Environmental Engineering Reference
In-Depth Information
1.1.4
Charged Particles in a Gas
We shall consider primarily a plasma whose properties are similar to those of a gas.
As in a gas, each particle of the plasma will follow a straight trajectory as a free par-
ticle most of the time. These free-particle intervals will occasionally be punctuated
by strong interactions with surrounding particles that will cause a change in energy
and the direction of motion. This situation occurs if the mean interaction potential
of the particle with its neighbors is small compared with the mean kinetic energy
of the particle. This is the customary description of the gaseous state of a system,
and a plasma that also satisfies this description is called an ideal plasma.
Let us formulate now a quantitative criterion for a plasma to be ideal. The
Coulomb interaction potential between two charged particles has the absolute val-
ue
e
2
/
R
,where
e
is the charge of an electron or a singly charged ion and
R
is the distance between interacting particles. Thus, the interaction potential at
the mean distance between particles
R
0
j
U
(
R
)
jD
e
2
N
1/
e
,andbecausethe
mean thermal energy of the particles is of the order of
T
(
T
is the plasma tempera-
ture expressed in energy units), the condition of the gaseousness of a plasma due
to interaction of charged particles is characterized by the smallness of the plasma
parameter
N
1/3
is
j
U
j
e
γ
,whichis
N
e
e
6
T
3
γ
D
1.
(1.3)
If the gaseousness condition (1.3) is fulfilled for a plasma, this plasma is ideal. In
the following, we shall deal primarily with a plasma whose parameters satisfy (1.3).
We define a weakly ionized gas as a gas with a small concentration of charged
particles. Nevertheless, some properties of the weakly ionized gas are governed
by the charged particles. For example, the degree of ionization in power-discharge
molecular lasers is 10
7
10
5
. In these lasers, the energy is first transferred from
an external source of energy to electrons, and then it is transformed to the ener-
gy of laser radiation. As we shall see, a relatively small concentration of electrons
determines the operation of this system.
Some properties of a weakly ionized gas are determined by the interaction
between charged and neutral particles, whereas other properties are created by
charged particles only. Although the concentration of charged particles in a plasma
is small, the long-range Coulomb interaction between them may be more im-
portant than the short-range interaction between neutral particles. We consider
below the plasma properties that are associated with the presence of charged par-
ticles. The short-range interaction of neutral particles is not important for these
properties.
We now study the penetration of an external electric field into a plasma. Since
this field leads to a redistribution of the charged particles of a plasma, it creates an
internal electric field that opposes the external field. This has the effect of screening
the plasma from an external field. To analyze this effect, we consider the Poisson
