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Clearly, to the extent that "electric breakdown" requires the presence of
a gas, it simply cannot happen in a vacuum.
To which brian wrote:
1) provide two adjacent point electrodes of "molecular"
sharpness.
2) Increase the electric field between the points,
taking care that the vacuum is maintained at the highest
obtainable levels by positioning in space or by means of
getters.
3) High field emission of electrons will soon create a
plasma discharge at a vacuum so high that it passes
Ludwik's standard of idealisation.
Of course you are right, but I wouldn't like to confuse field emission
with the more common phenomenon of "electric breakdown." I was responding
only to the clear and incorrect implication in your statement (quoted
above) that the kind of electrical discharges that are often observed in
moderately low pressure situations are somehow to be associated with "the
vacuum." Your statement that "the breakdown voltage is smaller for a
given vacuum gap than for an air gap," is simply not true in general even
*if* you expand the definition of "electric breakdown" to include field
emission.
John