Abstract
After introducing the basic phenomena, the simplest (free-boundary) model describing the change of phase of a superconducting material is formulated. In some situations the model is ill-posed, and it is shown that it can be regularised in a certain parameter regime (type-I superconductors) by the Ginzburg-Landau model. For other parameter regimes (type-II superconductors) the free-boundary model is not appropri- ate, and a bifurcation analysis indicates that the normally conducting (normal) region should comprise thin “flux tubes” (or vortices) rather than large domains. An asymptotic analysis determines the law of motion of these vortices, and they are then averaged to produce a vortex density model. Including vortex pinning by impurities in this model leads to the familiar Bean critical state model.
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Chapman, S.J. (2002). Asymptotic Analysis of Models of Superconductivity. In: Berestycki, H., Pomeau, Y. (eds) Nonlinear PDE’s in Condensed Matter and Reactive Flows. NATO Science Series, vol 569. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0307-0_17
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