Shear-Alfvén dynamics of toroidally confined plasmas

Recent developments in the stability theory of toroidally confined plasmas are reviewed, with the intention of providing a picture comprehensible to non-specialists. The review considers a class of low-frequency, electromagnetic disturbances that seem especially pertinent to modern high-temperature confinement experiments. It is shown that such disturbances are best unified and understood through consideration of a single, exact fluid moment: the shear-Alfvén law. Appropriate versions of this law and its corresponding closure relations are derived, essentially from first principles, and applied in a variety of mostly, but not exclusively, linear contexts. Among the specific topics considered are: flux coordinates (including Hamada coordinates), the Newcomb solubility condition, Shafranov geometry, magnetic island evolution, reduced MHD and its generalizations, drift-kinetic electron response, classical tearing, twisting, and kink instabilities, pressure-modified tearing instability (Δ-critical), collisionless and semi-collisional tearing modes, the ballooning representation in general geometry, ideal ballooning instability. Mercier criterion, near-axis expansions, the second stability region, and resistive and kinetic ballooning modes. The fundamental importance of toroidal topology and curvature is stressed