Please wait a minute...
Chin. Phys. B, 2022, Vol. 31(11): 110203    DOI: 10.1088/1674-1056/ac600d
GENERAL Prev   Next  

Application of Galerkin spectral method for tearing mode instability

Wu Sun(孙武)1, Jiaqi Wang(王嘉琦)1,†, Lai Wei(魏来)2, Zhengxiong Wang(王正汹)2, Dongjian Liu(刘东剑)1, and Qiaolin He(贺巧琳)3
1 College of Physics&Key Laboratory of High Energy Density Physics and Technology, Sichuan University, Chengdu 610065, China;
2 School of Physics, Dalian University of Technology, Dalian 116024, China;
3 School of Mathematics, Sichuan University, Chengdu 610065, China
Abstract  Magnetic reconnection and tearing mode instability play a critical role in many physical processes. The application of Galerkin spectral method for tearing mode instability in two-dimensional geometry is investigated in this paper. A resistive magnetohydrodynamic code is developed, by the Galerkin spectral method both in the periodic and aperiodic directions. Spectral schemes are provided for global modes and local modes. Mode structures, resistivity scaling, convergence and stability of tearing modes are discussed. The effectiveness of the code is demonstrated, and the computational results are compared with the results using Galerkin spectral method only in the periodic direction. The numerical results show that the code using Galerkin spectral method individually allows larger time step in global and local modes simulations, and has better convergence in global modes simulations.
Keywords:  Galerkin spectral method      tearing mode instability      magnetic reconnection      magnetohydrodynamics  
Received:  31 December 2021      Revised:  15 March 2022      Accepted manuscript online:  23 March 2022
PACS:  02.70.Hm (Spectral methods)  
  52.35.Py (Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.))  
  52.35.Vd (Magnetic reconnection)  
  52.65.Kj (Magnetohydrodynamic and fluid equation)  
Fund: Project supported by the Sichuan Science and Technology Program (Grant No. 22YYJC1286), the China National Magnetic Confinement Fusion Science Program (Grant No. 2013GB112005), and the National Natural Science Foundation of China (Grant Nos. 12075048 and 11925501).
Corresponding Authors:  Jiaqi Wang     E-mail:  jacky@scu.edu.cn

Cite this article: 

Wu Sun(孙武), Jiaqi Wang(王嘉琦), Lai Wei(魏来), Zhengxiong Wang(王正汹), Dongjian Liu(刘东剑), and Qiaolin He(贺巧琳) Application of Galerkin spectral method for tearing mode instability 2022 Chin. Phys. B 31 110203

[1] Giovanelli R G 1947 Mon. Not. R. Astron. Soc. 107 338
[2] Giovanelli R G 1946 Nature 158 81
[3] Tsuneta S 1996 Astrophys. J. 456 840
[4] Burch J L and Phan T D 2016 Geophys. Res. Lett. 43 8327
[5] Wyper P F, Antiochos S K and DeVore C R 2017 Nature 544 452
[6] Dungey J W 1961 Phys. Rev. Lett. 6 47
[7] Boozer A H 2012 Phys. Plasmas 19 092902
[8] Angelopoulos V, Artemyev A, Phan T D and Miyashita Y 2020 Nat. Phys. 16 317
[9] Phan T D, Eastwood J P, Shay M A, et al. 2018 Nature 557 202
[10] Furth H P, Rutherford P H and Selberg H 1973 Phys. Fluids 16 1054
[11] Rutherford P H 1973 Phys. Fluids 16 1903
[12] Von Goeler S, Stodiek W and Sauthoff N 1974 Phys. Rev. Lett. 33 1201
[13] Wang J, Xiao C, Wang X, Ji X and Liu Y 2012 Plasma Phys. Control. Fusion 54 122001
[14] Kim G, Yun G S, Woo M, Park H K and the KSTAR Team 2018 Plasma Phys. Control. Fusion 60 035009
[15] Parker E N 1957 J. Geophys. Res. 62 509
[16] Petschek H E and Thorne R M 1967 Astrophys. J. 147 1157
[17] Carmichael H 1964 The Physics of Solar Flares, Proceedings of AAS-NASA Symposium, 1964, Washington, D.C., USA, p. 451
[18] Sturrock P A 1966 Nature 211 695
[19] Hirayama T 1974 Sol. Phys. 34 323
[20] Kopp R A and Pneuman G W 1976 Sol. Phys. 50 85
[21] Su Y, Veronig A M, Holman G D, Dennis B R, Wang T, Temmer M and Gan W 2013 Nat. Phys. 9 489
[22] Dahlin J T, Antiochos S K and DeVore C R 2019 Astrophys. J. 879 96
[23] Angelopoulos V, McFadden J P, Larson D, Carlson C W, Mende S B, Frey H, Phan T, Sibeck D G, Glassmeier K H, Auster U, Donovan E, Mann I R, Rae I J, Russell C T, Runov A, Zhou X Z and Kepko L 2008 Science 321 931
[24] Priest E R 1985 Rep. Prog. Phys. 48 955
[25] Wesson J 2004 Tokamaks, 3rd edn. (Oxford: Clarendon Press) pp. 374-390
[26] Furth H P, Killeen J and Rosenbluth M N 1963 Phys. Fluids 6 459
[27] Canuto C, Hussaini M Y, Quarteroni A and Zang T A 1987 Spectral Methods in Fluid Dynamics (New York: Springer-Verlag) pp. 3-7, 183-278
[28] Canuto C, Hussaini M Y, Quarteroni A and Zang T A 2007 Spectral Methods: Evolution to Complex Geometries and Applications to Fluid Dynamics (Scientific Computation) (Berlin: Springer-Verlag) pp. 39-430
[29] Le Maȋtre O P and Knio O M 2010 Spectral Methods for Uncertainty Quantification: With Applications to Computational Fluid Dynamics (New York: Springer-Verlag) pp. 107-339
[30] Serre E and Pulicani J P 2001 Computers & Fluids 30 491
[31] Glasser A H, Sovinec C R, Nebel R A, Gianakon T A, Plimpton S J, Chu M S, Schnack D D and the NIMROD Team 1999 Plasma Phys. Control. Fusion 41 A747
[32] Lütjens H and Luciani J F 2008 J. Comput. Phys. 227 6944
[33] Wang S and Ma Z W 2015 Phys. Plasmas 22 122504
[34] Brennan D P, La Haye R J, Turnbull A D, Chu M S, Jensen T H, Lao L L, Luce T C, Politzer P A, Strait E J, Kruger S E and Schnack D D 2003 Phys. Plasmas 10 1643
[35] Granetz R, Whyte D G, Izzo V A, Biewer T, Reinke M L, Terry J, Bader A, Bakhtiari M, Jernigan T and Wurden G 2006 Nucl. Fusion 46 1001
[36] Lutjens H and Luciani J F 2010 J. Comput. Phys. 229 8130
[37] Halpern F D, Lütjens H and Luciani J F 2011 Phys. Plasmas 18 102501
[38] Zhang W, Wang S and Ma Z W 2017 Phys. Plasmas 24 062510
[39] Zhang W, Ma Z W, Zhang H W and Zhu J 2019 Phys. Plasmas 26 042514
[40] Bi H L, Wei L, Fan D M, Zheng S and Wang Z X 2016 Acta Phys. Sin 65 225201 (in Chinese)
[41] Pritchett P L, Lee Y C and Drake J F 1980 Phys. Fluids 23 1368
[42] Drake J F 1978 Phys. Fluids 21 1777
[43] Yagi M, Yoshida S, Itoh S I, Naitou H, Nagahara H, Leboeuf J N, Itoh K, Matsumoto T, Tokuda S and Azumi M 2005 Nucl. Fusion 45 900
[44] Gottlieb D and Hesthaven J S 2007 Spectral Methods for Time-Dependent Problems (Cambridge: Cambridge University Press) pp. 34-42
[1] Linear analysis of plasma pressure-driven mode in reversed shear cylindrical tokamak plasmas
Ding-Zong Zhang(张定宗), Xu-Ming Feng(冯旭铭), Jun Ma(马骏), Wen-Feng Guo(郭文峰), Yan-Qing Huang(黄艳清), and Hong-Bo Liu(刘洪波). Chin. Phys. B, 2023, 32(1): 015201.
[2] Collisionless magnetic reconnection in the magnetosphere
Quanming Lu(陆全明), Huishan Fu(符慧山), Rongsheng Wang(王荣生), and San Lu(卢三). Chin. Phys. B, 2022, 31(8): 089401.
[3] Physical aspects of magnetized Jeffrey nanomaterial flow with irreversibility analysis
Fazal Haq, Muhammad Ijaz Khan, Sami Ullah Khan, Khadijah M Abualnaja, and M A El-Shorbagy. Chin. Phys. B, 2022, 31(8): 084703.
[4] Effect of the magnetization parameter on electron acceleration during relativistic magnetic reconnection in ultra-intense laser-produced plasma
Qian Zhang(张茜), Yongli Ping(平永利), Weiming An(安维明), Wei Sun(孙伟), and Jiayong Zhong(仲佳勇). Chin. Phys. B, 2022, 31(6): 065203.
[5] Electron acceleration during magnetic islands coalescence and division process in a guide field reconnection
Shengxing Han(韩圣星), Huanyu Wang(王焕宇), and Xinliang Gao(高新亮). Chin. Phys. B, 2022, 31(2): 025202.
[6] Evolution of melt convection in a liquid metal driven by a pulsed electric current
Yanyi Xu(徐燕祎), Yunhu Zhang(张云虎), Tianqing Zheng(郑天晴), Yongyong Gong(龚永勇), Changjiang Song(宋长江), Hongxing Zheng(郑红星), and Qijie Zhai(翟启杰). Chin. Phys. B, 2021, 30(8): 084701.
[7] Spontaneous growth of the reconnection electric field during magnetic reconnection with a guide field: A theoretical model and particle-in-cell simulations
Kai Huang(黄楷), Quan-Ming Lu(陆全明), Rong-Sheng Wang(王荣生), Shui Wang(王水). Chin. Phys. B, 2020, 29(7): 075202.
[8] Formation of electron depletion layer and parallel electric field in the separatrix region of anti-parallel magnetic reconnection
Zisheng Li(李子圣), Huanyu Wang(王焕宇), Xinliang Gao(高新亮). Chin. Phys. B, 2019, 28(7): 075203.
[9] Preliminary investigation on electrothermal instabilities in early phases of cylindrical foil implosions on primary test stand facility
Guanqiong Wang(王冠琼), Delong Xiao(肖德龙), Jiakun Dan(但家坤), Yang Zhang(张扬), Ning Ding(丁宁), Xianbin Huang(黄显宾), Xiaoguang Wang(王小光), Shunkai Sun(孙顺凯), Chuang Xue(薛创), Xiaojian Shu(束小建). Chin. Phys. B, 2019, 28(2): 025203.
[10] Basic features of the multiscale interaction between tearing modes and slab ion-temperature-gradient modes
L Wei(魏来), Z X Wang(王正汹), J Q Li(李继全), Z Q Hu(胡朝清), Y Kishimoto(岸本泰明). Chin. Phys. B, 2019, 28(12): 125203.
[11] Effects of q-profiles of a weak magnetic shear on energetic ion excited q=1 mode in tokamak plasmas
Ze-Yu Li(李泽宇), Xian-Qu Wang(王先驱), Xiao-Gang Wang(王晓钢). Chin. Phys. B, 2016, 25(1): 015203.
[12] Out-of-plane shear flow effects on fast magnetic reconnection in a two-dimensional hybrid simulation model
Wang Lin (王琳), Wang Xian-Qu (王先驱), Wang Xiao-Gang (王晓钢), Liu Yue (刘悦). Chin. Phys. B, 2014, 23(2): 025203.
[13] Simulation for double shell pinch
Wang Gang-Hua (王刚华), Hu Xi-Jing (胡熙静), Sun Cheng-Wei (孙承纬). Chin. Phys. B, 2004, 13(12): 2105-2108.
No Suggested Reading articles found!