A Particle Phalanx is a lighter version of a Particle Beam mounting, with a dedicated linear accelerator feeding it, permanently set to fire a stream of antineutrons; and used as a point-defense system against starfighters or incoming projectile fire.
Due to the size of the particle accelerators, Particle Phalanxes can only mounted on warships destroyer-sized (about half a kilometer long) or larger. Smaller warships (corvettes, frigates, etc.) use light Plama Cannon instead, and these are called Plasma Phalanxes.
Behind the Scenes
There is a scene in the movie Aliens where Hudson is boasting of the Colonial Marine platoon's firepower, and he mentions an "Independently targeting particle beam phalanx." Bax originally intended this to be a much heavier weapons system, but that got retconned and replaced with the heavy version of the Particle Beam cannon, and the term Particle Phalanx got relegated to a point-defense system based on its similarity in name with the real world Vulcan Phalanx Close-in Weapons System.