Breakdown with Streamer Discharge(Streamer or Kanal Mechanism) S.Krishnaveni AP/EEE 1 Streamer or Kanal Mechanism In 1940,Raether and Meek and Loeb proposed the streamer theory against Townsend mechanism. S.Krishnaveni AP/EEE 2 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 -5 s 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 -8 s. 3. Discharges were found to be filamentary and irregular. S.Krishnaveni AP/EEE 3 • 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. Streamer or Kanal Mechanism S.Krishnaveni AP/EEE 4 • 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 (n 0 = 1) in a uniform field, corresponds to a value, • Streamer or Kanal Mechanism S.Krishnaveni AP/EEE 5 • x c is the length of avalanche in the field direction when it amplifies to its critical size. • or words, x c is the critical length of the electrode gap d c . • This means that the streamer mechanism is possible only when d ≥ x c . • If x c is longer than the gap length d (x c > d) then the initiation of streamer is unlikely as shown in Fig. Streamer or Kanal Mechanism Effect of space charge field E a of an avalanche of critical amplification on the applied uniform field. S.Krishnaveni AP/EEE 6 • 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. Streamer or Kanal Mechanism S.Krishnaveni AP/EEE 7 Condition for streamer in air by Raether • x c = d c gives the smallest value of α to produce streamer breakdown, where d c is given in cm. • For α x c = ln 10 8 , x c 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. S.Krishnaveni AP/EEE 8 • 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 E a ≈ E 0 . • Hence the above breakdown criterion becomes, α x c = 17.7 + ln x c • The minimum value of αx c required for breakdown in a uniform field αd c = 17.7 + ln x c ≈ 20 Condition for streamer in air by Raether S.Krishnaveni AP/EEE 9 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 10 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 11 • 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 S.Krishnaveni AP/EEE 12 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 E 0 produced by the space charge, at the radius ‘r’ is given by ( ) cm V p x e E x / 10 27 . 5 2 1 7 0 o o ÷ × = S.Krishnaveni AP/EEE 13 Streamer or Kanal Mechanism by Meek To determine minimum break-down voltage, let E 0 =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 o o o o o o o o o o Experimental values of o/p and E/p are used to solve the equation using trial and error method S.Krishnaveni AP/EEE 14 Paschen's Law The scientist, Paschen, established it experimentally in 1889 from the measurement of breakdown voltage in air, carbon dioxide and hydrogen. S.Krishnaveni AP/EEE 15 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. Conditions to apply Paschen's Law S.Krishnaveni AP/EEE 16 • In uniform fields, the Townsend's criterion for breakdown in electropositive gases is given by the following equation, ¸ (e αd -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 ¸ o o S.Krishnaveni AP/EEE 17 Paschen's Law In a uniform field electrode system of gap distance d, Sub o 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 pdf p E pdf = = ( ( ¸ ( ¸ ÷ | | . | \ | = = ( ( ¸ ( ¸ ÷ | | . | \ | | | . | \ | | | . | \ | S.Krishnaveni AP/EEE 18 Breakdown voltage vs pd characteristics in uniform field Paschen's curve S.Krishnaveni AP/EEE 19 • 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. Paschen's curve S.Krishnaveni AP/EEE 20 • 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. Paschen's curve S.Krishnaveni AP/EEE 21 • 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. Paschen's curve S.Krishnaveni AP/EEE 22 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 Paschen's law S.Krishnaveni AP/EEE 23 Paschen's law pressure atm and temp room at air for cm KV E gap long for cm KV E cm KV d d V E d d V K and Torr At T pd T pd V / 30 / 24 / 08 . 6 22 . 24 293 760 760 293 08 . 6 293 760 760 293 22 . 24 293 760 760 293 08 . 6 760 293 22 . 24 2 1 2 1 = = + = = ( ¸ ( ¸ × × × + ( ¸ ( ¸ × × × = ( ¸ ( ¸ + ( ¸ ( ¸ = Breakdown potential S.Krishnaveni AP/EEE 24 Breakdown voltage characteristics of atmospheric air in uniform fields S.Krishnaveni AP/EEE 25 S.Krishnaveni AP/EEE 26 Streamer or Kanal Mechanism In 1940,Raether and Meek and Loeb proposed the streamer theory against Townsend mechanism. S.Krishnaveni AP/EEE 2 It predicts a very diffused form of discharges. Discharges were found to be filamentary and irregular. 3 S. 3. Depends on gas pressure result of ionization process and gap geometry. Current growth occurs as a 1. only. practically 1. 3.Why Townsend mechanism failed Townsend mechanism But .Krishnaveni AP/EEE . It predicts time lags of the 2. 2. It was observed that time order of 10-5s lags of the order of 10-8s. • The space charge developed by the avalanche itself due to rapid growth of charge carriers. it is the 'eigen space charge' which produces the instability of the avalanche. S. transforms it into a conducting channel.Streamer or Kanal Mechanism • The streamer breakdown mechanism describes the development of spark breakdown directly from a single avalanche.Krishnaveni AP/EEE 4 . • As described by Raether. corresponds to a value. when the number of charge carriers increased to a critical value. • S. the transformation from avalanche to streamer began to develop from the head of an electron avalanche.Krishnaveni AP/EEE 5 .Streamer or Kanal Mechanism • By approximate calculations. • For an avalanche initiated by a single electron (n0 = 1) in a uniform field. Streamer or Kanal Mechanism • xc is the length of avalanche in the field direction when it amplifies to its critical size. • If xc is longer than the gap length d (xc > d) then the initiation of streamer is unlikely as shown in Fig. xc is the critical length of the electrode gap dc.Krishnaveni AP/EEE . S. 6 Effect of space charge field Ea of an avalanche of critical amplification on the applied uniform field. • This means that the streamer mechanism is possible only when d ≥ xc. • or words. • The interaction between the space charges and the polarities of the electrodes results in distortion of the uniform field. S. Raether developed the following empirical formula for the 'streamer breakdown criterion'.Streamer or Kanal Mechanism • On the basis of experimental results and some simple assumptions.Krishnaveni AP/EEE 7 . S. dc.Condition for streamer in air by Raether • xc = dc gives the smallest value of α to produce streamer breakdown. • For α xc = ln 108 . for streamer phenomenon to take place in atmospheric air in uniform field.Krishnaveni AP/EEE 8 . where dc is given in cm. xc works out to be equal to 2cm which can be considered to be critical gap distance. Condition for streamer in air by Raether • Field intensities towards the head and the tail of avalanche acquire a magnitude (Ea + Eo ). α xc= 17.7 + ln xc • The minimum value of αxc required for breakdown in a uniform field αdc = 17. while above the positive ion region.7 + ln xc ≈ 20 S. the field is reduced to a value (E0 . • Hence the above breakdown criterion becomes.Krishnaveni AP/EEE 9 .Ea) • The condition for transition from avalanche to streamer breakdown assumes that Ea ≈ E0. just behind the head. Streamer or Kanal Mechanism 1. and the positive ions in the tail of the avalanche stretch out across the gap 2. it does not constitute a breakdown in the gap.Krishnaveni AP/EEE 10 . The electrons are swept into the anode. S. A highly localized space charge field due to positive ions is produced near the anode but since the ion density elsewhere is low. which are directed towards the stem of the main avalanche 5.Streamer or Kanal Mechanism 3. In the gas surrounding the avalanche. secondary electrons are produced by photons and photo-electric effect from the cathode. The secondary electrons initiate the secondary avalanches. 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 11 . 4. 200 V/cm by Raether . taken in a gap of 3.Krishnaveni AP/EEE 12 .Streamer or Kanal Mechanism • Figure shows the photograph of an avalanche where secondary avalanches are feeding into the primary avalanche. S.6 cm in air at 270 Torr and a field intensity of about 12. 27 10 7 ex x p 2 1 V / cm S. at the radius ‘r’ is given by E0 5.Krishnaveni AP/EEE 13 . The field E0 produced by the space charge.Streamer or Kanal Mechanism by Meek He proposed a simple quantitative criterion to estimate the electric field that transforms an avalanche into streamer. 27 10 7 Take ln ln E 14.5 ln d d 1 ln p 2 ed d p 1 V / cm 2 d 1 ln p 2 d 1 ln p 2 ln E ln p 14. let E0=E and x=d in the above equation E 5.5 ln ln p d ln E ln p 14.Streamer or Kanal Mechanism by Meek To determine minimum break-down voltage.5 ln ln ed ln E 14.Krishnaveni AP/EEE 14 .5 ln p d d 1 ln p 2 Experimental values of /p and E/p are used to solve the equation using trial and error method S. Paschen.Paschen's Law The scientist. established it experimentally in 1889 from the measurement of breakdown voltage in air. carbon dioxide and hydrogen.Krishnaveni AP/EEE 15 . S. 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. S.Conditions to apply Paschen's Law 1.Krishnaveni AP/EEE 16 . At higher pressure 2. Paschen's Law • In uniform fields. (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. the Townsend's criterion for breakdown in electropositive gases is given by the following equation.e 1 p f1 p f2 E p 17 E S.Krishnaveni AP/EEE . Sub and in Townsend’s eqn.Paschen's Law In a uniform field electrode system of gap distance d. E E pdf1 p f 2 e 1 1 p V Let E d V V pdf1 pd e f2 1 1 pd So V f ( pd ) S.Krishnaveni AP/EEE 18 . Krishnaveni AP/EEE 19 .Paschen's curve Breakdown voltage vs pd characteristics in uniform field S. hence a lower voltage suffices to provide electrons the kinetic energy required for ionization by collision to achieve breakdown. 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.Krishnaveni AP/EEE 20 . a lower electric field intensity. S. • As the pressure is decreased.Paschen's curve • To explain the shape of the curve. and • Let the pressure decrease from a point Phigh on the curve at the right of the minimum. • It is convenient to consider a gap with fixed spacing (d = constant). • Since each collision results in loss of energy. Krishnaveni AP/EEE 21 . S. even if the kinetic energy of the electron is more than the energy required for ionization. the density of the gas becomes so low that relatively fewer collisions occur. • Under such conditions.Paschen's curve • When the minimum of the breakdown voltage is reached and the pressure still continues to be decreased. an electron may not necessarily ionize a molecule on colliding with it. an electron has a finite chance of ionizing which depends upon its energy. • In other words. • Under these conditions.Krishnaveni AP/EEE 22 . 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.Paschen's curve • The breakdown can occur only if the probability of ionization becomes greater by increasing the field intensity. Plow . S. • This explains the increase in breakdown voltage to the left of the minimum. • At low pressures. hence this phenomenon is applicable in high voltage vacuum tubes and switchgears. partial vacuum conditions exist. Voltage=f(Nd) where N-density of gas molecules From gas law PV=NRT N=PV/RT where V – volume of the gas R .Paschen's law To account the effect of temperature.Krishnaveni AP/EEE 23 .constant T – Temperature S. 22 KV / cm d d 24 KV / cm for long gap 30 KV / cm for air at room temp and atm pressure 1 S.08 760 293 760 293 V 6.Paschen's law Breakdown potential 293 pd 293 pd V 24.08 760 T 760 T At 760 Torr and 293K V E E E 1 2 293 760 d 293 760 d 2 24.Krishnaveni AP/EEE 24 .08 24.22 6.22 6. Breakdown voltage characteristics of atmospheric air in uniform fields S.Krishnaveni AP/EEE 25 . S.Krishnaveni AP/EEE 26 .