Nonlinear study of tearing modes and plasma flows around magnetic islands in tokamak plasmas

The behavior of non-linear tearing modes and the plasma flows around magnetic islands is studied numerically in a cylindrical geometry using the method of reduced magneto-hydro-dynamic simulation. The results show that the single tearing mode (STM) becomes stable in a short time. The magnetic islands of double tearing modes (DTMs) first develop to a sufficiently large scale and then couple together when entering the non-linear phase. It is also shown that, before the non-linear growth stage, the perturbed kinetic energy and magnetic energy of both the STM and DTM have a process from different signs to constant positive values. For the STM island and plasma flow, it is demonstrated that the shear flow is formed on both sides of the islands and the poloidal flow velocity around the O-point is larger than that around the X-point. For the DTM island and plasma flow, we found that the peak of the poloidal flow velocity is mainly distributed at the O-point edge and the X-point of the magnetic island and the plasma flow velocities at the magnetic island edges are opposite. In addition, the process of plasma flow accompanying the nonlinear evolution of tearing modes is also presented.