Chemistry Reference
In-Depth Information
1.0
0
.
0
0.2
0.4
0.6
0.8
1.
0
10
7
0
.
0
0.2
0.4
0.6
0.8
1.
0
1.0
10
7
j
+
/
j
0.8
0.8
10
6
10
6
n
+
0.6
0.6
10
5
10
5
j
= 3 µA/cm
2
j
= 3 µA/cm
2
0.4
0.4
10
4
10
4
n
e
0.2
0.2
10
3
10
3
j
e
/
j
0.0
0.0
10
2
10
2
0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
0.4
0.6
0.8
1.0
z
/
d
E
z
/
d
E
(a)
(b)
FIGURE 3.35
Characteristic axial profiles for the current density (a), and charge carrier
density (b) between the discharge gap for a Townsend discharge (
E
/
p
=
100 V (cm Pa)
−
1
,
α
·
d
E
=
5,
b
+
·
p
=
·
10
5
cm
2
·
Pa V
−
1
s
−
1
,
b
e
/
b
+
=
2
100).
It is to note the essential contribution of the ion current to the total current in the
most part of the gap. Furthermore, no quasi-neutral region and therefore no plasma
is observed because of the dominant positive ion density in the discharge gap, with
the exception directly in front of the anode, see Figure 3.35b.
3.7.3 G
LOW
D
ISCHARGES
3.7.3.1 Transition from the Townsend Discharge to the Glow Discharge
With increasing discharge current the raising positive space charge density determines
more and more the electric field strength in the discharge gap. At constant gap width
and neutral gas pressure, the transition from the Townsend to the glow discharge
regime may be defined for the special case that the electric field strength decreases
from the maximum value at the cathode (
z
=
0) to the value zero at the anode position
(
z
=
d
E
), see [43].
With the approximations
n
+
,
the 1D source equation for the electric space charge field is solved with the boundary
conditions
E
n
e
and
j
≈ |
j
+
| =
e
·
n
+
·
v
+
D
=
e
·
n
+
·
b
+
·
E
|
j
e
|
(
z
=
0
)
=
E
0
and
E
(
z
=
d
E
)
=
0
1
1
/
2
z
d
E
E
(
z
)
=
E
0
·
−
(3.287)
2
.
From the rearrangement of the expression for
E
0
in (3.287) to the total discharge
current density
j
and the multiplication with 1
1
/
with
E
0
=
((
2
·
j
·
d
E
) / (
ε
0
·
b
+
))
/
p
2
it follows
E
0
p
2
j
p
2
b
+
·
ε
0
·
E
0
p
p
=
ε
0
2
·
(
p
·
b
+
)
=
·
d
E
)
·
.
(3.288)
2
·
d
E
·
p
2
(
p
·
The relation
j
/
p
2
in terms of (
p
·
d
E
), (
E
0
/
p
), and (
p
·
b
+
) provides a further similarity
parameter in gas discharge physics.
