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Conefield method reveals regions without invariant tori in helical magnetic fields, indicating chaos and magnetic islands.
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.
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Martinez-del-Rio et al. (2025) studied this question.
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