Environmental Engineering Reference
In-Depth Information
is small compared with the tube radius. This is the equation for the longitudinal
electric field strength which determines the ionization rate compensated for by the
departure of electrons and ions to the walls.
We now analyze the character of motion of electrons and ions to the walls. Elec-
trons and ions attach to the walls and recombine there, and we have that the elec-
tron
j
e
and ion
j
i
fluxes to the walls are identical:
j
e
D
j
i
.
(4.126)
To fulfill this, it is necessary that the electric field at the walls precludes approach of
electrons to the walls, and this electric field arises if the walls are charged negatively.
Next, this electric field is damped by the Debye screening by the plasma as we
approach to the walls, and for definiteness we take the following relations between
plasma parameters:
λ
r
D
,
0
where
isthemeanfreepathofelectronsandionsand
r
D
is the Debye-Hückel
radius. Under these conditions we have that the processes under consideration pro-
ceed in a flat layer near the walls and plasma quasineutrality occurs near the walls,
where the field is absent. Then the action of the walls reduces to the potential
U
near the walls, which repels the electrons.
Thus, introducing the electron
T
e
and ion
T
i
temperatures, we have for the elec-
tron and ion fluxes to the walls
λ
N
e
s
T
e
2
N
i
s
T
i
2
j
e
D
,
j
i
D
,
(4.127)
π
m
e
π
m
i
where
N
e
and
N
i
are the electron and ion number densities near the walls and
m
e
and
m
i
are the electron and ion masses. Equality of the electron and ion fluxes is
governed by the wall electric potential
U
with respect to the plasma, which gives
N
i
exp
,
eU
T
e
N
e
D
which gives the following expression for the wall potential:
ln
T
e
m
i
T
i
m
e
.
T
e
2
eU
D
(4.128)
Thus, the plasma sheath is formed at the plasma boundary, and its parameters
may be different depending on the parameters of the ionized gas near the plasma
boundary. One more effect may follow from the nature of the double layer where
electron and ion fluxes toward the plasma boundary originate, because of interac-
tion of these fluxes with a surrounding plasma, and this interaction may lead to
instability of the double layer [101, 102].
