All ion engines are particle accelerators. You get to choose how big.
The fundamental problem for extended space exploration is one of mass. You might have some kind of nuclear reactor (preferably the fusion kind) to give you energy, but what you need is reaction mass also.
So in the future we'll have plenty of on-board energy but can't afford too much mass.
Fortunately, the thrust (or impulse, which is thrust over a period of time) is the product of the exhaust velocity (which comes from your energy source) and the mass you eject. So you accelerate your mass to the highest exhaust velocity you can, in order to maximize its impulse.
One further gain is that as you accelerate the fuel mass on board to near the speed of light, it gains significant mass (relative to the spacecraft frame of reference). Above 99%, every tenth, every hundredth, every thousandth part of the velocity you can give your reaction mass pays off in substantial increases in its effective mass, and therefore in its thrust per unit mass consumed.
If we could ever fully harness the deuterim-tritium fusion reaction in a rocket engine, we might have rocket efficiencies tens of thousands of times what can be obtained with any chemical rocket. It would completely change our relationship with space--both near-earth and interplanetary.
since 2000, physicists have been accelerating gold nuclei around a 2.4-mile underground ring to 99.995 percent of the speed of light and then colliding them
Why are they using Gold?