Exploring the link between coil non-planarity and magnetic surface geometry across a dataset of QI stellarators
Stellarator fusion devices confine plasma by means of complex, non-planar electromagnetic coils. Understanding how the shape of the plasma boundary determines the required complexity of the coil set is a central open question in stellarator design, with direct implications for engineering feasibility and the prospects of building next-generation fusion power plants. In this work we address this question using a large data-driven study. Starting from the Constellaration dataset of quasi-isodynamic (QI) stellarator plasma boundaries, we compute a set of filamentary coil configurations using constrained optimisation within SIMSOPT, and define quantitative coil-complexity metrics (torsion, SVD non-planarity score, inboard-side inclination angle, spectral width) together with a rich set of surface and magnetic geometry features (second fundamental form, principal-direction rotation rate, surface curvatures, and magnetic axis properties). Univariate and multivariate statistical analyses, reveal a strong, central role of the surface geometry: the principal-direction rotation rate of the plasma boundary is the single best predictor of coil non-planarity, while a Random Forest model using up to four surface features achieves R2 = 0.882 for the same target. These results provide quantitative evidence that the rate of change of the principal curvatures cross the plasma boundary are the primary drivers of coil non-planarity in this dataset of quasi-isodynamic stellarators.