Earlier quoted context omitted.
Basically: making charged particles change direction causes them to emit radiation, and the more they turn the more they radiate. This gets worse and worse at higher energies, so increasing the magnets but keeping the same angle means you waste more energy and your magnets get destroyed by the intense radiation.
My understanding is that is true of Electrons, but not Protons, which is why SLAC is a straight line, the only way to get electrons up to high energies. [Edit]Wrong! Turns out protons do emit energy as well... up to 6.7 KeV per turn. Source: https://en.wikipedia.org/wiki/Synchrotron_radiation
For this reason I've seen suggestions to do round electron-type accelerators but using the much heavier muons to get around the radiation problem.