We investigate theoretically how the proximity of an Abrikosov vortex influences the physical properties of a long Josephson junction. We find that ␦I c , the contribution to the critical current associated with the presence of the vortex, is generally positive ͑the critical current is increased͒ and is crucially dependent on the specific boundary conditions satisfied by the transport current. In the case in which the latter has a bulk component in the vicinity of the vortex, ␦I c is proportional to the coupling between the vortex and the junction. The situation is however more complex when the transport current is purely a surface phenomenon. In this case ␦I c strongly depends on the distance between the vortex and the edges of the junction, and is in general much smaller than that of the bulk current case unless a special commensurability condition is met. In particular we show that a contribution to ␦I c proportional to is obtained in this case only when an integer number of Josephson vortices can be accommodated between the location of the vortex and one of the edges of the junction
