Modal Theory of Skin Effect in Single and Multiple Turn Coils

The skin effect in circularly symmetric structures is formulated in terms of an integral equation, which may be solved in terms of the normal modes of the corresponding integral equation eigenvalue problem. The necessary modal functions are computed numerically, using a simple discrete model of the coil. The modal series solution easily accounts for electrical excitation of the coil as for external magnetic fields. A comparison with so-called "direct" calculation methods, as well as with published experimental results, shows that the method is capable of good accuracy, while effecting substantial economies in computation.