Periodic Korteweg-de Vries soliton potentials generate quasisymmetric magnetic field strength in a finite plasma-beta equilibrium

TL;DR

This paper reveals that the magnetic field strength in quasisymmetric stellarator equilibria can be described by a small set of flux functions linked to periodic soliton theory, providing a new global understanding beyond near-axis models.

Contribution

It demonstrates that the magnetic field strength in quasisymmetric equilibria is governed by a limited number of flux functions connected to periodic soliton solutions, offering a global perspective.

Findings

B on a flux surface is determined by 3-4 flux functions.

These flux functions are critical values of the derivative of B along field lines.

Results are consistent with near-axis models but are valid globally.

Abstract

Quasisymmetry (QS) is a hidden symmetry of the magnetic field strength, B, that enables effective confinement of charged particles in a fully three-dimensional (3D) toroidal plasma equilibrium. Such equilibria are typically modeled by the ideal magnetohydrostatic (MHS) equation. The nonlinear, overdetermined nature of the quasisymmetric MHS equations severely complicates our understanding of the interplay between 3D shaping, equilibrium properties such as pressure and rotational transform, and B. Progress has been made through expansions near the magnetic axis; however, a more comprehensive theory is desirable. Using a combination of analysis and regression on a large dataset of numerically optimized quasisymmetric stellarators, we demonstrate that there is a hidden lower dimensionality of B on a magnetic flux surface with connections to the theory of periodic solitons. We show that $B$ on a flux surface is determined by three or at most four flux functions, each of which is a critical value of the derivative of B along the field line. While being consistent with the near-axis models, our results are global and hold even on the last closed flux surface.