Asymptotic analysis of models of superconductivity

Conference item

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 appropriate, 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.

Authors: Chapman, S

• Publication status: Published
• Journal: NONLINEAR PDE'S IN CONDENSED MATTER AND REACTIVE FLOWS
• Volume: 569
• Pages: 375-398
• Publication date: 2002-01-01
• Event title: Conference of the NATO-Advanced-Study-Institute on PDEs in Models of Superfluidity, Superconductivity and Reactive Flows
• ISSN: 0258-2023
• ISBN: 1402009720
• Keywords: II SUPERCONDUCTORS; DYNAMICS; MOTION; VORTEX; LIMITS; HELE-SHAW; VORTICES; STEFAN