S OF TECHJ I
1,
27 1967
IB RA RI E
INVESTIGATIONS OF A
REFLEX DISCHARGE
by
ROGER JONES BREEDING
3. A., VWesleyan University
(1962)
SUBMITTED IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE
DEGREE OF MASTER OF
TIchi
SCIENCE
*1:"
7
at the
MASSACHUSETTS INSTI UTE OF
1IECHNOLOGY
September, 1965
Signature of Author.
Depar lient of Geology and
ophysics, August 31, 1965
Certified by...........
Thesis Supervisor
Accepted by......................
...
Chairman,
..
. .. .o m t
Departmental Committee
on Graduate Students
-2-
Investigations of a Reflex Discharge
Roger Jones Breeding
Submitted to the Department of Geology and Geophysics on August 31, 1965, in
partial fulfillment of the requirement for the degree of Master of Science
Radiation maxima near the gyrofrequency harmonics have been observed in a hot
cathode reflex discharge. Probe measurements were undertaken to determine the characteristics of the discharge. 7 he results of the probe explorations are not entirely
-3
satisfactory, but indicate that the densities encountered ranged from 2.0 to 20 x 10 18 m
1hese are higher densities than those at which gyrofrequency harmonics have previously
been observed. No change in the position of the maxima with density was observed.
Thesis Supervisor: Giorgio Fiocco
' itle: Assistant Professor of j44eJl
-3-
1 ABLE OF CON'I ENI S
Abstract ...........................................................
. 2
Ackno xledgernents ...................................................
. 5
Introduction ........................................................
. 6
I.
II.
S7
Background ...................................................
.11
Experimental Program .........................................
II-
.
II-2.
Description of Apparatus .................................
Figure i.
Line Drawing of Cavity .....................
Figure 2.
Photograph of Discharge ....................
Figure 3.
Photographs of Discharge ...................
Figure 4.
Block Diagram of Radiometer ................
.11
.12
16
.17
.19
Results .................................................
Figure 5.
Radiation vs. B for Three Pressures .........
Figure 6.
Radiation vs. B for Different Horn Orientations
and Cathode Conditions .....................
.20
.z1
T'able 1.
Peak Position for Various Pressures ..........
.22
Table 2.
Peak Position for Various Currents ...........
.23
Figure 7.
Probe Curves for Three Pressures ...... ........ 24
Figure 8.
Probe Curves for Three Pressures (Semilogarithmic) ...........................
'Table 3.
Plasma Characteristics for Three Pressures
Figure 9.
Figure 10.
Table 4.
Anomalous Probe Behavior ...............
Probe Current vs. B..................
Densities for Four Values of IDC..........
III.
Discussion ............................
IV.
Conclusion ................................................
...................
.25
.26
.28
.29
.30
.31
.35
-4-
iibliography
............................................................
36
Appendix A ...........................................................
40
Appendix B ...........................................................
41
-5-
ACKNOWLEDGEMENTS
The author is indebted to Assistant Professor G. Fiocco for suggesting this
experiment and for constant advice during its progress.
Discussions with Associate
Professor G. Bekefi concerning cyclotron harmonics and with Dr. J. Waymouth concerning probe measurements have been most helpful.
Much technical assistance
was obtained from various members of the staffs of the Research Laboratory of
Electronics end the Nationa l Magnet Laborator/y.
In particular, the patience of
G. Leach with the probe and the cathodes is appreciated.
This work was supported in part by the U. S. Army, the U. S. Air Force Office
of Scientific Research and the Office of Naval Research.
-6-
INTRODUCTION
This experimental research was undertaken to determine whether or not radiation
at the gyrofrequency harmonics could be detected, and if so, Nwhether any additions
could be made to the information already extant on their behavior.
Gyrofrequency harmonics were observed the very first time that the radiometer
vas connected to the discharge.
No change in the positions of the maxima of the radio-
meter output near the harmonics was observed
discharge current IDC were changed.
hblnthe neutral pressure No or the
Many other maxima were also observed, but
their behavior seemed directly related to the condition of the cathodes.
Probe measurements were made in order to determine how the electron thermal
energy kT e and the plasma density N.i varied with N, and IDC.
These measurements
were not entirely satisfactory, but indicated that N, varied over an order of magnitude
or so in a regular manner.
No inconsistancies with earlier work were found.
-7-
I.
BACKGROUND
T"Fhe reflex discharge provides a convenient method for plasma containment.
The
cathodes at each end of the cylindrical axis provide a potential well which traps the
electrons in their axial motion.
The externally-generated magnetic field along the
axis provides the impediment to radial escape from the plasma region.
TIhe specific
nature of the discharge depends on whether it has hot or cold cathodes, operates in
the low pressure - high impedance mode or the high pressure - low impedance mode,
and on the geometry.
7 he anodes usually have the form of annuli, cylinders, or
plates with a hole through which the discharge passes.
The names Penning or P. I. G.
(Penning or Philips Ionization Guage) are variously applied to some or all of these
discharges.
1 he mechanism of ionization is that of collisions due to electrons which have
been emitted at the cathode and accelerated into the plasma region through the cathode
potential fall.
With cold cathodes, electrons are mostly generated by secondary
emission due to heavy ion bombardment.
very severe (Backus, 1949).
( athode heating and disintegration can be
Hot cathode discharges, of course, rely on thermionic
emission.
In the low pressure and high impedance mode, only cold cathodes appear to have
been used (the early literature is cited in Jepsen, 1961).
These discharges have been
utilized as pressure gauges, ion sources and vacuum pumps as well as for plasma
production (Jepsen, 1961; Helmer and Jepsen, 1961; Dow, 1963).
on magnetrons is applicable because of the similar geometry.
Some of the work
Instabilities and micro-
wave radiation have been observed, and their connection with sheath phenomena and
electrons possessing anomalous energy is postulated (Hirsch, 1964; Knauer, 1963).
The transition to the low impedance mode has been found to take place between
10 - 4 Torr and 10- 2 Torr in a complicated manner for cold cathode systems.
Both
hot and cold cathodes have been used in the high pressure mode, but most of the papers
-8-
concerning discharges using them (Allen, 1963; Chen, 1962; Goler and Wagner, 1964)
have little bearing on the details sought for this discharge.
Chen and Cooper's (1962)
paper concerning electrostatic oscillations may be of interest, however, because of
the mechanism postulated for emission at the gyrofrequency harmonics.
Results of cold cathode discharges in the low impedance mode (Backus, 1949;
Backus, 1959; Backus and Huston, 1960) are not completely equilivant because of the
different emission mechanism and the higher voltages used.
Discharges with pres-
sures near 1 mTorr (= 10-3 ,Torr = 10-3 mm Hg) have generally been found to have
about 10A ionization with the thermal electron energy k'1e around 3 eV.
Noise and
oscillations between 104 and 1010 c/s have been reported (Agdur and Ternstrom,
1964; Kaganskii et al., 1)64).
Interest in the mechanisms by which energy is radiated by a plasma at multiples
of the electron gyrofrequency, and in the conditions under which this takes place, has
arisen from two different sources.
Radiation at gyrofrequency harmonics, or cyclo-
tron harmonics, has been observed from laboratory plasmas in a number of configurations.
Gyrofrequency harmonics and other allied frequencies have also been noted in
the results of topside ionospheric sounders.
'This is not truly a steady-state power
radiation that is observed, but rather a resonance which is excited by the sounder
and which dies away in time.
These ionospheric resonances were first noted by Knecht et al., (1961) in a
fixed-frequency sounder rocket flight.
and Russell, 1962).
A second flight gave similar results (Knecht
More detailed results were procured with the Alouette topside
sounder satellite (Lockwood, 1963).
Calvert and Goe (1963) extended Lockwood's
(1963) identification of the 'spikes' and advanced an explanation for some of the resonances based on electrostatic plasma oscillations.
Resonances always observed in-
cluded multiples of the electron gyrofrequency f , the plasma frequency fp, and the
hybrid, transverse, or Pythagoras frequency fh = (fp - f
) . Resonances were oc-
casionally observed at the fundamental electron gyrofrequency and at twice the hybrid
frequency.
Recently a large number of workers have published theories dealing with the
excitation and decay of these resonance phenomena (Wallis, 1965; Nuttall, 1965;
Fejer and Calvert, 1965; Johnston and Nuttall, 1964).
As these theories are quite
complex and it is not yet certain which is the correct approach, they will not be reviewed here.
Landauer (1962) was the first to observe electron gyrofrequency harmonics in
a laboratory discharge.
From his cold cathode P. I. G. discharge in 2 x 10- 2 T'orr
of Helium he detected radiation at frequencies nfg, where n, the harmonic number,
varied between 2 and 25.
His equipment did not permit him to observe the fundamental,
but the emission of cyclotron radiation (Waniek et al., 1964) seems to be due to an
entirely different mechanism and need not be discussed here.
i he next report concerning this problem was that of Bekefi et al., (1962) who
observed absorption as well as emission at the harmonics.
In the atbsorption mea-
surements they used the positive column of weakly ionized are discharge in Helium.
They found emission from a number of different discharges.
They found evidence that
the electrons did not have a Maxwelliam distribution and rejected Landauer's suggestion of quasirelativistic electrons.
Mitani et al., (A964), Kubo et al., (1964), and Tfanaka et al., (1963) have found
emission near gyrofrequency harmonics in Ne, Xe, Kr, and Ar at various pressures
in the range 10- 2 to I ' orr. 1They observed that the position of the emission peaks
changed with the pressure p and with the discharge current IDC in their arc discharge.
'Ihey pointed out that Bernstein (1958) had shown that electrostatic oscillations were
not allowed at multiples of the cyclotron frequency.
Mitani et al., also observed
structure near the harmonic, which has since been observed in absorption by Buchsbaum
and Hasegawa (1964) who offered an explanation of it which is in some agreement with
-10-
their experimental results.
Gyrofrequency harmonics have been found also in plasmas generated by electron
beams (Bekefi and Hooper, 1964; Gruber et al., 1964).
output increased very steeply with beam density.
It was found that the power
Crawford et al., (1964) have found
that microwave transmission between two probes in a positive column exhibited strong
resonances related to the gyrofrequency harmonics.
An early attempt to explain this radiation (Simon and Rosenbluth, 1963) by postulating that it came from single particles which have their or bits interupted by walls
or sheaths has been rejected because it seems completely unable to account for the
great intensity observed.
More promising has been the work of Stone and Auer (1965)
who have extended the work of Canobbio and Croci (1963).
They assume a non-Max-
wellian group of fast electrons and show that excitation of electrostatic waves propagating nearly perpendicular to the magnetic field is possible under their postulated
conditions.
Landau damping is slight for these waves.
By assuming certain values for various parameters, Lustig (1965) was able to
show substantial agreement betw.-een the theory of Stone and Auer and his experimental results.
Lustig's discharge tube passed through a microwave cavity which
was also used to measure the density.
He found three lines near the harmonic, two
of which could not be explained, and a strong dependence of radiated power on electron
density which the theory did not predict.
His discharge tube, filled with Ar at about
1 mf orr, handled currents of up to 0.35 A.
-11-
II.
EXPERIMENTAL PROGRAM
II- 1. Description
rThe main cavity of the demountable system in which the argon plasma was produced was a water-cooled, stainless steel cylinder (axis vertical) of inside diameter
19.7 cm and height 15.2 cm.
Ports of inside diameter 9.8 cm were located 30.5 cm
apart on the vertical axis and on perpendicular horizontal axis.
See Figure 1. 1 he
electrodes were mounted from the top and bottom ports so that the anodes were 10.2 cm
apart and the cathodes about 14 cm apart.
To the north port was attached a 203 cm
baffled black tube for use in future light scattering experiments.
The east port con-
nected to the pumping system, and the microwave horn antenna was introduced through
the east port.
A window occupied the south port.
In between the large ports in the
horizontal plane were smaller ports of 2.3 cm diameter.
'Ihe probe was introduced
through these ports.
The anodes were hollow copper annuli 1.8 cm high, inside diameter (i.d.) 3.8 cm
and outside diameter (o.d.) 5.7 cm.
7 Yo copper tubes supported the anode and gave
ingress and egress for the water circulation.
The anodes and the entire cavity -were
maintained at ground potential.
Indirectly heated barium oxide cathodes were tried first, but these did not perform satisfactorily, probably'due to poisoning, and they were replaced by spirals of
tungsten wire.
0.508 mm (z0 mil) and 0.635 (25 mil) wire were used.
had an i.d. 1.3 cm, o.d. 3.2 cm.
Heating to the neighborhood of 1800 0 C was ac-
complished by 60 c/s currents of about 15 A.
"hese cathodes gave off tungsten at a
con. iderable rate, so that the life of a cathode wvas 50 hours or less.
a visually uniform plasma for only ten hours or so.
uneven heating of the wire.
T he spirals
'They produced
This was presumable due to
As the wire diameter is not perfectly uniform, some
spots will be hotter than others, and these spots will therefore give off more tungsten than cooler areas, thus decreasing the diameter at the hot spots still further,
-12-
VIEW FROM TOP
WINDOW
T
N
80
TO
RADIOMETER
10"
WINDOW
Figure la. Line drawing of cavity as seen from above.
VIEW FROM NORTH
~
~
ANODE
TO PUMPS
TO RADIOMETER
ANODE
CATHODE
SPIRAL
Figure lb. Line drawing of cavity as seen from the north.
-13-
and increasing the rate of tungsten emission until it evaporated completely.
'1 hus
a spent cathode would be worn through in one place and be thin in a few others, while
much of the wire still remained near its original diameter.
7Ihe cavity eventually
became completely coated with tungsten.
Tlhe
DC supply for the discharge was a 400 V battery bank.
Since the discharge
was operated in the low impedance mode, the current control was by ballast resistors.
Pressure in the cavity was adjusted by changing the opening of a leak while
keeping the pumps in operation.
Desiccated cylinder argon was used. Tihe pressure
was measured by an NRC ionization gauge below 5 mi orr and by a thermocouple
gauge above that.
7I he magnetic field was generated by water cooled coils above and below the
the coils were 32 cm apart.
64 A DC.
input.
The center planes of
Each coil was 15 cm thick, i.d. 31 cm, o.d. 67 cm.
cavity.
i he power supply normally used could supply up to
It was sometimes programmed by a 10 V peak-to-peak triangular 0.01 c/s
A knowledge of the current passing through the coils was obtained by mea-
suring the voltage drop across a precise ion 0.05 ohm resistor in the power supply.
The magnetic field produced in the cavity was measured by a rotating coil component
magnetometer oriented for a maximum reading.
current I
'I he relationship between the coil
and the field B was found to be
B (G) = 23.67 Im(A)
where 1 Gauss (G) = 10 - 4 Tesla (T) = 10- 4
ieber/m
2
(Wb/m2).
(The unit 'lesla and
its abbreviation T were approved by the SUN Commission and the IUPAP, see Physics
Today, June, 1962, p. 19).
T he axis of the coils and the axis of the cavity were not
exactly aligned, but- since the field within 3 cmn of the cavity axis was measured to
depart by less than 15 from the field measured on the axis, it was not felt worthwhile to go to the considerable trouble of moving the coils.
Magnetic field measure-
ments were repeatable to about 3% for a given voltage reading.
-14-
When the cathodes were fairly new the plasma created appeared to be quite uniform to the eye.
As mentioned above, hot spots in the cathodes developed after some
hours of use, and this led to the development of bright vertical streaks or 'pencils'
in the plasma.
disappeared.
It aiways happened that one pencil soon became dominant and the others
The brightness of the plasma is related to the ionization, which in turn
is due to the enhanced electron emission from the hot spot.
At low magnetic fields,
of course, the electrons are not tightly collimated and the plasma appears uniform
as seen in Figure 2.
As the magnetic field is increased, Figure 3, the pencil forms.
Unless otherwise specified, all results were obtained under conditions when IDC was
evenly divided between the two cathodes.
This division was maintained and adjusted
by changing the AC heater currents to the cathodes.
'The shift to the high impedance mode for this system apparently occurred at
-5
about 5 Y 10-5 Torr since below that pressure the discharge vwas not visible and the
current dropped to near zero.
Pressure readings on the thermocouple gauge were
slow and unreliable so that pressures above 5 m'lorr were rarely used.
A block diagram of the X -band (8.2 - 12.4 Gc/s) radiometer is shown in Figure 4.
T he mixer-preamplifier had a noise figure of 10 db. The video or detected output
from the I. F. amplifier (gain 87 db) was fed to the P. A. R. lock-in amplifier.
'This
unit combined a tuned amplifier, a detector synchronous with the switching frequency,
a low-pass filter and a DC amplifier.
The 3 db bandwidth of the mixer and the I. 1.
amplifier was 20 Mc/s.
7The local oscillator (L. O.) was about 20 years old and left something to be
desired in frequency stability, power output stability, and tuning.
of 8.14 and 8.44 Gc/s were used.
L. O. frequencies
Since no filter was used between the mixer and the
horn, the radiometer was sensitive to radiation 50 to 70 Mc/s above the L. 0. frequency and 50 to 70 Mc/s below the L. 0. frequency.
the ferrite switch was left open.
The unused fourth port of
It probably should have been terminated with a load.
-15-
Figure 2.
Photograph of Discharge.
t = 0.01 Wb/m
2,
IDC = 0.8 A, p = 1.0 x 10 - 3
I he horn antenna may be seen behind the plasma.
orr.
-16-
2
Figure 3 a.
Photograph of Discharge.
B = 0.04 Wb/m
Figure 3 b.
Photograph of Discharge.
B = 0.12 WV/m 2,
ID
= 0.8 A, p = 1.0 x 10 -
3
7orr.
1.0 x 10-
3
lorr.
IDC = 0.8 A, p
It
IIKI i,
±i
1+-++
+HH++H-H I-H1+
-+-H-H+H-H+
i -H-lH-+ H-IH
' '
IW
tt
TR
Li :
i I
''l
:l
''
I
1i ?
I [:
1
~
.. .
V
!!
' ' ,,
~~I
H- III
,H_1
i IIi ;i
I
7W
IIi
I
I
II I
I
+--!I
I ::
II
:: :: :i I
+-4+A14- H+ HH1-H4+Ft+
r
i ii
Tm
M'H+r
1+H
iT
Tt
i.
4t
...
1
-11
-r
it
I
4V'
N
+
i,;i
-
'F4-
L1
...
3..-
L
_4--+--
F
4
±
I.
f
IM
~
'
,
_4
:$r
IL:
i
.......
4ii
; - ~1 ~ , ~
lj
I i1
!I!!!!C
"44i4
-Fi- T
Figure 4.
Block diagram of radiometer.
iFSt7ft-~~
~S!rlii
T
i;
:
'it
-18-
i he probe was introduced into the cavity through one of the 2.3 cm ports men-
tioned earlier.
A fitting adapting the port to a quick-release vacuum coupling was
used so that 1.27 cm glass tubing could be passed into the cavity and moved along its
axis through the quick-release coupling without breaking the seal.
the lead and a shield.
7 he tubing contained
On the vacuum side of the seal between the lead and the glass
4 or 5 cm of 0. 127 mm (5 mil) or 0. 152 mm (6 mil) wire was spot-welded to the lead.
All of the exposed metal except the last 2.54 mm was covered by an insulating coat
of aluminum oxide.
I he axis of the working surface, the uncoated 2.54 mm was per-
pendicular to the magnetic field.
it was in the pencil.
It was never possible to position the probe so that
Tungsten from the cathodes was deposited on the probe just as
it was on everything else inside the cavity.
-19-
II-2.
Results.
By feeding the radiometer output to the y input and the voltage drop across the
resistor in the magnet power supply into the x imput of the recorder plots of radiometer output against the magnetic field were obtained.
polts for various pressures.
plane of the horn antenna.
Figure 5 shows three such
Figure 6 shows the effect of the orientation of the E-
The top cathode being fairly new at the time, the plasma
was practically uniform when the top cathode was dominant, but showed a strong pencil
when the bottom cathode was dominant.
'7 he
value of the ratio
-
provides a convenient measure of position on the x
axis and makes the position of the integer multiples of the gyrofrequency obvious.
Ip
g
eB
-is the radian gyrofrequency and ,,, is the frequency of the local oscillator.
m
e
'i he positions of the radiometer maxima near the harmonics indicated are
given in ZIables I and 2.
7 he higher harmonics were chosen for 'Table 2 because the
peaks near n = 3 and n = 4 were seldom observed for IDC greater than 2 A.
Maxima near
-
=0.29 and
currents and large broad maxima near
observed for large currents.
tion.
= 0.22 were frequently observed for lower
-
= 0.29 and -i
0.39 were persistantly
Other maxima were chaotic in appearance and posi-
The peaks away from harmonics were not as repeatable as were those near
the harmonic numbers.
The intensity of the radiometer output increased with IDC' but was also dependent on the intensity of the pencil.
Probe curves for three different pressures are shown in Figure 7 where I
p
and V
are the probe's current and voltage with respect to the grounded anode. For
p
the usual temperature determination, points from Figure 7 are plotted in Figure 8
according to the method described in Appendix A.
Figure 7 is the result of several
cycles of the 0.02 c/s triangular wave generator over the range indicated.
Figure 9
-20-
,'D
iT-
=
Figure 5. Radiometer output as a function of magnetic field; IDC 0.8 A. The
vertical scale is arbitrary, except that the lowest curve has been amplified by
factor of 100 with respect to the others.
74t
~.
~ ~i!!!!]
~
mrm~~-r~r~T
r~..
...
..
..
...
..
LLLI lilr
LI
U1.. ....
i ......
![!!!![[!!!
!I
ffl=4'
F+
_ .t..
_if ..f.
r~T-. ..11t......
~ ~ iiil~i( ~i*
C
ill . i hmlt L tt,71
I
1,1HHiit 4
; !r
v .4WMN!
i
~i t,t
~
49V
:1x17mT
L
4
1 ;rGLTtilflfJ
. ..
Jil~ l r l l ] I111
J , l 1i
t ,
WI
I fl-,
tit-
F
ti'
TfftiV .
p-~~~ifi~ft
Il--t'i 'Uiiit 1+ F. .
?
0t
F
M
I!
a
-
1
1
"i
it
t
I- r~
/
T
V
I:T,
4"'
It~iijr:i
Flit
It~t~
77
77
it
''
ITT
Mi
I
i: H -
ta
I-
_
iT
ii
1 t-.
i iI I i
V
Mir
r
'
4: UTI
LiL
4
d4i!
1:S
rr
i
1/15
5 iE71:
;
~~i!
1/3
1/6
w/w
Figure 6.
Radiometer output as a function of the magnetic field, with the E-plane of
the horn oriented parallel to and perpendicular to the magnetic field. IDC = 1.3 A.
The upper curve in each pair is with the top cathode emitting 2/3 of the current and
the lower is with the bottom cathode emitting 2/3 of the current.
-22-
TABLE 1
Positions of peaks near
g
=
for harmonic numbers n = 3, 4, 5, and 6 for various
values of pressure with IDC = 0.8 A
DC1
(10
( = .167)
( 3 = .333)
( = .250)
0.1
.329
.246
203
0.2
.330
.248
.198
.164
0.5
.330
.245
.194
.161
0.8
.333
.249
.193
.162
1.0
.329
.247
.197
.162
2.0
.331
.248
.198
.164
3.0
.331
.248
.198
.164
.199
.165
P
-3
(1 = .200)
TIorr)
8.0
.171
-23-
7ABLE 2
= 1 for harmonic numbers n = 5, 6, 7, 8 and 9 for various
n
values of discharge current with p = 1.0 x 10-3 Torr
vcalues of discharge current with p 1.0 x 10
Torr
Positions of peaks near
1 =.200)
(6 = .167)
6.8
. 193
.153
6.0
.202
4.7
.204
1
1
= .143)
1
(- = .125)
(- = .111)
.132
.115
.101
.161
.132
.117
.104
.161
.137
.120
.104
4.4
.145
.125
.112
3.5
.136
.119
.100
IDC
(.A)
1.8
.1 95
.163
.138
.121
.108
1.6
.200
.166
.144
.123
.109
1.0
.193
.162
.138
.121
.106
0.6
.196
.161
.137
.124
41
t
,
T,
i~'
4;i:
F-,
-
I
TW"VTTHT44Iq
'4
t
Jl~Ti 42TW2T7IWi~m
7714i
i~fi;,~7rrr;
I-I L4
I
I
~-~
'F-
K~;~,tT
L
I
T
-I
-m
fT
rt
I
F~tti
'-
#F
4I~i
t
ii
Es
- 11 17T
I~cTC~~LrF
'l
42
-
k'-<
:
',
-171
44
p-
;
:ii
C
L
_i~
4-P2-TW
i7TF
-rrmmm
- -F -T- -
i
t
-T
T
iT
T1rT
+4--+4-
-
i i
-
+
1
i! 1AM tt t tI rl! 1tt
I1111
kA
4
i
VIT
tlit
##
Figure 7.
Change in probe curves with pressure; IDC = 0.8 A,
B = 0.03 Wb/m
2
i
i
-25-
Vp (V)
Figure 8.
Change in probe curves with pressure; IDC = 0.8 A,
B = 0.03 Wb/m
2
-26-
7ABLE 3
IDC
0.8 A, B = 0.03 Wb/m
2
=
0.3
1.0
3.0
kTe (eV)
=
3.9
3.2
2.6
q
=
1.6
1.4
1.4
(small q approximation)
=
2.9 (28%)
5.7 (16%)
7.6 (7%)
N.1 (1018 m3) (large q approximation)
=
1.6 (i4%)
1.9 (5%)
2.0 (2%)
p (10-
3
?orr)
N. (1018 m)
1
-27-
shows the anomalous behavior of the probe which became increasingly common as
the cathodes aged and the pencil effect became more and more prominant.
It was
not possible to obtain a satisfactory set of probe curves for various values of IDC
Figure 10 gives the change of probe current with magnetic field.
The values for the thermal electron energy k' e calculated according to Appendix A and the ion density N. calculated by the methods outlined in Appendix B
are given in 7 able 3 for three pressures.
around the probe to the radius of the proLbe.
q is the ratio of the radius of the sheath
The figures in parentheses are the
percentages of ionization.
Incomplete data indicates that the density N i for p = 1 m'orr and B = 0.03 Wb/m
increases sharply with IDC for values of IDC below 1 A and begins to level off above
1 A.
This is based on the small sheath approximation vhich appears to become less
valid with decreasing IDC.
in ' able 4.
he values computed are presented as tentative data
Not enough points were available to make use of the large sheath ap-
proximation, and the values 'were computed for Vp only -25 V so that some electrons
were still being collected.
rThe trend, howvever, is unmistakable.
2
Ie
ii
+HnIi
1
-I
=r
t-
it
4-4
T-,
Ii-<41 4; P;tH
-F-
4 rI 1
C-p~
1-;
____i
-44
2212t44 Ai~
bl
- l T
P>VTVJT-hI7tVR
271 2
i-~I~illtl
l
1
>
1-44-
i-u
LLU
ttt
mtbmfrzi~t
1u4--4
r
S-lL;
1>4
[TI[ II i I I II I I! I
Wi'I
[A [
i
rt i
. . . . . . . . . . .. . . . . . . . . . .
444- +4i+ -+1
-v
-30
-45
Figure 9.
VP (V)
Anomalous behavior of probe; IDC = 0.8 A,
-15
B = 0.03 Wb/m
2
E
m
B (Wb/m2)
Figure 10.
V
P
= 60 V,
Change in probe current with magnetic field; IDC = 0.7 A,
-3
p = 1.0 x 10
Torr.
The pencil effect was very pronounced.
-30-
TABLE 4
p = 1.0 x 103 Torr, B=0.03 \b/m
18
2
-3
IDC = 0.45 A
q = 1.9
0.65
1.4
3.4
(10%)
1.3
1.3
8.0
(23%)
2.0
1.2
12.5
(36 )
N =0.47 x 10
m
-31-
III.
DISCUSSION
Considering the accuracy of this system, no trends of the positions of the maxima
with either p (Table 1) or IDC (Table 2) are evident.
Lustig (1965) found three dif-
ferent peaks near the harmonic, two of which he observed did not change with the
density.
other.
two.
He seemed to be able to vary the relative intensity of these peaks with each
It is possible that the peaks observed here near the harmonic is one of these
Lustig, Mitani et al., (1964) and Buchsbaum and Hasegawa (1964) found that
the peak position changed with Ni only for the lower densities (or discharge currents).
For comparison with Figure 4 of Lustig or Figure 2 of Buchsbaum and Hasegawa, note
f2
2
that for this system N.
=
is the plasma frequency.
=1 .2 where
1018 m-3 corresponds t
=
In the theory of Stone and Auer (1965), if the value of the
parameter ) is large, no change of the peak position with density is indicated no
matter what the density.
(See Stone and Auer's Figure 1).
on the wave number perpendicular to the magnetic field.
of estimating a value of this for this experiment.
The parameter X depends
1 here seems to be no way
If the densities in TIables 3 and 4
are not too far off, however, this experiment has been done in density regions high
enough so that if a change in peak position had been detected, it would have contradicted all of the findings mentioned above.
The change in intensity of the peaks with the orientation of the horn in Figure 6
is less than one would expect since the gyration of the electrons is in a plane perpendicular to B. Landauer (1962) found a much greater change.
From Figure 6 it
is evident that the intensity of the peaks near the harmonics and the features of the
peaks away from the harmonics have a direct relation to the pencil effect.
'Ihere is
no doubt that the hot spot in the cathode wire results in a beam of energetic electrons
entering the plasma.
From Figure 10 it is noted that the density decreases with
magnetic field increase for most of the curve.
The confinement of the energetic electrons
-32-
more closely to the pencil as the magnetic field becomes strong makes the plasma
density at the probe lower than it had been for smaller fields when the electrons weie
not so closely bound to the pencil and could spread throughout the plasma region.
7 he
actual density in the pencil at high fields is probably several times greater than it is
outside the pencil.
'1he dependence of the intensity with the pencil intensity agrees roughly with the
findings from beam-plasma interactions (Bekefi and Hooper, 1964; Gruber et al., 1964).
It is possible that the beam is enhancing an instability in the plasma.
Such instabilities
have been noted (Agdur and 'lernstrom, 1964; Kaganskii et al., 1964; Chen and cooper,
1962), but the mechanism of the magnetic field dependence is not clear.
Ihe values obtained for kT e and N.i (small sheath approximation) do not appear
to be unreasonable and they agree with the findings of Backus (1959) and Backus and
Huston (1960) even though their discharges were quite different in detail (cold cathodes).
It is unfortunate that the sheath thickness is just in the region where neither approximation may be applied with confidence.
The use of the large sheath approximation
results to estimate the degree to which the small sheath approximation results may
be in error has been investigated by Chen (1965).
He found that under certain condi-
tions the large sheath approximation gives results near the correct values even though
it is not valid. It seem s that the conditions in this experiment are such that this is
the case.
The effect of the magneti field on the probe results should be slight. The probe
radius was 15 times sinaller than Lhe minimum gyroradius for ions with room temperature velocities.
Since the gyroradius varies as the square root of the energy, the
gyroradius would not approach the probe rddius even if the ion temperatures were
as high as I eV (Backus, 1959).
Th1
e magnetic fields were well below the critical
field strength at which Dote and Amemiya (1964) calculated the results would be affected.
-33-
1 he anomalous behavior of the probe as shown in Figure 9 is probably due to
tungsten deposition which increases the area of the probe by coating the aluminum
oxide with a coating of conducting material.
t hat this anomalous behavior was
noticed to increase with the length of time the probe was in the plasma, and that this
behavior was much more common at high values of IDC is entirely consistent with
this explanation.
this problem.
The use of a probe of the type used by Little (1964) would avoid
It is possible, however, that some instability is responsible.
Since
the percentage of ionization calculated from the anomalous protion of the curves is
2001,' or more this is unlikely.
Careful monitoring of the discharge current and
voltage would indicate whether or not a mechanism which affects the whole plasma
is acting.
Difficulties in the region where the probe collects large numbers of electrons
may be traceable to the fact that the cathodes are heated by, and the chopper in the
recorder driven by the 60 c/s line.
Dr. J. Waymouth mentioned that he had encoun-
tered cases where this effect was very important.
I he operating range of this probe was severly limited by overheating above
50 mA.
Either the ratio of the collecting area to the cross-section should be decreased
or some pulsed technique should be adapted in the future.
Another improvement in this system could be made by replacing the tungstenwire cathodes w *h something that would lead the generation of a more uniform plasma.
A beam over which one had more control would be advisable if one wished to do beam
interaction experiments.
Associate Professor G. Bekefi has suggested that a large
cathode of the type used in thyratrons might prove suitable for this application.
Once
activated it could not be exposed to air again as these cathodes can, but they are not
expensive so that this problem is not too important.
Although this system cannot be
baked out, poisoning could probably be avoided by keeping a very small amount of an
inert gas flowing through the cavity at all times.
-34-
Improved accuracy and sharper peaks on the radiometer-magnetic field plots
is greatly desirable.
It should be possible to obtain peaks as sharp as those of
Landauer (1962) or Lustig (1964) by eliminating simultaneous reception at two frequencies and narrowing the bandwidth.
A more precise magnetometer-magnet cur-
rent calibration and movement of the coils to make the coils axis coincident with the
cavity axis would be beneficial.
-35-
IV.
CONCLUSION
Experiments at high densities have shown no evidence for a change of the posi-
tion of radiometer maxima near the cyclotron harmonics with density.
accordance with previous results.
"Ihis is in
Densities between 2.0 and 20 x 1018 m -were
p-obably encountered, although the nature of the probe measurements makes the
exact range uncertain.
Suggestions for improvement of the system concerning the cathodes, the probe
and the radiometer should lead to more precise measurements over a greater range
of densities in the future.
-36-
iIBLIOGRAPHY
Agdur, 8., and V. Ternstrom, Instabilities in Penning Discharges, Phys. Rev. Letters
13, 5 (1964).
Allen, N/i. A., P. Chorney, and H. S. Maddix, Stabilization of a Hot-Cathode P. I. G.
Discharge in a Magnetic Field, Appl. Phys. Letters 3, 30 (1963).
Bekefi, G., J. D. Coccoli, E. B. Hopper, Jr., and S. J. Buchsbaum, Microwave
Emission and Absorption at Cyclotron Harmonics of a Warm Plasma, Phys. Rev.
ietters 9, 6 (1962).
Bekefi, G., and E. B. Hooper, Jr., Cyclotron Radiation of an Hg Plasma Generated by
an Electron Beam, App. Phys. Letters 4, 135 (1964).
Backus, J., Theory and Operation of a Philips Ionization Gauge Type Discharge, ' he
Cliaracteristics of Electrical Discharges in Magnetic Fields (A. Guthrie and
R. K. Wakerling, eds.) McGraw-Hill, New York (1949).
Backus, J., Studies of Cold Cathode Discharges in Magnetic Fields, J. Appl. Phys. 30,
1866 (1959).
Backus, J., and N. E. Huston, Ion Energies in a Cold Cathode Discharge in a Magnetic
Field, J. Appl. Phys. 31, 400 (1960).
Bernstein, I. B., Waves in a Plasma in a Magnetic Field, Phys. Rev. 109, 10 (1958).
Bohm, D., E. H. S. Burhop and H. S. W. Massey, The Use of Probes for Plasma
Exploration in Strong Magnetic Fields,
hle Characteristics of Electrical Dis-
charges in Magnetic Fields (A. Gutherie and R. K. Wakerling, eds.) McGrawHill, New York (949).
Buchsbaum, S. J., and A. Hasegawa, Excitation of Longitudinal Plasma Oscillations
Near Electron Cyclotron Harmonics, Phys. Rev. Letters 12, 685 (1964).
Calvert, W., and G. B. Goe, Plasma Resonances in the Upper Ionosphere, J. Geophys.
Res. 68, 6113 (1963).
Canobbio, E., and R. Crocci, Harmonics of the Electron Cyclotron Frequency in a
P. I. G. Discharge, Proc. of the Sixth Int. Conf. on Ionization Phenomena in
Gases, Paris, 1963, P. Hubert (ed.) Sterma, Paris (1964), Vol. 3, p. 269.
-37-
Chen, F. F., Saturation Ion Current to Langrnuir Probes, J. Appl. Phys. 36, 675 (1965).
Chen, F. F.
Radial Electric Field in a Reflex Discharge, Phys. Rev. Letters 8, 234
(1962).
Chen, F. F., and A. W. Cooper, Electrostatic 1urbulence in a Reflex Discharge,
Phys. Rev. Letters 9, 333 (1962).
Crawford, F. W., G. S. Kino and H. H. Weiss, Excitation of Cyclotron Harmonic
Resonances in a Mercury-Vapor Discharge, Phys. Rev. Letters 13, 229 (1964).
Dote, T., and H. Amemlya, Negative Characteristic of a Cylindrical Probe in a Magnetic
Field, J. Phys. Soc. Japan 19, 1915 (1964).
Dote, 1., H. Amemiya, and T, Ichimiya, Effect of a Magnetic Field upon the Saturation
Electron Current of an Electrostatic Probe, Japanese J. Appl. Phys. 3, 789 (1964).
Dow, D. G., Electron-Beam Probing of a Penning Discharge, J. Appl. Phys. 34, 2395
(1963).
Dreicer, H., Emission of Cyclotron Radiation from a P. I. G. Discharge, Bull. Am.
Phys. Soc. 9, 312 (1964).
Fejer, J. A., and WV.Calvert, Resonance Effects of Electrostatic Oscillations in the
Ionosphere, J. Geophys. Res. 69, 5049 (1964).
Geller, R., and D. Pigache, Mecanisme D'Equilibre d'une Decharge P. I. G. Reflex
et Determination Experimentale de D dans le Plasma, J. Nucl. Eng. C 4, 229
(1962).
Goler, S. V., and H. Wagner, Uber die Penning-Entladung mit heisser Kathode und
ihre Verwendung als Ionenquelle, Sixth Int. Conf. on Ionization Phenomena in
Gases, Paris, 1963, P. Hubert (ed.), S. E. R. M. A., Paris (1964), vol. 2,
p. 405.
Gruber, S., W. D. McBee and L. T. Shepherd, Observation of Spatially Growing Waves
at the Cyclotron Harmonics in an Electron-Beam-Generated Plasma. Appl. Phys.
Letters 4, 137 (1964).
-38-
Helmer, J. C., and R. L. Jepsen, Electrical Characteristics of a Penning Discharge,
Proc. IRE 49, 1920 (1961).
Hirsch, Ei. H., On the Mechanism of the Penning Discharge, Brit. J. Appl. Phys. 15,
1535 (1964).
Jepsen, R. L., Magnetically Confined Cold-Cathode Gas Discharges at Low Pressures,
J. Appl. Phys. 32, 2619 (1961).
Johnston, 7. W., and J. Nuttal, Cyclotron Harmonic Signals Received by the Alouette
Topside Sounder J. Geophys. tRes. 69, 2305 (1964).
Kaganskii, M. G., D. L. Kaminskii and A. N. Klyucharev, Coherent Oscillations in
a High-Voltage Penning Discharge, Sovy. Phys.-Tech. Phys. 9, 815 (1964).
Knauer, W. , A. Fafarman, and R. L. Poeschel, Instability of Plasma Sheath Rotation
and Associated Microwave Generation in a Penning Discharge, Appl. Phys. Letters
3, 111 (1963).
Knecht, R. W., and S. Russell, Pulsed Radio Soundings of the Topside of the Ionosphere in the Presence of Spread F, J. Geophys. Res. 67, 1178 (1962).
Knecht, R. W., T. E. Van Zandt and S. Russell, First Pulsed Radio Soundings of the
Topside of the Ionosphere, J. Geophys. Res. 66, 3078 (1961).
Kubo, H., K. Mitani, S. Tanaka, and Y. Terumichi, Microwave Radiation from a Plasma
in a Magnetic Field (II), J. Phys. Soc. Japan 19, 221 (1964).
Landauer, G., Generation of Harmonics of the Electron-Gyrofrequency in a Penning
Discharge, J. Nucl. Energy C 4, 395 (1962).
Langmuir, I., and K. T. Compton, Electrical Discharges in Gasses, II, Fundamental
Phenomena in Electrical Discharges, Rev. Mod. Phys. 3, 191 (1931).
Little, R. G., Experimental Determination of the Perturbation of a Plasma by a Probe,
M. S. Thesis, Massachusetts Institute of Technology (1964).
Lockwood, G. E. K., Plasma and Cyclotron Spike Phenomena Observed in Topside
lonograms, Can. J. Phys. 41, 190 (1963).
-39-
Loeb, L. B., Basic Processes of Gaseous Electronics, U. of Cal., Berkeley (1955).
Lustig, C. D., Electron Density Dependence of Cyclotron Harmonic Radiation from
a Plasma, Phys. Rev. 139, A63 (1965).
Mitani, K. H. Kubo, and S. Tanaka, Microwave Radiation from a Plasma in a Magnetic
Field (I), J. Phys. Soc. Japan, 19, 211 (1964).
Nuttall, J., 'heory of Collective Spikes Observed by the Alouette Topside Sounder,
J. Geophys. Res. 70, 1119 (1965).
Simon, A., and M. N. Rosenbluth, Single Particle Cyclotron Radiation near Val z4and
Sheaths, Phys. Fluids 6, 1566 (1963).
Spivak, G., and E. Reichrudel, 7uiz Allgemeinen "Theirie der Sonden Stroms in der
Gasentladung, Physikalische 7eitschrift der Sovietunion 9, 655 (1936).
Stone, P. M. and P. L. Auer, Excitation of Electrostatic Waves near Electron
Cyclotron Harmonic Frequencies, Phys. Rev. 138, A695 (1965).
Tanaka, S., Y. Terumichi, K. Mitani, and H. Kubo, Anomalous Microwave Radiation
at Cyclotron Resonance in Partially Ionized Plasmas, J. Phys. Soc. Japan 18,
1810 (1963).
Vasil'Eva, M. N., and E. M. Reikhrudel, Influence of Space Charge on The Kinetics
of Electrons in Penning-type 'ubes,
Sov. Phys.-Tech. Phys. 7, 528 (1962).
Verweij, W., Probe Measurements and Determination of Electron Mobility in the
Positive Column of a low-pressure Mercury-Argon Discharge, Ph. D. Thesis,
Utrecht, (1960).
Wallis, G., On the Harmonics of the Gyrofrequency Observed on Topside Ionograms,
J. Geophys. Rev. 70, 1113 (1965).
Waniek, R. W., R. T. Grannan, and D. G. Swanson, Anomalous Cyclotron Radiation
from a Plasma Discharge, App. Phys. Letters 5, 39 (1954).
-40-
APPENDIX A
Calculation of Thermal Electron Energies.
'I he well-known exponential dependence of the electron current to a probe negative
with respect to the plasma potential is (Loeb, 1955; Verweij, 1960):
I
where I
pe
eV
N ev S exp( -e
k e
4 e
is the electron current to the probe, V
is the probe potential with respect
to the plasma, Ne the electron density (assumed equal to the ion density Ni), v the
average velocity of the electrons, and S is the area of the probe.
Since Vp = V
constant, this is
eV
0.4343 log I
pe
=
a
kTe
constant
andgivesa straight line on a semi-logarthmic plot, the slope of which is determined by
k1e"
i he problem is that of accounting for the ionic current which is being collected
by the probe at the same time.
to be nonlinear.
Even though small, this contribution can cause the plot
Here the tangent to the probe curve between V
has been extended and taken as the ion current.
= -40 V and V
= -25 V
The values of I in Figure 8 are the
differences between the curve and the extended tangent in Figure 7.
More sophisticated methods of accounting for the ion current which insure that the
ion current goes to zero for values of Vp not too far from the plasma potential are
described in Loeb (1955), but for the portion of the probe curve used here this approach
is adequate.
It is thought best to use this lower portion of the probe curve anyway be-
cause it appears that the curve does not follow the exponential law near the plasma potential
when a magnetic field is present (Dote et al., 1964; Dote and Amamiya, 1964).
also 3ohm et al.,
1949).
(See
-41-
APPENDIX B
Calculation of Densities
I he saturation current to a cylindrical probe is complicated by the geometry because the surface area of the sheath is not the same as the surface area of the probe,
and, if the sheath is thick with respect to the probe, many of the electrons entering
the sheath may leave it without being collected by the probe.
7 ne theory for the ex-
treme cases of thick and thin sheaths for monoenergetic particles is presented in
Langmuir and Compton (1931).
1 he theory for a Maxwellian distribution may be found
After their work had been published, these authors dis-
in Dote and Amemiya (1964).
covered that some of their results had been obtained earlier by Spivak and Rleichrudel
(1936).
r
o determine the size of the sheath, the parameter
'4
is found from the Vp3/2
law (equation 332 of Langmuir and Compton) and the value of q, the ratio of the radius
of the sheath to the radius of the probe, is found from Langmuir and Compton's
Figure 43 or Figure 44.
For the larger probe used in this experiment, the equation is
V3/2
4
2
x 10
= 1.78
-
p
P
when I is in mA and V in v.
P
P
the thin sheath approximation is calculated using Dcte and
using
9 he density
Amemiya's equation (17)
I P = 2wrpq I P
(q)e N i exp (-
1 kfe ) 1/2
)
i
where rp is the probe radius, tp the length of the probe, Mi is the mass of the ion and
'
(q) is a correction for the end effect.
If this end correction is ignored (
the larger probe in this experiment we obtain (assuming ki e = 3 eV)
= 1). for
-42-
N. = 3.15 I /q
1
p
with I in mA, N. in 10
18
1
p
m
-3
2
For the large sheath, Ip is plotted against Vp and a straight line should result.
From Dote and Amemiya's equation (14) (corrected by the incorporation of the factor
2 -- 1/2) one finds
4
i2
p
. 2 exp(1)2 k'e
=
M.(
1
eV
e
2T.
kl
Fir the larger probe, this becomes
dI
with the assumption that
1/2
2
e
e
=
100 i.,and for I in mA and N. in 10
p
18
m
-3
.n