Self-field critical current of a conductor with an elliptical cross-section

Numerical calculations using the commercial finite-element code FEMLAB have been carried out to find the distribution of current density in a wire of elliptical cross-section from a hard superconductor carrying the critical current. Dependence of the critical current density on local magnetic field and its orientation has been taken into consideration in these calculations. The results of critical current calculations for wires of different shapes and dimensions clearly revealed how this quantity can be influenced by the distribution of the self magnetic field. The outcome found for wires with cross-sections resembling tapes made from a high-temperature superconductor Bi-2223 have been approximated by two engineering formulae: one can be used to cancel out the influence of the tape width, and the other allows us to perform a correction on the aspect ratio. These expressions would allow the quality of superconducting properties expressed by the self-field critical current density to be compared also for wires of different cross-sections.