Magnetohydrodynamic stability of a toroidal plasma's separatrix

Large tokamaks capable of fusion power production such as ITER, should avoid large edge localized modes (ELMs), thought to be triggered by an ideal magnetohydrodynamic instability due to current at the plasma's separatrix boundary. Unlike analytical work in a cylindrical approximation, numerical work finds the modes are stable. The plasma's separatrix might stabilize modes, but makes analytical and numerical work difficult. We generalize a cylindrical model to toroidal separatrix geometry, finding one parameter Delta' determines stability. The conformal transformation method is generalized to allow nonzero derivatives of a function on a boundary, and calculation of the equilibrium vacuum field allows Delta' to be found analytically. As a boundary more closely approximates a separatrix, we find the energy principle indicates instability, but the growth rate asymptotes to zero.