Permanent Magnet Modeling for Lorentz Force Evaluation

Lorentz force evaluation (LFE) is a technique to reconstruct defects in electrically conductive materials. The accuracy of the forward and inverse solution highly depends on the applied model of the permanent magnet. The resolution of the technique relies upon the shape and size of the permanent magnet. Furthermore, the application of an existing forward solution requires an analytic integral of the magnetic flux density. Motivated by these aspects, we propose a magnetic dipoles model (MDM), in which the permanent magnet is substituted with an assembly of magnetic dipoles. This approach allows modeling of magnets of arbitrary shape by appropriate positioning of the dipoles, and the integral can be expressed by elementary mathematical functions. We apply the MDM to cuboidal-shaped and cylindrical-shaped magnets and evaluate the obtained magnetic flux density by comparing it to reference solutions. We consider distances of 2-6 mm to the permanent magnet. The representation of a cuboidal magnet with 832 dipoles yields a maximum error of 0.02% between the computed magnetic field of the MDM and the reference solution. Comparable accuracy for the cylindrical magnet is achieved with 1890 dipoles. In addition, we embed the MDM of the cuboidal magnet into an existing forward solution for LFE and find that the errors of the magnetic flux density are partly compensated by the forward calculations. We conclude that our modeling approach can be used to determine the most efficient MDMs for LFE.