The Bean model of the critical state in a magnetically shielded superconductor filament

Yampolskii, S. V.; Genenko, Yuri A.; Rauh, H.; Snezhko, Alexey

doi:10.1088/1742-6596/43/1/142

Cited by 6 publications

(12 citation statements)

References 17 publications

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“…Similar behaviour has been found for the case of rounded SCFM heterostructures under applied magnetic field, with the AC losses behaviour explained for moderate to high magnetic fields, it relative to the full penetration field (H p = 2πJ c R SC ) of the bare SC of radius R 1 [30]. However, a physical explanation for the increment in the AC losses of SCFM heterostructures at self-field conditions, i.e., with an applied transport current but no external magnetic field, has not been reached yet.…”

Section: Introductionsupporting

confidence: 82%

Electric Field and Energy Losses of Rounded Superconducting/Ferromagnetic Heterostructures at Self-Field Conditions

Fareed

Robert

2019

IEEE Trans. Appl. Supercond.

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The AC losses induced by an alternating transport current in type-II superconductors is a well known phenomena which still attracts much attention due to its intrinsic relevance for the proper development of practical applications. In the case of single core superconducting cables of cylindrical crosssection, it is possible to find exact analytical solutions at self field conditions, and it has been believed for nearly two decades that the use of an ideal soft ferromagnetic sheath with negligible magnetization losses will not affect the electromagnetic properties of the superconducting wire, and on the contrary due to the shielding magnetic properties of the ferromagnet, the total AC losses of the SC wire have to be reduced or as maximum they must be equal to the one for the bare superconductor at self-field conditions, what contraries the experimental evidences that show a non-negligible increase on the AC losses. In this paper, we explain the physical nature of this mysterious increase on the AC losses for rounded superconducting/ferromagnetic heterostructures, which for the sake of generality, it has been solved within the critical state theory and, a magnetic multipolar expansion which enables the direct coupling of the magnetostatic properties of the superconductor and an ideal soft ferromagnet. A significant increase on the transient electric field during the excitation period has been observed, which might have utter implications on the adequate choosing of insulation materials for superconducting/ferromagnetic heterostructures.

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Section: Introductionsupporting

confidence: 82%

Electric Field and Energy Losses of Rounded Superconducting/Ferromagnetic Heterostructures at Self-Field Conditions

Fareed

Robert

2019

IEEE Trans. Appl. Supercond.

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“…3) Type-II superconducting tubes are able to shield lowfrequency magnetic fields in a more efficient way than a ferromagnetic cylinder would do [5], [6]. The axial and transverse magnetic shielding properties of HTS cylinders may even be improved by covering the HTS tube with a ferromagnetic sheath [19]- [24].…”

Section: ) An Increase In the Electrical Transport Abilities In Htsmentioning

confidence: 99%

Numerical Study of the Shielding Properties of Macroscopic Hybrid Ferromagnetic/Superconductor Hollow Cylinders

Lousberg

Fagnard

Ausloos

et al. 2010

IEEE Trans. Appl. Supercond.

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Abstract-We study the magnetic shielding properties of hybrid ferromagnetic/superconductor (F/S) structures consisting of two coaxial cylinders, with one of each material. We use an axisymmetric finite-element model in which the electrical properties of the superconducting tube are modeled by a nonlinear E-J power law with a magnetic-field-dependent critical current density whereas the magnetic properties of the ferromagnetic material take saturation into account. We study and compare the penetration of a uniform axial magnetic field in two cases: 1) a ferromagnetic tube placed inside a larger superconducting tube (Ferro-In configuration) and 2) a ferromagnetic tube placed outside the superconducting one (Ferro-Out configuration). In both cases, we assess how the ferromagnetic tube improves the shielding properties of the sole superconducting tube. The influence of the geometrical parameters of the ferromagnetic tube is also studied: It is shown that, upon an optimal choice of the geometrical parameters, the range of magnetic fields that are efficiently shielded by the hightemperature superconductor tube alone can be increased by a factor of up to 7 (2) in a Ferro-Out (Ferro-In) configuration. The optimal configuration uses a 1020 carbon steel with a thickness of 2 mm and a height that is half that of the superconducting cylinder (80 mm).Index Terms-Ferromagnetic/high-temperature superconductors (HTSs) hybrid structure, finite element, magnetic shield.

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“…According to the Bean concept of the critical state, the flux-penetrated regions carry a current of density j c directed parallel (antiparallel) to the z-direction. Generally, these regions evolve in a rather complicated manner [21][22][23][24]28 but, when magnetic flux completely penetrates the superconductor, the boundary between the re- gions of positive and negative induced currents coincides with the x = 0 plane of Cartesian coordinate system, as marked in Fig. 1.…”

mentioning

confidence: 99%

“…where H 0 f p = (2j c /π)(R 1 − R 0 ) is the field of full flux penetration in the superconductor constituent for an unshielded superconductor cylinder 23 . In the limit of R 0 → 0, H f p reduces to the known expression for the magnetically shielded superconductor filament 24 . In Fig.…”

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Magnetic cloaking by a paramagnet/superconductor cylindrical tube in the critical state

Yampolskii

Genenko

2014

Applied Physics Letters

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Cloaking of static magnetic fields by a finite thickness type-II superconductor tube being in the full critical state and surrounded by a coaxial paramagnet shell is studied. On the basis of exact solutions to the Maxwell equations, it is shown that, additionally to previous studies assuming the Meissner state of the superconductor constituent, perfect cloaking is still realizable at fields higher than the field of full flux penetration into the superconductor and for arbitrary geometrical parameters of both constituents. It is also proven that simultaneously the structure is fully undetectable under the cloaking conditions. Differently from the case of the Meissner state the cloaking properties in the application relevant critical state are realized, however, only at a certain field magnitude.A great research activity has been focused last time on electromagnetic metamaterials which exhibit many unique features, providing particularly cloaking of electromagnetic waves as well as of low frequency and static magnetic or electric fields [1][2][3][4][5][6][7][8] . A magnetic cloak is expected to retain undistorted the external field outside the cloak, thus being "invisible" for external observation, and, as far as possible, to protect its inner area from the external field penetration. To fulfill these requirements, different cloak designs have been proposed, including hybrid systems consisting of ferromagnet and superconductor constituents 8-13 which were recently experimentally realized in the forms of multilayered 14 or bilayered 15,16 magnet/superconductor hollow cylinder. An essential component of the proposed hybrid cylindrical designs is the inner superconducting layer which was assumed until quite recently to be an ideal diamagnetic medium with zero effective permeability in both analytical and finite-element considerations 10,15 . This assumption is, however, unrealistic because of (1) finite field penetration depth which can be comparable with superconductor thickness and (2) massive magnetic flux penetration followed by formation of the critical state typical of magnetic shielding applications [17][18][19] . The system with the finite penetration depth of magnetic field into a superconductor never completely protects the inner region (a central hole) from the penetration of weak external field even in the Meissner state 20 . On the other hand, a non-distorted uniform magnetic field outside the cloak can exist in a wide range of relative permeability and thickness values of the paramagnet sheath for both cases of thick and thin superconductor layers being in the Meissner state. At the same time, the magnetic moment of such a bilayer tube vanishes under the cloaking conditions (as well as all higher multipole moments) making this object magnetically undetectable. Moreover, penetration of magnetic flux into a superconductor in the form of single vortices produces rather small a) Electronic address: yampolsk@mm.tu-darmstadt.de paramagnetic moment of the system, thus breaking the perfect cloaking only slightl...

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The Bean model of the critical state in a magnetically shielded superconductor filament

Cited by 6 publications

References 17 publications

Electric Field and Energy Losses of Rounded Superconducting/Ferromagnetic Heterostructures at Self-Field Conditions

Electric Field and Energy Losses of Rounded Superconducting/Ferromagnetic Heterostructures at Self-Field Conditions

Numerical Study of the Shielding Properties of Macroscopic Hybrid Ferromagnetic/Superconductor Hollow Cylinders

Magnetic cloaking by a paramagnet/superconductor cylindrical tube in the critical state

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