Penetration of the magnetic field into 3D ordered Josephson medium

The physics of all processes taking place in ordinary superconductors (the Meissner image currents, vortices interacting with one another, etc.) is clear and the theory based on the Landau-Ginsburg equations had been constructed before the Bardeen-Cooper-Schrieffer (BCS) theory was developed. In ceramic HTSCs, the theoretical description of these processes faces some problems, which are connected with the cellular structure of the medium, when dielectric regions are located between the contacting superconducting granules. In the regions where the granules contact one another, the large quantity of the appearing Josephson contacts are sometimes called the Josephson media. All these Josephson contacts are nonlinear elements, which highly complicates the analysis of such media. In this monograph a model of a granulated HTSC is proposed, where the system of equations of fluxoid quantization in the cells is used as the basis for the mathematical description. This model is a cubic lattice consisting of superconducting wires, and each link of the lattice contains one Josephson contact. The proposed method makes it possible to analyze all details of current configurations.