scholarly journals Energy and vorticity of the Ginzburg–Landau model with variable magnetic field

2015 ◽  
Vol 93 (1-2) ◽  
pp. 75-114 ◽  
Author(s):  
K. Attar
Keyword(s):  
Magnetic Field ◽  
Variable Magnetic Field ◽  
Ginzburg Landau ◽  
Landau Model

On the minimizers of the Ginzburg–Landau energy for high kappa: the one-dimensional case

1997 ◽  
Vol 8 (4) ◽  
pp. 331-345 ◽  
Author(s):  
AMANDINE AFTALION
Keyword(s):  
Magnetic Field ◽  
Asymptotic Behaviour ◽  
Dimensional Case ◽  
Numerical Computations ◽  
Ginzburg Landau ◽  
Landau Model ◽  
One Dimensional ◽  
Landau Parameter ◽  
Convergence Results ◽  
The One

The Ginzburg–Landau model for superconductivity is examined in the one-dimensional case. First, putting the Ginzburg–Landau parameter κ formally equal to infinity, the existence of a minimizer of this reduced Ginzburg–Landau energy is proved. Then asymptotic behaviour for large κ of minimizers of the full Ginzburg–Landau energy is analysed and different convergence results are obtained, according to the exterior magnetic field. Numerical computations illustrate the various behaviours.

scholarly journals Effect of Background Magnetic Field on Type-II Superconductor under Oscillating Magnetic Field Simulated Using Ginzburg-Landau Model

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Hasnain Mehdi Jafri ◽  
Congpeng Zhao ◽  
Houbing Huang ◽  
Xingqiao Ma
Keyword(s):  
Magnetic Field ◽  
Carrier Concentration ◽  
Static Magnetic Field ◽  
Thermal Quenching ◽  
Phase Changes ◽  
Ginzburg Landau ◽  
Landau Model ◽  
Background Magnetic Field ◽  
Oscillating Magnetic Field ◽  
Energy Components

Cubic superconducting sample was simulated using time-dependent Ginzburg-Landau model under oscillating magnetic field with and without additional background static magnetic field. Vortex dynamics including entrance and exit from the sample was simulated. Magnetization and carrier concentration densities of the sample were studied as a function of external magnetic field variations. Anomalies in carrier concentration density were observed at certain values of the magnetic field which were correlated with the entrance and exit processes of vortices. Area swept by superconductor magnetization with magnetic field was observed to have a hysteresis-like behavior where area representing energy dissipated per cycle. This energy accumulation was suggested to cause instability in superconductor over the number of cycles and may result in thermal quenching. Temporal distribution of energy components showed consistency with the pattern observed for carrier concentration and magnetization under oscillating magnetic field. Rapid phase changes with magnetic oscillations resulted in oscillations in energy components, and irregular peaks and ripples in superconducting energy represent the situation of exit and entry of vortices. While the rise in interaction energy with cycles is referred to vortex relaxation time in a cycle, this energy is expected to accumulate and take other forms (e.g., heat) and is predicted to cause thermal quenching. In the presence of background static magnetic field, this energy dissipation was calculated to increase significantly while superconductor is subjected to oscillating magnetic field.

Superconductors With Structured Surfaces: Fields and Currents

1987 ◽  
Vol 101 ◽  
Author(s):  
Z.C. Wu ◽  
Daniel A. Jelski ◽  
Thomas F. George
Keyword(s):  
Magnetic Field ◽  
The Other ◽  
Ginzburg Landau ◽  
Landau Model ◽  
Structured Surfaces ◽  
Field Parallel ◽  
First Case ◽  
The Magnetic Field ◽  
Effect Of Structure ◽  
Effect Of Surface

ABSTRACTThis paper discusses the behavior of currents and fields along a structured superconductor. First the effect of surface structure on supercurrents is investigated. Then the effect of structure on the critical nucleation field is discussed in two cases, one with the magnetic field parallel to the ripples and the other with the field parallel to the grating wavenumber. In the first case, it is found that the critical field is reduced as a function of grating height, whereas in the latter case it is increased. Finally, the relevance of this work for laser-induced chemistry above a superconducting surface is discussed. The Ginzburg-Landau model is used throughout.

ON THE CONTINUITY OF THE RESPONSE MAP AND AN ALTERNATIVE SHOOTING METHOD FOR THE HALF-SPACE GINZBURG–LANDAU MODEL

2006 ◽  
Vol 16 (09) ◽  
pp. 1527-1558
Author(s):  
CATHERINE BOLLEY ◽  
BERNARD HELFFER
Keyword(s):  
Magnetic Field ◽  
Half Space ◽  
Shooting Method ◽  
The Other ◽  
Complete Analysis ◽  
Qualitative Properties ◽  
Ginzburg Landau ◽  
Landau Model ◽  
Ginzburg Landau Equations ◽  
Physical Literature

As a consequence of a rather complete analysis of the qualitative properties of the solutions of the Ginzburg–Landau equations, we prove, in this paper, both the continuity of a fundamental map σ, called response map in the physical literature on superconductors, and the convergence of an efficient algorithm for the computation of the graph of σ. The response map σ gives the intensity h of the external magnetic field for which the Ginzburg–Landau equations (in a half-space) have a solution such that the parameter order has a prescribed value at the boundary of the sample. Our study involves a shooting method on either one or the other unknown of the system; our algorithm has been introduced in Bolley–Helffer for small values of the Ginzburg–Landau parameter κ and extended in Bolley to any value of κ. Our preceding mathematical studies were not sufficient to prove the convergence, but a recent result (in Ref. 3) on the monotonicity of the solutions with respect to h, combined with a more extensive use of the properties of the solutions of the Ginzburg–Landau system, allow us to complete the proof and to get, as a by-product, the continuity of σ.

ON THE SECOND CRITICAL FIELD FOR A GINZBURG–LANDAU MODEL WITH FERROMAGNETIC INTERACTIONS

2004 ◽  
Vol 16 (02) ◽  
pp. 147-174 ◽  
Author(s):  
STAN ALAMA ◽  
LIA BRONSARD
Keyword(s):  
Magnetic Field ◽  
Critical Field ◽  
Order Parameter ◽  
Upper Critical Field ◽  
Average Energy ◽  
Spin Coupling ◽  
P Wave ◽  
Ginzburg Landau ◽  
Landau Model ◽  
Second Critical Field

We consider a two-dimensional Ginzburg–Landau model for superconductors which exhibit ferromagnetic ordering in the superconducting phase, introduced by physicists to describe unconventional p-wave superconductors. In this model the magnetic field is directly coupled to a vector-valued order parameter in the energy functional. We show that one effect of spin coupling is to increase the second critical field Hc2, the value of the applied magnetic field at which superconductivity is lost in the bulk. Indeed, when the spin coupling is strong we show that the upper critical field is no longer present, confirming predictions in the physics literature. We treat the energy density as a measure, and show that the order parameter converges (as the Ginzburg–Landau parameter κ→∞) in an average sense to a constant determined by the average energy.

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