Previous work by Johnson and Greene on resistive instabilities is extended to finite-pressure configurations. The Mercier criterion for the stability of the ideal magnetohydrodynamic interchange mode is rederived, the generalization of the earlier stability criterion for the resistive interchange mode is obtained, and a relation between the two is noted. Conditions for tearing mode instability are recovered with the growth rate scaling with the resistivity in a more complicated manner than η3/5. Nyquist techniques are used to show that favorable average curvature can convert the tearing mode into an overstable mode and can often stabilize it.

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A nominally axisymmetric plasma configuration, such as a tokamak or a spherical torus, is highly sensitive to nonaxisymmetric magnetic perturbations due to currents outside of the plasma. The high sensitivity means that the primary interest is in the response of the plasma to very small perturbations, i.e., ∣b⃗∕B⃗∣≈10−2 to 10−4, which can be calculated using the theory of perturbed equilibria. The ideal perturbed equilibrium code (IPEC) is described and applied to the study of the plasma response in a spherical torus to such external perturbations.

Application of resistive instability theory shows that toroidal effects can stabilize the tearing mode in devices like the Princeton Large Torus. Contraction of the current channel is destabilizing. Finite fluid compressibility is crucial to this phenomenon.