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托卡马克理想导体壁与磁流体不稳定性

沈勇 董家齐 何宏达 潘卫 郝广周

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托卡马克理想导体壁与磁流体不稳定性

沈勇, 董家齐, 何宏达, 潘卫, 郝广周

Ideal conductive wall and magnetohydrodynamic instability in Tokamak

Shen Yong, Dong Jia-Qi, He Hong-Da, Pan Wei, Hao Guang-Zhou
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  • 为了探索等离子体磁流体力学(MHD)不稳定性的导体壁效应以及壁设计思想, 研究了基于HL-2A托卡马克偏滤器位形的、自由边界和多种形式的理想导体壁条件下的等离子体MHD不稳定性与装置MHD运行β极限. 在稳定性计算中, 考虑的是n = 1扭曲模, 该模对托卡马克等离子体MHD不稳定性有决定性的影响. 研究着眼于验证多种形状导体壁抑制内、外扭曲模的有效性, 观察运行$ \beta $极限的变化, 并讨论分析相关物理. 研究发现在离等离子体适当距离处放置一个理想导体壁, 可有效抑制外扭曲模. 在壁与等离子体表面的平均距离相同、且足够小的条件下, 圆截面壁并不一定是最佳选择, 设置一个经过优化的多边形导体壁能更有效地抑制MHD不稳定性, 它使本装置的理想MHD运行β极限βN提高到2.73, 比自由边界条件下(即假设壁设置在无穷远处的)装置的运行β极限值($ \sim $2.56)提高了约6.5%. 这暗示需要根据有拉长、有变形的等离子体的极向截面形状, 优化制作一个离等离子体表面平均距离尽可能近的多边形导体壁, 才能取得抑制外扭曲模、提高β极限的最佳效果.
    In order to explore the conductive wall effect of plasma magnetohydrodynamic (MHD) instability and the wall designing idea, the various forms of ideal conductive walls based on divertor equilibrium configurations in the HL-2A Tokamak and their role in suppressing kink modes are studied. The MHD instabilities and the ideal MHD operational β limits under free boundary or ideal wall conditions are compared. In the stability calculation, n = 1 kink mode is considered, which has a decisive influence on the MHD instability of Tokamak plasma. The research focuses on verifying the effectiveness of various shapes of conductive walls in suppressing internal and external kink modes, and observing the operational β limit changes, and discussing and analyzing related physics. It is found that an ideal conducting wall placed at a suitable distance from the plasma can effectively suppress the external kink modes. Under the condition that the average distance between the wall and the plasma surface is the same and small enough, the circular cross-section wall is not necessarily the best option. Setting an optimized polygonal conductive wall can more effectively suppress the MHD instability. It makes the ideal MHD operational β limit of the device, βN, increase to 2.73, which is about 6.5% higher than that for the device with a wall assumed to be set at infinity ($ \sim $2.56). This implies that it is necessary to optimize and make a polygonal conductive wall as close as possible to the average distance from the plasma surface according to the poloidal-section shape of the elongated and shaped plasma, so as to achieve the suppression of external kink mode and increase the operational β limits. The physical mechanism of the stabilizing effect of the ideal wall on external kink modes is analyzed. With the development of the kink mode, when the plasma column is twisted closely to the wall, the plasma column will squeeze the magnetic field in the vacuum area, making the magnetic field line compressed and bent. At this time, the magnetic pressure and the component force of the magnetic tension in the opposite direction of the radial direction push the plasma back, thus stabilizing the kink mode. Finally, a conclusion is given.
      通信作者: 沈勇, sheny@swip.ac.cn
    • 基金项目: 国家自然科学基金(批准号: 12075077)和国家重点研发计划(批准号: 2017YFE0301200, 2019YFE03050003)资助的课题.
      Corresponding author: Shen Yong, sheny@swip.ac.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 12075077) and the National Key R&D Program of China (Grant Nos. 2017YFE0301200, 2019YFE03050003).
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    Petty C C, Kinsey J E, Holcomb C T, et al. 2016 Nucl. Fusion 56 016016Google Scholar

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    ITER Physics Expert Group on Disruptions, Palsma Control, and MHD and ITER Physics Basis Editors 1999 Nucl. Fusion 39 2251Google Scholar

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    Kerner W, Gautier P, Lackner K, Schneider W, Gruber R, Troyon F 1981 Nucl. Fusion 21 1383Google Scholar

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    Park J M, Ferron J R, Holcomb C T, Buttery R J, Solomon W M, Batchelor D B, Elwasif W, Green D L, Kim K, Meneghini O, Murakami M, Snyder P B 2018 Phys. Plasmas 25 012506Google Scholar

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    Howl W, Turnbull A D, Taylor T S, Lao L L, Helton F J, Ferron J R, Strait E J 1992 Phys. Fluids B 4 1724

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    Wesson J A, Sykes A 1985 Nucl. Fusion 25 85Google Scholar

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    Shen Y, Dong J Q, Peng X D Han M K, He H D, Li J Q 2022 Nucl. Fusion 62 106004Google Scholar

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    Yavorskij V, Goloborod'ko V, Schoepf K, Sharapov S E, Challis C D, Reznik S, Stork D 2003 Nucl. Fusion 43 1077Google Scholar

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    Taylor T S, Strait E J, Lao L, et al. 1989 Phys. Rev. Lett. 62 1278Google Scholar

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    Troyon F, Gruber R, Saurenmann H, Semenzato S, Succi S 1984 Plasma Phys. Controlled Fusion 26 209Google Scholar

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    Ferron J R, Chu M S, Helton F J, Howl W, Kellman A G, Lao L L, Lazarus E A, Lee J K, Osborne T H, Strait E J, Taylor T S, Turnbull A D 1990 Phys. Fluids B 2 1280Google Scholar

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    Taylor T S, St John H, Turnbull A D, Lin-Liu V R, Burrell K H, Chan V, Chu M S, Ferron J R, Lao L L, Haye R J La, Lazarus E A, Miller R L, Politzer P A, Schissel D P, Strait E J 1994 Plasma Phys. Control. Fusion 36 B229Google Scholar

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    Shen Y, Dong J Q, He H D, Shi Z B, Li J, Han M K, Li J Q, Sun A P, Pan L 2020 Nucl. Fusion 60 124001Google Scholar

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    沈勇, 董家齐, 何宏达, 丁玄同, 石中兵, 季小全, 李佳, 韩明昆, 吴娜, 蒋敏, 王硕, 李继全, 许敏, 段旭如 2021 物理学报 70 185201Google Scholar

    Shen Y, Dong J Q, He H D, Ding X T, Shi Z B, Ji X Q, Li J, Han M K, Wu N, Jiang M, Wang S, Li J Q, Xu M, Duan X R 2021 Acta Phys. Sin. 70 185201Google Scholar

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    Garofalo A M, Doyle E J, Ferron J R, et al. 2006 Phys. Plasmas 13 056110Google Scholar

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    Turnbull A D, Lin-Liu Y R, Miller R L, Taylor T S, Todd T N 1999 Phys. Plasmas 6 1113Google Scholar

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    Bernard L C, Moore R W 1981 Phys. Rev. Lett. 46 1286Google Scholar

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    胡希伟 2006 等离子体理论基础 (北京: 北京大学出版社) 第119—182页

    Hu X W 2006 Fundamentals of Plasma Theory (Beijing: Peking University Press) pp119–182 (in Chinese)

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    Chu M S, Ichiguchi K 2005 Nucl. Fusion 45 804Google Scholar

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    Hender T C, Gimblett C G, Robinson D C 1989 Nucl. Fusion 29 1279Google Scholar

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    Hao G Z, Liu Y Q, Wang A K, Qiu X M 2012 Phys. Plasmas 19 032507Google Scholar

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    Shen Y, Dong J Q, He H D, Turnbull A D 2009 Plasma Sci. Technol. 11 131Google Scholar

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    Lao L L, Ferron J R, Groebner R J, Howl W, John H St, Strait E J, Taylor T S 1990 Nucl. Fusion 30 1035Google Scholar

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    Lao L L, John H St, Stambaugh R D, Kellman A G, Pfeiffer W 1985 Nucl. Fusion 25 1611Google Scholar

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    Gruber R, Troyon F, Berger D, Bernard L C, Rousset S, Schreiber R, Schneider W, Roberts K V 1981 Comput. Phys. Commun. 21 323Google Scholar

  • 图 1  (a) HL-2A托卡马克极向截面图, 包括等离子体分界面(红线), 限制器(黑线), HL-2A真空室壁(深蓝线), 以及拟设新导体壁(淡蓝线); 预设4种导体壁, 概略图包含(b)原壁, (c) 圆截面壁, (d)多边形壁, 以及(e)优化多边形壁

    Fig. 1.  (a) Scheme of the poloidal cross-section of HL-2A Tokamak, including plasma separatrix (red line), limiter (black line), HL-2A vacuum chamber wall (dark blue line), and proposed new conductive wall (light blue line). Four kinds of conductive walls are preset, and the sketch is as follows: (b) Original wall, (c) circular section wall, (d) polygonal wall, and (e) optimized polygonal wall.

    图 2  $ {q}_{0}=1.05 $, (a) $ {\beta }_{\rm{p}}=0.45 $时与(b)$ {\beta }_{\rm{p}}=2.00 $时的平衡位形; (c)$ {\beta }_{\rm{p}}=2 $时, GATO计算的安全因子(q)剖面(由图2(a)图2(b)对比得知, $ {\beta }_{\rm{p}} $越大, 等离子体Shafranov位移越大)

    Fig. 2.  When $ {q}_{0}=1.05 $, the equilibrium configuration of (a) $ {\beta }_{\rm{p}}=0.45 $ and (b) $ {\beta }_{\rm{p}}=2.00 $, and (c) the safety factor (q) profile calculated by GATO at $ {\beta }_{\rm{p}}=2 $ (According to the comparison between Fig. 2(a) and Fig. 2(b), the larger the $ {\beta }_{\rm{p}} $, the larger the plasma Shafranov displacement).

    图 3  ${q}_{0} = 0.95$时, 较低$ {\beta }_{\rm{p}} $与较高$ {\beta }_{\rm{p}} $时模的极向投影与对应模径向扰动X的傅里叶分解结果 (a), (b) ${\beta }_{\rm{p}} = 0.45$; (c), (d) ${\beta }_{\rm{p}} = 2.5$

    Fig. 3.  When $ {q}_{0}=0.95 $, the poloidal projection of the mode and the Fourier decomposition of the radial perturbation of the corresponding mode $ \mathit{X} $ at lower $ {\beta }_{\rm{p}} $ and higher $ {\beta }_{\rm{p}} $: (a), (b) $ {\beta }_{\rm{p}}=0.45 $; (c), (d) $ {\beta }_{\rm{p}}=2.5 $.

    图 4  $ {q}_{0}=1.05 $, 自由边界条件下, 模位移矢量在极向平面的投影及扰动位移径向分量X的傅里叶分解结果图 (a), (b) ${\beta }_{\rm{p}}= $$ 0.45$, q95 = 4.37, $ \lambda =-0.4492\times {10}^{-7} $; (c), (d) $ {\beta }_{\rm{p}}=2 $, q95 = 5.35, $ \lambda =-0.1247\times {10}^{-6} $; (e), (f) $ {\beta }_{\rm{p}}=2.3$, q95 = 5.67, $\lambda = $$ -0.1198\times {10}^{-3}$; (g), (h) $ {\beta }_{\rm{p}}=2.5$, q95 = 5.80, $ \lambda =-0.4774\times {10}^{-3} $

    Fig. 4.  When $ {q}_{0}=1.05 $, the projection of the mode displacement vector on the poloidal plane and the radial component of Fourier decomposition of the perturbation $ \mathit{X} $: (a), (b) $ {\beta }_{\rm{p}}=0.45$, q95 = 4.37, $ \lambda =-0.4492\times {10}^{-7} $; (c), (d) $ {\beta }_{\rm{p}}=2$, q95 = 5.35, $\lambda = $$ -0.1247\times {10}^{-6}$; (e), (f) $ {\beta }_{\rm{p}}=2.3$, q95 = 5.67, $ \lambda =-0.1198\times {10}^{-3} $; (g), (h) $ {\beta }_{\rm{p}}=2.5 $, q95 = 5.80, $ \lambda =-0.4774\times {10}^{-3} $.

    图 5  (a) 优化理想导体壁条件下等离子体与壁的位置关系; (b) ${\beta }_{\rm{p}}=2.3,\; {q}_{95}=5.67$, $ \lambda =-0.1418\times {10}^{-5} $和(c) ${\beta }_{\rm{p}}=2.5, $$ {q}_{95}=5.8$, $ \lambda =-0.4985\times {10}^{-4} $时, 扰动位移在极向平面的投影; (d)${\beta }_{\rm{p}}=2.5,\;{ q}_{0}=1.05$情形下径向扰动X的傅里叶分解图

    Fig. 5.  (a) Under the condition of the ideal optimized conductive wall, the position relationship between plasma and wall; (b) the projection of perturbation displacement on the polar plane when ${\beta }_{\rm{p}}=2.3,\; {q}_{95}=5.67$, $ \lambda =-0.1418\times {10}^{-5} $ and (c) ${\beta }_{\rm{p}}=2.5, $$ {q}_{95}=5.8$, $ \lambda =-0.4985\times {10}^{-4} $; (d) Fourier decomposition diagram of radial perturbation X when $ {\beta }_{\rm{p}}=2.5 $, $ {q}_{0}=1.05 $.

    图 6  自由边界与各种壁条件下等离子体的几何位置及位形, 其中(a1) 自由边界位形, (b1) 原壁位形, (c1) 圆截面壁位形, (d1) 多边形壁位形, (e1) 优化壁位形; 在各种位形下, $ {q}_{0}=0.95 $ (图(a2)—(e2))与1.05 (图(a3)—(e3)) 时模的极向截面投影和对应的模特征值$ \lambda $, 其中(a2) $ \lambda =-0.2162\times {10}^{-2} $; (a3) $ \lambda =-0.4774\times {10}^{-3} $; (b2) $ \lambda =-0.2162\times {10}^{-2} $; (b3) $\lambda =-0.4315\times {10}^{-3}$; (c2) $ \lambda =-0.1846\times {10}^{-2} $; (c3) $ \lambda =-0.1991\times {10}^{-3} $; (d2) $ \lambda =-0.1761\times {10}^{-2} $; (d3) $ \lambda =-0.7246\times {10}^{-4} $; (e2) $\lambda = -0.1727\times $$ {10}^{-2}$; (e3) $ \lambda =-0.4985\times {10}^{-4} $

    Fig. 6.  Geometry and configuration of plasma under free boundary and various wall conditions: (a1) Free boundary configuration; (b1) original wall configuration; (c1) circular section wall configuration; (d1) polygonal wall configuration; (e1) optimized wall configuration. For each configuration, the poloidal projection of the mode is given respectively at $ {q}_{0}=0.95 $ (panel (a2)—(e2)) and 1.05 (panel (a3)—(e3)), and the corresponding mode eigenvalues $ \lambda $ are given under the projection diagrams: (a2)$\lambda = $$ -0.2162\times {10}^{-2}$; (a3) $ \lambda =-0.4774\times {10}^{-3} $; (b2) $ \lambda =-0.2162\times {10}^{-2} $; (b3) $ \lambda =-0.4315\times {10}^{-3} $ ; (c2) $ \lambda =-0.1846\times {10}^{-2} $; (c3) $\lambda = -0.1991\times $$ {10}^{-3}$; (d2)$\lambda = -0.1761\times {10}^{-2}$; (d3)$\lambda = -0.7246\times {10}^{-4}$; (e2) $\lambda = -0.1727\times {10}^{-2}$; (e3) $\lambda = -0.4985\times {10}^{-4}$

    图 7  模特征值绝对值$ \left|\lambda \right| $ (归一化增长率)随$ {\beta }_{\rm{p}} $的变化关系图 (a) 自由边界位形条件; (b)优化壁条件

    Fig. 7.  Absolute value of mode eigenvalue ($ \left|\lambda \right| $) variation with $ {\beta }_{\rm{p}} $: (a) Free boundary configuration; (b) the condition of optimized wall.

    表 1  $ {q}_{0}=0.95 $时, 自由边界条件下以及各种形状理想壁条件下计算的模特征值

    Table 1.  Eigenvalues calculated under free boundary and ideal wall conditions when $ {q}_{0}=0.95 $.

    βP$ \lambda $/10–3
    自由边界原理想壁优化多边形壁多边形壁圆截面壁
    0.10–0.9944–0.9944–0.9944
    0.30–0.8297–0.8297–0.8297
    0.45–0.7713–0.7713–0.7713
    1.05–0.9110–0.9101–0.9001
    2.00–1.2690–1.2410–1.1840–1.190
    2.20–1.4730–1.4620–1.1301–1.352
    2.50–2.1620–2.1260–1.7270–1.761–1.846
    3.00–5.9170–5.6920–3.6110
    4.00–21.930–20.700–9.7990
    下载: 导出CSV

    表 2  $ {q}_{0}=1.05 $时, 各种条件下计算的模特征值

    Table 2.  Eigenvalues calculated under different conditions when $ {q}_{0}=1.05 $.

    βP$ \lambda $/10–7
    自由边界原理想壁优化多边形壁多边形壁圆截面壁
    0.10–0.4284–0.4284–0.4284
    0.45–0.4492–0.4492–0.4492
    1.05–0.4647–0.4647–0.4647
    1.50–1.2230–1.2230–1.2200
    2.00–1.2470–1.2460–1.2380–1.2391.240
    2.20–393.40–313.70–1.2010–2.246–1.258
    2.30–1198.0–1054.0–14.180–60.220–195.20
    2.40–2460.0–2200.0–103.00–211.90–546.0
    2.50–4774.0–4315.0–498.50–724.60–1391
    3.00–38850–35570–9185.0–10780–15430
    下载: 导出CSV
  • [1]

    Ferron J R, Casper T A, Doyle E J, et al. 2005 Phys. Plasmas 12 056126Google Scholar

    [2]

    Holcomb C T, Ferron J R, Luce T C, et al. 2009 Phys. Plasmas 16 056116Google Scholar

    [3]

    Petty C C, Kinsey J E, Holcomb C T, et al. 2016 Nucl. Fusion 56 016016Google Scholar

    [4]

    Petty C C, Nazikian R, Park J M, et al. 2017 Nucl. Fusion 57 116057Google Scholar

    [5]

    Huysmans G T A, Hender T C, Alper B, Baranov Yu F, Borba D, Conway G D, Cottrell G A, Gormezano C, Helander P, Kwon O J, Nave M F F, Sips A C C, Söldner F X, Strait E J, Zwingmann W P, JET Team 1999 Nucl. Fusion 39 1489Google Scholar

    [6]

    ITER Physics Expert Group on Disruptions, Palsma Control, and MHD and ITER Physics Basis Editors 1999 Nucl. Fusion 39 2251Google Scholar

    [7]

    Phillips M W, Todd A M M, Hughes M H, Manickam J, Johnson J L, Parker R R 1988 Nucl. Fusion 28 1499Google Scholar

    [8]

    Kerner W, Gautier P, Lackner K, Schneider W, Gruber R, Troyon F 1981 Nucl. Fusion 21 1383Google Scholar

    [9]

    Park J M, Ferron J R, Holcomb C T, Buttery R J, Solomon W M, Batchelor D B, Elwasif W, Green D L, Kim K, Meneghini O, Murakami M, Snyder P B 2018 Phys. Plasmas 25 012506Google Scholar

    [10]

    Howl W, Turnbull A D, Taylor T S, Lao L L, Helton F J, Ferron J R, Strait E J 1992 Phys. Fluids B 4 1724

    [11]

    Wesson J A, Sykes A 1985 Nucl. Fusion 25 85Google Scholar

    [12]

    Shen Y, Dong J Q, Peng X D Han M K, He H D, Li J Q 2022 Nucl. Fusion 62 106004Google Scholar

    [13]

    Yavorskij V, Goloborod'ko V, Schoepf K, Sharapov S E, Challis C D, Reznik S, Stork D 2003 Nucl. Fusion 43 1077Google Scholar

    [14]

    Taylor T S, Strait E J, Lao L, et al. 1989 Phys. Rev. Lett. 62 1278Google Scholar

    [15]

    Troyon F, Gruber R, Saurenmann H, Semenzato S, Succi S 1984 Plasma Phys. Controlled Fusion 26 209Google Scholar

    [16]

    Ferron J R, Chu M S, Helton F J, Howl W, Kellman A G, Lao L L, Lazarus E A, Lee J K, Osborne T H, Strait E J, Taylor T S, Turnbull A D 1990 Phys. Fluids B 2 1280Google Scholar

    [17]

    Taylor T S, St John H, Turnbull A D, Lin-Liu V R, Burrell K H, Chan V, Chu M S, Ferron J R, Lao L L, Haye R J La, Lazarus E A, Miller R L, Politzer P A, Schissel D P, Strait E J 1994 Plasma Phys. Control. Fusion 36 B229Google Scholar

    [18]

    Shen Y, Dong J Q, He H D, Shi Z B, Li J, Han M K, Li J Q, Sun A P, Pan L 2020 Nucl. Fusion 60 124001Google Scholar

    [19]

    沈勇, 董家齐, 何宏达, 丁玄同, 石中兵, 季小全, 李佳, 韩明昆, 吴娜, 蒋敏, 王硕, 李继全, 许敏, 段旭如 2021 物理学报 70 185201Google Scholar

    Shen Y, Dong J Q, He H D, Ding X T, Shi Z B, Ji X Q, Li J, Han M K, Wu N, Jiang M, Wang S, Li J Q, Xu M, Duan X R 2021 Acta Phys. Sin. 70 185201Google Scholar

    [20]

    Garofalo A M, Doyle E J, Ferron J R, et al. 2006 Phys. Plasmas 13 056110Google Scholar

    [21]

    Turnbull A D, Lin-Liu Y R, Miller R L, Taylor T S, Todd T N 1999 Phys. Plasmas 6 1113Google Scholar

    [22]

    Bernard L C, Moore R W 1981 Phys. Rev. Lett. 46 1286Google Scholar

    [23]

    胡希伟 2006 等离子体理论基础 (北京: 北京大学出版社) 第119—182页

    Hu X W 2006 Fundamentals of Plasma Theory (Beijing: Peking University Press) pp119–182 (in Chinese)

    [24]

    Liu Y Q, Bondeson A, Chu M S, Favez J Y, Gribov Y, Gryaznevich M, Hender T C, Howell D F, La Haye R J, Lister J B, de Vries P, EFDA JET Contributors 2005 Nucl. Fusion 45 1131Google Scholar

    [25]

    Chu M S, Ichiguchi K 2005 Nucl. Fusion 45 804Google Scholar

    [26]

    Hender T C, Gimblett C G, Robinson D C 1989 Nucl. Fusion 29 1279Google Scholar

    [27]

    Hao G Z, Liu Y Q, Wang A K, Qiu X M 2012 Phys. Plasmas 19 032507Google Scholar

    [28]

    Shen Y, Dong J Q, He H D, Turnbull A D 2009 Plasma Sci. Technol. 11 131Google Scholar

    [29]

    Lao L L, Ferron J R, Groebner R J, Howl W, John H St, Strait E J, Taylor T S 1990 Nucl. Fusion 30 1035Google Scholar

    [30]

    Lao L L, John H St, Stambaugh R D, Kellman A G, Pfeiffer W 1985 Nucl. Fusion 25 1611Google Scholar

    [31]

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出版历程
  • 收稿日期:  2022-10-25
  • 修回日期:  2022-11-18
  • 上网日期:  2022-11-28
  • 刊出日期:  2023-02-05

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