Environmental Engineering Reference
In-Depth Information
We now analyze the character of plasma relaxation to ionization equilibrium in
the first stage when the gas is fully ionized, and one can ignore ionization of atoms.
Then relaxation results from recombination of electrons and ions according to the
scheme
A
C
!
A
!
2
e
C
e
C
e
C
A
,
(1.89)
and the balance equation for the electron number density is
dN
e
dt
KN
e
N
i
,
D
(1.90)
where for a quasineutral plasma the number densities of electrons and ions are
identical
N
e
N
i
,and
K
is the recombination coefficient for the three body pro-
cess (1.89). Subsequently, we analyze this process in detail, but now we find the
rate constant
K
from the dimension considerations, according to which it has di-
mensions centimeters to the sixth power per second and includes the parameters
e
2
,
m
e
,and
T
e
(
T
e
D
J
). Then the recombination coefficient is
ae
10
T
9/
e
m
1/2
K
D
,
(1.91)
e
where the numerical coefficient
a
1.
Ta k i ng
a
D
1, we obtain the balance equation (1.88) in the form
J
p
T
e
r
m
e
T
e
d
dt
J
T
e
KN
e
e
2
p
m
e
D
γ
3
e
2
J
3
D
γ
D
γ
,
τ
D
.
(1.92)
τ
As is seen, although a typical relaxation time
exceeds the atomic time, the dif-
ference between these times is not great. For example, for a hydrogen plasma and
T
e
τ
is about 10
15
s, whereas the minimum time for plasma genera-
tion is approximately 10
14
s for short-pulse lasers, and the minimum time of a
laser pulse exceeds a typical ionization relaxation time for this plasma. This means
that it is impossible to create a strongly coupled plasma of low temperature in a
two-component plasma consisting of electrons and ions only. Hence, the neutral
component of a plasma or external fields are of importance to support a plasma
with strong coupling, in contrast to an ideal plasma, where many of its properties
(such as plasma oscillations and interaction with electromagnetic waves) are inde-
pendent of its neutral components. Thus, the word “plasma” in its general sense
meaning a system of charged particles is not appropriate for a dense plasma of low
temperature, whereas it is a suitable description for ideal plasmas that are weakly
ionized gases at low temperature.
D
1000 K,
τ
1.3.4
Special Features of Strongly Coupled Plasmas
The above analysis of a strongly coupled plasma makes it possible to identify the
distinguishing features of such an object. We first present a contrast to a weakly
