quasisymmetry

Quasisymmetry is a property of magnetic fields used to confine plasmas in toroidal devices, particularly stellarators. It refers to a special kind of symmetry in the field strength B on magnetic surfaces: instead of depending on all three spatial coordinates, B is effectively a function of a single helically twisted angle. This hidden symmetry aims to preserve the guiding-center invariants of particle motion and thereby improve confinement in non-axisymmetric geometries.

In a common formulation, one uses Boozer or related magnetic coordinates (ψ, θ, φ). Quasisymmetry means B = B(ψ, χ), where χ = M θ − N φ with integers M and N that specify the field’s helicity. The toroidal variation of B around a field line is therefore periodic with that helicity, and the magnitude of B is invariant under the symmetry associated with χ. As a result, the canonical momentum associated with motion along the field line is approximately conserved, reducing neoclassical transport and improving confinement.

Quasisymmetry encompasses several practical realizations, notably quasi-axisymmetric and quasi-helically symmetric configurations. It guides stellarator design, and devices like the Wendelstein 7-X project aim to approximate this property to obtain good confinement without requiring axisymmetry. Achieving and maintaining quasisymmetry in operation is challenging, as real devices exhibit deviations due to coil geometry, plasma currents, and boundary shaping.

Status: Quasisymmetry remains a central concept in fusion plasma theory and stellarator design. It provides a framework for understanding transport in three-dimensionally structured fields and informs optimization strategies that balance confinement with engineering constraints.