Connections between quasisymmetric magnetic fields and anisotropic pressure equilibria in stellarators

Quasisymmetric stellarators are an attractive alternative to axisymmetric magnetic confinement devices. They replicate the good neoclassical behaviour of the latter while enabling flexibility in their three-dimensional design to avoid disruption-prone currents. However, until now, it has been accepted in the fusion community that global quasisymmetry in magnetostatic equilibria (which obeys j×B=▽p with p the isotropic pressure) is not achievable exactly in stellarators. As evidence, the Garren-Boozer overdetermination problem is often cited: construction of solutions by means of a near-axis expansion break down beyond second order due to the appearence of overdetermined equations. We show that this limitation is not inherent to quasisymmetry, but rather a result of requiring it in ideal MHD force balance. Extending the equilibria to include asymmetric forces avoids the overdetermination problem. Anisotropic pressure plays a central role in this extension, as not only does it avoid the overdetermination problem, but it can be shown to also be derivable as an energy minimum from a variational principle with global constraints in the manner of Kruskal and Kulsrud or Grad. Numerical solutions obtained by near-axis expansion are presented. The extended space of solutions opens the door to a more fundamental understanding of quasisymmetry and its practical construction for optimal design of future experiments. In particular, it suggests that there might exist solutions in MHD equilibria that are very close to exactly quasisymmetric.