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The CERN tunnels use klystrons to accelerate the protons

https://home.cern/science/engineering/accelerating-radiofrequency-cavities

But electron guns use an electric field to accelerate electrons. Theoretically, shouldn’t we be able to use the same device to accelerate protons? The Output of this design would be a continuous stream of high energy protons instead of bunches.

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    $\begingroup$ Because you need to keep accelerating the particles as they go round and round - so electrostatics isn't the way to do it. Essentially the LHC is a linac wrapped around on itself. $\endgroup$
    – Jon Custer
    Commented May 14, 2020 at 15:18
  • $\begingroup$ Imagine the source of protons connected to a tunnel that opens up into a ring which has a bunch of the ‘parallel plate capacitors’ spaced evenly around. It is described here physics.stackexchange.com/questions/12788/…. The protons should behave the same way electrons do - accelerating more and more each time they pass through another grid, no? $\endgroup$ Commented May 14, 2020 at 15:22
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    $\begingroup$ Nope, it just doesn't work that way - see, for example, cds.cern.ch/record/1982425/files/295-329%20Vretenar.pdf $\endgroup$
    – Jon Custer
    Commented May 14, 2020 at 15:25
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    $\begingroup$ Same for electron linacs, by the way. The ability to 'continuously' accelerate particles was the real advantage of linacs/cyclotrons/etc. over Cockroft-Walton or Van de Graaff electrostatic accelerators. $\endgroup$
    – Jon Custer
    Commented May 14, 2020 at 15:26
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    $\begingroup$ And, klystrons aren't magnets. $\endgroup$
    – Jon Custer
    Commented May 14, 2020 at 15:39

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