Energetic Ion Effects on Tearing Mode Instabilitie

This thesis consists of developing an analytic model of linear resistive tearing modes that occur within tokamak experiments, and the effect that high-energy ions have on this mode's stability. The drift-kinetic motion of high-energy ions interacting with the perturbed fields of a tearing mode described by a reduced modeling framework is found to contribute significantly to the stability of tokamak equilibrium states. Using the mathematical framework of a piecewise continuous basis function and an asymptotic matching method describing the tearing mode combined with the framework of pressure coupling of the ion drift-kinetics, we determine the effect on tearing stability due to changes in equilibrium parameters and energetic ion resonances. The result is a description of tearing stability that is dependent on the magnetic shear (s = [1/q( r)][dq(r)/dr]) across the equilibrium. The effect that energetic ion resonances have on the development of the mode is governed by the ions' kinetic contribution to the perturbed pressure, and this contribution is heavily dependent on the nature of the magnetic field line topology. The key findings of this thesis are that configurations with significant negative shear (s < scrit) in the core region interior to the rational surface can have a tearing mode resonant at that surface which is driven towards instability while configurations above this threshold in shear are driven towards stability by energetic ions. The effect is caused by shifts in the pitch angle resonance of the energetic ions as the magnetic shear varies, and the strength of its contribution is proportional to the pressure gradient. This is the first study to include a non-Maxwellian kinetic distribution in an analytic model and measure its effect on the stability of the tearing mode, resulting in a newfound understanding of the physics behind the puzzling results observed in experiments.