Energy minimization and flux domain structure in the intermediate state of a type-I superconductor

R. Choksi, R. V. Kohn, F. Otto

Research output: Contribution to journalArticlepeer-review

Abstract

The intermediate state of a type-I superconductor involves a fine-scale mixture of normal and superconducting domains. We take the viewpoint, due to Landau, that the realizable domain patterns are (local) minima of a nonconvex variational problem. We examine the scaling law of the minimum energy and the qualitative properties of domain patterns achieving that law. Our analysis is restricted to the simplest possible case: a superconducting plate in a transverse magnetic field. Our methods include explicit geometric constructions leading to upper bounds and ansatz-free inequalities leading to lower bounds. The problem is unexpectedly rich when the applied field is near-zero or near-critical. In these regimes there are two small parameters, and the ground state patterns depend on the relation between them.

Original languageEnglish (US)
Pages (from-to)119-171
Number of pages53
JournalJournal of Nonlinear Science
Volume14
Issue number2
DOIs
StatePublished - Mar 2004

ASJC Scopus subject areas

  • Modeling and Simulation
  • Engineering(all)
  • Applied Mathematics

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