-
Circular cross-section plasma is the most basic form of tokamak plasma and the fundamental configuration for magnetic confinement fusion experiments. This article is based on the HL-2A limiter discharge experiments to study the magnetohydrodynamic (MHD) equilibrium and MHD instability of tokamak plasmas in circular cross-section. The results showed that when q0=0.95, the internal kink mode of m/n=1/1 is always unstable. The increase in plasma β (=the ratio of thermal pressure to magnetic pressure) can lead to the appearance of external kink modes. The combination of axial safety factor q0 and edge safety factor qa determines the equilibrium configuration of the plasma and also affects the MHD stability of the equilibrium, but its growth rate is also related to the size of β. Under the condition of qa>2 and q0 slightly greater than 1, it is easy to achieve the stabilization of internal and surface kink modes. However the plasma becomes unstable again and the instability intensity increases as q0 continues to increase when q0 exceeds 1. As the poloidal specific pressure (βp) increases, the MHD instability develops, the equilibrium configuration of MHD elongates laterally, and the Shafranov displacement increases, which in turn has the effect for suppressing instability. Calculations have shown that the maximum β value imposed by the ideal MHD mode in a plasma with free boundary in tokamak experiments is proportional to the normalized current IN (=Ip(MA)/a (m)B0(T)), and the maximum specific pressure is calibrated as β(max)~2.01IN. The operational β limit of HL-2A circular cross-section plasma is approximately βNc≈2.0. A too high q0 is not conducive to MHD stability and leads to a decrease in the β limit. When q0=1.3, we obtain a maximum β_N of approximately 1.8. Finally, based on the existing circular cross-section plasma, some key factors affecting the operational β and the relationship between achievable high β and the calculated ideal β limits were discussed.
-
Keywords:
- circular cross-section plasma /
- magnetohydrodynamic (MHD) equilibrium /
- MHD instability /
- kink mode /
- β limit
-
[1] Buttery R J, Park J M, McClenaghan J T, Weisberg D, Canik J, Ferron J, Garofalo A, Holcomb C T, Leuer J, Snyder P B, The Atom Project Team 2021 Nucl. Fusion 61 046028.
[2] SarazinY, Hillairet J, Duchateau J L, Gaudimont K, Varennes R, Garbet X, Ghendrih Ph, Guirlet R, Pégourié B, Torre A 2020 Nucl. Fusion 60 016010.
[3] Hender T C, Wesley J C, Bialek J 2007 Nucl. Fusion 47 S128.
[4] Suzuki Y, Watanabe K Y, Sakakibara S 2020 Phys. Plasmas 27 102502.
[5] Liu Y, Chapman I T, Saarelma S, Gryaznevich M P, Hender T C, Howell D F, JET-EFDA contributors 2009 Plasma Phys. Control. Fusion 51 115005.
[6] Wolf R C, Biel W, Bock M F M de, Finken K H, Günter S, Hogeweij G M D, Jachmich S, Jakubowski M W, Jaspers R J E, Krämer-Flecken A, Koslowski H R, Lehnen M, Liang Y, Unterberg B, Varshney S K, Hellermann M von, Yu Q, Zimmermann O, Abdullaev S S, Donné A J H, Samm U, Schweer B, Tokar M, Westerhof E, the TEXTOR Team 2005 Nucl. Fusion 45 1700.
[7] Zhao K J, Lan T, Dong J Q, Yan L W, Hong W Y, Yu C X, Liu A D, Qian J, Cheng J, Yu D L, Yang Q W, Ding X T, Liu Y, Pan C H 2006 Phys. Rev. Lett. 96 255004.
[8] Chen W, Ding X T, Yang Q W, Liu Yi, Ji X Q, Zhang Y P, Zhou J, Yuan G L, Sun H J, Li W, Zhou Y, Huang Y, Dong J Q, Feng B B, Song X M, Shi Z B, Liu Z T, Song X Y, Li L C, Duan X R, Liu Y (HL-2A team) 2010 Phys. Rev. Lett. 105 185004.
[9] Zhong W L, Shen Y, Zou X L, Gao J M, Shi Z B, Dong J Q, Duan X R, Xu M, Cui Z Y, Li1, X. Q. Ji Y G, Yu D L, Cheng J, Xiao G L, Jiang M, Yang Z C, Zhang B Y, Shi P W, Liu Z T, Song X M, Ding X T, Liu Y (HL-2A Team1) 2016 Phys. Rev. Lett. 117 045001.
[10] Xu M, Duan X R, Liu Yi, Song X M, Liu D Q, Wang Y Q, Lu B, Yang Q W, Zheng G Y, Ding X T, Dong J Q, Hao G Z, Zhong W L, Shi Z B, Yan L W, Zou X L, Liu Y Q, Chen W, Xiao G L, Zhang Y P, Jiang M, Hou Y M, …, the HL-2A Team 2019 Nucl. Fusion 59 112017.
[11] Piovesan P, Igochine V, Turco F, Ryan D A, Cianciosa M R, Liu Y Q, Marrelli L, Terranova D, Wilcox R S, Wingen A, Angioni C, Bock C, Chrystal C, Classen I, Dunne M, Ferraro N M, Fischer R, Gude A, Holcomb C T, Lebchy A, Luce T C, Maraschek M, McDermott R, Odstrčil T, Paz-Soldan C, Reich M, Sertoli M, Suttrop W, Taylor N Z, Weiland M, Willensdorfer M, The ASDEX Upgrade Team, The DIII-D Team and The EUROfusion MST1 Team 2009 Plasma Phys. Control. Fusion 59 014027.
[12] Igochine V, Piovesan P, Classen I G J, Dunne M, Gude A, Lauber P, Liu Y, Maraschek M, Marrelli L, Dermott R Mc, Reich M, Ryan D, Schneller M, Strumberger E, Suttrop W, Tardini G, Zohm H, The ASDEX Upgrade Team and The EUROfusion MST1 Team 2017 Nucl. Fusion 57 116027.
[13] Todd A M M, Manickam J, Okabayashi M, Chance M S, Grimm R C, Greene J M, Johnson J L 1979 Nucl. Fusion 19 743.
[14] Bernard L C, Helton F J, Moore R W, Todd T N 1983 Nucl. Fusion 23 1475.
[15] Li Z-J, Chen W, Sun A-P, Yu L-M, Wang Z, Chen J-L, Xu J-Q, Li J-Q, Shi Z-B, Jiang M, Li Y-G, He X-X, Yang Z-C, Li J 2024 Acta Phys. Sin. 73 065202 (in Chinese) [李正吉, 陈伟, 孙爱萍, 于利明, 王卓, 陈佳乐, 许健强, 李继全, 石中兵, 蒋敏, 李永高, 何小雪, 杨曾辰, 李鉴2024 73 065202]
[16] Zhu X-L, Chen W, Wang F, Wang Z-X 2023 Acta Phys. Sin. 72 215210 (in Chinese) [朱霄龙, 陈伟, 王丰, 王正汹2023 72 215210]
[17] Shen Y, Dong J Q , He H D, Li J, Wu N, Zhao K J, Deng W 2024 J. Phys. Soc. Jpn. 93 104501.
[18] Shen Y, Dong J Q , Pend X D, He H D, Li J X 2025 Phys. Rev. E 111 025208.
[19] Lao L L, John H St, Stambaugh R D, Kellman A G, Pfeiffer W 1985 Nucl. Fusion 25 1611.
[20] Gruber R, Troyon F, Berger D, Bernard L C, Rousset S, Schreiber R, Kerner W, Schneider W, Roberts K V 1981 Comput. Phys. Commun. 21 323.
[21] Bernard L C, Helton F J, Moore R W 1981 Comput. Phys. Commu. 24 377.
[22] Lao L L, Strait E J, Taylor T S, Chu M S, Ozeki T, Howl W, Stambaugh R D, Burrell K H, Chance M S, DeBoo J C, Gohil P, Greene J M, Groebner R J, Kellman A G, Mahdavi M Ali, Osborne T H, Porter G, Turnbull A D 1989 Plasma Phys. Control. Fusion 31 509.
[23] Aydemir A Y, Kim J Y, Park B H, Seol J 2015 Phys. Plasmas 22, 032304.
[24] Bondeson A, Vlad G, and Léutjens H 1992 Phys. Fluids B 4 1889.
[25] Turnbull AD, Pearlstein LD, Bulmer .H, Lao LL, Haye RJ La 1999 Nucl. Fusion 39 1557.
[26] Kerner W, Gruber R, Troyon F 1980 Phys. Rev. Lett. 44 536.
[27] Troyon F, Gruber R, Saurenmann H, Semenzato S, Succi S 1984 Plasma Phys. Control. Fusion, 26, 209.
[28] Troyon F and Gruber R 1985 Phys. Lett. 110A 29.
[29] Bondeson A, Liu D-H, Söldner F X, Persson M, Baranov Yu F, Huysmans G T A 1999 Nucl. Fusion 39 1523.
[30] Shen Y, Dong J-Q, He H-D, Pan W, Hao G-Z 2023 Acta Phys. Sin. 72 035203 (in Chinese) [沈勇, 董家齐, 何宏达, 潘卫, 郝广周 2023 72 035203]
[31] Liu Y, Kirk A, Keeling D L, Kogan L, Du X D, Li L, Piron L, Ryan D A, Turnbull A D 2021 Nucl. Fusion 61 116022.
[32] Wang S, Liu Y Q, Xia G L, Song X M, Hao G Z, Li L, Li B, Zhang N, Dong G Q, Bai X, Zheng G Y 2021 Plasma Phys. Control. Fusion 63 055019.
[33] Haye R J La, Politzer P A, Brennan D P 2008 Nucl. Fusion 48 015005.
[34] Taylor T S, John H St, 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, Strait E J 1994 Plasma Phys. Control. Fusion 36 B229.
[35] Turnbull A D, Brennan D P, Chu M S, Lao L L, Snyder P B 2005 Fusion Sci. Technol. 48 875.
[36] Li G Q, Xu X Q, Snyder P B, Turnbull A D, Xia T Y, Ma C H, Xi P W 2014 Phys. Plasmas 21 102511.
Metrics
- Abstract views: 40
- PDF Downloads: 0
- Cited By: 0
下载:
