Multi-Billion dollar experiment.

Here's the bottom line. That particle accelerator likely costs on the order of a trillion dollars. Look it up online and call me wrong, but this is an order of magnitude estimate. Putting that into space would theoretically cost more than the money that is in the world, when you factor in the mass-cost of putting anything into orbit. Again, this is something you can look up, but roughly the cost of putting anything into orbit is a function of its mass (aka the fuel required), and it is expensive as hell. This particle accelerator is one massive piece of equipment, and a ballpark estimate could easily be found by simply considering its size and assuming a uniform mass density. As if that was not a problem enough, if I'm not mistaken it operates by providing a massive amount of power to electromagnets. When this is in orbit, where will this kind of power come from?

When talking about feasibility of putting this into space, then you're looking at somewhere on the science fiction time scale when the human race has large naval space-faring vessels. If this ever happens, and shipyards are in orbit and have material carried to them on either a space elevator, or something much, much, much more efficient than current methods, then yes this could be built in space. Save science fiction though, this will not be in space in the next 100 - 200 years, and that's making the assumption that science lags science fiction on the subject of space travel much as it has for other similar subjects.

By that time enough tests will have been conducted using this thing to know whether or not - by trial and error alone - it can destroy the human race.