Limits to the critical current in Bi₂Sr₂Ca₂Cu₃O_x tape conductors: The parallel path model

An extensive overview of a model that describes current flow and dissipation in high-quality Bi₂Sr₂Ca₂Cu₃O_x superconducting tapes is provided. The parallel path model is based on a superconducting current running in two distinct parallel paths. One of the current paths is formed by grains that are connected at angles below 4°. Dissipation in this strongly linked backbone occurs within the grains and is well described by classical flux-creep theory. The other current path, the weakly linked network, is formed by superconducting grains that are connected at intermediate angles (4°–8°) where dissipation occurs at the grain boundaries. However, grain boundary dissipation in this weakly linked current path does not occur through Josephson weak links, but just as in the strongly linked backbone, is well described by classical flux creep. The results of several experiments on Bi₂Sr₂Ca₂Cu₃O_x tapes and single-grained powders that strongly support the parallel path model are presented. The critical current density of Bi₂Sr₂Ca₂Cu₃O_x tapes can be scaled as a function of magnetic field angle over the temperature range from 15 K to 77 K. Expressions based on classical flux creep are introduced to describe the dependence of the critical current density of Bi₂Sr₂Ca₂Cu₃O_x tapes on the magnetic field and temperature.