Analytical study of current-sharing at power frequency between a type II superconducting composite with a normal metal backing

Current sharing in a two-layer composite is studied analytically by numerically solving the 1-dimensional diffusion equation in the normal metal and the phenomenological critical state model with field independent critical current density Jc(T) in the superconductor, with boundary conditions appropriate to a transmission line at each surface and the interface. It is found that with a sufficiently low resistivity (ρ) backing, and reasonable assumptions as to heat transfer, an appreciable fraction of a current density of several thousand amps per cm can be carried in the backing with the balance in a superconductor with high Tcsuch as Nb3Sn. The dependence of the dissipation on such parameters as thickness, Jc, ρ and frequency at constant temperature is given, and typical loss voltage waveforms presented.