Environmental Engineering Reference
In-Depth Information
2
Elementary Processes in Excited and Ionized Gases
2.1
Elastic Collision of Atomic Particles
2.1.1
Elementary Act of Collisions of Particles in a Plasma
If we deal with an ionized gas consisting of atoms or molecules with an admixture
of electrons and ions, the ionized gas is an ideal plasma, so each if its particles is
free and can interact with surrounding particles in short time intervals. As a result
of each act of strong interaction that is a collision of a test particle with surrounding
particles, the state of the test particle may be changed, and our goal is to define the
parameters of the elementary act of particle collision.
In considering the collision of a test particle
A
with particles
B
in a gas of these
particles, where the initial state of particle
A
changes as a result of these collisions,
we denote the initial state of particle
A
by subscript
i
and the final state by sub-
script
f
. Then the probability
P
(
t
)thatparticle
A
remains in the initial state up to
time
t
is governed by the equation
dP
dt
D
ν
if
P
,
(2.1)
in compliance with the nature of this process. Here
if
is the probability of this
transition per unit time, and we assume that the transition takes place only between
indicated states.
Let us use a coordinate frame where the test particle
A
is motionless. The transi-
tion probability per unit time
ν
if
is proportional to the incident flux
j
of particles
B
.
One can introduce as a characteristic of the elementary act of particle collisions the
cross section of this process, which is the ratio
ν
if
/
j
. It is important that this quan-
tity is independent of the number density [
B
]oftheparticles
B
. If all the particles
B
move with identical velocity
v
B
, the flux of gas particles is given by
ν
[
B
],
where
v
A
is the velocity of particle
A
. Thus, we have the following connection be-
tween the frequency of transition
j
v
A
v
B
j
ν
if
and the transition cross section
σ
if
:
ν
D
[
B
]
j
v
A
v
B
j
σ
if
.
(2.2)
if
