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An Elysian field was a technology, using cryogenetic extraction, that allowed a Time Lord to completely break down their body into its components, i.e. atoms and molecules, and rebuild themselves, editing their personality.
It was capable of regenerating its user, even if they were at the end of their regeneration cycle or were otherwise unable to regenerate. It was also capable of imbuing its user with an entirely new regeneration cycle. Because of the ease at which the technology could be used to cheat permanent death, its use was banned by the Time Lords. Another reason for this was that the use of an Elysian field created a "temporal tourniquet", severing the resurrected Time Lord from their past; the resurrected Time Lord could kill their former self with impunity without fear of causing a paradox. (AUDIO: The Lumiat)
When her previous incarnation shot her, wounding her beyond the ability to regenerate, (TV: The Doctor Falls) Missy used an Elysian field to survive and regenerate, all whilst granting herself a new regeneration cycle. In doing so, Missy chose to remove all her "snide" evil and leave only the kindness, in a final act of breaking the rules, in the hopes of impressing the Doctor. This new incarnation was almost entirely good, but did not retain very many of her memories. Leaving the name the Master behind, she choose to call herself the Lumiat. (AUDIO: The Lumiat)
Behind the scenes
In Greek mythology, the Elysian Fields were the section of the afterlife reserved for the heroic and pure of heart.