Numerical Study On MHD Instability Modes In Tokasmaks

The efficiency of Tokamak is confined by the beta (the ratio of the plasma pressure to magnetic field pressure) in the magnetic confinement of toroidal plasma, and the external kink mode(XKM) is the macroscopic MHD instabilities that limits the beta. The external kink mode can be driven by toroidal current or pressure gradient, and can be stabilized by a perfectly conducting wall, which is close enough to the plasma surface. But there is no perfectly conducting wall in the realistic devices, this external kink mode will excited to a new instability mode called the resistive wall mode(RWM) by the finite conductivity wall.The future advanced Tokamak device ITER, Reversed Field Pinch, and Tokamak devices at present, such as DIII-D, JT-60U and JET, are expected to run in the high beta mode. In the Tokamak plasma, resistive wall mode is normally driven by plasma equilibrium pressure, or plasma equilibrium current. In reversed field pinch, the resistive wall instability is always driven by the plasma equilibrium current, and disruptive instability occurs whenever the duration of the discharge is longer than the wall penetration time. Bondeson and Ward first discovered that RWM can be stabilized when the plasma rotates at some fraction of the sound speed in their numerical study in 1994, and it is be proved in the later experiment in DⅢ-D. And recent studies show that few or even no plasma rotation since the kinetic mechanisms is predicted as a significant stabilizing effect in current fusion devices, even the stability of ITER.In this thesis, we study on the character of the resistive wall instability which is driven by parallel current in the toroidal coordinate. This model takes into account plasma pressure, plasma rotation, viscosity and a resistive wall with a thin-wall approximate. In the model equations, the equilibrium current profile is from Wesson(1997) for external kinks in a tokamak. The most unstable mode is the low number mode, so in the thesis we focus on the m/n=2/1 (the ratio of poloidal number m to toroidal number n) mode whose rational surface is in the region of internal vacuum. The jump conditions are satisfied to connect the magnetic fields across the plasma-vacuum surface through Maxwell equations and the momentum equation. The axis symmetry condition is used on the axis.The main method that we carry on the research is solving the model equations as the eigenvalue problem. All the equilibrium functions are converted to the function of the poloidal fluxΨ0 only, and are calculated by using the code CHEASE. And then we attain the eigenmode equations deduced from MHD equations. Subsequently the finite element difference is made for the system, which leads to the eigenvalue problem. The MARS code is adopted to solve this eigenvalue problem.In the chapter 2, the main study is about the ideal external kink mode. In the chapter 3, the effect of parameter of the resistive wall on the MHD instabilities is investigated. In the chapter 4, we add the toroidal plasma rotation and study the effect of it on the MHD instabilities. Finally, a brief summary and discussion are given in the end of this thesis.