We propose a model for edge localized mode (ELM) evolution which goes beyond linear stability arguments by hypothesizing that peeling modes initiate a Taylor relaxation (a constrained minimization of the magnetic energy) of an outer annular plasma region. The relaxation has two effects on peeling mode stability: (a) As the relaxation process proceeds radially inwards it leaves in its wake a Taylor state, which for conventional tokamak ordering is simply a flattened equilibrium toroidal current density. This effect acting in isolation would provide a destabilizing effect (for conventional current profiles the edge current density would increase); (b) The formation of a (negative for conventional current profiles) skin current at the plasma–vacuum interface which has a counteracting stabilizing effect on peeling modes. For a finite relaxed annulus, these two opposing effects can balance and give a configuration that is stable to all possible peeling instabilities. The radial extent of the relaxed region required for stability can be calculated using this balance. This then leads to model predictions for ELM characteristics such as the widths and mode numbers, the magnitude of the attendant energy losses and the natural (deterministic) scatter in these quantities. We compare these model predictions with a number of experimentally observed ELM properties. Further, expanding the governing equations gives analytic expressions for ELM widths in terms of localized edge parameters. Peeling modes can occur even when the critical pressure gradient for the onset of ballooning modes has not been reached. For this reason 'type III' ELMs, which typically occur just above the threshold for L–H transitions, may be best described by this model.
A simple dynamical model of edge localized mode phenomena