Submitting Campus
Daytona Beach
Department
Mathematics
Document Type
Article
Publication/Presentation Date
8-23-2010
Abstract/Description
We solve the linear Ginzburg–Landau GL equation in the presence of a uniform magnetic field with cylindrical symmetry and we find analytic expressions for the eigenfunctions in terms of the confluent hypergeometric functions. The discrete spectrum results from an implicit equation associated to the boundary conditions and it is resolved in analytic form using the continued fractions formalism. We study the dependence of the spectrum and the eigenfunctions on the sample size and the surface conditions for solid and hollow cylindrical superconductors. Finally, the solutions of the nonlinear GL formalism are constructed as expansions in the linear GL eigenfunction basis and selected by minimization of the free energy. We present examples of vortex states and their energies for different samples in enhancing/suppressing superconductivity surroundings.
Publication Title
Journal of Mathematical Physics
DOI
https://doi.org/10.1063/1.3470767
Publisher
AIP Publishing
Scholarly Commons Citation
A. Ludu, J. Van Deun, M. V. Milošević, A. Cuyt, F. M. Peeters; Analytic treatment of vortex states in cylindrical superconductors in applied axial magnetic field. J. Math. Phys. 1 August 2010; 51 (8): 082903. https://doi.org/10.1063/1.3470767
Included in
Aerodynamics and Fluid Mechanics Commons, Ordinary Differential Equations and Applied Dynamics Commons, Partial Differential Equations Commons, Special Functions Commons
