A MEAN-FIELD MODEL OF SUPERCONDUCTING VORTICES IN THREE DIMENSIONS*

A mean-field model for the motion of vortices in a type II superconductor is for- mulated, drawing on analogies with vortices in an inviscid fluid. The model admits discontinuous solutions, and the conditions on such an interface are derived. In a natural limiting case the model is shown to reduce to a novel, vectorial nonlinear diffusion equation. Finally, generalizations of the model to incorporate vortex pinning and fluctuation effects are described. material will be in the superconducting state but above which it will revert to the normally conducting (normal) state. The transition between normal and supercon- ducting states as the applied magnetic field is raised or lowered through HC takes place by means of phase boundaries separating normal regions from superconducting regions sweeping through the material and is described in (10), (13), and (22).

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