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Critical currents of Josephson-coupled wire arrays

#### J. Kent Harbaugh and D. Stroud, Department of Physics,
The Ohio State University, Columbus, Ohio 43210

We calculate the current-voltage characteristics and
critical current I_c^{array} of an array of
Josephson-coupled superconducting wires. The array has two layers, each
consisting of a set of parallel wires, arranged at right angles, such that
an overdamped resistively-shunted junction forms wherever two wires cross.
A uniform magnetic field equal to f flux quanta per plaquette is applied
perpendicular to the layers. If f = p/q, where p and q are mutually
prime integers, I_c^{array}(f) is found to have sharp
peaks when $q$ is a small integer. To an excellent approximation, it is
found in a square array of n^2 plaquettes, that I_c^{array}(f)
is proportional to (n/q)^{1/2} for sufficiently large n. This result
is interpreted in terms of the commensurability between the array and the
assumed q X q unit cell of the ground state vortex lattice.