Accurate computation of Magnetostatic fields in axisymmetric geometries in the presence of ferromagnetic materials

In this paper the magnetic field is computed as the superposition of two contributions: B = B0 + ΔB. The vacuum field B0 due to the coil currents can be obtained with extreme accuracy using analytical methods. The field ΔB, due to the magnetizing currents in the iron or other perturbations like eddy currents in passive conductors, is computed numerically. The splitting yields a very high accuracy in all cases in which |ΔB| ≪ |B0|. The method, based on a calibration of the numerical results, is shown to be similar, but less expensive than perturbation techniques and reduced potential approaches. The effect of the outer magnetic shield on the field produced by an air core magnet for magnetic resonance is studied and compared to the analytical solution available for a particular shield geometry. An example of application is also shown for a dynamic case in the presence of eddy currents.