Critical currents in polycrystalline YBa2Cu3O7-x: Self-field and grain-size dependence

The critical state in a random 3D Josephson net created by transport current

The set of weak links connecting superconducting grains of ceramics forms a random three-dimensional Josephson net. The temperature and size dependences of the critical currents in bismuth-based and yttrium-based high-temperature superconducting ceramic samples consisting of randomly oriented grains have been studied in zero magnetic field. It is shown that the critical current in samples having various cross-sectional shapes can be presented as the product of temperature and size dependent factors. The transport critical current is a homogeneous function of the cross-sectional shape dimensions. The size dependent factor is a universal function describing properties of the weak link Josephson net. The exponent of this function is independent of the temperature, the type of superconducting material, the existence (or lack) of a Josephson net in the sample, and the method used for varying the sample cross-section. The transport critical current density and induced magnetic field are homogeneous functions of coordinates. It is shown that the critical current density has a power law dependence on the magnetic field.