UW-CPTC 07-10 Ballooning filament growth in the intermediate nonlinear regime

In this work we develop a theory of ballooning instability in the intermediate nonlinear regime for general magnetic configurations including tokamaks. The evolution equations for plasma filament growth induced by the ballooning instability are derived accounting for the dominant nonlinear effects in an ideal MHD description. The intermediate nonlinear regime of ballooning modes is defined by the ordering that the plasma filament length across field line in the direction of pressure gradient is comparable to the mode width in the same direction. In the tokamak case, this regime becomes particularly relevant for a transport barrier as the width of that barrier (or pedestal) region approaches the mode width of the dominant ballooning mode. The filament growth equations in the intermediate nonlinear ballooning regime is meant to quantify the precursor and pre-collapse phase of edge localized modes (ELMs) in both simulations and experiments.