Breakdown with Streamer Discharge
Breakdown with Streamer Discharge
(Streamer
Streamer
Streamer or
or Kanal
Kanal Mechanis
Mechanism
m
In 1940,Raether and Meek and Loeb proposed the In 1940,Raether and Meek and Loeb proposed the streamer theory against Townsend mechanism.
Why Townsend mechanism failed
Townsend mechanism
1. Current growth occurs as a result of ionization process only.
2. It predicts time lags of the order of 10-5s
3. It predicts a very diffused form of discharges.
But , practically
1. Depends on gas pressure and gap geometry.
2. It was observed that time lags of the order of 10-8s.
3. Discharges were found to be filamentary and irregular.
• The streamer breakdown mechanism describes the
development of spark breakdown directly from a single avalanche.
• The space charge developed by the avalanche itself due to
rapid growth of charge carriers, transforms it into a conducting channel.
• As described by Raether, it is the 'eigen space charge' which
produces the instability of the avalanche.
• By approximate calculations, the transformation from
avalanche to streamer began to develop from the head of an electron avalanche, when the number of charge carriers
increased to a critical value,
• For an avalanche initiated by a single electron (n0 = 1) in a
uniform field, corresponds to a value,
•
• xc is the length of avalanche in
the field direction when it amplifies to its critical size.
• or words, xc is the critical
length of the electrode gap dc.
• This means that the streamer
mechanism is possible only when d ≥ xc.
• If xc is longer than the gap
length d (xc > d) then the
initiation of streamer is unlikely as shown in Fig.
Streamer or Kanal Mechanism
Effect of space charge field Ea of an avalanche of critical amplification on the applied uniform field.
• On the basis of experimental results and some simple
assumptions, Raether developed the following empirical
formula for the 'streamer breakdown criterion'.
• The interaction between the space charges and the polarities
of the electrodes results in distortion of the uniform field.
Condition for streamer in air by
Raether• xc = dc gives the smallest value of α to produce streamer
breakdown, where dc is given in cm.
• For α xc= ln 108 , xcworks out to be equal to 2cm which can be
considered to be critical gap distance, dc, for streamer
• Field intensities towards the head and the tail of avalanche
acquire a magnitude (E a + E o ), while above the positive ion region, just behind the head, the field is reduced to a value
(E 0 - E a )
• The condition for transition from avalanche to streamer
breakdown assumes that Ea ≈ E0.
• Hence the above breakdown criterion becomes, α xc= 17.7 + ln xc
• The minimum value of αxc required for breakdown in a uniform
field
αdc = 17.7 + ln xc ≈ 20
Streamer or Kanal Mechanism
1. The electrons are swept into the anode, and the positive ions in the tail of the avalanche stretch out across the gap
2. A highly localized space charge field due to positive ions is
produced near the anode but since the ion density elsewhere is low, it does not constitute a breakdown in the gap.
Streamer or Kanal Mechanism
3. In the gas surrounding the avalanche, secondary electrons are produced by photons and photo-electric effect from the cathode.
4. The secondary electrons initiate the secondary avalanches, which are directed towards the stem of the main avalanche 5. The positive ions left behind by the secondary avalanches
effectively lengthen and intensify the space charge of the main avalanche in the direction of the cathode and the process develops a self propagating streamer breakdown
• Figure shows the photograph of an
avalanche where secondary avalanches are feeding into the primary avalanche, taken in a gap of 3.6 cm in air at 270 Torr and a field intensity of about 12,200 V/cm by
Raether .
Streamer or Kanal Mechanism by Meek
He proposed a simple quantitative criterion to estimate the electric field that transforms an avalanche into
streamer.
The field E0 produced by the space charge, at the radius
‘r’ is given by
x p
V cm e E x / 10 27 . 5 2 1 7 0 Streamer or Kanal Mechanism by Meek
To determine minimum break-down voltage, let E0=E and x=d in the above equation
p d d p p E p d d p p E p d d E p d d e E Take cm V p d d e E ln 2 1 ln 5 . 14 ln ln ln 2 1 ln ln 5 . 14 ln ln ln 2 1 ln 5 . 14 ln ln 2 1 ln ln 5 . 14 ln ln / 2 1 7 10 27 . 5
Experimental values of /p and E/p are used to solve the equation
using trial and error method
Paschen's Law
The scientist, Paschen, established it experimentally in 1889 from the measurement of breakdown voltage in air, carbon dioxide and hydrogen.
1. At higher pressure
2. Gaps of more than several mm
Breakdown characteristics is non linear.
It is a function of the product of the gas pressure and gap length.
• In uniform fields, the Townsend's criterion for breakdown in
electropositive gases is given by the following equation,
(eαd -1 ) = 1
or
αd = ln (1/ + 1)
• where the coefficients α and γ are functions of E/p and are
given as follows: i.e
Paschen's Law
p E f p E f p p E f p 2 1 1 Paschen's Law
In a uniform field electrode system of gap distance d, Sub and in Townsend’s eqn,
) ( 1 1 1 1 1 1 2 2 pd f V So e pd V f d V E Let e p E f pd V pd f p E pd f
Breakdown voltage vs pd characteristics in uniform field
• To explain the shape of the curve,
• It is convenient to consider a gap with fixed spacing
(d = constant), and
• Let the pressure decrease from a point Phigh 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, Plow , 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.
To account the effect of temperature,
Voltage=f(Nd) where N-density of gas molecules From gas law PV=NRT
N=PV/RT where V – volume of the gas R - constant
T – Temperature
