Chemistry Reference
In-Depth Information
to achieve the α coefficient
exp
. (3.268)
exp
(
−
z
ion
/
λ
ion
)
p
ε
ion
α
=
=
C
ion
·
−
λ
ion
k
B
·
T
gas
·
e
·
C
ion
·
k
B
·
T
gas
·
E
/
p
The constant
C
ion
depends on the ionization cross section of the used gas and the
electron velocity distribution function.
Finally, the pressure reduced first Townsend coefficient
exp
f
E
p
α
p
=
C
2
E
C
1
·
−
=
(3.269)
/
p
with
C
1
=
(
k
B
·
T
gas
·
C
ion
)
−
1
and
C
2
=
ε
ion
/(
e
·
k
B
·
T
gas
·
C
ion
)
is found as a function
of the reduced electric field strength
E
p
, only, firstly derived by Townsend.
The reduced electric field strength
E
/
/
p
expressed by
E
/
n
gas
is mostly given in
units of Townsend which is defined as
E
n
gas
=
1 Townsend
=
1Td
=
10
−
17
V
·
cm
2
.
The constants
C
1
and
C
2
in Equation 3.269 have to be determined experimentally
and they are available for a special kind of gas at constant temperature in a lim-
ited range of the reduced electric field strength
E
/
p
, see Figure 3.33, [3]. Thereby
the range of validity of the constant
C
2
is in the limit between about
C
2
/
2
≤
E
/
p
≤
3
C
2
[40].
0
100
200
300
400
500
600
7
7
6
Air
6
Ar
5
5
4
N
2
4
3
3
H
2
Ne
2
2
1
1
0
0
0
100
200
300
400
500
600
E
/
p
in V (Pa
.
m)
-1
FIGURE 3.33
Analytical calculation (3.269) of the pressure reduced first Townsend coeffi-
cient α
/
p
in dependence on
E
/
p
for different gases, using the corresponding values for
C
1
and
C
2
from literature.
