Superconductor in a hollow cylinder -- two different end states. Why?

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Discussion Overview

The discussion revolves around the behavior of magnetic fields in superconductors, specifically in a hollow cylindrical superconductor under different conditions of cooling and magnetic field application. Participants explore the implications of these conditions on magnetic flux and the resulting states of the superconductor.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants propose that when a magnetic field is applied during the cooling of a superconductor, the field penetrates through the hole of the hollow cylinder, while applying the field after cooling results in the field being expelled.
  • Others argue that in the superconducting state, the magnetic flux through the loop cannot change, leading to the trapping of any existing flux when cooled with a magnetic field present.
  • A participant questions the mechanism behind the expulsion of the magnetic field when the field is applied after cooling, suggesting that the size of the hole and the screening currents may play a role.
  • Another participant notes that the magnetic field cannot be arbitrarily strong, as exceeding a critical field strength would break down superconductivity, and this reasoning may not fully apply to type II superconductors.
  • One participant emphasizes that the initial magnetic flux state before the transition to superconductivity determines the final state, indicating a key asymmetry in the behavior of the superconductor.

Areas of Agreement / Disagreement

Participants express differing views on the mechanisms at play regarding the behavior of magnetic fields in superconductors, particularly concerning the conditions under which magnetic flux is trapped or expelled. The discussion remains unresolved with multiple competing perspectives.

Contextual Notes

Participants mention limitations related to the size of the hole in the superconductor and the critical field strength, which may affect the behavior of magnetic fields but do not resolve these aspects fully.

annaphys
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When a magnetic field is applied to a SC during cool down, the field goes through the hole of the hollow cylinder. When the cool down first takes place and then later a magnetic field is applied, the magnetic field does not go through the hole of the hollow cylinder but rather is expelled to the exterior of the cylinder. Why does this happen? Why is there a difference between the two?
 
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Inside the bulk of the superconductor, there can't be a magnetic field. So the field inside the hole get's trapped.
You can also show that the field can't have arbitrary values but gets quantized.
 
Hi thanks for the comment. What do you mean it gets trapped and which state are you referring to?
 
In the superconducting state, the magnetic flux through the loop cannot change. If there was a flux inside, before cooling down, it gets trapped, i.e. you can't change it any more when the loop has become superconducting.
 
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Ok that makes sense. And for the other case, i.e. when first cool down then magnetic field, what makes it that no flux goes through the hole? Is this simply because the hole is relatively small and the screening current on all sides pushes the magnetic field out of the hole? If we had a cylinder, with a meter wide hole, could we see flux going through it?
 
annaphys said:
Is this simply because the hole is relatively small and the screening current on all sides pushes the magnetic field out of the hole? If we had a cylinder, with a meter wide hole, could we see flux going through it?
Yes, this is principally the explanation. The magnetic field cannot be made arbitrary strong, as this will make superconductivity to break down (critical field stength). The reasoning is also not completely applicable to type II superconductors, as small flux packets can enter the superconductor (Superconductivity vanishes at the location of the flux lines).
 
DrDu said:
the magnetic flux through the loop cannot change

This is the key to the asymmetry. Whatever the flux was before the transition is what you have after. If it was zero before, it';s zero after. If it was non-zero before, it's non-zero after.
 

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