Ballooning filament growth in the intermediate nonlinear regime

A theory is developed for the description of ballooning instability in the intermediate nonlinear regime for general magnetic configurations including toroidal systems such as tokamaks. The evolution equations for the 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 displacement across the magnetic surface is comparable to the linear mode width in the same direction. In the tokamak case, this regime could become particularly relevant for a transport barrier as the width of that barrier (or pedestal) region approaches the mode width of the dominant ballooning mode. A remarkable feature of the nonlinear ballooning equations is that solutions of the associated local linear ballooning mode equations continue to be valid solutions into the intermediate nonlinear regime. The filament growth equations for the intermediate nonlinear ballooning regime may be applicable to the precursor and pre-collapse phase of edge localized modes (ELMs) observed in both simulations and experiments.