Critical State Theory for Nonparallel Flux Line Lattices in Type-II Superconductors

Badı́a, A.; López, Carlos Monge

doi:10.1103/physrevlett.87.127004

Cited by 54 publications

(59 citation statements)

References 17 publications

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“…Along this line, some recent papers 1,3,4,5,11,12 have considered the importance of transverse flux effects. Of particular interest is the magnetization decay induced by the oscillations of a perpendicular magnetic field.…”

Section: Discussionmentioning

confidence: 99%

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Critical-state analysis of orthogonal flux interactions in pinned superconductors

Badía-Majós

López

2007

Phys. Rev. B

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We show that, based on the critical state model for flux-line pinning in hard superconductors, one can assess the magnetic moment relaxation induced by the oscillations of a perpendicular magnetic field. Our theory follows a recent proposal of using phenomenological 2D modeling for the description of crossed field dynamics in high-Tc superconductors [arXiv:cond-mat/0703330].Stationary regimes with either saturation to metastable configurations, or complete decay to the thermodynamic equilibrium are obtained. The transition between both types of response is related to the disappearance of a flux free core within the sample. As a common feature, a step-like dependence in the time relaxation is predicted for both cases. The theory may be applied to long bars of arbitrary and non homogeneous cross section, under in-plane magnetic field processes.

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Section: Discussionmentioning

confidence: 99%

“…4,5 However, the latter studies refer to magnetic field vectors with mutually perpendicular components, but parallel to the surface of the sample. This mathematical simplification implies an important physical assumption: the dynamics of transverse flux lines includes cutting effects between them.…”

Section: Introductionmentioning

confidence: 99%

Critical-state analysis of orthogonal flux interactions in pinned superconductors

Badía-Majós

López

2007

Phys. Rev. B

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“…Unlike existing models, which aim to calculate the true critical state in type-II superconductors with cross-flow effects, 12,14,[26][27][28][29][30][31][34][35][36][37] the approach adopted here simply considers an E ϰ J n power law ͑with n = 21 in the present case͒. One of the reasons for the good agreement between the predictions of the model and the experimental results is that the n value in real HTSs is finite and probably very close to 21 for melt-textured YBCO at 77 K, although there is significant discrepancy between n values determined by different experimental techniques.…”

Section: A Validity Of An E-j Power Law With Finite N Valuementioning

confidence: 99%

“…This variational approach was generalized by Badía and López who modeled the electrodynamic response of the superconductor by minimizing an appropriate functional related to magnetic field changes within the material. [29][30][31] In this work, the boundary conditions are determined by the external magnetic field source and the two components of the local current density vector are such that its extremity is constrained to "stay" on some locus defined by the geometry-dependent critical-state model employed. Such geometries include ͑i͒ a disk of constant radius ͑isotropic Bean model͒, ͑ii͒ a rectangle ͑double-critical-state model͒, ͑iii͒ an ellipse ͑elliptic model͒, or ͑iv͒ a disk whose radius is a function of the magnetic field angle with respect to a reference axis ͑"pseudoisotropic model"͒.…”

Section: Introductionmentioning

confidence: 99%

Behavior of bulk high-temperature superconductors of finite thickness subjected to crossed magnetic fields: Experiment and model

et al. 2007

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Crossed-magnetic-field effects on bulk high-temperature superconductors have been studied both experimentally and numerically. The sample geometry investigated involves finite-size effects along both ͑crossed-͒ magnetic-field directions. The experiments were carried out on bulk melt-processed Y-Ba-Cu-O single domains that had been premagnetized with the applied field parallel to their shortest direction ͑i.e., the c axis͒ and then subjected to several cycles of the application of a transverse magnetic field parallel to the sample ab plane. The magnetic properties were measured using orthogonal pickup coils, a Hall probe placed against the sample surface, and magneto-optical imaging. We show that all principal features of the experimental data can be reproduced qualitatively using a two-dimensional finite-element numerical model based on an E-J power law and in which the current density flows perpendicularly to the plane within which the two components of magnetic field are varied. The results of this study suggest that the suppression of the magnetic moment under the action of a transverse field can be predicted successfully by ignoring the existence of flux-free configurations or flux-cutting effects. These investigations show that the observed decay in magnetization results from the intricate modification of current distribution within the sample cross section. The current amplitude is altered significantly only if a field-dependent critical current density J c ͑B͒ is assumed. Our model is shown to be quite appropriate to describe the cross-flow effects in bulk superconductors. It is also shown that this model does not predict any saturation of the magnetic induction, even after a large number ͑ϳ100͒ of transverse field cycles. These features are shown to be consistent with the experimental data.

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“…In particular, we justify the use of restricted variational principles in applied superconductivity for the so-called hard materials. At a first approximation, these superconductors are treated by a nonfunctional law, in which the electrical resistivity jumps from zero to infinity, when a critical value in the current density is reached [13].…”

Section: Introductionmentioning

confidence: 99%

Geometric treatment of electromagnetic phenomena in conducting materials: variational principles

Badía-Majós

Cariñena

López

2006

J. Phys. A: Math. Gen.

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Abstract.The dynamical equations of an electromagnetic field coupled with a conducting material are studied. The properties of the interaction are described by a classical field theory with tensorial material laws in space-time geometry. We show that the main features of superconducting response emerge in a natural way within the covariance, gauge invariance and variational formulation requirements. In particular, the Ginzburg-Landau theory follows straightforward from the London equations when fundamental symmetry properties are considered. Unconventional properties, such as the interaction of superconductors with electrostatic fields are naturally introduced in the geometric theory, at a phenomenological level. The BCS background is also suggested by macroscopic fingerprints of the internal symmetries.It is also shown that dissipative conducting behavior may be approximately treated in a variational framework after breaking covariance for adiabatic processes. Thus, nonconservative laws of interaction are formulated by a purely spatial variational principle, in a quasi-stationary time discretized evolution. This theory justifies a class of nonfunctional phenomenological principles, introduced for dealing with exotic conduction properties of matter [Phys. Rev. Lett. 87, 127004 (2001)].

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Critical State Theory for Nonparallel Flux Line Lattices in Type-II Superconductors

Cited by 54 publications

References 17 publications

Critical-state analysis of orthogonal flux interactions in pinned superconductors

Critical-state analysis of orthogonal flux interactions in pinned superconductors

Behavior of bulk high-temperature superconductors of finite thickness subjected to crossed magnetic fields: Experiment and model

Geometric treatment of electromagnetic phenomena in conducting materials: variational principles

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