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You are indeed wrong to think that electric breakdown does not occur in the
vacuum. It is intuitively plausible but in fact, the breakdown voltage
is smaller for a given vacuum gap than for an air gap. This was a matter of
considerable practical importance when high power radars were carried to
great heights, where they proceeded to misbehave until their waveguides
were pressurized.
Clearly, to the extent that "electric breakdown" requires the presence of
a gas, it simply cannot happen in a vacuum.
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.