THEORY OF PHASE-LOCKING IN SIMPLE 2-DIMSENSIONAL JOSEPHSON-JUNCTION ARRAYS WITH SMALL INDUCTANCES

Several elementary two-dimensional Josephson junction arrays have been investigated mainly analytically with the special emphasis an phase l ocking. For this purpose, a novel perturbation scheme appropriate for the handling of small loop inductances has been developed and applied to (i) a single SQUID cell, (ii) two cells coupled by an inductive Lin e, and (iii) an externally loaded two-cell configuration with more gen eral internal shunt. While internal in-phase lacking within the cells call easily be achieved as long as the normalized ring inductances are small compared to unity, the inter-cell coupling tends to favor an an tiphase regime. A mechanism is proposed for circumventing this problem and the boundaries separating both regimes are determined. The influe nce of an external load is considered as well.