Environmental Engineering Reference
In-Depth Information
transverse to the field is identical in both cases, the kinetic energy of ions in the
field direction varies from
T
/2 to 2
T
in these cases, and in the second case, ac-
cording to (4.96) we have
eE
λ
D
4
T
.Taking
T
D
300 K and
σ
D
43 Å
2
at this
res
temperature, we find
E
/
N
a
40 Td. Note that the electric field strength of the elec-
tron energy doubling is 0.07 Td according to (3.39) for the regime of high electron
density. From this it follows that in some range of electric field strengths the ener-
gy of plasma electrons exceeds significantly the energy of plasma ions and neutral
particles.
D
4.4.3
Diffusion of Atomic Ions in Gases in External Fields
At low electric field strengths the diffusion coefficient of ions is expressed through
the ion mobility by the Einstein relation [13, 15, 20] according to (4.38). Formula
(4.90) gives the diffusion coefficient of ions in a foreign gas when ion-atom po-
larization interaction dominates. In the same manner we have for the diffusion
coefficient of ions in a parent gas without external fields
0.34
r
T
M
1
D
i
D
res
(
p
9
T
/
M
)
.
(4.101)
N
a
σ
The argument in the cross section
res
of resonant charge exchange indicates the
collision velocity in the laboratory frame of reference at which this cross section
is taken. The indicated velocity corresponds to the ion energy in the laboratory
frame of reference of 4.5
T
. If we express the diffusion coefficient in this formula
in square centimeters per second, take the normal number density of atoms
N
a
σ
D
10
19
cm
3
, give the gas temperature
T
in Kelvin, represent the ion mass
in atomic mass units (1.66
2.69
10
24
g), and express the cross section of resonant
res
in units of 10
15
cm
2
, this formula takes the form
charge exchange
σ
34.6
r
T
300
1
K
D
.
(4.102)
σ
res
(2.1
v
T
)
For determination of the ion diffusion coefficient in a gas in an external electric
field we use the kinetic equation for the ion distribution function (3.4) that has the
form
e
M
@
f
@
v
D
(
v
w
)
f
C
I
col
(
f
),
r
and the ion diffusion coefficient in this gas
D
is defined as
j
i
D
D
i
r
N
i
.
Here
j
i
is the ion current density due to the gradient of the ion number density,
which is small at a distance of the order of the mean free path of ions in a gas.
