Environmental Engineering Reference
In-Depth Information
2.2.2
Atom Ionization by Electron Impact
Processes in which ions and free electrons are either introduced into a plasma or
removed from it are fundamental to the establishment of plasma properties. Below
we analyze basic processes of this type. We consider first the ionization of an atom
by electron impact:
A
C
.
e
C
A
!
2
e
C
(2.59)
In this process the incident electron interacts with a valence electron, transfers to
it part of its kinetic energy, and causes the detachment of the valence electron from
the initially neutral atom. We can analyze this process in terms of a simple mod-
el developed by J.J. Thomson [94], in which it is assumed that electron collisions
can be described on the basis of classical laws, and that the electrons do not in-
teract with the atomic core in the course of the collision. Despite the fact that the
atom is a quantum system, this model gives a correct qualitative description of the
process because the cross sections for elastic collisions governed by the Coulomb
interaction are identical in the classical and quantum cases.
In determining the ionization cross section, we ignore the interaction of incident
and bound electrons with the charged core during energy transfer between these
electrons, and this is a model assumption. Next, we assume the bound electron
to be motionless at the beginning and consider scattering into small angles. Then
the differential cross section of collision with exchange of energy
is given by the
Rutherford formula (2.35), and the atom ionization occurs if the energy transferred
to the valence electron exceeds the atomic ionization potential
J
. This leads to the
following expression for the ionization cross section [94]:
Δ
ε
1
J
.
Z
ε
e
4
ε
σ
D
π
1
ε
σ
D
d
(2.60)
ion
J
This expression for the ionization cross section is called the Thomson formula.
Although this result is for an atom with one valence electron, it can be generalized
for atoms with several valence electrons.
Since the process was treated classically, the ionization cross section depends on
classical parameters of the problem:
m
e
(the electron mass),
e
2
(the interaction pa-
rameter),
(the electron energy), and
J
(the ionization potential). The most general
form of the cross section expressed through these parameters is
ε
f
J
,
e
4
J
2
D
π
σ
(2.61)
ion
where
f
(
x
) is, within the framework of the approach we employ, a universal func-
tion which is identical for all atoms. In particular, for the Thomson model this
function is
1
x
1
x
2
f
(
x
)
D
.
