Phenomenological description of flux pinning in non-uniform high-temperature superconductors in magnetic fields lower than the self-field

Critical currents measured on a commercial Bi-2223/Ag tape in applied magnetic fields ranging from zero to 100 mT are analysed in order to demonstrate the validity of the phenomenological description proposed by the authors for flux pinning in polycrystalline high-temperature superconductors in low magnetic fields. The four-parameter model is a generalization of the Kim formula describing the magnetic field dependence of the critical current density. When combined with the finite-element calculation, it is able to predict the critical currents measured in different field orientations with an average accuracy better than 0.2%. The volume density of the flux pinning force is easily evaluated from the parameters of the model. Particular attention is paid to the problem of a possible sample non-uniformity. In fact, the experimental data can be better explained assuming the hypothesis of better filament texturing in outer filaments. This also means that the accurate determination of critical currents in low magnetic fields can be used to reveal a non-uniformity in the current-carrying capability of the superconducting material.