Model For type-II Superconductors Research Articles

3D FEM Modeling of ${\mathrm CORC}$ Commercial Cables With Bean’s Like Magnetization Currents and Its AC-Losses Behavior

The Conductor on Rounded Core (CORC) cables manufactured by Advanced Conductor Technologies with current densities beyond 300 Amm^-2 at 4.2 K, and bending diameter of up to 3.5 cm, are considered as one of the strongest candidates for the next generation of high field power applications and magnets. In this paper, we present a full 3D FEM model for their monolayer and bilayer CORC cables made with up to three and six superconducting tapes respectively, disclosing the full curve of AC losses for the monolayer cable at magnetic fields beyond 60 mT, and the actual distribution of current density along and across the thickness of the superconducting tapes in both designs. The model is based on the so-called H-formulation, allowing to incorporate the true three-dimensionality of the tapes without recurring to 2D thin-film approaches where non-physical surface currents that do not follow the celebrated Bean's model for type-II superconductors appear. Likewise, good agreement with the experimentally measured AC-losses for the monolayer and bilayer cable have been obtained, with all the details of the model disclosed in this paper.

General p-curl systems and duality mappings on Sobolev spaces for Maxwell equations

We study a general p-curl system arising from a model of type-II superconductors. We show several trace theorems that hold on either a Lipschitz domain with small Lipschitz constant or on a C^{1,1} domain. Certain duality mappings on related Sobolev spaces are computed and used to establish surjectivity results for the p-curl system. We also solve a nonlinear boundary value problem for a general p-curl system on a C^{1,1} domain and provide a variational characterization of the first eigenvalue of the p-curl operator.
 For more information see https://ejde.math.txstate.edu/Volumes/2020/116/abstr.html

Equilibrium States in Two-Temperature Systems.

Systems characterized by more than one temperature usually appear in nonequilibrium statistical mechanics. In some cases, e.g., glasses, there is a temperature at which fast variables become thermalized, and another case associated with modes that evolve towards an equilibrium state in a very slow way. Recently, it was shown that a system of vortices interacting repulsively, considered as an appropriate model for type-II superconductors, presents an equilibrium state characterized by two temperatures. The main novelty concerns the fact that apart from the usual temperature T, related to fluctuations in particle velocities, an additional temperature was introduced, associated with fluctuations in particle positions. Since they present physically distinct characteristics, the system may reach an equilibrium state, characterized by finite and different values of these temperatures. In the application of type-II superconductors, it was shown that , so that thermal effects could be neglected, leading to a consistent thermodynamic framework based solely on the temperature . In the present work, a more general situation, concerning a system characterized by two distinct temperatures and , which may be of the same order of magnitude, is discussed. These temperatures appear as coefficients of different diffusion contributions of a nonlinear Fokker-Planck equation. An H-theorem is proven, relating such a Fokker-Planck equation to a sum of two entropic forms, each of them associated with a given diffusion term; as a consequence, the corresponding stationary state may be considered as an equilibrium state, characterized by two temperatures. One of the conditions for such a state to occur is that the different temperature parameters, and , should be thermodynamically conjugated to distinct entropic forms, and , respectively. A functional is introduced, which presents properties characteristic of an entropic form; moreover, a thermodynamically conjugated temperature parameter can be consistently defined, so that an alternative physical description is proposed in terms of these pairs of variables. The physical consequences, and particularly, the fact that the equilibrium-state distribution, obtained from the Fokker-Planck equation, should coincide with the one from entropy extremization, are discussed.

An A-ϕ Scheme for Type-II Superconductors

AbstractA fully discrete A-ϕ finite element scheme for a nonlinear model of type-II superconductors is proposed and analyzed. The nonlinearity is due to a field dependent conductivity with the regularized power-law form. The challenge of this model is the error estimate for the nonlinear term under the time derivative. Applying the backward Euler method in time discretisation, the well-posedness of the approximation problem is given based on the theory of monotone operators. The fully discrete system is derived by standard finite element method. The error estimate is suboptimal in time and space.

Vortex velocity laws to I-V data for flat superconductors

A vortex-density model for type-II superconductors is used to study the transport current in a strip in flux-flow conditions. Flux pinning is incorporated using a stick-slip vortex velocity law. Current and vortex density profiles are calculated, and the effect of applied magnetic fields and pinning strength is analysed. The I-V characteristics are determined and related to the local vortex velocity law. Initial comparisons of the results with experimental data show good agreement.

Two-dimensional numerical modeling of superconductors with imposed currents by the finite element method

A finite element method is proposed for modeling the imposed currents in several long conductors. Numerical examples are presented for the Bean critical state model of type II-superconductors.

Vortex-liquid-vortex-crystal transition in type-II superconductors.

We present in detail a functional renormalization group (FRG) study of a Landau-Ginzburg model of type-II superconductors (generalized to {ital N}/2 complex fields) in an external magnetic field, both for a pure system and also in the presence of quenched random impurities. If the coupling functions are restricted to the space of functions with nonzero support only at reciprocal lattice vectors corresponding to the Abrikosov lattice, we find a stable FRG fixed point in the presence of disorder for 1{lt}{ital N}{lt}4, identical to that of the disordered {ital O}({ital N}) model in {ital d}{minus}2 dimensions. This implies a continuous transition from the vortex crystal to vortex liquid in the presence of disorder, but only for {ital d}{gt}4. The nonzero-temperature transition will disappear in physical dimensions. The pure system has a stable fixed point only for {ital N}{gt}4. Therefore the physical case ({ital N}=2) is likely to have a first-order transition in the absence of quenched disorder. We give a full discussion of both the motivation of the model and the details of the FRG calculation. We also place our results in context with regard to the current experimental scene concerning the high-{ital T}{sub {ital c}} compounds. In particular, we discussmore » the relevance of our results to the recently discovered critical end point in the phase diagram of Bi-Sr-Ca-Cu-O. The main results of this analysis were previously reported in the form of a Letter [M.A. Moore and T.J. Newman, Phys. Rev. Lett. {bold 75}, 533 (1995)]. {copyright} {ital 1996 The American Physical Society.}« less

Magnetization in a generalized critical-state model for type-II superconductors

This paper describes the magnetization of type-II superconductors in the critical state, where the critical current density, J c has a field dependence of the form J c (B) = J 0 /(1 + B/B 0 ) n . Explicit formulae are derived for the various branches of the complete high-field hysteresis loop. The geometry under consideration is that of an infinitely long rectangular bar placed in a parallel applied field. In the discussion, emphasis is put on the behaviour of the vertical width, ΔM, of the hysteresis loop, and a simple graphical method to fit model parameters to experimental data is outlined.

Vortex Configurations in Type-II Superconducting Films

This article is concerned with the numerical solution of the Ginzburg-Landau (GL) model for type-II superconductors in thin films (two-dimensional periodic domains). A new gauge is defined that reduces the coupling between the equations for the nonzero components of the vector potential. The GL equations are written in a symmetric form by means of continuous link variables. A second-order accurate scheme is used for the numerical approximation. Numerical experiments demonstrate that the discrete GL model leads to asymmetric solutions in the plane; symmetry is recovered only in the limit as the mesh size goes to zero. Results of computational experiments to find the upper critical field and an empirical power law for vortex interactions are given.