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托卡马克中低频磁流体不稳定性协同作用引起快粒子输运的混合模拟研究

朱霄龙 陈伟 王丰 王正汹

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托卡马克中低频磁流体不稳定性协同作用引起快粒子输运的混合模拟研究

朱霄龙, 陈伟, 王丰, 王正汹

Hybrid numerical simulation on fast particle transport induced by synergistic interaction of low- and medium-frequency magnetohydrodynamic instabilities in tokamak plasma

Zhu Xiao-Long, Chen Wei, Wang Feng, Wang Zheng-Xiong
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  • 在托卡马克实验中, 通常会有多种磁流体不稳定性同时存在并与快粒子发生相互作用, 引起非常显著的快粒子输运和损失, 破坏装置第一壁导致放电淬灭. 因此, 理解磁流体不稳定性引起快粒子输运的物理机制, 对未来聚变堆稳态长脉冲运行是亟需解决的重要物理问题. 本文基于球形托卡马克装置NSTX上观测到的非共振内扭曲模与撕裂模发生协同相互作用的实验现象, 采用全局非线性磁流体-动理学混合模拟程序M3D-K, 比较了两种情况下的快粒子损失、输运和再分布的特征, 包括情况1: 非共振内扭曲模与撕裂模同时存在并且发生协同相互作用, 研究了这种协同作用引起快粒子输运的物理机理; 情况2: 只有非共振内扭曲模存在. 研究结果表明, 非共振内扭曲模与撕裂模的协同相互作用可以显著提升快粒子损失和输运水平, 主要原因是这种协同作用可以提供一种快粒子沿径向从等离子体芯部向等离子体边界运动的通道, 从而提升了快粒子输运、损失和再分布水平. 这些结果有助于理解未来聚变堆中低频磁流体不稳定性协同作用引起快粒子输运和损失的物理机理, 为寻找控制和缓解未来聚变堆中快粒子损失和输运水平的策略提供一定的新思路.
    In tokamak experiments, various magnetohydrodynamic (MHD) instabilities usually co-exist and interact with fast particles. It can cause the fast particles to significantly transport and lose, which results in damaging the first wall and quenching discharge in tokamak. Therefore, the understanding of the physical mechanism of fast particle transport caused by MHD instabilities is crucial and this physical problem needs solving urgently for the steady-state long pulse operation of future reactor-graded devices. According to the phenomenon of synergy between non-resonant internal kink mode and tearing mode, observed experimentally on NSTX, a spherical tokamak device, we utilize the global nonlinear hybrid-kinetic simulation code M3D-K to study and compare the characteristics of loss, transport and redistribution of fast particles in the two cases: 1) the synergy between the non-resonant internal kink mode and tearing mode and 2) only non-resonant internal kink modes. The physical mechanisms of transport, loss, and redistribution of fast particles caused by such synergy are studied, respectively. The results show that the synergy between the non-resonant internal kink mode and the tearing mode can significantly enhance the loss and transport of fast particles. The main reason is that such a synergy can provide a radial channel for fast particles to migrate from the plasma core to the plasma boundary accompanied with the total stochasticity of the magnetic topology. These results can help understand the physical mechanism of the transport and loss of fast particles caused by the synergy of low-frequency MHD instabilities in future fusion reactors, and provide some new ideas for finding strategies to control and mitigate the loss and transport level of fast particles in future fusion reactors.
      通信作者: 王正汹, zxwang@dlut.edu.cn
    • 基金项目: 国家自然科学基金(批准号: 12205034, 11925501, 12125502)和中国博士后科学基金(批准号: 2021M700674)资助的课题.
      Corresponding author: Wang Zheng-Xiong, zxwang@dlut.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 12205034, 11925501, 12125502) and the Post-doctoral Science Foundation of China (Grant No. 2021M700674).
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    Ferrari H E, Farengo R, Garcia-Martinez, Clauser C F 2023 Plasma Phys. Control. Fusion 65 025001Google Scholar

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  • 图 1  模拟中采用的平衡剖面—NSTX上 134020 炮$ t= $$ 0.64\, \mathrm{s} $的实验剖面 (a)安全因子剖面 q (红色实线), 对应下文中情况1, 向下平移后的安全因子剖面 q (黑色虚线), 对应下文中情况2; (b)总压强剖面 p, 包括快离子压强和热压强; (c)等离子体密度剖面 n. 蓝色点划线表示$ q=2 $

    Fig. 1.  Equilibrium profiles used in the simulation, namely the experimental profiles at $ t = 0.64\, \mathrm{s} $ on NSTX shot 134020: (a) Safety factor profile q denoted by red solid line corresponding to case 1, the down-shifted q profile denoted by black dotted line corresponding to case 2; (b) total pressure profile p including fast ion pressure and thermal plasma pressure; (c) plasma density profile n. Blue dotted line denotes $ q=2 $.

    图 2  (a) $ t=300\tau_{\rm{A}} $$ m/n=1/1 $非共振内扭曲模和$ m/n=2/1 $撕裂模存在协同作用情况时的模结构U, 图中从内向外的红色圆圈分别表示$ q=1.24 $$ q=2 $两个共振面; (b) 扰动磁场在环向角$ \phi=0 $位置处的庞加莱图($t=300\tau_{\rm{A}} $); (c) $ t=750\tau_{\rm{A}} $$ m/n=1/1 $非共振内扭曲模和$ m/n=2/1 $撕裂模存在协同作用情况时的模结构U

    Fig. 2.  (a) Mode structure U of coupled $ m/n=1/1 $ non-resonant kink mode and $ m/n=2/1 $ tearing mode at $ t=300\tau_{\rm{A}} $, the two red circles from inner to outer respectively denotes $ q=1.24 $ and $ q=2 $ resonant surfaces; (b) the Poincare plot for the perturbed magnetic field line at toroidal angle $ \phi=0 $ ($t=300\tau_{\rm{A}} $); (c) the mode structure U of coupled $ m/n=1/1 $ non-resonant kink mode and $ m/n=2/1 $ tearing mode at $ t=750\tau_{\rm{A}} $.

    图 3  (a) $ m/n=1/1 $非共振内扭曲模和$ m/n=2/1 $撕裂模存在协同作用情况时模幅度非线性演化; (b) $ m/n= $$ 1/1 $非共振内扭曲模和$ m/n=2/1 $撕裂模存在协同相互作用情况的频谱演化

    Fig. 3.  (a) Nonlinear evolution of amplitude for coupled $ m/n=1/1 $ non-resonant kink mode and $ m/n=2/1 $ tearing mode; (b) the evolution of frequency spectrum of coupled $ m/n=1/1 $ non-resonant kink mode and $ m/n= $$ 2/1 $ tearing mode.

    图 4  (a) $ t=150\tau_{\rm{A}} $$ m/n=1/1 $非共振内扭曲模的模结构, 图中的红色圆圈表示$ q=1.24 $共振面所在的位置; (b) 扰动磁场在环向角$ \phi=0 $位置处的庞加莱图($t=150\tau_{\rm{A}} $); (c) $ t=300\tau_{\rm{A}} $$ m/n=1/1 $非共振内扭曲模的模结构

    Fig. 4.  (a) Mode structure of coupled $ m/n=1/1 $ non-resonant kink mode at $ t=150\tau_{\rm{A}} $, the red circle denotes the location of $ q= $$ 1.24 $ resonance surface; (b) the Poincare plot for the perturbed magnetic field line at toroidal angle $ \phi=0 $ ($t=150\tau_{\rm{A}} $); (c) the mode structure of coupled $ m/n=1/1 $ non-resonant kink mode at $ t=300\tau_{\rm{A}} $.

    图 5  (a) $ m/n=1/1 $非共振内扭曲模幅度$ U_{{\rm{cos}}} $非线性演化; (b) $ m/n=1/1 $ 非共振内扭曲模的频谱演化

    Fig. 5.  (a) Nonlinear evolution of amplitude for $ m/n=1/1 $ non-resonant kink mode; (b) the evolution of frequency spectrum of $ m/n=1/1 $ non-resonant kink mode.

    图 6  $ m/n=1/1 $非共振内扭曲模非线性演化过程中, 在初始时刻(a) $ t=0 $, 初始饱和时刻(b) $ t=201\tau_{\rm{A}} $, 非线性饱和前期(c) $ t=300\tau_{\rm{A}} $, 非线性饱和后期(d) $ t=400\tau_{\rm{A}} $, 在($ P_\phi, E $)空间中磁矩$ \mu=0.3343 $附近的快粒子分布函数F的演化

    Fig. 6.  During the nonlinear evolution of $ m/n=1/1 $ non-resonant kink mode, the distribution function F around magnetic moment μ = 0.3343 in ($P_\phi, E $) space at the initial moment (a) $ t=0 $, the initial saturation moment (b) $ t=201\tau_{\rm{A}} $, the late saturation moments (c) $ t=300\tau_{\rm{A}} $ and (d) $ t=400\tau_{\rm{A}} $.

    图 7  耦合的$ m/n=1/1 $非共振内扭曲模和$ m/n=2/1 $撕裂模非线性演化过程中, 在初始时刻(a) $ t=0 $, 非线性扫频阶段(b) $ t=400\tau_{\rm{A}} $, 出现零频分量的阶段(c) $ t=600\tau_{\rm{A}} $, 非线性饱和后期只有零频分量的阶段(d) $ t=900\tau_{\rm{A}} $, 在($ P_\phi, E $) 空间中磁矩$ \mu=0.3343 $附近的快粒子分布函数F的演化

    Fig. 7.  During the nonlinear evolution of coupled $ m/n=1/1 $ non-resonant kink mode and $ m/n=2/1 $ tearing mode, the distribution function F around magnetic moment μ = 0.3343 in ($P_\phi, E $) space at the initial moment (a) $ t=0 $, the initial saturation moment (b) $ t=400\tau_{\rm{A}} $, the late saturation moments (c) $ t=600\tau_{\rm{A}} $ and (d) $ t=900\tau_{\rm{A}} $.

    图 8  耦合的$ m/n=1/1 $非共振内扭曲模和$ m/n= $$ 2/1 $撕裂模中, 不同模幅度$ A_{{\rm{max}}} $与快粒子损失份额$ f_{{\rm{loss}}} $的定标关系

    Fig. 8.  In the case of coupled $ m/n=1/1 $ non-resonant kink mode and $ m/n=2/1 $ tearing mode, lost particle fraction $ f_{{\rm{loss}}} $ as a function of the mode amplitude.

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    Heidbrink W W, White R B 2020 Phys. Plasmas 27 030901Google Scholar

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    Chen W, Yu L M, Xu M, Ji X Q, Shi Z B, He X X, Li Z J, Li Y G, Wang T B, Jiang M, Gong S B, Wen J, Shi P W, Yang Z C, Fang K R, Li J, Wei L, Zhong W L, Sun A P, Cao J Y, Bai X Y, Li J Q, Ding X T, Dong J Q, Yang Q W, Liu Y, Yan L W, Wang Z X, Duan X R 2022 Fundam. Res. 2 667Google Scholar

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    Yu L M, Chen W, Jiang M, Shi Z B, Ji X Q, Ding X T, Li Y G, Ma R R, Shi P W, Song S D, Yuan B S, Zhou Y, Ma R, Song X M, Dong J Q, Xu M, Liu Y, Yan L W, Yang Q W, Xu Y H, Duan X R, HL-2A Team 2017 Nucl. Fusion 57 036023Google Scholar

    [4]

    Zhu X L, Wang F, Chen W, Wang Z X 2022 Plasma Sci. Technol. 24 025102Google Scholar

    [5]

    Li E Z, Igochine V, Dumbrajs O, Xu L, Chen K, Shi T, Hu L 2014 Plasma Phys. Control. Fusion 56 125016Google Scholar

    [6]

    Chen W, Zhu X L, Wang F, Jiang M, Ji X Q, Qiu Z Y, Shi Z B, Yu D L, Li Y G, Yu L M, Shi P W, Ding X T, Xu M, Wang Z X 2019 Nucl. Fusion 59 096037Google Scholar

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    Wang Z X, Tang W K, Wei L 2022 Plasma Sci. Technol. 24 033001Google Scholar

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    Chen W, Wang Z X 2020 Chin. Phys. Lett 37 125001Google Scholar

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    Shi P W, Chen W, Duan X R 2021 Chin. Phys. Lett 38 035202Google Scholar

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    Chen W, Yu L M, Shi P W, Ma R, Ji X Q, Jiang M, Zhu X L, Shi Z B, Yu D L, Yuan B S, Li Y G, Yang Z C, Cao J Y, Song S D, Zhong W L, He H D, Dong J Q, Ding X T, Yan L W, Liu Y, Yang Q W, Xu M, Duan X R 2018 Nucl. Fusion 58 014001Google Scholar

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    Zhu X L, Chen W, Wang F, Wang Z X 2020 Nucl. Fusion 60 046023Google Scholar

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    Cai H S, Fu G Y 2012 Phys. Plasmas 19 072506Google Scholar

    [17]

    Gao B F, Cai H S, Gao X, Wan Y X 2021 Nucl. Fusion 61 116070Google Scholar

    [18]

    Ferrari H E, Farengo R, Garcia-Martinez, Clauser C F 2023 Plasma Phys. Control. Fusion 65 025001Google Scholar

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    Clauser C, Farengo R, Ferrari H 2019 Comput. Phys. Commun. 234 126Google Scholar

    [20]

    Zhu X L, Yu L M, Chen W, Shi P W, Ge W L, Wang F, Luan Q B, Sun H E, Wang Z X 2023 Nucl. Fusion 63 036014Google Scholar

    [21]

    Bonofiglo P J, Podesta M, Vallar M, Gorelenkov N N, Kiptily V, White R B, Giroud C, Brezinsek S, JET Contributors 2022 Nucl. Fusion 62 112002Google Scholar

    [22]

    Yang J, Fredrickson E D, Podesta M, Poli F M 2022 Plasma Phys. Control. Fusion 64 095005Google Scholar

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    Yang J, Podesta M, Fredrickson E D 2021 Plasma Phys. Control. Fusion 63 045003Google Scholar

    [24]

    Podesta M, Gorelenkova M, White R B 2014 Plasma Phys. Control. Fusion 56 055003Google Scholar

    [25]

    Podesta M, Gorelenkova M, Teplukhina A A, Bonofiglo P J, Dumont R, Keeling D, Poli F M, White R B, Jet Contributors 2022 Nucl. Fusion 62 126047Google Scholar

    [26]

    Park W, Belova E V, Fu G Y, Tang X Z, Strauss H R, Sugiyama L E 1999 Phys. Plasmas 6 1796Google Scholar

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    Zhu X L, Wang F, Wang Z X 2020 Chin. Phys. B 29 025201Google Scholar

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    Zhu X L, Chen W, Podesta M, Wang F, Liu D, Wang Z X 2022 Nucl. Fusion 62 016012Google Scholar

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    Shi P W, Zhu X L, Liang A S, Chen W, Shi Z B, Wang T B, Yang Z C, Yu L M, Jiang M, He X X, Bai X Y, Ji X Q, Zhong W L, Xu M, Wang Z X, Duan X R 2022 Nucl. Fusion 62 106009Google Scholar

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    Wang F, Fu G Y, Breslau J A, Liu J Y 2013 Phys. Plasmas 20 102506Google Scholar

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    Wang F, Fu G Y, Shen W 2017 Nucl. Fusion 57 016034Google Scholar

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    Duan S Z, Fu G Y, Cai H S, Li D 2022 Nucl. Fusion 62 056002Google Scholar

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    Yang Y R, Chen W, Ye M Y, Yuan J B, Xu M 2020 Nucl. Fusion 60 106012Google Scholar

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    Ge W L, Wang J L, Wang F, Wang Z X 2021 Nucl. Fusion 61 116037Google Scholar

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    Ge W L, Wang Z X, Wang F, Liu Z X 2023 Nucl. Fusion 63 016007Google Scholar

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    Mynick H E 1993 Phys. Fluids B 5 1471Google Scholar

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    Briguglio S, Wang X, Zonca F, Vlad G, Fogaccia G, Di Troia C, Fusco V 2014 Phys. Plasmas 21 112301Google Scholar

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    Zhang H W, Ma Z W, Zhu J, Zhang W, Oiu Z Y 2022 Nucl. Fusion 62 026047Google Scholar

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    Zhu J, Ma Z W, Wang S, Zhang W 2018 Nucl. Fusion 58 046019Google Scholar

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    Cai H S, Li D 2022 Natl. Sci. Rev. 9 nwac019Google Scholar

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出版历程
  • 收稿日期:  2023-04-17
  • 修回日期:  2023-05-30
  • 上网日期:  2023-06-20
  • 刊出日期:  2023-11-05

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