• To explain the shape of the curve in last slide, it is convenient to consider a gap with fixed spacing (d = constant), and let the pressure decrease from a point P_high on the curve at the right of the minimum. As the pressure is decreased, the density of the gas decreases, consequently the probability of an electron making collisions with the molecules goes down as it travels towards the anode. Since each collision results in loss of energy, a lower electric field intensity, hence a lower voltage suffices to provide electrons the kinetic energy required for ionization by collision to achieve breakdown.
• When the minimum of the breakdown voltage is reached and the pressure still continues to be decreased, the density of the gas becomes so low that relatively fewer collisions occur. Under such conditions, an electron may not necessarily ionize a molecule on colliding with it, even if the kinetic energy of the electron is more than the energy required for ionization. In other words, an electron has a finite chance of ionizing which depends upon its energy. The breakdown can occur only if the probability of ionization becomes greater by increasing the field intensity. This explains the increase in breakdown voltage to the left of the minimum. At low pressures, P_low , partial vacuum conditions exist, hence this phenomenon is applicable in high voltage vacuum tubes and switchgears. Under these conditions, the effect of electrode material surface roughness plays an important role on the breakdown voltage especially at small gap distances and the Paschen's law is no more valid to the left of the minimum of this curve.

With the help of many scientists, Schumann, Sohst and Schröeder, the following equation for breakdown voltage of air in uniform field was derived.

where p is given in bar and d in cm, therefore pd in bar.cm

• Calculated values of breakdown voltages using Equation 10.3 for uniform field in air have been compared with the available experimental results from different authors by Dakin et al. [2.15] as shown in Fig. 10.2. The peak values of the breakdown voltages in kV and pd in bar. mm are plotted on a double logarithmic scale paper. As seen in this figure, the calculated and the measured results agree with each other well, except for the very low values of pd. In this region where the Elp values are quite high due to low pressures, the equation 10.3 no longer holds good and the Paschens law is no more valid. In this region or in the pressure range of ≤ 25Torr till upto 10^-3 Torr, the phenomenon of Faraday Glow occurs. The air acquires a plasma state on applying quite low voltages depending upon the actual pressure.