Environmental Engineering Reference
In-Depth Information
Substituting this expression into the relationship derived from the continuity equa-
tion yields
q
2
cos
α
ν
,
w
0
w
N
e
N
e
2
H
D˙
ω
C
ν
(5.144)
where cos
the angle between vectors
w
and
k
. Substitution of
this into (5.142) gives, with the help of (5.139),
α
D
k
x
/
k
,with
α
3
N
e
T
e
2
ω
.
dW
0
dt
d
dt
H
sin 2
α
T
e
2
J
N
e
m
e
w
2
cos
2
D
D
α
ν
ν
(5.145)
If the term on the right-hand side of this equation is positive, any random deviation
of the electron number density from its equilibrium value continues to increase,
that is, instability develops. This term has a maximum when tan 2
α
D
ω
H
/
ν
.
For this direction of vector
k
, (5.145) has the form
0
@
1
A
q
2
H
C
ν
2
ω
dW
0
dt
T
e
2
J
N
e
m
e
w
2
D
ν
1
.
(5.146)
ν
From this it follows that this instability has a threshold, stated by
ω
H
/
ν
(
T
e
/
J
)
1/2
. When the ratio
is large, ionization instability develops for per-
turbations propagating at an angle
ω
H
/
ν
45
ı
to the direction of the current. If this
ratio is small, the most unstable perturbations propagate in a direction almost per-
pendicular to the current.
α
D
5.5.5
Attachment Instability of a Molecular Gas
Several different instabilities are possible during the formation of negative ions by
attachment of electrons to molecules. This process is related to the formation of
positive ions by loss of electrons, and to recombination events. All of these pro-
cesses can create ionization structures and waves in a plasma. As an example, we
shall consider attachment as it occurs in the plasma of an excimer laser, where
a strong dependence of the attachment rate for electrons on the vibrational state
of the molecule may lead to attachment instability. Then vibrational excitation of
molecules causes acceleration of the electron attachment process and may produce
a decrease in the electric current.
In an excited molecular gas (e.g., HCl) the attachment rate constant increases
with an increase of the vibrational temperature. The positions of electronic states,
as illustrated in Figure 5.13, determine the properties of this process. It proceeds
according to the following scheme:
(
AB
)
,
AB
)
!
B
,
AB
)
!
AB
C
AB
C
e
!
A
C
e
. (5.147)
