First- and second-order transitions for a superconducting cylinder in a magnetic field obtained from a self-consistent solution of the Ginzburg-Landau equations

2001 ◽  
Vol 63 (22) ◽  
Author(s):  
G. F. Zharkov
Keyword(s):  
Magnetic Field ◽  
Second Order ◽  
Ginzburg Landau ◽  
Superconducting Cylinder ◽  
Self Consistent ◽  
Consistent Solution ◽  
Ginzburg Landau Equations

Critical fields of a superconducting cylinder

Open Physics ◽  
2004 ◽  
Vol 2 (1) ◽  
Author(s):  
G. Zharkov
Keyword(s):  
Axial Magnetic Field ◽  
Second Order ◽  
The Self ◽  
Critical Fields ◽  
Penetration Length ◽  
Ginzburg Landau ◽  
Superconducting Cylinder ◽  
Self Consistent ◽  
Consistent Solution ◽  
Ginzburg Landau Equations

AbstractThe self-consistent solutions of the nonlinear Ginzburg-Landau equations, which describe the behavior of a superconducting mesoscopic cylinder in an axial magnetic field H (provided there are no vortices inside the cylinder), are studied. Different, vortex-free states (M-, e-, d-, p-), which exist in a superconducting cylinder, are described. The critical fields (H 1, H 2, H p, H i, H r), at which the first or second order phase transitions between different states of the cylinder occur, are found as functions of the cylinder radius R and the GL-parameter $$\kappa $$ . The boundary $$\kappa _c (R)$$ , which divides the regions of the first and second order (s, n)-transitions in the icreasing field, is found. It is found that at R→∞ the critical value, is $$\kappa _c = 0.93$$ . The hysteresis phenomena, which appear when the cylinder passes from the normal to superconducting state in the decreasing field, are described. The connection between the self-consistent results and the linearized theory is discussed. It is shown that in the limiting case $$\kappa \to {1 \mathord{\left/ {\vphantom {1 {\sqrt 2 }}} \right. \kern-\nulldelimiterspace} {\sqrt 2 }}$$ and R ≫ λ (λ is the London penetration length) the self-consistent solution (which correponds to the socalled metastable p-state) coincides with the analitic solution found from the degenerate Bogomolnyi equations. The reason for the existence of two critical GL-parameters $$\kappa _0 = 0.707$$ and $$\kappa _0 = 0.93$$ in, bulk superconductors is discussed.

scholarly journals Weakly Nonlinear Magnetic Convection in a Nonuniformly Rotating Electrically Conductive Medium Under the Action of Modulation of External Fields

2020 ◽  
Keyword(s):  
Magnetic Field ◽  
Angular Velocity ◽  
Landau Equation ◽  
Temperature Modulation ◽  
External Fields ◽  
Ginzburg Landau ◽  
Electrically Conductive ◽  
Weakly Nonlinear ◽  
Conductive Fluid ◽  
Ginzburg Landau Equations

In this paper we studied the weakly nonlinear stage of stationary convective instability in a nonuniformly rotating layer of an electrically conductive fluid in an axial uniform magnetic field under the influence of: a) temperature modulation of the layer boundaries; b) gravitational modulation; c) modulation of the magnetic field; d) modulation of the angular velocity of rotation. As a result of applying the method of perturbation theory for the small parameter of supercriticality of the stationary Rayleigh number nonlinear non-autonomous Ginzburg-Landau equations for the above types of modulation were obtaned. By utilizing the solution of the Ginzburg-Landau equation, we determined the dynamics of unsteady heat transfer for various types of modulation of external fields and for different profiles of the angular velocity of the rotation of electrically conductive fluid.

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.

scholarly journals Existence and uniform boundedness of strong solutions of the time-dependent Ginzburg-Landau equations of superconductivity

2005 ◽  
Vol 2005 (8) ◽  
pp. 863-887
Author(s):  
Fouzi Zaouch
Keyword(s):  
Magnetic Field ◽  
Existence And Uniqueness ◽  
Uniform Boundedness ◽  
Strong Solutions ◽  
Time Dependent ◽  
Dynamical Process ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equations ◽  
Uniformly Bounded ◽  
Weak And Strong Solutions

The time-dependent Ginzburg-Landau equations of superconductivity with a time-dependent magnetic fieldHare discussed. We prove existence and uniqueness of weak and strong solutions withH1-initial data. The result is obtained under the “φ=−ω(∇⋅A)” gauge withω>0. These solutions generate a dynamical process and are uniformly bounded in time.

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