Townsend’s Criterion for Breakdown
- Equation I = I0 ead
/ I – γ (ead – 1) gives the total average current in a gap before the occurrence of breakdown. As distance between electrodes d is increased, the denominator of the equation tends to zero, and at some critical distance
d = ds
1 – γ (exp (αd) – 1)
= 0
- For values of d < ds, I is approximately equal to I0 and if the external source for the supply of I0 is removed, I becomes zero.
- If d = ds, I → ∞ and current will be limited only by the resistance of the power supply and the external circuit. This condition is called Townsend’s breakdown criterion and can be written as y (exp (αd) – 1) = 1
- Normally, exp (αd) is very large, and hence the above equation reduces to γ exp (αd) = 1.
- For a given gap spacing and at a given pressure the value of the voltage V which gives the values of α and y satisfying the breakdown criterion is called the “Spark breakdown voltage (Vs)” and the corresponding distance is called the “Sparking distance (ds )”. Thus, the Towsend’s mechanism explains the phenomenon of breakdown only at low pressures i.e. corresponding to p x d (gap pressure x gap distance) values of 1000 Torr.cm and below.
Limitations or Drawbacks of Townsend’s Theory of Breakdown
- Townsend stated that breakdown is due to current growth and current growth is due to primary and secondary ionization (α and γ) But in practice, breakdown is also dependent on gas pressure (P) and gap distance (d) [breakdown voltage = f ( p x d) as per Paschens law].
- This mechanism predicts time lag is of the order of 10-5 sec while actual breakdown occurs in very short time i.e. 10-8 sec.
- Townsend predicted diffused and regular form of discharge while actual discharge is irregular and filamentary.
Remedies
As Townsend failed to explain all these observed phenomenon, around 1940 Raether, Meek and Loeb proposed a theory called as Streamer theory.