(coexisting on another dimensional plane)
This page contains information regarding Star Trek: Discovery, and thus may contain spoilers.
The field was apparently a secret from everyone except Marlena Moreau, and to others it seemed that Kirk's enemies had a tendency to "simply disappear." The field was used by Moreau to save the prime Kirk when he was trapped in the mirror universe. Before leaving the ISS Enterprise, the prime Kirk attempted to convince Spock to reform the Terran Empire before it collapsed as a result of its own brutality. When Spock expressed doubts about his ability to survive if he attempted dissent from imperial policy, Kirk revealed the existence of the Tantalus field to him, telling him it would make him invincible. Kirk apparently hoped that Spock could survive long enough to change the Empire for the better. (TOS: "Mirror, Mirror")
In a story planned for an unrealized William Shatner guest appearance on Star Trek: Enterprise, it would have been revealed that the Tantalus field did not kill its victims, but transported them to a different time. In the story, it would have been revealed that, sometime after the events of "Mirror, Mirror", Spock had used the device on Kirk, depositing him on a remote planet in the 2120s, where he would have later been discovered by the crew of the Enterprise NX-01 in the 2150s, shortly before the "mirror universe" was to have diverged from the standard Trek universe as an alternate timeline.
The device was never seen or mentioned in any of the other "mirror" episodes in Star Trek: Deep Space Nine or Star Trek: Enterprise. An identical control-panel device was seen in the background behind Jane Wyatt as Spock's mother Amanda Grayson in "Journey to Babel", and probably not meant to depict the Tantalus Field as seen in "Mirror, Mirror".
In the novel Dark Mirror by Diane Duane, Jean-Luc Picard looks up Spock's history, and finds that he managed, briefly, to become a very powerful and influential figure in the Empire, largely because his enemies had a way of "disappearing" when they became too threatening.
In The Sorrows of Empire, Spock takes possession of the device after he slays Captain Kirk. Spock was able to use it with more frightening efficiency, as he was able to wipe out the entire crew of a Klingon battle cruiser and a Romulan Bird-of-Prey within a year of taking control of it. These incidents – plus the "disappearance" of Uhura for plotting to mutiny against Spock – lead to rumors that Spock is unleashing some previously-unknown Vulcan psionic power. The Tantalus field's power fuels a rapid rise through the imperial ranks that, by 2277, culminates with his becoming Emperor of the Terran Empire. In 2293, after announcing the foundation of a Terran Republic, Spock – knowing the Republic would be short-lived – destroys the device with a phaser to prevent another tyrant from taking possession of it.
A version of the Tantalus field appears in the prime universe in Star Trek Online. A player ship equipped with all four pieces of the "Delta Alliance Assault" set (shield, deflector, impulse engine, and either a singularity core for Romulan ships or a warp core for all others) can deploy a "Prototype Tantalus Field", which immediately destroys any targetable torpedoes (heavy plasma torpedoes for instance), mines, or fighter craft in a radius around the player's ship.