As others said, they are a sniper weapon. And they do need quite a bit of reseach.
They generally have two uses for me:
1) You are faster than the enemy. Make sure you stay at a distance just slightly shorter than your max range. Since you can dictate the range of the engagement, you will almost surely do more damage per 5 seconds at that range than the enemy
2) You know the enemy designs are heavily reliant on armor. In that case, the armor penetration of the particle weapon can score early critical hits.
I would probably not make massive usage of them though, unless I also HEAVILY invest in speed to make sure I always outpace the enemy...
Or for RP, which I often do
Ultimately, all beam weapons (expect gauss which has other purposes) have to contend with the fact that lasers are the best generalist beam weapon. Because of their flexibility, lasers can be used in just about any situation, and they do great damage for any extended brawl while still performing adequately at range.
The main constraint is really the research cost. In a situation where you're short on research, it's best to just research lasers and gauss, and with that you can be sure you will have enough to cover at least adequately any situation.