Exact Modal Decomposition of Axial Currents in Bulk and Hollow Conducting Cylinders

The modal decomposition of eddy current problems is commonly treated numerically via integral formulations or via the imposition of arbitrary homogeneous boundary conditions at some distance from the sources in the case of differential formulations. In this article, the eigenvalues and eigenvectors for axial currents in an infinitely long conducting cylinder surrounded by vacuum are computed analytically, rigorously accounting for the solution of the outer magnetostatic problem. The analytically derived eigenvalues and eigenvectors are compared against the results of a specifically developed numerical model based on an integral formulation. The two approaches mutually confirm each other's validity. The procedure highlighted is general and could be extended to different geometries.