Environmental Engineering Reference
In-Depth Information
in accordance with (1.8). But in this case only electrons partake in screening of ion
fields and hence the Debye-Hückel radius is given by
s
T
e
4
r
D
D
π
N
0
e
2
instead of (1.9). For an ideal plasma (1.3) this effect is weak for the maximum of
the distribution function
E
E
0
.
1.1.9
Beam Plasma
We considered above a quasineutral plasma as a widespread plasma type. In re-
ality, plasma boundaries (called plasma sheaths, or double layers) contain a non-
neutral plasma. Plasma properties in this region depend on processes that occur
there. If charged particles are generated by a metallic surface or charged particles
recombine on walls, an intermediate layer of nonneutral plasma arises between
the plasma and the surface. A nonneutral plasma also occurs if charged particles
are collected in certain regions or traps, and if they are transported through space
by the action of external fields in the form of beams. Thus, a nonneutral plasma
is a specific physical object [25, 26], so the primary characteristic of a nonneutral
plasma arises from the strong fields created by the particle charge, and that re-
stricts the plasma density. As an illustration, we shall consider a classic example of
anonneutralplasmaformednearahotcathode.
We start from a simple estimation. Let a beam of electrons have number density
N
e
10
10
cm
3
(the minimum boundary of the electron number density for a
glow discharge) and beam radius
1 cm. Then from the Poisson equation (1.4)
we have the following estimation for the electric voltage
0
'
between the beam center
and its boundary:
2
0
'
4
π
eN
e
20 keV .
This shows the necessity of using specific electric optics to conserve this plasma.
One can generate an electron beam in a simple way by heating a metallic sur-
face in a vacuum; this will cause the surface to emit an electron flux as a result of
thermoemission. Using electric fields allows us to accelerate electrons and remove
them from the surface in the form of a beam. But the parameters of this beam can
be limited by internal electric fields that arise from electron charges. We can find
the properties of such a beam, created between two flat plates a distance
L
apart,
with an electric potential
U
0
between them.
The electron current density
i
is constant in the gap because electrons are not
produced nor do they recombine in the gap. This gives
i
D
eN
e
(
x
)
v
e
(
x
)
D
const ,
w
here
x
is th
e distance from the cathode,
N
e
is the electron number density,
v
e
D
p
2
e
'
(
x
)/
m
e
is the electron velocity, and the electric potential is zero at the cathode
