Interaction energy of Abrikosov and Josephson vortices in a long Josephson junction

We calculate the interaction energy of a Josephson vortex (fluxon) in a long Josephson junction with an Abrikosov vortex, trapped in one of the superconducting electrodes of the junction. The Abrikosov vortex we consider as penetrating a top superconducting film and spreading out in the tunnel barrier area between the films. In the quasi-one-dimensional approximation we show that the interaction potential for the Josephson vortex is analogous to those of a local magnetic impurity, pinned in the tunnel barrier. The sign of interaction depends on the transverse coordinate of the Abrikosov vortex in the junction. The experiment agrees well with the theoretical model proposed.