A topological approach to magnetic nulls

TL;DR

This paper introduces a topological method using isotropes to analyze magnetic nulls, providing analytical tools to understand their behavior and locations in magnetic fields, which is crucial for understanding magnetic reconnection.

Contribution

It presents a novel topological framework based on isotropes to study magnetic nulls and derives analytical expressions for null locations in specific magnetic field configurations.

Findings

Analytical expressions for null locations in dipole fields

Topological framework using isotropes for magnetic null analysis

Application to fields from Hopf fibration

Abstract

Magnetic nulls are locations where the magnetic field vanishes. Nulls are the location of magnetic reconnection, and they determine to a large degree the magnetic connectivity in a system. We describe a novel approach to understanding movement, appearance, and disappearance of nulls in magnetic fields. This approach is based on the concept of isotropes, or lines where the field direction is constant. These lines are streamlines of a vector field whose flux is sourced by the topological indices of nulls, and can be conceptualized as corresponding "lines of force" between nulls. We show how this topological approach can be used to generate analytical expressions for the location of nulls in the presence of external fields for dipoles and for a field defined by the Hopf fibration.