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磁场对激光驱动Kelvin-Helmholtz不稳定性影响的二维数值研究

孙伟 安维明 仲佳勇

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磁场对激光驱动Kelvin-Helmholtz不稳定性影响的二维数值研究

孙伟, 安维明, 仲佳勇

Two-dimensional numerical study of effect of magnetic field on laser-driven Kelvin-Helmholtz instability

Sun Wei, An Wei-Ming, Zhong Jia-Yong
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  • Kelvin-Helmholtz不稳定性(KHI)是流体和等离子体的基本物理过程, 广泛存在于自然、天体物理以及高能量密度物理现象中. 本文提出一种新的实验方案产生磁化KHI. 利用开源的FLASH 模拟程序对激光驱动调制靶产生的KHI进行了二维的数值模拟, 考察和比较了KHI涡旋在毕尔曼自生磁场、外加磁场和无磁场情况下的演化. 模拟结果表明自生磁场在KHI演化过程中基本不会改变KHI 涡旋的形貌, 而平行于流体方向的外加磁场对剪切流有致稳作用, 主要稳定长波扰动. 该研究结果可为在高能量密度激光装置中开展强磁环境下KHI 实验提供理论指导.
    Kelvin-Helmholtz instability is the basic physical process of fluids and plasmas. It is widely present in natural, astrophysical, and high energy density physical phenomena. With the construction of strong laser facilities, the research on high energy density physics has gained new impetus. However, in recent years the magnetized Kelvin-Helmholtz instability was rarely studied experimentally. In this work, we propose a new experimental scheme, in which a long-pulsed nanosecond laser beam is generated by a domestic starlight III laser facility. The whole target consists of two parts: the upper part that is the CH modulation layer with lower density, and the lower part that is the Al modulation layer with higher density. The laser beam is injected from one side of the CH modulation layer and generates a CH plasma outflow at the back of the target. During the transmission of the CH plasma outflow, the Al modulation layer is radiated and ionized, which makes the Al modulation layer generate an Al plasma outflow. The interaction between the Al plasma outflow and the CH plasma outflow produces a velocity shear layer, and then Kelvin-Helmholtz instability will gradually form near the Al modulation layer. In this paper, the open-source FLASH simulation program is used to conduct a two-dimensional numerical simulation of the Kelvin-Helmholtz instability generated by the laser-driven modulation target. We use the FLASH code, which is an adaptive mesh refinement program, developed by the Flash Center at the University of Chicago, and is well-known in astrophysics and space geophysics, to create a reference to the magnetohydrodynamic solution in our experiment. At present, this code introduces a complete high-energy-density physical modeling module, which is especially suitable for simulating intense laser ablation experiments. The equation of state and opacity tables of targets are based on the IONMIX4 database. The evolution of Kelvin-Helmholtz vortices, separately, in the Biermann self-generated magnetic field, the external magnetic field, and no magnetic field are investigated and compared with each other. It is found that the self-generated magnetic field hardly changes the morphology of the Kelvin-Helmholtz vortex during the evolution of Kelvin-Helmholtz instability. The external magnetic field parallel to the fluid direction can stabilize the shear flow. The magnetic field mainly stabilizes the long wave disturbance. The study results in this work can provide theoretical guidance for the next step of the Kelvin-Helmholtz experiment under a strong magnetic environment in the high energy density laser facility.
      通信作者: 仲佳勇, jyzhong@bnu.edu.cn
    • 基金项目: 国家自然科学基金委员会-中国工程物理研究院联合基金 (批准号: U1930108)、科学挑战计划 (批准号: TZ2016005) 和中国科学院战略重点研究计划(批准号: XDA25030700)资助的课题
      Corresponding author: Zhong Jia-Yong, jyzhong@bnu.edu.cn
    • Funds: Project supported by the Joint Fund of the National Natural Science Foundation of China and the China Academy of Engineering Physics (Grant No. U1930108), the Science Challenge Project, China (Grant No.TZ2016005), and the Strategic Priority Research Program of Chinese Academy of Sciences (Grant No. XDA25030700)
    [1]

    Li X, Zhang J, Yang S, Hou Y, Erdelyi R 2018 Sci. Rep. 8 8136Google Scholar

    [2]

    Steinbusch B, Gibbon P, Sydora R D 2016 Phys. Plasmas 23 052119Google Scholar

    [3]

    Price D J, Rosswog S 2006 Science 312 719Google Scholar

    [4]

    Kiuchi K, Cerdá-Durán P, Kyutoku K, Sekiguchi Y, Shibata M 2015 Phys. Rev. D 92 124034Google Scholar

    [5]

    Foullon C, Verwichte E, Nakariakov V M, Nykyri K, Farrugia C J 2011 Astrophys. J. Lett. 729 L8Google Scholar

    [6]

    Li X, Narayan R 2004 Astrophys. J. 601 414Google Scholar

    [7]

    Yuan D, Shen Y, Liu Y, Li H, Feng X, Keppens R 2019 Astrophys. J. Lett. 884 L51Google Scholar

    [8]

    Ershkovich A I 1980 Space Sci. Rev. 25 3Google Scholar

    [9]

    Dittrich T R, Hammel B A, Keane C J, McEachern R, Turner R E, Haan S W, Suter L J 1994 Phys. Rev. Lett. 73 2324Google Scholar

    [10]

    Hammel B A, Haan S W, Clark D S, Edwards M J, Langer S H, Marinak M M, Patel M V, Salmonson J D, Scott H A 2010 High Energy Dens. Phys. 6 171Google Scholar

    [11]

    Clark D S, Haan S W, Cook A W, Edwards M J, Hammel B A, Koning J M, Marinak M M 2011 Phys. Plasmas 18 082701Google Scholar

    [12]

    Zhou Y, Remington B A, Robey H F, Cook A W, Glendinning S G, Dimits A, Buckingham A C, Zimmerman G B, Burke E W, Peyser T A, Cabot W, Eliason D 2003 Phys. Plasmas 10 1883Google Scholar

    [13]

    Zhou Y 2017 Phys. Rep. 720-722 1Google Scholar

    [14]

    Chandrasekhar S 1961 Hydrodynamic and Hydromagnetic Stability (Oxford: Clarendon Press) pp481−512

    [15]

    范征锋, 叶文华, 孙彦乾, 郑炳松, 李英骏, 王立锋 2009 物理学报 58 6381Google Scholar

    Fan Z F, Ye W H, Sun Y Q, Zheng B S, Li Y J, Wang L F 2009 Acta Phys. Sin. 58 6381Google Scholar

    [16]

    范征锋, 叶文华, 李英骏, 王立锋 2009 物理学报 58 4787Google Scholar

    Fan Z F, Ye W H, Li Y J, Wang L F 2009 Acta Phys. Sin. 58 4787Google Scholar

    [17]

    Mak J, Griffiths S D, Hughes D W 2017 Phys. Rev. Fluid 2 113701Google Scholar

    [18]

    Liu Y, Chen Z H, Zhang H H, Lin Z Y 2018 Phys. Fluids 30 044102Google Scholar

    [19]

    Harding E C, Hansen J F, Hurricane O A, Drake R P, Robey H F, Kuranz C, Gillespie R S 2009 Phys. Rev. Lett. 103 045005Google Scholar

    [20]

    Wan W C, Malamud G, Shimony A, Stefano C A, Trantham M R, Klein S R, Drake R P 2015 Phys. Rev. Lett. 115 145001Google Scholar

    [21]

    Wan W C, Malamud G, Shimony A, Di Stefano C A, Trantham M R, Klein S R, Kuranz C C 2017 Phys. Plasmas 24 055705Google Scholar

    [22]

    Sun W, Zhong J, Zhang S, Tong B W, Wang L F, Zhao K G, Liu J Y, Han B, Zhu B J, Yuan D W, Yuan X X, Zhang Z, Li Y T, Zhang Q, Peng J M, Wang J Z, Ping Y L, Xing C Q, Wei H G, Liang G Y, Xie Z Y, Wang C, Zhao G, Zhang J 2019 High Energy Dens. Phys. 31 47Google Scholar

    [23]

    Fryxell B, Olson K, Ricker P, Timmes F X, Zingale M, Lamb D Q, Macneice P, Rosner R, Truran J W, Tufo H M 2000 Astrophys. J. Suppl. Ser. 131 273Google Scholar

    [24]

    Macfarlane J J 1989 Comput. Phys. Commun. 56 259Google Scholar

    [25]

    Rutter E M, Grosskopf M J, Malamud G, Kuranz C C, Harding E C, Keiter P A, Drake R P 2013 High Energy Dens. Phys. 9 148Google Scholar

    [26]

    Farmer W A, Koning J M, Strozzi D J, Hinkel D E, Berzak Hopkins L F, Jones O S, Rosen M D 2017 Phys. Plasmas 24 052703Google Scholar

    [27]

    Woolsey N C, Courtois C, Dendy R O 2004 Plasma Phys. Controlled Fusion 46 B397Google Scholar

  • 图 1  利用激光驱动调制靶产生KHI的实验方案(虚线框是模拟区域)

    Fig. 1.  Experimental scheme for KHI using the laser-driven modulation targets. The dashed line box is the simulation domain.

    图 2  无磁场时不同时刻的电子密度分布图 (a) 20 ns; (b) 40 ns; (c) 60 ns; (d) 80 ns

    Fig. 2.  Snapshots of the electron density distribution at different times without magnetic field: (a) 20 ns; (b) 40 ns; (c) 60 ns; (d) 80 ns.

    图 3  x方向外加0.4 T磁场时不同时刻的电子密度分布图 (a) 0 ns; (b) 40 ns; (c) 80 ns; (d) 120 ns

    Fig. 3.  Snapshots of the electron density distribution at different times with 0.4 T in x direction: (a) 0 ns; (b) 40 ns; (c) 80 ns; (d) 120 ns.

    图 4  (a) 考虑毕尔曼自生磁场, 在120 ns时毕尔曼自生磁场强度的分布情况; (b)忽略毕尔曼自生磁场, 在120 ns时外加磁场在模拟平面的分布情况

    Fig. 4.  (a) Considering the Biermann self-generated magnetic field, the distribution of the Bierman self-generated magnetic field strength at 120 ns; (b) ignoring the Bierman self-generated magnetic field, the distribution of the applied magnetic field in the simulated plane at 120 ns.

    图 5  x方向外加0.4 T磁场时不同时刻外加磁场的分布情况 (a)静态参考图像(0 ns); (b) 40 ns的磁场分布图像; (c) 80 ns的磁场分布图像; (d) 120 ns的磁场分布图像

    Fig. 5.  Snapshots of the magnetic field distribution at different delay times with 0.4 T in x direction: (a) Reference image (0 ns); (b) 40 ns. (c) 80 ns; (d) 120 ns

    图 6  (a) 120 ns时磁压力的分布情况; (b) 120 ns的磁张力的分布情况

    Fig. 6.  (a) Distribution of magnetic pressure at 120 ns; (b) distribution of magnetic tension at 120 ns.

    图 7  (a) 有无外加磁场的情况下, KHI涡旋的生长情况; (b) x方向外加0.4 T磁场, 初始扰动波长不同时, KHI涡旋的生长情况

    Fig. 7.  (a) Growth of the KHI vortex with or without an external magnetic field; (b) the growth of the KHI vortex when a 0.4 T magnetic field is applied in the x direction and the initial disturbance wavelength is different.

  • [1]

    Li X, Zhang J, Yang S, Hou Y, Erdelyi R 2018 Sci. Rep. 8 8136Google Scholar

    [2]

    Steinbusch B, Gibbon P, Sydora R D 2016 Phys. Plasmas 23 052119Google Scholar

    [3]

    Price D J, Rosswog S 2006 Science 312 719Google Scholar

    [4]

    Kiuchi K, Cerdá-Durán P, Kyutoku K, Sekiguchi Y, Shibata M 2015 Phys. Rev. D 92 124034Google Scholar

    [5]

    Foullon C, Verwichte E, Nakariakov V M, Nykyri K, Farrugia C J 2011 Astrophys. J. Lett. 729 L8Google Scholar

    [6]

    Li X, Narayan R 2004 Astrophys. J. 601 414Google Scholar

    [7]

    Yuan D, Shen Y, Liu Y, Li H, Feng X, Keppens R 2019 Astrophys. J. Lett. 884 L51Google Scholar

    [8]

    Ershkovich A I 1980 Space Sci. Rev. 25 3Google Scholar

    [9]

    Dittrich T R, Hammel B A, Keane C J, McEachern R, Turner R E, Haan S W, Suter L J 1994 Phys. Rev. Lett. 73 2324Google Scholar

    [10]

    Hammel B A, Haan S W, Clark D S, Edwards M J, Langer S H, Marinak M M, Patel M V, Salmonson J D, Scott H A 2010 High Energy Dens. Phys. 6 171Google Scholar

    [11]

    Clark D S, Haan S W, Cook A W, Edwards M J, Hammel B A, Koning J M, Marinak M M 2011 Phys. Plasmas 18 082701Google Scholar

    [12]

    Zhou Y, Remington B A, Robey H F, Cook A W, Glendinning S G, Dimits A, Buckingham A C, Zimmerman G B, Burke E W, Peyser T A, Cabot W, Eliason D 2003 Phys. Plasmas 10 1883Google Scholar

    [13]

    Zhou Y 2017 Phys. Rep. 720-722 1Google Scholar

    [14]

    Chandrasekhar S 1961 Hydrodynamic and Hydromagnetic Stability (Oxford: Clarendon Press) pp481−512

    [15]

    范征锋, 叶文华, 孙彦乾, 郑炳松, 李英骏, 王立锋 2009 物理学报 58 6381Google Scholar

    Fan Z F, Ye W H, Sun Y Q, Zheng B S, Li Y J, Wang L F 2009 Acta Phys. Sin. 58 6381Google Scholar

    [16]

    范征锋, 叶文华, 李英骏, 王立锋 2009 物理学报 58 4787Google Scholar

    Fan Z F, Ye W H, Li Y J, Wang L F 2009 Acta Phys. Sin. 58 4787Google Scholar

    [17]

    Mak J, Griffiths S D, Hughes D W 2017 Phys. Rev. Fluid 2 113701Google Scholar

    [18]

    Liu Y, Chen Z H, Zhang H H, Lin Z Y 2018 Phys. Fluids 30 044102Google Scholar

    [19]

    Harding E C, Hansen J F, Hurricane O A, Drake R P, Robey H F, Kuranz C, Gillespie R S 2009 Phys. Rev. Lett. 103 045005Google Scholar

    [20]

    Wan W C, Malamud G, Shimony A, Stefano C A, Trantham M R, Klein S R, Drake R P 2015 Phys. Rev. Lett. 115 145001Google Scholar

    [21]

    Wan W C, Malamud G, Shimony A, Di Stefano C A, Trantham M R, Klein S R, Kuranz C C 2017 Phys. Plasmas 24 055705Google Scholar

    [22]

    Sun W, Zhong J, Zhang S, Tong B W, Wang L F, Zhao K G, Liu J Y, Han B, Zhu B J, Yuan D W, Yuan X X, Zhang Z, Li Y T, Zhang Q, Peng J M, Wang J Z, Ping Y L, Xing C Q, Wei H G, Liang G Y, Xie Z Y, Wang C, Zhao G, Zhang J 2019 High Energy Dens. Phys. 31 47Google Scholar

    [23]

    Fryxell B, Olson K, Ricker P, Timmes F X, Zingale M, Lamb D Q, Macneice P, Rosner R, Truran J W, Tufo H M 2000 Astrophys. J. Suppl. Ser. 131 273Google Scholar

    [24]

    Macfarlane J J 1989 Comput. Phys. Commun. 56 259Google Scholar

    [25]

    Rutter E M, Grosskopf M J, Malamud G, Kuranz C C, Harding E C, Keiter P A, Drake R P 2013 High Energy Dens. Phys. 9 148Google Scholar

    [26]

    Farmer W A, Koning J M, Strozzi D J, Hinkel D E, Berzak Hopkins L F, Jones O S, Rosen M D 2017 Phys. Plasmas 24 052703Google Scholar

    [27]

    Woolsey N C, Courtois C, Dendy R O 2004 Plasma Phys. Controlled Fusion 46 B397Google Scholar

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出版历程
  • 收稿日期:  2020-07-21
  • 修回日期:  2020-08-13
  • 上网日期:  2020-11-27
  • 刊出日期:  2020-12-20

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