The Stability of the Normal State of Superconductors in the Presence of Electric Currents
Author:
- 1 January 2008
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Mathematical Analysis
- Vol. 40 (2) , 824-850
Abstract
The stability of the normal state of superconductors in the presence of electric currents is studied in the large domain limit. The model being used is the time-dependent Ginzburg–Landau model, in the absence of an applied magnetic field, and with the effect of the induced magnetic field being neglected. We find that if the current is nowhere perpendicular to the boundary, or if the minimal current on the boundary, at points where it is perpendicular to it, is greater than the critical current in the one-dimensional case, then the normal state is stable. We also prove some short-time instability when the current is both perpendicular to the boundary and smaller than the one-dimensional critical current.Keywords
This publication has 10 references indexed in Scilit:
- Surface superconductivity in 3 dimensionsTransactions of the American Mathematical Society, 2004
- NON LINEAR EIGENVALUE PROBLEMSMatemática Contemporânea, 2004
- Josephson Behavior of Phase-Slip Lines in Wide Superconducting StripsPhysical Review Letters, 2003
- Current-Voltage Characteristics of Quasi-One-Dimensional Superconductors: An-Shaped Curve in the Constant Voltage RegimePhysical Review Letters, 2003
- A Hierarchy of Models for Superconducting Thin FilmsSIAM Journal on Applied Mathematics, 2003
- Wild Spectral Behaviour of Anharmonic OscillatorsBulletin of the London Mathematical Society, 2000
- High-Kappa Limits of the Time-Dependent Ginzburg–Landau ModelSIAM Journal on Applied Mathematics, 1996
- Electric currents and resistive states in thin superconductorsAdvances in Physics, 1984
- Sur un probleme aux valeurs propres non line aireIsrael Journal of Mathematics, 1980
- Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions IICommunications on Pure and Applied Mathematics, 1964