Phenomenological model of vortex dynamics in arrays of Josephson junctions

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Abstract
A phenomenological model for arrays of Josephson junctions is developed in the continuum limit. This model gives a unified treatment of various types of behavior in arrays, such as charge solitons, vortices, collective modes, and the mass of the vortex. This model is then used to describe vortex dynamics when there is no pinning. We calculate the flux-flow resistivity due to vortex motion as well as consider the possibility of ballistic motion of vortices. We compare these results to the analogous situations in a conventional superconductor as well as for granular systems.