Generalized Boozer coordinates: a natural coordinate system for quasisymmetry

TL;DR

This paper introduces generalized Boozer coordinates, a new magnetic field coordinate system that simplifies the analysis of quasisymmetric magnetic configurations in toroidal plasma devices.

Contribution

It proves the existence of generalized Boozer coordinates for certain magnetic fields and demonstrates their usefulness in analyzing quasisymmetry and equilibrium properties.

Findings

Existence of generalized Boozer coordinates under specific conditions.

All quasisymmetric fields satisfy the integral condition for coordinate existence.

Analytical insights into differences between strong and weak quasisymmetry.

Abstract

We prove the existence of a straight-field-line coordinate system we call generalized Boozer coordinates. This coordinate system exists for magnetic fields with nested toroidal flux surfaces} provided $ \oint\mathrm{d}l/B\:(\mathbf{j}\cdot\nabla\psi)=0$, where symbols have their usual meaning, and the integral is taken along closed magnetic field lines. All quasisymmetric fields, regardless of their associated form of equilibria, must satisfy this condition. This coordinate system presents itself as a convenient form in which to describe general quasisymmetric configurations and their properties. Insight can be gained analytically into the difference between strong and weak forms of quasisymmetry, as well as axisymmetry, and the interaction of quasisymmetry with different forms of equilibria.