Annular Josephson tunnel junctions in an external magnetic field: The statics

We have investigated the static configurations of the phase inside an annular Josephson tunnel junction in the presence of an externally applied magnetic field. We report here a detailed study of the dependence on the magnetic field of the critical current for different annular geometries. The periodic conditions for the phase difference across the barrier are derived from fluxoid quantization. For rings having a radius less than the Josephson penetration depth analytical results are derived which are in excellent agreement with the experimental data. For longer junctions numerical analysis is carried out after the derivation of the appropriate perturbed sine-Gordon equation. We find that a number of different phase profiles may exist for a given applied field which differ according to the number of fluxon-antifluxon pairs present in the line. Experimental data support the theoretical analysis provided self-field effects are taken into account in real devices.