Conservation of Flux by a Superconducting Torus

Dolecek, R. L.; Launay, Jules de

doi:10.1103/physrev.78.58

Cited by 4 publications

(7 citation statements)

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“…Karlsson [45], however, was probably the first to notice that the solution minimizes magnetic energy for constant flux. Dolecek and de Launay [48] verified experimentally that a type I superconducting torus behaves exactly as the corresponding classical perfectly diamagnetic system for field strength below the critical field. Here we treat two simpler cases involving constant external fields: a cylinder in a transverse magnetic field, and a sphere.…”

Section: A2 Explicit Solutions With Minimum Magnetic Energymentioning

confidence: 92%

“…In the electrostatic case charge conservation prevents the energy minimum from being the trivial zero field solution. In the magnetic ideal conductor case a corresponding conservation law is the conservation of magnetic flux through a hole [48]. But, as long as one conductor of the system has a hole with conserved flux there will be a non-trivial magnetic field.…”

Section: Previous Workmentioning

confidence: 99%

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Minimum magnetic energy theorem predicts Meissner effect in perfect conductors

Fiolhais,

Essen,

Providencia

2009

Preprint

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A theorem on the magnetic energy minimum in a perfect, or ideal, conductor is proved. Contrary to conventional wisdom the theorem provides a classical explanation of the expulsion of a magnetic field from the interior of a conductor that loses its resistivity. It is analogous to Thomson's theorem which states that static charge distributions in conductors are surface charge densities at constant potential since these have minimum energy. This theorem is proved here using a variational principle. Then an analogous result for the magnetic energy of current distributions is proved: magnetic energy is minimized when the current distribution is a surface current density with zero interior magnetic field. The result agrees with currents in superconductors being confined near the surface and indicates that the distinction between superconductors and hypothetical perfect conductors is artificial.

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Section: A2 Explicit Solutions With Minimum Magnetic Energymentioning

confidence: 92%

Section: Previous Workmentioning

confidence: 99%

Minimum magnetic energy theorem predicts Meissner effect in perfect conductors

Fiolhais,

Essen,

Providencia

2009

Preprint

View full text Add to dashboard Cite

show abstract

“…Karlsson [12], however, was probably the first to notice that the solution minimizes magnetic energy for constant flux. Dolecek and de Launay [15] verified experimentally that a type I superconducting torus behaves exactly as the corresponding classical perfectly diamagnetic system for field strength below the critical field. Here we treat three cases all involving a constant external field.…”

Section: Appendix B Explicit Solutions With Minimum Magnetic Energymentioning

confidence: 99%

“…In the electrostatic case charge conservation prevents the energy minimum from being the trivial zero field solution. In our magnetic ideal conductor case the corresponding conservation law is the conservation of magnetic flux through a hole [15,16]. As long as one conductor of the system has a hole with conserved flux there will be a non-trivial magnetic field.…”

Section: Previous Workmentioning

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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“…In the past, the work on toroids has focused on the vector potential and magnetic fields of such currents [3][4][5][6][7][8][9][10][11][12][13][14][15], on their inductance and energy [16][17][18][19][20][21][22], as well as on force free configurations of such currents [23][24][25][26][27]. In particular the problem of surface currents, either due to skin effect, or due to superconductivity or perfect conductivity of the tori, has been investigated [28][29][30][31][32][33][34].…”

Section: Introductionmentioning

confidence: 99%

Magnetic Energy of Surface Currents on a Torus

Essén¹,

Stén²,

Nordmark³

2013

PIER B

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Abstract-The magnetic energy and inductance of current distributions on the surface of a torus are considered. Specifically, we investigate the influence of the aspect ratio of the torus, and of the pitch angle for helical current densities, on the energy. We show that, for a fixed surface area of the torus, the energy experiences a minimum for a certain pitch angle. New analytical relationships are presented as well as a review of results scattered in the literature. Results for the ideally conducting torus, as well as for thin rings are given.

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Conservation of Flux by a Superconducting Torus

Cited by 4 publications

References 0 publications

Minimum magnetic energy theorem predicts Meissner effect in perfect conductors

Minimum magnetic energy theorem predicts Meissner effect in perfect conductors

Magnetic Field and Current Are Zero Inside Ideal Conductors

Magnetic Energy of Surface Currents on a Torus

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