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Because of the Meissner effect, magnetic fields can only infiltrate superconductors as discrete flux tubes.

Normally, a flux tube has two ends where magnetic fields enter and exit the superconductor, but what if the flux tube is circular without any open ends? Would such circular tubes collapse and disappear inside the superconductor?

What if there are two circular tubes interlocked to each other?

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  • $\begingroup$ Some theoretical discussion here of knotted/braided flux tubes. More theory is for braids (not knots or links) where the ends of the flux tubes are fixed at defects. $\endgroup$ Commented 2 days ago

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I am not an expert on this, but I strongly think that the answer to this is a resounding yes.

Consider a superconductor made into a torus and wind some insulated wire around it as if it were supposed to be a inductive choke. Have the wire pass a large current so that the magnetic field is strong, and then activate the superconductivity by lowering the temperature from above the superconducting temperature to beneath. Mind you, this temperature is dependent upon the imposed magnetic field too.

Then, by the geometry, there is no way for the magnetic flux to escape, and so there must be some circular flux tube.

I welcome some expert weighing on whether my argument is correct, but I have very little doubts at this point.

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On the first glance one would think such circular flux tubes should be commonplace. They are analogous to vortex rings in superfluid helium which exist and have been observed.

The simplest scenario would be a straight superconducting wire carrying some current. The current will generate magnetic field that will have flux lines in the form of closed loops. The field that is in the superconducting material should then lead to formation of the closed loop flux tubes (Abrikosov vortex rings).

But the vortex rings in superconductors are more of a theory rather than a well established observation (see e.g. here). The surface of the superconductor acts as a barrier for the vortex lines that run parallel to the surface (here). So it is actually hard to form a ring by "pushing" it in from the outside as in the example above. The other thing is that once inside the superconductor the ring energy is proportional to its radius (here) - it will tend to collapse.

All that being said, I would not call myself an expert either.

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    $\begingroup$ What makes you think that that those rings will want to collapse? They contain energy, after all, and energy must be conserved. That is, in order to collapse, they must give off their energy. And that's kinda hard to do within a superconductor, which does not allow photons to propagate. So, how would you create/destroy such a ring? $\endgroup$ Commented 2 days ago
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    $\begingroup$ I'm citing a paper there - PRB 49 6950, fig2 and end of section II. Vortex motion in type ii superconductor can generate heat and effectively lead to non zero resistance. I guess the collapsing ring would just be a special case of that. $\endgroup$ Commented 2 days ago
  • $\begingroup$ Ah, I wasn't aware of this heat generation effect. With that in mind, it's obvious that you are correct. Thanks for the clarification. $\endgroup$ Commented yesterday

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