Theory of the Critical Current Density in YBa₂Cu₃O₇ Ceramics

Abstract

Two dimensional Josephson junction array model are used to study the effect of grain boundary on the critical current density of YBa₂Cu₃O₇ superconducting ceramics. The model is a network of superconducting grains. The grain boundary angle θ has a Gaussian distribution. Each grain boundary has a critical current density J _c(θ) and normal state resistance R(θ). The current-voltage characteristics is calculated numerically for different grain boundary angle distribution. The scaling law and statistics of extremes introduced by Duxbury, Beale, and Leath (DBL) for general breakdown behavior, based on the most critical defect (normal region) in the network, are tested and found to be accurate for the predicted critical-current distribution of random samples. When the applied current is larger than but close to its critical value, there is periodic V(t) with discrete power spectra. When the applied current get larger, chaotic behavior appears with nearly continuous power spectra.