Environmental Engineering Reference
In-Depth Information
where
v
T
m
e
)]
1/2
isthemeanelectronvelocity.
Equation (4.78) together with the corresponding expressions for the kinetic coef-
ficients allow us to determine the electron heat flux under different conditions in
the plasma. Let us determine the effective thermal conductivity coefficient in the
direction perpendicular to an external electric field
E
. If the plasma is placed into
a metallic enclosure, the transverse electric field is absent,
E
D
[8
T
e
/(
π
0, and the first
equation (4.78) coincides with (4.69). If the walls are dielectric ones, we have
j
D
D
0,
which corresponds to the regime of ambipolar diffusion when electrons travel to-
gether with ions. In the electron scale of values this gives
j
D
0, that is, an electric
field of strength
E
D
D
T
r
ln
T
e
/(
N
e
K
) arises. Let us represent the heat flux in the
form
q
D
C
T
e
,
r
e
where the coefficient
C
is
e
α
D
T
C
D
1
e
T
e
N
e
K
.
Let us take the velocity dependence for the rate of electron-atom collisions as usual
as
n
,thatis,
0
z
n
/2
,where
z
2
/(2
T
e
). Using the Einstein
ν
v
ν
(
)
D
ν
D
m
e
v
v
relation
D
D
KT
e
/
e
,weget
C
α
n
C
D
1
.
e
As a result, we obtain
n
C
2
C
D
n
.
(4.80)
2
As is seen, the effective thermal conductivity coefficient for electrons in the two
cases considered of metallic and dielectric walls depends on
n
.For
n
D
0, this
value is identical in both instances. For
n
D
1, it is greater by a factor of 3 in the
second case than in the first.
4.3.6
Townsend Energy Coefficient
The Townsend energy coefficient for electrons is introduced as
eED
?
Tw
D
eD
?
TK
e
η
D
,
(4.81)
where
D
?
is the transverse diffusion coefficient for electrons in a gas,
K
e
is their
mobility, and
T
is the gas temperature. For a Maxwell distribution function for elec-
tronswiththegastemperature,
1 according to the Einstein relation (4.38). In
the regime of high electron number densities with a Maxwell distribution function
η
D
