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?
reuse and re-acceleratesounds like the particles that did not collide, slowed down at the end of the linear section. Why should they? $\endgroup$