Abrikosov vortices in long Josephson junctions

We have developed a theory of the critical current I-c of a long Josephson junction in the presence of a finite density of Abrikosov vortices trapped in the electrodes in the immediate vicinity of the plane of the junction. We show that under these conditions the Josephson phase difference can be finite even well inside the junction in such a way as to result in a nonmonotonous dependence of I-c on the concentration of the perturbing vortices, a behavior at variance with that of a short junction. As the average distance between the vortices decreases, I-c reaches a maximum. The location, magnitude, and sharpness of this feature are strongly dependent on the ratio psi lambda(J)/r(0), where r(0) and psi are respectively the range and the strength of the effective interaction between the Abrikosov Vortices and the Josephson fluxons while lambda(J) is the Josephson penetration length. The results obtained are used to discuss the behavior of the critical current recently observed in Josephson junctions based on Nb films. [S0163-1829(98)10437-X].