2. CONDUCTION and BREAKDOWN IN GASES
2.1 Gases as Insulating Media
The most common dielectrics are gases. Many electrical apparatus use air as the insulating medium, in a few cases other gases such as N, CO, CClF (freon) and SF (hexafluoride) are used. 22226
Various phenomena occur in gaseous dielectrics when a voltage is applied.
-When low voltage is applied, small current flow between the electrodes and the insulation retains its electrical properties.
-If the applied voltage is large, the current flowing through the insulation increases very sharply and an electrical breakdown occur. A strongly conducting spark formed during breakdown, practically produces a short circuit between the electrodes. The maximum voltage applied to the insulation at the moment of breakdown is called the breakdown voltage.
In order to understand the breakdown phenomenon in gases, the electrical properties of gases should be studied. The processes by which high currents are produced in gases is essential. The electrical discharges in gases are of two types;
i) non-sustaining discharges
ii) self-sustaining types.
The breakdown in a gas (spark breakdown) is the transition of a non-sustaining discharges into a self-sustaining discharge. The build up of high currents in a breakdown is due to the ionization in which electrons and ions are created from neutral atoms or molecules, and their migration to the anode and cathode respectively leads to high currents. Townsend theory and Streamer theory are the present two types of theories which explain the mechanism of breakdown under different conditions as pressure, temperature, electrode field configuration, nature of electrode surfaces and availability of initial conducting particles.
2.2 Ionization Process
Consider a simple electrode arrangement as shown in the fig 2.1, having two parallel plate electrodes separated by a distance d and immersed in a gas at pressure p. A uniform E is applied between two electrodes. Due to
any external radiation (ultra violet illumination) free electrons are liberated at the cathode. When an electron, e
is placed in an E it will be accelerated with a force eE towards the anode, and it gains an energy
12u！eEx！mv (eqn. 2.1) where x is the distance traveled by the electron from the cathode, m is the mass 2
and v is the velocity of the electron.
This electron collides with the other gas molecules while it is traveling towards the anode. If the energy of the electron is sufficiently large (about 12.2 eV for N or 15.5 eV for O), on collision it will cause a break-up of the 22
atom or molecule into positive ion and electron, so the new electrons and positive ions are created. Thus created electrons form a group or an avalanche and reach the anode. This is the electric current and if it is sufficiently large it results in the formation of a conducting path between the electrodes resulting in the breakdown of the gap.
Townsend conducted experiments on the growth of these currents which led to breakdown under d.c. voltage conditions, and he proposed a theory to explain the phenomenon.
_ + I0
R Current limiting d resistor
_ _ + A
Adjustable HV source
Fig. 2.1 Arrangement for study of a Townsend discharge
2.3 Townsend’s Current Growth Equation
Assuming n electrons are emitted from the cathode and when one electron collides with a neutral particle, a 0
positive atom and electron formed. This is called an ionization collision. Let be the average number of (
ionizing collisions made by an electron per centimeter travel in the direction of the field where it depends on gas pressure p and E/p, and is called the Townsend’s first ionization coefficient. At any distance x from the cathode
when the number of electrons, n , travel a distance of dx they give rise to () electrons. Then, the number (ndxxx
of electrons reaching the anode at x=d, n will be (eqn. 2.2) n！nd0xx！0
dn(xxor (eqn. 2.3) and n！ne！(n0xxdx(x (eqn. 2.4) at x=d. n！ne0d
nn？(d0dThe number of new electrons created, on the average, by each electron is (eqn. 2.5). e1？！n0
Therefore the average current in the gap, which is equal to the number of electrons traveling per second will be
(d (eqn. 2.6) where I is the initial current at the cathode. I！Ie00
2.4 Current Growth in the Presence of Secondary Processes
When the initial set of electrons reaches the anode the single avalanche process is completed. Since the
(damplification of electrons is occurring in the field, the probability of additional new electrons being liberated e
by other mechanisms increases, and created further avalanches and are called as secondary electrons. The other mechanisms are
i) The positive ions liberated may have sufficient energy to cause liberation of electrons from the cathode when they impinge on it.
ii) The exited atoms or molecules in avalanches may emit photons, and this will lead to the emission od electrons due to photo-emission.
iii) the metastable particles may diffuse back causing electron emission.
Defining the Townsend’s secondary ionization coefficient in the same way as, then the net number of ；(
secondary electrons produced per incident positive ion, photon, excited particle or metastable particle and the total value of due to the three different processes is and is function of gas pressure p and E/p. ；！；？；？；；123
Following Townsend’s procedure for current growth, let us assume
' number of secondary electrons produced due to secondary processes. ；n！0
''Let total number of electrons leaving the cathode. n！0
'''Then (eqn. 2.7) n！n？n000
the total number of electrons n reaching to the anode becomes,
''(d'(d'' and n！；[n？(n？n)]n！ne！(n？n)e000000((ddneIe'00Eliminating , or (eqn. 2.8) n！I！n0dd((1？；(e？1)1？；(e？1)
2.5 Townsend’s Criterion for Breakdown
Eqn. 2.8 give the total average current in a gap before the occurrence of breakdown. As the distance between the electrodes d is increased the denominator of equation tend to zero and at some critical distance d=d s(d (eqn. 2.9) 1？；(e？1)！0
For values of d<d, is approximately equal to and if the external source for the supply of is removed, IIIIs00
becomes zero. If d=d and the current will be limited only by the resistance of power supply and the I?；s,(dexternal circuit. This condition is called Townsend’s Breakdown Criterion and can be written as. ；(e？1)！1
(dNormally, is very large, and hence the above equation reduces to e
(d (eqn. 2.10) ；e！1
For a given gap spacing and at a given pressure the value of voltage V which gives the values of and ；(
satisfying the breakdown criterion is called the spark breakdown voltage V, and the corresponding distance d is
called the sparking distance.
Townsend Mechanism explains the phenomena of breakdown only at low pressures, corresponding to p?d
values of 1000 torr-cm and below.
2.6 Breakdown in Electronegative Gases
One process that gives high breakdown strength to a gas is the electron attachment in which free electrons get attached to a neutral atoms or molecules to form negative ions.
Since negative ions like positive ions are too massive to produce ionization due to collisions, attachment represents an effective way of removing electrons which otherwise would have led to current growth and breakdown at low voltages. The gases in which attachment plays an active role are called electronegative gases. Two types of attachment are encountered in gases as;
a) Direct attachment: An electron directly attaches to form a negative ion.
b) Dissociative attachment: The gas molecules split into their constituent atoms and the electronegative atom forms a negative ion.
A simple gas for this type is the oxygen and others are sulphur hexafluoride, Freon, carbon dioxide and fluorocarbons. In these gases, ‘A’ is usually sulphur or carbon atom and ‘B’ is oxygen atom or one of the halogen atoms or molecules.
The Townsend current growth equation is modified to include ionization and attachment with such gases. The current reaching the anode, can be written as,
(，)?)?(，(？)d is the number of attaching collisions where ，？e????(，(，？？，?，?made by one electron drifting one centimeter in (2.11) ！II0the direction of the field( )?((？，)d；1？e？1??(，？，?
The Townsend breakdown criterion for attaching gases can also be deduced from the denominator as,
()?((？，)d；. When , breakdown is always possible irrespective of the values of . (,，and；(，，1？e？1！0??(，？，?
(，；(If then an asymptotic form is approached with increasing value of, or！ ！1(，，d(，1？；？
？4Normally is very small and the above equation can be written. This condition puts a limit for ;；；：10(！，
E below which no breakdown is possible irrespective of the value of , and the limit value is called the dp
-1-1-1-1Ecritical. For SF it is 117 Vcmtorr, for CClF 121 Vcmtorr both at 20?C. values can also ，622p
2.7 Time Lags for Breakdown
Theoretically the mechanism of spark breakdown is considered as a function of ionization processes under uniform field conditions. In practical engineering designs, the breakdown due to rapidly changing voltages or impulse voltages is of great importance. Actually there is a time difference between the application of a voltage sufficient to cause breakdown and the occurrence of breakdown itself. This time difference is called as the time lag.
The Townsend criterion for breakdown is satisfied only if at least one electron is present in the gap between the electrodes as in the case of applied d.c. or slowly varying (50 Hz a.c.) voltages. With rapidly varying voltages of -6short duration (?10s), the initiatory electron may not be present in the gap that the breakdown can not occur.
2.8 Streamer Theory of Breakdown in Gases
According to the Townsend theory;
- firstly, current growth occurs as a result of ionization process only. But in practice, breakdown voltages
were found to depend on the gas pressure and the geometry of the gap; -5 - secondly, the mechanism predicts time lags of order of 10s, but practically it was observed to occur at -8a very short time of 10 s.
- Also the Townsend mechanism predicts a very diffused form of discharge, that actually discharges were
found to be filamentary and irregular.
Townsend mechanism failed to explain all these observed phenomena and as a result The Streamer theory was proposed.
The theory predicts the development of a spark discharge directly from a single avalanche in which the space
charge develop by the avalanche itself is said to transform the avalanche into a plasma steamer. In the fig 2.2, a
single electron starting at the cathode by ionization builds
up an avalanche that crosses the gap. The electrons in the
avalanche move very fast compared with the positive ions. + anode By the time the electrons reach the anode the positive ions
are in their original positions and form a positive space
>E Echarge at the anode. This enhances the field, and the 1
secondary avalanches are formed from a few electrons
produced due to the photo-ionization in the space charge - region. This occurs first near the anode where the space
charge is maximum and a further increase in the space E + charge. This process is very fast and the positive space
E>E charge extends to the cathode very rapidly resulting in the 3
formation of a streamer. Comparatively narrow luminous
tracks occurring at breakdown at pressures are called
streamers. As soon as the streamer tip approaches to the
cathode, a cathode spot is formed and a stream of
electrons rush from the cathode to neutralize the positive
- cathode space charge in the streamer; the result is a spark and the
spark breakdown has occurred. Fig.2.2 Effect of space charge produced by an
A simple quantitative criterion to estimate the electric field avalanche on the applied electric field
which is produced by the space charge, at the radius r Er
and that transforms an avalanche into streamer is given by
(xeV(？7E where is the Townsend’s first ionization coefficient, is the gas pressure in torr ！5.27?10p(rcmxp
and is the distance to which the streamer has extended in the gap. When and the equation E！Exx！dr
above simplifies into;
dE((Ed？ln！14.5？ln？0.5ln. This equation is solved between at which a given andp(ppppp
and satisfy the equation. The breakdown voltage is given by the corresponding product . dEd
It is generally assumed that forvalues below 1000 torr-cm and gas pressures varying from 0.01 to 300 torr, pd
The Townsend mechanism operates, while at higher pressures and values the streamer mechanism plays pd
the dominant role in explaining the breakdown phenomena. However controversies still exist n these statements.
2.9 Paschen’s Law
(dEThe breakdown criterion (2.9) where and are functions of, i.e. 1？；(e？1)！0；(p
????V(EE and . Also . ！f；！fE！?：?：12pdpp(，(，
Substituting for E in the expressions and and rewriting equation (2.9) we have ；(
Vpdf()1)?pd??Vfe？1！1. This equation shows a relationship between V and pd, and implies that the ?：2??pd(，，?
breakdown voltage varies as the product varies. Knowing the nature of functions we can write the pdfandf12
equation ;； known as Paschen’s law and has been experimentally established for many gases. V！fpd
Paschen’s law is a very important law in high voltage engineering.
The relationship between is not linear and has has a minimum value for any gas. The minimum Vandpd
breakdown voltages for various gases are as follow;
Gas Vmin(V) pd at Vmin(torr-cm) ss
Air 327 0.567
H 273 1.15 2
CO 420 0.51 2
O 450 0.7 2
SO 457 0..33 2
Helium 156 4.0
The existence of a minimum sparking potential in Paschen’s curve may be explained as follows:
For values electrons crossing the gap make more frequent collisions with gas molecules than ;；pd，pdmin
, but the energy gained between collisions is lower. Hence to maintain the desired ionization more ;；pdmin
voltage has to be applied.
For electron may cross the gap without even making a collision or making only less number of ;；pd，pdmin
collisions. Hence more voltage has to be applied for breakdown to occur.
For the effect of temperature, the Paschen’s law is generally stated as where N is the density of the ;；V！fNd
gas molecules. This is necessary since the pressure of the gas changes with temperature according to the gas law .The breakdown potential of air is expressed due to the experimental results as; pv！NRT
At 760 torr and 293?K
)?6.08VkVkV. This equation yields a limiting value for E of 24 for long gaps and a E！！24.22？??dcmcmd，?
293pd)?kVvalue of 30 for ！1, which means a pressure of 760 torr at 20?C with 1 cm gap. This the ??cm760T，?
breakdown strength of air at room temperature and at atmospheric pressure.
2.10 Post-Breakdown Phenomena and Applications
Post-Breakdown phenomenon is of technical importance which occurs after the actual breakdown has taken place. Glow and arc discharges are the post-breakdown phenomena and there are many devices that operate over these regions. In a Townsend discharge (see Fig 2.3) the current increases gradually as a function of the applied voltage from point A. Further to this point B only the current increases and the discharge
(VOLTS) Abnormal Townsend dark 500 Glow
E A B
F Transition from Transition
Dark to Glow from 250 discharge Glow to Arc
Glow C D
-15-12-90 -6-3310 10 10 10 10 1 10
Fig.2.3 d.c. voltage current characteristic at an electrical discharge with
electrodes having no sharp points or edges
changes from the Townsend type to Glow type (BC). Further increase in current results in a very small reduction I voltage across the gap (CD) corresponding to the normal glow region. The gap voltage again increases (DE), when the current increase more, but eventually leads a considerable drop to the applied voltage. This is the region of the Arc discharge (EG). The phenomena occur in the region CG are the post-breakdown phenomena consisting of glow discharge CE and the arc discharge EG.
A glow discharge is characterized by a diffused luminous glow. The color of the glow discharge depends on the cathode materials and the gas used. The glow discharge covers the cathode partly and the space between the cathode and the anode will have intermediate dark and bright regions. In a glow discharge the voltage drop between the electrodes is substantially constant, ranging from 75 to 300 V over a current range of 1 mA to 100 mA depending on the type of the gas. The properties of the glow discharge are used inj many practical applications, such as, voltage regulation (VR) tubes, for rectification and as an amplifier.
If the current in the gap is increased to about 1 A or more, the voltage across the gap suddenly reduces to a few volts (20-50 V). The discharge becomes very luminous and noisy (region EG). The current density over the cathode region increases to very high
37Avalues of 10 to 10. Arcing is associated with high temperature, ranging from 1000?C to several 2cm
thousands degrees celcius. The discharge contain very high density of electrons and positive ions, and called as arc plasma. The study of arcs is important in circuit breakers and other switch contacts. It is convenient high temperature high intensity light source. It is used for welding and cutting of metals. It is the light source in lamps such as carbon arc lamp. High temperature plasmas are used for generation of electricity through magneto-hydro dynamic or nuclear fusion processes.
1. Describe the current growth phenomenon in a gas subjected to uniform electric fields.
2. Define Townsend’s first and second ionization coefficients. How is the condition for
breakdown obtained in a Townsend discharge?
3. What are electronegative gases? Why is the breakdown strength higher in these gases
compared to that in other gases?
4. Derive the criterion for breakdown in electronegative gases.
5. Explain the Streamer theory of breakdown in air at atmospheric pressure.
6. What are the anode and the cathode streamers? Explain the mechanism of their
formation and development leading to breakdown.
7. What is Paschen’s law? How do you account for the minimum voltage for breakdown
under a given ‘p×d’ conditions?
8. Describe the various factors that influence breakdown in a gas.