Abstract
Single-valued conformal flux (magnetic) coordinates can always be introduced on arbitrary toroidal magnetic surfaces. It is shown how such coordinates can be obtained by transforming Boozer magnetic coordinates on the surfaces. The metrics is substantially simplified and the coordinate grid is orthogonalized at the expense of a more complicated representation of the magnetic field in conformal flux coordinates. This in turn makes it possible to introduce complex angular flux coordinates on any toroidal magnetic surface and to develop efficient methods for a complex analysis of the geometry of equilibrium magnetic surfaces. The complex analysis reveals how the plasma equilibrium problem is related to soliton theory. Magnetic surfaces of constant mean curvature are considered to exemplify this relationship.
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