Minimal spatial symmetry description for quasi-symmetric equilibria

Establish whether the hypothesized spatial symmetry—defined such that an equilibrium shape is uniquely determined by the magnetic axis, a selected flux-surface cross-section, and the geometric relationship between them—provides a minimal description of ideal-MHD quasi-helical-symmetric or quasi-axisymmetric equilibria.

Background

The paper argues that in axisymmetric tokamaks, a minimal geometric description of the entire equilibrium shape can be given by the magnetic axis, one poloidal cross-section, and the position of that cross-section relative to the axis. Motivated by this, the authors define an analogous spatial symmetry for non-axisymmetric equilibria in which the entire shape would be uniquely determined by the magnetic axis, an appropriately selected cross-section, and the geometric relationship between the two.

They suggest that such a symmetry, if it exists, would both provide a minimal description for quasi-helical or quasi-axisymmetric equilibria and enable more systematic investigations into relationships between equilibrium shaping and figures of merit, potentially facilitating direct construction of quasi-symmetric equilibria without heavy optimization.