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

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.