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At CERN for example, what is actually providing the current? It cannot be a battery because when the load resistance is less that the internal resistance then the load sees no voltage...

So do they use a current source? A transformer and then a rectifier to make it DC?

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CERN is powered from the French national grid, with a backup power line from the Swiss national grid. Details are available in this document.

You specifically ask about the magnets: superconducting magnets use a controlled current power supply like this one or this one, or many others a short Google away. Those two examples are intended for applications like NMR or MRI where the power requirements are relatively modest, but the controlled current PSUs at the LHC will be basically similar but larger. I think, though I wouldn't swear to it, that the PSUs for some if not all of the LHC magnets were built by Ocem.

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  • $\begingroup$ No kidding about "powered by [the] grid". Back in the 1990s Fermilab used to call Illinois Power about an hour before they planned to run up the big accelerators and warn them to bring some spare capacity on-line. As in get at least one more significant power-plant up to steam. Superconducting magnets and cavities help, but the beam still takes a lot of power and there are losses outside the superconductors. $\endgroup$ – dmckee Nov 25 '16 at 20:38

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