Instabilities Of Plasma With Both Sheared Magnetic Field And Shear Flow

In this thesis, we have investigated plasma instabilities with both sheared magnetic field and plasma flow within the framework of magnetohydrodynamics. The plasma flow is always chosen to be parallel to the magnetic field. In Cartesian coordinate,the plasma flow and magnetic field can be written as:u=(0, u0tanh(x/dv),0),B=(0, Bo tanh(x/d).0), respectively. The param-eters u0, dx, Bo, d are the flow speed, flow shear thickness, magnetic field strength, and current sheet thickness, respectively. In this configuration, both tearing instability and Kelvin-Helmholtz instability may develop under proper conditions.In the second chapter, we studied effects of sub-Alfvenic shear flows on plasma instabilities in an incompressible MHD model. With sub-Alfvenic shear flows, Kelvin-Helmholtz instability does not occur while tearing mode is unstable. It is found that the shear flow can either stabilize or destabilize the tearing mode, depending on both the speed and the shear thickness of the plasma flow. In the extreme case Ro=(u0d)/(B0dv)=1.0, the tearing mode is fully suppressed by the shear flow.In Chapter3, we investigate roles of super-Alfvenic shear flows on plasma instabilities in a compressible MHD model. The compressibility of plasma is important when the flow speed is super-Alfvenic. In the linear growth phase, there are two parameter regimes of plasma flows: one with tearing mode instability only and another with Kelvin-Helmholtz instability dominantly. The shear flow with a relative small thickness drives a Kelvin-Helmholtz instability in accompany with a tearing mode instability. But for the super-Alfvenic flow with a large shear thickness, the tearing mode becomes unstable only. For the KH instability, the mode could be pure growing or oscillating growing, which depends on the flow speed. For the cases with the tearing mode dominant, two Alfvenic resonant layers always show up on both sides of the current sheet.In Chapter4, we checked influences of resistivity and hall effect on plasma instabilities. In the KH dominating case, resistivity has little effect on the linear growth rate. But in the nonlinear stage, for smaller resistivity, the plasma reaches the saturate stage earlier. A secondary tearing instability shows up when the resistivity is small enough. In the tearing mode dominating case, resistivity is a key factor of the linear growth rate. But the scaling law also depends on flow speeds.Finally, we give a brief summary and discussion in the last chapter.