Tokamak Axisymmetric Stability : Vertical Displacements and their Consequences
Creators: name: Windridge, Melanie Jane
Publisher: name: Imperial College London
Year: 2009

description: Vertical Displacement Events (VDEs) are a major concern for future tokamak operation since their consequences—halo currents and the associated j × B forces on the vacuum vessel—have the potential to be very damaging when scaled up to ITER-size devices. VDEs become more likely for elongated plasmas, which are inherently vertically unstable and most tokamaks, including ITER, will operate with elongated plasmas to take advantage of the higher [Beta], and therefore higher efficiency. Plasma stability to vertical displacement and halo current mitigation are therefore critical areas of study for future tokamak devices. The extreme geometry of Spherical Tokamaks (STs) makes them interesting machines on which to investigate stability and halo current behaviour, and none more so than the Mega Amp`ere Spherical Tokamak (MAST), which has a unique open vacuum vessel design. This thesis combines simple analytic exploration, theoretical modelling, and experimental work and analysis on the MAST tokamak. The vertical stability of the plasma is studied in MAST with a view to determining whether the non-linearity in the vertical feedback controller is increased in STs compared to conventional tokamaks. It is thought that the higher curvature of the vertical field index in STs will play a role, along with the deterioration in efficacy of the vertical feedback with progressing excursion from equilibrium. The open design of the MAST vessel brings an extra dimension to the problem, with the passive stabilisation being provided by internal coil casings. Contrary to the design of many other tokamaks, where a toroidal shell with coils outside is used, the MAST vessel is cylindrical with poloidal field coils hanging on the inside. The origin of non-linearity in the plasma response is explored by way of a simple heuristic analytic model of an up-down symmetric plasma. Simulations are made using the non-linear equilibrium evolution code DINA-CH to model plasma discharges subject to a sinusoidal perturbation. Both MAST and a hypothetical conventional aspect ratio tokamak are investigated. The responses of the plasma are subjected to harmonic analysis to determine the non-linearity in the systems and enhanced non-linearity is found in MAST. Experiments undertaken specifically to explore this effect in the MAST tokamak are also detailed. These non-linear effects in plasma control require consideration by controller designers. Having examined plasma stability in MAST, one of the primary consequences of VDEs—halo currents—are explored in detail. Forced VDE experiments are described and the data analysed to give a picture of where in the MAST vessel halo currents flow. A new method is developed for use with the DINA code to calculate the halo currents flowing in the different passive conductors, based on summing over flux surfaces. Further investigation is made into the stability of the MAST plasma at high displacements from equilibrium, and it is found that MAST has a region of extreme instability, where both the feedback and the passive stabilisation are insufficient to hold the plasma and thus the plasma acceleration is very rapid. The mechanisms for generating halo currents are considered in detail and an analytic circuit-equation model is used to demonstrate the consistency of our understanding and to investigate the relative strength of the main drivers in MAST.