Magnetization Profiles of AC Type-II Superconducting Wires Exposed to DC Magnetic Fields

The macroscopic electromagnetic behavior of a type-II superconducting (SC) wire for alternating current (ac) 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 I
_tr
(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 behavior 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 semianalytical 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 for a rounded SC wire define an adequate benchmark for the implementation of flux-tracking approaches in other two-dimensional symmetries, such as SC strips, where the flux-front profile for isolated excitations can be formulated by exact geometrical expressions.