Static Josephson effects in circularly symmetric annular junctions

Static Josephson effects in circularly symmetric annular junctions are discussed. When the annular width W of a junction is smaller than λ_J, analytic solutions can be obtained. For annular width W of a junction larger than λ_J, the self-field effects must be considered; the solutions can be obtained numerically. For these two cases, called "small junction" and "large junction," respectively, the magnetic field dependence of the critical current I _m of a circularly symmetric annular junction is obtained. Further, for a width W larger than λ_J, the current density distribution is also given for several magnetic fields. In addition, for a given external magnetic field, when the feeding current I is smaller than the critical current I _m of the circular symmetric annular junction, there are multisolutions under such physical conditions. Finally, the stability of these solutions is also discussed.