Stochastic single-stage stellarator optimization using fixed-boundary equilibria

Abstract

In this paper, single-stage stellarator optimization is combined with stochastic coil optimization to improve the robustness of the stellarator as compared to deterministic methods. The plasma boundary, solved with an MHD solver in fixed-boundary mode, is linked to a set of randomly perturbed coils via the squared flux. The optimizer avoids sharp local minima and can reach improved configurations. Two different configurations obtained with our method, one quasi-axisymmetric and one quasi-helically symmetric, are compared against both the standard stochastic stage II method and the single-stage method. The new configurations shown here yield improved squared flux, quasisymmetry, and particle loss following a posteriori perturbation of the coils.

Figures (13)

• Figure 1: Illustration of 10 perturbed coils in a QA stellarator with 5-coils per half field period using the Gaussian Process approach. The blue surface is the last closed flux surface.
• Figure 2: Left: Distributions of the squared flux for different coil perturbation amplitudes $\sigma$ for a HSX-like 4 field period QH stellarator with 1 m major radius. Right: Distributions of the squared flux for different coil perturbation wavelengths $L$.
• Figure 3: Left: Quasisymmetry measured from the final optimized fixed-boundary equilibrium object as a function of the initialized perturbation amplitude $\sigma$. Right: Run time versus number of cores used. Between 64 and 512 cores, the runtime decreases as expected due to parallelization for the stochastic single-stage (blue). However, after this point, concurrency issues, most likely arising from the standard single-stage run (red), appear and delay the optimization.
• Figure 4: Total minimizing function during the optimization for both standard single-stage (blue) and stochastic single-stage (red). Results are normalized with regards to the respective initial value for comparison. The stochastic single-stage approach appears to not get stuck earlier during the optimization allowing the minimizer to reach deeper minima.
• Figure 5: Results of the stochastic single stage method applied to the quasi-axisymmetric case. Coils obtained from a stage II warm-start and stochastic single stage (a), coils obtained from stochastic stage II (b), coils obtained from standard single stage without coil length penalty (c), coils obtained from standard single stage with coil length penalty (d).