1. Prepared By:- Nisarg Amin
Topic:- Streamer Theory

2. STREAMER THEORY

3. STREAMER THEORY
 Streamer theory breakdown mainly arises due to the added effect of the space-
charge field of an avalanche and photo-electric ionization in the gas volume.
Streamer theory overcomes the drawbacks of Townsend’s theory which are
mentioned below:
a) According to the Townsend theory, current growth occurs as a result of
ionization process only. But in practice, breakdown voltages were found to
depend on the gas pressure and the geometry of the gap.
b) The mechanism predicts time lags ( the time that elapses between the application
of the voltage to a gap sufficient to cause breakdown of the order of 10^6 s,
while in actual practice breakdown was observed to occur at very short time of
the order of 10^8 s.
c) While the Townsend mechanism predicts a very diffused form of discharge, in
actual practice, discharge were found to be filamentary and irregular.

4.  Due to Townsend mechanism failed to explain all these observed
phenomena.
 In 1940, Rather, Meek and Loeb proposed the Streamer theory.
 The streamer mechanism breakdown mainly arises due to the added
effect of the space-charge field of an avalanche and pho-electric
ionization in the gas volume.
 Streamer theory predicts the development of a spark discharge directly
from a single avalanche.
 The space charge produced in the avalanche causes sufficient distortion
of the electric field that those free electrons move towards the
avalanche head and in so doing generate further avalanches in a
process that rapidly becomes cumulative.

6.  As the electrons advance rapidly, the positive ions are left behind in a
relatively slow-moving tail.
 The field will be enhanced in front of the head. Behind the head the
field between the electrons and the positive ions is in the opposite
direction to applied field and hence the resultant field strength is less.
 Again between the tail and the cathode the field is enhanced.

7. ANODE
CATHODE
STREAMER BREAKDOWN

8.  Due to enhanced field between the head and the anode, the space
charge increase and causing a further enhancement of the field
around the anode.
 The process is very fast and the positive space charge extends to the
cathode very rapidly resulting in the formation of a steamer as shown
in Figure 1.8.

9.  Meek proposed a simple quantitative criterion to estimate the
electric field that transform an avalanche into streamer.
 The field Er produced by the space charge, at the radius r, is given by
Er = 5.27 x 10^-7
∝exp(∝𝑥)
𝑥/𝑝1/2 V/cm
 Where ∝ is Townsend first coefficient, p is the gas pressure in torr
and x is the distance to which the streamer has extended in the gap.

10.  According to Meek, the minimum breakdown voltage is obtained
when Er = E and x = d in the above equation.
 The equation simplifies into,
∝ 𝑑 + ln
∝
𝑝
= 14.5 + ln
𝐸
𝑃
+
1
2
ln
𝑑
𝑝