Numerical Modelling of Dynamic Resistance in a Parallel-Connected Stack of HTS Coated-Conductor Tapes

Dynamic resistance is observed in type-II superconductors carrying a DC transport current while simultaneously exposed to an alternating magnetic field. The appearance of a nonzero resistance is attributed to the interaction between the transport current and moving fluxons. This effect is relevant to many superconductor applications such as high-temperature-superconductor (HTS) flux pumps, DC/AC magnets, synchronous machines, and persistent current switches. Here, we present a finite element method (FEM) analysis of both the time averaged dynamic resistance and the instantaneous current sharing behaviour in a cable comprised of a stack of four YBCO thin films connected in parallel. Numerical modelling was performed using the H-formulation method implemented in the commercial software COMSOL. The model employs experimentally measured values of the angular dependence of the critical current I.(B, 8) and the flux creep exponent n(B, 8). A single threshold field is observed, above which a finite dynamic resistance is observed in all tapes simultaneously. The time-averaged dynamic resistance of individual tapes tends to be larger for the exterior tapes than the interior tapes, but this difference decreases as the total transport current in the cable increases. We attribute this to shielding currents flowing in the exterior tapes during the majority of the cycle, which displace net DC current into the interior tapes. However, the relative proportion of DC transport current flowing in the exterior and interior tapes is also observed to vary periodically once per half cycle of the applied field. This is due to the periodic trapping of return screening currents in the interior tapes.