Conefield approach to identifying regions without flux surfaces for magnetic fields

TL;DR

This paper introduces a conefield-based Converse KAM method to identify regions in magnetic fields where invariant flux surfaces do not exist, effectively detecting magnetic islands and chaotic zones in toroidal geometries.

Contribution

It presents a novel conefield approach for efficiently locating non-flux-surface regions in 3D magnetic fields, extending the capability to analyze complex magnetic structures.

Findings

Successfully identifies regions without invariant flux surfaces.

Detects magnetic islands and chaotic zones in perturbed magnetic fields.

Provides bounds on invariant tori slopes to extend non-existence regions.

Abstract

The conefield variant of a Converse KAM method for 3D vector fields, identifying regions through which no invariant 2-tori pass transverse to a specified direction field, is tested on some helical perturbations of an axisymmetric magnetic field in toroidal geometry. This implementation computes bounds on the slopes of invariant tori of a given class and allows to apply a subsidiary criterion to extend the non-existence region, saving significant computation time. The method finds regions corresponding to magnetic islands and chaos for the fieldline flow.