Error magnetic fields in a cylindrical plasma: Stability with zero pressure

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Abstract
The importance of error magnetic fields is that, if large enough, they cause the destruction of magnetic surfaces. In this paper error fields in a cylindrical plasma are described by nonlinear tearing mode theory, which deals with plasma equilibria having concentrated currents flowing along closed magnetic field lines. Because of the small spatial scale of the current distribution, resistive diffusion is significant even for small resistivity and, in certain cases, causes instability. An energy principle exists and is discussed. This conceptual framework is used in a study of the stability of zero pressure equilibria toward spontaneous generation of error fields, relevant for the reversed field pinch program. Cylindrical Ohmic states are shown to be extremely unstable. Relaxed states (having flattened current profiles) have much better stability. Both completely relaxed states of the Taylor type and partially relaxed Robinson‐type states are studied. A new class of metal–liner stabilized profiles is found, which offers one explanation for the apparent stability observed in experiments with distant conducting shells. The possibility that relaxed states have weakly stochastic magnetic field lines is discussed.