From The TimeSplitters Wiki

The Plasma Auto Rifle is a futuristic machine gun with a very high rate of fire. In Timesplitters 2, (I don't see why this gun and it's sibling in TS2 are consider two different guns) in shot bright white lazer and shot plasma grenades as secondary fire. In TS3, it shot red skinny lasers ,but lost the plasma grenades (which became a stand alone weapon). Thoughout the series, well at least in TS2 and TS3 it shot lazers at an increasingly speed untill it overheated. After which, it then cools down. Also, in TS3 it has up to 400 shots. It is found in TS3 in these levels: Time to Split, Machine Wars, Something to Crow About, and finally (it's last appearance in TS3's story) The Hooded Man.

Little know fact, it may have appeared in two of TS2 cutscenes and shot regular grenades (as seen in the final cutscene).