Analysis of perturbed magnetic fields via construction of nearby integrable fields

For a given nonintegrable toroidal magnetic field, a nearby integrable magnetic field is constructed from quadratic-flux minimizing surfaces. A new mathematical definition and derivation of quadratic-flux minimizing surfaces, which directly exploits the analogy between toroidal magnetic fields and 112 degree of freedom Hamiltonian systems, is given. The width and phase of magnetic islands (calculated from the shear of the integrable field and the magnitude and phase of the perturbation harmonics) are in excellent agreement with detailed Poincaré plots.