CHAPTER V: BREAKDOWN
IN GASES
1. Introduction
2. Breakdown in uniform field
3. Ionization
4. Photo-ionization
5. Thermal ionization
6. Ionization by collision
7. Townsend discharge/Townsend avalanche theory
8. Breakdown in electronegative gases
9. Paschen law
10. Streamer theory
1. Introduction
 Gases are generally insulators (air, SF6, N2, etc. )
 To use gases as insulators, it needs to:
o Understand V-A characteristics of gases
o Explain pre-breakdown and breakdown phenomena
o Describe the influence of external factors on breakdown
phenomenon
 Used in both opened system and enclosed system
 Opened system: air
 Enclosed system: air and other gases at high pressure
 Advantages: capable of self-healing after discharge
 Disadvantages: lower dielectric strength than liquids and solids
2. Breakdown in uniform field
 Uniform field: the value of the field strength is the same at all
points (field between two parallel charged plates)
 Low field: small electronic conduction  insulators
 High field: high conduction  discharges/breakdown 
conductors
 Breakdown time: ns  s
 Breakdown in gases largely depends on gaseous types and
pressure  breakdown originates from gases inside electrode
gap
3. Ionization processes
 The process of liberating an electron from a gas molecule with the
simultaneous production of a positive ion is called ionization
 Types of ionization:
o Ionization by collision (primarily responsible for the
breakdown in gases)
o Photo-ionization (for non-uniform field)
o Thermal ionization (electrical arc)
4. Photo-ionization
 Occurs when the amount of radiation energy absorbed by an atom
or molecule exceeds its ionisation potential
 Photon energy
Planck constant
W  hf
Frequency of
radiation
h  6,626 .10 34 ( J .s )
 Excited equation
Ionization energy
hf Vi
hf  A  A
 Ionization equation
Vi
hf  A hf
 A  e 
*
Excited atom
Where:
c
hc
hc
f   hf 
 Vi   


Vi
 Ex. Given a gas with an ionization energy of about 10 eV, calculate
the wavelength of the radiation that can cause ionization of the gas.
6,626.10 34 ( J .s)  3.108 (m / s)
7
m


1
,
242
.
10
19
10 1,6.10 ( J )
 124,2 nm (UV  C )
5. Thermal ionization
 Mean kinetic energy per atom
3
Wk  kT
2
Boltzmann constant (1,38.10-23 J/K
= 8,617.10-5 eV.K-1 )
 When Wk  Vi: cause ionization by collision of the gas
atoms/molecules with each other
 At room temperature: low Wk  unable to cause ionization
 Ex. Calculate Wk at room temperature (300K)
3
3
Wk  kT   8,617 .10 5 (eV .K 1 )  300 ( K )
2
2
 0,039 eV  10eV
6. Ionization by collision
 Process of removing electrons from neutral atoms/molecules by
collision.
 Excited equation
Ionization energy
Vi
e   A 

 e  A*
 Ionization equation

 Vi


e  A 
 e  A  e

: accumulated energy between 02 collisions
7. Discharge-avalanche
theory/Townsend mechanism
a. Conditions of application
 Uniform field
 Small electrode gaps: d = mmcm
 Atmospheric pressure (p  1 atm)
 p.d  1000 mmHg.cm
 Some initial free electrons in the electrode gaps
b. Experimental circuit
 V = 0 (E = 0): random motion of electrons  I= 0
 V > 0 (E > 0): Free electrons move at a constant acceleration in
the opposite direction of the electric field  collide with neutral
particles  may cause ionization  electron avalanche 
current pulses
 Electrons collide with neutral atoms when moving across
the electrode gap
 Energy received by electrons between two collisions:
Nguyên tử
-
+
Điện tử
W  Fe  qEe
1 n
e   i
n i 2
Average mean free path between
two collisions
 Properties of e:
1
e 
n
 The ideal gas law:
pV  nRT
1 RT
 
n pV
n: density of molecule/atom
p: gas pressure
1
e 
p
 Energy received by electrons between two collisions is
proportional to: :
o Electric field E
o e (e  1/p)
 Probability of ionization by collision (probability that one
collision causes ionization)
E
Pr  f  
 p
 The number of collisions per unit length in the direction of
electron travel
Nc  p
 Probability that one collision causes one ionization by collision
per unit length in the direction of electron motion (the first
ionization coefficient)
E
E
  N c Pr  N c f    pf  
 p
 p
c. Current growth
 An increase in the number of free
electrons along a distance dx
-
Nec
Ne(x)+dNe
Ne(x)
x
dNe  N e  x dx
+
dx

dNe
dNe
 dx  
  dx
N e x 
N e x 
 ln N e  x  ln C
 ln N e  ln C  x
 At x = 0  exp(0)=1  C=Nec
(the number of electrons
generated at cathode in 1s)
 Ne(x) = Nec exp(x)
N 
 ln  e   x
C 
  N 
 exp ln  e    exp x 
  C 
 N e  C exp x 
 The number of positive ions generated along a distance dx
dN  Ne x dx  Nec expx dx
 The number of positive ions generated between x = 0 and x
x
N  x   N ec  expx dx  N ec
o
1

expx 
x
o
 N ec expx   1
 The total number of electrons between the electrodes
Ned   Nec expd  *
 The total number of positive ions between the electrodes
N d   Nec expd   1  **
 N d   Ned   Nec
 Positive ions travel towards the cathode and impact on it  release the
secondary electrons
 Nec  No  N d 
The number of secondary electrons released
by positive ion impact
Primary electrons at the
cathode due to natural
ionization (sunlight, UV,
radiation, cosmic rays, etc.)
ee-
: the second ionization coefficient (the
probability that one electron is
released from the cathode for each
generated positive ion)
e-
-
+
N ec  N o  N d 
 N o  N ec exp d   1
No
 N ec 
1   exp d   1
 The total number of electrons reaching the anode per second
N ed   N ec expd 
N o exp d 

1   exp d   1
 Current
N o qe exp d 
i  ie  N e d qe 
1   exp d   1
io exp d 

1   exp d   1
 Townsend’s criterion for breakdown: i =   denominator = 0
1   exp d   1  0
  exp d   1  1