Analytical solution of the induced currents in multilayer cylindrical conductors under external electromagnetic sources

We present a closed-form solution for the induced losses in round conductors consisting of several concentric layers. The geometry under study corresponds to an infinitely-long and isolated multilayer cylinder where layers can have different electromagnetic properties and the number of layers is not restricted. The multilayer conductor is under an external time-varying magnetic field which induces currents and, accordingly, generates Joule dissipation. Total induced losses are obtained by integrating the losses of each layer. Mathematical expressions of the current distribution in each layer are derived from the solution of Maxwell's equations. These expressions consist of a combination of Bessel functions of different kinds and orders. The current distribution in a particular layer not only depends on the properties of the layer but also on the properties of the rest of layers. Consequently, matrix formalism is adopted for describing current distribution of layers. Matrix description is numerically solved and results are compared with finite element simulations for different arrangements and cases.