What is generally used to cool down superconductive elements?

A magnet levitating above a high-temperature superconductor, cooled with liquid nitrogen. (Wikipedia)

It will almost always be liquid nitrogen or liquid helium. Liquid nitrogen is the cheapest cryogenic that can cool existing superconductors below the critical temperature. In fact, the development of "high temperature" superconductors that can operate above the boiling point of liquid nitrogen (77K) was a godsend. Before that you had to use liquid helium, which is much more expensive and more of a pain to use. Unfortunately for certain applications (e.g. MRIs) you are still stuck using liquid helium, which tends to drive up the cost.

Of course, it would be great if we could develop superconductors that could be cooled with water or which wouldn't require any cooling at all. That would drastically reduce the costs of superconductors and open up many new applications. Unfortunately, we are not quite there yet, and at this point it's not clear whether such materials may exist.

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