Search

Article

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

One-dimensional integrated simulations of magnetized liner inertial fusion

Zhao Hai-Long Xiao Bo Wang Gang-Hua Wang Qiang Zhang Zheng-Wei Sun Qi-Zhi Deng Jian-Jun

Citation:

One-dimensional integrated simulations of magnetized liner inertial fusion

Zhao Hai-Long, Xiao Bo, Wang Gang-Hua, Wang Qiang, Zhang Zheng-Wei, Sun Qi-Zhi, Deng Jian-Jun
PDF
HTML
Get Citation
  • Magnetized liner inertial fusion (MagLIF) integrates the advantages of traditional magnetic confinement fusion with those of inertial confinement fusion, and thus has promising potentials because theoretically it can dramatically lower the difficulties in realizing the controlled fusion. For the systematic simulating of MagLIF, we build up an integrated one-dimensional (1D) model to describe the complex process, which includes the terms of magnetization, laser preheating, liner implosion, fusion reaction, end loss effect, and magnetic flux compression. According to this model we develop an integrated 1D code–MIST (magnetic implosion simulation tools) , and specifically we propose a simplified model to describe the end loss effect based on the flow bursting theory, so the code is able to consider two-dimensional effects within 1D calculations. We also present a specific expression of magnetic diffusion equation where the Nernst effect term is taken into consideration, which is very important if there exists a temperature gradient perpendicular to magnetic field lines. Such conditions are fully satisfied in the MagLIF process. We use experimental data of aluminum liner implosions to verify the magneto-hydrodynamic module of our code, those shots (0607 & 0523) are performed on FP-1 facility (2 MA, 7.2 μs), and results show good agreement with the calculated velocity of inner flyer or target surface and other measurements. Comparison with code LASNEX and HYDRA (used by Sandia Laboratory) is also made to assess the fusion module, and the results show that our calculations are physically self-consistent and roughly coincide with the results from LASNEX and HYDRA, a key difference appears at fuel temperature, and the factors that might cause this difference are discussed. With this integrated model and 1D code, our work would provide a powerful tool for the future experimental research of MagLIF.
      Corresponding author: Zhao Hai-Long, ifp.zhaohailong@qq.com
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No.11205145)
    [1]

    Sinars D B, Campbell E M, Cuneo M E, Jennings C A, Peterson K J, Sefkow A B 2016 J Fusion Energy 35 78Google Scholar

    [2]

    Ding B J, Bonoli P T, Tuccillo A, Goniche M, Kirov K, Li M, Li Y, Cesario R, Peysson Y, Ekedahl A, Amicucci L, Baek S, Faust I, Parker R, Shiraiwa S, Wallace G M, Cardinali A, Castaldo C, Ceccuzzi S, Mailloux J, Napoli F, Liu F, Wan B 2018 Nucl. Fusion 58 095003Google Scholar

    [3]

    Makwana K D, Keppens R, Lapenta G 2018 Phys. Plasmas 25 082904Google Scholar

    [4]

    Shimomura Y, Spears W 2004 IEEE Trans. Plasma Sci. 14 1369

    [5]

    Clark D S, Weber C R, Milovich J L, Pak A E, Casey D T, Hammel B A, Ho D D, Jones O S, Koning J M, Kritcher A L, Marinak M M, Masse L P, Munro D H, Patel M V, Patel P K, Robey H F, Schroeder C R, Sepke S M, Edwards M J 2019 Phys. Plasmas 26 050601Google Scholar

    [6]

    Perkins L J, Logan B G, Zimmerman G B, Werner C J 2013 Phys. Plasmas 20 072708Google Scholar

    [7]

    McCrory R L, Meyerhofer D D, Betti R, Craxton R S, Delettrez J A, Edgell D H, Glebov V Yu, Goncharov V N, Harding D R, Jacobs-Perkins D W, Knauer J P, Marshall F J, McKenty P W, Radha P B, Regan S P 2008 Phys. Plasmas 15 055503Google Scholar

    [8]

    Chen Y Y, Bao X H, Fu P, Gao G 2019 Chin. Phys. B 28 015201Google Scholar

    [9]

    Zhang Y K, Zhou R J, Hu L Q, Chen M W, Chao Y 2018 Chin. Phys. B 27 055206Google Scholar

    [10]

    Tikhonchuk V, Gu Y J, Klimo O, Limpouch J, Weber S 2019 Matter Radiat. Extremes 4 045402Google Scholar

    [11]

    薛全喜, 江少恩, 王哲斌, 王峰, 赵学庆, 易爱平, 丁永坤, 刘晶儒 2018 物理学报 24 094701Google Scholar

    Xue Q X, Jiang S E, Wang Z B, Wang F, Zhao X Q, Yi A P, Ding Y K, Liu J R 2018 Acta Phys. Sin. 24 094701Google Scholar

    [12]

    Wu F Y, Chu Y Y, Ramis R, Li Z H, Ma Y Y, Yang J L, Wang Z, Ye F, Huang Z C, Qi J M, Zhou L, Liang C, Chen S J, Ge Z Y, Yang X H, Wang S W 2018 Matter Radiat. Extremes 3 248Google Scholar

    [13]

    Ding N, Zhang Y, Xiao D L, Wu J M, Dai Z H, Yin L, Gao Z M, Sun S K, Xue C, Ning C, Shu X J, Wang J G 2016 Matter Radiat. Extremes 1 135Google Scholar

    [14]

    Slutz S A, Herrmann M C, Vesey R A, Sefkow A B, Sinars D B, Rovang D C, Peterson K J, Cuneo M E 2010 Phys. Plasmas 17 056303Google Scholar

    [15]

    Slutz S A, Vesey R A 2012 Phys. Rev. Lett. 108 025003Google Scholar

    [16]

    Sefkow A B, Slutz S A, Koning J M, Marinak M M, Peterson K J, Sinars D B, Vesey R A 2014 Phys. Plasmas 21 072711Google Scholar

    [17]

    Slutz S A 2018 Phys. Plasmas 25 082707Google Scholar

    [18]

    Gomez M R, Slutz S A, Sefkow A B, Sinars D B, Hahn K D, Hansen S B, Harding E C, Knapp P F, Schmit P F, Jennings C A, Awe T J, Geissel M, Rovang D C, Chandler G A, Cooper G W, Cuneo M E, Harvey-Thompson A J, Herrmann M C, Hess M H, Johns O, Lamppa D C, Martin M R, McBride R D, Peterson K J, Porter J L, Robertson G K, Rochau G A, Ruiz C L, Savage M E, Smith I C, Stygar W A, Vesey R A 2014 Phys. Rev. Lett. 113 155003Google Scholar

    [19]

    Awe T J, McBride R D, Jennings C A, Lamppa D C, Martin M R, Rovang D C, Slutz S A, Cuneo M E, Owen A C, Sinars D B, Tomlinson K, Gomez M R, Hansen S B, Herrmann M C, McKenney J L, Nakhleh C, Robertson G K, Rochau G A, Savage M E, Schroen D G, Stygar W A 2013 Phys. Rev. Lett. 111 235005Google Scholar

    [20]

    Seyler C E, Martin M R, Hamlin N D 2018 Phys. Plasmas 25 062711Google Scholar

    [21]

    赵海龙, 张恒第, 王刚华, 王强 2017 强激光与粒子束 29 072001

    Zhao H L, Zhang H D, Wang G H, Wang Q 2017 High Power Laser and Particle Beams 29 072001

    [22]

    Basko M M, Kemp A J, Meyer-ter-Vehn J 2000 Nucl. Fusion 40 59Google Scholar

    [23]

    Ramis R, Meyer-ter-Vehn J 2016 Comput. Phys. Commun. 203 226Google Scholar

    [24]

    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, and Seidel D B 2013 Phys. Rev. ST Accel. Beams 16 120401Google Scholar

    [25]

    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, and Maron Y 2017 Phys. Rev. ST Accel. Beams 20 010401Google Scholar

    [26]

    Slutz S A 2012 Sandia National Laboratory Report SAND2012-1734 C

    [27]

    Sefkow A B, Koning J M, Marinak M M, Nakhleh C W, Peterson K J, Sinars D B, Slutz S A, Vesey R A 2012 Sandia National Laboratory Report SAND2012-0876C

  • 图 1  MagLIF过程示意图(包含3个主要阶段)

    Figure 1.  Schematic of MagLIF process, including three main stages.

    图 2  端面效应简化模型示意图

    Figure 2.  Schematic of simplified model describing end loss effect.

    图 3  磁通压缩与扩散过程示意图

    Figure 3.  Schematic of magnetic flux compression and diffusion process.

    图 4  FP-1装置0523与0607发次实验驱动电流测量曲线

    Figure 4.  Experimental current curves of shot 0523 & 0607.

    图 5  MIST计算得到的自由面速度曲线与实验测量结果的比较 (a) 0607发次; (b) 0523发次

    Figure 5.  Comparison of inner surface velocity curves between the calculations and measurements: (a) 0607 shot; (b) 0523 shot.

    图 6  MIST程序计算得到的(a)监测点、(b)套筒内爆速度、(c)燃料温度, 以及(d)聚变产额等随时间的演化曲线

    Figure 6.  Calculated results of (a) grid position, (b) implosion velocity, (c) fuel temperature, and (d) fusion yield evolving with time.

    图 7  端面效应与Nernst效应影响下, 套筒内(a)燃料质量与(b)磁通随时间的演化

    Figure 7.  (a) Fuel mass and (b) magnetic flux evolving with time with consideration of end loss and Nernst effect.

    表 1  系数C0C7的取值

    Table 1.  Values of coefficient C0C7

    C0 /keV1/3C1/cm3·s–1C2/keV–1C3/keV–1
    6.661643.41×10–1615.136×10–375.189×10–3
    C4/keV–2C5/keV–2C6/keV–3C7/keV–3
    4.6064×10–313.5×10–3–0.10675×10–30.01366×10–3
    DownLoad: CSV

    表 2  MIST与LASNEX和HYDRA程序一维计算结果的对比

    Table 2.  Comparison of calculated results between MIST and LASNEX, HYDRA.

    程序名称燃料密度/g·cm–3燃料温度/keV磁场强度/103 T压缩比峰值压力/Gbar聚变产额/kJ
    LASNEX0.586—13233500
    MIST0.478.57162.7620
    HYDRA0.8—1.06—88—22225565
    MIST0.569.58173.3725
    DownLoad: CSV
  • [1]

    Sinars D B, Campbell E M, Cuneo M E, Jennings C A, Peterson K J, Sefkow A B 2016 J Fusion Energy 35 78Google Scholar

    [2]

    Ding B J, Bonoli P T, Tuccillo A, Goniche M, Kirov K, Li M, Li Y, Cesario R, Peysson Y, Ekedahl A, Amicucci L, Baek S, Faust I, Parker R, Shiraiwa S, Wallace G M, Cardinali A, Castaldo C, Ceccuzzi S, Mailloux J, Napoli F, Liu F, Wan B 2018 Nucl. Fusion 58 095003Google Scholar

    [3]

    Makwana K D, Keppens R, Lapenta G 2018 Phys. Plasmas 25 082904Google Scholar

    [4]

    Shimomura Y, Spears W 2004 IEEE Trans. Plasma Sci. 14 1369

    [5]

    Clark D S, Weber C R, Milovich J L, Pak A E, Casey D T, Hammel B A, Ho D D, Jones O S, Koning J M, Kritcher A L, Marinak M M, Masse L P, Munro D H, Patel M V, Patel P K, Robey H F, Schroeder C R, Sepke S M, Edwards M J 2019 Phys. Plasmas 26 050601Google Scholar

    [6]

    Perkins L J, Logan B G, Zimmerman G B, Werner C J 2013 Phys. Plasmas 20 072708Google Scholar

    [7]

    McCrory R L, Meyerhofer D D, Betti R, Craxton R S, Delettrez J A, Edgell D H, Glebov V Yu, Goncharov V N, Harding D R, Jacobs-Perkins D W, Knauer J P, Marshall F J, McKenty P W, Radha P B, Regan S P 2008 Phys. Plasmas 15 055503Google Scholar

    [8]

    Chen Y Y, Bao X H, Fu P, Gao G 2019 Chin. Phys. B 28 015201Google Scholar

    [9]

    Zhang Y K, Zhou R J, Hu L Q, Chen M W, Chao Y 2018 Chin. Phys. B 27 055206Google Scholar

    [10]

    Tikhonchuk V, Gu Y J, Klimo O, Limpouch J, Weber S 2019 Matter Radiat. Extremes 4 045402Google Scholar

    [11]

    薛全喜, 江少恩, 王哲斌, 王峰, 赵学庆, 易爱平, 丁永坤, 刘晶儒 2018 物理学报 24 094701Google Scholar

    Xue Q X, Jiang S E, Wang Z B, Wang F, Zhao X Q, Yi A P, Ding Y K, Liu J R 2018 Acta Phys. Sin. 24 094701Google Scholar

    [12]

    Wu F Y, Chu Y Y, Ramis R, Li Z H, Ma Y Y, Yang J L, Wang Z, Ye F, Huang Z C, Qi J M, Zhou L, Liang C, Chen S J, Ge Z Y, Yang X H, Wang S W 2018 Matter Radiat. Extremes 3 248Google Scholar

    [13]

    Ding N, Zhang Y, Xiao D L, Wu J M, Dai Z H, Yin L, Gao Z M, Sun S K, Xue C, Ning C, Shu X J, Wang J G 2016 Matter Radiat. Extremes 1 135Google Scholar

    [14]

    Slutz S A, Herrmann M C, Vesey R A, Sefkow A B, Sinars D B, Rovang D C, Peterson K J, Cuneo M E 2010 Phys. Plasmas 17 056303Google Scholar

    [15]

    Slutz S A, Vesey R A 2012 Phys. Rev. Lett. 108 025003Google Scholar

    [16]

    Sefkow A B, Slutz S A, Koning J M, Marinak M M, Peterson K J, Sinars D B, Vesey R A 2014 Phys. Plasmas 21 072711Google Scholar

    [17]

    Slutz S A 2018 Phys. Plasmas 25 082707Google Scholar

    [18]

    Gomez M R, Slutz S A, Sefkow A B, Sinars D B, Hahn K D, Hansen S B, Harding E C, Knapp P F, Schmit P F, Jennings C A, Awe T J, Geissel M, Rovang D C, Chandler G A, Cooper G W, Cuneo M E, Harvey-Thompson A J, Herrmann M C, Hess M H, Johns O, Lamppa D C, Martin M R, McBride R D, Peterson K J, Porter J L, Robertson G K, Rochau G A, Ruiz C L, Savage M E, Smith I C, Stygar W A, Vesey R A 2014 Phys. Rev. Lett. 113 155003Google Scholar

    [19]

    Awe T J, McBride R D, Jennings C A, Lamppa D C, Martin M R, Rovang D C, Slutz S A, Cuneo M E, Owen A C, Sinars D B, Tomlinson K, Gomez M R, Hansen S B, Herrmann M C, McKenney J L, Nakhleh C, Robertson G K, Rochau G A, Savage M E, Schroen D G, Stygar W A 2013 Phys. Rev. Lett. 111 235005Google Scholar

    [20]

    Seyler C E, Martin M R, Hamlin N D 2018 Phys. Plasmas 25 062711Google Scholar

    [21]

    赵海龙, 张恒第, 王刚华, 王强 2017 强激光与粒子束 29 072001

    Zhao H L, Zhang H D, Wang G H, Wang Q 2017 High Power Laser and Particle Beams 29 072001

    [22]

    Basko M M, Kemp A J, Meyer-ter-Vehn J 2000 Nucl. Fusion 40 59Google Scholar

    [23]

    Ramis R, Meyer-ter-Vehn J 2016 Comput. Phys. Commun. 203 226Google Scholar

    [24]

    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, and Seidel D B 2013 Phys. Rev. ST Accel. Beams 16 120401Google Scholar

    [25]

    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, and Maron Y 2017 Phys. Rev. ST Accel. Beams 20 010401Google Scholar

    [26]

    Slutz S A 2012 Sandia National Laboratory Report SAND2012-1734 C

    [27]

    Sefkow A B, Koning J M, Marinak M M, Nakhleh C W, Peterson K J, Sinars D B, Slutz S A, Vesey R A 2012 Sandia National Laboratory Report SAND2012-0876C

  • [1] Hao Bao-Long, Li Ying-Ying, Chen Wei, Hao Guang-Zhou, Gu Xiang, Sun Tian-Tian, Wang Yu-Min, Dong Jia-Qi, Yuan Bao-Shan, Peng Yuan-Kai, Shi Yue-Jiang, Xie Hua-Sheng, Liu Min-Sheng, ENN TEAM. Optimizing numerical simulation of beam ion loss due to toroidal field ripple on EXL-50U spherical torus. Acta Physica Sinica, 2023, 72(21): 215215. doi: 10.7498/aps.72.20230749
    [2] Ji Yang, Chen Mei-Ling, Huang Xun, Wu Yong-Zheng, Lan Bing. Simulation of random photon loss in boson sampling of different optical networks. Acta Physica Sinica, 2022, 71(19): 190301. doi: 10.7498/aps.71.20220331
    [3] Gong Zhen-Zhou, Wei Hao, Fan Si-Yuan, Sun Feng-Ju, Wu Han-Yu, Qiu Ai-Ci. Circuit simulation of current loss in magnetically insulated transmission line system in 15- MA Z-pinch driver. Acta Physica Sinica, 2022, 71(10): 105202. doi: 10.7498/aps.71.20212378
    [4] Zhao Shi-Hang, Zhang Yuan, Lü Si-Yuan, Cheng Shao-Bo, Zheng Chang-Lin, Wang Lu-Xia. Numerical simulation of strong coupling between silver nanorod and dielectric layer detected by electron energy loss spectrum. Acta Physica Sinica, 2022, 71(14): 147302. doi: 10.7498/aps.71.20220194
    [5] Zou Xiong, Qi Xiao-Bo, Zhang Tao-Xian, Gao Zhang-Fan, Huang Wei-Xing. Numerical simulation of filling and evacuating process of impurity gas in target capsule of inertial confinement fusion. Acta Physica Sinica, 2021, 70(7): 075207. doi: 10.7498/aps.70.20201491
    [6] Hao Bao-Long, Chen Wei, Li Guo-Qiang, Wang Xiao-Jing, Wang Zhao-Liang, Wu Bin, Zang Qing, Jie Yin-Xian, Lin Xiao-Dong, Gao Xiang, CFETR TEAM. Numerical simulation of synergistic effect of neoclassical tearing mode and toroidal field ripple on alpha particle loss in China Fusion Engineering Testing Reactor. Acta Physica Sinica, 2021, 70(11): 115201. doi: 10.7498/aps.70.20201972
    [7] Zhao Hai-Long, Xiao Bo, Wang Gang-Hua, Wang Qiang, Kan Ming-Xian, Duan Shu-Chao, Xie Long, Deng Jian-Jun. One-dimensional modeling and simulation of end loss effect in magnetized liner inertial fusion. Acta Physica Sinica, 2021, 70(6): 065202. doi: 10.7498/aps.70.20201587
    [8] Zhao Hai-Long, Wang Gang-Hua, Xiao Bo, Wang Qiang, Kan Ming-Xian, Duan Shu-Chao, Xie Long. Evolution characteristic of axial magnetic field and Nernst effect in magnetized liner inertial fusion. Acta Physica Sinica, 2021, 70(13): 135201. doi: 10.7498/aps.70.20202215
    [9] Li Zhi-Xuan, Yue Ming-Xin, Zhou Guan-Qun. Three-dimensional numerical simulation of electromagnetic diffusion problem and magnetization effects. Acta Physica Sinica, 2019, 68(3): 030201. doi: 10.7498/aps.68.20181567
    [10] Xu Ping, Yang Wei, Zhang Xu-Lin, Luo Tong-Zheng, Huang Yan-Yan. Two-dimensional distribution design of micro-prism for partial integrated light guide plate. Acta Physica Sinica, 2019, 68(3): 038502. doi: 10.7498/aps.68.20181684
    [11] Zhang Xu-Lin, Yang Wei, Luo Tong-Zheng, Huang Yan-Yan, Lei Lei, Li Gui-Jun, Xu Ping. Two-dimensional distribution expressions of micro-prism on bottom surface of partial integrated light guide plate. Acta Physica Sinica, 2019, 68(21): 218501. doi: 10.7498/aps.68.20190854
    [12] Luo Xu-Dong, Niu Sheng-Li, Zuo Ying-Hong. Diffusing loss effects of radiation belt energetic electrons caused by typical very low frequency electromagnetic wave. Acta Physica Sinica, 2015, 64(6): 069401. doi: 10.7498/aps.64.069401
    [13] Wang Shi-Ping, Zhang A-Man, Liu Yun-Long, Yao Xiong-Liang. Numerical simulation of bubbles coupled with an elastic membrane. Acta Physica Sinica, 2011, 60(5): 054702. doi: 10.7498/aps.60.054702
    [14] Yang Huan, Zhang Sui-Meng, Wu Xing-Ju. A theoretical study on final channel screening and exchange effects in large energy loss geometry. Acta Physica Sinica, 2009, 58(10): 6938-6945. doi: 10.7498/aps.58.6938
    [15] Zhao Zheng-Yu, Wang Xiang. Numerical simulation of the ionization effects of low-and high-altitude nuclear explosions. Acta Physica Sinica, 2007, 56(7): 4297-4304. doi: 10.7498/aps.56.4297
    [16] Zhang Xin-Lu, Wang Yue-Zhu, Li Li, Ju You-Lun. Fractional thermal loading and thermal lensing in end-pumped Tm,Ho:YLF lasers. Acta Physica Sinica, 2007, 56(4): 2196-2201. doi: 10.7498/aps.56.2196
    [17] Guan Jun, Li Jin-Ping, Cheng Guang-Hua, Chen Guo-Fu, Hou Xun. Experimental study on thermal lensing of end-pumped solid-state lasers. Acta Physica Sinica, 2004, 53(6): 1804-1809. doi: 10.7498/aps.53.1804
    [18] Liu Wen-Biao, Zhu Jian-Yang, Zhao Zheng. . Acta Physica Sinica, 2000, 49(3): 581-585. doi: 10.7498/aps.49.581
    [19] SONG YUAN-HONG, WANG YOU-NIAN, GOND YE. GRAZING SCATTERING AND ENERGY LOSS OF H+ MOVING NEAR A SOLID SURFACE. Acta Physica Sinica, 1999, 48(7): 1275-1281. doi: 10.7498/aps.48.1275
    [20] LI YUE-LIN, XU ZHI-ZHAN, CHEN SHI-SHENG. A NUMERICAL STUDY OF RADIATIVE LOSSES IN ALUMINUM PLASMAS. Acta Physica Sinica, 1990, 39(12): 1915-1920. doi: 10.7498/aps.39.1915
Metrics
  • Abstract views:  5536
  • PDF Downloads:  56
  • Cited By: 0
Publishing process
  • Received Date:  16 September 2019
  • Accepted Date:  08 November 2019
  • Published Online:  05 February 2020

/

返回文章
返回