On the non-uniqueness of ideal MHD equilibria, with implications for tokamak calculations

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Abstract
Non-linear ideal MHD equilibria in axisymmetric systems are examined, both in diffuse and free boundary cases. Attention is restricted to the situation in present low-β tokamak experiments, in which there are no current reversals. Both general qualitative results on the uniqueness and bifurcation of solutions are provided and exact solutions of several problems in a circular cylinder are given, exhibiting bifurcation phenomena. In particular sufficient conditions for bifurcation behaviour are conjectured, for both diffuse and free boundary equilibria.