Destruction of invariant surfaces and magnetic coordinates for perturbed magnetic fields

Straight-field-line coordinates are constructed for nearly integrable magnetic fields. The coordinates are based on the robust, noble-irrational rotational-transform surfaces, whose existence is determined by an application of Greene’s residue criterion. A simple method to locate these surfaces is described. Sequences of surfaces with rotational-transform converging to low order rationals maximize the region of straight-field-line coordinates.