Environmental Engineering Reference
In-Depth Information
In particular, for an argon plasma and temperatures
T
e
D
2eVand
T
i
D
400 K of
electrons and ions, this formula gives
x
D
2.6, which leads to the particle charge
Z
D
4
10
3
e
for the particle radius
r
0
D
1
μ
m.
1 if a change of cluster charge by
one leads to a small variation of the electron and ion fluxes. In particular, in the
case of identical electron and ion temperatures (
T
i
Formula (6.21) holds true in the limit
j
Z
j
D
T
e
), this formula gives
ln
r
m
i
m
e
.
1
x
D
(6.22)
1
C
x
Table 6.1 gives the solution of this equation for a quasineutral ionized inert gas
(and nitrogen) with positive atomic ions (and
N
2
ions for nitrogen).
We now consider the limit of small cluster size
e
2
T
when clusters are neutral or singly charged and are in a quasineutral ionized gas
with different temperatures of electrons
T
e
and ions
T
i
. The charging processes
involving electrons, ions
A
C
,andclusters
M
C
Z
n
r
0
consisting of
n
atoms and having
charge
Z
proceed according to the scheme
M
N
,
M
n
e
C
M
n
!
e
C
!
M
N
,
A
C
C
M
N
C
A
,
A
C
C
M
N
C
M
n
!
M
n
!
A
.
This scheme gives the following set of balance equations for the number density
of neutral clusters
N
0
, singly negatively charged clusters
N
, and singly positively
charged clusters
N
C
:
k
i
1
N
i
N
C
k
e
1
N
e
N
e
,
dN
0
dt
D
e
2
r
0
T
i
e
2
r
0
T
e
k
e
N
e
N
0
k
i
N
i
N
0
C
C
C
k
e
1
N
e
N
e
,
e
2
r
0
T
e
dN
C
dt
D
k
i
N
i
N
0
C
k
i
1
N
i
N
e
2
r
0
T
i
dN
dt
D
k
e
N
e
N
0
C
.
Here
k
i
is the rate constant for ion attachment to a neutral cluster and
k
e
is the rate
constant for electron attachment to a neutral cluster according to
s
8
T
i
π
s
8
T
e
π
r
0
r
0
k
i
D
π
,
k
e
D
π
.
m
i
m
e
Ta b l e 6 . 1
The solution of (6.22) [41].
Buffer gas
He
Ne
Ar
Kr
Xe
N
2
x
3.26
3.90
4.17
4.47
4.65
4.03
