The breakdown voltage is defined by the Paschen equation and graph.
The ionization percentage is defined by the Saha equation (and other mechanisms).
However, the Paschen theory only works up to 1400ºC, as beyond that point, the gas gets ionized, and the breakdown voltage is reduced.
On the other hand, I suppose that the Saha equation provides the percentage of ionization, which should be higher if the plasma is subjected to a high voltage.
Is there a formula that describes the dependence of breakdown voltage on temperature?
Is there a formula that provides the percentage of ionization of plasma subjected to a high DC voltage?
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