A RING OF JOSEPHSON-JUNCTIONS IN A MAGNETIC-FIELD

We studied the magnetic properties of the ring of a Josephson junctions in a magnetic field at different capacitance of superconducting regions. We found that the capacitance which is the characteristic of the size of the superconducting region, does not change qualitatively the magnetic properties of the ring of junctions. At half-quantum of the flux through the ring there appears the magnetic phase transition which is characterised by the singularity in magnetization and in sucseptibility. At the transition there is the trapping of the one quantum of the flux by the ring. The interpretation of experiments, describing the inverse kinetic inductance as a function of a flux per plaquette of a lattice of two- dimensional arrays of the Josephson junctions is proposed. The new singularities in this dependency are predicted.