What provides the centripetal force for Cooper pairs flowing in a toroidal superconductor?
I asked myself this question, which led me to realize I also don't really know the answer to a more basic question: What provides the centripetal force for ordinary current (electrons) flowing in a circular wire?
Are either or both of these forces a Lorentz force, as a result of the magnetic field generated by other moving electrons/Cooper pairs? (I suspect no, since if I were to add more electrons/Cooper pairs into the conductor/superconductor, then the centripetal force on individual charge carriers will increase and their motion will follow a tighter circle, perhaps ejecting the surplus charge carriers from the conductor/superconductor. But I don't think this really happens? And this apparently fails to explain the forces experienced by charge carriers flowing in closed loops other than circles, e.g. forces that cause charge carriers to "turn the corners" in a square loop.)
These thoughts prompt the question: does the ion lattice itself exert a centripetal force? Is the mechanism by which the lattice exerts a centripetal force different for Cooper pairs in a superconductor than for ordinary electrons in an ordinary conducting wire? (I suspect some kind of "yes" to these questions, though I don't understand the mechanism by which the ion lattice would exert a force, especially for Cooper pairs in a superconductor. I figure ordinary electrons can at least "bump" themselves around the lattice in a circular wire -- which I suppose would mean that for extraordinarily narrow wires, the resistance of the wire could be a function of its geometry (!) -- but for Cooper Pairs to do so without resistance of course feels like a miracle.)
