Environmental Engineering Reference
In-Depth Information
where
r
is the distance from the charge considered. If this charge is located in a
vacuum, the right-hand side of this equation is zero, and the solution has the form
' D
q
/
r
,where
q
is the charge. Requiring the solution of the above equation to
be coincident with this one at
r
!
0, we obtain for the potential of a test charged
particle in a plasma
r
exp
.
q
r
r
D
' D
(1.10)
Hence, the interaction potential
U
of two charged particles with charges
q
1
and
q
2
is as follows:
exp
.
q
1
q
2
r
r
r
D
U
(
r
)
D
(1.11)
Thus, the Debye-Hückel radius is a typical distance at which fields in a plasma are
shielded by the charged particles. The field of a charged particle is eliminated on
this scale by fields of surrounding particles.
Now we shall check the validity of the condition
e
T
,whichallowedusto
simplify the equation for the electric field strength. Because this condition must
work at distances of the order of
r
D
,ithastheform
'
e
6
N
0
T
3
1/2
e
2
r
D
T
1.
This condition according to criterion (1.3) characterizes an ideal plasma.
We can determine the number of charged particles that participate in shielding
the field of a test particle. This value is of the order of magnitude of the number of
charged particles located in a sphere of radius
r
D
. The number of charged particles
is, to within a numerical factor,
s
T
3
N
0
e
6
r
D
N
0
1.
Figure 1.4
The distribution of the electric potential in a gap containing an ionized gas. 1 - the
Debye-Hückel radius is large compared with the gap size; 2 - the Debye-Hückel radius is small
compared with the gap size.
