Constrained stellarator coil curvature optimization with FOCUS

Krüger, Thomas; Zhu, Caoxiang; Bader, A.; Anderson, David T.; Singh, Luquant

doi:10.1017/s0022377821000106

Cited by 9 publications

(17 citation statements)

References 12 publications

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“…For the longer QA-III [22] and QA-III[24] coils, the (small) particle losses are comparable to those for QA-II [22] and QA-II[24] respectively, despite significantly better quasi-symmetry throughout the volume. We note that this imperfect correlation between quasi-symmetry and energetic particle confinement is consistent with the findings in Bader et al (2021), and in Landreman & Paul (2022) where the QA+Well configuration had lower particle losses than the QA configuration despite worse quasi-symmetry. For 3/2 eff (Nemov et al 1999) we observe significant improvement compared to the coils of Wechsung et al (2022), and our procedure is even able to improve the results from the target field of Landreman & Paul (2022).…”

Section: Coil-coil Separationsupporting

confidence: 89%

“…The second contribution of this article is the formulation of a single-stage optimization problem for highly accurate quasi-symmetry and a target rotational transform on an arbitrary number of surfaces subject to engineering constraints for the coils. Penalty terms are constructed to favor simpler coils by constraining their minimum pairwise distance, length, maximum curvature, and mean squared curvature, similar to constraints used for two-stage coil design (Zhu et al 2017;Kruger et al 2021;Singh et al 2020). We consider zero-thickness filament coils for simplicity, but our approach can be generalized to coils of finite thickness, e.g., following the method proposed in Singh et al (2020).…”

Section: Introductionmentioning

confidence: 99%

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Direct computation of magnetic surfaces in Boozer coordinates and coil optimization for quasi-symmetry

Giuliani,

Wechsung,

Landreman

et al. 2022

Preprint

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We propose a new method to compute magnetic surfaces that are parametrized in Boozer coordinates for vacuum magnetic fields. We also propose a measure for quasisymmetry on the computed surfaces and use it to design coils that generate a magnetic field that is quasi-symmetric on those surfaces. The rotational transform of the field and complexity measures for the coils are also controlled in the design problem. Using an adjoint approach, we are able to obtain analytic derivatives for this optimization problem, yielding an efficient gradient-based algorithm. Starting from an initial coil set that presents nested magnetic surfaces for a large fraction of the volume, our method converges rapidly to coil systems generating fields with excellent quasi-symmetry and low particle losses. In particular for low complexity coils, we are able to significantly improve the performance compared to coils obtained from the standard two-stage approach, e.g. reduce losses of fusion-produced alpha particles born at half-radius from 17.7% to 6.6%. We also demonstrate 16-coil configurations with alpha loss < 1% and neoclassical transport magnitude 3/2 eff less than approximately 5 × 10 −9 .

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Section: Coil-coil Separationsupporting

confidence: 89%

Section: Introductionmentioning

confidence: 99%

Direct computation of magnetic surfaces in Boozer coordinates and coil optimization for quasi-symmetry

Giuliani,

Wechsung,

Landreman

et al. 2022

Preprint

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“…• Curvature To design coils that are more easily manufacturable, a constraint to reduce the curvature of the coils is present. While different forms have been implemented in FOCUS [17],…”

Section: Existing Focus Cost Functions Used In This Workmentioning

confidence: 99%

“…It has a major radius of 1.2 m with 4 field periods and 12 magnets per period divided in 2 sets of 6 magnets related by the stellarator symmetry. In this section, the coils obtained using the spline representation are compared with the coils presented in [17], obtained using the constrained curvature function and already shown to be an improvement over the actual coils.…”

Section: Hsxmentioning

confidence: 99%

Stellarator coil design using cubic splines for improved access on the outboard side

Lonigro,

Zhu

2021

Preprint

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In recent years many efforts have been undertaken to simplify coil designs for stellarators due to the difficulties in fabricating non-planar coils. The FOCUS code removes the need for a winding surface and represents the coils as arbitrary curves in 3D. In the following work, the implementation of a spline representation for the coils in FOCUS is described, along with the implementation of a new engineering constraint to design coils with a straighter outer section. The new capabilities of the code are shown as an example on HSX, NCSX, and a prototype quasi-axisymmetric reactor-sized stellarator. The flexibility granted by splines along with the new constraint will allow for stellarator coil designs with improved accessibility and simplified maintenance.

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“…2021; Kruger et al. 2021) as well as using permanent magnets to replace 3-D coils (Helander et al. 2020; Zhu et al.…”

Section: Introductionmentioning

confidence: 99%

Existence of an optimized stellarator with simple coils

Feng

Jiang

et al. 2022

J. Plasma Phys.

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An optimized compact stellarator with four simple coils is obtained from direct optimization via a coil shape. The new stellarator consists of two interlocking coils and two vertical field coils similar to those of the Columbia Non-neutral Torus (CNT) (Pedersen et al., Phys. Rev. Lett., vol. 88, 2002, pp. 205002). The optimized configuration has a global magnetic well and a low helical ripple level comparable to that of Wendelstein 7-X (W7-X) (Wolf et al., Nucl. Fusion, vol. 57, 2017, pp. 102020). The two interlocking coils have a smooth three-dimensional shape much simpler than those of advanced stellarators such as W7-X. This result opens up possibilities of future stellarator reactors with simplified coils.

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Constrained stellarator coil curvature optimization with FOCUS

Cited by 9 publications

References 12 publications

Direct computation of magnetic surfaces in Boozer coordinates and coil optimization for quasi-symmetry

Direct computation of magnetic surfaces in Boozer coordinates and coil optimization for quasi-symmetry

Stellarator coil design using cubic splines for improved access on the outboard side

Existence of an optimized stellarator with simple coils

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