Why vacuum and high-pressure gas are stronger

By Paschen's law the breakdown voltage of a gas gap depends on the product $pd$ (pressure × gap). Air at normal pressure with usual gaps (1 cm gives $pd = 760$ torr·cm) lies on the right-hand rising branch of the Paschen curve, far from the minimum at about 0.57 torr·cm, and has a moderate strength of about 30 kV/cm. Raising the pressure moves the gap further up this branch, so $V_b$ increases. Reducing the pressure towards vacuum moves $pd$ far to the left of the minimum, where $V_b$ rises very steeply; in high vacuum, collision ionization stops altogether. So both vacuum and high-pressure gas are stronger than air at normal pressure.

Vacuum (low pressure)

• Very few gas molecules: the electron mean free path is longer than the gap.
• An electron crosses the gap with almost no collisions, so collision ionization ($\alpha$) cannot build an avalanche.
• Breakdown can occur only by electrode processes (field emission, particle exchange, clumps), which need very high fields: about $10^5$–$10^6$ V/cm for short gaps.

High-pressure gas

• Molecules are packed closely: the mean free path $\lambda$ is very short.
• Energy gained between collisions, $eE\lambda$, is small, so most collisions are non-ionizing.
• A much larger field is needed for ionization, so $V_b$ rises almost linearly with pressure (basis of SF₆ at 3–6 bar in GIS).