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