Meissner state in a 3D ordered Josephson medium

A system of difference equations describing current configurations in a 3D ordered Josephson medium is obtained. The system is based on the fluxoid quantization conditions in the cells. A method for the exact solution to the system is proposed for the Meissner configuration for any values of the parameters. The current configurations for the Meissner regime are computed, as well as the values of the critical fields above which the Meissner configuration does not exist. Approximate analytic solutions are obtained for the system of difference equations, which correctly describe the exact solution for the major part of the range of the parameters.