Tempo di lettura stimato: 6 minuti

We are finally about to reach our goal, Billy. The wait is over. This is the last chapter of our long, strenuous, yet satisfying exploration of the phenomenon of superconductivity.

Like any self-respecting season finale, this article deserves its own  “Previously on… Superconductivity and magnetic levitation”:

  • Chapter 1: we introduced superconductivity as a phase transition that takes place at a specific critical temperature, typically in the cryogenic range, and requires some applied field and current density requirements to be fulfilled. Its main properties are null resistance and the Meissner effect. Moreover, we emphasized the fact that superconductivity can be described from different points of view, but it is still far from full comprehension.
  • Chapter 2: we briefly summarized the most important moments in superconductivity’s history; in particular, we have mentioned Onnes (discovery), Meissner, the London brothers (electromagnetic approach), Ginzburg and Landau (II order phase transition), Abrikosov (vortices) and finally Feynman, Bardeen, Cooper, and Schrieffer (microscopic theory).
  • Chapter 3: we said that there exist 2 kinds of superconductors: I type and II type superconductors, that are provided with an additional third intermediate state, the vortex state. The latter envisions 2 possible varieties as well, reversible and irreversible superconductors. Vortices play a fundamental role in irreversible superconductors, which are the material we are interested in for magnetic levitation.
  • Chapter 4: we focused on irreversible II type superconductors and depicted their peculiar hysteretical behaviour, resulting from the interaction of vortices with pinning centres (defects of the material able to block vortices since they represent energetically favourable sites).

My dear Billy, this was a demanding, but necessary premise to eventually get into the core of our dissertation: magnetic levitation and its counterpart, magnetic suspension. Here we are, at last. I am sure, Billy, that you are a big fan of “Fisici Senza Palestra” and that you have loyally and accurately read all our articles, Monday by Monday. Then, now I suppose you are sufficiently prepared to engage to a pure and formal physical experiment. I can feel your goose bumps, both of pleasure and concern.

Let’s begin first with magnetic levitation, which is performed in Zero Field Cooling operating mode.

As we already described in the first article, the ZFC technique consists in subjecting the superconducting sample to the effect of a magnet, after is has already been cooled down below its critical temperature. The sample we use is a textured Y Ba2Cu3O7 material, an irreversible II type superconductor whose critical temperature is Tc = 92 K. It undergoes the action of a Nd-Fe-B permanent magnet. Given Tc, liquid nitrogen is suitable as cooling bath, since its boiling point is attained at T = 77 K < Tc. The experimental setup of this experience follows:

As we approach the magnet to the superconductor once it has reached T = 77 K uniformly, it does not come into contact with the sample, but it levitates above it. The physical interpretation of such a behaviour is due to pinning. The displacement of the magnet modifies the distribution of the vortices, but the pinning force reacts trying to oppose to any variation. Vortices find difficulties in entering the material because of the pinning centers; therefore, the magnet is repelled by the superconductor. It levitates at a height given by Fp = Fg = mg, where the weight of the magnet is perfectly counterbalanced by the force exerted by the superconductor (equilibrium). When the magnet is perturbed by an external force, it responds like it was connected to the superconductor through a spring: restoring forces tend to bring the magnet back to its original position through oscillations, until it reaches equilibrium thanks to damping. Stiffness is another important parameter that characterizes any spring: it is a measure of the resistance to deformations, so, in this case, it is related to the stability of the levitation. We aim at obtaining the most stable possible interaction between the magnet and the superconductor, implying then the higher the stiffness, the smaller the oscillations, the better the stability. At the same time, damping introduces energy losses, so it might seem detrimental to the phenomenon. However, damping is essential for stability as well since it extinguishes oscillations, otherwise uncomfortable in practical applications, for example the Japanese MAGLev trains. No one wishes to travel on a bouncy train, do they Billy?

Magnetic suspension can be considered the dual of levitation. In fact, it must be accomplished in Field Cooling mode, which performs the inverse procedure with respect to ZFC: firstly, an external magnetic field is applied to the superconductor; then, the sample is cooled down below its critical temperature. The experimental setup follows:

Here, the geometry of the setup is also reversed. Since we are investigating suspension, now the superconductor must be located above the magnet with a proper support. Once liquid nitrogen has been poured in the container and the temperature of the sample has become 77 K, we can observe the desired phenomenon: the magnet floats in the air, correspondingly to the sample position. The cause of such a phenomenon is still pinning, yet with an opposite result. In the previous article we said that Meissner effect is not the best proof for showing superconductivity. In fact, this is a piece of evidence for it. In ZFC, the sample felt no magnetic field before the phase transition to the superconducting state, then no vortices were contemplated inside the sample, due to the pinning’s repulsion effect. On the contrary, in FC the material is fully penetrated by a magnetic field before becoming effectively superconducting, then, as soon as T < Tc, the sample is inhabitated by plenty of vortices. The Lorentz-like force tries to expel them, but they are blocked inside the superconductor by the pinning centers. Some of them could survive also when H < Hc1, then Meissner effect does not take place. The tendency of the sample to retain vortices results in an attraction effect. This is the reason why the magnet is suspended in the air, provided that Fp ≥ F = mg.

Let’s celebrate Billy, we have crossed the finish line! I am proud of your commitment, effort and curiosity! I hope you have really appreciated our travel through the mysteries of superconductivity. But don’t feel sated, new adventures are coming!

Pubblicato da Giulia Maffeis

Crede che esistano due cose infinite: l'universo e il suo amore per la fisica, ma riguardo la prima nutre ancora dei dubbi.