The advantages of this would be the extremely high specific impulse (particles in an accelerator can get to high fractions of C), an adequate thrust (particles near the speed of light increase in thrust), and low fuel usage (you'd just need something like hydrogen or xenon). This would also need a lot of power, needing something like a polonium RTG or nuclear reactor), but not completely impossible. Particle accelerators are big, but recent advancements have made them much smaller. Plasma acceleration and nanophotonic accelerators are reaching the size where the smallest functional ones can even fit on your thumb. Such high thrust would allow direct thrust trajectories between planets. A preliminary calculation, back of the napkin, shows that a 500 kg probe could accelerate at 1 g with one engine unit. This would need a lot of power, yes, but this could be supplied with a polonium RTG or solar panels for near-Sun operation.
I did some calculations on how much a trip to Mars would cost, energy wise, and yeah. It'd take some 2.78 × 10¹⁵ J for the trip. I suck at math, so this might be off, but this means you'd need WAY too much polonium for 1g constant acceleration.