基于MULTI2D-Z程序的Z箍缩动态黑腔形成过程模拟

陈忠旺; 宁成

doi:10.7498/aps.66.125202

摘要

对辐射流体力学程序MULTI-2D进行改造，增加磁场演化方程程序模块，自洽地在运动方程模块中增加洛伦兹力，在能量方程模块中增加欧姆加热，将它改造成辐射磁流体力学程序MULTI2D-Z.验证了新增磁场程序模块的可靠性，并发现温度和密度的增大会抑制磁场的扩散，负径向速度梯度的流体对流也会抑制磁场的扩散.利用改造好的MULTI2D-Z程序模拟了峰值为8 MA的脉冲电流驱动的钨丝阵Z箍缩动态黑腔形成过程.得到了X光功率（约30 TW）和能量（约300 kJ）、泡沫辐射温度（约120 eV）、箍缩轨迹等模拟结果.在动态黑腔形成过程中，磁场主要分布在钨主体等离子体中；辐射向内传播，烧蚀泡沫柱而使它膨胀；辐射热波在被撞击的泡沫柱中传播，其传播速度比物质温度传播得快，当辐射热波传播到中心轴时泡沫柱中的辐射场变得比较均匀，并且除了冲击波处外辐射温度与物质温度基本上没有分离.这些模拟结果可增强人们对磁场扩散和对流规律以及动态黑腔形成机制的理解，同时表明了MULTI2D-Z程序可成为Z箍缩及其应用的新的程序模拟工具.

关键词:

Abstract

The radiation hydrodynamics code MULTI-2D, which was developed by Ramis et al. in 2009 (2009 Comput. Phys. Commun. 180 977) and adopted the single temperature fluid and unstructured lagrangian mesh, is modified into a radiation magnetohydrodynamics code MULTI2D-Z by adding the program module of evolution equation of magnetic field, and self-consistently considering the Lorentz force in the module of motion equation and the Ohmic heating in the module of energy equation. The newly developed module for magnetic field was validated to be reliable. The module is used to study the magnetic field diffusion process, and it is found that the diffusion is weakened due to the increasing of plasma temperature and density and the fluid convection, in which there is minus grads of velocity in radial direction. The new code MULTI2D-Z is used to simulate the formation process of dynamic hohlraum driven by tungsten wire-array Z-pinch at an 8 MA current level. The obtained results are that X-ray power and energy are, respectively, ～30 TW and ～300 kJ, radiation temperature in foam is ～120 eV, and the implosion trajectory of wire-array is also obtained. The calculated results reveal that the magnetic field is mainly distributed in the outside of tungsten plasma during the hohlraum formation. The foam expands due to the radiation heating from the shock wave created by the collision between wire-array plasma and the foam. The thermal radiation wave, which is characterized by radiation temperature, spreads towards the central axis faster than the plasma temperature. When the thermal radiation wave spreads to the central axis, the radiation temperature becomes comparatively uniform in space, and is almost equal to the plasma temperature except at the place of the shock wave. These results help the people to better understand the magnetic field diffusion and convection in Z-pinch, as well as the formation mechanism of dynamic hohlraum driven by wire-array Z-pinch. It is also indicated that the newly developed code MULTI2D-Z can be considered as a new tool for simulating Z-pinch and its applications, such as inertial confinement fusion and magnetically accelerated flyer plates.

Keywords:

作者及机构信息

陈忠旺,
宁成

1.
北京应用物理与计算数学研究所, 北京 100088

通信作者: 宁成, ning_cheng@iapcm.ac.cn

基金项目: 国家自然科学基金（批准号：11675025）和国家自然科学基金重点项目（批准号：11135007）资助的课题.

Authors and contacts

1.
Institute of Applied Physics and Computational Mathematics, Beijing 100088, China

Corresponding author: Ning Cheng, ning_cheng@iapcm.ac.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11675025) and the Key Program of the National Natural Science Foundation of China (Grant No. 11135007).

参考文献

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[16]	Ruiz C L, Cooper G W, Slutz S A, Bailey J E, Chandler G A, Nash T J, Mehlhorn T A, Leeper R J, Fehl D, Nelson A J, Franklin J, Ziegler L 2004 Phys. Rev. Lett. 93 015001
[17]	Zimmerman G B, Kruer W B 1975 Comments Plasma Phys. Control. Fusion 2 51
[18]	Slutz S A, Peterson K J, Vesey R A, Lemke R W, Bailey J E, Varnum W, Ruiz C L, Cooper G W, Chandler G A, Rochau G A, Mehlhorn T A 2006 Phys. Plasmas 13 102701
[19]	Meng S J, Huang Z C, Ning J M, Hu Q Y, Ye F, Qin Y, Xu Z P, Xu R K 2016 Acta Phys. Sin. 65 075201 (in Chinese) [蒙世坚, 黄展常, 甯家敏, 胡青元, 叶繁, 秦义, 许泽平, 徐荣昆 2016 65 075201]
[20]	Xiao D L, Sun S K, Xue C, Zhang Y, Ding N 2015 Acta Phys. Sin. 64 235203 (in Chinese) [肖德龙, 孙顺凯, 薛创, 张扬, 丁宁 2015 64 235203]
[21]	Xiao D L, Ding N, Ye F, Ning J M, Hu Q Y, Chen F X, Qin Y, Xu R K, Li Z H, Sun S K 2014 Phys. Plasmas 21 042704
[22]	Ramis R, Ramirez J, Meyer-ter-Vehn J 1988 Comput. Phys. Commun. 49 475
[23]	Ramis R, Meyer-ter-Vehn J, Ramirez J 2009 Comput. Phys. Commun. 180 977
[24]	Ramis R, Meyer-ter-Vehn J, Ramirez J 2016 Comput. Phys. Commun. 203 226
[25]	Liberman M A, De Groot J S, Toor A 2003 Physics of High-Density Z-Pinch Plasmas (Beijing: National Defence Industry Press) (in Chinese) [Liberman M A, De Groot J S, Toor A 著 (孙承纬译) 2003 高密度 Z 箍缩等离子体物理学 (北京: 国防工业出版社)
[26]	Ning C, Yang Z H, Ding N 2003 Acta Phys. Sin. 52 415 (in Chinese) [宁成, 杨震华, 丁宁 2003 52 415]
[27]	Murakami M, Meyer-ter-Vehn J, Ramis R 1990 J. X-Ray Sci. Technol. 2 127
[28]	Salamann D 1998 Atom Physics in Hot Plasmas (New York: Oxford University Press) p28
[29]	Kemp A J, Meyer-ter-Vehn J 1998 Nucl. Instrum. Meth. A 415 674
[30]	More R, Warren K H, Yong D A, Zimmermann G 1988 Phys. Fluids 31 3059

施引文献

[1]	Matzen M K 1997 Phys. Plasmas 4 1519
[2]	Qiu A C, Kuai B, Wang L P, Wu G, Cong P T 2008 High Power Laser and Particle Beams 20 1761 (in Chinese) [邱爱慈, 蒯斌, 王亮平, 吴刚, 丛培天 2008 强激光与粒子束 20 1761]
[3]	Huang X B, Zhou S T, Dan J K, Ren X D, Wang K L, Zhang S Q, Li J, Xu Q, Cai H C, Duan S C, Ouyang K, Chen G H, Ji C, Wei B, Feng S P, Wang M, Xie W P, Deng J J, Zhou X W, Yang Y 2015 Phys. Plasmas 22 072707
[4]	Dan J K, Ren X D, Huang X B, Zhang S Q, Zhou S T, Duan S C, Ouyang K, Cai H C, Wei B, Ji C, He A, Xia M H, Feng S P, Wang M, Xie W P 2013 Acta Phys. Sin. 62 245201 (in Chinese) [但加坤, 任晓东, 黄显宾, 张思群, 周少彤, 段书超, 欧阳凯, 蔡红春, 卫兵, 计策, 何安, 夏明鹤, 丰树平, 王勐, 谢卫平 2013 62 245201]
[5]	Jiang S Q, Ning J M, Chen F X, Ye F, Xue F B, Li L B, Yang J L, Chen J C, Zhou L, Qin Y, Li Z H, Xu R K, Xu Z P 2013 Acta Phys. Sin. 62 155203 (in Chinese) [蒋树庆, 甯家敏, 陈法新, 叶繁, 薛飞彪, 李林波, 杨建伦, 陈进川, 周林, 秦义, 李正宏, 徐荣昆, 许泽平 2013 62 155203]
[6]	Deeney C, Nash T J, Spielman R B, Seaman J F, Chandler G C, Struve K W, Porter J L, Stygar W A, McGum J S, Jobe D O, Gilliland T L, Torres J A, Vargas M F, Ruggles L E, Breeze S, Mock R C, Douglas M R, Fehl D L, McDaniel D H, Matzen M K, Peterson D L, MatuskaW, Roderick N F, MacFarlane J J 1997 Phys. Rev. E 56 5945
[7]	Spielman R B, Deeney C, Chandler G A, Douglas M R, Fehl D L, Matzen M K, McDaniel D H, Nash T J, PorterJ L, Sanford T W L, Seaman J F, Stygar W A, Struve K W, Breeze S P, McGurn J S, Torres J A, Zagar D M, Gilliland T L, Jobe D O, McKenney J L, Mock R C, Vargas M, Wangoner T, Peterson D L 1998 Phys. Plasmas 5 2105
[8]	Stygar W A, Ives H C, Fehl D L, Fehl D L, Cuneo M E, Mazarakis M G, Bailey J E, Bennett G R, Bliss D E, Chandler G A, Leeper R J, Matzen M K, McDaniel D H, McGurn J S, McKenney J L, Mix L P, Muron D J, Porter J L, Ramirez J S, Ruggles L E, Seamen J F, Simpson W W, Speas C S, Spielman R B, Struve K W 2004 Phys. Rev. E 69 046403
[9]	Lebedev S V, Mitchell I H, Aliaga-Rossel R, Bland S N, Chittenden J P, Dangor A E, Haines M G 1998 Phys. Rev. Lett. 81 4152
[10]	Harvey-Thompson A J, Lebedev SV, Patankar S, Bland S N, Burdiak G, Chittenden J P, Colaitis A, de Grouchy P, Doyle H W, Hall G N, Khoory E, Hohenberger M, Pickworth L, Suzuki-Vidal F, Smith R A, Skidmore J, Suttle L, Swadling G F 2012 Phys. Rev. Lett. 108 145002
[11]	Swadling G F, Lebedev S V, Harvey-Thompson A J, Rozmus W, Burdiak G, Suttle L, Patankar S, Smith R A, Bennett M, Hall G N, Suzuki-Vidal F, Bland S, Yuan J 2015 Phys. Plasmas 22 072706
[12]	Leeper R J, Alberts T E, Asay J R, Baca P M, Baker K L, Breeze S P, Chandler G A, Cook D L, Cooper G W, Deeney C, Derzon M S, Douglas M R, Fehl D L, Gilliland T, Hebron D E, Hurst M J, Jobe D O, Kellogg J W, Lash J S, Lazier S E, Matzen M K, McDaniel D H, McGurn J S, Mehlhorn T A, Moats A R, Mock R C, Muron D J, Nash T J, Olson R E, Porter J L, Quintenz J P, Reyes P V, Ruggles L E, Ruiz C L, Sanford T W L, Schmidlapp F A, Seamen J F, Spielman R B, Stark M A, Struve K W, Stygar W A, Tibbetts-Russell D R, Torres J A, Vargas M, Wagoner T C, Wakefield C, Hammer J H, Ryutov D D, Tabak M, Wilks S C, Bowers R L, McLenithan K D, Peterson D L 1999 Nucl. Fusion 39 1283
[13]	Ning C, Feng Z X, Xue C 2014 Acta Phys. Sin. 63 125208 (in Chinese) [宁成, 丰志兴, 薛创 2014 63 125208]
[14]	Bailey J E, Chandler G A, Slutz S A, Bennett G R, Cooper G, Lash J S, Lazier S, Lemke R, Nash T J, Nielsen D S, Moore T C, Ruiz C L, Schroen D G, Smelser R, Torres J, Vese y R A 2002 Phys. Rev. Lett. 89 095004
[15]	Rochau G A, Bailey J E, Maron Y, Chandler G A, Dunham G S, Fisher D V, Fisher V I, Lemke R W, MacFarlane J J, Peterson K J, Schroen D G, Slutz S A, Stambulchik E 2008 Phys. Rev. Lett. 100 125004
[16]	Ruiz C L, Cooper G W, Slutz S A, Bailey J E, Chandler G A, Nash T J, Mehlhorn T A, Leeper R J, Fehl D, Nelson A J, Franklin J, Ziegler L 2004 Phys. Rev. Lett. 93 015001
[17]	Zimmerman G B, Kruer W B 1975 Comments Plasma Phys. Control. Fusion 2 51
[18]	Slutz S A, Peterson K J, Vesey R A, Lemke R W, Bailey J E, Varnum W, Ruiz C L, Cooper G W, Chandler G A, Rochau G A, Mehlhorn T A 2006 Phys. Plasmas 13 102701
[19]	Meng S J, Huang Z C, Ning J M, Hu Q Y, Ye F, Qin Y, Xu Z P, Xu R K 2016 Acta Phys. Sin. 65 075201 (in Chinese) [蒙世坚, 黄展常, 甯家敏, 胡青元, 叶繁, 秦义, 许泽平, 徐荣昆 2016 65 075201]
[20]	Xiao D L, Sun S K, Xue C, Zhang Y, Ding N 2015 Acta Phys. Sin. 64 235203 (in Chinese) [肖德龙, 孙顺凯, 薛创, 张扬, 丁宁 2015 64 235203]
[21]	Xiao D L, Ding N, Ye F, Ning J M, Hu Q Y, Chen F X, Qin Y, Xu R K, Li Z H, Sun S K 2014 Phys. Plasmas 21 042704
[22]	Ramis R, Ramirez J, Meyer-ter-Vehn J 1988 Comput. Phys. Commun. 49 475
[23]	Ramis R, Meyer-ter-Vehn J, Ramirez J 2009 Comput. Phys. Commun. 180 977
[24]	Ramis R, Meyer-ter-Vehn J, Ramirez J 2016 Comput. Phys. Commun. 203 226
[25]	Liberman M A, De Groot J S, Toor A 2003 Physics of High-Density Z-Pinch Plasmas (Beijing: National Defence Industry Press) (in Chinese) [Liberman M A, De Groot J S, Toor A 著 (孙承纬译) 2003 高密度 Z 箍缩等离子体物理学 (北京: 国防工业出版社)
[26]	Ning C, Yang Z H, Ding N 2003 Acta Phys. Sin. 52 415 (in Chinese) [宁成, 杨震华, 丁宁 2003 52 415]
[27]	Murakami M, Meyer-ter-Vehn J, Ramis R 1990 J. X-Ray Sci. Technol. 2 127
[28]	Salamann D 1998 Atom Physics in Hot Plasmas (New York: Oxford University Press) p28
[29]	Kemp A J, Meyer-ter-Vehn J 1998 Nucl. Instrum. Meth. A 415 674
[30]	More R, Warren K H, Yong D A, Zimmermann G 1988 Phys. Fluids 31 3059

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