Analysis of critical-state problems in type-II superconductivity

Prigozhin, Leonid

doi:10.1109/77.659440

Cited by 139 publications

(127 citation statements)

References 20 publications

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“…The approach of Prigozhin mathematically treats the electric field as a subdifferential of a critical energy density which takes either the value 0 if the current density does not exceed some critical value or infinity otherwise. By analyzing the subdifferential formulation, the magnetic penetration and the current distribution around the superconductor in 2D situation were intensively investigated by Prigozhin (1996bPrigozhin ( ,1997Prigozhin ( ,1998Prigozhin ( ,2004. Adopting the variational formulation by Prigozhin, Elliott et al (2004) reported a numerical analysis of the Bean critical state model modelling the magnetic field and the current density.…”

Section: Introductionmentioning

confidence: 99%

A finite-element analysis of critical-state models for type-II superconductivity in 3D

Elliott

Kashima

2007

IMA Journal of Numerical Analysis

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We consider the numerical analysis of evolution variational inequalities which are derived from Maxwell's equations coupled with a nonlinear constitutive relation between the electric field and the current density and governing the magnetic field around a type-II bulk superconductor located in three dimensional space. The nonlinear Ohm's law is formulated using the sub-differential of a convex energy so the theory is applied to the Bean critical state model, a power law model and an extended Bean critical state model. The magnetic field in the nonconductive region is expressed as a gradient of a magnetic scalar potential in order to handle the curl free constraint. The variational inequalities are discretized in time implicitly and in space by Nédélec's curl conforming finite element of lowest order. The non-smooth energies are smoothed with a regularization parameter so that the fully discrete problem is a system of nonlinear algebraic equations at each time step. We prove various convergence results. Some numerical simulations under a uniform external magnetic field are presented.Keywords: macroscopic models for superconductivity, variational inequality, Maxwell's equations, edge finite element, convergence, computational electromagnetism.

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Section: Introductionmentioning

confidence: 99%

A finite-element analysis of critical-state models for type-II superconductivity in 3D

Elliott

Kashima

2007

IMA Journal of Numerical Analysis

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“…This nonlinear constitutive relation is given in the Bean model by a m ultivalued monotone graph: (Here we h a ve adopted units in which the critical current density j c = 1.) The magnetization model with this current-voltage law is equivalent t o a n e v olutionary variational inequality, see 15], and such a f o r m ulation is convenient for both the numerical approximation and theoretical study of these magnetization problems 15,16,17,18]. In simple cases the solution to the Bean model can be found analytically see, e.g., the two examples in the next section.…”

Section: Introductionmentioning

confidence: 99%

Bean's critical-state model as the p→∞ limit of an evolutionary -Laplacian equation

Barrett

Prigozhin

2000

Nonlinear Analysis: Theory, Methods & Applications

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We consider magnetization of type-II superconductors characterized by a m ultivalued current-voltage relation (the Bean model) and show that for the longitudinal and thin-lm con gurations the problems are equivalent to similar evolutionary variational inequalities with a gradient constraint. It is proved that the unique solutions to these inequalities are the p ! 1 limits of the solutions to the evolutionary p-Laplacian equations that appear in the corresponding magnetization models obeying the power current-voltage law with exponent p ; 1.

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“…15, with the constraints that the net current must be zero and the current density does not exceed the J c . Introducing the J c ͑H i ͒ dependence by means of a first-order iterative algorithm, it is found that, following the notation of Prigozhin, 16 minimizing this functional with the current density J is equivalent to minimizing a functional FЈ with the current density variation ␦J defined as the difference, at present field H, between the present current density J͑r , H͒ and the previous current density Ĵ͑r , H͒ ͑at the first step of H a , Ĵ͑r , H͒ is assumed zero͒. The functional FЈ is defined as…”

Section: Tunability Of the Critical-current Density In Superconductormentioning

confidence: 99%

Tunability of the critical-current density in superconductor-ferromagnet hybrids

Del-Valle

Navau

Sanchez

et al. 2011

Applied Physics Letters

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Important modifications on the magnetization loops of the superconductor have been observed in superconductor-ferromagnet hybrids due to the effects of the ferromagnetic components, which can be used for tuning the superconductor critical-current density Jc to desirable values. Here, a model based on an energy minimization procedure is presented to analyze the complex interaction between the superconductor and the ferromagnets. We show how the geometry and orientation of the ferromagnets can be chosen for shifting the position of the peaks appearing in the magnetization to positive or negative applied fields, and, consequently, to tune Jc in superconductor-ferromagnet hybrids.

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Analysis of critical-state problems in type-II superconductivity

Abstract: An efficient numerical scheme is proposed for modeling the hysteretic magnetization of type-II superconductors. Numerical examples are presented for the Bean and Kim critical state models. It is shown that Bean's model is a Hele-Shaw type problem.

Cited by 139 publications

References 20 publications

A finite-element analysis of critical-state models for type-II superconductivity in 3D

A finite-element analysis of critical-state models for type-II superconductivity in 3D

Bean's critical-state model as the p→∞ limit of an evolutionary -Laplacian equation

Tunability of the critical-current density in superconductor-ferromagnet hybrids

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