Download - k Streamer Theory

Transcript
Page 1: k Streamer Theory

Breakdown with Streamer Discharge (Streamer or Kanal Mechanism)

S.Krishnaveni AP/EEE 1

Page 2: k Streamer Theory

Streamer or Kanal Mechanism

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

S.Krishnaveni AP/EEE 2

Page 3: k Streamer Theory

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

Page 4: k Streamer Theory

• 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

Page 5: k Streamer Theory

• 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

Page 6: k Streamer Theory

• 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

Page 7: k Streamer Theory

• 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

Page 8: k Streamer Theory

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 , 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

Page 9: k Streamer Theory

• 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,

α xc= 17.7 + ln xc

• The minimum value of αxc required for breakdown in a uniform field

αdc = 17.7 + ln xc ≈ 20

Condition for streamer in air by Raether

S.Krishnaveni AP/EEE 9

Page 10: k Streamer Theory

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

Page 11: k Streamer Theory

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

Page 12: k Streamer Theory

• 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

Page 13: k Streamer Theory

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

cmV

px

eE

x

/1027.52

1

7

0

S.Krishnaveni AP/EEE 13

Page 14: k Streamer Theory

Streamer or Kanal Mechanism by Meek

To determine minimum break-down voltage, let E0=E and x=d in the above equation

p

dd

ppE

p

ddppE

p

ddE

p

ddeE

Take

cmV

pd

deE

ln2

1ln5.14lnln

ln2

1lnln5.14lnln

ln2

1ln5.14ln

ln2

1lnln5.14ln

ln

/

21

71027.5

Experimental values of /p and E/p are used to solve the equation using trial and error method

S.Krishnaveni AP/EEE 14

Page 15: k Streamer Theory

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

Page 16: k Streamer Theory

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

Page 17: k Streamer Theory

• 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

Ef

p

Efp

p

Ef

p

2

1

1

S.Krishnaveni AP/EEE 17

Page 18: k Streamer Theory

Paschen's Law

In a uniform field electrode system of gap distance d,

Sub and in Townsend’s eqn,

)(

11

11

1

1

2

2

pdfVSo

epd

Vf

d

VELet

ep

Ef

pd

Vpdf

p

Epdf

S.Krishnaveni AP/EEE 18

Page 19: k Streamer Theory

Breakdown voltage vs pd characteristics in uniform field

Paschen's curve

S.Krishnaveni AP/EEE 19

Page 20: k Streamer Theory

• 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

Page 21: k Streamer Theory

• 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

Page 22: k Streamer Theory

• 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

Page 23: k Streamer Theory

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

Page 24: k Streamer Theory

Paschen's law

pressureatmandtemproomatairforcmKVE

gaplongforcmKVE

cmKVdd

VE

ddV

KandTorrAt

T

pd

T

pdV

/30

/24

/08.6

22.24

293760

76029308.6

293760

76029322.24

293760

760

29308.6

760

29322.24

21

21

Breakdown potential

S.Krishnaveni AP/EEE 24

Page 25: k Streamer Theory

Breakdown voltage characteristics of atmospheric air in uniform fields

S.Krishnaveni AP/EEE 25

Page 26: k Streamer Theory

S.Krishnaveni AP/EEE 26


Top Related