Stabilizing Effect Of Equilibrium Flow And Feedback Control On Resistive Wall Modes

In the Tokamak plasmas, the plasma pressure is limited by the external kink mode because of its global structur. And this mode can lead to disruption directly, for its great growth rate. Therefore, the external kink mode is one of the most dangerous magnetohydrodynamic modes in the high pressure and bootstrap current tokamaks. Fortunately, this kind of external kink mode can be stabilized totally by a perfect wall surrounding the plasma, then the plasma pressure can be enhanced. However, another new instability called resistive wall mode (RWM) can be excited when there is finite resistivity on the conducting wall, the growth rate of which is smaller than the external kink mode significantly, and it is still dangerous when the discharge time of the device exceeds the wall diffusion time. So, the stabilization of the RWM is also improtrant for us.In the recent study, it is found that the RWM can be stabilized with two methods. The one is by the plasma rotation when there is the viscosity in the plasma, but we still do not understand clearly the mechanism. And the other one is by taking the active feedback control system into system, which is a new but effective way to control the growth rate of the MHD instability in the tokamaks. However, there is very little work to study on the evolution of the instability and the effective control logic after the power saturation of the feedback system. In this thesis, we study on the MHD instabilities in the system with resistive wall, and the way of the stabilization of them.In Chapter Ⅰ, a brief review on our topic is given, and then the meaning of the resistive wall mode and the evolution how to make them stabilized are explained.In Chapter Ⅱ, we adopt the non-ideal MHD equation with the plasma viscosity to describe the plasma in our model and the thin wall approximation to simulate the resistive wall, and used initial value way to solve all of these equations. Afterward, LARWM code is carried out to study on the MHD instabilities in the plasma with the resistive wall. After the benchmark of our code, we confirm the wall diffusion time.In Chapter Ⅲ, we apply the LARWM code to study the effect of the heating driven by current on the external kink mode in no-wall model. The numerical results illuminate that the equilibrium current bump on the tail is the thinner and higher the better, even the external kink mode can be stabilized totally. In addition, the growth rate of the external kink mode can be decreased while being close to the plasma region, where the critical position is rcr=0.85. In Chapter IV, the resistive wall is taken into account to investigate the stabilizing effect of the shear equilibrium flow on the RWMs, including the global and local structures. It is found that the inertia energy of the equilibrium plasma flow is the most important for the stabilization of the RWMs. However, there is no obvious effect of the structure in the center of plasma on the stabilization of the RWMs.In Chapter V, the active feedback control system is taken into the cylinder model to study the effective control schemes of the stabilization of the RWMs, when the control system achieves power saturation. It can be seen that, just flux-to-current logic and flux-to-voltage logic are effective after the power saturation. But the flux-to-current logic is very sensitive to the signal on the active coils in the closed loop, and cannot tolerate the saturation of the control coil current. On the contrary, the flux-to-voltage logic can allow a certain degree of saturation, without the loss of the closed loop stability.In Chapter VI, a slab model is employed to describe the ideal plasma with the resistive wall. By eigen mode analysis, three eigen modes are obtained in this system, where one is the normal mode in plasma which is always stable, the second one is the Kelvin-Helmholtz instability, and the last one is the instable mode driven by the plasma flow. After taking the viscosity into account, the second mode can be stabilized and the stable boundary is also changed, so that a second stable region appears. However, the stable boundary of the instability driven by the plasma flow does not move, even though the growth rate of it has been decreased by the plasma viscosity.Finally, a brief summary ends this thesis.