A group of experimental physicists recently proposed reviving the Superconducting Supercollider, because its location (in Texas) happens to have the lowest tunneling costs of any known site. Particle accelerators have to be in tunnels, for a few reasons. First of all, they’re huge. The LHC is 27 kilometers in circumference, and the proposed future accelerators are up to 10 times that size. They have to be perfectly level, so you can’t just run them along the ground, unless you put them up on pilings or in trenches wherever the level varies. Also, they spray X-rays when they’re running, so you generally don’t want them in the open air.
The proposed plan at the SSC site has an estimated tunneling cost of $4,900/meter … much cheaper than the $23,000/meter estimate at CERN, but still more expensive than the actual magnets in the tunnel (which they estimate at $2,700/meter). If you imagine that accelerators will continue to get bigger as physicists pursue higher energies, this cost is going to be increasingly problematic. But apart from underground, where else can you go that’s huge, perfectly flat, uninhabited, and reasonably accessible?
I expect the ring would float a few meters below the surface to allow boat traffic to pass, with periodic buoys to keep it in place. It would be constructed with just slightly below neutral buoyancy (to minimize catenary hang), and elastic tethers to dampen the effects of surface waves. Small deformations in the ring would be easily accounted for by slightly varying the magnetic field along the way, to steer the beam. On these scales, iron pipe (with a coat of marine grade paint) is flexible enough to allow portions of the ring to be surfaced for repairs as necessary.
For a 270km ring, the investment in invention may not be economical, but if you consider approaching the limits of particle physics on Earth, I think undersea accelerators may be the logical conclusion. Where else can you put a ring that’s 27,000 km in circumference?