Circular and annular two-dimensional Josephson junction: statics and dynamics

We present the results of the numerical analysis of circular and annular two-dimensional planar Josephson junctions. The static and dynamical states of a junction with or without an externally applied uniform magnetic field have been investigated. Our model is based on the assumption that junction electrodes are sufficiently long and have a uniform cross section. Such a configuration allows to find analytically and numerically the boundary conditions, which are given by the surface current distribution on the electrodes. We found static and dynamical states of a large-area two-dimensional junction and present some of the resulting patterns. Surprisingly, in contrast to a circular one-dimensional structure ( ring), we found that in a circular or annular large-area junction, the fluxons circulating along the junction border do not exist. The boundary conditions play an essential role and determine the trajectory of fluxons. Finally, we analyze a junction surrounding a current-carrying wire.