Simplified models of axisymmetric MHD instabilities

Itis 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, 6W, the simplified models are shown to satisfy the inequalities SW. > 6Wc > 8 Wm, where subscripts i, c and m refer to the uniform ideal flux-shift, uniform current-shift and minimizing eigenmode respectively.Thus, of the simplified models, the current-shift is always a better estimate than the flux-shift.