Application of Galerkin spectral method for tearing mode instability

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 of 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.

Effects of diamagnetic drift on nonlinear interaction between multi-helicity neoclassical tearing modes

“…[1][2][3] The tearing mode (TM), one kind of the most dangerous instabilities in this context, will occur in the presence of finite resistivity. [4][5][6][7][8] Due to resistive dissipation effects, TMs can alter the topology of the magnetic surfaces through magnetic reconnection, leading to the formation of magnetic islands in the vicinity of rational surfaces. When seed islands in the system reach a sufficient size, the flattening of pressure gradients inside the magnetic islands induces a significant loss of bootstrap current, [9,10] which in turn widens the magnetic islands.…”