Chemistry Reference
In-Depth Information
10
-1
10
0
10
1
10
2
10
3
10
4
10
5
10
5
10
4
10
4
Air
Ar
10
3
10
3
10
2
10
2
10
-1
10
0
10
1
10
2
10
3
10
4
p
.
d
E
in (Pa
.
m)
FIGURE 3.34
Breakdown voltage in dependence on
p
·
d
E
with the Paschen minimum
calculated by (3.282) with γ
=
=
·
m)
−
1
,
C
2
=
·
m)
−
1
)andair
0.05 in Ar (
C
1
9(Pa
135 V(Pa
(
C
1
=
11.3(Pa
·
m)
−
1
,
C
2
=
275 V(Pa
·
m)
−
1
).
j
=
j
eC
(
0
)
+
j
+
C
(
0
)
=
j
eC
(
0
)
+
1
/
γ
·
j
eC
(
0
)
and anode
j
=
j
eA
(
d
E
)
, we obtain after
integration over
z
for the electron and ion current density
γ
j
e
(
z
)
=
j
eC
·
exp
(
α
·
z
)
=
j
·
γ
·
exp
(
α
·
z
)
1
+
1
.
(3.284)
γ
j
+
(
z
)
=
j
·
−
γ
·
exp
(
α
·
z
)
+
1
Replacing γ in (3.284) with the breakdown condition (3.279) permits the rearrange-
ment of the current densities
j
e
(
z
)
=
j
·
exp
[
α
(
z
−
d
E
)
]=
e
·
n
e
·
b
e
·
E
(3.285)
j
+
(
z
)
=
j
·[
1
−
exp
[
α
(
z
−
d
E
)
]] =
e
·
n
+
·
b
+
·
E
and the calculation of electron and positive ion density
E
p
−
1
j
1
b
e
·
j
n
e
(
z
)
=
E
·
exp
[
α
(
z
−
d
E
)
]=
C
be
·
·
exp
[
α
(
z
−
d
E
)
]
e
·
e
·
E
p
−
1
j
1
b
+
·[
j
n
+
(
)
=
E
·
−
[
(
−
d
E
)
]] =
C
b
+
·
·[
−
[
(
−
d
E
)
]]
(3.286)
z
1
exp
α
z
1
exp
α
z
·
·
e
e
with 0
≤
z
≤
d
E
and
b
·
p
=
C
b
=
const
. in the discharge gap, see Figure 3.35.
