Influence of toroidal equilibrium plasma rotation on m/n=2/1 resistive tearing modes is studied numerically using a 3D toroidal MHD code (CLT). It is found that the toroidal rotation with or without shear can suppress the tearing instability and the Coriolis effect in the toroidal geometry plays a dominant role on the rotation induced stabilization. For a high viscosity plasma (τ R /τ V >>1, where τ R and τ V represent resistive and viscous diffusion time, respectively.), the effect of the rotation shear combined with the viscosity appears to be stabilizing. For a low viscosity plasmas (τ R /τ V <<1), the rotation shear shows a destabilizing effect when the rotation is large.

The tearing instability in a current sheet, which has a sub-Alfvénic or super-Alfvénic plasma flow in the current layer, is investigated based on the linearized compressible magnetohydrodynamic (MHD) equations. An initial-value method is employed to obtain the linear growth rate and eigenmode profiles of the fastest growing mode. The results show that for a sub-Alfvénic plasma flow parallel to the neutral sheet, the growth rate of the tearing instability is only slightly larger than that of the pure tearing mode without the flow. On the other hand, a large increase in the growth rate of the most unstable mode is observed, when the streaming speed V0m in the central region of the current sheet increases above a critical speed VC≂1.2VA∞. Here VA∞ is the Alfvén speed far away from the current layer. This study shows that when the electric resistivity η is zero, the sausage mode is excited because of a super-Alfvénic plasma flow parallel to the current sheet. This flow-induced sausage mode is called the streaming sausage mode. In the presence of a finite resistivity, the streaming sausage mode becomes a mixed sausage–tearing mode, because of the presence of magnetic field line reconnections in the current sheet. This mixed sausage–tearing mode, or simply the streaming tearing mode, has a high growth rate, γ≂0.1τ−1A, where τA is the Alfvén transit time across the current layer. This growth rate is larger than the growth rate of the pure tearing mode, which is approximately the inverse of the geometric mean of the Alfvén time τA and the diffusion time τD across the current layer.

Tearing mode instability is one of the most important dynamic processes in space and laboratory plasmas. Hall effects, resulted from the decoupling of electron and ion motions, could cause the fast development and perturbation structure rotation of the tearing mode and become non-negligible. A high accuracy nonlinear MHD code (CLT) is developed to study Hall effects on the dynamic evolution of tearing modes with Tokamak geometries. It is found that the diamagnetic rotation of the mode structure is self-consistently contained in the Hall MHD model. The self-consistently generated rotation largely alters the dynamic behaviors of the double tearing mode.

The influence of driven current on the m/n=2/1 resistive tearing mode is studied systematically using a three-dimensional toroidal magnetohydrodynamic code. A uniform driven current with Gaussian distribution in the radial direction is imposed around the unperturbed rational surface. It is found that the driven current can locally modify the profiles of the current and safety factor, such that the tearing mode becomes linearly stable. The stabilizing effect increases with the increase of the driven current Icd or the decrease of its width δcd, unless an excessively large driven current reverses the magnetic shear near the rational surface and drives other instabilities such as double or triple tearing modes. The stabilizing effect can be negligible or becomes reversed if the maximum driven current density is not at the unperturbed rational surface.

The influences of helical driven currents on nonlinear resistive tearing mode evolution and saturation are studied by using a three-dimensional toroidal resistive magnetohydrodynamic code (CLT). We carried out three types of helical driven currents: stationary, time-dependent amplitude, and thickness. It is found that the helical driven current is much more efficient than the Gaussian driven current used in our previous study [S. Wang et al., Phys. Plasmas 23(5), 052503 (2016)]. The stationary helical driven current cannot persistently control tearing mode instabilities. For the time-dependent helical driven current with fcd=0.01 and δcd&lt;0.04, the island size can be reduced to its saturated level that is about one third of the initial island size. However, if the total driven current increases to about 7% of the total plasma current, tearing mode instabilities will rebound again due to the excitation of the triple tearing mode. For the helical driven current with time dependent strength and thickness, the reduction speed of the radial perturbation component of the magnetic field increases with an increase in the driven current and then saturates at a quite low level. The tearing mode is always controlled even for a large driven current.

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