Maximum Entropy Distributions Describing Critical Currents in Superconductors

Maximum entropy inference can be used to find equations for the critical currents (Jc) in a type II superconductor as a function of temperature, applied magnetic field, and angle of the applied field, θ or . This approach provides an understanding of how the macroscopic critical currents arise from averaging over different sources of vortex pinning. The dependence of critical currents on temperature and magnetic field can be derived with logarithmic constraints and accord with expressions which have been widely used with empirical justification since the first development of technical superconductors. In this paper we provide a physical interpretation of the constraints leading to the distributions for Jc(T) and Jc(B), and discuss the implications for experimental data analysis. We expand the maximum entropy analysis of angular Jc data to encompass samples which have correlated defects at arbitrary angles to the crystal axes giving both symmetric and asymmetric peaks and samples which show vortex channeling behavior. The distributions for angular data are derived using combinations of first, second or fourth order constraints on cot θ or cot . We discuss why these distributions apply whether or not correlated defects are aligned with the crystal axes and thereby provide a unified description of critical currents in superconductors. For J//B we discuss what the maximum entropy equations imply about the vortex geometry.