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I know that circular accelerators, due to the radiation emitted by accelerated particles, are limited by their size in what energies they can reach. Linear accelerators (linacs) instead could reach any energy, provided you can make one long enough, but another problem they suffer is that the particles of the two beams colliding that do not partake in any scattering process are lost, while in circular accelerators they can be recirculated and reused. This is important when we are interested in effects and phenomena that have very low scattering cross-sections.

My question is, does it exist (or at least is it planned to be built) an accelerator that is partially linear and partially circular? (here is a sketch just to be clear)

This way one could accelerate the particles in the linear sections, making the two beams collide in the center of one of these, and then reuse and re-accelerate in another lap the particles that did not partake in any scattering process.

I'm curious if this has been done or if someone is planning to do it. If not, why? What other disadvantages would one of these accelerators have?

More generally, are there other geometries (other than circular and linacs) that are used to accelerate particles?

enter image description here

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    $\begingroup$ en.wikipedia.org/wiki/… $\endgroup$
    – Solomon Slow
    Nov 28, 2022 at 20:32
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    $\begingroup$ While we call them circular accelerators, you'll find that large synchrotrons are actually composed of bend sections interspersed with straight sections. For example RHIC is almost like a hexagon, and the LHC has eightfold symmetry. $\endgroup$
    – mng
    Nov 29, 2022 at 6:30
  • $\begingroup$ Eventually, the radius of the circular section would be the main constraint. In a sense, you still have all the limitations of the circular machines (powerful magnets, synchrotron radiation). $\endgroup$
    – Martino
    Dec 2, 2022 at 13:03
  • $\begingroup$ reuse and re-accelerate sounds like the particles that did not collide, slowed down at the end of the linear section. Why should they? $\endgroup$
    – Martino
    Dec 2, 2022 at 13:04
  • $\begingroup$ They could slow down in the circular section @Martino $\endgroup$
    – Rhino
    Dec 2, 2022 at 13:17

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It exists! One example is the racetrack microtron:

enter image description here

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The electron beamline at the SLAC facility was originally a linac, to which several circular sections were subsequently added over the years at the end section to act as storage rings. Those rings needed to be powered so as to maintain the energy levels of the particles that the linac had injected into them; I do not know if further acceleration was applied to the circulating particles to add more energy to the beam or if energy was simply maintained in the rings.

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