Periodic Korteweg-de Vries soliton potentials generate magnetic field strength with exact quasisymmetry

Quasisymmetry (QS) is a hidden symmetry of the magnetic field strength, B, that confines charged particles effectively in a nonsymmetric toroidal plasma equilibrium. Recent numerical breakthroughs have shown that excellent QS can be realized in a toroidal volume. Here, we show that the hidden symmetry of QS has a deep connection to the underlying symmetry that makes solitons possible. In particular, we demonstrate that a class of quasisymmetric B is described by a periodic finite-gap soliton potential of the well-known Korteweg-de Vries (KdV) equation. Our exact and non-perturbative method drastically reduces the number of independent B parameters on a magnetic flux surface to just three, which could make stellarator optimization schemes significantly more efficient. Furthermore, we deduce an upper bound on the maximum toroidal volume that can be quasisymmetric. In the neighborhood of the outermost surface, B approaches the form of the 1-soliton reflectionless potential.