Environmental Engineering Reference
In-Depth Information
1.3
Rarefied and Dense Plasmas
1.3.1
Criteria for an Ideal Plasma
Many varieties of plasmas are known, with most of them composed of weakly in-
teracting particles (see Figures 1.1-1.3). These plasma systems are analogues of
gaseous systems of neutral particles. When they experience weak interactions, the
system of charged particles is an ideal plasma, with the criterion for plasma ideality
expressed by (1.3) between plasma parameters. The small parameter of the theory,
the plasma parameter, has the form [69]
N
e
e
6
T
e
γ
D
,
(1.78)
and the condition to have an ideal plasma is
γ
1. Specific values for
γ
can be
estimated on the basis of fundamental physical considerations.
The first criterion for an ideal plasma refers to the condition that the mean in-
teraction energy of a plasma particle with its neighbors must be small compared
with its kinetic energy 3
T
/2. (We assume in the following that electrons and other
plasma particles have the same temperature.) The electric potential arising from a
charged plasma particle is given by (1.10), and close to the nucleus it is
q
r
q
r
D
,
' D
r
r
D
,
where
q
is the particle charge,
r
is the distance from this particle, and
r
D
is the
Debye-Hückel radius. The first term in this expression is the particle potential
in a vacuum, and the second term is the electric potential that is created by the
neighboring plasma particles. This means that the average interaction energy of a
particle of charge
e
with other plasma particles is
e
2
/
r
D
, and the criterion for an
ideal plasma (
e
2
/
r
D
3
T
/2) leads to the value
9
32
γ
D
0.09 .
(1.79)
π
A second criterion follows from the condition that many charged particles are
located in the sphere of radius
r
D
,thatis,4
r
D
N
e
/3
π
1. This gives the value
1
96
γ
D
0.003 .
(1.80)
π
Criteria (1.79) and (1.80) both contain identical combinations of parameters, but
yield different numerical values. Criterion (1.79) is preferred, because it encom-
passes a larger region in which the ratio of the potential energy of a particle to its
kinetic energy can be a small parameter, and thus is useful for expansion of plasma
parameters. Nevertheless, Figures 1.1 and 1.2 display criteria (1.79) and (1.80) as
boundaries between an ideal plasma and a dense plasma.
