A comprehensive exploration of quasisymmetric stellarators and their coil sets

TL;DR

This work expands the QUASR repository to include vacuum-field stellarators with quasiaxisymmetry and quasihelical symmetry, along with their coil sets, enabling a globalized coil-design workflow over roughly 370{,}000 configurations. It combines near-axis quasisymmetry landscapes with PCA-based dimensionality reduction to visualize high-dimensional device data and compare QUASR designs to literature, uncovering low-dimensional structure and clusters driven by symmetry goals and rotational-transform constraints. The study demonstrates that 2–3 principal components capture most variability in targeted subsets, revealing continua within clusters and highlighting the interplay between geometry, QS quality, and engineering constraints. These insights facilitate rapid exploration of coil geometries, guide future optimization strategies, and provide a scalable framework for analyzing large stellarator design datasets with potential impact on coil-design workflows and reactor-relevant configurations.

Abstract

We augment the `QUAsi-symmetric Stellarator Repository' (QUASR) to include vacuum field stellarators with quasihelical symmetry using a globalized optimization workflow. The database now has almost 370,000 quasisaxisymmetry and quasihelically symmetric devices along with coil sets, optimized for a variety of aspect ratios, rotational transforms, and discrete rotational symmetries. This paper outlines a couple of ways to explore and characterize the data set. We plot devices on a near-axis quasisymmetry landscape, revealing close correspondence to this predicted landscape. We also use principal component analysis to reduce the dimensionality of the data so that it can easily be visualized in two or three dimensions. Principal component analysis also gives a mechanism to compare the new devices here to previously published ones in the literature. We are able to characterize the structure of the data, observe clusters, and visualize the progression of devices in these clusters. The topology of the data is governed by the interplay of the design constraints and valleys of the quasisymmetry objective. These techniques reveal that the data has structure, and that typically one, two or three principal components are sufficient to characterize it. The latest version of QUASR is archived at https://zenodo.org/doi/10.5281/zenodo.10050655 and can be explored online at quasr.flatironinstitute.org.

Figures (16)

• Figure 1: Globalized coil design workflow.
• Figure 2: Notable QH devices and their coil sets in the QUASR.
• Figure 3: The top row shows the landscape of quasisymmetric stellarators for $n_{\text{fp}}=4$, the red dot on the leftmost panel corresponds to the HSX device. There are four quasisymmetry phases delineated by poorly quasisymmetric (dark color) devices. Devices optimized for QA and QH in QUASR plotted on top of the landscape with blue and red dots, respectively. The second row and third rows of plots correspond to $n_{\text{fp}}=4$ and 5, respectively.
• Figure 4: Data $\mathbf x_i \in \mathbb R^3$ from three Gaussians are shown on the left, and the optimal projection $\tilde{\mathbf x}_i$ onto a two-dimensional plane is shown on the right. The transparent ellipsoids correspond to the 95% confidence interval of each Gaussian.
• Figure 5: Conditions that the surface parametrization must satisfy so that the feature vector of Fourier coefficients is unique. The left image illustrates how the surface coordinates satisfy $x(0, 0) \geq x(0, \pi)$, $\frac{\partial z}{\partial \theta}(0, 0) \geq 0$, $\frac{\partial y}{\partial \varphi}(0, 0) \geq 0$, and that the $Z$-coordinate of the magnetic axis (in red) satisfies $Z'(\phi) \geq 0$. The right image is a view in the $\sm Z$ direction onto the $XY$ plane, showing that the radius of the magnetic axis satisfies $R(0) \geq R(\pi/n_{\text{fp}})$. The grid lines on the magnetic surface correspond to lines of constant toroidal and poloidal Boozer angles.