Improved performance of stellarator coil design optimization

Abstract

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.

Global Stochastic Optimization of Stellarator Coil Configurations

“…Numerically, the perturbations are independent of the coil discretization by considering additive perturbations modeled by Gaussian Processes (GPs). Similar approaches to model coil perturbations for stellarators have been presented in [21,34]. Compared to [34], instead of a squared exponential kernel with added periodicity, we take the period kernel as the basis for our perturbations.…”

“…This allowed the reduction of engineering coil tolerances significantly [16]. Furthermore, recent work has shown that stochastic optimization is a promising method to improve the robustness of the generated magnetic field to fabrication and alignment errors in the associated coils [21,34]. However, all aforementioned approaches do not globally explore the coil design space.…”

“…We define the components of the optimization model precisely in Section 3. Similarly to [21], we consider fabrication errors to be spatially correlated Gaussian perturbations to the coils. In order to optimize (1), we present a two-step global-to-local algorithm for stochastic optimization.…”

Combined plasma–coil optimization algorithms

“…The 3-D optimization effort is encouraged by recent Wendelstein 7-X results (Klinger et al 2019), which was optimized for neoclassical transport (Nührenberg & Zille 1986). There are new methods in coil-design, such as using permanent magnets (Helander et al 2020;Landreman & Zhu 2020;Zhu et al 2020) and designing coils with generous tolerances (Lobsien, Drevlak & Pedersen 2018;Lobsien et al 2020).…”

“…2020) and designing coils with generous tolerances (Lobsien, Drevlak & Pedersen 2018; Lobsien et al. 2020).…”