Positron Rifle (Prototype 20 with toroidal accelerator) Edit
The positron cannon was used in episode 6 by EVA-01 to defeat the 5th angel Ramiel.
The way NERV got hold of this prototype technology is due to Misato "borrowing" it from JSSDF's R&D labs, where it was known as the SDF's Automated Positron Rifle.
How Does It Work: Edit
Due to our worlds current knowledge of science the Positron Rifle works by colliding a positron (charged electron which a +1 charge) with a normal electron (-1 charge.) When these two collide annihilation occurs and sends out gamma ray photons which in the anime is what we see as the laser beam like ray that exits the gun when it fires. The reason it is made out to be such a hard task for Shinji is because electrons are affected by almost any other particle it collides with, so for example changes in magnetic flux density around them can cause them to change direction could change direction, also because of the Earth curvature gravity will affect it also.
Why Does It Need So Much Power: Edit
The reason this certain operation put Japan into a country wide power outage is because to create a positron we need to shift a normal electron from its native charge, -1, to a positive charge, +1. An approximate amount of power needed to do this is about 1 terra watt.