2012
DOI: 10.1088/0953-2048/25/10/104004
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Electromagnetics close beyond the critical state: thermodynamic prospect

Abstract: Abstract. A theory for the electromagnetic response of type-II superconductors close beyond the critical state is presented. Our formulation relies on general physical principles applied to the superconductor as a thermodynamic system. Equilibrium critical states, externally driven steady solutions, and transient relaxation are altogether described in terms of free energy and entropy production. This approach allows a consistent macroscopic statement that incorporates the intricate vortex dynamic effects, reve… Show more

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Cited by 19 publications
(35 citation statements)
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“…9 Nevertheless, nowadays, it is well known that the two-velocity hydrodynamic model cannot explain all the experimental facts observed in type-II superconductors. 16 Moreover, due to the recently reported possibility to extend and compare the E-J power law models with the material law of the critical state theory, 17 the critical state is still the strongest candidate to explain the electromagnetic behavior of type-II superconductors. In this approach, the equilibrium configurations of flux quanta are treated by the macroscopic relation jJ Â Bj F p between the volume pinning force and the average values of the current density and magnetic flux density, i.e., a maximum value for the pinning force is equivalent to a critical value in the component of the current density perpendicular to the local magnetic induction, J ?…”
mentioning
confidence: 99%
“…9 Nevertheless, nowadays, it is well known that the two-velocity hydrodynamic model cannot explain all the experimental facts observed in type-II superconductors. 16 Moreover, due to the recently reported possibility to extend and compare the E-J power law models with the material law of the critical state theory, 17 the critical state is still the strongest candidate to explain the electromagnetic behavior of type-II superconductors. In this approach, the equilibrium configurations of flux quanta are treated by the macroscopic relation jJ Â Bj F p between the volume pinning force and the average values of the current density and magnetic flux density, i.e., a maximum value for the pinning force is equivalent to a critical value in the component of the current density perpendicular to the local magnetic induction, J ?…”
mentioning
confidence: 99%
“…However, in terms of its practical implementation an accurate sizing of the amount of material needed is a serious challenge which depends on the physical properties of the entire system. For instance, in the case of low J c materials, and assuming that the superconductor heats up uniformly during a broad transition beyond the critical state [4], the amount of material needed can be roughly estimated by the need to drop the supply voltage on the SFCL once the transition to the normal state is reached by the condition J > J c . On the other hand, for high J c materials the amount of material is mainly determined by the need to absorb the thermal energy in a fault without irreversible degradation, but the material volume must still be low enough for heating up above T c before reaching the rated time for the aperture of a protective circuit breaker.…”
Section: Practical Implementation Of Sfcl: Field Test Status and mentioning
confidence: 99%
“…with the unit vector along the current density at each point of the superconductor, and ρ ff the material property (resistivity) that may acquire an involved tensorial character [12], [13]. The second equation means that Faraday's law may be enforced by the use of the magnetic vector potential.…”
Section: D Modeling Of Levitating Experimentsmentioning
confidence: 99%
“…In many practical situations, transitions are rather steep and the induced electric fields are such that E 0 /ρ ff J c is a small parameter. This means that J goes very little beyond J c and the term ∆t W JE may be just replaced by the critical state condition |J| ≤ J c , holding "quasistatically" along the time [12].…”
Section: D Modeling Of Levitating Experimentsmentioning
confidence: 99%
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