Superheating fields of superconductors: Asymptotic analysis and numerical results

Abstract

The superheated Meissner state in type-I superconductors is studied both analytically and numerically within the framework of Ginzburg-Landau theory. Using the method of matched asymptotic expansions we have developed a systematic expansion for the solutions of the Ginzburg-Landau equations in the limit of small $\kappa$, and have determined the maximum superheating field $H_{\mathrm{sh}}$ for the existence of the metastable, superheated Meissner state as an expansion in powers of ${\kappa }^{1/2}$. Our numerical solutions of these equations agree quite well with the asymptotic solutions for $\kappa <0.5$. The same asymptotic methods are also used to study the stability of the solutions, as well as a modified version of the Ginzburg-Landau equations which incorporates nonlocal electrodynamics. Finally, we compare our numerical results for the superheating field for large-$\kappa$ against recent asymptotic results for large-$\kappa$, and again find a close agreement. Our results demonstrate the efficacy of the method of matched asymptotic expansions for dealing with problems in inhomogeneous superconductivity involving boundary layers.

14 pages, 8 uuencoded figures, Revtex 3.0

Cited by in corpus (18)

• Dynamics of vortex penetration, jumpwise instabilities and nonlinear surface resistance of type-II superconductors in strong rf fields
• Superheating field of superconductors within Ginzburg-Landau theory
• Temperature dependence of the superheating field for superconductors in the high-k London limit
• Effect of Impurities on the Superheating field of Type II superconductors
• Theoretical estimates of maximum fields in superconducting resonant radio frequency cavities: Stability theory, disorder, and laminates
• The surface barrier in mesoscopic type I and type II superconductors
• Role of surface defects and material inhomogeneities for vortex nucleation in superconductors within time-dependent Ginzburg-Landau theory in 2 and 3 dimensions
• Analysis of Magnetic Vortex Dissipation in Sn-Segregated Boundaries in Nb${}_3$Sn Superconducting RF Cavities
• Niobium in clean limit: an intrinsic type-I superconductor
• Vortex nucleation barrier in superconductors beyond the Bean-Livingston approximation: A numerical approach for the sphaleron problem in a gauge theory
• The Battle of the Bulge: Decay of the Thin, False Cosmic String
• Nucleation and Growth of the Superconducting Phase in the Presence of a Current
• Ginzburg-Landau theory of the superheating field anisotropy of layered superconductors
• Topological Defect Densities in Type-I Superconducting Phase Transitions
• A Time-Dependent Ginzburg-Landau Framework for Sample-Specific Simulation of Superconductors for SRF Applications
• Significant improvement of the lower critical field in Y doped Nb: potential replacement of basic material for the radio-frequency superconducting cavity
• Superheated and Dissipative Ginzburg-Landau Superconductors
• Discrepancies in Determinations of the Ginzburg-Landau Parameter