A Mean-field Model of Superconducting Vortices in three dimensions

S. J. Chapman

A mean-field model for the motion of vortices in a type-II superconductor is formulated, 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.