How Does the Meissner Effect Cause a Superconductor to Levitate?

[wasia]

I have been considering a situation, where a piece of superconducting (SC) material is put onto a magnet and then cooled through SC transition. As I understand, repulsion occurs and the SC piece gets away from the magnet (is it correct?).

Assuming this happens, the SC piece may shoot upwards resisting gravity. In this case work is done (against gravity) and energy should be conserved. Where does this energy come from?

Yes, I have done a search on this and did not find an answer. Thank you.

 

[marcusl]

The energy to consider is the Helmholtz free energy of the SC. When the transition temperature is crossed, electrons in the metal form Cooper pairs and condense into a lower energy state. This released energy does the mechanical work you observe. The free energy was first examined by the London brothers ("London equations"), and developed fully by Ginzburg and Landau ("Ginzburg-Landau Theory"). Tinkham's book "Introduction to Superconductivity" has a full discussion.