II.
A.
MICROWAVE GASEOUS DISCHARGES
Prof. S. C. Brown
L. Gould
J. J. McCarthy
Prof. W. P. Allis
N. W. Donelan
J. W. Lathrop
D. H. Looney
K. -B. Persson
G. J. Schulz
CHARACTERISTICS OF MAINTAINING FIELDS IN MICROWAVE GAS
DISCHARGES
A perturbation solution for the electron energy distribution function has been
obtained.
It was found that such a solution gave an accurate representation of the exper-
imental measurements, provided the electron density present remained below that
necessary for plasma resonance to occur.
Schumann (1) has shown that when a portion of the plasma is
microwave electric field tends to be strongest in this region.
in resonance,
the
Thus when electron den-
sities are present in a resonant cavity in excess of the plasma resonance densities, a
nonuniform electric field will result.
incorporated in the theory.
This is an effect which had not previously been
Allis, Brown, and Everhart (2) have considered the varia-
tion of the electric field in predicting the spatial electron distribution.
It is possible,
by a method similar to theirs, to take the nonuniformity of the electric field into account.
The result is a nonuniform ionization frequency, which can be related to the uniform
ionization frequency.
In this way, uniform field data are used to predict the nonuniform
field data.
Experimentally this is a difficult region in which to work.
A 1000-watt c-w magne-
tron was obtained for use in taking the high density measurements.
The measurements
in this region seem to agree with the theoretical values within the experimental
(10-20 percent) error.
B.
ELECTRON-ION RECOMBINATION IN HYDROGEN
Earlier measurements of the recombination coefficient for hydrogen (3, 4) with
microwave methods do not agree and have not yet been theoretically explained.
The
measurements have been made on a decaying plasma obeying the following equation,
in which it is assumed that there are only electrons and one kind of ion in the plasma.
an =
2
2
anD aV n - an
at
a
(1)
where n = electron density, Da = ambipolar diffusion coefficient, a = recombination
coefficient.
At higher electron densities (n = 108 - 10 9 electrons/cm 3 )the experimental
results have been explained by the relation
1-=- 1 + at
n n
o
-6-
(2)
(II.
MICROWAVE GASEOUS DISCHARGES)
which is the solution of Eq. 1 when uniform electron density is assumed. This, however,
is a contradictory assumption because if the density is uniform in the bottle or the cavity
containing the plasma, the wall effects cannot be neglected, the diffusion term may be
dominating, and the time dependence of the decaying plasma has to be a function of the
diffusion coefficient, the recombination coefficient, the spatial form of the probing
microwave signal, and the initial spatial distribution of electron density.
However, the two loss processes, diffusion and recombination, have different pressure and energy dependence;
and therefore, with an experimental setup to measure the
time dependence of the decaying electrons as a function of pressure and average energy
it should be possible to separate the two pro-
over ranges that are sufficiently large,
cesses and calculate the recombination coefficient.
This may be checked with a pertur-
bation calculation when the initial conditions are known.
The experimental setup for measuring the pressure and energy dependence of the
decay function in the afterglow,
as shown in Fig. II-1,
is practically ready.
It consists
of a microwave cavity in the 10-cm region in the form of a rectangular parallelepiped.
The dimensions of the cavity are designed so that the fundamental modes resonate at
10. 5 cm,
10 cm and 9. 5 cm wavelength.
to each other.
The E fields of these modes are perpendicular
A variable coupling mechanism in the form of a disc on the end of the
inner conductor of the coaxial line going into the cavity has been developed.
Fig. II-1
Block diagram of experimental apparatus for measuring electron
decay as a function of the average electron energy.
-7-
It is
(II.
MICROWAVE GASEOUS DISCHARGES)
essentially a capacitive coupling which, because of its rotational symmetry, couples
only to that fundamental mode whose E field is perpendicular to the disc. Use has been
made of this property of the disc coupling to load down one of the modes of the cavity so
that QU of that mode may be varied from 10, 000 to 200. A quartz bottle, small in relation to the dimensions of the cavity, contains the gas discharge and is introduced in
the center of the cavity.
The Q of the mode mentioned above may be made essentially
independent of the change in loss because of the changing electron density during the
decay period.
This mode is used to heat the electrons, and the E field of the mode is
measured in the same way as in breakdown measurements. The other two modes are
used for the pulsed breakdown signal and the probing signal. The electron density as
a function of time is measured in the customary way. In principle, the average energy
of the electrons may be calculated from a measurement of the ambipolar diffusion coefficient.
This leads to the possibility of relating the average energy of the electrons to
the applied heating field and of experimentally determining the decay process as a function of the average energy of the electrons and pressure.
C.
OSCILLATIONS IN DC DISCHARGES
The recent theoretical treatment of plasma oscillations by Bohm and Gross (5)
indicates that high-frequency oscillations may be generated in a gas discharge plasma
by a high-velocity electron beam. The electron beam supplies energy to the oscillation
and is modulated by the plasma oscillation.
The presence of the beam should modify the
frequency of oscillation in the manner indicated by Eq. 3
2
Wpp
22
n
1+
2
where (2
-
(3)
Vb
b
no 4o
2
= electron plasma frequency = ne
/mE
; n
= density of electrons in the
exciting beam; Vb = accelerating potential of the beam; n o = plasma electron density;
and o = potential of the oscillation generated. This formula indicates that the density
and accelerating potential of the electron beam are the variables associated with deviations of the observed frequency from the plasma electron frequency. This electron
beam can be generated by the use of a mercury discharge as a cathode in the structure
shown in Fig. 11-2. Electrons in discharge A move through a hole in the kovar cup C
which acts as an anode for discharge A. These electrons are accelerated by the potential Vb and enter the main plasma B. This gun produces a high-density beam for relatively low accelerating potentials when the gas pressure through the tube is of the order
of 1 to 5 4 and eliminates any necessity for differential pumping. It should be noted that
-8-
Fig. II-2
Electron gun section. C and D are kovar assemblies.
Diameter of beam is 0. 042 inch.
REGION
Fig. II-3
Mercury discharge tube for plasma oscillation study.
-9-
(II.
MICROWAVE
GASEOUS DISCHARGES)
the density of electrons in the beam may be varied in a linear manner by changing the
current passed by the gun discharge A, while the accelerating potential Vb may be
varied independently of the beam density to a first order. This structure incorporates
the proper variables indicated by Eq. 3.
The final tube, now being assembled, is shown in Fig. 1I-3.
D.
BREAKDOWN IN HYDROGEN AT 100 MC/SEC
Work on the breakdown of hydrogen
at a frequency of 100 Mc/sec has been
completed and no further work is being
contemplated at this time. The meas-
3000o
2000-
urements of breakdown covered a range
of pressures from 1 cm to 1 atmosphere
1000700-
of hydrogen, obtained from a palladium
leak, and up to 2 atmospheres with the
500 -
S200
100-
addition of tank hydrogen.
Figure II-4
shows a plot of the data.
The results
-THEORY
at low pressures, if extended,
D 100-Mc DATA
3000-Mc DATA
good agreement with those obtained by
are in
70 -
others (6)
at microwave frequencies.
At intermediate pressures the results
50-
follow the ~enerl
20
0
-xxx
nre]irtinns nf the
theory up to a p/E of 0. 11,
10
point there is
002 004 006 008 010 0.12 014 016
p/E (mm Hg-
018
020
This
cm/volts)
has
progress
at which
a departure from theory.
in a previous
been discussed
report
(7).
No
way was
found
Fig. II-4
to eliminate this effect in the present
Breakdown data at 100 Mc/sec.
experiment. This might be due to the
fact that the large cavity could not be
outgassed well enough to remove small
traces of 02.
Further work on the breakdown of hydrogen at high pressures will be
conducted at microwave frequencies,
because high purity conditions (due to the smaller
size of the cavity) are more easily obtained and a new 1000-watt c-w tunable magnetron (Litton Industries - 5607 magnetron) is
-10-
now available.
MICROWAVE
(II.
GASEOUS DISCHARGES)
References
Z.
1. W. O. Schumann:
P.
Allis, S.
Physik 7,
121,
1942
Phys. Rev. 84,
C. Brown, E. Everhart:
519,
1951
2.
W.
3.
M. A. Biondi, S. C. Brown:
4.
L. J.
5.
D. Bohm, E. P.
6.
A. D.
7.
Quarterly Progress Report, Research Laboratory of Electronics,
1951, p. 11
Varnerin, Jr.:
Phys. Rev. 84, 563,
Gross:
MacDonald,
Phys. Rev. 76,
Phys. Rev.
S. C. Brown:
75,
1697,
1949
1951
1851 and 1864,
Phys. Rev.
-11-
76,
1949
1634, 1949
M. I. T. Oct.
15,