Environmental Engineering Reference
In-Depth Information
The diffusion of the electrons is seen to lead to damping of the drift wave because
the dependence of electron parameters on time has the form exp(
t
). As a result
of electron diffusion, the perturbation region increases in size and the perturbation
dissipates.
The behavior of the drift wave depends on the type of ionization processes in the
gas. Under certain conditions, the interaction of drift waves with the ionization pro-
cess of gas atoms by electron impact leads to amplification of the drift waves. This
phenomenon is called ionization instability. Various types of ionization instability
can occur depending on the particular properties of a plasma and the processes
within it. The development of ionization instability leads to the formation of struc-
tures in the plasma that will be considered below.
i
ω
5.5.2
Ionization Instability from Thermal Effects
A common causal mechanism for ionization instability is to be found in the pos-
itive column of an arc, where the instability arises from thermal processes. The
equilibrium electron number density depends strongly on the plasma temperature,
whereas the temperature dependence of the heat transport coefficient is weak. At
high intensities, thermal instability occurs because the heat transport mechanism
due to atom thermal conductivity is unable to provide heat release. This instability
may lead to contraction of the plasma that increases heat release or it can cause the
formation of new types of structures in the plasma. A simple example of this phe-
nomenon arises when the heat transport in a cylindrical discharge tube depends
upon thermal conductivity. The heat balance equation in this case has the form
d
d
)
dT
d
1
(
C
p
(
)
D
0 ,
(5.130)
where
is the distance from the tube axis,
is the thermal conductivity coefficient,
and
p
(
iE
is the specific power of heat release, where
i
is the current den-
sity and
E
is the electric field strength. We assume that the rate of heat release is
strongly dependent on the local plasma temperature, and is a function only of this
temperature.
This model is descriptive of arc discharges at high currents and high pressures.
If the gas discharge plasma is in equilibrium, the electron and gas temperatures
are similar, and the electron number density can be estimated from the Saha for-
mula (1.52) to behave as
N
e
)
D
J
/(2
T
)], where
J
is the ionization potential of
the gas atoms, and it is usually true that
T
exp[
J
. The specific power of heat release
is
p
iE
, where the electric field strength
E
does not vary over the discharge cross
section, and the variation of the current density
i
is proportional to
N
e
.Thespecific
power of heat release in an arc discharge is determined not only entirely by the
temperature, but also has a strong dependence on the temperature. In this case the
equilibrium between ionization and recombination is maintained at each point in
the plasma, that is, local ionization equilibrium is supported in the plasma.
D
