# What is the smallest amount of He you can use to cool a superconducting magnet?

This is an engineering question, but it is adressed to physicists who build accelerators. This question: An electromagnetic space elevator? notices that a NbSn superconducting ring around the equator will launch itself into orbit. The question is whether there is enough He to cool such a massive structure.

What is the minimum amount of He required to maintain a stable 4-degree temperature safely throughout a long cylindrical wire? Is is necessary to use a fluid at all, or can one stably and safely maintain a stable He-range temperature in a very long wire without a liquid coolant?

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Now this amount is converted: $$\mathrm{mass_{He}} = 147\cdot 10^9\, \mathrm{m}^3 \cdot 0.18\, \mathrm{ kg/m^3} = 2.6\cdot 10^{10}\,\mathrm{kg}$$ Which is much more than the $1.7\cdot 10^{8}\,\mathrm{kg}$ necessary for a ring with similar specifications as the LHC. You can greatly reduce the necessary amount by using pulse tube refrigerators and relax the specifications a bit by allowing slightly higher temperatures. Then the conduction via the metal itself might be enough to cool the wire as NbSn wires are embedded in copper.