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

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