We develop and apply a theory for the structure of an isolated vortex parallel to the layers in a Josephson-coupled layer model of a high-T, copper oxide superconductor. This model takes into account the discreteness of the copper oxide planes, which is expected to become important below the crossover temperature where the coherence length g, (T) becomes less than the lattice constant c. We apply the layer model to the motion of a vortex parallel to the planes and calculate the viscous drag coefficient. This result is contrasted with that of the anisotropic Bardeen-Stephen model.
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