Stellarator coil optimization towards higher engineering tolerances

Lobsien, Jim-Felix; Drevlak, M.; Pedersen, T. S.; Team, W X

doi:10.1088/1741-4326/aad431

Cited by 25 publications

(60 citation statements)

References 14 publications

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“…This is consistent with but does not prove that the field error values obtained here are close to a global field error minimum of a coil configuration that meets the geometric constraints necessary to build Wendelstein 7-X. Comparing the results to our previous design study (Lobsien et al 2018) shows that the absence of most of the geometric constraints in the first phase of the design process in combination with an increased sample size and fully 3-D perturbations yielded lower field error values. We conclude that geometric constraints are responsible for the creation of local less performing minima in which the optimizer got stuck.…”

Section: Discussionsupporting

confidence: 63%

“…In this section, we investigate the effects of stochastic stellarator coil optimization using 3-D perturbations. We follow the coil design process described in § 2.4 that Improved performance of stellarator coil design optimization 9 Coil configuration Maximal field error Average field error Stochastic case 2 mm 3.73 × 10 −2 1.3 × 10 −2 Stochastic case 5 mm 6.64 × 10 −2 2.01 × 10 −2 Reference case HYBRID 4.0 × 10 −2 0.53 × 10 −2 Reference case ONSET 5.71 × 10 −2 1.37 × 10 −2 Stochastic case 8000 (Lobsien et al 2018) 6.1 × 10 −2 1.59 × 10 −2 consists of three phases. Two coil configurations are optimized using the stochastic version of ONSET with average perturbation amplitudes of 2 mm and 5 mm.…”

Section: Resultsmentioning

confidence: 99%

“…In this manuscript, we build on the results obtained in Lobsien et al (2018) and study the effects of stochastic stellarator coil optimization with three-dimensional (3-D) perturbations on a different coil design process for the original W7-X plasma boundary. First, we solely concentrate on the field error, then implement the geometric and vacuum magnetic field properties in two subsequent phases.…”

Section: And Othersmentioning

confidence: 99%

“…The design sequence described here is slightly different from the one used in the previous study (Lobsien et al 2018). There, the geometric properties are optimized simultaneously to the field error such that phases I and II are combined into a single phase.…”

Section: Design Sequencementioning

confidence: 99%

“…Maximal field error Average field error Stochastic case 2 mm 4.32 × 10 −2 1.09 × 10 −2 Stochastic case 5 mm 3.66 × 10 −2 0.95 × 10 −2 Reference case HYBRID 3.45 × 10 −2 0.72 × 10 −2 Stochastic case 8000 (Lobsien et al 2018) 6.08 × 10 −2 1.56 × 10 −2 (1.16 × 10 9 evaluations of f ). Closely behind follows the reference case HYBRID, which needed 86 000 evaluations of the objective function f to complete phases II and III.…”

Section: Coil Configurationmentioning

confidence: 99%

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Improved performance of stellarator coil design optimization

et al. 2020

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Following up on earlier work which demonstrated an improved numerical stellarator coil design optimization performance by the use of stochastic optimization (Lobsien et al., Nucl. Fusion, vol. 58 (10), 2018, 106013), it is demonstrated here that significant further improvements can be made – lower field errors and improved robustness – for a Wendelstein 7-X test case. This is done by increasing the sample size and applying fully three-dimensional perturbations, but most importantly, by changing the design sequence in which the optimization targets are applied: optimization for field error is conducted first, with coil shape penalties only added to the objective function at a later step in the design process. A robust, feasible coil configuration with a local maximum field error of 3.66 % and an average field error of 0.95 % is achieved here, as compared to a maximum local field error of 6.08 % and average field error of 1.56 % found in our earlier work. These new results are compared to those found without stochastic optimization using the FOCUS and ONSET suites. The relationship between local minima in the optimization space and coil shape penalties is also discussed.

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Section: Discussionsupporting

confidence: 63%

Section: Resultsmentioning

confidence: 99%

Section: And Othersmentioning

confidence: 99%

Section: Design Sequencementioning

confidence: 99%

Section: Coil Configurationmentioning

confidence: 99%

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Improved performance of stellarator coil design optimization

et al. 2020

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Combined plasma–coil optimization algorithms

et al. 2021

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Combined plasma–coil optimization approaches for designing stellarators are discussed and a new method for calculating free-boundary equilibria for multiregion relaxed magnetohydrodynmics (MRxMHD) is proposed. Four distinct categories of stellarator optimization, two of which are novel approaches, are the fixed-boundary optimization, the generalized fixed-boundary optimization, the quasi-free-boundary optimization, and the free-boundary (coil) optimization. These are described using the MRxMHD energy functional, the Biot–Savart integral, the coil-penalty functional and the virtual casing integral and their derivatives. The proposed free-boundary equilibrium calculation differs from existing methods in how the boundary-value problem is posed, and for the new approach it seems that there is not an associated energy minimization principle because a non-symmetric functional arises. We propose to solve the weak formulation of this problem using a spectral-Galerkin method, and this will reduce the free-boundary equilibrium calculation to something comparable to a fixed-boundary calculation. In our discussion of combined plasma–coil optimization algorithms, we emphasize the importance of the stability matrix.

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Global stochastic optimization of stellarator coil configurations

et al. 2022

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In the construction of a stellarator, the manufacturing and assembling of the coil system is a dominant cost. These coils need to satisfy strict engineering tolerances, and if those are not met the project could be cancelled as in the case of the National Compact Stellarator Experiment (NCSX) project (R.L. Orbach, 2008, https://ncsx.pppl.gov/DOE_NCSX_052208.pdf). Therefore, our goal is to find coil configurations that increase construction tolerances without compromising the performance of the magnetic field. In this paper, we develop a gradient-based stochastic optimization model which seeks robust stellarator coil configurations in high dimensions. In particular, we design a two-step method: first, we perform an approximate global search by a sample efficient trust-region Bayesian optimization; second, we refine the minima found in step one with a stochastic local optimizer. To this end, we introduce two stochastic local optimizers: BFGS applied to the sample average approximation; and Adam, equipped with a control variate for variance reduction. Numerical simulations performed on a W7-X-like coil configuration demonstrate that our global optimization approach finds a variety of promising local solutions at less than $0.1\,\%$ of the cost of previous work, which considered solely local stochastic optimization.

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Stellarator coil optimization towards higher engineering tolerances

Cited by 25 publications

References 14 publications

Improved performance of stellarator coil design optimization

Improved performance of stellarator coil design optimization

Combined plasma–coil optimization algorithms

Global stochastic optimization of stellarator coil configurations

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