We present a robust optimization algorithm for the design of electromagnetic coils that generate vacuum magnetic fields with nested flux surfaces and precise quasi-symmetry. The method is based on a bilevel optimization problem, where the outer coil optimization is constrained by a set of inner least squares optimization problems whose solutions describe magnetic surfaces. The outer optimization objective targets coils that generate a field with nested magnetic surfaces and good quasi-symmetry. The inner optimization problems identify magnetic surfaces when they exist, and approximate surfaces in the presence of magnetic islands or chaos. We show that this formulation can be used to heal islands and chaos, thus producing coils that result in magnetic fields with precise quasi-symmetry. We show that the method can be initialized with coils from the traditional two-stage coil design process, as well as coils from a near-axis expansion optimization. We present a numerical example where island chains are healed and quasi-symmetry is optimized up to surfaces with aspect ratio 6. Another numerical example illustrates that the aspect ratio of nested flux surfaces with optimized quasi-symmetry can be decreased from 6 to approximately 4. The last example shows that our approach is robust and a cold-start using coils from a near-axis expansion optimization.
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Direct stellarator coil optimization for nested magnetic surfaces with precise quasi-symmetry
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April 2023
Research Article|
April 13 2023
Direct stellarator coil optimization for nested magnetic surfaces with precise quasi-symmetry
Andrew Giuliani
;
Andrew Giuliani
a)
(Conceptualization, Methodology, Software, Visualization, Writing – original draft, Writing – review & editing)
1
Courant Institute of Mathematical Sciences, New York University, New York
, New York 10012-1185, USA
a)Author to whom correspondence should be addressed: giuliani@cims.nyu.edu
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Florian Wechsung
;
Florian Wechsung
(Conceptualization, Methodology, Software, Writing – original draft, Writing – review & editing)
1
Courant Institute of Mathematical Sciences, New York University, New York
, New York 10012-1185, USA
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Antoine Cerfon
;
Antoine Cerfon
(Conceptualization, Funding acquisition, Methodology, Supervision, Writing – original draft, Writing – review & editing)
1
Courant Institute of Mathematical Sciences, New York University, New York
, New York 10012-1185, USA
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Matt Landreman
;
Matt Landreman
(Conceptualization, Funding acquisition, Methodology, Software, Supervision, Writing – original draft, Writing – review & editing)
2
Institute for Research in Electronics and Applied Physics, University of Maryland, College Park
, Maryland 20742, USA
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Georg Stadler
Georg Stadler
(Conceptualization, Funding acquisition, Methodology, Supervision, Writing – original draft, Writing – review & editing)
1
Courant Institute of Mathematical Sciences, New York University, New York
, New York 10012-1185, USA
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a)Author to whom correspondence should be addressed: giuliani@cims.nyu.edu
Phys. Plasmas 30, 042511 (2023)
Article history
Received:
October 06 2022
Accepted:
March 13 2023
Citation
Andrew Giuliani, Florian Wechsung, Antoine Cerfon, Matt Landreman, Georg Stadler; Direct stellarator coil optimization for nested magnetic surfaces with precise quasi-symmetry. Phys. Plasmas 1 April 2023; 30 (4): 042511. https://doi.org/10.1063/5.0129716
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