Usually you cannot find a Beam Rifle in Campaign mode. Start the mission, get in the Warthog, and wait for the marine to open the door. Once he opens the door, drive out of the cave. When you are out, listen very carefully to the Marines. When a marine says "Snipers", get out of the Warthog and kill the Jackals close to a flying platform (the purple ones lifted with a big grav lift which has turrets on it). Both of those Jackals have Beam Rifles.