Outside and inside a magnetic island: different perspectives to describe the same observables

TL;DR

This paper compares three different theoretical approaches—perturbative and non-perturbative—to describe magnetic islands in toroidal plasmas, highlighting their respective perspectives and limitations.

Contribution

It introduces and contrasts three distinct methods for modeling magnetic islands, providing insights into their applicability and the observables they describe.

Findings

Different approaches yield consistent observables in certain limits

Perturbative methods are effective for small islands

Non-perturbative description captures full geometric details

Abstract

We compare three different approaches to describe a magnetic island in a generic toroidal plasma: (i) perturbative, from the perspective of the equilibrium magnetic field and the related action in a variational principle formulation, (ii) again perturbative, based on the integrability of a system with a single resonant mode and the application of a canonical transformation onto a new island equilibrium system, and (iii) non-perturbative, making use of a full geometric description of the island considered as a stand-alone plasma domain. For the three approaches, we characterize some observables and discuss the respective limits.