Environmental Engineering Reference
In-Depth Information
at any ele
ct
ric field strength. If
σ
(
v
)
D
const, in the limit of high electric field
strengths
ε
T
, the distribution functions (3.27) yield
1/4
s
eE
0.427
s
M
0.897
m
e
M
λ
m
e
0.530
Mw
e
,
w
e
D
,
ε
D
m
e
eE
λ
D
(3.29)
σ
).
As follows from (3.26), the electron drift velocity depends on the electric field
strength
E
through the reduced electric field strength
E
/
N
a
, which is usually mea-
sured usually in Townsends (Td) [33] (1 Td
where the mean free path for electrons is
λ
D
1/(
N
a
10
17
Vcm
2
). Table 3.1 contains the
values of the electron drift velocity in some gases depending on the reduced electric
field strength. In addition, Figures 3.1 and 3.2 give the measured drift velocity of
electrons in helium and argon as a function of the reduced electric field strength.
Let us give the criterion for validity of this regime for electron drift in a gas.
We ignored collisions between electrons compared with electron-atom collisions,
which corresponds to assumption
I
ea
(
f
0
)
D
I
ee
(
f
0
) in the second equation of the
set (3.25). This criterion may be represented in the form
B
ea
B
ee
,wherethe
electron diffusion coefficient
B
ea
in the energy space for electron-atom collisions
is given by (3.10), and this coefficient for electron-electron collisions in accordance
with (3.19) and (3.20) is
e
4
N
e
T
e
m
e
v
4
π
B
ee
D
ln
Λ
.
Correspondingly, the criterion for this regime of electron drift takes the form
2
σ
ea
N
e
N
a
m
e
M
T
T
e
ε
,
(3.30)
2
π
e
4
ln
Λ
Ta b l e 3 . 1
The experimental electron drift velocity
w
e
in gases expressed in units of 10
5
cm/s for
the regime of a low electron number density [32].
E
/
N
a
,Td He
Ne
Ar
Kr
Xe
H
2
N
2
0.001
0.028
0.35
0.15
0.015
0.004
0.020
-
0.003
0.080
0.55
0.53
0.038
0.013
0.052
-
0.01
0.25
0.89
1.0
0.13
0.040
0.17
0.39
0.03
0.64
1.3
1.2
0.90
0.16
0.46
1.0
0.1
1.4
2.1
1.7
1.4
0.86
1.4
2.3
0.3
2.7
3.5
2.4
-
1.1
3.2
3.1
1
4.8
-
3.1
-
1.4
6.2
4.5
3
8.6
-
4.0
-
1.8
10
7.7
10
22
-
11
-
6.0
19
18
30
72
-
26
-
18
37
42
100
-
-
74
-
53
130
100
