Computing Flux-Surface Shapes in Tokamaks and Stellarators

Fuente: arXiv
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Main Authors: Gerard, M. J., Pueschel, M. J., Stewart, S., Hillebrecht, H. O. M., Geiger, B.
Format: Preprint
Published: 2025
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author Gerard, M. J.
Pueschel, M. J.
Stewart, S.
Hillebrecht, H. O. M.
Geiger, B.
author_facet Gerard, M. J.
Pueschel, M. J.
Stewart, S.
Hillebrecht, H. O. M.
Geiger, B.
contents There is currently no agreed-upon methodology for characterizing a stellarator magnetic field geometry, and yet modern stellarator designs routinely attain high levels of magnetic-field quasi-symmetry through careful flux-surface shaping. Here, we introduce a general method for computing the shape of an ideal-MHD equilibrium that can be used in both axisymmetric and non-axisymmetric configurations. This framework uses a Fourier mode analysis to define the shaping modes (e.g. elongation, triangularity, squareness, etc.) of cross-sections that can be non-planar. 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. Using this method, a shaping analysis is performed on non-axisymmetric configurations with precise quasi-symmetry and select cases from the QUASR database spanning a range of quasi-symmetry quality. Empirically, we find that quasi-symmetry results from a spatial resonance between shape complexity and shape rotation about the magnetic axis. The quantitative features of this resonance correlate closely with a configuration's rotational transform and number of field periods. Based on these observations, it is conjectured that this shaping paradigm can facilitate systematic investigations into the relationship between general flux-surface geometries and other figures of merit.
format Preprint
id arxiv_https___arxiv_org_abs_2512_24544
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Computing Flux-Surface Shapes in Tokamaks and Stellarators
Gerard, M. J.
Pueschel, M. J.
Stewart, S.
Hillebrecht, H. O. M.
Geiger, B.
Plasma Physics
There is currently no agreed-upon methodology for characterizing a stellarator magnetic field geometry, and yet modern stellarator designs routinely attain high levels of magnetic-field quasi-symmetry through careful flux-surface shaping. Here, we introduce a general method for computing the shape of an ideal-MHD equilibrium that can be used in both axisymmetric and non-axisymmetric configurations. This framework uses a Fourier mode analysis to define the shaping modes (e.g. elongation, triangularity, squareness, etc.) of cross-sections that can be non-planar. 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. Using this method, a shaping analysis is performed on non-axisymmetric configurations with precise quasi-symmetry and select cases from the QUASR database spanning a range of quasi-symmetry quality. Empirically, we find that quasi-symmetry results from a spatial resonance between shape complexity and shape rotation about the magnetic axis. The quantitative features of this resonance correlate closely with a configuration's rotational transform and number of field periods. Based on these observations, it is conjectured that this shaping paradigm can facilitate systematic investigations into the relationship between general flux-surface geometries and other figures of merit.
title Computing Flux-Surface Shapes in Tokamaks and Stellarators
topic Plasma Physics
url https://arxiv.org/abs/2512.24544