Environmental Engineering Reference
In-Depth Information
3
Physical Kinetics of Ionized Gases
3.1
Kinetics of Atomic Particles in Gases and Plasmas
3.1.1
The Boltzmann Kinetic Equation
An ensemble of identical atomic particles may be described in different manners.
In hydrodynamic terms, we deal with average parameters of atoms of a gaseous
system, in particular, with the drift velocity
w
(
r
) of gas atoms at a given coordinate
r
. In kinetics, the distribution function is used at a given space point
f
(
v
,
r
), so
fd
v
is the number density of atoms with velocities in a range between
v
and
v
C
d
v
.
In a general case, we define the distribution function
f
(
v
,
J
,
r
,
t
) that relates to
time
t
, and the parameter
J
characterizes all internal quantum numbers of atomic
particles. The normalization condition for the distribution function has the form
Z
f
(
v
,
J
,
r
,
t
)
d
v
,
X
N
(
r
,
t
)
D
(3.1)
J
where
N
(
r
,
t
) is the number density of atomic particles (atoms) at point
r
and time
t
.
The distribution function gives detailed information about an ensemble of atomic
particles and its evolution. In particular, the drift velocity of particles is given by
Z
D
X
J
w
(
r
,
t
)
v
f
(
v
,
J
,
r
,
t
)
d
v
.
(3.2)
The characteristic behavior of a test particle in a gas is such that most of the time
it moves along straightforward trajectories, and sometimes it interacts with sur-
rounding particles. This particle behavior in a gas is governed by the gaseous state
criterion (2.27)
N
3/2
is the cross section of pairwise collisions of
gas particles. If this criterion holds true, the probability of collision of a test particle
with any gas particle at a given time is of the order of
N
σ
1, where
σ
3/2
1, the probability of
simultaneous collision of three gas particles is of the order of (
N
σ
3/2
)
2
1, and so
on. Hence, most of the time the test particle does not interact with surrounding gas
particles, and its state changes as a result of pairwise collisions with gas particles.
σ
