What would happen if you put a superconductor shell around a magnetic monopole?
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What would happen if you put a superconductor shell around a magnetic monopole?
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David Kahana, physicist unhinged
Answered Nov 1, 2016 · Upvoted by Paul Mainwood, Degrees in Physics and Philosophy, Doctorate in Philosophy …
Wow, nice question!
Alan Guth, or rather, his and Andre Linde’s inflationary cosmology after appropriate fine-tuning, long ago supposedly explained why there are no magnetic monopoles found in the observable universe, when, by the general understanding of the standard model, and certainly in any grand unified theory or string theory it is highly probable that there would be a lot of monopoles around.
Still, for theoretical reasons it would be very nice if Guth were a bit wrong and there were at least one monopole, since even one would be enough to explain the quantization of electric charge.
If it is a ’t Hooft-Polyakov monopole, and the thickness of the superconducting shell is finite but large enough, meaning probably very large indeed, and there is spherical symmetry, then I believe that the magnetic flux of the monopole will penetrate the superconductor along two or possibly more Abrisokov flux tubes (assuming a type II superconductor) inside of which the magnetic flux is oppositely directed.
Supercurrents will flow inside the superconductor around the flux tubes, and there will be a normal conductor inside the tubes.
Outside the superconducting shell the fields will return asymptotically to the ’t Hooft Polyakov solution, the magnetic field of which tends to the field of the Dirac monopole at large radii.
The field inside the flux tubes will be above the transition field which drives the superconductor to go normal - and will likely be just at the transition field at the boundaries of the flux tubes.
You could either imagine that the superconducting shell is brought below the transition temperature with the magnetic monopole alrready at rest inside, or imagine that the monopole is pulled slowly inside the shell, through the superconductor, into the centre.
In either case the superconductor will try to expel the magnetic field of the monopole due to the Meissner effect, but it will not be possible to do so completely, since for the ’t Hooft Polyakov monopole the magnetic field is topologically trapped and cannot be unwound, since it connects to the magnetic field/gauge field/Higgs field configuration at spatial infinity.
So as the superconductor tries to push the magnetic field out - it will end up instead pinching all the magnetic flux into a number of thin flux tubes, and probably only two in the limit of very thick superconducting shell, that cut right through the superconducting shell.
You would need to do a numerical study using a Polyakov monopole, to prove that this is what happens - it involves a smooth deformation of all of the fields of the ’t Hooft Polyakov solution to produce the flux tubes and you need to know the change in energy of the configuration inside the superconductor too. The Polyakov solution itself has finite energy, and is classically stable: it is a topological soliton.
You would need to show that it’s still locally stable when the superconductor goes normal inside the flux tubes.
This of course depends on how strong the magnetic field of the monopole is and how thick the superconducting shell is and what the characteristics of the superconductor are: if the magnetic field is extremely strong - and certainly, when the Dirac quantization condition is satisfied and the electric charge is small - the magnetic charge of the monopole is very large, then the result may be simply that the whole superconducting shell is driven to the normal state instead, and the field of the monopole simply penetrates right through.
I’ld expect flux tubes to form when the monopole field is small enough compared with the maximum field the superconductor will tolerate without quenching, or when the spherical superconducting shell is large enough and located far enough away from the monopole.
That’s not a proof of course - it’s only my intuition.
This question previously had details. They are now in a comment.
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3 ANSWERS

David Kahana, physicist unhinged
Answered Nov 1, 2016 · Upvoted by Paul Mainwood, Degrees in Physics and Philosophy, Doctorate in Philosophy …
Wow, nice question!
Alan Guth, or rather, his and Andre Linde’s inflationary cosmology after appropriate fine-tuning, long ago supposedly explained why there are no magnetic monopoles found in the observable universe, when, by the general understanding of the standard model, and certainly in any grand unified theory or string theory it is highly probable that there would be a lot of monopoles around.
Still, for theoretical reasons it would be very nice if Guth were a bit wrong and there were at least one monopole, since even one would be enough to explain the quantization of electric charge.
If it is a ’t Hooft-Polyakov monopole, and the thickness of the superconducting shell is finite but large enough, meaning probably very large indeed, and there is spherical symmetry, then I believe that the magnetic flux of the monopole will penetrate the superconductor along two or possibly more Abrisokov flux tubes (assuming a type II superconductor) inside of which the magnetic flux is oppositely directed.
Supercurrents will flow inside the superconductor around the flux tubes, and there will be a normal conductor inside the tubes.
Outside the superconducting shell the fields will return asymptotically to the ’t Hooft Polyakov solution, the magnetic field of which tends to the field of the Dirac monopole at large radii.
The field inside the flux tubes will be above the transition field which drives the superconductor to go normal - and will likely be just at the transition field at the boundaries of the flux tubes.
You could either imagine that the superconducting shell is brought below the transition temperature with the magnetic monopole alrready at rest inside, or imagine that the monopole is pulled slowly inside the shell, through the superconductor, into the centre.
In either case the superconductor will try to expel the magnetic field of the monopole due to the Meissner effect, but it will not be possible to do so completely, since for the ’t Hooft Polyakov monopole the magnetic field is topologically trapped and cannot be unwound, since it connects to the magnetic field/gauge field/Higgs field configuration at spatial infinity.
So as the superconductor tries to push the magnetic field out - it will end up instead pinching all the magnetic flux into a number of thin flux tubes, and probably only two in the limit of very thick superconducting shell, that cut right through the superconducting shell.
You would need to do a numerical study using a Polyakov monopole, to prove that this is what happens - it involves a smooth deformation of all of the fields of the ’t Hooft Polyakov solution to produce the flux tubes and you need to know the change in energy of the configuration inside the superconductor too. The Polyakov solution itself has finite energy, and is classically stable: it is a topological soliton.
You would need to show that it’s still locally stable when the superconductor goes normal inside the flux tubes.
This of course depends on how strong the magnetic field of the monopole is and how thick the superconducting shell is and what the characteristics of the superconductor are: if the magnetic field is extremely strong - and certainly, when the Dirac quantization condition is satisfied and the electric charge is small - the magnetic charge of the monopole is very large, then the result may be simply that the whole superconducting shell is driven to the normal state instead, and the field of the monopole simply penetrates right through.
I’ld expect flux tubes to form when the monopole field is small enough compared with the maximum field the superconductor will tolerate without quenching, or when the spherical superconducting shell is large enough and located far enough away from the monopole.
That’s not a proof of course - it’s only my intuition.
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Hola mate !! ✨✨
here's your answer...⬇️⬇️
▶️Thoug magnetic monopoles are not practically possible. But if theoretically, we put a superconductor shell around the magnetic monopole then the flux of monopole will induce the current also known as super current inside the superconductor.
hope it helps !! ❤️❤️
here's your answer...⬇️⬇️
▶️Thoug magnetic monopoles are not practically possible. But if theoretically, we put a superconductor shell around the magnetic monopole then the flux of monopole will induce the current also known as super current inside the superconductor.
hope it helps !! ❤️❤️
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