This word takes us back to the third century BC, to the Greek philosophy schools of Pyrrhonism, Epicureanism and Stoicism. All of them held, for various reasons, that true happiness (eudaimonia) came from a state in which a person was free from worry or preoccupations and in particular had adopted a tranquil spirit. This state of freedom from passion or disturbance of mind was called ataraxia, stoical impassiveness, a word created from a-, not, and tarassein, to disturb.
In English the word occasionally turns up from the seventeenth century onwards as ataraxy or sometimes ataraxia.
It is lucky for us that President Grevy has such sound teeth. To that fact must be attributed his unchanging calm, his ataraxy, the perfect equilibrium of his physical and intellectual functions, which have made him the most prudent of statesmen and the most constitutional of presidents.
Logansport Journal (Logansport, Indiana), 12 Jun. 1886.
In the middle 1950s it was borrowed to coin ataractic (also written ataraxic), a term for what are more commonly called tranquillisers, whose main aim is to induce calmness without causing confusion of mind. For a while, the term was fashionable in fiction:
It had never proved effective against the psychoses; those had to be attacked pharmacologically, by regulating serotonin metabolism with ataraxics — the carefully tailored chemical grandchildren of the countess’s crude smokes.
A Case of Conscience, by James Blish, 1959.