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General Electric's medical electron synchroton from 1956 looked like a toaster for a 100-foot giant
(hexbear.net)
https://broughttolight.ucsf.edu/2013/12/03/stones-synchrotron/
This compelling photograph (which, despite appearances, is not a scene from a sci-fi movie) depicts Dr. Robert Stone with the machine he created, the 70MeV electron synchroton. The synchrotron was a type of particle accelerator used to treat cancer patients with radiation from 1956 to 1964. Stone’s work contributed greatly to the safe clinical use of radiation.
Ah okay I think I've figured out the reason for the difference. My CERN article is talking about "synchrotron radiation" which is a secondary radiation emitted during acceleration of the particle beam, sort of like electronics losing a certain amount of power to heat. Your article seems to be referring to shooting an x-ray beam at something, which I imagine is produced by shooting the electron beam at some sort of target to produce x-rays.
As for size requirements, it seems that it's mostly due to those synchrotron radiation losses. The losses scale with energy to the fourth power, and decrease with the turning radius, so if you want to run a higher energy beam, you need vastly higher radius.
Oh, damn, great observation. I never even considered that they'd use them for an electron beam for a secondary source, since electron synchrotrons now are pretty much only used for radiation emitted from the beam. (Although they have much fancier means of extracting the radiation than the simple bending magnets now.
As for size, ~3 GeV machines span an order of magnitude in circumference so at least part of it is to do with how many beamlines you want to fit around it, but yeah I'm sure the electron energy makes a lower bound.