Shear Alfven continua and discrete modes in the presence of a magnetic island

Shear Alfven instabilities are of considerable interest to plasma confinement and will become even more important in ITER and future devices containing strong energetic particle drive. In this dissertation, we investigate the effects of a magnetic island on the shear Alfven continuum both analytically and numerically. Using an island coordinate system and a WKB approximation of the linearized ideal MHD equations, a shear Alfven dispersion relation for the continuum is found globally in the presence of an island; the first time this has been obtained analytically. The island is shown to cause an upshift in the continuum accumulation point frequency. The minimum of the frequency spectrum is shifted from the rational surface to the island separatrix. This analytic result confirms previous numerical work.;The theory is used to explain some previously uncategorized Alfvenic activity observed on the Madison Symmetric Torus (MST) reversed-field pinch during neutral beam injection. A sizable n = 5 island exists in the plasma core that has not been included in past simulations of the MST Alfven spectrum. The theoretical Alfven continua in the core of the island provide a gap in which the observed n = 4 Alfvenic bursts reside, suggesting that these modes may arise from a coupling due to the island. A novel code for computing Alfven eigenmodes called SIESTAlfven is described. SIESTAlfven utilizes 3D MHD equilibria with an island obtained using the SIESTA code. The Alfven modes are computed by solving the generalized eigenvalue problem obtained from the Hessian matrix of the potential energy along with the inertia matrix of the SIESTA equilibrium. Numerical simulations using SIESTAlfven and the STELLGAP/AE3D codes are used to identify the Alfven bursts on MST as the first observation of an Island-induced Alfven Eigenmode (IAE). The IAE arises from a helical coupling of mode numbers inside the island core. Additional n=-1 activity on MST is shown to be consistent with a second type of island-induced mode residing below the lowest continuum branch, named here the Island-induced Global Alfven Eigenmode (IGAE). The continuum theory also explains the Beta-induced Alfven Eigenmode (BAE) frequencies observed during tearing modes on tokamaks including EAST and FTU.