Chemistry Reference
In-Depth Information
10
4
1
0
0
10
1
10
2
10
4
Electrons
10
3
10
3
10
2
10
2
Ions
10
1
10
1
10
0
10
0
10
-1
10
-1
10
0
10
1
10
2
in V Pa
-1
cm
-1
E
0
/
p
FIGURE 3.38
Ions and electrons arriving the electrode from the discharge center represented
by the product
d
E
·
ω in dependence on the reduced electric field strength
E
/
p
according to
(3.303) with
b
+
·
p
=
C
+
=
2
·
10
5
cm
2
Pa(V s)
−
1
and
b
e
/
b
+
=
100.
Furthermore, the transit time
3
·
s
Child
v
0
τ
+
=
(3.304)
(with
v
0
=
(
1
/
2
) of the ions through the plasma sheath is important
which is estimated by use of the Child-Langmuir sheath model and time-averaged
sheath thickness and potential.
As the consequence, at higher electric field frequencies the breakdown voltage
depends on both, the product
p
·
·
ϕ
Child
/
m
+
)
2
e
d
E
.
Firstly, a qualitative overview is given about the characteristic changes in the
discharge mechanisms with increasing electric field frequency.
Standard line frequency
50 Hz
·
d
E
and ω
·
ω
pe
, ω
+
: At very low frequency case the
discharge processes are considered to be similar to the static electric field (quasi-
stationary conditions). For example, at the standard line frequency of 50 Hz, the
low-pressure discharge represents an alternating DC glow discharge. For each half
cycle an electric breakdown (ignition) and the development of the discharge regions
(e.g., cathode sheath, negative glow) is observed. If the voltage goes down the dis-
charge disappears. At the zero point of the cycle no charged particles are present
due to ambipolar diffusion to the electrodes/walls and recombination. With increas-
ing voltage at the next half cycle the discharge starts at the breakdown voltage
completely new.
Mid-frequency range
10
4
ω
p
+
: At mid-frequencies the loss
of charged particles by ambipolar diffusion and recombination per time unit is in
the order with the electric field frequency. No complete new ignition is necessary for
−
10
5
Hz
ω
pe
,
<
