Environmental Engineering Reference
In-Depth Information
and according to the definition of the dimension
l
of the particle field region we
have
Q
D
Q
i
C
Q
tr
Dj
Z
j
.
(6.48)
Using this relation as the equation for
l
, we introduce the part of the screening
charge
that is created by trapped ions as
Q
tr
D
.
(6.49)
Q
i
C
Q
tr
In evaluating these parameters of the particle field screening we use (6.46) or (6.47)
for the number densities of free and trapped ions. Note that in the range of compe-
tition of these screening channels, the difference in the results for these versions
is not remarkable. In particular, for the above example of the argon dusty plas-
ma (
T
e
10
10
cm
3
D
1eV,
T
i
D
400 K,
r
0
D
1
μ
m) at
N
0
D
the contribution of
trapped ions to the particle screening is
0.43, respectively, if we
use (6.46) or (6.47) for the number densities of free and trapped ions, and the size
l
of the particle field is 30
D
0.40 and
D
m, respectively, for these cases.
The above formulas exhibit the scaling law according to which the parameters
of the length dimension are proportional the particle radius, and the dependence
on the number density of electrons and ions
N
0
far from the particle is through
N
0
r
0
. In particular, free and trapped ions give the same contribution to the screen-
ing charge if
N
0
r
0
D
μ
mand31
μ
70 cm
1
, which means that at
r
0
D
1
μ
m the correspond-
10
9
cm
3
and at
r
0
ing number density of the plasma is
N
0
D
7
D
10
μ
mthis
10
7
cm
3
. Next, trapped ions disappear at
N
0
r
0
D
10
3
cm
1
, which corresponds to
N
0
number density is
N
0
D
7
10
11
cm
3
for
r
0
D
1
D
1
μ
m, and the num-
10
9
cm
3
ber density is
N
0
m. From the last value it follows
that trapped ions are not important for electric probes in a plasma at
r
0
D
1
for
r
0
D
10
μ
10
μ
m
but are significant for a rare dusty plasma in the solar system.
Figure 6.6 shows the dependence of the part of the screening charge
(6.49) that
iscreatedbytrappedionsonthereducednumberdensity
N
0
r
0
of a surrounding
plasma, and Figure 6.7 gives the dependence of the reduced size of the particle field
on this parameter. Figure 6.8 shows the reduced number densities of free
N
i
r
0
and
trapped
N
tr
r
0
ions as a function of the reduced distance
R
/
r
0
from the particle.
These number densities correspond to the reduced number density of a surround-
ing plasma
N
0
r
0
D
100 cm
1
at which the contribution from trapped ions to the
particle screening is approximately 40%. Comparing the results of the two cases in
Figures 6.6 and 6.7 where the number densities of ions are determined by (6.46)
or (6.47), one can estimate the accuracy of the above operations as approximately
10%.
We note one more aspect of this phenomenon. We consider the case
R
0
r
0
,
which allows us to divide the ion trajectories from which an ion attaches to the par-
ticle or goes into the surrounding plasma. Next, the nearest elliptic ion orbit is far
from the particle. All this according to (6.32) is possible only for a nonequilibrium
plasma where
T
e
T
i
, as is realized in a gas discharge plasma containing dust
