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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 quasisymmetric 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 quasisymmetry and low particle losses. In particular for low complexity coils, we are able to significantly improve the performance compared with 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 $$\epsilon _{\text {eff}}^{3/2}$$ less than approximately $$5\times 10^{-9}$$ .
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Stochastic and a posteriori optimization to mitigate coil manufacturing errors in stellarator design
Abstract It was recently shown in Wechsung et al (2022 Proc. Natl Acad. Sci. USA 119 e2202084119) that there exist electromagnetic coils that generate magnetic fields, which are excellent approximations to quasi-symmetric fields and have very good particle confinement properties. Using a Gaussian process-based model for coil perturbations, we investigate the impact of manufacturing errors on the performance of these coils. We show that even fairly small errors result in noticeable performance degradation. While stochastic optimization yields minor improvements, it is not possible to mitigate these errors significantly. As an alternative to stochastic optimization, we then formulate a new optimization problem for computing optimal adjustments of the coil positions and currents without changing the shapes of the coil. These a-posteriori adjustments are able to reduce the impact of coil errors by an order of magnitude, providing a new perspective for dealing with manufacturing tolerances in stellarator design.
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- Award ID(s):
- 1820852
- PAR ID:
- 10392041
- Date Published:
- Journal Name:
- Plasma Physics and Controlled Fusion
- Volume:
- 64
- Issue:
- 10
- ISSN:
- 0741-3335
- Page Range / eLocation ID:
- 105021
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1088/1361-6587/ac89ee
