On the Topological Characterization of Near Force-Free Magnetic Fields, and the work of late-onset visually-impaired Topologists

TL;DR

This paper uses topological methods to characterize near force-free magnetic fields relevant to plasma physics, revealing new conditions for force-free fields and exploring the role of visually impaired topologists in understanding complex 3D structures.

Contribution

It introduces a topological framework for near force-free magnetic fields and establishes necessary and sufficient conditions for force-free configurations, linking mathematics, physics, and cognitive science.

Findings

Topological characterization of near force-free magnetic fields

Necessary and sufficient conditions for force-free magnetic fields

Connections between topology, visualization, and cognitive science

Abstract

The Giroux correspondence and the notion of a near force-free magnetic field are used to topologically characterize near force-free magnetic fields which describe a variety of physical processes, including plasma equilibrium. As a byproduct, the topological characterization of force-free magnetic fields associated with current-carrying links, as conjectured by Crager and Kotiuga, is shown to be necessary and conditions for sufficiency are given. Along the way a paradox is exposed: The seemingly unintuitive mathematical tools, often associated to higher dimensional topology, have their origins in three dimensional contexts but in the hands of late-onset visually impaired topologists. This paradox was previously exposed in the context of algorithms for the visualization of three-dimensional magnetic fields. For this reason, the paper concludes by developing connections between mathematics and cognitive science in this specific context.