Optimizing stellarators with hidden symmetry

Abstract

Stellarators confine fusion plasmas using three-dimensional magnetic fields composed of nested toroidal magnetic surfaces. In generic stellarators, trapped particles can drift across these surfaces and degrade plasma confinement. Certain topological properties of the magnetic field strength can suppress these drifts. However, conventional stellarator design approaches typically enforce restrictive constraints to realize such properties, thereby segmenting and limiting the accessible configuration space. In this work, we reformulate the conditions for efficient confinement as constraints on a homeomorphic straightening transformation of the field contours. Within this framework, the various families of stellarator magnetic fields optimized for plasma confinement arise naturally as specific realizations of a unified mapping. This new perspective provides a significantly more comprehensive description of viable stellarator configurations, enabling systematic exploration of trade-offs among confinement quality, geometric complexity, and engineering requirements. We illustrate this approach by presenting a highly compact stellarator design that nevertheless achieves plasma performance comparable to that of leading reactor-scale designs with much larger aspect ratios.

Figures (6)

• Figure 1: Stellarator configurations and the new optimization method.a, A general stellarator with nested flux surfaces. The colours represent the magnetic field strength $B(s, \theta, \zeta)$, where $s$ is the radial label, $\theta$ is the poloidal angle, and $\zeta$ is the toroidal angle. b, Variation of $B$ in Boozer coordinates $(\theta_B, \zeta_B)$ on a magnetic surface. c, Various stellarator fields that could serve as the basis for reactor candidates. Quasisymmetry is a subset of omnigenity. Omnigenity can be generalized to pseudosymmetry (preserving no locally closed $B$ contours) and piecewise omnigenity (preserving $\partial \mathcal{J} / \partial\alpha = 0$), which can in turn be combined with omnigenity. d, Flow of the new optimization method. e, All configurations can be transformed to symmetry-aligned coordinates with special homeomorphic mappings.
• Figure 2: Quasisymmetric and pseudosymmetric configurations.a, 3D plots of the plasma boundary (from left to right: QA, QP, QH, PS). b,$B$ contours in Boozer coordinates on the outermost surface. Dashed lines correspond to the field line.
• Figure 3: Confinement properties of all configurations.a, Neoclassical transport coefficient. b, Collisionless loss fractions of alpha particles at reactor scale.
• Figure 4: Precisely omnigenous configurations.a, 3D plots of the plasma boundary (from left to right: TO, HO, PO). b,$B$ contours in Boozer coordinates on the outmost surface. c, The distribution of the normalized second adiabatic invariant $\tilde{\mathcal{J}} (\alpha, b^*)$ on the outmost surface ($b^*$ is the relative field strength). d, Comparison of the new omnigenous configurations (stars) with reference QI stellarators (crosses) and the ConStellaration database (dots) in the aspect ratio and QI quality space. The reference QI stellarators include W7X-HMdinklageMagneticConfigurationEffects2018, QPS Spong1998, QIPC Subbotin2006, QI-NFP1jorgeSinglefieldperiodQuasiisodynamicStellarator2022, Precise-QI3goodmanConstructingPreciselyQuasiisodynamic2023, and CIEMAT-QI4sanchezQuasiisodynamicConfigurationGood2023.
• Figure 5: The PO-pwO-A6 configuration.a, 3D plot of the plasma boundary. b,$B$ contours in Boozer coordinates on the outmost surface. c, Cross-sections of QP, PO, and PO-pwO-A6 configurations at toroidal angles of 0 and $\pi/n_\text{fp}$. d,$\mathcal{J}$ on the outmost surface as a function of $b^*$. There are multiple invariant branches in high-field regions. The mean absolute relative error (MARE) is below 1% in each region. e, The minimum magnetic gradient scale length $L^*_{\nabla B}$ of three configurations.