Environmental Engineering Reference
In-Depth Information
The quantity selected to characterize a plasma may not be
γ
,butmayinstead
maybesomefunctionof
of the plasma,
introduced as the ratio of the Coulomb interaction potential of a charged particle
with its nearest neighbors to the thermal energy,
γ
. Often one uses the coupling constant
Γ
4
1/3
e
2
r
W
T
D
πγ
3
Γ
D
,
(1.81)
N
e
/3)
1/3
is the Wigner-Seitz radius. A dense plasma is one with
where
r
W
D
(4
π
1, and is called a strongly coupled plasma. The condition for the plasma to be
ideal is
Γ
Γ
1, which implies that
3
4
γ
D
0.2 .
(1.82)
π
We can express plasma properties as a function of the plasma coupling constant
. The ratio of the average interaction energy of a charged plasma particle with
other particles to its mean kinetic energy has the form
Γ
3
p
2
)
3/2
2
1/2
e
2
r
D
(
2
2
3
T
D
4
Γ
πγ
D
.
Thenumberofelectronsinasphereofradius
r
D
is
r
D
N
e
3
4
π
1
6
p
8
1
0.07
Γ
N
D
D
D
D
D
3/2
,
πγ
)
3/2
(6
Γ
and the criterion
N
D
0.2.
Note that the plasma under consideration consists of electrons and ions with a
single charge. For a plasma with multicharged ions, the ideality criterion (1.5) is
violated at low ion density. In particular, for interaction between ions after chang-
ing in criterion (1.5)
e
to
Ze
,where
Z
is the ion charge, we obtain the plasma
parameter (1.78) in the form
1 of an ideal plasma gives
Γ
Z
6
e
6
N
i
T
3
γ
D
.
10
3
,thenumber
In particular, for a dusty plasma with typical parameters [70]
Z
D
10
3
cm
3
,and
T
density of particles
N
p
D
D
400Kwehavefortheplasmaparam-
10
5
, that is, in this example one can consider the plasma to have strong
eter
γ
coupling.
1.3.2
Conditions for Ideal Equilibrium Plasmas
We expect a plasma to fail to be an ideal plasma as the plasma density increases,
but if a plasma is prepared from a gas and ionization equilibrium is supported
between electrons and atoms, this plasma is ideal. Below we convince ourselves
