On the abrupt growth dynamics of nonlinear resistive tearing mode and the viscosity effects

The nonlinear evolution of the resistive tearing mode exhibits an abrupt growth after an X-point collapse once the magnetic island exceeds a certain critical width Delta'w(c) for large instability parameter Delta', leading to a current sheet formation [N. F. Loureiro et al., Phys. Rev. Lett. 95, 235003 (2005)]. In this work, we investigate the underlying mechanism of the X-point collapse as well as the current sheet formation including the viscosity effects, based on a secondary instability analysis. The secondary instability is excited due to the quasilinear current modification by the zonal current. In particular, it is identified that the current peaking effect is plausibly responsible for the onset of the X-point collapse and the current sheet formation, leading to the explosive growth of reconnected flux. In the presence of finite viscosity, the Delta'w(c) scaling with the resistivity gets modified. A transition behavior is revealed at P-r approximate to 1 for the viscosity dependence of Delta'w(c) and the linear tearing instability. However, the explosive growth seems to be independent of the viscosity in the magnetic Prandtl number P-r < 1 regime, while large viscosity plays a strong dissipation role. (C) 2014 AIP Publishing LLC.