G H, Yang L, Xiao B, Wang G L 2015 High Power Laser and Particle Beams 27 125001 (in Chinese)[阚明先, 张朝辉, 段书超, 王刚华, 杨龙, 肖波, 王贵林 2015 强激光与粒子束 27 125001]
[31]	Yang L B, Sun C W, Liao H D, Hu X J 2002 High Power Laser and Particle Beams 14 767 (in Chinese)[杨礼兵, 孙承纬, 廖海东, 胡熙静 2002 强激光与粒子束 14 767]
[32]	Zhang Z W, Wei Y, Sun Q Z, Liu W, Zhao X M, Zhang Z H, Wang G L, Guo S, Xie W P 2016 High Power Laser and Particle Beams 28 045017 (in Chinese)[章征伟, 魏懿, 孙奇志, 刘伟, 赵小明, 张朝辉, 王贵林, 郭帅, 谢卫平 2016 强激光与粒子束 28 045017]
[33]	Zhang S L, Zhang Z W, Sun Q Z, Liu W, Zhao X M, Zhang Z H, Wang G L, Jia Y S 2017 High Power Laser and Particle Beams 29 105002 (in Chinese)[张绍龙, 章征伟, 孙奇志, 刘伟, 赵小明, 张朝辉, 王贵林, 贾月松 2017 强激光与粒子束 29 105002]
[34]	Liao H D, Hu X J, Yang L B, Feng S P 1998 Chinese Journal of High Pressure Physics 12 174 (in Chinese)[廖海东, 胡熙静, 杨礼兵, 丰树平 1998 高压物理学报 12 174]
[35]	Steinberg D J, Cochran S G, Guinan M W 1980 J. Appl. Phys. 51 1498
[36]	Lee Y T, More R M 1984 Phys. Fluids 27 1273
[37]	Liu H F, Song H F, Zhang Q L, Zhang G M, Zhao Y H 2016 Matter and Radiation at Extremes 1 123

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Vol. 67, Issue 8 - 2018-04-20

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