Designing stellarator coils by a modified Newton method using FOCUS

Zhu, Caoxiang; Hudson, S. R.; Song, Yuntao; Wan, Yuanxi

doi:10.1088/1361-6587/aab8c2

Cited by 28 publications

(33 citation statements)

References 34 publications

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“…Coils to reproduce the vacuum boundary were produced by the FOCUS code (Zhu et al. 2018) using an initial coil set generated by the REGCOIL code (Landreman 2017). The FOCUS code targets the average normal field on the magnetic boundary (a quantity to minimize) and the minimal radius of curvature for the coils (a quantity to maximize).…”

Section: Coil Constructionmentioning

confidence: 99%

Advancing the physics basis for quasi-helically symmetric stellarators

et al. 2020

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A new optimized quasi-helically symmetric configuration is described that has the desirable properties of improved energetic particle confinement, reduced turbulent transport by three-dimensional shaping and non-resonant divertor capabilities. The configuration presented in this paper is explicitly optimized for quasi-helical symmetry, energetic particle confinement, neoclassical confinement and stability near the axis. Post optimization, the configuration was evaluated for its performance with regard to energetic particle transport, ideal magnetohydrodynamic stability at various values of plasma pressure and ion temperature gradient instability induced turbulent transport. The effects of discrete coils on various confinement figures of merit, including energetic particle confinement, are determined by generating single-filament coils for the configuration. Preliminary divertor analysis shows that coils can be created that do not interfere with expansion of the vessel volume near the regions of outgoing heat flux, thus demonstrating the possibility of operating a non-resonant divertor.

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Section: Coil Constructionmentioning

confidence: 99%

Advancing the physics basis for quasi-helically symmetric stellarators

et al. 2020

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“…Furthermore, in order to optimize multi-filament coils in the current framework, a single-filament representation needs to be obtained first. An explanation of the single-filament optimization, as used in FOCUS (Zhu et al 2018), is given in this section. A Fourier series representation for single-filament coils in three-dimensional space is employed.…”

Section: Filament Optimizationmentioning

confidence: 99%

“…Fast calculation of target function derivatives with respect to the coil coefficients is available using analytic derivatives. More details can be found in Zhu et al (2018).…”

Section: The Single-filament Modelmentioning

confidence: 99%

Optimization of finite-build stellarator coils

et al. 2020

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Finding coil sets with desirable physics and engineering properties is a crucial step in the design of modern stellarator devices. Existing stellarator coil optimization codes ultimately produce zero-thickness filament coils. However, stellarator coils have finite depth and thickness, which can make the single-filament model a poor approximation, particularly when coil build dimensions are relatively large compared to the coil–plasma distance. In this paper, we present a new method for designing coils with finite builds and present a mechanism to optimize the orientation of the winding pack. We approximate finite-build coils with a multi-filament model. A numerical implementation has been developed, and applications to the Helically Symmetric eXperiment stellarator and a new UW-Madison quasihelically symmetric configuration are shown.

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“…ONSET has several optimizers, but we use Brent's method (Gegenfurtner 1992) which approximates the Hessian of f in an iterative process and optimizes along its principal axes. FOCUS, on the other hand, computes the gradient and Hessian (Zhu et al 2018b) of f analytically. FOCUS also has several optimizers to minimize the objective function f , but in this study, we will mainly use the conjugate gradient method.…”

Section: And Othersmentioning

confidence: 99%

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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Designing stellarator coils by a modified Newton method using FOCUS

Cited by 28 publications

References 34 publications

Advancing the physics basis for quasi-helically symmetric stellarators

Advancing the physics basis for quasi-helically symmetric stellarators

Optimization of finite-build stellarator coils

Improved performance of stellarator coil design optimization

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