Environmental Engineering Reference
In-Depth Information
where the above integral is limited at small
max
impact parameters.
The lowest limit is determined by violation of the assumption of small scattering
angles and is estimated as
min
and large
. The upper limit is because of
screening of the Coulomb field of interacting particles in a plasma, so the interac-
tion potential of two charged particles in a plasma at a distance
r
from each other
is
e
2
exp(
#
1, or
e
2
/
ε
min
r
/
r
D
)/
r
,where
r
D
is the Debye-Hückel radius. Hence, the upper lim-
it is
r
D
, and the diffusion cross section for the scattering of two charged
particles in a plasma is [47]
max
e
4
r
D
e
2
ε
σ
D
π
ln
Λ
,
Λ
D
,
(2.37)
ε
2
and the Coulomb logarithm ln
Λ
is determined within the accuracy up to a con-
stant factor under logarithm.
Formula (2.37) leads to different diffusion cross sections for electron-electron
and electron-ion scattering in a plasma. From this the diffusion cross section for
scattering of a fast electron by a plasma electron is
e
4
4
π
σ
ee
D
ln
Λ
,
(2.38)
2
ε
2
/2, and
where the energy of the fast electron is
is the velocity of the fast
electron. In the case of electron-ion scattering, if the electron velocity exceeds the
ion velocity significantly, the diffusion cross section of electron-ion scattering is
ε
D
m
e
v
v
e
4
σ
ei
D
π
ln
Λ
.
(2.39)
ε
2
Let us estimate a typical value of the Coulomb logarithm for a plasma of a glow
gas discharge, taking the number density of electrons and ions
N
e
10
12
cm
3
,
a typical electron energy
ε
1 eV, and the temperature of atoms and ions
T
D
10
4
cm, and the
400 K. Under these conditions, the Debye-Hückel radius is
r
D
e
2
/
T
e
for strong interaction of two charged particles involving an
distance
min
electron is
7. As is seen,
the value of the logarithm is large, which justifies the approximation used. Next,
we use this value of the Coulomb logarithm in subsequent estimates.
10 Å. For the Coulomb logarithm this gives ln
Λ
D
min
2.1.9
Elastic Ion-Atom Collision and Resonant Charge Exchange
Two types of processes involving ions are of importance for ionized gases, elastic
ion scattering of gas atoms and the resonant charge exchange process. The basic
type of ion-atom interaction at large distances
R
between interacting particles has
a polarization character and takes the form [2]
e
2
2
R
4
,
D
α
U
(
R
)