Environmental Engineering Reference
In-Depth Information
Note that if electrons are located in an external electric field, along with a nonsym-
metric part due to the electron number density gradient, there is another nonsym-
metric part of the distribution function due to an electric field. In deriving (4.64)
we separate these parts, which is valid if they correspond to different directions.
Hence, if an electric field influences the distribution function for electrons, the ex-
pression (4.64) for the electron diffusion coefficient holds true for the transverse
diffusion coefficient only.
In the absence of an electric field, if the velocity distribution function for elec-
trons is a Maxwell one, (3.26) gives
v
2
eE
3
T
eED
e
T
w
e
D
D
,
(4.64)
ν
which corresponds to the Einstein relation (4.38). In addition, the diffusion coef-
ficient of electrons is identical in different directions. This holds true also for the
regime of a high number density of electrons when we have the Einstein relation
in the following form instead of (4.38)
eED
e
T
e
w
e
D
,
(4.65)
where
T
e
is the electron temperature. Table 4.8 gives the reduced zero-field mo-
bilities of electrons in inert gases at room temperature,
K
e
N
a
(
K
e
is the electron
mobility,
N
a
is the number density of gas atoms), and the values of the reduced
diffusion coefficients of electrons,
D
e
N
a
.
An external electric field influences the character of electron drift in a gas and the
value of the diffusion coefficient. If
ν
D
const, the diffusion coefficient is propor-
tional to the average electron energy, and the diffusion coefficients in the transverse
and longitudinal directions are the same. In other cases only the diffusive motion
in the transverse direction with respect to the electric field is separated from elec-
tron drift, and the dependence on the electric field strength is connected with the
dependence of the diffusion cross section of elastic electron-atom collision on the
electron energy. We give in Figures 4.2 and 4.3 the coefficients of transverse diffu-
sion of electrons in helium and argon on the basis of experimental data [37]. As is
seen, in the argon case with the Ramsauer effect for elastic electron-atom scatter-
ing, the dependence of the diffusion coefficient on the electric field strength has a
nonmonotonic character.
Let us consider the case when the diffusion cross section of elastic electron-atom
collision is independent of the electron energy, which corresponds to the helium
Ta b l e 4 . 8
Electron drift parameters in inert gas atoms at zero field and room temperature [37].
Gas
He
Ne
Ar
Kr
Xe
D
e
N
a
,10
21
(cm s)
1
7.2
72
30
1.6
0.43
K
e
N
a
,10
23
(cm s V)
1
.9 9 2 . 2 . 7
