Phases and phase-transitions in quasisymmetric configuration space

TL;DR

This paper investigates the topological structure of quasisymmetric magnetic configurations, revealing distinct phases characterized by topological invariants and proposing a new approach to stellarator design based on magnetic axes.

Contribution

It introduces a topological framework for classifying quasisymmetric configurations and links phases to self-linking numbers, advancing stellarator optimization methods.

Findings

Configurations are divided into well-separated phases by topology.

Self-linking number characterizes different symmetry phases.

Phase transitions correspond to quasi-isodynamic configurations.

Abstract

We explore the structure of the space of quasisymmetric configurations identifying them by their magnetic axes, described as 3D closed curves. We demonstrate that this topological perspective divides the space of all configurations into well-separated quasisymmetric phases. Each phase is characterized by the self-linking number (a topological invariant), defining different symmetry configurations (quasi-axisymmetry or quasi-helical symmetry). The phase-transition manifolds correspond to quasi-isodynamic configurations. By considering some models for closed curves (most notably torus unknots), general features associated with these phases are explored. Some general criteria are also built and leveraged to provide a simple way to describe existing quasisymmetric designs. This constitutes the first step in a program to identify quasisymmetric configurations with a reduced set of functions and parameters, to deepen understanding of configuration space, and offer an alternative approach to stellarator optimization that begins with the magnetic axis and builds outward.