Some mathematics for quasi-symmetry

TL;DR

This paper explores the mathematical conditions and restrictions for quasi-symmetry in steady magnetic fields, deriving new equations and insights into their structure and properties.

Contribution

It introduces new restrictions on quasi-symmetry and derives an analogue of the Grad-Shafranov equation for quasi-symmetric magnetohydrostatic fields.

Findings

Derived restrictions on quasi-symmetry possibilities

Formulated an analogue of the Grad-Shafranov equation for quasi-symmetric fields

Enhanced understanding of the mathematical structure of quasi-symmetric magnetic fields

Abstract

Quasi-symmetry of a steady magnetic field means integrability of first-order guiding-centre motion. Here we derive many restrictions on the possibilities for a quasi-symmetry. We also derive an analogue of the Grad-Shafranov equation for the flux function in a quasi-symmetric magnetohydrostatic field.