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轴向磁场是磁化套筒惯性聚变(magnetized liner inertial fusion, MagLIF)有别于其他惯性约束聚变构型的主要标志之一. 本文在建立集成化物理模型并编写一维模拟程序的基础上, 通过对ZR装置驱动能力下典型MagLIF负载参数的模拟, 系统研究并获得MagLIF各个阶段轴向磁场演化与分布特征, 发现预加热引起的压力不平衡导致燃料中磁通保有量并未呈现随时间单调递减的关系, 而是反复震荡甚至出现局部短时间内反而增加的演化曲线. 通过在磁场演化方程中引入控制项来讨论Nernst效应的影响, 计算结果表明随着初始磁场强度降低(30, 20, 10 T), Nernst效应越发明显, 磁通损失增大(28%, 44%, 73%), α粒子能量沉积比例则大幅降低(44%, 27%, 4%), 因此初始磁场强度不宜太低; 预加热结束后应使燃料中温度径向分布尽量均匀、平缓, 有助于减少Nernst效应的影响. 所取得的研究结果有助于加深对MagLIF中磁通压缩和磁扩散过程的物理图像认知和理解, 对未来实验负载参数设计也有重要的指导作用.Axial magnetic field is one of the main parameters of magnetized liner inertial fusion (MagLIF), which is greatly different from other traditional inertial confinement fusion configurations. The introduce of axial magnetic field dramatically increases energy deposit efficiency of alpha particles, when initial Bz increases from 0 to 30 T, the ratio of deposited alpha energy rises from 7% to 53%. In the MagLIF process, the evolvement of magnetic flux in fuel can be roughly divided into three main stages: undisturbed, oscillation, and equilibrium. The distributions and evolution characteristic of axial magnetic field are both determined by the liner conductivity, fuel conductivity, and the fluid dynamics. The pressure imbalance between fuel and liner, caused by laser injection, is the source of fluid oscillation, which is an intrinsic disadvantage of laser preheating method. This fluid oscillation does not lead the magnetic flux to decrease monotonically in the fuel during implosion process, but oscillate repeatedly, even increase in a short time. Nernst effect plays a negative role in MagLIF process. As initial axial magnetic field decreases from 30 to 20 to 10 T, the Nernst effect causes magnetic flux loss to increase from 28% to 44% to 73% correspondingly, and the deposited alpha energy ratio drops from 44% to 27% to 4% respectively. So the initial magnetic field is supposed to be moderately high. The radial distribution of temperature in fuel should be as uniform as possible after preheating, which is helpful in reducing the influence of Nernst effect. Compared with Nernst effect, the end loss effect is much responsible for rapid drawdown of fusion yield. A large number of physical images are acquired and summarized through this work, which are helpful in understanding the process of magnetic flux compression and diffusion in MagLIF process. The simulation can act as a powerful tool and the simulation results can serve as a useful guidance for the future experimental designs.
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Keywords:
- MagLIF /
- axial magnetic field /
- Nernst effect
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图 1 磁通压缩与扩散过程示意图(含Nernst效应)
Fig. 1. Schematic of magnetic flux compression and diffusion process (including Nernst effect).
图 2 ZR装置95 kV充电电压下驱动电流随时间演化曲线[13]
Fig. 2. Driving current from ZR facility with charging voltage 95 kV.
图 3 燃料中不同位置磁雷诺数随时间演化曲线
Fig. 3. Magnetic Reynolds numbers at different positions in fuel.
图 4 套筒内轴向磁通保有量随时间演化曲线(归一化)
Fig. 4. Evolvement curve of remained magnetic flux in fuel (unified).
图 5 MIST计算得到的64 ns时 (a) 密度和(b) 轴向磁场分布曲线
Fig. 5. Distributions of (a) density and (b) axial magnetic field at 64 ns calculated by MIST.
图 6 MIST计算得到的80 ns时 (a) 密度和(b) 轴向磁场分布曲线
Fig. 6. Distributions of (a) density and (b) axial magnetic field at 80 ns calculated by MIST.
图 7 MIST计算得到的86.6 ns时 (a) 温度和(b) 压强分布曲线
Fig. 7. Distributions of (a) temperature and (b) pressure at 86.6 ns calculated by MIST.
图 8 MIST计算得到的94 ns时 (a) 温度和(b) 轴向磁场分布曲线
Fig. 8. Distributions of (a) temperature and (b) axial magnetic field at 94 ns calculated by MIST.
图 9 MIST计算得到的101 ns时 (a) 温度和(b) 轴向磁场分布曲线
Fig. 9. Distributions of (a) temperature and (b) axial magnetic field at 101 ns calculated by MIST.
图 10 MIST计算得到的112 ns时 (a) 温度和(b) 轴向磁场分布曲线
Fig. 10. Distributions of (a) temperature and (b) axial magnetic field at 112 ns calculated by MIST.
图 11 MIST计算得到的124 ns时 (a) 压强和(b) 轴向磁场分布曲线
Fig. 11. Distributions of (a) pressure and (b) axial magnetic field at 124 ns calculated by MIST.
图 12 MIST计算得到的136 ns时 (a) 温度, (b) 轴向磁场分布曲线
Fig. 12. Distributions of (a) temperature and (b) axial magnetic field at 136 ns calculated by MIST.
图 13 MIST计算得到的迟滞时刻 (a) 压强, (b) 轴向磁场分布曲线
Fig. 13. Distributions of (a) pressure and (b) axial magnetic field at stagnation time calculated by MIST.
图 14 是否考虑Nernst项给出的 (a) 磁通演化和(b) 迟滞时刻磁场分布对比曲线
Fig. 14. Comparisons between (a) magnetic flux evolvements and (b) magnetic field distributions at stagnation time with or without Nernst effect.
图 15 考虑Nernst效应后计算得到迟滞时刻燃料中 (a) 温度和 (b)密度分布曲线
Fig. 15. Distributions of (a) temperature and (b) magnetic field at stagnation time calculated by MIST with Nernst effect.
图 16 初始10 T磁场下计算得到的 (a)磁通和(b)产额随时间演化曲线
Fig. 16. Comparisons between (a) magnetic flux and (b) fusion yield evolvements with or without Nernst effect (Bz0 = 10 T).
图 17 不同初始磁场下计算得到的迟滞时刻磁场分布曲线 (a) Bz0 = 10 (b) Bz0 = 20 T
Fig. 17. Distributions of magnetic field at stagnation time with initial (a) Bz0 = 10 and (b) Bz0 = 20 T.
图 18 初始20 T磁场下计算得到的 (a)磁通和(b)产额随时间演化曲线
Fig. 18. Comparisons between (a) magnetic flux and (b) fusion yield evolvements with or without Nernst effect (Bz0 = 20 T).
图 19 同一能量不同预加热分布计算得到的 (a)磁通演化和(b)磁场分布曲线
Fig. 19. Calculated (a) magnetic flux evolvements and (b) magnetic field distributions with different preheat results.
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[1] Gao Z 2016 Matter Radiat. Extremes 1 153
Google Scholar
[2] 章太阳, 陈冉 2017 66 125201
Google Scholar
Zhang T Y, Chen R 2017 Acta Phys. Sin. 66 125201
Google Scholar
[3] Kazuhiko Horioka 2018 Matter Radiat. Extremes 3 12
Google Scholar
[4] Kawata S, Karino T, Ogoyski A I 2016 Matter Radiat. Extremes 1 89
Google Scholar
[5] Chen Y Y, Bao X H, Fu P, Gao G 2019 Chin. Phys. B 28 015201
Google Scholar
[6] Zhang Y K, Zhou R J, Hu L Q, Chen M W, Chao Y 2018 Chin. Phys. B 27 055206
Google Scholar
[7] Liu D Q, Zhou C P, Cao Z, Yan J C, Liu Y 2003 Fusion Eng. Des. 66 147
Google Scholar
[8] Liu D Q, Lin T, Qiao T, Li Q, Li G S, Bai G Y, Ran H, Cao Z, Cai L J, Zou H, Li Y 2015 Fusion Eng. Des. 96 298
[9] Tikhonchuk V, Gu Y J, Klimo O, Limpouch J, Weber S 2019 Matter Radiat. Extremes 4 045402
Google Scholar
[10] 薛全喜, 江少恩, 王哲斌, 王峰, 赵学庆, 易爱平, 丁永坤, 刘晶儒 2018 24 094701
Google 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 094701
Google Scholar
[11] 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 3 248
Google Scholar
[12] 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 1 135
Google Scholar
[13] 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 056303
Google Scholar
[14] Paradela J, García-Rubio F, Sanz J 2019 Phys. Plasmas 26 012705
Google Scholar
[15] Perkins L J, Logan B G, Zimmerman G B, Werner C J 2013 Phys. Plasmas 20 072708
Google Scholar
[16] Slutz S A, Vesey R A 2012 Phys. Rev. Lett 108 025003
Google Scholar
[17] 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 072711
Google Scholar
[18] Slutz S A 2018 Phys. Plasmas 25 082707
Google Scholar
[19] Gomez M R, Slutz S A, Sefkow A B, et al. 2014 Phys. Rev. Lett 113 155003
Google Scholar
[20] Awe T J, McBride R D, Jennings C A, et al. 2013 Phys. Rev. Lett 111 235005
Google Scholar
[21] Seyler C E, Martin M R, Hamlin N D 2018 Phys. Plasmas 25 062711
Google Scholar
[22] Shipley G A, Awe T J, Hutsel B T, Slutz S A, Lamppa D C, Greenly J B, Hutchinson T M 2018 Phys. Plasmas 25 052703
Google Scholar
[23] Gourdain P A, Adams M B, Davies J R, Seyler C E 2017 Phys. Plasmas 24 102712
Google Scholar
[24] 赵海龙, 肖波, 王刚华, 王强, 章征伟, 孙奇志, 邓建军 2020 69 035203
Google Scholar
Zhao H L, Xiao B, Wang G H, Wang Q, Zhang Z W, Sun Q Z, Deng J J 2020 Acta Phys. Sin. 69 035203
Google Scholar
[25] Basko M M, Kemp A J, Meyer-ter-Vehn J 2000 Nucl. Fusion 40 59
Google Scholar
[26] Braginskii S I 1965 Reviews of Plasma Physics (New York: Consultants Bureau) p205.
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