Abstract
Necessary analytic constraints for a force-free, single harmonic, single helicity, magnetic-field configuration to be an Ohmic equilibrium are derived. These conditions imply that the typical configuration possesses an m=1 helical structure and has only open magnetic flux surfaces. The conclusion is drawn that Taylor’s helical state is not a steady state in the presence of resistive dissipation, no matter how small. Nevertheless, the field configurations that commonly have been associated with Taylor’s minimum energy states retain significance because they may represent either the mean configuration of a temporally fluctuating state or the zero-resistivity limit of a (hypothetical) three-dimensional, Ohmic equilibrium. Examples of single harmonic, single helicity, reversed-field, Ohmic equilibria are presented.
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