  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.
