Toroidicity

Toroidicity is the property of having a torus-like, donut-shaped geometry. In mathematics and geometry, it describes objects or surfaces that resemble a torus, including aspects such as curvature and symmetry around a central hole. In plasma physics and magnetic confinement fusion, toroidicity refers to the torus-shaped arrangement of the confinement system and its magnetic flux surfaces.

In devices such as tokamaks and stellarators, the confined plasma lies on nested toroidal magnetic flux surfaces. The degree of toroidicity is closely related to the system’s aspect ratio, defined as the major radius to the minor radius (R0/a). A smaller a/R0 (weaker toroidicity) approaches cylindrical geometry, while larger a/R0 enhances toroidal effects and curvature. Toroidicity also leads to variations in the magnetic field strength around the torus, affecting transport and stability through features such as toroidal field ripple in devices with discrete coil structures.

The geometry of toroidic confinement is described, in axisymmetric approximations, by equilibrium models like the Grad-Shafranov equation, where the toroidal shape influences the configuration of magnetic surfaces, shear, and stability properties. In stellarators, toroidicity is an inherent aspect of the three-dimensional magnetic configuration, whereas tokamaks rely on a primarily toroidal symmetry with controlled deviations.

Understanding toroidicity is important for predicting confinement quality, neoclassical transport, and magnetohydrodynamic stability, and it informs coil design, plasma shaping, and error-field control in fusion experiments.