Static properties of annular Josephson tunnel junctions

We have investigated the static configurations of the phase inside an annular Josephson tunnel junction in the presence of an externally applied magnetic field. For rings having a circumference less than the Josephson penetration depth analytical results are derived which extend the previous theory to (i) rings having finite width and (ii) rings with trapped fluxons. For longer junctions an analysis based on a perturbative approach is carried out in order to find the different phase profiles existing for a given applied field. This perturbative analysis reproduces the threshold curves found numerically.