Abstract
Based on a previously developed analytical procedure combining ideas from the first harmonic approximation with those from the slowly varying phase we obtain some rigorous analytical results on the dynamics of two-dimensional Josephson-junction ladder arrays composed of an arbitrary number of cells. We are able to derive a general analytic expression for the reduced equations governing phase locking of the cells. While solving these reduced equations seems not to be possible in general, we were able to evaluate them up to the end for three experimentally relevant cases: (i) arrays composed of strongly damped junctions and small ring inductances without an external shunt, (ii) arrays composed of strongly damped junctions and small ring inductances with an external shunt, and (iii) arrays composed of strongly damped junctions and large ring inductances without an external shunt.
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