Magnetohydrodynamic stability of tokamak edge plasmas

A new formalism for analyzing the magnetohydrodynamic stability of a limiter tokamak edge plasma is developed. Two radially localized, high toroidal mode number $n$ instabilities are studied in detail: a peeling mode and an edge ballooning mode. The peeling mode, driven by edge current density and stabilized by edge pressure gradient, has features which are consistent with several properties of tokamak behavior in the high confinement “H”-mode of operation, and edge localized modes (or ELMs) in particular. The edge ballooning mode, driven by the pressure gradient, is identified; this penetrates ${\mathrm{\sim n}}^{\text{1/3}}$ rational surfaces into the plasma (rather than ${\mathrm{\sim n}}^{\text{1/2}},$ expected from conventional ballooning mode theory). Furthermore, there exists a coupling between these two modes and this coupling provides a picture of the ELM cycle.