Dwindling fossil fuel resources, and the undesirable environmental effects associated with their use in power generation, are a powerful impetus in the search for clean, reliable and inexpensive methods of generating electricity. Fusion is a process wherein light nuclei are able to fuse together, releasing large amounts of energy. Magnetic Confinement Fusion is one concept for harnessing this energy for electricity production. The tokamak reactor confines the plasma in a toroidal configuration using strong magnetic fields to minimise particle and heat losses from the plasma. However, this plasma can become unstable, resulting in loss of plasma confinement, or plasma disruption.
In particular, the instability known as the Resistive Wall Mode (RWM) is of concern for operating scenarios which are designed to optimise the fusion process, yet lie close to mode stability boundaries. The RWM is a global instability, which can cause plasma disruption. The mode is so named because it is only present when the plasma is surrounded by a resistive wall. Theoretical and experimental studies have found that plasma rotation is able to stabilise the RWM; yet in projected operating scenarios for ITER, the plasma rotation will fall below the levels found in present tokamaks. Understanding the stability of the RWM in 'advanced' scenarios is crucial, and requires non-linear physics to incorporate all the characteristics of the mode.
In this thesis, the Introduction describes the need for the development of fusion energy, and why the RWM is an important consideration in planning for future experimental programmes. The Literature Review summarises the current state of knowledge surrounding the RWM and its stability in tokamak plasmas. In Chapter 3, an analytic study of the RWM is presented. In this study, the mode is coupled to a different mode, known as the Neoclassical Tearing Mode. A system of non-linear equations describing the coupling of the modes in a rotating plasma is derived. In Chapter 4, these equations are solved for limiting solutions, and solved numerically, to show how the RWM may be responsible for an observed phenomenon called the triggerless NTM. Chapter 5 and Chapter 6 focus on simulations of RWMs. Chapter 5 describes the implementation of a resistive wall in the non-linear MHD code JOREK, carried out by M. Holzl. This implementation is benchmarked successfully against a linear analytic formula for the RWM growth rate. In Chapter 6, initial simulations using the resistive wall in JOREK are carried out. These simulations are carried out in ITER geometry, with the resistive wall modelling the ITER first wall. Chapter 7 summarises the conclusions of the research chapters and lays out future work which could be undertaken in both analytic modelling and simulations.
