Global stochastic optimization of stellarator coil configurations

Glas, Silke; Padidar, Misha; Kellison, Ariel; Bindel, David

doi:10.1017/s002237782200023x

Cited by 4 publications

(10 citation statements)

References 27 publications

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“…and the decision variables x represent coil shape parameters and the coil currents. The quadratic flux is a standard metric used to find coils in the stage-two problem (Merkel 1987;Landreman 2017;Zhu et al 2017;Singh et al 2020;Kruger et al 2021;Glas et al 2022;Wechsung et al 2022a). To solve the bi-objective coil problem, (3.5), we use the coil optimization framework implemented in SIMSOPT.…”

Section: Problem 2: the Coil Length And Quadratic Flux Trade-offmentioning

confidence: 99%

Understanding trade-offs in stellarator design with multi-objective optimization

Bindel,

Landreman,

Padidar

2023

J. Plasma Phys.

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In designing stellarators, any design decision ultimately comes with a trade-off. Improvements in particle confinement, for instance, may increase the burden on engineers to build more complex coils, and the tightening of financial constraints may simplify the design and worsen some aspects of transport. Understanding trade-offs in stellarator designs is critical in designing high performance devices that satisfy the multitude of physical, engineering and financial criteria. In this study, we show how multi-objective optimization (MOO) can be used to investigate trade-offs and develop insight into the role of design parameters. We discuss the basics of MOO, as well as practical solution methods for solving MOO problems. We apply these methods to bring insight into the selection of two common design parameters: the aspect ratio of an ideal magnetohydrodynamic equilibrium and the total length of the electromagnetic coils.

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Section: Problem 2: the Coil Length And Quadratic Flux Trade-offmentioning

confidence: 99%

Understanding trade-offs in stellarator design with multi-objective optimization

Bindel,

Landreman,

Padidar

2023

J. Plasma Phys.

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“…Coil design problems can admit multiple local minima (Miner et al 2001;Zhu et al 2017) with large variability in performance of the discovered designs (Wechsung et al 2022). One remedy of this problem is to use stochastic optimization (Glas et al 2022;Wechsung et al 2022), which appears to reduce the variability of the discovered minima. Stochastic optimization of coils has also been explored in Lobsien, Drevlak & Pedersen (2018); Lobsien et al (2020).…”

Section: Introductionmentioning

confidence: 99%

“…Another approach is to use global optimization algorithms that attempt to fully explore the range of allowable stellarator coil designs. Glas et al (2022) combine both remedies by FIGURE 1. Current workflow wraps phase I (the near-axis expansion algorithm, Giuliani et al 2022a) in globalization subroutines (Eriksson et al 2019) to generate interesting initial guesses for the subsequent volume QA optimizations in phase II (Giuliani et al 2022b) and III (Giuliani et al 2023).…”

Section: Introductionmentioning

confidence: 99%

“…For this algorithm, the user must provide lower and upper bounds on the design variables, known as box constraints. This algorithm has been used before in coil design problems (Glas et al 2022), but our approach is notably different as we reformulate our optimization problem to accept constraints on the geometry of the coils in physical, rather than Fourier space.…”

Section: Introductionmentioning

confidence: 99%

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

Giuliani

2024

J. Plasma Phys.

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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’.

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“…In an effort to lessen the impact of errors, stochastic optimization approaches have recently drawn significant attention in the stellarator community [9,[17][18][19]28]. The core idea underlying the various approaches is the following: by including coil errors explicitly as part of the optimization problem, one hopes to find minimizers that perform well even when the coils are not built or placed perfectly.…”

Section: Introductionmentioning

confidence: 99%

Stochastic and a posteriori optimization to mitigate coil manufacturing errors in stellarator design

Wechsung¹,

Giuliani²,

Landreman³

et al. 2022

Plasma Phys. Control. Fusion

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It was recently shown in [Wechsung et. al., Proc. Natl. Acad. Sci. USA, 2022] 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 able 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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Global stochastic optimization of stellarator coil configurations

Cited by 4 publications

References 27 publications

Understanding trade-offs in stellarator design with multi-objective optimization

Understanding trade-offs in stellarator design with multi-objective optimization

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

Stochastic and a posteriori optimization to mitigate coil manufacturing errors in stellarator design

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