The main constraint is power usage. In principle you want to accelerate your fuel particles as fast as possible. At a fixed electric power though, the faster yo

The main constraint is power usage. In principle you want to accelerate your fuel particles as fast as possible. At a fixed electric power though, the faster you accelerate each individual particle, the less particles you can accelerate. This conserves propellant but reduces thrust. Consider that you could use a photon rocket, basically a flashlight, where your propellant is moving at the maximum possible speed. This will have great propellant efficiency but you won't move much unless you have TW of power. Since you want to get somewhere in a finite time and don't have unlimited power, in practice you want something with lower propellant efficiency. So yes, you could use a particle accelerator to accelerate ions, and it might be quite efficient, but you would need a ton of power if you wanted a reasonable amount of thrust.