Conefield approach to identifying regions without flux surfaces for magnetic fields

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 the bounds on the slopes of invariant tori of a given class and allows us 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.