Environmental Engineering Reference
In-Depth Information
will no longer decay as a result of electron diffusion. Thus, the ionization wave can
amplify in the range of wave vectors
k
1
s
J
s
k
ion
N
B
T
e
<
k
<
.
(5.170)
D
a
If this condition is satisfied, ionization waves can develop, and striations arise. The
plasma then exhibits a striped structure with a specific periodicity.
Considering the striations as ionization waves gives an understanding of some
aspects of this problem [85, 86]. One can formulate conclusions which follow from
the above analysis of striations as instabilities of ionization waves in a gas discharge
plasma. For low gas discharge currents this instability proceeds only in an interme-
diate range of electron number densities where the ionization rate depends on the
number density of electrons (the Rother condition (5.166)). Next, we have differ-
ent regions in the spatial distributions of species, so the wave distribution of the
electron number density is shifted with respect to the electron temperature.
5.5.9
Self-Consistent Structure of Striations
In considering striations as ionization waves, we divide a region into elements with
the length of a wave for each element, so plasma parameters are repeated in each
element. According to the Pupp classification [107-109], for striations of low pres-
sure and discharge electric currents, the wavelengths of striations as oscillations
in a plasma of inert gases are small compared with the mean free path electrons
with respect to energy change in elastic electron-atom collisions, but are large in
comparison with the mean free path of electrons with respect to electron scattering
by atoms. According to the properties of waves, the electric voltage
'
(
λ
) between
two points a distance of one wave period
λ
apart is the same
Z
λ
'
(
λ
)
D
E
(
x
)
dx
D
const ,
0
where
E
(
x
) is the electric field strength at point
x
and
is the wavelength for
striations. According to the Novak rule [116], the voltage per striation is almost
constant for a given striation type, that is, this value is independent of the electric
current and pressure. As a demonstration of this, Table 5.1 gives the values of the
voltage per striation for three striation types (P, R, S) in gas discharge of inert gases,
where these values are compared with the atomic excitation energy
λ
Δ
E
,theatomic
ionization potential
J
and the ionization potential
J
for a metastable atom.
Our goal is to understand the nature of striations as ionization waves in an atom-
ic gas of low density if the mean free path of electrons is small compared with a
striation length (the spatial period of oscillations), but the mean free path of elec-
trons with respect to variation of their energy as a result of elastic collisions with
