Regions without flux surfaces of given class for magnetic fields in toroidal geometry

A Converse KAM method for 3D vector fields, establishing regions through which pass no invariant 2-tori transverse to a given direction field, is tested on some helical perturbations of an axisymmetric magnetic field in toroidal geometry. It finds regions corresponding to magnetic islands and chaos for the fieldline flow. Minimization of these regions is proposed as a tool to help in the design of plasma confinement devices of tokamak and stellarator type.