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The real story has to do with ions. Once the air is ionized, the ions stay
in the vicinity for many milliseconds before they recombine. If there is a
field, the ions carry a current. The moving ions undergo violent
collisions with air molecules, which produces more ions, so the arc can
sustain itself under a wide range of conditions. Under a fairly-wide
subset of these conditions, if you manage to extinguish the arc, it will
stay extinguished.
These phenomena have very great practical importance, because every switch
and every circuit breaker must deal with this. It does not suffice to move
the contacts apart; the hard part is to extinguish the arc. ... I am
fascinated by the tricks they use to switch the really high-power circuits at
power plants and substations.
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