Environmental Engineering Reference
In-Depth Information
of neutral particles in an ionized gas, and therefore the character of reacting to
external fields as well some plasma collective phenomena in ionized gases are de-
termined by charged particles only and are independent of the presence of atoms
or molecules in an ionized gas. As a result, collective phenomena in ionized gases
have a universal character and may be identical for various ionized gases if the gas
criterion holds true for neutral and charged particles.
1.1.7
Interaction of Charged Particles in an Ideal Plasma
We now calculate the average potential energy of a charged particle in an ideal
plasma and the distribution function for the interaction potential of charged parti-
cles. From the interaction potential (1.11) for two charged particles, we have for its
average value
Z
1
h
N
0
exp
T
N
0
exp
e
T
i
d
r
.
e
U
D
e
'
0
˙
e
and use (1.10)
We assume the charges of electrons and ions in a plasma to be
'
C
e
,thatis,
for the electric potential
from an individual plasma particle of charge
r
exp
.
e
r
r
D
' D
The above formula for the average interaction potential in an ideal plasma accounts
for pairwise interactions of all the charged particles in a volume that have a Boltz-
mann distribution. In the case of an ideal plasma, the principal contribution to the
integral occurs at small interactions
e
'
T
,whichgives
Z
1
2
N
0
T
4
π
N
0
r
D
T
e
2
2
r
D
T
,
)
2
4
r
2
dr
U
D
(
e
'
π
D
D
(1.14)
0
where we used expression (1.7) for the Debye-Hückel radius. Thus, the average
energy of a charged particle in an equilibrium plasma is
3
T
2
e
2
2
r
D
.
ε
D
(1.15)
U
of the interaction potential for a charged particle
in a plasma, we assume this value to be determined by positions of other charged
particles in a sphere of the Debye-Hückel radius centered on the test particle. The
mean number of char
ge
d particles in this region is
n
To estimate fluctuations
Δ
N
0
r
D
1, with fluctua-
tions of the order of
p
n
. Hence, the fluctuation of the interaction potential of the
test charged particle in a plasma is
p
n
e
2
e
2
N
1/2
0
r
1/
D
.
U
r
D
Δ
(1.16)
