A quasi-linear analytical model is used to describe the nonlinear growth and saturation of tearing modes with mode number m⩾2. The saturation of the magnetic island growth is the quasi-linear development of a single mode rather than a mode coupling process. The saturation amplitude, which is dependent on the form of the resistivity, is in good agreement with results obtained previously by numerically advancing the full set of nonlinear equations.

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The authors study the hypothesis that sawtooth oscillations or internal disruptions are the result of a cyclic process in which the plasma core is resistively heated until the safety factor drops below unity, causing the m = 1 tearing mode to become unstable, to grow with an accelerating growth rate, and ultimately to flatten the electron temperature and safety factor profiles. A model based on this hypothesis compares favourably with experimental data from the Oak Ridge Tokamak (ORMAK) in explaining (1) the rate at which a sawtooth rises, (2) the radial dependence of the precursor and main sawtooth oscillation amplitudes, (3) the accelerating growth of the m = 1 precursor oscillations, and (4) the repetition time of the sawteeth. The heat lost from the central region during the internal disruption is found to transport diffusively through the exterior plasma with a conduction coefficient that agrees within a factor of two with the value inferred from the observed electron power balance.