Environmental Engineering Reference
In-Depth Information
These examples illustrate the above conclusion for a strongly coupled plasma:
namely, that its properties are determined by interactions involving both neutral
and charged particles. Different physical objects of this type do not have general
properties determined only by the charged particles. Therefore, when one describes
a system as a “strongly coupled plasma”, the immediate implication is that it is not
one of a general class with identical properties as in the case of an ideal plasma.
1.3.5
Quantum Plasmas
We can treat a dense, low-temperature plasma of metals as a degenerate Fermi
gas. Because of the low temperature and high density, the system has quantum
properties. Let us consider the limit when
T
0, and take into consideration the
Pauli principle, according to which two electrons cannot be in the same state. With
the positive charge distributed uniformly over the plasma volume, this plasma is
a degenerate electron gas. At zero temperature the plasma electrons have distinct
momenta
p
in the interval 0
D
p
p
F
.TheFermimomentum
p
F
is found from
the relation
2
Z
d
p
d
r
(2
n
D
,
π
„
)
3
where
n
is the total number of plasma electrons, the factor 2 accounts for the two
possible directions of the electron spin, and
d
p
and
d
r
are elements of the elec-
tron momentum and the plasma volume. Introducing the electron number densi-
ty
N
e
n
/
R
d
r
,wehave
p
F
2
3
N
e
)
1/3
D
D
(3
π
„
for the Fermi momentum, and the
Fermi energy is
p
F
2
m
e
D
2
N
e
)
2/3
2
(3
π
„
ε
D
.
(1.93)
F
2
m
e
T
or
r
D
N
1/3
a
0
.
We define a quantum plasma to be a charged particle system characterized by the
small parameter
The parameters of a classical plasma satisfy the relation
ε
F
e
T
ε
η
D
,
(1.94)
F
exactly opposite to the condition for a classical plasma. The Fermi energy is a funda-
mental parameter of a degenerate electron gas, and it is the parameter that is used
for the analysis of a quantum plasma. We introduce the parameter characterizing
the ideal nature of a quantum plasma by analogy with the plasma parameter (1.3)
as the ratio of the Coulomb interaction energy of electrons to the Fermi energy, or
e
2
/
r
W
ε
2
5/3
0.337
a
0
N
1/3
D
D
D
,
(1.95)
a
0
N
1/3
3
π
F
e
e
where
r
W
is the Wigner-Seitz radius and
a
0
is the Bohr radius. The ideal degener-
ate electron gas has a high density compared with the characteristic atomic density,
