Islands and current singularities in quasisymmetric toroidal plasmas

TL;DR

This paper investigates current singularities in quasisymmetric toroidal plasmas, showing how quasisymmetry influences singularity localization and the effects of pressure-driven currents, with implications for plasma stability and magnetic island formation.

Contribution

It demonstrates that quasisymmetry effectively isolates Pfirsch-Schl"uter singularities to a single resonant surface and analyzes the impact of higher-order geometric effects on current singularities.

Findings

Quasisymmetry confines Pfirsch-Schl"uter singularities to a single resonant surface.

Pressure-driven currents can reduce but not eliminate magnetic islands.

Higher-order Fourier components influence resistive stability and quasisymmetry's effectiveness.

Abstract

The presence of current singularities in a quasisymmetric magnetic field is explored. Quasisymmetry is shown effective in isolating Pfirsch-Schl\"{u}ter singularities, to leading order, to a single magnetic surface resonant with the helicity of the symmetry. The effects of pressure driven currents are analysed, indicating that exclusion of this surface from the plasma volume reduces the potential opening of islands, but does not generally eliminate them completely due to higher order asymmetric geometric effects. These three-dimensional effects are contained in quasisymmetry and indicate the complexity of finding consistent solutions and their potential sensitivity. The $\delta$-function current singularities show a distinct quasisymmetric behaviour only when the higher-order Fourier content of $B$ is relevant for the resistive stability parameter $D_R$ (not included in leading-order near-axis expansions). In such scenarios, quasisymmetry proves advantageous, both in simplicity and avoidance of amplification by low-order rational surfaces.