Abrikosov vortices in long Josephson junctions

Consistently with the results of the one vortex analysis of Ref. 10 we show that in the presence of a finite concentration of trapped Abrikosov vortices the critical current of the junction can actually be larger than that of a vortex free junction. The present paper is organized as follows: In Sec. II the model and the theory of the coupling between the junction and the perturbing vortices are introduced. There three common geometrical configurations for the AV’s with respect to the junction plane are also discussed. In Sec. III we present the theory for the case in which the AV’s are well separated ~as compared to the range of their interaction with the junction!. In Sec. IV we tackle the opposite case of a high concentration of AV’s, a regime which requires a rather different approach. Finally Sec. V provides a discussion of our results and the conclusions.