...protons are accelerated to 800Gev in a 1 km radius superconducting-magnet synchrotron with a residence time of 40 sec, at a substantial fraction of the speed of light,

The effective centripetal acceleration required to maintain the circular orbit is 9 * 10^13 m/sec/sec

For an equivalent linear accelerator (LINAC),you would need a linear accelerator stretching 12 million km - 30 times the Earth-Moon distance, and 8% of the distance from the Earth to the Sun, in order to obtain the storage time and ultimate velocity (energy).

Note that in a Newtonion approximation, you would only need a LINAC 1 km long, but the trick is that we need long residence times at speeds near to c in order to continue to add energy to the particles.

There is a paradox with synchrotrons that, in the absence of losses, you can accelerate particles to an almost infinite energy, since they are STILL orbiting at the speed of light, no matter how "fast" they go (we're looking at tiny fractions below c, whatever the energy). In practice, the losses constrain the capacity of any synchrotron.

Heavier ions DO accelerate slower down the tube (according to mass^-1), and have a higher centrifugal force (scaled as mass^+1). (or strictly speaking as mass/charge, and be aware that heavy nuclei can usefully be multiply-ionised which makes things easier)

however, the issue of residence time is critical. If you want low-energy particles, then a LINAC is the easy solution. for high energy (relativistic) particles, the size of BOTH the LINAC and synchrotron scales as mass/charge. A synchrotron only 244 km in radius can theoretically accelerate singly-ionised plutonium nuclei to 800 Gev with the same superconducting magnets as used by CERN. The equivalent LINAC would be approx 20 AU in size.