Model for the angular dependence of critical currents in technical superconductors

We propose a model for the effect of anisotropic pinning on the critical currents in superconductor wires as a function of the direction of an external magnetic field. The model emphasizes the statistical distribution of the pinning encountered by a vortex as determining the functional forms observed. If we assume anisotropic defect populations with normal distributions of pinning then we can derive exact functions for the critical current as a function of angle: J c (θ). The model predicts that the combination of extended defects in the c -axis and ab -plane directions can lead to peaks at intermediate angles. The predicted forms agree well with experiments on superconductors with layered structures including cases where peaks occur at intermediate angles. The results suggest that common features of J c (θ) can be identified with combinations of defects. We discuss some implications of the statistical model including a possible sample thickness dependence of critical currents.