S² Engine
The S² — or Super Solenoid — Engine (S²機関) is an organ located within the cores of Angels which grants them a limitless source of energy. For unknown reasons, Evangelions are not born with S² Engines, and thus can only function without external power cables for about 5 minutes of internal battery power. (This time period can sometimes be extended when an Eva goes berserk, however.)
A mostly-intact S² Engine is obtained from the corpse of Shamshel and sent to Germany for further study by the Third Branch's Energy Analysis Unit. [#05] After the S² Engine is restored, Nerv's Second Branch in Nevada undertakes an experiment to install it into EVA-04, which results in the disappearance of the Eva, related facilities, and everything else within an 89 kilometer radius. Ritsuko suggests, “In all probability, they were swallowed by a Sea of Dirac, just like EVA-01 was” Episode 17, which implies a connection between the Super Solenoid and the Dirac Sea.
Despite the loss of the restored S² Engine, the research data is preserved in Germany. The project continues, ultimately producing nine Mass Production Evangelions outfitted with S² Engines.
A berserk EVA-01 is eventually able to obtain an S² Engine from the Angel Zeruel by physically devouring the organ and assimilating it as her own. According to Seele, this acquisition makes EVA-01 an "absolute being" and the living embodiment of a god.
An intact S² Engine is never seen in the show, although it is known to be double-helical in structure, much like DNA. (Regular solenoids are shaped like spirals.) Why the name "engine" is given to what is inarguably a flesh and blood organ (as seen in #19) is never stated, but it is consistent with the show's tendency to disguise the inherently biological with terms of mechanical connotation. (Incidentally, written with different kanji (器官), "kikan" does mean "organ".) Dr. Katsuragi had intended to create an actual engine based on the principles established with his S² Theory, but this never came to be.
The S² Engine is equated to the Fruit of Life.