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This paper addresses the inverse problem of the existence of surface current MHD equilibria in toroidal geometry with vanishing magnetic field inside. The term "inverse" implies that the plasma-vacuum interface is given and conditions at the external wall or conductors remain to be determined. The problem is therefore reformulated to discover what toroidal surfaces with analytic parametrisation allow a simple analytic covering by geodesics. All known equilibria (with zero and infinite rotational transform, and symmetric equilibria in the case of finite rotational transform) are found to be solutions of separable cases of a nonlinear partial differential equation of the Hamilton-Jacobi type whose coefficients are combinations of the metric elements of the surface. Finally the analyticity requirement is considered, and implications for volume current equilibria are discussed.

Additional information

Authors: KAISER R, Universität Bayreuth, Lehrstuhl für Angewandte Mathematik (DE);SALAT A, Max-Planck-Institut für Plasmaphysik, Garching bei München (DE)
Bibliographic Reference: Report: IPP 6/315 EN (1993) 41 pp.
Availability: Available from Max-Planck-Institut für Plasmaphysik, 8046 Garching bei München (DE)
Record Number: 199311121 / Last updated on: 1994-11-29
Original language: en
Available languages: en