Hostname: page-component-848d4c4894-wg55d Total loading time: 0 Render date: 2024-06-07T13:31:33.177Z Has data issue: false hasContentIssue false
  • English
  • Français

Direct stellarator coil design using global optimization: application to a comprehensive exploration of quasi-axisymmetric devices

Published online by Cambridge University Press:  16 May 2024

Andrew Giuliani Open the ORCID record for Andrew Giuliani [Opens in a new window]
Andrew Giuliani*
Affiliation:
Flatiron Institute, 162 Fifth Avenue, New York, NY 10010, USA
*
†Email address for correspondence: agiuliani@flatironinstitute.org
Get access Rights & Permissions [Opens in a new window]

Abstract

Many stellarator coil design problems are plagued by multiple minima, where the locally optimal coil sets can sometimes vary substantially in performance. As a result, solving a coil design problem a single time with a local optimization algorithm is usually insufficient and better optima likely do exist. To address this problem, we propose a global optimization algorithm for the design of stellarator coils and outline how to apply box constraints to the physical positions of the coils. The algorithm has a global exploration phase that searches for interesting regions of design space and is followed by three local optimization algorithms that search in these interesting regions (a ‘global-to-local’ approach). The first local algorithm (phase I), following the globalization phase, is based on near-axis expansions and finds stellarator coils that optimize for quasisymmetry in the neighbourhood of a magnetic axis. The second local algorithm (phase II) takes these coil sets and optimizes them for nested flux surfaces and quasisymmetry on a toroidal volume. The final local algorithm (phase III) polishes these configurations for an accurate approximation of quasisymmetry. Using our global algorithm, we study the trade-off between coil length, aspect ratio, rotational transform and quality of quasi-axisymmetry. The database of stellarators, which comprises approximately 200 000 coil sets, is available online and is called QUASR, for ‘quasi-symmetric stellarator repository’.

Keywords

plasma confinementplasma devices
Type
Research Article
Information
Journal of Plasma Physics , Volume 90 , Issue 3 , June 2024 , 905900303
Check for updates
Copyright
Copyright © The Author(s), 2024. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bertolazzi, E., Ghiloni, R. & Specogna, R. 2019 Efficient computation of linking number with certification, arXiv:1912.13121.Google Scholar
Bindel, D., Landreman, M. & Padidar, M. 2023 Understanding trade-offs in stellarator design with multi-objective optimization. J Plasma Phys 89 (5), 905890503.CrossRefGoogle Scholar
Boozer, A.H. 2019 Curl-free magnetic fields for stellarator optimization. Phys. Plasmas 26 (10), 102504.CrossRefGoogle Scholar
Eriksson, D., Pearce, M., Gardner, J., Turner, R.D. & Poloczek, M. 2019 Scalable global optimization via local Bayesian optimization. In Advances in Neural Information Processing Systems (eds. Wallach, H., Larochelle, H., Beygelzimer, A., d'Alché-Buc, F., Fox, E. & Garnett, R.), vol. 32. Curran Associates, Inc. https://proceedings.neurips.cc/paper_files/paper/2019/file/6c990b7aca7bc7058f5e98ea909e924b-Paper.pdfGoogle Scholar
Giuliani, A., Wechsung, F., Cerfon, A., Landreman, M. & Stadler, G. 2023 Direct stellarator coil optimization for nested magnetic surfaces with precise quasi-symmetry. Phys. Plasmas 30 (4), 042511.CrossRefGoogle Scholar
Giuliani, A., Wechsung, F., Cerfon, A., Stadler, G. & Landreman, M. 2022 a Single-stage gradient-based stellarator coil design: optimization for near-axis quasi-symmetry. J. Comput. Phys. 459, 111147.CrossRefGoogle Scholar
Giuliani, A., Wechsung, F., Stadler, G., Cerfon, A. & Landreman, M. 2022 b Direct computation of magnetic surfaces in Boozer coordinates and coil optimization for quasisymmetry. J. Plasma Phys. 88 (4), 905880401.CrossRefGoogle Scholar
Glas, S., Padidar, M., Kellison, A. & Bindel, D. 2022 Global stochastic optimization of stellarator coil configurations. J. Plasma Phys. 88 (2), 905880208.CrossRefGoogle Scholar
Goodman, A.G., Camacho Mata, K., Henneberg, S.A., Jorge, R., Landreman, M., Plunk, G.G., Smith, H.M., Mackenbach, R.J.J., Beidler, C.D. & Helander, P. 2023 Constructing precisely quasi-isodynamic magnetic fields. J Plasma Phys 89 (5), 905890504.CrossRefGoogle Scholar
Halır, R. & Flusser, J. 1998 Numerically stable direct least squares fitting of ellipses. In Proc. 6th International Conference in Central Europe on Computer Graphics and Visualization. WSCG, vol. 98, pp. 125–132.Google Scholar
Hudson, S.R., Monticello, D.A. & Reiman, A.H. 2001 Reduction of islands in full-pressure stellarator equilibria. Phys. Plasmas 8 (7), 3377–3381.CrossRefGoogle Scholar
Landreman, M. 2023 PyQSC version 0.1.2. https://github.com/landreman/pyQSC.Google Scholar
Landreman, M., Medasani, B., Wechsung, F., Giuliani, A., Jorge, R. & Zhu, C. 2021 SIMSOPT: a flexible framework for stellarator optimization. J. Open Source Softw. 6 (65), 3525.CrossRefGoogle Scholar
Landreman, M. & Sengupta, W. 2018 Direct construction of optimized stellarator shapes. Part 1. Theory in cylindrical coordinates. J. Plasma Phys. 84 (6), 905840616.CrossRefGoogle Scholar
Landreman, M., Sengupta, W. & Plunk, G.G. 2019 Direct construction of optimized stellarator shapes. Part 2. Numerical quasisymmetric solutions. J. Plasma Phys. 85 (1), 905850103.CrossRefGoogle Scholar
Lee, B.F., Paul, E.J., Stadler, G. & Landreman, M. 2022 Stellarator coil optimization supporting multiple magnetic configurations. Nucl. Fusion 63 (1), 014002.CrossRefGoogle Scholar
Lobsien, J.-F., Drevlak, M., Kruger, T., Lazerson, S., Zhu, C. & Pedersen, T.S. 2020 Improved performance of stellarator coil design optimization. J. Plasma Phys. 86 (2), 815860202.CrossRefGoogle Scholar
Lobsien, J.-F., Drevlak, M., Pedersen, T.S., & W7-X Team. 2018 Stellarator coil optimization towards higher engineering tolerances. Nucl. Fusion 58 (10), 106013.CrossRefGoogle Scholar
Miner, W.H., Valanju, P.M., Hirshman, S.P., Brooks, A. & Pomphrey, N. 2001 Use of a genetic algorithm for compact stellarator coil design. Nucl. Fusion 41 (9), 1185.CrossRefGoogle Scholar
Padidar, M., Zhu, X., Huang, L., Gardner, J. & Bindel, D. 2021 Scaling Gaussian processes with derivative information using variational inference. Adv. Neural Inf. Process. Syst. 34, 6442–6453.Google Scholar
Rodriguez, E., Sengupta, W. & Bhattacharjee, A. 2022 Phases and phase-transitions in quasisymmetric configuration space. Plasma Phys. Control. Fusion 64 (10), 105006.CrossRefGoogle Scholar
Wechsung, F., Giuliani, A., Landreman, M., Cerfon, A. & Stadler, G. 2022 Single-stage gradient-based stellarator coil design: stochastic optimization. Nucl. Fusion 62 (7), 076034.CrossRefGoogle Scholar
Zhu, C., Hudson, S.R., Song, Y. & Wan, Y. 2017 New method to design stellarator coils without the winding surface. Nucl. Fusion 58 (1), 016008.CrossRefGoogle Scholar