Environmental Engineering Reference
In-Depth Information
D
v
/
p
2
T
/
M
is the reduced ion velocity (
m
is the ion mass,
T
is the gas
temperature). The optimal index value for the ion mobility is
n
where
u
3/2, and in the
first approximation we restrict ourselves to the Sonin polynomial with
k
D
0, which
is equal to 1. Hence, in the first Chapman-Enskog approximation the quantity
D
ψ
is independent of the ion velocity and may be found from (4.19), which has the
following form in this approximation:
Z
σ
(
g
)
v
eEN
i
D
ψ
g
x
g
'
'
a
)
d
v
d
v
a
μ
(
v
)
(
v
x
Z
g
2
D
3
μ
σ
(
g
)
'
(
v
)
'
(
v
a
)
d
v
d
v
a
.
From the definition of the ion drift velocity
w
i
we have
Z
v
f
(
v
)
d
v
D
3
h
v
2
w
i
D
i
.
This leads to the following connection between the ion drift velocity in a weak
electric field
K
I
and the cross section of ion-atom collision in the first Chapman-
Enskog approximation:
3
e
p
π
8
N
a
Z
1
1
2
D
μ
g
2
2
T
σ
(
x
)
e
x
x
2
dx
,
K
I
D
σ
p
2
T
,
σ
(
T
)
D
x
.
(4.21)
μ
0
4.1.6
Excitation of an Ionized Gas in an Electric Field
A plasma is a convenient means to accomplish energy transfer from an external
electric field to a gas. It is used in plasma generators, gas lasers, and other devices
for transformation of electric energy to other forms of energy. We can find the
specific power transformed by a gas discharge plasma in the low electric current
regime when interaction of charged particles is nonessential, and electric currents
in a gas do not change its properties significantly. One electron moving in a gas
in an external electric field of strength
E
transfers to gas atoms the power
eEw
e
,
where
w
e
is the electron drift velocity. Therefore, the power transformed per unit
volume of a plasma is
P
D
N
e
eEw
e
D
N
e
N
a
w
e
,
(4.22)
where
N
e
is the electron number density and
N
a
is the number density of atoms or
molecules of the gas, and the electron drift velocity
w
e
depends on the ratio
eE
/
N
a
.
For an understanding of the practical physical quantities associated with the en-
ergy transformation process, Table 4.1 gives the parameters in (4.22) for mean elec-
tron energies of 1 and 3 eV, and the rate of the temperature change in this table is
determined by formula
dT
dt
D
N
e
eE
N
a
w
e
c
p
(4.23)
