Geoscience Reference
In-Depth Information
PARTICLE SIZE (in nm)
0
10
20
30
40
50
60
1.2
Q=2, q=1
Q=q=1
Q=1, q=2
1.0
ε
=5
0.8
0.6
0.4
0.2
0.0
0.2
0.4
0.6
0.8
1.0
PARTICLE SIZE (in units of l
c
)
Fig. 3.12
Influence of particle (ion) charge on double charging efficiency. Shown are the
suppression factors ".a/ as the function of 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
ˇe
2
D
momenta corresponding to the ion trajectories intersecting the particle surface. The
analysis becomes somewhat nontrivial because we consider the flux from a sphere
of
finite
radius
R
. In what follows we introduce the notation L
a
for the separating
angular momentum (its value depends on the ion energy).
3.6.1.1
Nonsingular Attraction
Let us begin by considering attractive nonsingular potentials
j
U.r/
j /
r
˛
, ˛<2.
The function L
2
.r/
D
2mr
2
.E
U.r// is shown schematically in Figs.
3.13
and
3.14
for
E
> 0and
E
< 0. It is seen that ions with L
2
<2m.E
U.a//
are able to reach the particle surface. At
E
< 0 the situation changes; if
2mR
2
.
j
E
j C j
U.R/
j
/<2ma
2
.
j
E
j C j
U.a/
j
/, then the trajectories with
