Geoscience Reference
In-Depth Information
Fig. 3.10
Influence of
particle (ion) charge on
recombination efficiency.
Shown are the enhancement
factors ".a/ as the function of
the particle size at different
particle and ion charges
Q
and
q
.
Lower horizontal axis
shows particle size in units of
the Coulomb length l
c
PARTICLE SIZE (in nm)
0
10
20
30
40
50
60
50
Q=2, q=1
Q=q=1
Q=1, q=2
ε
=5
40
ˇe
2
D
30
20
10
0
1
PARTICLE SIZE (in units of l
c
)
We have also obtained the analytical expression for the image potential
(Eq.
3.131
). The integral on the right-hand side of this expression can be expressed
in terms of the hypergeometric function. At "
D
1 this integral is expressed in
terms of elementary functions. The approximation Eq.
3.136
is very efficient. The
numerical study shows that this approximation reproduces exact results with the
precision 1% within 2<"<
1
.
3.6
Particle Charging in the Transition Regime
Charging of small neutral and charged particles suspended in a weakly ionized
plasma is investigated under the assumption that the Coulomb
C
image forces and
diffusion contribute to the ion transport in the carrier plasma and define the rate of
charging processes (Brock
1970
; Burtcher and Schmidt-Ott
1985
; Khachatourian
and Wistrom
2001
). Our approach is based on the flux-matching theory already
described. The collisionless kinetic equation is solved, and the ion concentration
profile in the free molecule zone (at distances less than the ion mean free path)
