Charged particles radiate away energy if you accelerate them (force them on a curved path), this energy loss is larger for larger accelerations / smaller radii.

Charged particles radiate away energy if you accelerate them (force them on a curved path), this energy loss is larger for larger accelerations / smaller radii. To bend the particle beam you need magnetic fields. Particles with more energy need larger fields. Larger radius means less field strength for given energy or larger energy for given field strength. So a circular accelerator needs strong magnets nearly everywhere to force the beam on a circular path. In case you would put it in outer space, it's not like you just bounce the beam between some small number of spacecraft, that wouldn't gain much if at all, you would need something very similar to the structure in the LHC.