Evolution from the vortex state to the critical state in a square-columnar Josephson-junction array

The remanence of a 25x25 square-columnar Josephson-junction array with normalized maximum junction current i(max), is calculated from the de and ac Josephson equations, the Ampere theorem, and the gauge invariance. It is shown that with increasing i(max) the remanence changes from zero to nonzero. The field profile in the nonzero remanence state has multiple peaks at smaller i(max) but a single peak at greater i(max) indicating a transition from the vortex state to the critical state.