Self-generated flux in Josephson junctions with alternating critical current density

We study an interesting state with a self-generated magnetic flux in a long Josephson junction. The critical current density (Formula presented) is assumed to alternate randomly along the tunnel contact on a length scale much less than the local Josephson penetration depth. The phase difference is then a sum of an alternating term and a smooth term which self-consistently contribute to the formation of a stationary state with self-generated flux. Two types of Josephson vortices are found in this state, one with magnetic flux (Formula presented) and another one with magnetic flux (Formula presented).