Electrodynamic model connecting superconductor response to magnetic field and to rotation

Essén, Hanno

doi:10.1088/0143-0807/26/2/007

Cited by 10 publications

(16 citation statements)

References 30 publications

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“…Here the energy is written in terms of the field A and its source j. There are many ways of combining (19) and (20) to get an energy expression, but it turns out that (21) is the one that gives the simplest results. Starting from (21) and adding the constraint ∇ · j = 0, the integration is split into interior, surface, and exterior regions.…”

Section: G a Purely Classical Derivation From Magnetostaticsmentioning

confidence: 99%

Meissner effect, diamagnetism, and classical physics—a review

Essén

Fiolhais

2012

American Journal of Physics

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We review the literature on what classical physics has to say about the Meissner effect and the London equations. We discuss the relevance of the Bohr-van Leeuwen theorem for the perfect diamagnetism of superconductors and conclude that the theorem is based on invalid assumptions. We also point out results in the literature that show how magnetic flux expulsion from a sample cooled to superconductivity can be understood as an approach to the magnetostatic energy minimum. These results have been published several times but many textbooks on magnetism still claim that there is no classical diamagnetism, and virtually all books on superconductivity repeat Meissner's 1933 statement that flux expulsion has no classical explanation.

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Section: G a Purely Classical Derivation From Magnetostaticsmentioning

confidence: 99%

Meissner effect, diamagnetism, and classical physics—a review

Essén

Fiolhais

2012

American Journal of Physics

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“…Based on more detailed studies Cole [15] has also concluded that plasmas are diamagnetic. In our model plasma diamagnetism is seen to be closely related to the diamagnetism of superconductors, as discussed by Essén [16]: the external field induces a current that screens the external field and reduces it inside. In the absence of resistance this screening current persists.…”

Section: Plasma Energy and Diamagnetismmentioning

confidence: 82%

“…Here A e = 1 2 B × r is the vector potential of the external field. Starting from (11) and (16) we find that,…”

Section: Relative Rotational Motionmentioning

confidence: 97%

Magnetic dynamics of simple collective modes in a two-sphere plasma model

Essén

2005

Physics of Plasmas

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A plasma blob is modeled as consisting of two homogeneous spheres of equal radius and equal but opposite charge densities that can move relative to each other. Relative translational and rotational motion are considered separately. Magnetic effects from the current density caused by the relative motion are included. Magnetic interaction is seen to cause an inductive inertia. In the relative translation case the Coulomb attraction, approximately a linear force for small amplitudes, causes an oscillation. For a large number of particles the corresponding oscillation frequency will not be the Langmuir plasma frequency, because of the large inductive inertia. For rotation an external magnetic field is included and the energy and diamagnetism of the plasma in the model is calculated. Finally it is noted how the neglect of resistivity is motivated by the results.

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“…The vector potential produced by this current density can be found using the methods of Essén [28], see also [29][30][31]. If we introduce ξ = a/R, we find,…”

Section: A02 Current In Sphere Due To Rigidly Rotating Chargementioning

confidence: 99%

Magnetic Field and Current Are Zero Inside Ideal Conductors

Fiolhais¹,

Essén²,

Providência³

et al. 2011

PIER B

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Abstract-We prove a theorem on the magnetic energy minimum in a system of perfect, or ideal, conductors. It is analogous to Thomson's theorem on the equilibrium electric field and charge distribution in a system of conductors. We first prove Thomson's theorem using a variational principle. Our new theorem is then derived by similar methods. We find that magnetic energy is minimized when the current distribution is a surface current density with zero interior magnetic field; perfect conductors are perfectly diamagnetic. The results agree with currents in superconductors being confined near the surface. The theorem implies a generalized force that expels current and magnetic field from the interior of a conductor that loses its resistivity. Examples of solutions that obey the theorem are presented.

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Electrodynamic model connecting superconductor response to magnetic field and to rotation

Cited by 10 publications

References 30 publications

Meissner effect, diamagnetism, and classical physics—a review

Meissner effect, diamagnetism, and classical physics—a review

Magnetic dynamics of simple collective modes in a two-sphere plasma model

Magnetic Field and Current Are Zero Inside Ideal Conductors

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