Magnetohydrodynamic tokamak plasma edge stability

The edge of a tokamak plasma is interesting due to its geometrical structure that is difficult to model mathematically and computationally, its tendency to form 'transport barriers' with increased confinement of energy and momentum, and the edge-localized instabilities associated with transport barriers that threaten the lifetime of components in large tokamaks. Ideal magnetohydrodynamics (MHD) is generally well understood, but only in the past decade has a good theoretical understanding emerged of MHD stability near the plasmas' separatrix when one or more X-points are present. By reviewing and discussing our theoretical understanding of ideal MHD stability of the plasma's edge, a clear picture emerges for its ideal stability. Conclusions are: ideal MHD will limit the width of strong transport barriers at the plasma's edge, a strong edge transport barrier will be associated with ELMs, ELMs will have a maximum toroidal mode number, will be preceded by smaller precursor instabilities, and can be triggered by sufficient changes to either the edge or the core plasma. Observations are made for the mechanisms responsible for edge transport barriers and ELMs, some leading to experimental predictions, others highlighting important open questions.