# k streamer theory

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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 10-5s 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. 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 (n0 = 1) in a uniform field, corresponds to a value, Streamer or Kanal Mechanism S.Krishnaveni AP/EEE 5 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. 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 xc = dc gives the smallest value of to produce streamer breakdown, where dc is given in cm. For xc = ln 108 , xc works out to be equal to 2cm which can be considered to be critical gap distance, dc, 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 (Ea + Eo ), while above the positive ion region, just behind the head, the field is reduced to a value (E0 - Ea) The condition for transition from avalanche to streamer breakdown assumes that Ea E0. Hence the above breakdown criterion becomes, xc= 17.7 + ln xc The minimum value of xc required for breakdown in a uniform field dc = 17.7 + ln xc 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 E0 produced by the space charge, at the radius r is given by ( )cm Vp xeEx/ 10 27 . 52170oo =S.Krishnaveni AP/EEE 13 Streamer or Kanal Mechanism by Meek To determine minimum break-down voltage, let E0=E and x=d in the above equation ( )||.|

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\| + + = =pddpp Epdd p p Epdd Epdde ETakecm Vp ddeEln21ln 5 . 14 ln lnln21ln ln 5 . 14 ln lnln21ln 5 . 14 lnln21ln ln 5 . 14 lnln/21710 27 . 5ooo oo oooooExperimental 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, (ed -1 ) = 1 or d = ln (1/ + 1) where the coefficients and are functions of E/p and are given as follows: i.e Paschen's Law ||.|

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\|=pEfpEf ppEfp211ooS.Krishnaveni AP/EEE 17 Paschen's Law In a uniform field electrode system of gap distance d, Sub o and in Townsends eqn, ) (1 11 11122pd f V SoepdVfdVE LetepEfpdVpdfpEpdf==(((

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\|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 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. 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, 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. 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 Egap long for cm KV Ecm KVddVEd dVK and Torr AtTpdTpdV/ 30/ 24/08 . 622 . 24293 760760 29308 . 6293 760760 29322 . 24293 76076029308 . 676029322 . 242121==+ = =((

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=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