Environmental Engineering Reference
In-Depth Information
4.4
Transport of Atomic ions and Clusters in Plasma
4.4.1
Zero-Field Mobility of Ions in Gases
The ion mobility
K
i
is defined as the ratio of the ion drift velocity
w
to the electric
field strength
E
according to (4.37)
w
i
E
K
i
D
,
and is independent of the electric field strength at low fields according to criteri-
on (4.20):
eE
λ
T
.
At low field the connection between the ion mobility and the cross section of ion-
atom scattering in the first approximation of the Chapman-Enskog method is giv-
en by (4.21), and according to the Einstein relation (4.38) the diffusion coefficient
of ions in gases is given by
3
p
π
T
D
i
D
N
σ
p
2
,
(4.86)
8
N
a
μ
where the average cross section of ion-atom scattering is given in (4.21). The dif-
fusion coefficient does not depend on the direction until the distribution function
forionsisisotropic.
We have two types of ion-atom scattering depending on the ion and atom
species. In the first case, the types of ion and atom are different, and the scattering
cross section in (4.21) and (4.86) corresponds to elastic ion-atom scattering. In the
second case, atomic ions move in a parent atomic gas, and the resonant charge
exchange process that proceeds according to the scheme
C
A
C
!
A
C
C
A
A
(4.87)
determines the ion mobility. Indeed, if the cross section of the resonant charge
exchange process exceeds significantly the cross section of elastic ion-atom colli-
sion, the effective ion scattering proceeds as a result of the Sena effect [40, 41], as
shown in Figure 4.6. Ion scattering results in charge transfer from one atomic core
to the other one, and hence the charge exchange cross section characterizes the ion
mobility.
In the case of ion drift in a foreign gas in a weak electric field we use (2.40) for the
ion-atom diffusion cross section of elastic scattering assuming polarization char-
acter of ion-atom interaction. Then the diffusion cross section is inversely propor-
tional to the collision velocity, and the ion mobility follows from (4.19). We obtain
the Dalgarno formula [42] for the ion mobility
K
in the form
36
p
αμ
K
D
.
(4.88)
