Geoscience Reference
In-Depth Information
2
3
L 2
L 2
SINGULAR (r)
1
L 2
NONSINGULAR (r)
L 2
2
1
a
r
DISTANCE
Fig. 3.7 Nonsingular and singular ion-particle interactions. Shown are the maximal admissible
angular momenta L 2 .r/ as the functions of r . Ions with the trajectories 1 can reach the particle
surface and be captured by the particle. Ions of trajectories 2 pass aside from the particle. The
finite trajectory 3 cannot be populated in the free molecule regime and thus does not contribute to
the particle charging efficiency
function of r ) in the admissible interval of L . The latter is defined by two conditions:
(1) 0<L 2 <L 2 .r/ (this condition provides the existence of the square root on the
right-hand side of Eq. 3.23 ), and (2) the finite ion trajectories do not contribute to
the ion distribution. These trajectories can appear as the bound states of attractive
potentials at negative E or at E > 0 if the function L 2 .r/ has a minimum at r D r >
a as it takes place, for example, in the case of attractive potentials (see Fig. 3.7 ).
Hence,
f s .r;E;L/ D B s .E;L/ L 2 m .r/ L 2
(3.105)
with .x/being the Heaviside step function. The function B s .E;L/ is still arbitrary.
Its dependence on E is defined by the condition that f s / e ˇE .E/ as r !1 .
Here, ˇ D 1=kT . The factor .E/ excludes the bound states of ions, for they do
Search WWH ::




Custom Search