Chin. Phys. B, 2022, Vol. 31(11): 110203    DOI: 10.1088/1674-1056/ac600d
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# 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