MHD Simulations About Impact Of Shear Flows On Double Tearing Modes

Double tearing mode (DTM) has been observed in space plasmas as well as in fusion plasmas with the reversed magnetic shear configuration. The DTM is believed to be one of the most important mechanisms leading to the sudden loss of the confinement in tokamak and the fast reconnection in the astrophysical plasmas due to the interplay of two islands formed on two rational surfaces. In order to suppress such events, sheared plasma flows have been considered to be one of the plausible candidates. The shear flows induced by the momentum input through the neutral beam injection and/or wave drive in tokamak and by the solar activities, such as the solar wind, in space plasmas have been reported. Thus, understanding the influence of the shear flow on the DTM is of significant importance. Although the influence of various kinds of shear flows on the DTM has been studied extensively, the stabilization or possible destabilization mechanisms have not been fully understood. Meanwhile, due to the complexity of the nonlinear dynamics, to thoroughly address the influence of the shear flow on the evolution of the DTM remains a challenge for the theory and the simulation. In this thesis, we perform simulations using the eigenvalue method and the initial perturbation method to study the linear and nonlinear dynamics of the DTM with shear flows.In Chapter1, a brief overview of the background, fundmental characteristics of the DTM and the work progress about the influence of the shear flow on the DTM are introduced.In Chapter2, the reduced resistive MHD model, basic equilibriums of the magnetic field and shear flows as well as the numerical methods are described.In Chapter3, the DTM with shear flows are linearly simulated by the eigenvalue analysis based on the reduced resistive MHD model in slab geometry. Shear flows with antisymmetric profile are focused. The even (odd) DTM is stabilized (destabilized) by weak shear flows through the distortion of magnetic islands mainly due to the global effect of shear flows. For the medium flows, two eigenmodes with the same growth rate but opposite propagating direction are identified. Due to the Alfven resonance, two eigenmodes of the DTM show the similar structure to the single tearing mode and may be destabilized. In addition, the electromagnetic Kelvin-Helmholtz (KH) instability coexisting with DTMs is also discussed.In Chapter4, the generation dynamics and the structural characteristics of the zonal flow are investigated in the DTM with the weak and the medium shear flows. For the weak flows, zonal flows grow oscillatorily in the Rutherford regime resulting from the nonlinear interaction between the distorted islands and the zonal flow. Moreover, the weak flow has little influence upon the global reconnection of the DTM. For the medium flows, an oscillatory growing zonal flow occurs in the linear phase originating from the three-wave mode coupling pumped by two DTM eigenmodes. Furthermore, impacts of the oscillatory zonal flows on the DTM islands and the global reconnection are also discussed briefly.In Chapter5, the nonlinear interactions between the DTM and the KH instability are numerically investigated. For a relative weak KH instability, after the linear growth, the zonal flow saturates and damps the KH fluctuations. Then in the turbulent background, the DTM evolves and the interchange of the magnetic islands and the full reconnection of the magnetic field lines terminates the whole evolution. For the strong KH instability, the vortex-driven magnetic reconnection is dominant. And the medium KH instability may be understood as the transition phase of the cases with the weak and the strong KH instabilities.In Chapter6, a brief summary and the plan of the future work are presented.