Simplified models of axisymmetric magnetohydrodynamic instabilities

Abstract

It is shown that simplified models of the axisymmetric vertical instability in elongated plasmas, based on uniform shifts of current or of ideal flux surfaces, are not equivalent. In comparison with the ideal MHD eigenmode that minimizes the magnetic energy change, δW, the simplified models are shown to satisfy, under certain general conditions, the inequalities δWi ≥ δWC ≥ δWm (the subscripts i, c and m refer to the uniform ideal flux shift, the uniform current shift and the minimizing eigenmode, respectively). Thus, of the simplified models, the current shift is always a better estimate than the flux shift, although it is not indicated quantitatively how much better.