A mathematical property of optimized stellarator magnetic fields that makes particle confinement nearly as good as in a tokamak — the theoretical breakthrough enabling the modern stellarator renaissance.
ReviewedLast reviewed: 9 Aug 2026·Category: Glossary
The Problem
In a tokamak, the magnetic field strength depends only on the major radius (it is axisymmetric). This symmetry ensures that trapped-particle orbits are well-confined. In a general stellarator, the three-dimensional magnetic field breaks this symmetry, causing trapped particles to drift out of the plasma — leading to unacceptable neoclassical transport losses.[1]
The insight: In 1988, Juergen Nührenberg and Rainer Zille showed that it is possible to design stellarator magnetic fields where the field strength B, expressed in Boozer coordinates, depends on only one angular coordinate — even though the field geometry is fully three-dimensional. This “quasi-symmetry” restores the good confinement properties of axisymmetry.
Types of Quasi-Symmetry
Quasi-helical symmetry (QHS): B depends on a helical angle. Demonstrated in the HSX stellarator at the University of Wisconsin. Quasi-axisymmetry (QA): B depends on the toroidal angle (like a tokamak). Being pursued by CFQS and Princeton Stellarators. Quasi-isodynamicity (QI): All trapped particles have zero average drift. Implemented in Wendelstein 7-X.[2]
Impact
Quasi-symmetry has transformed the stellarator from a historical curiosity into a serious reactor candidate. Several private companies (Type One Energy, Princeton Stellarators, Proxima Fusion) are building on quasi-symmetric optimization for commercial stellarator designs.[3]
Sources
Nührenberg, J. and Zille, R. "Quasi-helically symmetric toroidal stellarators." Physics Letters A, 129, 113, 1988.
Helander, P. "Theory of plasma confinement in non-axisymmetric magnetic fields." Reports on Progress in Physics, 77, 087001, 2014.
Landreman, M. and Paul, E. "Magnetic fields with precise quasisymmetry for plasma confinement." Physical Review Letters, 128, 035001, 2022.