@article{article,
  author = {M. J. Gerard and M. J. Pueschel and S. D. Stewart and H. Hillebrecht and B. Geiger},
  title = {Characterizing Flux-Surface Shapes in Tokamaks and Quasi-Symmetric Stellarators},
  abstract = {Modern stellarator designs routinely attain high levels of magnetic-field quasi-symmetry through flux-surface shaping. Here, we examine different methods for characterizing stellarator flux-surface shapes in a manner analogous to flux-surface shaping in tokamaks. The methods considered use a Fourier analysis to define the shaping modes (e.g., elongation, triangularity, squareness, etc.) of equilibrium cross sections. Relative to an axisymmetric equilibrium, the additional degree of freedom in a non-axisymmetric equilibrium manifests as a rotation of each shaping mode about the magnetic axis. This analysis is performed on non-axisymmetric configurations with a high degree of quasi-symmetry and equilibria with varying quasi-symmetry quality from the quasi-symmetric Stellarator Repository database. One method in particular is shown to reduce shape complexity in quasi-symmetric equilibria by defining a set of cross sections that efficiently fill out an equilibrium volume. This is accomplished by defining a cross section as the set of points that occupy the shortest distance between the magnetic axis and an equilibrium flux surface across all quasi-symmetry contours. Using this method, we find empirically that an equilibrium geometry can be described with significantly fewer non-negligible shaping modes relative to other shape characterization methods. Moreover, the method reveals that quasi-symmetry quality is strongly correlated with equilibrium shapes that exhibit a highly constrained linear distribution of shaping modes, where an increase in shape complexity is proportional to an increase in shape rotation about the magnetic axis. It is therefore argued that this method provides a way to efficiently characterize the shape of quasi-symmetric equilibria in a manner analogous to how equilibrium shapes are described in tokamaks.},
  year = {2026},
  journal = {Physics of Plasmas},
  volume = {33},
  pages = {092507},
  url = {https://arxiv.org/abs/2512.24544},
  doi = {10.1063/5.0320418},
  language = {eng},
}