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Abstract
A quasilinear perturbation analysis of the time independent MHD equations has lead to the formulation of a set of equations suitable for the study of saturated tearing modes. The quasilinear analysis allows the effects of the magnetic island on the background equilibrium to be modelled in a self consistant way in a toroidal plasma of arbitrary aspect ratio, beta, and cross section.
The most important finding of this study is the effect of the current density profile within a magnetic island vs the width of a magnetic island. "Peaking" or "anti-peaking" the current density profile within a magentic island can cause large differences in the saturated magnetic island width; furthermore the width of the magnetic island is found to be sensitive to this parameter.
Modification of the background current density profile by the presence of multiple islands can and does cause nonlinear destabilization of magnetic islands; also toroidicity and elongation are shown to have a linear coupling effect that can also destabilize otherwise stable magnetic islands. By themselves, toroidicity and elongation are shown to modestly reduce the saturated magnetic island width and a general trend of smaller magnetic island width with the inward shift of the mode rational surface is noted.
