Computing Flux-Surface Shapes in Tokamaks and Stellarators
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866908741097488384 |
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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 |
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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 |