Paschen, in 1889, studied the breakdown physics of gases in planar gap regions [13]. The
result of Paschen showed that breakdown process is a function of the product of the gas
pressure and the distance between the electrodes. Paschen showed that
pd d
l
where p is the pressure, d is the distance between the plates and l is the mean free path of the
electrons. From the work of Paschen, a universal curve was established which followed
the same characteristics independent on the gas in the gap. The Paschen curve is a plot of the
logarithm of the breakdown voltage, VBD, as a function of the logarithm of the product of the
pressure and gap distance,
VBD ¼ f pd ð Þ
At very low values of the p-d product, electrons must accelerate beyond the ionization
limit to produce an avalanche process because the likelihood of impacts is too few. In this
region, the breakdown voltage decreases with increasing value of the pressure-gap product.
This occurs until a minimum condition is reached. At very high values of the pressure-gap
product, the number of inelastic collisions is higher and the breakdown voltage increases.
This U-shaped dependence is characteristic of gas phenomenon. At the high gas pressure,
secondary processes, such as light emissions occur. Figure 1.3 shows the Paschen curve highlighting
its U-shaped characteristic.