Numerical determination of the threshold magnetic field in superconducting strips and coils triggering dynamic resistance

The threshold magnetic field is a key parameter for evaluating the current decay caused by dynamic resistance in superconducting windings and magnets. For a DC-carrying superconducting slab under an AC parallel magnetic field, the analytical theory clearly shows that there is only one electric central line (ECL) across the slab width at the onset of dynamic-resistance. However, threshold magnetic fields in superconducting strips and coils have not been fully investigated. Based onthe one-ECL criterion, this paper first presents a method for numerically determining the threshold magnetic field via the evolving internal magnetic field in superconducting strips and coils. By probing transient electromagnetic behaviours, interestingly, we found a distinctive feature of superconducting strips in which a wide region of zero electrical field is observed when dynamic resistance/loss initially occurs. With increasing magnetic fields, this region gradually shrinks and eventually become the ECL. More importantly, this numerical method can analyse the local threshold magnetic field in a targeted coil turn. The ability to quantify threshold magnetic field provides a clear guidance on the acceptable level of ripple and harmonic magnetic fields for coil windings in superconducting maglev trains and field windings of superconducting machines operating at persistent current mode.