Penetration depth of shielding currents due to crossed magnetic fields in bulk (RE)-Ba-Cu-O superconductors

Exposure to time-varying magnetic fields causes shielding currents to flow beneath the surface of a superconductor up to a field-dependent penetration depth. In trapped field applications of bulk superconductors, in which the decay of trapped field due to external AC magnetic fields is caused by current redistribution (and not by helating and temperature rise), this penetration depth determines the degree of current redistribution in the superconductor and, in turn, the degree of decay of trapped field. In this study we propose and validate experimentally a model to explain the rate of decay of trapped field in a single grain bulk GdBa2Cu3O7-8 (GdBCO) superconductor exposed to an AC magnetic field in a crossed-field configuration. The model is based on calculating the time dependence of the trapped field using the Biot-Savart law and assuming that the time dependence of the current density changes at the depth of penetration of the induced shielding currents. Inside the superconductor, where the crossed-field has not penetrated, the time dependence is assumed to be logarithmic and the decay of current density due to flux creep, whereas within the penetration depth of the surface the time dependence is assumed to be exponential and the decay of current density due to its redistribution. The penetration depth was measured separately using SQUID magnetometry and used as an input parameter to the model. The model was compared subsequently with measurements of the decay of trapped field and found to be in excellent agreement with the observed behaviour.