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I'm not sure if it's up to the task (yet?), but thermoelectric coolers are routinely used for CCDs that operate below -80 °C (an overview: https://www.azom.com/article.aspx?ArticleID=14681). I suspect someone will come up with a solution once the technology starts to mature.

At those temperatures things get weird. Cryocoolers are established technology, but anything colder than the xx K range very quickly stops being easy in any way.

That said, LH2 temperatures aren't really hard and can easily fit in a 2U rackmount device, providing power/classical-RF uses of type2 superconductors. Think EMI shielding, power conditioning, ~50 GHz traces that can span a full backplane without fancy signal conditioning, etc.

Thermoelectric coolers are not even able to keep up with modern CPUs. Or rather, they can, but they are very energy hungry. As much or more so than the CPU itself.

Mostly: thermometric coolers are bad for >50K difference and >10W heat flux on the cold side. Most uses are better off with a sterling cooler or maybe even an absorption refrigerator, which can have no mechanical parts (just fluids, plumbing and heat exchanges) and could theoretically provide human-centric AC/refrigeration based on server waste heat.

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