II.
MICROWAVE GASEOUS DISCHARGES
L. Gould
J. J. McCarthy
Prof. W. P. Allis
J. W. Lathrop
K.
Dr. F.
D. H. Looney
A. V.
Phelps
G. J.
Schulz
Prof. S. C.
Brown
Reder
N. W. Donelan
A.
-B.
Persson
THE STEADY STATE DISCHARGE IN HYDROGEN
A steady state microwave gas discharge occurs when the electron losses due to
This may be written as
diffusion equal the electrons gained due to ionization (1).
D
s
(1)
A2
where v. is the ionization frequency,
D
1
presence of space charge,
S
the diffusion coefficient of electrons in the
and A is the cavity diffusion length.
Equation 1 may be
rewritten in the form
D
D
The problem is now resolved into essentially two parts:
a calculation of (D_/vi) from
distribution function theory, and a calculation of (Ds/D
from boundary conditions.
(D /v)
of nA
should be a function of EeA and p/E
2
_)
while (D /D_)
e
should mainly be a function
(2).
Rewriting Eq.
1 of Ref.
I gives
2
.f+
xl
df
3v
Vc AZ
(f + u
s u-
2
) -
1
3-
d
3/2
u df
3m
u
v u
+
du
c
c u
M
(3)
where
eE
uc =
my
2
e
(4)
2
c
The distribution function, f, may be obtained quite readily if the terms in Eq. 3
containing 1/A
2
are neglected.
This gives
o
M
4f
m
n (v+
x
v
1
)
exp (-w)
v
-1
c
v
-3
exp(w) dw
(5)
w
where w is defined as
w
3m m
e
M
c
E
u is the energy of the electrons and v their velocity.
-10-
(6)
u
Vx,
i are the respective average
(II.
excitation and ionization frequencies.
MICROWAVE GASEOUS DISCHARGES)
The distribution function of Eq. 5 may be used
to give a perturbation solution of Eq. 3 which when combined with Eq. 2 gives as the
steady state equation
D
E
(ek
v
+v
i
X
(EeA)
w
w
1
/2
exp(w)
$(w)
dw dw
w
wow
V.
1
w3/2
1
w
0
w3/
2
exp (-w)
wl/2 exp (w) (w)dw dw
exp (-w)
0
L.
12
o
°
Vx + Vi
+
3/2
1 1
i
Vx
_-W
w
- 1/ 2
-
exp(w) dw dw
w
O0
3(w) is defined as
w 3/
d (w)
w
2
w3
exp (-w)
2
exp (w) dw
(8)
dw
w
0
is an effective excitation potential and varies as p/E.
u
For breakdown (D s = D_) only the.&(w ) terms need to be considered, since u
and EeA is so large as to make the uE term negligible.
= 0
The.'(wo) terms are just those
which would occur if a perturbation solution had not been used.
This indicates that the
distribution function of Eq. 5 is adequate for breakdown.
For steady state all the terms are important, since EeA is much smaller than in
breakdown.
The two perturbation terms tend to cancel except at low p/E where the
2
uE term predominates and causes a deviation from the nonperturbed solution. Figure
II- 1 shows the perturbed and nonperturbed solutions together with the experimental
data for a particular density.
B.
Other densities will have a similar shape.
OSCILLATIONS IN A D-C MERCURY ARC
The oscillations appearing in a tungsten filament mercury vapor arc were studied
as functions of the arc voltage and the filament heating current.
The maximum arc
current which can be drawn at a relatively fixed tube voltage is a function of the filament
heating current.
If a current higher than the maximum is drawn, the tube voltage
-11-
HYDROGEN
A = 0.2 cm
X = 9.40cm
100
-
EXPERIMENT -S
BREAKDOWN
THEORY
xX
Sxx
ELECTRON DENSITY
x
X
Xxx
X
X
xX/
x
n
A2 =4.1x106 cm
X
10
x
UNPERTURBED
PERTURBED
-
MOLECULAR ION -He
CURRENT
+
S
I
I ,
0.02
004
p/E
e
,
ATOMIC ION - He
CURRENT
I
006
b
P---
I00
008
TIME AFTER DISCHARGE - MILLISECONDS
TIME AFTER DISCHARGE- MILLISECONDS
mmHg-cm/volts
Fig. II- I
IU
I
12
Fig. II- 2
Comparison of theory and experiment
for steady state and breakdown in
hydrogen.
Electron density and helium ion current
during afterglow of pulsed discharge at
1.6 mm of Hg and A = 0.9 cm 2 .
IUo
RUNS I AND 4
s8RUN 2
60-
RUN 3
40-
X\THEORY PLOT
""
-
RUN5 \
-
. .
30-
RUNS
o
1,2
AND 3 -
CAVITY,LIOUID He TRAP
RUN 4 -
CAVITY, LIQUID He TRAP
RUN 5--
CAVITY, LIQUID N 2 TRAP
I
2
3
I
4
1
i
I
6
8
10
L
I
1
15
20
30
40
Ee/p--
Fig. II-3
Breakdown voltage in pure helium.
12-
I
60
80
100
(II.
MICROWAVE GASEOUS DISCHARGES)
increases rapidly as the current increases and the electric field in the discharge is
increased. The frequency of the oscillation is strongly correlated to the tube voltage.
As the tube voltage increases rapidly the frequency of the oscillations also increases
rapidly. Both the waveform and mode of oscillation are influenced by a weak magnetic
field while a strong magnetic field disrupts the oscillation into noise. This behavior
coupled with the electric field effect described above indicates the oscillation is caused
by the motion of charged particles through the discharge tube.
Donohue and Dieke (3) have reported low-frequency oscillations in glow discharges
and related these to traveling striations in the discharge column. The waveform and
modes of oscillation are very similar to those observed here, but their frequencies
are much lower. Basically, the phenomena appear to be very similar. Since our
experiments were performed to discover a plasma suitable for the generation of plasma
electron oscillations, this particular line of investigation has been carried no further.
C.
POSITIVE ION ANALYSIS
Observations have been made on the positive ion currents reaching the wall of a
microwave cavity during the afterglow of a pulsed helium discharge for gas pressures
ranging from 0.5 mm to 5.3 mm in a cavity with a diffusion length of about 1 cm. At
pressures above about 4 mm only molecular ions, He 2 ,. are observed at times later
than a few milliseconds after the breakdown pulse, while only atomic ions, He
, are
observed in the afterglow at 0. 5 mm.
Figure II-2 shows a typical set of ion current and electron density curves. At all
except the lowest pressures, the ion current and the electron density curves show the
rise due to metastable ionization reported by Biondi (4). The delay in the time of
maximum ion current with respect to the maximum of the electron density is believed
to be due to the fact that most of the ions are produced near the center of the cavity
and require times of the order of milliseconds to diffuse to the walls.
Future work will be directed toward the improvement of the means of recording
the ion current and the formulation of a consistent, quantitative picture of the ion
production process, the conversion of He+ into He2, and the diffusion of the ions and
electrons to the cavity walls.
With the present apparatus the primary impurity appears
+
to be neon and results in a negligible Ne current until very late in the afterglow.
D.
PURE HELIUM BREAKDOWN
Runs have been taken with the usual microwave arrangement for breakdown measurements, using a one-quarter-inch cavity and a liquid helium trap. The resonant wavelength was 10.6 cm.
The results are plotted in an EeA,
Ee/p system, compared with
the measurements in a one-eighth-inch cavity, previously taken by MacDonald (5), and
with theoretical values (Fig. 11-3). These values have been calculated by Varnerin for
-13-
(II.
MICROWAVE
GASEOUS DISCHARGES)
pure helium gas by inserting the proper helium values into the equations originally
derived for H 2 breakdown.
This theory gives an asymptotic solution valid only in the
low-pressure region (Ee/p > 15 volt/cm-mm of Hg).
The various runs show good agree-
ment with each other for Ee/p > 8 volt/cm-mm of Hg and give values of EeA lying about
10 percent below the theoretical values in this region.
The obvious tendency of lowering the EeA values in the high-pressure region from
run to run with the same cavity seems to indicate a slow contaminating process inside
the cavity and will be investigated more carefully. The necessity of using liquid helium
traps is clearly pointed out by comparing the results in the high-pressure region of runs
taken with liquid He and liquid N 2 traps.
However, there is no appreciable difference
for a high Ee/p, as can be expected from the Penning effect (6).
References
1.
Quarterly Progress Report, Research Laboratory of Electronics, M.I.T. p. 11,
October 15, 1950
2.
Quarterly Progress Report, Research Laboratory of Electronics, M.I.T. p. 11,
July 15, 1950
3.
T. M. Donohue, G. H. Dieke:
4.
M. A. Biondi:
5.
A. D. MacDonald, S. C. Brown:
6.
M. J. Druyvesteyn, F. M. Penning:
Phys. Rev. 81,
Phys. Rev. 82, 453,
248, 1951
1951
Phys. Rev. 76, 1634, 1949
Rev. Mod. Phys. 12, 99, 1940
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