Filamentary plasma eruptions in tokamaks

The early stages as well as the crash of explosive, filamentary eruptions in magnetised plasmas, such as Edge Localised Modes (ELMs) in tokamaks, are investigated by modelling the ballooning mode envelope equation which can be derived from non-linear ideal MHD. The ballooning mode envelope equation describes the growth of a plasma filament amplitude; however it is not generally analytically tractable. Wilson and Cowley derived this equation for tokamak-like geometry, and provided numerical solutions for the two-dimensional non-linear differential equation, which can involve fractional temporal derivatives, but is often second order in time and space. We have extended those simulations to evolve through linear marginal stability instead of starting with a highly unstable state. This enables one to explore more realistic scenarios of these explosive events. Building on this, we have developed a new heuristic approach for the energy ejected in the plasma eruptions that could form the basis for a first-principle ELM model for tokamaks and, indeed, plasma eruption events in other plasma systems. If successfully benchmarked against tokamak data (future work), this method would help to make confident predictions for ELMs in ITER.