Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



The bifurcation structure of a thin superconducting loop swith small variations in its thickness

Author: G. Richardson
Journal: Quart. Appl. Math. 58 (2000), 685-703
MSC: Primary 82D55; Secondary 70K50
DOI: https://doi.org/10.1090/qam/1788424
MathSciNet review: MR1788424
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Abstract: We study bifurcations between the normal and superconducting states, and between superconducting states with different winding numbers, in a thin loop of superconducting wire, of uniform thickness, to which a magnetic field is applied. We then consider the response of a loop with small thickness variations. We find that close to the transition between normal and superconducting states lies a region where the leading-order problem has repeated eigenvalues. This leads to a rich structure of possible behaviours. A weakly nonlinear stability analysis is conducted to determine which of these behaviours occur in practice.

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DOI: https://doi.org/10.1090/qam/1788424
Article copyright: © Copyright 2000 American Mathematical Society

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