Synchronization of overdamped Josephson junctions shunted by a superconducting resonator

Synchronization was investigated numerically as well as by the method of slowly varying amplitudes for two Josephson junctions with McCumber parameters near 1 shunted by a superconductor and a dividing capacitor building up a resonator for ac currents. Because of the current resonance in the system the synchronizing ac current increases and provides phase locking up to 15% spread of critical currents. Thresholds of the phase-locked state at small as well as at large values of system parameters were explained in the developed model. Conditions of forming the phase-locked state are investigated in the many-junction array in which ac currents between neighbor junctions are formed through the superconducting shunt with a divided capacitance. It is shown that at certain conditions the total phase locking of all junctions switched into the voltage state appears when their quantity exceeds some critical value.