Quasi-symmetry in magnetic fusion energy confinement devices

Quasi-symmetry in three-dimensional magnetic confinement devices provides a path for external control of the confining magnetic field while achieving confinement comparable to axisymmetric configurations. In a quasi-symmetric toroidal configuration, magnetic field strength in magnetic flux coordinates depends primarily on two coordinates, $B\left( \psi, \theta, \zeta \right) \approx B\left( \psi, M\theta + N\zeta \right)$ where $M$ and $N$ are integers. Here, $\psi$ is the flux coordinate (analogous to a toroidal radial coordinate) while $\theta$ and $\zeta$ are the poloidal and toroidal angles in magnetic flux coordinates (a coordinate system in which the magnetic field lines are straight). In this work, different classes of quasi-symmetric configurations are compared from quasi-axisymmetric ($M=1,N=0$) to quasi-helically symmetric ($M\ne 0, N\ne 0$) to quasi-poloidally symmetric ($N=1,M=0$). This is a numerical investigation in which equilibria are optimized for different quasi-symmetries but with other parameters such as average field strength, major radius, and aspect ratio, equivalent across the configurations. Equilibrium and transport characteristics will be compared across the configurations.