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

The remanence of a 25×{}25 square-columnar Josephson-junction array with normalized maximum junction current iₘₐₓ is calculated from the dc and ac Josephson equations, the Amp\`ere theorem, and the gauge invariance. It is shown that with increasing iₘₐₓ the remanence changes from zero to nonzero. The field profile in the nonzero remanence state has multiple peaks at smaller iₘₐₓ but a single peak at greater iₘₐₓ, indicating a transition from the vortex state to the critical state. {} 1996 The American Physical Society.