|“||Well, this massive-recoiling fella did hit me big time. It doesn't seem I can use it as I please.||”|
–Bando, acknowledging one of the few drawbacks of the Desert Eagle
In real life
The Desert Eagle originated from Bernard C. White of Magnum Research, who filed a US patent application for a mechanism for a gas-actuated pistol in January 1983. This design established the basic layout of the Desert Eagle. A second patent application was filed in December 1985, after the basic design had been refined by IMI (Israel Military Industries) for production, and this is the form that went into production.
The Desert Eagle uses a gas-operated mechanism typically found in rifles, as opposed to the short recoil or blowback designs most commonly seen in semi-automatic pistols. When the gun fires a round, gases are ported out through a small hole in the barrel near the breech. These travel forward through a small tube under the barrel, to a cylinder near the front of the barrel. The separate bolt carrier/slide has a small piston on the front that fits into this cylinder; when the gases reach it, they push the piston rearward. The bolt carrier rides backwards on two rails on either side of the barrel, operating the mechanism.
All in all, it makes for a deadly and powerful weapon. Many other fictional characters, including Resident Evil's Leon Kennedy, take advantage of this now-iconic handgun. While in fact, this weapon is impractical in many of the fictional situations it's presented in, its capability of handling heavier rounds proves perfect for Bando's plans of revenge. His model appears to be a Mark VII, or at least a model well before the Mark XIX.
In the series
Over the course of Elfen Lied, the weapon becomes Bando's trademark weapon when fighting. His version is a modified .50AE Desert Eagle that fires Tungsten bullets, which are too heavy, and too powerful for an average Diclonius to block or deflect. Later on in the Manga, the Agent would use one too, alongside the Unknown Man's Crossbow.
The Desert Eagle has a sadly memorable moment when it is employed by Kouta at the conclusion of the series when he is forced to use it to kill the dying Lucy. As best as can be discerned, it comes off the body of a soldier murdered in the last fight with Lucy's body, possessed at that point only by the DNA Voice.