Optimizing stellarators with hidden symmetry
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.