Magnetization profiles of AC type-II superconducting wires exposed to DC magnetic fields

The macroscopic electromagnetic behaviour of a type-II superconducting wire for alternating current power transmission under constant magnetic field conditions is captured by the numerical solution of the Maxwell equations under the framework of the critical state principle and the so-called integral formulation, also known as J-formulation. Time-dependent distributions for the flux front profiles of local current density, magnetic flux, and cycles of magnetic moment are presented. We have found that, regardless of the intensity of the applied magnetic field, the first cycle of Itr(t) defines the period of magnetic stabilization of the SC wire where two plateaus with constant magnetic moment can be measured. Then, a cyclic monotonic behaviour with well-defined flux-front boundaries has been identified, with clear signatures of current-like and field-like flux front profiles. This observation has allowed us to establish semi-analytical approaches of flux-tracking for the local dynamics of current density of AC SC wires immersed in a constant transverse magnetic field, from which all the macroscopical electromagnetic quantities of interest such as the magnetic field, magnetic moment, and power density of energy losses can be calculated. The observations reported define an adequate benchmark for developing flux-tracking approaches in other 2D symmetries, such as SC strips.