Global stellarator coil optimization with quadratic constraints and objectives
Most present stellarator designs are produced by costly two-stage optimization: the first for an optimized equilibrium, and the second for a coil design reproducing its magnetic configuration. Few proxies for coil complexity and forces exist at the equilibrium stage. Rapid initial state finding for...
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IOP Publishing
2025-01-01
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| Series: | Nuclear Fusion |
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| Online Access: | https://doi.org/10.1088/1741-4326/ada810 |
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| author | Lanke Fu Elizabeth J. Paul Alan A. Kaptanoglu Amitava Bhattacharjee |
| author_facet | Lanke Fu Elizabeth J. Paul Alan A. Kaptanoglu Amitava Bhattacharjee |
| author_sort | Lanke Fu |
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| description | Most present stellarator designs are produced by costly two-stage optimization: the first for an optimized equilibrium, and the second for a coil design reproducing its magnetic configuration. Few proxies for coil complexity and forces exist at the equilibrium stage. Rapid initial state finding for both stages is a topic of active research. Most present convex coil optimization codes use the least square winding surface method by Merkel (NESCOIL), with recent improvements in conditioning, regularization, sparsity, and physics objectives. While elegant, the method is limited to modeling the norms of linear functions in coil current. We present QUADCOIL, a global coil optimization method that targets combinations of linear and quadratic functions of the current. It can directly constrain and/or minimize a wide range of physics objectives unavailable in NESCOIL and REGCOIL, including the Lorentz force, magnetic energy, curvature, field-current alignment, and the maximum density of a dipole array. QUADCOIL requires no initial guess and runs nearly $10^2\times$ faster than filament optimization. Integrating it in the equilibrium optimization stage can potentially exclude equilibria with difficult-to-design coils, without significantly increasing the computation time per iteration. QUADCOIL finds the exact, global minimum in a large parameter space when possible, and otherwise finds a well-performing approximate global minimum. It supports most regularization techniques developed for NESCOIL and REGCOIL. We demonstrate QUADCOIL’s effectiveness in coil topology control, minimizing non-convex penalties, and predicting filament coil complexity with three numerical examples. |
| format | Article |
| id | doaj-art-d31669e4a10f429ebcad2875a1556a44 |
| institution | Kabale University |
| issn | 0029-5515 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | Nuclear Fusion |
| spelling | doaj-art-d31669e4a10f429ebcad2875a1556a442025-01-22T10:56:46ZengIOP PublishingNuclear Fusion0029-55152025-01-0165202604510.1088/1741-4326/ada810Global stellarator coil optimization with quadratic constraints and objectivesLanke Fu0https://orcid.org/0000-0002-6845-387XElizabeth J. Paul1https://orcid.org/0000-0002-9355-5595Alan A. Kaptanoglu2Amitava Bhattacharjee3Princeton Plasma Physics Laboratory , Princeton, NJ, United States of America; Department of Astrophysical Sciences, Princeton University , Princeton, NJ, United States of AmericaDepartment of Applied Physics, Columbia University , New York, NY, United States of AmericaCourant Institute of Mathematical Sciences, New York University , New York, NY, United States of AmericaDepartment of Astrophysical Sciences, Princeton University , Princeton, NJ, United States of AmericaMost present stellarator designs are produced by costly two-stage optimization: the first for an optimized equilibrium, and the second for a coil design reproducing its magnetic configuration. Few proxies for coil complexity and forces exist at the equilibrium stage. Rapid initial state finding for both stages is a topic of active research. Most present convex coil optimization codes use the least square winding surface method by Merkel (NESCOIL), with recent improvements in conditioning, regularization, sparsity, and physics objectives. While elegant, the method is limited to modeling the norms of linear functions in coil current. We present QUADCOIL, a global coil optimization method that targets combinations of linear and quadratic functions of the current. It can directly constrain and/or minimize a wide range of physics objectives unavailable in NESCOIL and REGCOIL, including the Lorentz force, magnetic energy, curvature, field-current alignment, and the maximum density of a dipole array. QUADCOIL requires no initial guess and runs nearly $10^2\times$ faster than filament optimization. Integrating it in the equilibrium optimization stage can potentially exclude equilibria with difficult-to-design coils, without significantly increasing the computation time per iteration. QUADCOIL finds the exact, global minimum in a large parameter space when possible, and otherwise finds a well-performing approximate global minimum. It supports most regularization techniques developed for NESCOIL and REGCOIL. We demonstrate QUADCOIL’s effectiveness in coil topology control, minimizing non-convex penalties, and predicting filament coil complexity with three numerical examples.https://doi.org/10.1088/1741-4326/ada810stellaratorcoilswinding surfaceoptimizationconvex relaxation |
| spellingShingle | Lanke Fu Elizabeth J. Paul Alan A. Kaptanoglu Amitava Bhattacharjee Global stellarator coil optimization with quadratic constraints and objectives Nuclear Fusion stellarator coils winding surface optimization convex relaxation |
| title | Global stellarator coil optimization with quadratic constraints and objectives |
| title_full | Global stellarator coil optimization with quadratic constraints and objectives |
| title_fullStr | Global stellarator coil optimization with quadratic constraints and objectives |
| title_full_unstemmed | Global stellarator coil optimization with quadratic constraints and objectives |
| title_short | Global stellarator coil optimization with quadratic constraints and objectives |
| title_sort | global stellarator coil optimization with quadratic constraints and objectives |
| topic | stellarator coils winding surface optimization convex relaxation |
| url | https://doi.org/10.1088/1741-4326/ada810 |
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