Stellarator divertor design by optimizing coils for surfaces with sharp corners

TL;DR

This paper tackles the challenge of designing a stellarator divertor with sharp-edge X-points by directly optimizing modular coils toward a toroidally sharp target surface. It introduces the rotating lemon surface and three optimization variants—standard $B_n$ minimization, Weighted Squared Flux (WSF) emphasizing corner fidelity, and manifold optimization (MO) targeting field-line endpoints after one period—implemented within SIMSOPT. Results show that a baseline lemon coil set yields a clean, low-chaos separatrix compared to the chaotic LHD edge, while the WSF coil set improves engineering metrics but exhibits LHD-like separatrix chaos, and the MO coil set substantially reduces primary resonances’ chaos with minimal visual change. The study demonstrates that modular coils can realize a LHD-like helical divertor, but achieving simultaneously sharp edge topology and favorable core confinement requires integrating edge-topology optimization with realistic plasma boundary design and wall/neutral physics; future work should address detachment, heat-flux width, and robustness to coil perturbations.

Abstract

In stellarators, achieving effective divertor configurations is challenging due to the three-dimensional nature of the magnetic fields, which often leads to chaotic field lines and fuzzy separatrices. This work presents a novel approach to directly optimize modular stellarator coils for a sharp X-point divertor topology akin to the Large Helical Device's (LHD) helical divertor using a target plasma surface with sharp corners. By minimizing the normal magnetic field component on this surface, we target a clean separatrix with minimal chaos. Notably, this approach demonstrates the first LHD-like helical divertor design using optimized modular coils instead of helical coils. Separatrices are produced with significantly lower chaos than in LHD, demonstrating that a wide chaotic layer is not intrinsic to the helical divertor. Additional optimization methods are implemented to improve engineering feasibility of the coils and reduce chaos, including weighted quadrature and manifold optimization, a method which does not rely on normal field minimization. The results outline several new strategies for divertor design in stellarators, though it remains to achieve these edge divertor features at the same time as internal field qualities like quasisymmetry.

Figures (6)

• Figure 1: Lemon target surface showing the weight used for the weighted squared flux objective and an optimized coil set. One half field period is shown. Near the sharp corners of the lemon, the weight approaches 1 (red). Away from the corners, the weight decreases according to eqn. \ref{['eqn:WSF_weights']} (blue). The coils shown are the result of weighted squared flux optimization and correspond to the Poincare section in figure \ref{['fig:all_poincares']}(d).
• Figure 2: Illustration of manifold optimization
• Figure 3: Three-dimensional rendering of the rotating lemon divertor structure. The divertor legs are well-separated and non-chaotic.
• Figure 4: (a): Coil set of the rotating lemon after typical $B_n$ minimization with field lines shown. (b): Poincare sections for the lemon coil set at several toroidal angles.
• Figure 5: Poincaré sections of (a) the lemon, (c) Manifold-optimized, (d) Weighted Squared Flux coil sets and (b) the LHD divertor for comparison. Panel (b) is reproduced from Ref LHD_figure.