Numerical Studies Of External Kink Mode And Resistive Wall Mode In Tokamaks

The external kink mode (XKM) is long known as an important macroscopic magnetohydrodynamic (MHD) instability, mainly driven by plasma current and/or pressure. In fusion experiments, in particular in advanced tokamaks, it is desirable to confine the plasma to achieve the highest possible pressure. But this may cause dangerous consequences. One such is that the fusion plasma globally kinks, often causing a major disruption, which results in the complete loss of the plasma confinement and the ultimate direct contact of the plasma with materials walls. Theoretically, XKM can be completely suppressed by a closely surrounding, perfectly conducting wall. In reality, the material walls (e.g. vacuum vessels, conducting plates, etc.) normally have finite resistivity, and the XKM can not be completely suppressed due to the leakage of the radial magnetic flux. On the other hand, a highly conducting wall helps to substantially reduce the growth rate (from the Alfven time scale τA to the wall eddy current decay time υw) of the XKM, resulting in an instability which in some aspects still resembles XKM (e.g. the global mode structure measured in terms of the plasma displacement), but in many other aspects can be viewed as a new type of instability. This new instability is called the resistive wall mode (RWM). RWM did not draw much attention, in earlier study, due to its relatively slow growth time scale. For advanced tokamaks, a long pulse (τ>>τw), steady-state fusion plasma is required. Thus, the study on the RWM is very important. In this Thesis, the effect of the plasma equilibrium current density profile on XKM is numerically studied, followed by a numerical investigation, using the MARS-F and MARS-K codes, of the effect of parallel sound wave damping and drift kinetic damping on the stability of the RWM stability, assuming various plasma rotation profiles. The effect of plasma shear flow on the RWM stability in an ITER steady state advanced scenario is also systematically studied. Details are as follows:In Chapter I, the backgrounds, motivations and methods of the investigation are briefly presented. The energy crisis issue and the prospect of renewable energy resources from controlled thermal nuclear fusion are briefly reviewed. The energy principle approach and the normal mode approach are described as two important methods for studying MHD instabilities. The physics models of the MARS-F/K code are also presented.In Chapter II, based on a linearized MHD model, the effect of the equilibrium current density profile on XKM in tokamaks is studied by using the MARS-F code. Three types of current profiles are adopted in this work. Firstly, a set of parabolic equilibrium current profiles are chosen. The effects of the current gradient and jump on the growth rate of XKM are investigated. It is found that the current jump, which causes the q profiles to change, plays an important role in the XKMs in tokamaks. Secondly, a set of step equilibrium current profiles with different jump positions are chosen. The effect of jump position on XKMs is discussed. Thirdly, a set of parabolic equilibrium current profiles with current bumps are chosen for the case of off-axis heating. The effects of height, width and position of the current bumps on XKMs are analyzed.In Chapter III, The effect of sound wave damping (SWD) and drift kinetic damping (DKD) on the stability of the RWM is numerically investigated for one of the advanced steady state scenarios in ITER. The key element of the investigation is to study how different plasma rotation profiles affect the stability prediction. The single fluid, toroidal magnetohydrodynamic (MHD) code MARS-F and the MHD-kinetic hybrid code MARS-K are used for this purpose. Three extreme rotation profiles are considered:(a) a uniform profile with no shear, (b) a profile with negative flow shear at the q=2 rational surface (q is the equilibrium safety factor), and (c) a profile with positive shear at q=2. The parallel viscous force is found to be effective for the mode stabilization at high plasma flow speed (about a few percents of the Alfven speed) for profiles (a) and (b), but the stable domain does not appear with the rotation profile (c). The predicted eigenmode structure is different with different rotation profiles. With a self-consistent inclusion of the magnetic precession drift resonance of thermal particles in MARS-K computations, lower critical flow speed, i.e. the minimum speed needed for full suppression of the mode, is obtained. Likewise the eigenmode structure is also modified by different rotation profiles in the kinetic results.In Chapter IV, Rotational stabilization of the RWM (RWM), with varying ExB flow shear and the radial location of peak shear, is systematically investigated using the MARS-K code, following a non-perturbative magnetohydrodynamic-kinetic hybrid approach. The equilibrium is based on 9MA steady state target plasma from the ITER design, except for the plasma flow profile, which is significantly varied in this study. Generally two branches of unstable n=l kinetic RWM are computed (n is the toroidal mode number), depending on the flow amplitude. The first unstable branch, which is normally the more unstable one, is sensitively affected by both the local flow shear as well as the radial location of the peak amplitude of the shear. On the contrary, the second unstable branch, which is often weakly unstable, is less affected by the flow shear. Consequently, stability domains are computationally mapped out in relevant two-dimensional parameter spaces.Chapter V summarizes the work as well as discusses the future work.