[math-fun] superconducting magnet confusion
Richard E. Howard raised the point that type-II superconductors can permit magnetic field to penetrate thru them via "pinned flux tubes" which might permit a topologically-ball shaped permanent superconducting magnet to exist. This could overcome my "there's a huge magnetic field" objection to the claim neutron stars had superfluid+superconductive interior. --WDS: sorry, I should have pointed this out myself. However, I object that if the material is a "superfluid", not a "solid crystal lattice with crystal defects" then I find it hard to understand how we could have an "Abrikosov latttice of flux tubes pinned by crystal defects." On the contrary I would expect any flux tube to be mobile and hence be expelled. Therefore I would expect neutron star stuff, if really superfluid+superconductor, to be "type I" and hence to expel all magnetic field extremely quickly (result: exactly 0 field throughout the super-region). Also, the Earth's magnetic field is caused by convection currents in hot normal-conductive fluid forming a "dynamo." Ditto sun's field. But I would think there would be no such thing as convection currents in a superfluid. Instead in liquid helium heat is transmitted via "second sound", a wavelike rather than diffusive phenomenon quite unlike heat transmission in normal matter (including unlike it in liquid helium above the super-transition temperature). I suppose you might argue that a thin outer layer of non-super matter in a neutron star might be able to convect and might also be responsible for the magnetic field. But in that case we'd be speaking of an essentially TWO-dimensional "dynamo" quite unlike the Earth and Sun's 3D one and it seems dubious (?) such a thing could exist generating a macroscopic dipole field. Also, although I guess I should admit the logical possibility that a ball-shaped chunk of super-matter could be a permanent magnet if it is type-II, I am unaware of any actual example of this logical possibility. As far as I know, nobody has ever engineered a super-magnet that is topologically ball-shaped, and so it is not clear to me it really IS a logical possibility. Is it really? After a bit of thinking, I think yes, it really is possible as follows. Place your ball of type-II superconductor -- but heated well above Tc -- in a huge external field. Now cool it below Tc. Now the field presumably would be "frozen in" in the form of a flux-tube lattice even after we remove external field. So anyhow, at the very least I think one should concede these matters are subtle and worth analysis+discussion -- which I remind you, the "neutron stars have super interiors!" papers DID NOT DO AT ALL. At the worst, it might even be this all just kills the entire hypothesis.
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Warren D Smith