k Streamer Theory

Breakdown with Streamer Discharge (Streamer or Kanal Mechanism)

S.Krishnaveni S.Krishnave ni AP/EEE

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Streamer or Kanal Mechanism Mechanis m

In 1940,Raether and Meek and Loeb proposed the streamer theory against Townsend mechanism.

S.Krishnaveni S.Krishnave ni AP/EEE

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Why Townsend mechanism failed Townsend mechanism

But , practically

1. Current growth occurs as a 1. Depends on gas pressure result of ionization process and gap geometry. only. 2. It predicts time lags of the order of 10-5s 3.

It predicts a very diffused form of discharges.

2. It was observed that time lags of the order of 10-8s. 3. Discharges were found to be filamentary and irregular.

S.Krishnaveni AP/EEE

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Streamer or Kanal Mechanism •

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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.

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Streamer or Kanal Mechanism •

•

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,

•

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Streamer or Kanal Mechanism •

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Effect of space charge field Ea of an avalanche of critical amplification on the applied uniform field.

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 d c. 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.

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Streamer or Kanal Mechanism •

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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.

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Condition for streamer in air by Raether  •

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xc = dc gives the smallest value of α to produce streamer breakdown, where dc is given in cm.

For α xc = ln 108 , xc works out to be equal to 2cm which can be considered to be critical gap distance, d c, for streamer phenomenon to take place in atmospheric air in uniform field.

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Condition for streamer in air by Raether  •

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 )

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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

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The minimum value of αxc required for breakdown in a uniform field αdc = 17.7 + ln xc

≈ 20

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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. S.Krishnaveni AP/EEE

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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 S.Krishnaveni AP/EEE

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Streamer or Kanal Mechanism •

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 .

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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  E 0



5.27  10



7

e

 

 x

 

 x  p 

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V  / cm

1 2

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Streamer or Kanal Mechanism by Meek To determine minimum break-down voltage, let E 0=E and x=d in the above equation

  E   5.27  10

7



  

d  Take

e  d   p 

V   /  cm

1 2

ln

 14.5 

ln   



ln  E  

 14.5 

ln   

   d  

ln

  d      2    p     d    ln   p       1

d  e   

ln  E  

ln  E   ln

 p   14.5 

ln   

ln  E   ln

 p   14.5 

ln

  

 p

1 2



ln

ln 

 p    d  

   d  

1 2

1 2

  d       p    

ln 

  d         p  

ln 

Experimental values of /p and E/p are used to solve the equation using trial and error method S.Krishnaveni AP/EEE

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Paschen's Law

The scientist, Paschen, established it experimentally in 1889 from the measurement of breakdown voltage in air, carbon dioxide and hydrogen.

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Conditions to apply Paschen's Law 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.

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Paschen's Law •

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:    E       f      p    p    

 

i.e

1

   E      p    f      p          E           f      p      

 

1

2

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Paschen's Law In a uniform field electrode system of gap distance d, Sub   and   in Townsend’s eqn,   E      E     pd f      p     f  2   1  1   p  e        1

 Let   E  

V  d 

  V       V      pd f      pd       f  2   1  1   pd   e        So V     f  ( pd ) 1

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Paschen's curve Breakdown voltage vs pd characteristics in uniform field

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Paschen's curve • •

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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 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.

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Paschen's curve •

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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.

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Paschen's curve •

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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. S.Krishnaveni AP/EEE

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Paschen's law 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

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Paschen's law

Breakdown potential  293 pd    293 pd   V   24.22   6 . 08   760 T    760 T      At 760 Torr  and 

1 2

293K 

 293  760  d    293  760  d   V   24.22   6 . 08   760  293   760  293     E    E  

V 

 24.22 

d  24 KV  /  cm

6.08

d 

1 2

KV  /  cm

 for long gap

 E   30 KV  /  cm  for  air  at  room temp and  atm  pressure

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Breakdown voltage characteristics of  atmospheric air in uniform fields

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