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I think the Bremsstrahlung happens as a strong radiation emitted by the accelerated particle stream. As in this question is visible, it is the main cause of the energy loss in such big particle accelerators as the Fermilab or the LHC.

Are there existing plans to get this energy somehow back? The technology don't seem especially hard to this for me (at least, theoretically: taking the radiation energy with a lattice and using the induced current), especially because this very well controlled stream has probably a very stable BS.

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It is not clear what you mean by "get this energy back". Back to the individual particle? Not lose it as energy? You realize that all these particles run around in a vacuum and vacuum technologies are not that simple? –  anna v May 13 at 11:53
    
@annav Back to the energy provider of the accelerator. Of course, indirectly the particles will get it back. I know that vacuum technologies aren't really simple, I thought only about the theoretical complexity. –  Peter Horvath May 13 at 11:57
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Many old accelerators use their Bremsstrahlung for Chemistry/ Biology type experiments after new bigger machines are built. This is the case with DESY, which is now lots of Chemistry and Biology experiments set up around the ring. Would you count this as "getting back" the radiation. It is indeed being used for experimentation. –  Flint72 May 13 at 12:03
    
@Flint72 No. I am thinking reusing the energy of an active, big accelerator which the goal of the reduction of the total energy need. –  Peter Horvath May 13 at 12:05
    
Thousands of very intelligent people designed the particle accelerators you listed, I sincerely doubt that all of them missed on this one. –  Kyle Kanos May 13 at 12:31

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In the LHC the synchrotron radiation will waste approximately 13.5 kW with two beams each at 7 TeV which is something similar to 30 desktop computers (there are many more at CERN!!); but since this small power is lost at a small temperature, there is a huge workload for the cryogenic system which eats up a power of 40 MW to keep the superconducting magnets at 2K (although there are some thermal leaks also from the outside of the vessels).

You may think why not using room temperature magnets? They were used in LEP but:

  1. they have ohmic losses which still lead you to waste much more power than synchrotron radiation, and,
  2. more important, they do not allow you to push the field to the now-a-days required values.

Still we didn't take into account the energy wasted:

  1. in the generation and operation of the radio-frequency electric fields which are required to accelerate particles and keep the beam stable for a time that can go up to many hours,
  2. by the vacuum system,
  3. by the electronics and instrumentation to control and operate the machine.

There are some projects that point to recover part of the energy wasted by a particle accelerator for instance by heating the laboratory buildings, this going on for example with the SwissFEL project at PSI in Switzerland. However forcing this energy somehow back to the beam is simply too inefficient and too expensive; this is not a technology limitation, but a thermodynamic one!

Still, if you can find a very compact and cheap material (beampipes are few centimeters large) that can efficiently absorb photons in the keV range without emit secondary particles (which pollutes the vacuum and disturb the beam) and converting them to something more noble than heat, you are very welcome by the accelerator community!

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