Exact non-symmetric closed line vacuum magnetic fields in a topological torus

TL;DR

This paper derives explicit non-symmetric vacuum magnetic fields with closed lines in a topological torus and demonstrates their use in constructing 3D MHD equilibria, advancing stellarator design methods.

Contribution

It provides a closed-form expression for a class of vacuum magnetic fields with closed lines in a topological torus, including invariants and equilibrium construction.

Findings

Explicit closed-form vacuum magnetic fields with closed lines derived.

Invariants of these magnetic fields explicitly obtained.

Construction of 3D low beta MHD equilibria from these fields demonstrated.

Abstract

Non-symmetric vacuum magnetic fields with closed magnetic field lines are of interest in the construction of stellarator equilibria. Beyond the result of D.Lortz (ZAMP \textbf{21}, 196 (1970)), few results are available. This work presents a closed-form expression for a class of vacuum magnetic fields in a topological torus with closed field lines. We explicitly obtain the invariants of such a field. We finally show that a three-dimensional low beta magnetohydrodynamic (MHD) equilibrium may be constructed in a topological torus starting with these closed line vacuum magnetic fields.