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AN EXPERIMENTAL INVESTIGATION OF SURFACE IONIZED ALKALI AND ALKALINE EARTH PLASMAS CONFINED BY AN INCANDESCENT X-BAND MICROWAVE CAVITY

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University
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Kim, Kwang Seok
AN EXPERIMENTAL INVESTIG ATIO N OF SURFACE IONIZED ALKALI
AND ALKALINE EARTH PLASMAS CONFINED BY AN INCANDESCENT
X-BAND MICROWAVE C A V ITY
New York University
University
Microfilms
International
Ph.D. 1983
300 N. Zeeb Road, Ann Arbor, M I 48106
Copyright 1983
by
Kim, Kwang S e o k
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AN EXPERIMENTAL INVESTIGATION OF
SURFACE IONIZED ALKALI AND ALKALINE EARTH PLASMAS
CONFINED BY AN INCANDESCENT X-BAND MICROWAVE CAVITY
Kwang S t Kim
February 1983
A dissertation in the Department of Physics submitted
to the faculty of the Graduate School of Arts and
Sciences in partial fulfillment of the requirements
for the degree of Doctor of Philosophy at New York
University.
Supervised by Howard H. Brown
Approved
AN EXPERIMENTAL INVESTIGATION OF
SURFACE IONIZED ALKALI AND ALKALINE EARTH PLASMAS
CONFINED BY AN INCANDESCENT X-BAND MICROWAVE CAVITY
Kwang S. Kim
ABSTRACT
A homogeneous and near thermal equilibrium plasma device with
optical and microwave diagnostics has been designed and constructed.
The surface ionized plasma is confined by an incandescent x-band
microwave cavity.
The cylindrical cavity is supported by two
refractory metal waveguides, and is heated by radiation from two
larger ohmically heated tungsten cylinders concentric with the cylin­
drical cavity.
The microwave resonant frequencies of the cavity are
shifted by the plasma.
These shifts have been measured and are used
for a very accurate plasma density measurement.
The feasibility of
using laser induced fluorescence for a direct and localized plasma
ion density measurement has been demonstrated using a cw dye laser
beam and a Ba
plasma.
Using K and Cs plasmas, the microwaves have
been used at low power (~1 mw) to detect low frequency oscillations
(<100 kHz) in the cavity.
The nature of these oscillations is not
certain, but some possibilities are discussed.
At high microwave
power, low frequency ion acoustic oscillations have been observed
in the cavity.
There is evidence that these result from the parametric
decay of the microwaves.
The microwave resonant frequencies of the
plasma filled cavity shift as the microwave power is increased due to
the ponderomotive force rearranging the plasma.
been measured as a function of microwave power
These shifts have
and compared to a
calculation in which the modified electric field in the cavity is
calculated in a self-consistent manner.
At higher powers, the cal­
culated frequency shifts are less than the experimentally measured
shifts and do not fall within the estimated error bars of the data
points.
ACKNOWLEDGEMENTS
Many thanks are due the following people for their help throughout this work:
My wife Wi, who patiently supported me;
Professor Howard H. Brown, my thesis adviser, who taught me physics, guided
me in the lab, and provided constant encouragement. Without his help this
work would not have been possible;
Professor Benjamin Bederson who kindly took time away from his busy schedule
to give advice;
Professor Bernardo Jaduszliwer who gave me many useful suggestions;
Professor Harold Weitzner of the Courant Institute for helpful discussions;
Professor Leonard Yarmus, who generously lent me many microwave components
and advised me on microwave techniques;
Dr. Daniel Taggart, who worked with me on the construction of the apparatus;
Professor I. Bernstein and Dr. R. Jensen of Yale University for their interest
in this work and their calculations of the damping of acoustic modes in a
cavity;
Mr. Aubrey Hanley and his staff in the machine shop for their suggestions
and kindness;
Ms. Johnnie Foy, Ms. Pauline Maloni and Ms. Meredith Storer for their help
with the paper work;
All my colleagues in the lab who provided constant help and support:
Phyllis Weiss, Tom Guella, Bob Kremens.
Al Tino,
CONTENTS
page
1. Introductory Description of the Plasma, Apparatus, and Experiments
1.1
Introduction
1
1.2
The Apparatus
2
1*3
1.3.1
Experiments
4
Microwave Density Measurement
4
1.3.2
Laser Diagnostics
6
1.3.3
Resonant Microwave Frequency Shift due to the
Ponderomotive Force
6
1.3.4
Undriven Low Frequency Oscillations
1.3.5
Driven Low Frequency Oscillations
7
2.1
The Hot Box Plasma
8
2.2
Microwave Plasma Density Measurements
11
2.3
Laser Diagnostics
15
2.4
Resonant Microwave Frequency Shift due to the
Ponderomotive Force
27
2.5
Undriven Low Frequency Oscillations
41
2.6
Driven Low Frequency Oscillations
43
6
• 6
Theory
Apparatus
3.1
General Description of the Apparatus
45
3.2
Details of the Apparatus
46
3.2.1
Vacuum Chamber Main Cover Flange
46
3.2.2
Heating Element Flange Assembly
48
3.2.3
Oven Flange
51
3.2.4
Waveguide Flange and Waveguide Feedthrough
53
3.2.5
Heating Element Assembly
54
3.2.6
Tantalum Heating Shields
59
3.2.7
Water Cooled Copper Heat Shield
60
3.2.8
Microwave Cavity
60
3.2.9
Refractory Metal Waveguides
65
3.2.10 Waveguide Heatshields
68
3.2.11 Plasma Material Feed Tube
70
3.2.12 Wire Probes
71
3.2.13 Stabilization of the Heating Element Current
73
3.2.14 Microwave System
75
3.2.15 Laser Diagnostic System
77
(
3.2.16 Helmholtz Coils
3.2.17 Rhenium Plating
r
82
82
4. Experimental Work
4.1
Microwave Plasma Density Measurements
85
4.2
Laser Diagnostics
89
4.3
Cavity Resonant Frequency Shift due to the
Ponderomotive Force
92
4.4
Observation of Undriven Low Frequency Oscillations
H6
4.5
Observation of Driven Low Frequency Oscillations
129
5. Conclusion and Recommendation for Future Work
133
References
136
Appendix
Computer Program for the Self ConsistantField Calculation
138
1.
1.1
INTRODUCTORY DESCRIPTION OF THE PLASMA. APPARATUS. AND EXPERIMENTS
Introduction
Many plasma phenomena have been studied in the past few decades
using discharge plasmas and Q machine plasmas ^ . In addition,
discharge plasmas generally possess much higher electron temperatures
than ion temperatures.
For some purposes density gradients and
particle temperature differences are an intrinsic part of the phenomena
being studied.
For other purposes, particularly the study of plasma
properties near thermodynamic equilibrium, density arid temperature
gradients should be made as small as possible.
A few critical plasma
studies have been made using "hot box" or Saha plasmas, in which
density gradients and particle temperature differences are minimal.
A homogeneous and near thermal equilibrium plasma device has been
developed and used at NYU
2-5
. This plasma is produced by introducing
the plasma material into an incandescent refractory metal cylinder.
In thermal equilibrium the fractional ionization is determined by the
Saha equation which predicts that reasonably high ionization can be
obtained.
For example, the fractional ionization is about 67% for a
Cs plasma with a density of 5 x lO
of 2100° K.
10
cm
—3
and with a wall temperature
Except under special combinations of parameters, the hot
box plasma, like practically all plasmas, is separated from the walls
by a non-neutral sheath.
The sheath plus the hot box wall form the
plasma boundary, and this composite boundary affects the reflection
and absorption of incident waves.
Discharge plasmas are usually posi­
tive with respect to the wall, while Q machine and hot box plasmas may
be positive or negative depending on the wall work function, plasma
density, and temperature.
Because of the high temperature of the hot box, plasma diagnos­
tics with a conventional plasma probe are very difficult to perform.
The plasma phenomena studied in the past were limited to those where
the information could be transmitted by particle beams or by light
spontaneously emitted from the plasma.
A new plasma device^with
improved diagnostics and broadened capabilities has been built.
new diagnostics are microwaves
The
and dye laser induced resonance fluo'
i
rescence.
The capabilities of the new apparatus have been demonstrated, and
a number of plasma phenomena studied.
The microwave system has been
used to obtain plasma density measurements, induce parametric decay
oscillations, observe low frequency undriven oscillations, and measure
ponderomotive force effects.
Additionally, laser diagnostics have
been shown to be feasible.
1.2
The Apparatus
The plasma chamber is fabricated into a cylindrical microwave
cavity.
The cavity is held by two x-band waveguides made out of
tantalum foil (See Fig. 1.1).
Two waveguides are used so that both
reflected and transmitted waves from the cavity can be observed.
The cavity is made out of foil plated with Re to increase the proba­
bility of surface ionization at the walls.
To compensate for small
plasma losses from diagnostic holes in the cavity wall, a small tube
-2-
WAVE GUIDES
WAVEGUIDE WINDOW
,STAINLESS STEEL
•PIPES
.TOP -FLANGE
LASER WINDOW
WAVEGUIDE FLANGE
FLEXABLE WAVEGUIDES •
PLASMA SOURC
OVEN •
COPPER TUBING
FOR COOLING
OVEN f l a n g :
<— UPPER FLANGE
'WAVEGUIDE_
HEAT SHIELDS
<— LOWER FLANGE
HEAT SHIELDS_ PLASMA SOURCE
FEEDTHROUGH
TANTALUM
WAVEGUIDES
r “HEATING ELEMENTS
MICROWAVE CAVITY
HEAT SHIELDS
Fig. 1.1
CAVITY-IIEATING ELEMENT ASSEMBLY
made out of Ta foil continually supplies plasma material to the cavity.
The plasma chamber is heated by radiation emitted from a surrounding
ohmic element.
This element is coaxial and is heated by ~10 kW of
filtered dc power.
The coaxial configuration minimizes the magnetic
field produced in the plasma by the heating current.
The suspension
of the heating element from the water cooled flanges supplying the
heating current is shown in Fig. 1.1.
apparatus is shown in Fig. 1.2.
The overall layout of the
The plasma chamber and its supporting
flanges are inside a 45.72 cm diam vacuum chamber with multiple window
and access ports.
An originally horizontal dye laser beam enters the
vacuum chamber near the bottom, and is reflected to the vertical dir­
ection by a mirror that is rotatable about two axes and translatable
along one axis.
The laser beam emerges from a small optical glass
port in the vacuum chamber main cover flange.
When using barium, plasma
ion fluorescence emanating from small holes in the side of the plasma
chamber is observed through a large side port.
1.3
Experiments
1.3.1
Microwave Density Measurements
Plasma density measurements are discussed.
and highly accurate.
The method is direct
It uses the resonant frequency shift of the micro­
wave cavity due to the dielectric properties of the plasma in the cavity.
Sec. 2.2 contains a brief review of the theory, and Sec. 4.1 contains
experimental results. •
-b-
Eh
55
W
5%
W
,
w
8
t=>
W
O
55
M
Eh
CO
o
Q
.55
M
<£
s
CO 52
-a; w
>
P-.-D
w
5C
l
c 4 - ~ = —
HI
i
LAYOUT OF APPARATUS
< 1
1
' 1 i. .........
i%=
•'•..JO
/■
w
<
1^1
to
g
Fig. 1.2
STAINESS STEEL PIPES
FOR POWER AND COOLING
o
CO
«
Eh fcl
O
p: w
P=3Eh
£=<M
55 M
H
H Pi
s
Pi
K
W
3
a.
«
»•
t=>
Pi
-5-
1.3.2
Laser Diagnostics
A non-perturbative optical diagnostic is discussed.
Ba , which
has several transitions in the optical range, is used as the plasma
ion.
To excite the ions, resonant light from a tunable dye laser is
directed into the plasma which is confined in the incandescent micro­
wave cavity.
From the intensity and line shape of the light fluoresced
by the plasma ions, the ion motions and density can be found.
Sec. 2.3
contains the theory and Sec. 4.2 contains the experimental result.
1.3.3
Resonant Microwave Frequency Shift due to the Ponderomotive Force
The resonant frequencies of the plasma filled cavity depend on
the microwave power as well as the plasma density.
The measured micro­
wave power dependence of the resonant frequency of the cavity is compared
with the theory.
sistent way.
The resonant frequency is calculated in a self con­
The theory and an outline of the numerical calculation
are given in Sec. 2.4 and the experimental work is given in Sec. 4.3.
1.3.4
Undriven Low Frequency Oscillations
When the microwave power is low, the microwaves are often amplitude
modulated by low frequency (<100 KHz) oscillations in the plasma filled
cavity.
No threshold with microwave power is observed, and it is believed
that the microwaves are detecting existing oscillations, not causing
them.
For microwave power >1 W, the oscillations disappear.
lations are sensitive to an applied magnetic field.
The oscil­
An applied radial
field of ~1 G will significantly alter the amplitudes and frequencies
-6-
of the oscillations, and an applied radial field of ~5 G will make
them disappear.
Such low frequncy oscillations must be due to the
plasma ions, but the exact nature of the oscillation is not certain
at this time.
Some possibilities are discussed in Sec. 2.5, and the
experimental work is discussed in Sec. A.3.
1.3.5
Driven Low Frequency Oscillations
When the microwave power is high, low frequency oscillations with
well defined frequencies and large amplitudes are observed.
These
oscillations are not sensitive to an externally applied magnetic field
of ~1 G and disappear in the presence of vertically applied field of
>40 G.
These oscillations are most likely the ion acoustic oscillation
of a parametric decay process due to the high microwave power.
Stable
oscillations occur above a certain plasma density threshold, depending
on the microwave power.
Sec. 2.6 contains a brief review of the theory
and Sec. 4.5 contains the experimental observations.
-7-
2.
THEORY
2.1 Hot Box Plasma
A hot box plasma device has been developed and used in earlier
2-5
experiments
. The new "hot box" is similar in many ways to the old
one.
If a given number of atoms are introduced into an isothermal
enclosure at temperature T, some fraction of the atoms will be ionized.
The equilibrium plasma density np and neutral density riQ are related
by the Saha equation,
'Tip -
M i
„ ( 2 t m ek J ) % v n l £ t
where V,. „ is the ionization potential of the atoms, g , g., and g
I.P.
r
e
i
o
are the statistical weights of the electron, ion and neutrals respec­
tively, and the other symbols have their usual meaning.
For T = 2500° K
and using alkali or alkaline earth elements, the Saha equation predicts
useful plasma densities.
Fig. 2.1 is a graph of the fractional ioniza­
tion of a thermal Ba plasma vs. plasma temperature with plasma density
as a parameter and Fig. 2.2 is that of a K plasma.
2
The plasma cylinder has typically 0.28 cm
2
74.3 cm
of total hole area and
of wall area, and a particle, on the average, collides with
the wall several hundred times before escaping from the cavity.
For
ionization equilibrium to be established it is necessary for the atoms
to have a reasonable probability of being ionized before exiting from
the cavity.
The probability
that an atom or ion hitting the wall
-8-
FRACTIONAL IONIZATION OF AN EQUILIBRIUM BA PLASMA VS. TEMPERATURE
5x10'
1x10
H
fV
o
H
h
1x1 O'
5x10'
1800
2000
2200
TEM PER A TU R E
Fig. 2.1
-9-
2600
.2800
FRACTIONAL IONIZATION OF EQUILIBRIUM K PLASMA VS TEMPERATURE
o
c
^ 0.9
c
^
0.8
a
o
0.3
1800
2000
2200
TE M P E R A TU R E
Fig. 2.2
-
10 -
2400
260 0°K
6
comes off as an ion is given by
where W is the work function of the metal wall.
At 2500° K, P^ for
Ba is 0.57 with a Re wall, 0.082 with a W wall, and 0.014 with a Ta
wall.
For a Ba plasma, pure Ta might not produce the desired degree
for ionization, W may be satisfactory, and Re is the best available
material.
Constructing the cavity out of Re foil was considered, but
found to be very expensive.
A procedure for plating Ta foil with Re
was developed, and present cavities are constructed with this combination
of materials.
2.2
Microwave Plasma Density Measurements
Density measurements of a plasma in a microwave cavity have been
7-12
studied and used for many years ' . The resonant frequency fg and the
quality factor Q are the two quantities characterizing a particular
cavity resonance.
The resonant frequency is a function of the cavity
dimensions, the dielectric properties of the material in the cavity, and
the configuration of the electromagnetic fields within the cavity.
Q of a resonance is — —
Af
, where Af is the full width at half maximum
of the power transmission curve of the cavity plotted as a function
of the frequency.
The
Q is the loaded Q and is given by
-11-
1 =
Q
^
+
do
fi&
}
(2.2.1)
where Qe is the external Q associated with the energy loss through
the coupling holes used to make the measurement, and Qq is the unloaded
which depends only on the losses through other holes and at the cavity
walls.
A plasma placed inside a cavity changes f
and Q due to changes
in the real and imaginary part of the plasma dielectric constant.
For
0)
a transversely polarized wave and if
number k in an
< 0) and —
«
1 the wave
unmagnetized plasma is given by ^
2
'm \s
1
c 2 1
where co, (0^, and
u
)
,
(2.2.2)
are the microwave frequency, the electron plasma
frequency, and the collision frequency of the electrons with the plasma
ions and neutral atoms.
The factor in brackets is identified as the
square of the plasma index of refraction, y,so that
2
ii2 —
i
f.|
_
Vqn *t* ^0
'
.
• HtA
’
(2.2.3)
When the plasma is not distributed uniformly in the cavity, perturbation
theory is used to derive an expression for the change in Q and f
duced by the presence of the plasma.
-12-
The change of Q is given by
pro­
/ i
/ [ i f J t & i j v __
^Q'
JEo 'Eo^V
wi + A n
v
JE0‘Eo^
(2.2.4)
and the fractional shift in the resonant frequency is
I
eUv _
$0~Z
|
I
StirEoEjv
2. COo+Vm
^.£^(2.2.5)
where the subscripts I and R refer to the imaginary and real parts of
2
")■
y respectively and Eq is the electric field of the cavity mode corre-
spending to fQ =
CO
^
, the resonant frequency of the empty cavity.
The literature has been followed in that Af = (f - f), so that with
o
a plasma dielectric where the resonant frequency is raised, Af is a
negative number.
In Ref. 12 a similar Eq. for the fractional shift in
the resonant frequency is derived rigourously, assuming
E = ( E 0 +
E , ) e i(u ;o + S u ,)I
N
>
(2.2.6)
where E^ and 6^ are the perturbed electric field and the resonant
frequency shift due to the plasma.
When the whole cavity is uniformly
filled with the plasma Eq. (2.2.5) becomes
-13-
—
- -L
So
^
a)o + u
In this experiment,
«
2.
.
0), and may be neglected.
(2.2.7)
The plasma density
then may be calculated from Eq. (2.2.7), and one gets
-3
7lp=2.4Sx i o A f 0 *
with fQ and Af in H^.
C7TI
L j
« - 2-8>
This is the expression actually used to cal­
culate the plasma density.
An exact Eq. for the resonant frequency
when V = 0 is
m
f =
So
-
So
0)Z^
)
and Eq. (2.2.8) may be obtained by expanding Eq. (2.2.9).
For the
parameters of this experiment, the difference between Eq. (2.2.8) and
Eq. (2.2.9) is negligible.
To estimate the accuracy to which n^ can be measured, let 5
before a quantity represent the uncertainty in that quantity.
From Eq. (2.2.8),
i
s(np=2.48xio*[8i0xhj:l+
As
g jo Ol S K |
STlf ~
’ and
%»
f0x s | 4 n
.
(2 .2 .10)
Sto ’ we have
x /0*x to X S \ * j o \ .
(2-211)
The Q's for the cavity modes usually fall between 500 and 1000.
a typical value of f
fi|Af | is ± 2 MHz.
With
being 10*° Hz, a rather conservative value for
The absolute uncertainty in n^ is then 6n^ -± 5 x 10^
cm
As the plasma densities used range from about 1 x 1 0 ^ to 1 x 10^^
_3
cm , the density is known with a relative accuracy from 5% to 0.5%.
2.3
Laser Diagnostics
Laser diagnostics by fluorescence have been discussed by many
authors
13-17
+
. The fluorescence to be expected from a Ba plasma when
the fluorescence is induced by a tunable dye laser is calculated below.
Ba
has five allowed transitions in the optical region that occur
between five energy levels.
not drawn to scale.
These are shorn in
Fig. (2.3), which is
The two D states are metastable.
Ba is the even-even isotope
71.7% of natural
138, so that isotope shifts and hyperfine
structure are not a significant complication.
For convenience, each
energy level has been numbered successively, with the ground state
numbered 1.
For each transition is given the wavelength X in X, the
absorption oscillator strength fmn> the spontaneous emission probability
A ,
nm*
insec \ the induced emission coefficient B ,and the absorption
’
nm*
coefficient Bmn , where it has been assumed that m < n.
The Bmn and Bnm
coefficients are those of Milne and have units of sec. g
All the
transitions shown can be used for diagnostics, as the metastable states,
2 and 3, have significant populations.
levels 1, 2 and 3 are shown below.
-15-
The percentage populations of
Level Number
State
Percentage Population (T=2500° K)
1
62Si /2
80.6
2
52D3/2
10.0
3
52D5/2
9.4
It can be advantageous to excite one line and look at the fluorescence
of another line.
We estimate what physical processes dominate some of the transitions
between energy levels 1 through 5.
For these purposes it is assumed
that a cw dye laser can produce 50 mw at 4554 R and 240 mw at 6142 &
in a bandwidth of 0.1 R, and that the laser beam has a cross section of
-2
10
2
cm . These specifications are obtainable in an "off the shelf"
laser.
It is also assumed that the laser mode structure is rapidly
averaged over the 0.1 X line width either by noise or an acoustic
device.
Defining
—
»
I_____
(laser power)
4-71
(area of laser beam)
where Av is the frequency spreadof the laser beam in Hz, we have
1^ (4554
R) =
2.74x10 ^ erg
sec ^ cm 2
1^ (6142
R) =
2.40x10
sec ^ cm 2 V
erg
V \
and
(2 3 2)
I
The probability of a laser induced transition is then B
I , sec.
v
.
nm v
-1
Table 2.1, which uses the above values for laser induced processes, has
probabilities for laser induced absorption, spontaneous decay, exci-
-16-
Energy Level of Ba+(Not To Scale)
2.72 (5)
2.51
5854 A
•4554 A
f 15= .0.74
A^^«= 1.19xl08sec *
B-,= 2.83xl010sec g"1
51
B,c= 5.66xl0*8sec g ^
D
'
0.70
(3)
0.60
(2)
‘ *0
(1)
X
«= 6497 A
f25*= 0.025 .
f24= 0.105
Aj^ta 4.87xl0^sec *
9
-1
B ^ 2=
2 . 4 6 x 1 0
sec g
9
-1
B^a 2.46x10 sec g
A.0
42=s 0.332xl08sec"1
B,,= 2.29xl010sec g"1
, ,r ..10
-1
B24= 1.15x10. sec g
X a 4934 X
X a 6142 A
f,.= 0.35
14
A,,= 0.955x108sec_1
41
2.89xl0*8sec g *
f35= 0.14
A^3= 0.37xl08sec
B14.= 2.89xl010scc g"1
B^^a 1.44xl0^8sec g ^
B^a 2.16xl0^8sec g ^
•52 D,
5/2
V
V
V
V
-52D.3/2
-62S1/2
'Fig.
2.3
-17-
TABLE 2.1
Probability for transitions between levels 1-5 by different physical
processes.
T = 2500
K; n£ = 1 0
3.1
3
cm . Starred probabilities scale
with n .
e
Physical Process
Levels
Probability (sec
laser induced absorptions
1 to 5
1.55x10
(Vv>
1 to 4
7.92x10
<B354>
3 to 5
3.46x10
5 to 1
1.19x10
4 to 1
0.955x10
5 to 3
0.37xl08
spontaneous decay (A^)
1 to 2 or 3
excitation by electrons
It
deexcitation by electrons
II
excitation by black body radiation
II
II
8
104
wall collision probability
II
8
6.2xl05
replacement probability in 1 mm"
II
7
II
-18-
5.5xl03 *
1 to 4 or 5
1.3
*
4 or 5 to 1
1.2x10
*
2 or 3 to 1
7.1x10
*
1 to 4
7.14x10
1 to 5
8.39x10
tation by electrons, and de-excltation by electrons.
two, an electron density of 10
11
For the latter
-3
cm
has been assumed, and theoretical
estimates given in references 13 and 14 used.
Also given are the "wall
collision probability," which is the average collision rate of the Ba
ions with the plasma chamber walls, and the "replacement probability
-3
3
in 10
cm ."
The latter is the approximate replacement rate of Ba
-3
3
ions in the interaction volume of about 10
cm , which is the inter­
section of the laser beam and the observing optical system.
The
fluorescence intensity observed is directly proportional to this rate
because the laser intensity is sufficient to completely depopulate the
lower level of the excited transitions.
We note that excitation or
deexcitation by electrons or black body radiation are negligible except
possibly for the excitation of the ground state ions to the metastable
states.
The equilibrium populations of the metastable states will most
likely be maintained by wall collisions rather than electronic excitation.
The choice of which transition to excite with the laser is partly
determined by the need to keep the plasma optically thin to the incident
laser radiation.
The line profiles are Doppler, and the photon mean
18
free path A at resonance is given by
p
(2.3.3)
>
where N is the population of the lower level involved in the transition.
This X is conservative, as the photons off resonance have a longer mean
D
-19-
free path .
Below are listed for the 5 transitions the densities N
and corresponding total plasma densities for
= 10 cm.
A plasma
temperature of 2500° K is assumed.
Transition
N=density of lower level (cmn-3i
)
J for
.
.
ri of
-r 10
in
photon
mean free
path
cm
1
n = plasma
„
P^density
j ---^
/(cm
-- ~>)
1 -*■
5
1.08xl010
1.34xl010
1
4
2.12xl010
2.63xl010
3
5
4.25xl010
4.52X1011
2 -*•
4
5.37xl010
5.37X1011
2
5
2.50X1011
2.50xl012
There are suitable transitions for any plasma density contemplated.
The interaction volume has linear dimensions of the order of 10 ^
cm, and a plasma ion spends about 1.8x10 ^ sec there.
By solving the
rate equations for an ion entering a laser beam for this length of time,
we have calculated the maximum number of photons that will be emitted
£
from a given transition, and the laser intensity I
90% of this number of photons.
Table 2.2.
that will produce
These calculations are summarized in
The vertical column gives the transition that is excited
by the laser, and the horizontal column the transition that is observed.
The numbers in rows (a) are “ , the number of photons that are emitted
per ion entering the interaction region, where it has been assumed that
this ion has states 1, 2, and 3 populated according to Botzmann statis­
tics.
For a given excited line and a given observed line, the maximum
number of photons fluoresced is the number in the. table (oO multiplied
by the total number (all states) of ions entering the interaction
-20-
sit
<*
»
o
mx
I
o
rH
rH
X
o
o
X
X
X
CM
CO
CM
£
c
o
vO
to foH
ci
4J
4d-1 *o
0)
4o
-1
rH
4H
O
D
'O
d
d
1c
fH
•H
10
o
o
(0
d
m
Cl
>
•H
to
O
d
o
M
O
«4H
03
Cl
44
44
•rl
l*H
o
(X 44
d
d
4-1
to
JO
V)
d
•o
Cl
•H
rH
Cl
CX
g
•rl fH
4J
1
CO
c
rH
o
O
I
o
rH
X
CO
o
X
CO
m
<ro
X
rH
C
O
CO
4J
rH
d
d
to
CM
CO
CM
0
•c
p*
•s
d
o
<3vO
CO
CM
o
X
(0
d
o
d
rH
d
rH
t
in
CM
rH
o
rH
X
m
o
pH
X
vO
CM
HT
CO
CM
CM
o
O
O
1
o
rH
X
r*.
o
X
00
CM
ro
o
rH
X
ON
<r
CM
t
O
X
CM
<r
rH
X
CO
-o
rH
CM
N
t
O
rH
X
H
CM
rH
I
X
CO
vO
X
CO
VO
CO
•
CM
g
B
UH
2.2
(0
4J
d
M CO
1_
03
e
d
d
d
o o
U rH
to O
rH
•X
o
X
rt in
o
X
o
CO
d
o
on
o
o
CO
ON
rH
CO
O
X
CM
m
X
X
co
<r
<r
CM
CM
X
CN
N
O
Table
d
fH
U
Cl
u
d
o
00
o
rH
rH
X
X
VO
m
00
vO
CM
CM
o
g 4-1
Cl
o
rH
I
o
X
CM
CO
CM
OIN
on
d
0)
0)
>
o
r*
CM
/■N r-N rH
JO
O
O
V/
O
>
o
PS
CO
S»
O
P5
o
H
X
co
o
m
rH
<T
CO
m
in
1o <ro
o
rH
rH
X
m
2
rH
<r
rlM
CM
o
X
H
I
O
rH
0
0
m
X
<r
<■
o
X
<r
n
co
X
VO
o
-x
CO
o
r*f
I
O
X
co
O
m
o
x
o
o
co
44
0)
d
h)
•d
"
o
K
w
in
S
H
t
m
t
^
-21 -
rH
OXN HX
*** f**
CM
m
1
1
1
CM
co
CM
volume.
The numbers in the last column are the 1 fs necessary for
90% of these photons to be emitted.
.1
These values of I are less
than what is available from a standard tunable dye laser, and it may
be assumed that laser power is available to completely depopulate
the lower state of the excited transition and produce the maximum
number of photons.
Consider Fig.
2.4 . Let F equal the flux of ions (all states)
entering the interaction region per sec from the volume not irradiated
by the laser, £2 the acceptance solid angle of the observing optics in
sr, and t the transmittance of the optics.
The cw detector signal will
be
photons sec
-1
(2.3.4)
If the interaction volume is a cylinder D in diameter and H high, and
if F is the number of ions entering this volume from the side, we have
(2.3.5)
F = O A ) n pvTTDH ,
where v is the average speed of the ions.
The ions entering the
interaction volume from the ends are not included as the laser beam
will have depopulated the lower state of the excited transition.
—
4
_i
For D=H=0.1 cm, and v = 6.19x10 cm sec ,
(2.3.6)
\
-22-
CO
M-
<r
Pig. 2.if
o
co
C
CJ
•5 O
4.**
O
V
I ,
OJU-
- 23I
_3
where n is in cm . The interaction region is 22.9 cm from the
P
vacuum window, and the window is 3.18 cm in diameter, giving 0, = 0.015
sr.
The combination of this solid angle and a 10 ^ cm hole in the
plasma chamber for observation only degrades the spatial resolution
slightly.
If the photon signal is passed through an optical system
having a bandwidth larger than AX^, the Doppler bandwidth in cm, and
having an overall transmission of 0.4, the signal is
0*232 x oc x n
S =
•C*
photons sec“ ^#
•(2^3.7)
In the conditions prevailing in this experiment, most of the back­
ground and noise will be black body radiation emitted into the solid
angle
by the cavity.
The specific intensity for black body radiation,
1^, can be written as
L =
X
0 hr
"I
—3
~6/hi;, T— r era •sec cm
X ( e %fe«T - l )
D
.
<2.3.8)
We assume that the light from the plasma chamber is passed through an
interference filter of bandwidth AX^ cm and a Fabry-Perot of bandwidth
AXp cm and free spectral range AXg. With the condition AX^ > AX^ > AX^,
the black body background
will then be
C - i x ^XPx
3b
M
x ilxAxt photm sec1
^
As
(2.3.9)
where A = area of exit hole from the plasma cylinder, and AX^/AXg is
the number of times the bandwidth of the Fabry-Perot appears within
the bandwidth of the interference filter. Taking values of AX^ = 10 X,
.
O
AX = 0.05 A, and A = 7.85x10
cm , we have
P
IQ*1 x exp f- 5.16 x 10 % \ photons sec"'
1 L
J
O
with X the wavelength of the observed line in A.
(2.3.10)
The transmission of
the interference filter and Fabry-Perot have been taken as 0.5 and 0.8,
giving t = 0.4.
The ratio of the fluorescent signal to the black body
signal is
X
= (0 .4 ! x I020) <x71p\4 e x p [5.76 X 10%)
(2.3.11)
Defining
ft= (o.4lx|030M
4exp[5.16xlO%] ; -then -§;= (3^.
(.2.3.12)
Values of 3 are listed in Table 2.2 in rows (b). Experimentally, the
black body background will be averaged to zero by modulating the laser
beam and using phase sensitive detection.
If T = the time constant of
the detection system, the signal-to-noise ration S/N will be
-25-
%
=
f
f
e
*
.13)
•
Values of S/N are listed in Table 2.2 in rows (c) for T = 1 sec
and n^ = 5 x 10
10
-3
cm . A particularly attractive combination of
lines that emerges from this analysis is to excite 3
5 -*• 1.
The photon mean free path of the 3
enough for plasma densities up to ~10
11
5 and observe
5 transition is long
-3
cm , and the wavelength
falls near the peak power for the easily used dye Rhodamine 6G.
The emitted photon is relatively "hard," and scattered laser light
is not a problem as one is observing at a frequency different from
the laser frequency.
For the fluoresced laser light, we have estimated signal to
4
noise ratios >10
for a 1 sec time constant. This is more than
adequate for precision density measurements and for spectroscopic
analysis.
From the point of view of measuring plasma ion density,
greater signal to noise ratios could be obtained by using a pulsed
tunable dye laser and gating the photo detection system on just
to observe the fluorescence.
to noise using a cw laser.
There is, however, sufficient signal
A cw detection system also lends itself
to further diagnostics, such as analysis of fluctuations, waves, etc.
-26-
2.4
Resonant Microwave Frequency Shift due to the Ponderomotive Force
Assuming suitable boundary conditions, a plasma confined by a micro­
wave cavity will have a uniform density if the fields in the cavity are
low.
As the field intensity is increased, the plasma density will become
non-uniform due to the effects of the ponderomotive force and the microwave resonant frequencies of the cavity will shift.
H. Motz19-20 has
made a self-consistent numerical calculation of the plasma configuration
and resonant frequencies for a plasma in the TM011 mode of a cylindrical
cavity.
In this work the algorithm for the numerical calculation is
similar to that of H. Motz, but has been adapted for the TM010 mode.
Since the resonant frequency of TM010 mode does not depend on the cavity
length, by using this mode the number of mesh points can be reduced
to save computing time and computer memory space.
However, the calcula­
tion is set up in such a way that modes depending on the axial coordinate
can be included at a later time if desired.
The quasi-potential energy ip of the electrons in a R-F field is
given by
(2.4.1)
)
-27-
2
where E is the time average of the electric field squared and other
quantities have their usual meaning.
The electron density is given by
Xt— 2-
e £
~
<y\j 0, 4-OTtto 4 b T
(2.4.2)
For the TM010 mode all the electric field components can be obtained
from the azimuthal components of,magnetic field strength Hq . This is
easily seen from the Maxwell's equations,
V x E =
~~Ao
(2.4.3)
and
v * H
=
e
#
-
_
(2.4.4)
—
6 = e (f)= & K = e .(i
-
.
For this mode ^ = 0, and Hz = 0.
39
Assuming the time dependence elWt, eq. (2.4.3) gives
(2.4.5)
lia :
-
,
dZ
&r
1
< *( r£e)
r
ar
am i
(2.4.6)
~ q
‘
(2-4-7)
-26-
As Eg = 0 on all metal boundaries, from Eq. (2.4.7) it vanishes everywhere.
From Eq. (2.4.4) ,
^ ^
—
K^o-kCOEr
y
3b7ld
(2.4.8)
(2.4.9)
By substituting Eq. (2.4.8) and Eq. (2.4.9) into Eq. (2.4.6), and
defining <J> = (rHg), one gets
Eq. (2.4.10) plus appropriate boundary conditions defines an eigenvalue
problem.
The eigenvalues yield the resonant frequencies of the cavity,
and the eigen solutions the cavity fields.
Eq. (2.4.10) is solved on a computer.
The partial derivatives
in Eq. (2.4.10) are replaced by the following central finite difference
where Ax is the mesh length.
Eq. (2.4.10) now becomes
%
,5
.
(2.4.13)
where
i_
,
IUi/1 “
.
*
K;,i
.
[_
__
~ KU
1//1 — __L
•\
A
-
-
3 Ki-i
&Z
2 K<■/)
1
C2-
Ap
j
2171a
Cb
;
(2.4.14)
(2.4.15)
A*
■
a r ’ 2 K« j .>
>
(2.4.16)
C2.4.17)
(2.4.18)
<>
;
K t/j
>
9 Km
2 K&
0 = J L = JL
Ji
2
2 fry.
Ki,j
K U
ci
dr
ajf-Kw
—
=
9 K u
a ^ jK ij
vn
__L
IU i' i " Ki,j
K4i'i “
,
•
-30-
The mesh length In both directions, AZ and Ar, Is taken as a.
For
8Ki 1
notatlonal simplicity, the quantity — r— ^ has not been written out in
difference form.
X. . in the above equations is the quantity at a
j
point located at Z = ia and r = ja, and the center of the cavity is
located at Z = i = o and r = j = 0.
The mesh plane is taken as a cross
section of the cavity containing the cavity axis.
points is 12 in each direction.
The number of mesh
Boundary conditions for the TM010
mode are
1
<f>
2
d>.■ = d>, . , ., or d> is independent of Z, and
i,j
i + l,j
3
The
ljU
= 0 or <f> = 0 on the Z-axis,
derivative of cf> normal to the metal boundary is zero, or
the tangential component of the electric field at the boundary vanishes.
With the above boundary conditions Eq. (2.4.13) can be written as the
matrix equation
0
)
(2.4.19)
where f is a column vector with 121 components (the values of <j> at the
121 mesh points) and A is a 121 x 121 matrix, of which the elements are
given by Eqs. (2.4.14 - 18).
Eq. (2.4.19) be f
and
Let the eigenvectors and eigenvalues of
By definition
0
-31-
(2.4.20)
An arbitrary trial vector g(0) with 121 components can be written
in the form
—
-p
*
^ (0 ) = biji
+
*T
W fa + • • * • •
where the b's are numerical coefficients.
+ bn'JVn
,
(2.4.21)
If the matrix A is non
singular, Eq. (2.4.19) can be written in the fern*
j
+
r
XA
\^
^
j
=
0
,
(2.4.22)
-1
where A
is the inverse of A.
The result of operating with A
-I 71-*
times on g(0) will be denoted by g(n), or
§ M = L A 3
-1
n
. (2.4.23)
From Eqs. (2.4.20), (2.4.21), and (2.4.23),
If n is large and A^ is taken to be the smallest eigenvalue, all terms
-V
except the first term can be neglected.
->■
Then f^ « g(n), and the eigen­
value A^ is obtained from
ft(0Wl) "* A ftfa) -
Al
co2 a2
This "inner" iteration gives A^ = ---^—
-32-
•
» where co^ is the lowest
(2.4.25)
eigenfrequency of the plasma filled cavity, and f^, whose components are
the values of c|> at the mesh points.
The "outer" iteration consists of
using these values of A^ and (j) to calculate new values of E, n^, K, and
the elements of the matrix A.
In each outer iteration, the total number
of plasma electrons,
N = f f [ n , e 4'n’“'^ T ,27ir]cJrdZ = J | parciz
(2.4.26)
is evaluated, and n^ is adjusted to keep N constant from iteration to
iteration.
The integral is evaluated numerically by dividing r - z space
into blocks, each block consisting of four a x a squares as shown below.
<»------------6>--------- -—
y<\
4t>
/\
4k
A
%
M
...
..
The integral over each block is then 4a
factors
©
21
are shown in the diagram
E wij^ij* w^ere t^ie weighting
The complete integral is obtained
by summing these results for all the blocks.
The electric field intensity
is normalized to the input microwave power using the relation
q)W
Qwl-
P
(2.4.27)
-33-
where the field energy stored in the cavity is ]/\J
P is the net power delivered into the cavity and
Sec. 4.3.
JfeKE^TTr<tr4z ,
is defined in
2
As in the expression for the ponderomotive force, E is a
time average of the electric field squared.
The integral for W is
evaluated numerically in the same way as the integral for N.
The computer program has been checked in a number of ways.
First,
the effect of the mesh size on the two dimensional computer program
was investigated by calculating the lowest resonant frequency of the
empty cavity and comparing it with the analytic value of 9.036 GHz.
Table 2.3 shows the error as the number of mesh points is increased from
9x9=81 to 16x16=256.
For this last value, the error is 30 MHz.
Table
2.3 also shows the c.p.u. time necessary for each number of mesh points.
As expected,.the cpu time increases sharply as the number of mesh points
increases.
An error of less than 1 MHz has been obtained by changing
to a one dimensional program and dividing the radius of the cavity into
60 segments.
This technique was used to obtain the curve in Fig. (2.5)
which shows the frequency of the lowest mode, the TM010 mode, as a
function of microwave power.
density of 8.4x10
10
A temperature of 2,073° K and a plasma
-3
cm
were assumed.
For powers < 0.5 W, the computer
generated resonant frequency, and the resonant frequency calculated
analytically assuming uniform plasma density, agree to within 1 MHz.
There is no analytic theory for higher power where the plasma density
becomes non-uniform.
However, it is to be expected that as the power
is increased and the plasma is pushed out of the regions where there is
-34-
TABLE 2.3
// of mesh points
size of matrix A
Error (MHz)
cpu time
106 MHz
15.7 sec,
9x9 =
81
64x64
10x10
= 100
81x81
84
30
11x11
= 121
100x100
68
55.7
12x12
= 144
121x121
56
97.7
13x13 = 169
16x16 = 256
‘
144x144
47
163.7
225x225
30
586
-35-
electric field, the resonant frequency should tend toward the empty
cavity value.
This is born out by the curve, which approached to
within 3 MHz of the exact empty cavity value at a power of 800 W.
For a plasma temperature of 2,073° K, Figs (2.6) and (2.7)
show the radial dependence of the plasma density at various power
levels for plasma densities of 5.4x10
tively.
10
-3
11
-3
cm
and 1x10
cm
respec­
An interesting feature of both Figs. is that all the curves
cross at the same point.
This fact may be due to a peculiarity of
the TM010 mode; the electric field is everywhere perpendicular to the
gradients in the electric field and the gradients in the plasma density.
This results in an electric field configuration that is independent
of the microwave power.
This is verified by the computer calculation.
Fig. 2.8 shows the electric field vs. cavity radius for a number
of microwave powers as calculated by the computer program.
If the
curves are normalized at one radius, they fall on top of each other.
This is a further check on the computer program.
-36-
O — r—S--0OXVj—
— 11—
-11-—
- P r
BZEGtZS;
.r~. r
jjzii+iq!
::r^L
W::Ph:
ca-~.f.
W
O!
-o -M
r«fl— E*i
AX-iW
PA
IDS K
;asb
(z h d )AONanbaaa iMVwosaa
Fig. 2.5
-37-
MICROWAVE POWER(W)
r— i
-gSr
TT..
•!: :
.t
...t— ~
T F F T
1
t :i:
r r
c
±_[
: • j.. i;. j
I:
i • r.. i
5 £ j | - T “r - r a ~
I:
. l:.
. ..t
i
:i •
- !'•
• •
: I.
i
■■I
—r
l i••
!• ill
i-!
...
m r
" m
.r;-
__Li.
• I Ju.
■; f " i " !' •
i.
.!
I
r?rv?! ■ i-
LilILii
.
..r:
rti-
P
: ! .i': i i' v■ ; "!'
i ..........
i
*
! :>_ Li
!_ K j _ - . -j: i- I’, y - ' j - / . i
i
••• ?
•
-l
I :-i : : J_: L_iL_i : 1
•i; •
! .!
I:
——
K--—
ri
f - : —; ~7
f*m ”?3 .
©Q = 516
,©
8-.o:w-:
2.0 v/
o.'pyiT'r": ,
S_5o.
w l
(?rr
c
:j-r H " j :' j ;- p i ! / 6 ! : j 2 R /6 , ■i: 3R /6 v p R / 6 1 ' | ^R/6 : '::j ^R /6 r ' j ' ; >
_ l_. i.
T iiZ . j l ’L iL .I ..1 .1 .:!... j.PiSTANCS FRQMl CAVITY AXIS : •]; 1 .1 L i . : ..!.. .j. !.. ■ . i .I
!
11 1
Fig. 2.6
-38-
i
n ' VS. RADIAL DISTANCE
,Q=i.poo ;
•n-= 1x10-1•CM'
.
11-0
20.00 IV
o
8.00 V/
2.00 W
0.05 V/
J
H
9.0
8.0
1R/6
!
2R/6
3R/6
4R/6
5E/6 ;6R/6
DISTANCE FRO!I CAVITY AXIS ...
Fig. 2.7
-39-
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ELECTRIC FIELD INTENSITY (VOLTS/CM) .
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2.5
Undriven Low Frequency Oscillations
The nature of the undriven low frequency (10 ~ 100 KHz) oscillations
in the cavity is not understood at this time.
In this section, a few
possibilities are considered and brief outlines of the theories involved
are given.
The frequencies observed are in the region of ion acoustic oscil­
lations', and there is the possibility that the oscillations are normal
mode ion acoustic oscillations in the cavity.
For infinite plane ion
22
acoustic waves, the dispersion relation obtained from fluid theory, is
(2.5.1)
where 0), k, k^, ra^, Te, and T^ are the wave frequency, wave number,
Boltzmann constant, electron temperature, and ion temperature respectively.
It is assumed that the electrons are isothermal, and that the ion com­
pression is adiabatic.
The principal objection to assuming that the
oscillations are ion acoustic is that at least for infinite plane
running waves, a more detailed theory utilizing the particle distribution
functions shows these waves to be heavily attenuated by Landau damping
when Tg < 1\.
On the experimental side, the observed oscillations often
have Q's of 100 or more, far above that
damping
23
to be expected with Landau
when T^ = T^.
At the time of the observations, the theory for
Landau damping had only
been worked out for running plane waves, not for
standing waves, and not
for normal mode oscillations in a cavity.
-VI-
It
was conceivable that for these situations Landau damping was reduced.
The problem of Landau damping of ion acoustic waves in bounded geometry
was discussed with I. Bernstein and R. Jensen of Yale University, who
solved the problem
24
for cue dimensional geometry, that is, a plasma
confined by 2 parallel and infinite plates.
The one dimensional Vlasov
Eq. was used for the ions and the perturbed electron density was
(no
6(D
» where <}> is the electric potential.
Two boundary conditions
■■
*B
were investigated.
In one, the ions were absorbed by the wall and re­
emitted with a thermal distribution, and in the other, the ions were
reflected from the wall.
In the latter case, they found that the damping
rates were comparable to that of the unbounded problem.
For the absorbed
boundary condition, they found that the damping was even greater.
Bernstein and Jensen feel the results are suggestive enough to pretty
much rule out the possibility that in two and three dimensional geometries
normal mode ion acoustic oscillations might have reduced damping.
find the mathematics of these higher geometries intractable.
They
On the other
hand, in finite cylindrical geometry the field lines will be curved
while the particles will travel in fairly straight lines.
It is conceiv­
able that the particles will not stay with the field lines long enough
to experience the very high damping rate associated with plane geometry.
It has been mentioned that a very low magnetic field (~ few Gauss)
can significantly affect these oscillations.
With such fields, the ions
would be unmagnetized, but the electrons would be partially magnetized,
or fully magnetized if the field strength was increased to ~10 G.
-42-
There
are a large number of waves and instabilities associated with magnetized
plasmas in which gradients in density, temperature, and magnetic field
exist.
For example, Kadomtsev
25
discusses drift waves associated
with a homogeneous magnetic field, but a gradient in plasma density.
Such waves might exist in the region near the coupling slits where
density gradients occur.
An effort was made to fit the dispersion
relationships for some of these waves to the data using parameters of
the experiment, but no really convincing comparison could be made.
Further possibilities need to be explored.
Eichenbaum and Hernqvist
26
examined theoretically a collisionless
plasma formed between two parallel plates, both of which were emitting
electrons and ions in Maxwellian distributions.
If the charged particles
were injected at a rate such as to give overall charge neutrality, the
resulting state was found to be unstable.
Both positive and negative
potential states were found, and both these were found to be stable.
In an accompanying experiment, under some conditions they observed
oscillations associated with transitions between these two states.
The frequency they observed, 500 kHz, is much higher than the undriven
low frequency oscillations seen in the present experiment (5100 kHz).
2.6
Driven Low Frequency Oscillations
When the microwave frequency f
is tuned to a cavity resonance, and
the microwave power is increased, two additional microwave frequencies
f
± Af are observed arranged symmetrically about the original frequency.
~k3-
If the reflected or transmitted microwaves are detected and the resulting
signal fed into a low frequency spectrum analyzer, the frequency Af is
seen as a very strong component of the spectrum analyzer output.
Furthermore, at more microwave power, there may be additional micro­
wave frequencies generated and additional low frequencies observed with
the low frequency spectrum analyzer.
Unlike the undriven low frequency
oscillations, these observations have a definite threshold with micro­
wave power.
The most probable explanation of this phenomenon is that
the microwaves generate the additional frequencies by a parametric
process.
For infinite plane waves of various kinds, parametric instabilities
27
have been extensively studied
. An electron plasma wave can decay
into another electron plasma wave and an ion acoustic wave, and an
electromagnetic wave can decay into an electron plasma wave and an ion
acoustic wave.
In addition, an electromagnetic wave can decay into
another electromagnetic wave and an ion acoustic wave.
It is this
last possibility that would appear to be what is occuring in the exper­
iment.
For the infinite plane wave case, this instability has been the
subject of a number of theoretical and experimental efforts, especially
near the electron plasma frequency where the threshold is lowest.
Time
has not permitted an exhaustive literature search, but at the moment no
theoretical analysis of this instability is known for the case of a
bounded plasma.
-M+-
3.
3.1
APPARATUS
General Description of the Apparatus
An existing two part stainless steel cylindrical vacuum system
including two I beams and a concrete base were used in the new
apparatus which is shown in Figs. 1.1 and 1.2.
The vacuum chamber
rests on two parallel I beams, each 2.13 m long and separated by 0.84 m.
The I beams are supported by a one-piece concrete base.
The vacuum
chamber was previously located in the middle of the I beams.
To have
a convenient mounting structure for the laser, the vacuum chamber was
moved to one end of the I beam platform.
between the I beams.
The forepump sat on the floor
To reduce vibration to the laser, and reduce the
possibility of the forepump exhaust contaminating the optics with oil,
the forepump was moved to a corner of the room near a wall vacuum outlet,
and the exhaust of the forepump was hooked to this outlet.
isolation from the forepump now appears adequate.
Vibration
As shown in Fig. 1.2,
the laser beam enters the vacuum chamber horizontally, and is reflected
upward by a mirror.
channel.
Both pump laser and dye laser rest on a single
To support this channel, a laser support I beam was bolted
beneath and between the two I beams supporting the vacuum chamber.
The channel itself is supported by a cross piece and an "optics plate,"
both resting on the laser support I beam.
The optics plate provides a
table-like space to insert optical components such as a beam expander, and
also a chopper, into the dye laser beam.
-*f5-
3.2
Details of New Apparatus
3.2.1
Vacuum Chamber Main Cover Flange
The layout of the new main cover flange for the vacuum chamber is
shown in Fig. 3.1.
This flange supports the water cooled flanges for
the heating element, and contains a number of electrical feed throughs,
two microwave waveguide windows, a laser beam window, a mechanically
operated laser beam flag, and Quick Couplers for water lines.
The circu­
lar 304 stainless steel flange is 2.54 cm thick and 60.01 cm in diam.
Two symmetrically positioned 2.070 cm radius holes separated by 20.07 cm
are made for the 4.128 cm diam pipes supporting the heating element
assembly (see Sec. 3.2.2).
These two pipes are vacuum sealed by two
Quick Coupler type annular flanges with 9.144 cm o.d. and 4.140 cm i.d.
One of the inside edges of these flanges is chamfered to accomodate an
0-ring.
The water cooled flanges are held in place vertically by
attaching to the pipes split bushing type clamps which are supported by
10.16 cm long screws resting on the top of the main cover flange.
The
split bushing clamps are made of 2.54 cm thick and 12.70 cm square brass
blocks, which are also used as junction blocks for the electrical cables
from the heating element power supply.
A 6.223 cm radius hole is made
at the center of the main cover flange for the waveguide flange (see
Sec. 3.2.4).
A pair of 5.029 cm radius holes separated by 30.48 cm and
a pair of 3.713 cm radius separated by 40.03 cm are made in diametric
positions respectively.
One of the 3.713 cm radius holes and one of the
5.029 cm radius holes are used for the electrical feedthrough for the
heaters of the plasma material oven, the thermocouples, etc.
-
46 -
The other
3.7/3 Oftl
Fig. 3.1
-47\
3.713 cm radius hole is used for the Cu tubing from the Cu heat shield.
Eight pin ceramic insulated feedthroughs are soft soldered into holes
made on the flanges.
All of the small flanges on the main cover flange
are made of 9.525 mm thick 304 stainless steel and are vacuum sealed
with standard 0-rings.
The main cover flange with the water cooled flanges, plasma chamber,
and heat shields attached, can be lifted as a unit out of the vacuum
chamber after the vacuum chamber has been taken off the concrete base
and put on the floor.
For this operation, the cover flange and/or
vacuum chamber is attached to a ceiling chain hoist by two diametrically
positioned 1.27 cm diam threaded rods and a yoke.
3.2.2
Heating Element Flange Assembly
The heating element flange assembly holds the inner and outer
cylinders of the plasma heating element and supplies electric power
to this element in a way that minimizes magnetic fields from the
heating current.
The flange assembly consists of two water cooled
28.96 cm diam annuluses made of 304 stainless steel.
Cooling
water and electric current for the heating element are supplied through
a pair of 4.216 cm o.d. and 2.134 cm i.d. pipe assemblies on the
upper flange and a pair of 9.525 mm o.d. pipes on the lower flange.
Fig. 3.2 shows the assembled flanges and Fig. 3.3 shows the top ends of
the pipe assembly, the vacuum seal, and the water line connections.
The upper and lower flanges are electrically insulated from each other
using 7.630 mm diam and 3.810 mm long alumina insulators in the clearance
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ASSEMBLY
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IN S U L A T O R
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screw holes on the lower flange.
The inner and outer heating element
cylinders are attached to the bottom side of the upper flange and the
top side of the lower flange respectively using 304 stainless steel
annuluses and eight 10-32 screws on each flange.
Eight 10-32 screw holes
on the top side of the upper flange are made to mount the oven flange
(.see Sec. 3.2.3).
The flange assembly is supported by screws resting
on the main cover flange as described in Sec. 3.2.1.
"Watlube," a heat
release and transfer agent (manufactured by Watlow Electric, 12001
Lackland Rd., St. Louis, Mo.) is used on all screws used in the assembly
to prevent the screw threads from seizing due to the heat radiation.
All
of the screw holes on the flanges are clearance holes to prevent air from
being trapped in the holes.
Each of the two flanges described above is
hollow to allow for water cooling.
The flanges are machined in two
pieces, and then tungsten inert gas (TIG) welded together.
The lower
flange, adjacent to the heating element, is subject to the radiation from
the heating element and leaked after a while, as have earlier lower
flanges.
This problem seems to have been solved by having the TIG welds
reworked by a particularly gifted welder, Mr. Ralph Gardner, of Nevis
Laboratory, Dobbs Ferry, N.Y.
3.2.3
Oven Flange
The circular oven flange is shown in Fig. 3.4.
It is 14.22 cm in
diam, 9.525 mm thick, and is mounted on the upper heating element flange.
The oven flange supports the plasma material oven and serves as a connec­
tion between the two flexible waveguides and the two refractory waveguides
-51-
0.635
0.952
cm diam Holes
For
C u Tubing.
cm d iam hole
For Bla3ma Material
Feed T u b e N .
/
Holes vor Microwave
\ '
C e r a m i c Rods/
For Oven
i
0.317 cm/diam Hole
F o r L a s e r ,Beam
14.22 cm.
F ig.
3 .k
OVEN
-52-
FLANGE
(see Sec. 3.2.9) which support the plasma chamber.
The position of the
plasma chamber is adjusted for the alignment of the diagnostic holes by
adjusting the angle and position of the oven flange with respect to the
upper heating element flange.
The flange position is adjusted by means
of three spring and washer loaded screws.
The flange has a 0.317 cm
diam hole at the center for the laser beam, two 1.016 x 2.28 cm rectan­
gular holes for the waveguides and a 0.952 cm diam hole for the plasma
material feed tube.
A pair of 17.78 cm long Be-Cu alloy flexible wave­
guides (obtained from Microtech Inc., Cheshire, Conn.), are brazed into
the top side of the flange.
Also three 3.175 mm diam holes for the
alumina rods which support the plasma material oven are made.
Then
3.175 mm diam alumina rods are put tightly in the holes, sticking about
3.81 mm above the flange for thermal insulation.
facing the oven are sharpened.
The ends of the rods
The sharpened ends fit into alignment
grooves on the bottom of the oven.
3.2.4 Waveguide Flange and Waveguide Feedthroughs
In the design of the microwave system, the choice had to be made
between waveguide or coaxial microwave feed to the cavity.
Because of the
high temperatures at which the cavity is operated, only refractory metals
can be used, and it was thought easier to construct a waveguide system
entirely out of this material than a coaxial one.
With this decision in
hand, it was also decided to keep almost all the microwave system wave­
guide rather than coaxial.
Contributing to this latter decision was the
availability of many waveguide components from Prof. Leonard Yarmus of
-53-
N.Y.U.
The two standard x-band waveguides are fed into the vacuum system
through a 304 stainless steel circular flange which is 16.51 cm in diam
and 9.525 mm thick.
is shown in Fig. 3.6.
This is shown in Fig. 3.5.
The waveguide feedthrough
The flange is mounted in the center of the main
vacuum chamber cover flange.
The waveguides are inserted into 4.127 cm
diam stainless steel tubes, and the tubes and waveguides are sealed
together at one end by an insert brazed to both.
The two tubes with the
waveguides inside are passed through two Quick Couplers diametrically
mounted on the waveguide flange.
7.62 cm.
The Quick Couplers are separated by
The insides of the two waveguides are vacuum sealed above the
Quick Couplers by three iris resonance type glass to kovar waveguide win­
dows (supplied by Microwave Associates, Burlington, Mass.).
The above
design enables the oven flange, with the two pieces of flexible waveguide
brazed to it on the top and the plasma chamber suspended underneath, to be
detached from the waveguide flange and the rest of the apparatus.
This
feature is almost a necessity due to the complexities of mounting the
refractory metal waveguides, plasma chamber, and heat shields underneath
the oven flange.
As shown in Fig. 3.5, the waveguide flange also has a hole in the
center for the laser beam, two holes for Cu tubing, and a hole for a rod
that actuates a laser beam flag.
3.2.5
Heating Element Assembly
The heating element and heat shields are shown in Fig. 1.1.
Two
coaxial cylinders made out of refractory metal foil are used as a resistive
heating element to maintain the plasma chamber temperature,
-54-
The first
Beam
0.^53.Oyy^
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Quick Coupler Holes
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Fig. 3.5 WAVEGUIDE FLANGE
-55-
Waveguides
Waveguide Windows
•.Quick Couplers
Waveguide
Flange
It,12? cm diam
Stainless Stes
Tubes
Fig. 3.6 WAVEGUIDE FEEDTHROUGH
-
56-
1
heating element was made of 25. A y Ta foil.
The diameters of the cylinders
were larger than they are now since the heating element was then being
considered for both s-barid and x-band cavities.
Diam of the inner cylinder
was 11.A3 cm and that of the outer cylinder 12.70 cm.
After repeated
uses, the round Ta cylinders tended to deform into cylindrical polygons.
This occasionally produced a short circuit.
It was found that heating
elements made from 25.A y W foil were much more stable in their shape and
this material is now used exclusively.
It was also decided to reduce the
size of the heating element so that only x-band cavities could be accomo­
dated.
The inner and outer cylinders were reduced to diamters of 6.985 cm
and 9.208 cm respectively.
Two 0.51 mm thick annular Ta adaptors were
made for the smaller diam heating element.
The dimensions of the adaptor for the inner heating element cylinder
are 8.255 cm i.d. and 11.51 cm o.d., and those for the outer heating
element cylinder 9.525 cm i.d. and 13.3A cm o.d.
36.20 cm lpng and the outer 3A.A8 long.
The inner cylinder is
At the bottom the two cylinders
are split into tabs approximately A.76 mm wide.
The tabs of both cylin­
ders are bent outward and spot welded onto a 50.8 y thick and 9.8A3 cm o.d.
Ta annulus, forming a closed resistive circuit.
annulus as Ta-W
W-W spot welding.
Ta is chosen for this
spot welding is easier and makes stronger welds than
Usually the upper parts of the cylinders deteriorated
before the lower parts.
This was probably due to the large temperature
gradients in the upper part which are close to the water cooled flanges.
To reinforce the upper parts a 5.08 cm wide and 50.8 y thick Ta strap
-57-
Is spot welded onto the top end of each cylinder and 1.87 mm tabs are made
from the Ta strap.
The use of 50.8 ]i Ta straps for the tabs and reinforce­
ment made welding between the cylinder and the adaptors easy and strong,
resulting in longer life time of the heating element.
Both the inner and
outer heating cylinders have one 1.270 cm diam hole at bottom for the
laser beam, three 9.525 mm diam side holes for the fluorescent signal
detection, and two 9.525 mm side holes for the hot wire detector and the
optical pyrometer observations.
To cut the W foil with scissors, the
scissors are heated up with a Bunsen burner before cutting.
This prevents
cracks forming along the cutting lines.
To make the holes in the foil, the
foil
Several sharp drill bits are used
is clamped between two Al plates.
in order of increasing size until the desired hole size is obtained.
If
the foil is broken around the hole either the plates are not clamped
hard enough or the drill bits are not sharp enough.
For spot welding the
seams of the W cylinders, a 12.7 y thick Ta strap is used between the W
foil.
The use of special W alloy electrodes (Hughes, EH-125, and EL-125)
greatly facilitates the welding of the W foil.
is spot welded to the adaptor using the Ta tabs.
The outer heating element
Then two dylindrical Ta
heat shields with diameters of 10.16 and 11.43 cm are spot welded onto the
same adaptor.
These two concentric heat shields form the first and second
heat shields of the seven total coaxial heat shields for the heating ele­
ment Csee Sec. 3.2.6).
Fig. 1.1 shows the heating element assembly
including the two inner heat shields and the adaptors.
assembly, including the two inner heat shields,
-58-
The heating element
is installed on the
upper and lower flanges by clamping the adaptors on the flanges using an
annulus and eight 10-32 screws on each flange.
3.2.6
Tantalum Heat Shields
The heat shield assembly, shown in Fig. 1.1, provides five additional
cylindrical heat shields that are coaxial with the plasma chamber.
The
shields are fabricated out of 25.A y Ta foil, have diameters of 15.24,
17.78, 20.32, 22.35 , and 24.13 cm, and holes that line up with the
diagnostic holes in the heating element and plasma cavity.
most shield has a height of 45.085 cm.
The outer­
These heat shields are covered
at the bottom, and are spot welded to a Ta support at the top.
This
support is attached to the bottom side of the lower water cooled flange
by eight 10-32 screws on a 24.89 cm diam bolt circle.
To make the support a 12.70 cm diam hole is made in a 15.24 x 15.24 x
0.051 cm Ta plate and eight 1.905 cm wide and 0.51 mm thick tantalum
straps are spot welded onto the plate to extend the dimension of the
plate to the screw holes on the bottom side of the lower water cooled
flange.
Stainless steel screws had originally been used to connect
the straps to the Ta plate.
After the apparatus had been cycled to
operating temperature a few times, it was found that the screw material
vaporized and the Ta heat shields and support deteriorated where the screw
material was deposited.
An attempt was made to spot weld the straps to
the plate using the same spot welder used for the foils, but this was
unsuccessful.
A heavy duty spot welder, in the machine shop satisfactorily
joined the 0.51 mm straps to the 0.51 mm plate.
-59-
Recently a large piece
of 0.51 mm thick Ta plate has been acquired which will be fabricated
into a one piece annular support for the heat shields.
3.2.7
Water-Cooled Cu Heat Shield
In order to keep the vacuum chamber wall cool a water-cooled Cu
heat shield is made in addition to the Ta foil heat shield assembly.
This heat shield sits on the vacuum chamber middle flange which separates
the top and bottom vacuum chamber cylinders.
Dimensions of the cylin­
drical heat shield are 38.10 cm in diam, 48.26 cm in length and 3.17 mm
in thickness.
The shield has twelve 3.493 cm diam holes and four 9.208
cm diam holes positioned in accordance with the locations of the obser­
vation ports on the upper vacuum chamber cylinder.
by 6.35 mm o.d. Cu tubing which carries water.
The shield is cooled
The tubing runs up and
down the shield 16 times and is soldered to the shield.
Fig. 3.7
shows the layout of the Cu plate before being formed into the cylindrical
heat shield.
High temperature, high strength and low- vapor pressure
solder (Eutectic //157 silver alloy) was used for soldering the tubing
onto the cylinder.
The two Cu tubes for the input and output cooling
water are fed into the vacuum system using two Quick Couplers brazed to
the flange covering one of the 3.713 cm radius holes on the vacuum
chamber main cover flange (see Sec. 3.2.1).
3.2.8
Microwave Cavity
The microwave cavity in which the plasma is confined and the two
supporting waveguides are shown in Fig. 3.8.
The dimensions of the
cavity when cold are 2.54 cm in diam and 8.052 cm long.
-
60-
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Fig. 3.8 MICROWAVE CAVITY
-62-
ratio is chosen to get the maximum separation of the TM012 mode from
other adjacent modes in the x-band frequency range.
The cavity walls are made out of 50.8 y Ta foil plated with Re to
increase the ionization probability.
Before 50.8 y W foil was used to
fabricate the cavity, 25.4 y Ta foil and 25.4 y W foil were tried.
It
was found that the Re plated 25.4 y Ta foil was deformed considerably
after being used several times.
W foil became excessively brittle and
fragile after being heated up to operating temperature and was often
damaged when the system was disturbed.
These two problems, deformation
and brittleness, are negligible with the 50.8 y Ta foil.
After the foil is cut into a rectangular form, tabs about 2.4 mm
wide and 1.9 mm long are cut on the top and bottom sides of the foil,
and five 0.7938 mm diam holes for the diagnostics are made.
Then the
foil is Re plated (see Sec. 3.2.17) and spot welded into a cyliner
using a 2.54 cm diam mandril.
After the cylinder is formed a hole
approximately 0.51 mm in diam is made diametric to one of the existing
0.7938 mm holes using a hole on the cavity mandril.
This hole is made
after the cylinder is formed to insure that it is diametric to an
existing hole.
The 0.51 mm hole is used for the alignment of the optical
detection system.
A 50.8 y thick and 3.175 cm diam Ta disc with a 3.175
mm diam hole at the center is spot welded to the tabs at the bottom of the
cylinder.
It has been found easier to first spot weld the top of the
cavity, or coupling plate, to the refractory metal waveguides (see Sec.
3.2.9) before spot welding it to the cavity.
The coupling plate shown
in Fig. 3.9 is made of 0.51 nun thick and 4.445 cm diam Ta plated with Re.
-
63-
0-0508 x 1.113 CM SLITS
FOR MICROWAVE COUPLING
1.930 CM
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FOR LASER BEAM' AND PLASMA
MATERIAL FEEDTHROUGH
Pig*'3.9 CAVITY COUPLING PLATE
-b k -
Two 0.0508 x 1.143 cm microwave coupling slits and two 0.277 cm diam
circular holes for the outcomlng laser beam and the plasma material
feedthrough are made on the plate.
To reduce the number of particles
leaking into the waveguides two narrow slits rather than circular irises
are made.
The coupling slits are parallel to the long dimension of the
waveguides and serve as capacitive irises.
They are made where the
\
amplitude of the microwave magnetic field in the cavity is maximum
for TM01N modes.
H =
28
For these modes, the magnetic field H is given by
N u 7
-Hq
Jq *
(2.405 r/a) cos(—
), where
Jq '
is the derivative of the
Bessel function Jq , a = radius of cavity, and L = height of the cavity.
The first maximum of Jq ' gives the appropriate slit positions.
the coupling is designed
Although
for TM modes, TE modes are excited as well.
However, when the slits are made so long that they reach the cavity
side wall, all the TM modes disappear.
Since the coupling increases as the thickness of the coupling
aperture decreases
29
, the thickness of the slits
than 0.254 mm using a small grinding tool.
is reduced to less
When the cavity is cold
(.room temperature) some modes are almost critically coupled and others
are usually undercoupled.
3.2.9
Refractory Metal Waveguides
The waveguides are used to hold the microwave cavity in position
as well as to feed the microwaves into the cavity.
One of the wave­
guides is used for the transmitted waves and the other for the reflected
-
6.5-
waves.
As in fabrication of the cavity, a few different materials were
tried for the waveguides.
It is found that 50.8 y Ta foil reinforced
with 0.254 mm thick Ta ribbon is better than any other combination of
materials tried.
guides.
Fig. 3,10 shows the large dimension side of the wave­
They are 17.15 cm long, and fabricated by wrapping the foil
around a 1.016 x 2.286 cm rectangular mandril whose dimensions are
exactly the same as standard x-band waveguide.
Five 1.59 mm x 0.952 cm
slits are made on each waveguide to pump out the plasma.
The slits
are located in the center of the large dimension of the guide where the
waveguide wall current is zero.
slots on the waveguide mode.
This minimizes the perturbation of the
After the foil is spot welded into a
standard x-band waveguide five 0.635 cm wide and 0.254 mm thick Ta
ribbons are spot welded onto each of the waveguides.
Since the impedance
of a microwave waveguide depends sensitively on the geometry of the
waveguide, it is important to reinforce the foil waveguide with the
ribbons to prevent deformation due to the high temperature in the system.
After the waveguides are made the cavity coupling plate is spot welded
at the bottom side of the waveguides in such a way that the coupling
slits are parallel to the long dimension of the waveguides and each
slit is at the center of each waveguide.
It is also important that the
two waveguides have exactly the same length, be perpendicular to the
coupling plate and be spot welded at the right positions without being
forced, so that no mechanical tension is exerted on the coupling plate.
The mechanical tension on the coupling plate, in spite of its relatively
-66-
>1.59 Mia x .952 ca slits
17.15 cm
0.635 crn Ta ribbons
cn
Fig. 3.10 REFRACTORY METAL WAVEGUIDE
-67-
large thickness, makes the plate deform at high temperatures.
happened in the first cavity.
This
The microwave resonant frequencies
increased discontinuously by more than 100 MHz as the temperature
increased from 1500° C to 1700° C.
To make the waveguides perpendicular to the coupling plate, the
tabs on the waveguides are spot welded to the plate with mandrils in
the waveguides.
The ends of the mandrils are carefully squared off
at 90° and butted onto the coupling plate during the spot welding.
Then the waveguide heat shields are installed on the waveguides using
3.175 mm Ta straps (see Sec. 3.2.10).
The assembly including the
waveguides, cavity and heatshields is attached to the center of the
bottom side of the oven flange using a waveguide support which is shown
in Fig. 3.11.
The waveguide support is made of a 3.302 x 4.064 cm
and 0.51 mm thick rectangular Ta plate.
This plate has two rectangular
1.066 x 2.336 cm holes separated by 1.930 cm which accomodate the two
waveguides.
A circular 4.763 mm diam hole allows the laser beam to
pass through.
3.2.10
Waveguide Heat Shields
Fig. 1.1 shows the cavity, waveguide, heat shields, and oven flange
The oven flange has to be kept at low temperature since the flexible
waveguides are brazed into this flange using silver alloy brazing
material.
support.
Stainless steel screws are used for the refractory waveguide
Four 5.08 cm disk type heat shields are used to reduce the
heat radiation to this flange.
The disks are made out of 25.4 y Ta
foil reinforced with 127 y x 3.175 mm circular Ta rings along the cir-
■'4.064 CM
0.476 CM DIAM
LASER .H O LE
3.302 CM
PLASMA MATERIAL
1.066 * 2.336 CM
FEEDTHROUGH HOLE
WAVEGUIDE HOLE
KLg. -3.11
W AVEGUIDE. SUPPORT
-69-
cumferences.
The 5.08 cm diam rings are spot welded to the Ta disks
using 3.175 x 3.175 mm tabs made along the circumferences of the disks.
Each disk has two approximately 1.270 x 2.54 cm rectangular holes
separated by 1.930 cm for the waveguides, a 4.763 mm diam hole at the
center for the probe or the laser beam, and a 4.763 mm diam hole about
1.270 cm away from the center for the plasma material feedthrough.
The four disks are assembled together by spot welding 50.8 y 3.175 mm
Ta straps on the edge of each disk.
The end of each strap is spot-
welded on the top side of the waveguide support after the disk heat
shields are installed on the waveguides.
The gap between the shields
is about 1.275 cm and the top shield is approximately 6.35 cm below
the oven flange.
The heat shields have to be installed on the wave­
guides carefully so that they do not deform the waveguide structure
at high temperatures.
3.2.11
Plasma Material Feed Tube
A thin tube is used to transport the plasma material from the oven
flange to the microwave cavity in which the material is ionized.
The
19.05 cm long feed tube is made of 1.270 cm wide and 25.4 y thick Ta
foil.
To make the tube the strap is wound in a spiral on a 3.175 mm
diam rod and the rod is removed after the strap is spot welded to form
the tube.
The feed tube is not spot welded directly to the cavity
coupling plate as some initial flexibility is needed between the tube
and the plate so that the tube does "not deform the plate when the
cavity is first heated.
The tube is inserted into a cylindrical sleeve spot welded to the
-70-
coupling plate.
The 9.525 mm long sleeve is made of 25.4 y Ta foil
and is spot welded around a hole on the plate using tabs about 6.4
mm long.
The i.d. of the sleeve is made as nearly as possible the same
as the o.d. of the feed tube so there is a slight friction fit between
them.
After several temperature cycles, the tube and sleeve are
welded together.
The top end of the feed tube sticks out about
1.6 cm above the oven flange and loosely fits into the oven nozzle.
This fit allows for expansion when the cavity is heated.
The tube is
shown in Fig. 3.8.
3.2.12
Wire Probes
Originally, the microwaves and laser beam were the only two
diagnostics for the plasma in the cavity.
More recently, a two wire
diagnostic probe has been added using holes made for the laser beam.
The present probe system, which is shown in Fig. 3.8 cannot be used
simultaneously with the laser beam.
Due to the high temperatures at
which the probe must function, and uncertainties in the high tempera­
ture properties of various insulators, some experimentation was
necessary before a working probe was produced.
to be satisfactory.
The present probe seems
The two wire probe consists of 0.38 mm Ta wires
held in place by a cylindrical double bore insulator which is 22.86 cm
long, has 3.175 mm diam, and two 1.016 mm diam bore holes.
The in­
sulator material chosen was Omegatite 450, which according to the
manufacturer (Omega Engineering Corp., Stamford, -Conn.) has a maximum
service temperature of 19.50° C.
The insulator is held between the
-71-
refractory waveguides by 5 supports of 127 y Ta straps, and is
clamped to a 6.35 mm diam Cu rod attached to a split bushing clamp
on one of the 4.128 cm diam water cooling pipes on the upper flange.
The bottom end of the insulator is held approximately 6.35 mm above
the cavity coupling plate.
The bottom ends of the probe wires are
fed into the plasma chamber using the 2.778 mm diam hole for the
laser beam at the center of the coupling plate, and the top ends are
attached mechanically to the beam flag on the waveguide flange and
then connected to a pair of electrical feedthroughs on the main cover
flange.
Since the wires are flexible enough, by changing the beam
flag position, the penetration depth of the probe wires into the plasma
chamber can be changed or the probe completely removed from the plasma
chamber without breaking the vacuum.
The electrical resistance and
mechanical strength of the insulator decreases significantly as the
temperature increases.
In some of the earlier probe schemes the
insulator deteriorated and broke by itself after a few runs.
To keep
the insulator at low temperature it is wrapped with a piece of Ta
foil which serves as a radiation shield.
The resistance of the insu­
lator decreases and increases repeatedly as the cavity temperature
is increased slowly.
After the value changes several times, the resis­
tance between the wires and ground settles down to the order of
1 kS) at 2,100
°K.
In use, a signal is applied or measured between
the two wires, or the two wires are shorted together and the signal
is applied or measured between the two shorted wires and ground.
-72-
3.2.13
Stabilization of the Heating Element Current
Originally the heating element current was supplied solely by a
large dc power supply (General Electric, 0156A4838) consisting of Si
rectifiers in a three phase full wave bridge circuit and a filter of
inductors and capacitors.
The maximum current output is 480 A at 125 V.
Because the current was not regulated the heating element current
fluctuated up to 10%, especially from 4 o'clock to 6 o ’clock in the
afternoon.
In the previous experiments without the microwave
diagnostics, plasma density fluctuations due to heating element
current fluctuations were not recognized.
In the present apparatus
plasma density changes less than 0.1% can be seen and often the micro­
wave frequency had to be readjusted due to the plasma density changes.
For this reason, it was decided to try and stabilize the heating element
current if at all feasible without buying a very large and expensive
regulated power supply.
One approach would have been to buy or build
a pass regulator to tack onto the output of present GE supply.
This
would have been fairly expensive in itself, and a simpler approach
which ultimately worked well, was tried.
A few small regulated Hewlett-
Packard power supplies with remote sensing capability were borrowed
and connected in parallel with the large supply.
The remote sensing
terminals were connected across the heating element, and the supplies
adjusted to operate in the middle of their output range.
As hoped,
\
the output of the small supplies varied in such a way as to compensate
--
for the output fluctuations of the large supply.
-73-
The only difficulty
SENSING
terminals
HP 6269B
OUTPUT'
. TERMINALS
0.0625A
FUSES
(+)(-)
ECG 6020
MAIN PO'.VER SUPPLY
HEATING ELEMENT
Fig. 3.12 CURRENT STABILIZATION CIRCUIT
FOR THE HEATING ELEMENT
-7 k-
was the limited output current of the supplies, which was not sufficient
to compensate for the larger fluctuations.
With the basic idea shown
to be viable a large 50 A power supply (Hewlett-Packard, Model 6269B)
was purchased.
The current of the main supply is now stabilized by
connecting the HP 6269.B power supply in parallel with the main GE
supply.
Fig. 3.12 shows the schematic diagram of the system.
A high
current diode (ECG 6020) is used in the output of the 6269B power supply
to protect it from the voltage of the main power supply and also a
1/16 A fuse is used on each sensing wire to protect the control cir­
cuit of the 6269B power supply.
With, the regulating supply the heating
element current fluctuations are now less than 1%.
3.2.14
Microwave System
Most of the microwave components, such as wavemeters, attenuators,
matching devices, isolators, directional couplers, and traveling probes,
are standard x-band waveguide components.
to this:
There are some exceptions
The input and output of the 20 W traveling wave tube amplifier
(.TWTA) (Varian VZX69.81G3A) are for coaxial cable, which is also used
to connect the waveguide to a microwave spectrum analyzer.
As shown
in Fig. 3.13, both the reflected and transmitted microwaves from the
cavity are studied.
As an x-band microwave source, a HP 8620C sweep
oscillator is used with a 86245A RF plug-in.
Two wide band x-tal
detectors (Hewlett-Packard, X421) are used at the transmission and
reflection side of the system.
Their outputs are connected to an
-75-
OS
CO
O
Fig, 3.13 MICROWAVE SYSTEM
M
o
CO
M
O
to
>1 O
X1 H
w
-76-
oscilloscope and a low frequency spectrum analyzer (Hewlett-Packard,
3580A) respectively.
When the R-F source frequency is swept the ramp
output from the sweep oscillator is used as the horizontal sweep
signal for the oscilloscope.
When the microwave spectrum analyzer
(Polarad, 2992B) is used, the detector in the reflection side is
removed and a waveguide to coaxial adaptor and a coaxial cable
(CG 92/U) is used for the analyzer.
3.2.15
Laser Diagnostic System
The overall geometry of the laser diagnostic system is shown in
Fig. 1.2.
Spectra Physics manufactured both the cw dye laser (model
375) and the pump laser (model 164-09).
The linewidth of the dye
laser is 10 X, and is determined by a Spectra Physics //G0059-002
wedge and a Spectra Physics #0411-6502 fine tuning etalon.
The dye
used is rhodamine 6G, which has a bandwidth of from -5,720 X to
~6,400 X.
The mirror which deflects the initially horizontal laser
beam vertically upward is movable from outside the vacuum envelope
so that slight changes in the position and orientation can be compen­
sated for.
The mirror control motor assembly is shown in Fig. 3.14
and Fig. 3.15.
In Fig. 3.14 the laser beam travels from left to right
and is reflected toward the top of the paper, and in Fig. 3.15 the
beam is directed into the paper and reflected toward the top of the
paper.
Referring to Fig. 3.14, the mirror can be translated along the
original axis of the laser beam, rotated about that axis, and rotated
-77-
VACUUM CHAMBER WALL
co
W
TSS
S
t5
M,0
I
< S t^T,~
REFLECTED
LASER
W
W
-78-
Fig. 3.H
o
BEAM
o
o
MIRROR CONTROL
MOTOR ASSEMBLY
SUPPORTING BLOCK
HI
MIRROR
O
CONTROL
o
MOTOR
Hi
ASSEMBLY
CQ
3.1-5
p3pv
w
M
O
bO.
£
O
about a horizontal axis perpendicular to the original and reflected
laser beams.
These motions are produced by three synchronous motors
mounted inside the vacuum system.
The mirror is attached directly
to the shaft of "motor //l" at an angle of 45 deg.
Motor //I rotates
the mirror about the axis of the original laser beam at a rate of
1.5 deg./s.
Motor //I is attached to the horizontal axis of "motor
//2"; and when run, rotates the mirror and motor //I about an axis
perpendicular to the initial and reflected laser beam at a rate of 4 deg/s.
The mirror and both motors r/1 and if2 are all attached to a stainless
steel block which has two rods running through it.
One of the rods
is threaded and is turned by motor if3, which translates the mirror
assembly at 25 y/s.
The second rod prevents the stainless steel
block from turning.
Power for the motors is produced by a General
Radio 1305-A oscillator feeding a Bogen audio amplifier.
The motion
can be slower or faster than stated above by changing the frequency
of the oscillator.
To protect the motors from the heat radiation all the motors are
shielded by water-cooled heat shields made out of 1.587 mm thick Cu
cylinders and 3.175 mm o.d. Cu tubing.
All the water lines for the
shields are connected in series and 6.35 mm o.d. flexible stainless
steel tubing is used between the heat shields to allow for the motions
of the motor.
In addition to the water cooled heat shields a 7.62 x
12.7 cm Ta heat shield is installed above the mirror assembly.
The
electrical wires for the motors are fed through an 11 pin flange type
feedthrough on one of the side ports on the lower vacuum chamber cylinder.
-80-
The optical detection system senses the fluorescence from the
excited by the laser beam.
All the optical components are mounted on an
optical bench made out of 7.62 x 8.89 cm A1 L-beam.
The L beam is
installed on a 12.7 cm wide, 78.7 cm long A1 channel attached to the
middle flange of the vacuum chamber, and aligned with the cavity and
heating element holes through the 8.90 cm diam observation port on
the upper cylinder of the vacuum chamber.
The system consists of
lenses, apertures, optical filters, and a photomultiplier.
All the
optical components are supported by holders made of 6.35 mm thick A1
plate.
Their positions can be adjusted using slots on the bottom of
the holders.
Screws are
holes on the optical bench.
inserted through the slots and into threaded
A point on the cavity axis is brought to a
focus by a 14.28 cm diam convex lens with a focal length of 21.8 cm.
This lens is about 5.08 cm from the vacuum chamber.
To reduce the
radiation from the heating element a 6 cm diam adjustable iris is used
at the point where the heating element hole is focused.
At this 'point
a 1.58 cm diam adjustable aperture is installed to cut the radiation
from the cavity wall, leaving only the image of the cavity hole.
Then
a 5.08 cm diam concave lens with 8.38 cm focal length is put 59.7 cm
away from the first lens to make the image from the cavity axis a
parallel beam for the optical filters.
A Fabry-Perot interferometer and
a 2.54 x 2.54 cm interference filter (Quantum Detector Technology,
Burlington, Mass.) are put between the second lens and the photomulti­
plier (EMI if9524S). This tube is put in a 4.12 cm diam PVC tube to
shield it from room light and protect it from physical damage.
— 81 —
The
Whole system is covered with a sheet of opaque cloth.
3.2.16
Helmholtz Coils
It is found that some of the characteristics of the plasma oscil­
lations in the cavity are quite sensitive to changes in the magnetic
field.
For this reason, provisions are made to impose a magnetic field
of the order of a few G perpendicular to the cavity axis and ~100 G
parallel to the axis.
Two pairs of Helmholtz coils for the horizontal
magnetic field and a pair for the vertical magnetic field are installed
on the outside of the vacuum chamber.
Each of the coils for the horiz­
ontal field is formed by winding 200 turns of 0.8 mm diam transformer
wire on a 34.3 cm diam cylinder.
The coils are attached to a 9 x 61 cm
A1 plate after they are removed from the cylinder.
The plates with the
coils are mounted on the vacuum chamber main cover flange.
The resis­
tance of each coil is approximately 0.2 £2, and with two coils in
series 1.506 G/A is produced.
Each coil for the vertical field is
made by winding seven turns of high current cable on the upper cylinder
of the vacuum chamber.
3.2.17
These coils are 20 cm apart and produce 0.323 G/A.
Rhenium Plating
To increase the probability of Ba ionization, the cavity walls are
Re plated.
The plating used to be done after the Ta foil was fabricated
into a cylindrical form to make the spot welding easier.
After obtaining
the W alloy spot welding electrodes the plating is done before the foil
is fabricated into the cylinder.
The spot welding of Re plated foil
with the W alloy electrodes is as easy as that of unplated foil.
Plating
on the unfabricated
foil is much easier than that on the cylinder
because the anode (Re rod) can be kept away from the cathode (the foil)
during plating on the foil.
To plate the cylinder, the anode has to
be put inside the cylinder to get a thick enough deposit on the inner
wall and the two electrodes, being close to each other, get shorted
because of the agitation required during the plating process.
results in damage to the cavity wall.
This
Several different cleaning
procedures for the Ta were tried, including those in Ref. 30.
The
plating is not successful unless the surface is polished with emery
cloth.
After polishing, it is ultrasonically cleaned in acetone
and rinsed in distilled water.
operating conditions
2
31
The plating solution components and
are shown in Tables 3,1 and 3,2.
For plating
a 1 cm
surface with a 1 y thickness of Re, about 0.28 mg of Re is
needed.
After plating, the foil is rinsed in distilled water and
kept in a warm oven until installed in the vacuum chamber.
If it is
exposed in humid air longer than a day, instead of being kept dry,
tiny liquid droplets which look very much like water condensation
appear on the surface and the Re comes off easily where the droplets
are.
However this does not happen once the cavity is heated up to
operating temperature.
-83-
Table 3.1
Plating Solution Composition
Chemicals
Quantity (g/l)
KReO.
4
1
h 2so 4
10
Mg/S03(NH2)2
30
(NH4)2S04
25
Table 3.2
Operating Conditions for Plating
pH
1 - 1.5
Temperature
60° - 80° C
current density
0.1 - 0.15 A/cm2
agitation
moderate
-8Jf-
4.
4.1
EXPERIMENTAL WORK
Microwave Plasma Density Measurements
As described in Sec. 2.2, the plasma density is determined by
measuring the shift in the cavity resonances due to the plasma.
microwave system for doing this is shown in Fig. 3.13.
The
Referring to
Fig. 4.1, the top curve shows several cavity resonances in a microwave
transmission measurement with the cavity temperature at 290° K and the
oven cold.
The middle curve shows the same resonances with the cavity
temperature at 2,150° K and the oven cold.
The resonant frequencies
have been shifted down due to the thermal expansion of the cavity.
There is some plasma in the cavity, which tends to raise the resonant
frequencies, but the effect of the thermal expansion is dominant.
In the bottom curve, the cavity temperature is 2,150° K and the oven
10
-3
has been heated so a plasma of density n^ = 5 x 10
cm
is in the
cavity.
The resonant frequencies have moved higher due to the plasma.
The curves in Fig. 4.1 are of better than average quality and were
chosen for clarity of presentation.
always obtained.
Curves of this quality are not
Due to impedance mismatches, the amplitude of some
cavity peaks in some frequency ranges decrease significantly and become
comparable to or smaller than noise peaks.
The impedance mismatches
are caused by slight thermal deformation of the refractory waveguides,
and by small amounts of plasma in these waveguides.
the real peaks then becomes difficult.
Identification of
When this happens the real peaks
can usually be identified by changing the heating element current
slightly, because the cavity peaks shift as the cavity temperature
-
85-
8.80
•
9.00
-86MICROWAVE
9.20
.
9.^0
FREQUENCY(GHz)
OVEN COLD
OJ
9.60
'
9.80
changes while the noise peaks are unlikely to move.
Sometimes they can
be identified by comparing the spectrums in transmission and reflection
as the noise peaks are unlikely to show up on both sides.
Fig. 4.2 is a plot of the frequency of a cavity mode vs. the cavity
temperature.
For this data, the oven is kept cold.
the points lie on a straight line.
Below 1,500° C,
This is to be expected if there is
a non-measurable amount of plasma in the cavity, and the cavity is
expanding in a linear way as the temperature is increased.
The sharp
rise in resonant frequency as the temperature is increased above 1,500° C
is due to plasma filling the cavity.
cold.
This happens even with the oven
It is necessary to know the resonant frequency of the hot empty
cavity if the plasma density is to be accurately determined.
as that in Fig. 4.2 are used to obtain this quantity.
Data such
The linear portion
of the curve is extrapolated to higher temperatures, and is used to find
the resonant frequency at higher temperature.
of a resonance is now easily obtained.
obtain the plasma density n^.
The frequency shift Af
This is used in Eq. (2.2.8) to
The error associated with this extrapolation
is <1 MHz, and for this reason is not included in the error analysis of
Sec. 2.2.
Data taken in a similar manner to that in Fig. 4.2 also showed a
defect in an early cavity design.
The resonant frequencies of the cavity
would change abruptly as the temperature was changed.
This was attri­
buted to thermal stresses which caused the top cover of the cavity to
suddenly deform.
This defect was corrected by the cavity-waveguide
design described in Secs. 3.2.8 and 3.2.9.
-87-
OJ
CO
•
cO
0
O
1—
CO
•
O
O
CO
•
00
00
-88-
O
ON
<N
•
CO
(zHD)A0tranb3aj
O
CO
O•
CO
0-
O
c^.
•
00
1000
1100
1300
FREQUENCY
uoo
150.0
OF CAVITY
TEMPERATURES C)
120Q
RESONANCE
1600
1.700
1800
4.2
Laser Diagnostics
One of the first endeavors with the new plasma apparatus was to
get the laser diagnostic working.
Laser induced fluorescence from
t
the plasma was observed, showing that a laser diagnostic is feasible.
Nevertheless, observing the
fluorescence was very difficult and the
signal to noise ratio was marginal.
The principal difficulty is
that the fluorescence has to be observed through a very large back­
ground of thermal radiation emitted from the cavity, heating element,
✓
and heat shields.
In this early endeavor, the heating current had
not been stabilized.
This caused fluctuations in the thermal radiation
which compounded the problem.
The laser aspects of the apparatus
were put aside while the microwave diagnostic was worked on and
improved.
As the heating current is much more stable now than
formerly, there is every reason to believe that laser fluorescence
will be observed more easily in the future.
Below we outline the
optical and electronic systems, and the apparatus conditions, under
which fluorescence was observed.
The optical system is described in Sec. 3.2.15.
detection system is shown in Fig. 4.3.
(model 415A) is used for the PM tube.
The signal
A fluke high voltage supply
The PM tube output is amplified by
an electrometer (Keithley 602), whose output is fed into a lock-in ampli­
fier (Princeton Applied Research, model JB-5). Table 4.1 shows typical
experimental conditions for the observation of the fluorescence
-89-
HV SUPPLY
FLUKE Z fl 5 A
IN T E R F E R E N C E
F IL T E R
APERTURES
PM T U B E
EM I 9 5 2 *f
LENSES
C A V IT Y
ELECTRO M ETER
K E I T I IL E Y 6 0 2
L A S E R BEAM
L O C K - IN
A M P L IF IE R
PAR J B -5
C H O P P ER
F ifi.
b*3
-90-
F L U O R E S C E N C E D E T E C T IO N
SYSTEM
TABLE A.1
pump laser output
2 W
dye laser output
100 mW
oven temperature
1
800° C
cavity temperature
1900° C
plasma density
i i n 11 cm" 3
1x10
system vacuum pressure
1.6x10 ^ torr
PM tube output
-4
9.5x10
amp
diam of the front aperture
3.5 cm
diam of the second aperture
1 mm
chopping frequency
-120 Hz
time constant of Lock
In amplifier
~1 sec
-91-
signal.
The wavelengths of the laser beam and fluoresced photon
are 6142 R and 4554 R respectively.
For approximate tuning of the
laser beam a small spectrometer (Bausch and Lomb Optical Co.) is
used and then the fine tuning etalon knob on the cw laser is
adjusted for the maximum signal amplitude.
without the Fabry-Perot interferometer.
The signal is detected
After the signal is
detected arid maximized the interferometer is put in place.
Because
of instability, the signal usually disappears before the inter­
ferometer is installed and adjusted.
The relatively long term
instability seems to be due to heating element current fluctuations,
resulting in the plasma density fluctuation and poor alignments
in the optical system.
Since these observations, the plasma
density stability has been greatly improved.
4.3
Cavity Resonant Frequency Shift Due to the Ponderomotice Force
The resonant frequencies of the plasma filled cavity shift to lower
values as the power to the cavity is increased.
This effect is due to
the ponderomotive force which pushes the plasma out of the regions where
the electric field is most intense.
In one sense, the "shift" in the
resonant frequencies with power is easy to measure as obtaining the
-92-
resonance curves at higher powers is a relatively straightforward
procedure.
At the highest powers used, the exact meaning of "shift"
becomes somewhat unclear, as it is found that the resonance curves
become increasingly distorted and broadened as the power is increased.
This effect, and also the shift with power, is illustrated in Fig 4.4
which shows the TM011 mode measured in transmission.
resonances are inverted in this plot.
Note that the
The power levels shown are the
power levels at the maxima of the curves.
The spikes at the peaks of
the 2.8 and 1.65 W curves are due partly to recorder overshoot, but
also appear to have a component caused by plasma oscillations excited
by the very hard onset of microwave power.
For these two curves, the
power levels are those at the base of the spikes.
curve is relatively symmetric.
For 5.96 mW, the
At higher powers, the curves steepen on
the low frequency side, and broaden on the high frequency side.
Measuring the power that is actually delivered to the cavity is
rather difficult, and some time has been spent in developing a procedure
that yields reasonably accurate results.
I begin by discussing a method
that is no longer used, as a newer method is believed to yield better
results.
A discussion of this earler method illuminates some of the
difficulties encountered.
It is convenient to divide the microwave system into two parts:
the vacuum microwave system and the air microwave system.
separated by the two microwave vacuum windows.
presents relatively little difficulty.
-93-
These are
The air microwave system
The components are standard,
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and their absorption and reflection characteristics can he measured
and checked.
The vacuum microwave system is more of a problem.
Many
of the components are not standard, and while the components can be
studied while the vacuum system is open and the plasma chamber is cold,
they cannot be individually studied while the vacuum chamber is closed
and the plasma chamber is hot.
As might be expected, the vacuum micro­
wave system has somewhat different properties hot than cold.
It is
important to know the amount of power absorbed by the vacuum waveguide
system when the cavity is hot in order to know how much power is actually
being delivered to the cavity.
The first method used to measure the frequency shift vs. power
was as follows.
For a given power level, the microwave frequency was
adjusted so that the response of a cavity mode was maximum.
into and out of the vacuum system was measured.
The power
The difference of these
powers represents the power delivered to the vacuum microwave system,
or the "vacuum microwave absorption."
To determine what part of this
power is delivered to the cavity, the microwave frequency is changed so
that the cavity mode is no longer on resonance and practially all of
the power is being reflected by the cavity.
The power then being
absorbed by the microwave system is the power being absorbed by all
vacuum components except the cavity.
resonant microwave absorption."
We call this power the "non­
The power delivered to the cavity at
resonance is then obtained by subtracting the non-resonant microwave
absorption from the microwave absorption at resonance.
-95-
There are a
number of difficulties and sources of errors associated with this
approach.
The microwave generator and plasma density stability must
be good enough so small drifts do not move the mode off resonance
while the power measurements are being made.
Of more fundamental
concern is the fact that the non-resonant microwave absorption depends
on frequency.
It may not be the same to one side of a cavity resonance
as it is on the cavity resonance.
Finally, a technical point that
introduces some uncertainty into the measurement.
High microwave
power is not measured directly as the instrument we use has a maximum
rating of 15 mW.
A small fraction of the power is tapped off using
a directional coupler, and it is the diverted power that is measured.
The directional coupler used has a specification of 20 ± 1 dB.
This
means that nominally 1.00% of the power is diverted, but deviations
about this value are +1.26% to -0.79%.
power may vary by roughly ±25%.
The magnitude of the diverted
These deviations are not in the
cdlibration of the directional coupler, which can be done very accurately
at a fixed frequency, but in the broad band design that introduces many
wiggles in the diverted power vs. frequency characteristics.
If one
were unlucky, there could be an error of 25% in measuring the non­
resonant microwave absorption, and then an additional 25% error at
resonance in determining the power to the cavity.
For all these reasons,
this method of measuring the power to the cavity has been discontinued
and the data obtained is not presented in this thesis.
The most recent measurements of resonant frequency shift vs. micro­
wave power are now discussed.
The microwave system for these measurements
is specialized, and differs in enough ways from the system described
in Sec. 3.2.14 to merit a description in this section.
shows the set-up.
drive the TWTA.
Fig. 4.5
The HP-8620 microwave sweep oscillator is used to
The microwave power level is adjusted with a Waveline
attenuator connected to the output of the TWTA.
It might appear to
be more logical to adjust the power level at the input to the TWTA
where the power level is low, but this mode of operation was not as
stable.
The microwave power goes into port 1 and out of port 2 of the
circulator.
When the microwave frequency is detuned from any cavity
resonance, practically all of the microwaved power incident on the cavity
coupling aperture is reflected at the entrance to the cavity and goes
back to port 2.
When the microwave frequency is tuned to a cavity
resonance, a fraction of the power enters the cavity.
This power is
absorbed in the cavity walls and the plasma, radiated from diagnostic
holes, and also radiated into the second refractory waveguide.
This
second waveguide has an attenuator and a HP421A crystal detector in
series, and a shunt waveline 698DR cavity wavemeter.
Port 3 is connected
to a 20 dB directional coupler (Struthers Electronics, Farmingdale, NY),
and the undiverted, power goes to an attenuator and a HP-486A waveguide
mounted thermistor.
power meter.
The output of the thermistor goes to a HP-431B
The power diverted by the 20 dB directional coupler goes
to a precision HP-382A attenuator, cavity wavemeter, waveguide to co­
axial adaptor, and a HP-423 coaxial Low Barrier Schottly diode detector.
The output of this detector is connected to a HP-700A x-y recorder.
Port 4 of the circulator is terminated by a matched load.
The primary
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power measuring
standard is the HP-486A waveguide mounted thermistor
used with the HP-431B power meter.
Both these items were calibrated
on 9/15/82 by Test Equipment Service Inc., S. Plainfield, NJ (Files
10241 and 10242), and the combination is accurate'to ±5% of full
scale value.
This combination is used to calibrate the HP-423B diode
detector which is used to take the data.
It was found that the time
constant of the HP-431B thermistor detector was slightly too long
for the present method of data taking, and was less stable than the
diode detector at low power levels.
The data is now taken by a frequency sweep method.
The microwave
oscillator is set so that it sweeps ~150 MHz at an appropriate point in
the X-band range.
For a given series of measurements, the frequency
sweep limits are not touched, and the plasma temperature is held constant.
The success of the method depends on the observed fact that at a given
plasma temperature and a given input microwave power level, the power
reflected from the vacuum microwave system is relatively independent
of plasma density for frequencies that are detuned from cavity resonances.
Restated, the "non-resonant reflected (microwave) power" is relatively
independent of plasma density.
discussed.
The reasons for this observed fact are
The vacuum microwave system is complicated, with many small
reflections occurring for the power traveling in both directions.
In
addition, there will be non-negligible power absorption in the hot
waveguide where the wall resistivity is high.
At a given temperature,
the geometry of the hot microwave system will be constant, and the
impedance of the microwave system at all points will not change due to
-99-
waveguide dimensional changes.
Another factor influencing waveguide
impedance is the dielectric, or plasma, in the waveguide.
As the plasma
density changes, the amount of plasma in the waveguide changes, and
the impedance in the waveguide will change.
The plasma density in the
waveguide is kept low by the pump-out slots, and the electron plasma
frequency in the waveguide for all points except very close to the
cavity coupling apertures can be estimated to be several orders of
magnitude below the microwave frequency.
One would then expect that
impedance changes due to dielectric changes would be very small except
perhaps very close to the coupling apertures.
A final factor is the
impedance which the cavity represents at the end of a waveguide.
This
will be inductive or capacitive for a given cavity resonance. Furthermore,
more than one mode may contribute significantly.
For a given microwave
frequency, this impedance will change as the plasma density changes
because a plasma density change also changes the cavity resonant fre­
quencies.
While this change in the termination impedance of the waveguide
does not in itself produce a significant change in absorption (it is
mostly inductance or capacitance), it could conceivably rearrange the
reflections in the waveguide system in such a way that the waveguide
absorption changes.
Data at two power levels is given in Figs. 4.6 and 4.7.
Using the
x-y recorder, the x-axis of these Figs. is the frequency sweep, and the
y-axis is the microwave power reflected from the vacuum microwave system.
Note that an increase in reflected microwave power corresponds to a
decreased y value.
Several small narrow peaks in these Figs. marked
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with frequencies correspond to wavemeter calibration points.
In each
Fig., there are essentially three curves markes 1, 2, and 3 which
10
-3
correspond to plasma densities of 2.9, 6.7, and 9.6 x 10
cm
respect­
ively.
The double trace of curve 1 in Fig. 4.6 was due to an extra
sweep made in a period when the plasma density was changing rapidly.
Excluding the extreme left hand portions of the graphs, the curves
represent non-resonant reflected power except for the TM011 mode for
curves 1, the TM010 mode for curves 2, and TE113 mode for curves 3.
The peaks due to these modes are easily distinguishable from the
non-resonant reflected power as their frequencies change in a definite
way as the plasma density changes.
This effect is easily seen by the
double trace of curve 1 in Fig. 4.6.
On the other hand, the portions
of these curves representing only non-resonant reflected power are
largely independent of plasma density.
Again, excluding the extreme
left hand portions of the graphs, the left halves of the two graphs
have no cavity modes present.
These portions of the graphs indicate
to what extent the non-resonant reflected power does depend on plasma
density.
In the data analysis, it is assumed that the non-resonant
reflected power does not depend on plasma density, and these portions
of the curves allow an accurate estimate to be made of the error intro­
duced by this assumption.
The data is analyzed as follows.
Using the data in Figs. 4.6 and
4.7 as examples, most of curve 3 is non-resonant reflected power.
The
effect of the TE113 modes is very small at the peak values of the TM011
and TM010 modes of curves 1 and 2 respectively.
Therefore, the peak
power to these modes is obtained by subtracting the values of curves
-103-
3 from curves 1 and 2 at the resonant frequencies.
The one other quantity necessary to relate the measurements of
frequency shifts and microwave power to the computer calculations
is the appropriate Q of the cavity for the mode being used.
The theory
. invoked is given in Ref. 32 , but for clarity a different notation is
used here.
The microwave power actually measured is the power delivered
by one of the waveguides to the cavity.
This power is dissipated in
the walls of the cavity and the plasma, and lost through the coupling
slot of the other waveguide and through diagnostic holes.
The power
absorbed by the plasma and radiated out the diagnostic holes is small,
and is neglected in the following analysis.
The power balance in the
cavity is then dominated by wall losses and the losses through both
coupling apertures.Define
1
Q
1
2tt
by
___________ W1___________
Energy stored in Cavity
^
where W1 is the energy lost in the cavity walls per cycle plus the
energy lost through one coupling aperture per cycle.
The subscript on
means that this quantity is defined so as to
include wall losses and the loss through one coupling aperture, the
aperture not supplying power to the cavity.
The field intensity in
the cavity
may thenbe obtainedby noting
the cavity
is givenby (Q^P)/(2 tt), where P is the powerdelivered
the cavity though the other waveguide.
that the stored energy in
to
was obtained in two ways for
the TM011 mode and one way for the TM010 mode.
.o'
In the transmission method of obtaining
microwave power is
fed to the cavity through one waveguide, and measured in the other
-104-
waveguide.
The frequency is varied, and the two frequencies f^ and
f2 at which the transmitted power falls to half its peak value are
measured.
If f
is the resonant frequency (frequency of maximum
power transmission), the quantity
is given by f /
2 ~^1 ^’
w^ere
Q^2 Includes wall losses plus the losses through both coupling aper­
tures.
Defining
as including only the loss in the walls,
Qw2 are related by Qw =
+
+ ^
where
coupling coefficients for each coupling aperture.
and
an(* ^2 are the
As these are con­
structed as nearly identical as possible, 3^ = 32 = 3 in th® present
situation.
is then calculated with standard expressions
using a resistivity of 90 x 10
—6
-I
ohm cm
and 3 is then obtained
1
from 3 = ^(7;— - 1) • Recalling that to a high degree of approximation
W2
3
is given by
„ ~ energy loss through coupling aperture per cycle
energy loss in walls per cycle
*
it follows that Qt =QIT/(l+3). This method gave Qt =369 for the TM010
W1 w
W1
mode, and Q ^=736 for the TM011 mode.
In using this method, it is
important that the power be measured in the second waveguide, and a
crystal detector would most likely not be satisfactory.
The calibrated
combination of waveguide mounted thermistor and power meter
was used.
In the second method of obtaining Q^» °ne waveguide is terminated
in a matched load, and the power is fed through the other waveguide
which is fitted with a slotted line section (HP model 809B). Measure­
ments are made of the voltage standing wave ratio (VSWR) vs. frequency,
-105-
and of the position of a voltage minimum vs. frequency.
These pro­
cedures were carried out for the TM011 mode, and the results are
shown in Figs. A.8 and 4.9.
Referring to Fig. 4.8, the data points
on both sides of resonance fall on straight lines, but the lines for
each side of resonance are displaced from one another.
that this results from over coupling, or 3 > 1.
Theory shows
Knowing that the
cavity is overcoupled, the VSWR at resonance, (VSWR)q, is equal to
3.
(For undercoupling, (VSWR)q =1/B). From Fig. 4.9, (VSWR)q = B = 1.30.
The VSWR at the half power points, (VSWR)^^*
calculated from
(VSWR)
This is used in Fig. 4.9 to find f^ and f^, the frequencies at the half
power points.
Again, letting fQ = the resonant frequency,
fQ/(f2 - f-^) = 648, differing by 12% from the value obtained from the
transmission method.
This method was not used on the TM010 mode because
the low Q of this mode makes the method inaccurate.
The agreement
between the two methods for the TM011 mode is comforting, but may be
a bit fortuitous.
For the purposes of assigning error bars to the
data points, an uncertainty of ±20% is assumed in the Q^'s.
The data taken up to the time of this writing are presented in
Figs. 4.10 to 4.12.
Figs.4.13 to4.15 are expanded versions of parts of
these Figs. The^data;.of Fig..4.10 are for the TM010 mode at a plasma
-10
-3
density of 6.7 x 10
cm . Data for the TM011 mode is presented in Figs.
-106-
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4.11 and 4.12 for plasma densities of 5.4 x 1 0 ^ and 7.9 x 1 0 ^ cm~^
respectively.
The theory for the TM010 mode is given by the solid line
in all three Figs. as the theory for the TM011 mode has not yet been
worked out on the computer.
Bars representing experimental uncertainties
are given for representative points in all the Figs.
The vertical
uncertainty of ~ ± 2 MHz represents the uncertainties in reading the
peaks of the curves and in reading the wavemeter.
An additional
uncertainty has been added if the plasma density drifted noticibly
during the measurement.
The horizontal uncertainty includes the
uncertainties in calibration ±5%, in non-resonant reflected power
(2 to 10%, depending on data),and .in the .Q of the cavity (±20%).
For powers above > 0.5 W, all the. measured frequency shifts are
greater than the shifts predicted by the theory for the TM010 mode.
This can be seen most clearly in Fig. 4.13 to 4.15 where the scales
have been expanded.
For powers < 0.1 W, the uncertainties in the
measured points are large enough so that the uncertainty bars overlap
with the theoretical curve.
-109-
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-113-
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-114-
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B H E
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-115-
4.4
Observation of Undriven Low Frequency Oscillations
Quite by accident, it was found that the microwaves were being
amplitude modulated by low frequency (10-100 kHz) oscillations in
the plasma.
Using the experimental set up shown in Fig. (3.13) but
without the TWTA, a cavity resonance was being displayed on the
oscilloscope by sweeping the microwaves across the mode, detecting the
microwaves in a crystal, and feeding the crystal output into the
vertical axis of the oscilloscope.
seen on the curve.
A barely discernible hash was
The hash appeared to be less on the horizontal
top of the cavity resonance curve than on the steep sides of the
curve.
This indicated the hash might not be noise.
Changing to a
cw mode, a 0-50 kHz HP-3580A spectrum analyzer was used to analyze
the detected microwaves.
prisingly narrow.
Two narrow peaks were found that were sur­
The Q's were ~100.
coherent low level oscillations.
The hash was therefore fairly
Checks were made with the cavity
cold and no plasma present to see if the oscillations disappeared.
They did.
In studying these oscillations, this check had to be
continually repeated because occasionally oscillations appeared,
usually at unfamiliar frequencies, which were not due to the plasma,
but were due to pick-up from an unknown source.
The amplitude of the oscillations was studied by feeding the
detected microwave signal into the amplifier-rectifier circuit of
Fig. 4.16. The output of this circuit is fed into the y-axis of an
x-y recorder.
The result appears in Fig. 4.17, The bottom curve in
this Fig. is the standard cavity resonance.
The top curve is the output
F ig .
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CIRCUIT
FOR
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FREQUENCY
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-118-
of the amplifier-rectifier circuit, and shows the amplitude of the
oscillation as a function of frequency.
This curve bears out the
oscilloscope observation in that the amplitude is smaller at the
peak of the resonance curve compared to the sides of the resonance
curve.
This makes sense if one assumes that plasma oscillations are
displacing the cavity resonance curve at the same frequency, or
possibly at double the frequency, of the plasma oscillations.
The curves in Figs.
reflected microwaves.
4 . 1 8
to
4 . 2 0
were obtained by detecting the
For the top curves, the microwave frequency was
set to the side of a cavity resonance, the diode detected microwave
signal was put into the HP spectrum analyzer, and the output of the
spectrum analyzer connected to the y-axis input of the x-y recorder.
A ramp output of the spectrum analyzer, proportional to the frequency,
is fed into the x-axis of the recorder.
These curves are typical of
those obtained over a period of time with a horizontal magnetic field
of
0 - 2
G applied to the plasma.
Initially, the role of a small magnetic
field was not appreciated, but when a small magnet was brought near
the vacuum chamber, changes in the spectrum indicated that a field
of a few G can significantly alter the oscillations.
Helmholtz coils were installed.
Fig.
4iJ.8
to
4 . 2 0
See Sec.
3 . 2 . 1 6 .
At this point,
All of the data of
were taken with no applied vertical field, an
applied
horizontal field of 1.9 G East, and an applied horizontal field to the
South as indicated in the Figs.
It is interesting to note that two
peaks can merge into one peak at certain values of the applied magnetic
-119-
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field.
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Another observation was that an applied horizontal field of
greater than ~5 G quenched the oscillations.
More information about the resonances in Figs. 4.IB to 4.20 was
obtained by detuning the microwaves well off the microwave resonance
being used.
The microwaves then do not enter the cavity but are re­
flected at the coupling aperture.
taken in this way.
The lower curves in the Figs. are
It is seen that the higher frequency oscillations
extend to some extent into the wave guide.
It would have been informa­
tive to take data using the other waveguide to see if both peaks were
still seen, and if so, if the lower frequency peak extended into that
waveguide.
Unfortunately, before this was tried, the heating element
assembly had to be changed, and the spectrum of the low frequency
oscillations changed.
With the new heating element, only very low
levels of oscillations were seen unless a few G were applied to the
plasma.
It is possible that the older heating element, due to asymme­
tries, imposed a field of a few G on the plasma, and the newer heating
element did not.
A small field may be necessary for reasonable amplitudes
of these oscillations.
The data of Fig. 4.24* shows that the frequencies of these oscil­
lations is independent of plasma density.
With an applied vertical
magnetic field of 18 G, and a constant plasma temperature of 2,073° K,
10
-3
the K plasma density was varied from 6 to 14 x 10
cm . The frequency
of the observed resonances remained very close to 27 kHz.
cular feature is suggestive of ion acoustic waves.
-123-
This parti­
50 kHz Spectrum Analysis
of Detected Microwave
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The effect of an applied vertical field is shown in Figs. 4.21^
to 4.23.
The plasma density and temperature are held constant.
In
Fig. 4.21, with a vertical field of 21.8 G down, a resonance occurs
at 29 kHz with a Q of 29.
As the vertical magnetic field is increased,
the resonance frequency approaches ~25 kHz, and the Q increases.
This is seen in Figs. 4.22 and 4.23 for vertical fields of 36.3 and
50.9 G respectively.
For Cs, the resonance disappears for a vertical
field of about 55 G.
For K, the data is similar, but the resonance
persists to higher field.
The highest applied field, 80 G, is not quite
sufficient to completely quench the resonance, but the trend of the Q's
suggests that a still higher field would do so.
The above observations are independent of the microwave mode being
used.
They are also independent of microwave power if- the power is
<1 W.
No threshold with power is observed.
As the microwave power
is lowered to <1 mW, the low frequency resonances just drop into the
noise.
This strongly suggests that the microwaves are detecting the
oscillations, and are not causing them.
-128-
4.5
Observation of Driven Low Frequency Oscillations
Some preliminary data was taken using high microwave power and
available spectrum analyzers.
It is found that with enough power,
additional frequencies appear in the microwaves processed by the cavity.
These additional frequencies simultaneously arise in the low frequency
spectrum analysis of the detected microwaves, and in the range of the
microwave frequencies being used.
These additional oscillations,
unlike the undriven low frequency oscillations, have a very definite
threshold with microwave power, and are assumed to be caused by the
microwave fields.
The experimental set up for observing these driven oscillations
is shown in Fig. 3.13.
The high microwave power is supplied by a
20 W traveling, wave tube ampliflier (Varian, model VZX6981G3A). Referring
to the high power asymmetric microwave resonance curves of Fig. 4.24, 4.25
the microwave frequency was adjusted to be somewhat on the high fre­
quency side of the sharp low frequency drop off of these curves.
microwaves are analyzed two ways.
The
First, they are passed through a
crystal detector whose output is fed into a Tektronix (model 5L4N)
0-100 kHz spectrum analyzer.
is believed reliable.
This is a fairly modern instrument, and
Second, the microwaves are fed directly into
an ancient Polarad model 2992B microwave spectrum analyzer of uncertain
condition.
The frequency sweep of this analyzer is somewhat nonlinear,
but it was felt qualitative results could be obtained by using it.
Typical of the results obtained are the curves in Figs. 4.24 and
4.25.
Fig. 4.24 is a 0-100 kHz spectrum analysis of the detected
-129-
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microwaves.
The frequencies of the two peaks, 46.5 and 92.5 kHz,
are obtained by an internal calibrator in the Tektronix spectrum
analyzer, and are more accurate than can be obtained from the curves.
The frequency of the 92.5 kHz peak is not exactly double that of the
lower frequency peak.
Both peaks are pulled somewhat with power, but
as the power is raised, the 92.5 kHz peak appears.
The power thresholds
are found to be lower as the plasma density is raised.
The same
frequencies are found for different microwave modes, but these driven
low frequency oscillations are not seen for all modes.
This could
possibly be due to a sensitivity to mode structure, but could also
be due to the fact that some modes are not so strongly coupled to the
waveguides and less power is delivered to the cavity for these modes.
Fig. 4.25 shows the output of the microwave spectrum analyzer.
For
reasons already stated, caution must be used in interpreting the
spectrum.
wave power.
The central peak at 9.3 kHz represents the incident micro­
It is the only peak present at low power.. As the power is
raised, the peaks marked A
and C appear simultaneously with the 46.5
kHz peak in the low frequency spectrum.
Taking into account the state
of the microwave spectrum analyzer, these additional peaks could be
construed as representing new microwave frequencies at 9.3 GHz ± 46.5 kHz.
As the power is raised futher, peaks B appear simultaneously with the
92.5 kHz peak in the low frequency spectrum.
The location of this peak
is not understood.
The driven oscillations are detected by the wire probe as well as
by the microwaves.
In this respect the driven oscillations are
different from the undriven oscillations which are not detected by
the wire probe.
It could not be determined with certainty whether
this was a lack of probe sensitivity, or an indication of a fundamental
difference between the two kinds of oscillations.
Oscillations with
the same frequencies are observed with low microwave power when a
dc voltage is applied between the wire probe and the cavity wall.
It is believed that the high Q oscillations are the eigenmodes of ion
acoustic oscillations in the cavity with a high growth rate due to the
drift velocities caused by the applied dc voltage.
-132-
5.
CONCLUSIONS AND RECOMMENDATIONS FOR FUTURE WORK
A new thermal plasma device that differs significantly from
previous thermal plasma devices has been built, tested, and used for
studying several plasma phenomena.
The device consists of a hot
refractory metal box fabricated into a cylindrical microwave cavity.
The cavity is suspended from two X-band waveguides.
It has been
shown that with the cavity at ~2,100° K, low power microwaves can
be used as a diagnostic, and high power microwaves can be used for
the study of the interaction of electromagnetic waves with plasmas.
The microwaves have been used to measure the plasma density by
measuring the shifts in the cavity resonant frequencies caused by the
presence of plasma.
The primary challenge to an accurate density
measurement was to determine the resonant frequency of the hot empty
cavity, as the hot cavity always has some measurable plasma in it.
This was done by an extrapolation technique.
The resonant frequencies
were measured as a function of temperature for temperatures low
enough so that no measurable plasma was present in the cavity.
These
results were extended to higher temperatures to yield the resonant
frequencies of the hot empty cavity.
The plasma density is measured
with an uncertainty estimated to be ± 5 x
8
—3
10 cm
The capability of using a tunable dye laser beam as a diagnostic
on a Ba ion plasma was built into the apparatus.
The dye laser beam
enters and leaves the cavity through small holes in the ends of the
cavity, and travels along the axis of the cylindrical cavity.
-133-
The
laser beam can excite any of several Ba ion energy levels, and
fluorescence can be observed through small holes in the cylindrical
wall of the cavity.
The fluorescence has to be observed through
a very large amount of thermal radiation emitted by the cavity,
heating element, and heat shields.
Fluorescence was marginally observed,
but not used for any actual measurements.
Improvements in the stability
of the apparatus made since the observations of fluorescence should
help the signal to noise ratio of this diagnostic.
The signal to noise
ratio might also be considerably improved by putting an acoustic modu­
lator in the path of the laser beam.
The modulator would be used
to rapidly smear the modes of the laser beam into the entire Doppler
width of the Ba ions so that a larger fraction of these would be
excited.
This diagnostic is capable of yielding localized density
and velocity information of the plasma ions.
This kind of information
is always among the most difficult to obtain, but also of great impor­
tance.
Efforts should be made to further develop this diagnostic
capability.
The most important measurements made with the new apparatus are
the shifts in resonant frequencies of the cavity as the microwave power
I
is increased. These shifts can be directly related to the ponderomotive
force, so the experiment becomes a test of the theoretical expressions
for this important quantity.
This new apparatus is particularly suited
for this measurement because significant frequency shifts can be obtained
by using microwave power levels that neither heat nor ionize the plasma
significantly.
Both these effects, when present, make analysis of
experimental results much more difficult.
In addition to measuring
the frequency shifts as a function of microwave power, these quantities
were also calculated on a computer for the TM010 mode.
For low power
levels, the computer generated curve fell within the error bars of the
measurements, although the actually measured shifts always lay above
the computer calculated shifts.
For higher power levels, the measured
shifts were significantly larger than the computer calculated shifts.
The latter did not lie within the error bars of the data points.
Because of the potential significance of these results, more data
should be taken and further possible sources of error pursued.
Although it is not believed to be a factor in the reduction of the
data for the purposes of determining the ponderomotive force, it
would bd of interest to have a theory for the line shapes at high
microwave power.
A considerable amount of work was done in investigating undriven
low frequency oscillations in the cavity.
was never convincingly ascertained.
The nature of the oscillations
The laser diagnostic would be a
useful addition to the apparatus for studying these oscillations.
By using this diagnostic, it could be determined whether the oscillations
were localized, such as near the coupling slits, or were filling the
entire cavity.
At higher powers, additional microwave and acoustic frequencies were
observed in the cavity.
It is felt that these are parametric decay
oscillations, and merit further investigation.
-135-
REFERENCES
1.
See, for example, "Plasma Phenomena in Gas Discharges," by R.N,
Franklin (Clarendon Press, Oxford, 1976).
2.
I.L. Klavan, D.M. Cox, H.H. Brown, Jr., and B. Bederson, Phys.
Rev. Lett. 28, 1254 (1972).
3.
D.M. Cox, H.H. Brown Jr., I.K. Klavan, and B. Bederson, Phys. Rev.
A10, 1409 (1974).
4.
D.M. Cox, H.H. Brown Jr., L. Schumann, F. Murray, and B. Bederson,
Phys. Rev. A10, 1711 (1974).
5.
D. Taggart, L. Schumann, and H.H. Brown Jr., Phys. Fluids 24,
1180 (1981).
6.
R.W. Motley,"Q Machines’(Academic Press, 1975), p. 10.
7.
J.C. Ingraham and S.C. Brown, Technical Report //454 (MIT-1842-36).
8. S.J. Buchsbaum and S.C. Brown, Phys. Rev. 106, 196 (1957).
9. D.J. Rose and S.C. Brown, J. Appl. Phys. ^3, 719 (1952).
10. V.E. Golant, Soviet Phys. Tech. Phys. j>, 1197 (1961).
11. K.B. Persson, Physical Review, 106, 191 (1957).
12. R.A. Waldron, "The Theory of Waveguides and Cavities," (Maclaren
and Sons Ltd., London, 1967).
13.
E. Hinnov, and N. Rynn, Phys. Fluids 6^, 1779 (1963)
14.
F.W. Hofmann, Phys. Fluids, 1, 532 (1964).
15.
R.M. Measures, J.A.P., 39, 5232 (1968).
16.
D. Dimock, et. al., Phys. Fluids, 3L2_, 1730 (1969).
17.
R.A. Stern, et. al., Phys. Rev. Lett. 37, 833 (1976).
18.
A.C.G. Mitchel and M.W. Zemansky, "Resonance Radiation and Excited
Atoms"(Mcmillan, 1934).
19.
H. Motz, "Ionization Phenomena in Gases"(Munich, 1961), Vol. 2, p. 1484.
-136-
20.
H. Motz, "Numerical Solution of Ordinary and Partial Differential
Equations"(ed. by L. Fox, Pergamon Press, 1962), p. 469.
21.
Carl-Erik Frdberg, "Introduction to Numerical Analysis"(AddisonWesley Publishing Co., 1965).
22.
F.F. Chen, "Introduction to Plasma Physics"(Plenum Press, 1977).
23.
A.Y. Wong, R.W. Motley, and N. D'Angelo, Phys. Rev. 133, A436, (1964).
24.
I. Bernstein and R. Jensen, Private Communication
25.
B.B. Kadomotsev, "Plasma Turbulance," (Academic Press, New York,
1965)"
26.
A.L. Eichenbaum and K.G. Hernqvist, J. Appl. Phys., 32, 16 (1961).
27.
See, for example, E.A. Jackson, Phys. Rev. 153, 235 (1967), and
references cited there.
28.
C.G. Montgomery, "Techniques of Microwave Measurements,"
Book Co., N.Y., 1947).
29.
C.P. Poole, Jr., "Electron Spin Resonance," (Interscience Publishers,
1967), p. 280.
30.
F. Rosebury, "Handbook of Electron Tube and Vacuum Techniques" (Addison
and Wesley, Reading, Mass., 1965).
31.
A.R. Meyer, Trans. Inst. Metal Finishing, 46_, 209 (1968).
32.
E.L. Ginzton, "Microwave Measurements,"
N.Y., 1957).
-137-
(McGraw-Hill
(McGraw-Hill Book Co., Inc.,
P R O G R A M M w A V E ( I S P U T / O U T P U T / T A P E 5« I N P U T / T A P E 6* 0U T P U T / T A P E 2)
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THE I N ITIAL
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IMPLICIT PEAL(A-H/Q-Z)
IMPLICIT INTEGER(I-N)
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+ BK2(121)/3i<3(i21)/3KA(121)/cKLM121)/BK5{12I)/BK 6(121)/
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N 1 IS T O T A L H OF M E S H P O I N T S IN R (R A D I A L ) D I R E C T I O N I N C L U D I N G
T H E O R I G I N A N D S I D E V.ALL.
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“138-
RESPECTIVELY
i
CONTINUE
0=1500.
SET D I E L E C T R I C C O N S T . « ! .
TO S T A R T
DO 1 I ■ 1 * M l
DO 1 J » 1 * N 1
D K (I,J )= 1 .0
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‘
DK2(I*J)=G.O
CONTINUE
GDTAIN
T HE T R I A L
F U N C T I O N F OR T H E
READ ( 2 )
X
E P S 1 I S THf c C O N T R O L I N G P A R /
E P S 5 I S F OR O U T E R 1 T E R A T I G N
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♦ ♦♦♦START
OUT ER
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THE
VECTOR
INNER
F POM
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11=1*100
ICCUNT=ICCUNT+1
P P E P A R E T HE E L E M E N T S FOR
MATRIX
A
C A L C U L A T E L - I E L E C T W I C C O N S T A N T AND I T S D E R I V A T I V E S
AT E A C H M E S H
POINT.
ME S H P O I N T S ON R - A X 1 S A N D Z - A X I S
AR E N OT I N C L U D E D I N " A ( M* N ) "
DO 3 1 = 2 * M l
J K=1
DO 3 J = 2 * N 1
J M= JK + 1
D = F LO A T ( J K - l )
BKCC(I,J)=2.0/DK( I*J)
B K C 1 (I* J )= 1 .0 /C K (I* J )+ 1 .0 /(2 .0 ? D K (I»J ) * D ) +
# OKPC I * J > ^ A 6 / ( 2 : . C = * !C J r < { I » J ) = » C < ( I , J ) )
B K C 2 ( I , J ) = 1 .C/O K( 1*J ) +DKZ( I * J ) + A 6 / ( 2 . 0 * C K ( I , J ) * D K < I * J ))
B K C 3 1 I * J ) = 1 . 0 / O K I 1 * J ) —1« 0 / ( S . CR‘ D J>CDK { I * J ) )
# - C K P . ( I * J )* A t> / ( 2 .
( I * J >* 0i << I * J ) I
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B K C 5 II*J )= A .O /D K (I,J )'
B K C 6 { I , J ) = ? . KC5 ( I * J ) - E r t C 2 < I * J )
CONTINUE
CHANGE B K C ( M 1 * N 1 )
I1*G
. DC 4 I = 2 * M l
DC 4 J = 2 * N1
MATRICES
TO
8K«S(M*N»1)
MATRICES
.
11=11+1
BKO ( 1 1 ) = Bi XCO( 1 * J )
B K K I l ) = BK C1(I* J)
3 K 2 ( I 1 ) = B. <CE ( I * J )
BK3( I I ) = B K C 3 ( I * J )
B K A ( 11 ) = B K C A ( I * J )
BK 5 ( I I ) = b K C 5 ( I * J )
B K 6 (Il)= 3 K C t(I*J )
CONTINUE
FILL
DEFINF
UP
MATRIX
INDEX
A
WI TH
VARIABLES
T HE
ELEMENTS
WITH
BK«S.
'
MATRIX
c
c
NM1-NM-1
NMN* NM- N
NMN1*NM-(N-1)
NM2-NM+1
C
C
C
C
FILL
UP
DO
12
13
14
11
A d ,
DC 12
A( I,
DO 1 3
A ( I ,
DO 1 4
A( I,
DC
15
16
19
20
21
25
c
c
c
c
c
15
A d ,
DO 1 6
A( I,
OC 1 9
A( I , I +
DC 2 0
A ( I , I DO 2 1
A( 1 , 1 DO 2 5
A ( I , I )
INVERT
CALL
C
C
I-l)= C .O
1=1,NMl,1
I +l) = - B K 3 d
I=N,NMN,N
I+l)=G.O
DC
c.
23
24
ICO
26
• '•
22
)
1 = 1 , NMN, 1
N ) = —3 K 4 ( I )
1=N1, FMN,1
N ) = —4 K 2 ( I )
I = N M N 1» N H , 1
N)=-3K0(I)
I = I , N, 1
= 3 K6 d )
MATRIX
MATINV(
S T A R T THE
NORMALIZE
XC= X ( I )
22
FIRST
I=Nl,NM ,l
n =iJK5d)
1 = 2,NM,1
I - l ) = - 3 * l d >
I = N , N M, N
1 - 1 ) =- B O ( I )
I=N1
, NMN1 , N
♦♦♦LINEAR
C
C
0.
DC 1 C 1 = 1 , N M , 1
DG 1 0 J = 1 , N M , 1
A ( I , J ) = C.O
CONTINUE
10
11
WITH
"A' '
a
,NM,OE
E I G E N VALUE
PRC3LEM**+
INNER I TE RAT I ON
THE T R I A L F U N C T I O N
1 = 1 , NM
xm=xm/xo
INITIALIZE
T HE E I G E N V A L U E
EI C- EN1 = 0 . 0
DO I C C J J = 1 , 1 0 0
DC 2 3
1 = 1 , NM
Y (1) *0 .0
DO 2 3 J = 1 , N M
Y ( I) = Y (I) + A (I,J ) * X C J )
EIGEN»Y(NN)
D C 2 4 1 = 1 , NM
X(1)=Y (I)/EIG EN
IF
(ASS(EIGcN-£IGENl).LE.EPSl)
E I GF . N l = t I G E N
WRI TE
(6,95)
GG T O 1 0 7
EIGEN*1.C/E1GEN
.
-1 Z|0-
GO
TO
26
c
c
c
WPITE(t,6A)
WRI TE
(6,96)
JJ
EIGEN
CHANGE C O L U N M E I G E N V E C T E P )
M A T R I X T O SO' J ARE M A T R I X
X2(M1»N1)
I S C O M P O N E N T S OF E I G E N V E C T O R I N T HE G E O M E T R I C A L
J1«0
DO 2 7 I x ^ , M l
DC 2 7 J = 2 , N 1
J1*J1+1
X 2 (I,J )= X (J 1 )
27
C
C
28
C
C
CONTINUE
ALONG Z - A X I S
DO 2 3
1 = 1 , Ml
X2 ( 1 , 1)=0.0
'
-
ALONG R - A X I S
DO 2 9 J 3 1 , N 1
29
X2 (1,J )=X?(2,J )
C
C
C«2.998F8
CHARGE 3 1 . 6 0 2 E - 1 9
EPSILGS=3.aSAE-12
EMASS=9.109E-31
AKB3 1 < 3 8 E - 2 3
W x S C » T ( E I G E N ) *C / A6
W1=W/(3.1A15A*2.)
WPITE(6,9A)
to1
WR I T c ( 6 , 8 9 - )
C
C
C
C
C
C
♦♦♦♦CALCULATE
E-F1FLDS
IN
Z-
THIS
AND
R-COMPUNtNTS
PRCGRAM
ARE
PEAK
OF
E-FIELD**+*
VALUES
AND
U**2=E+E/2
C
C
C
C
A1
D C A 1 1= 1 , Ml
DO A1 J = 1 , N 1
Cl(I,J)=1.0/(A6*DK(I,JJ+EPSILON+W)
C
DC A3
1=2,M
0=0.0
-
<. 3
C
C
31
C
C
DO A3 J = 2 , N
D-D+1.0
E Z ( I , J ) = C 1 ( I , J ) / D M X 2 ( I , J - U ) - X I ( I , J - 1 ) ) / { 2 . 0 + A6.)
E R ( I » J ) 3- C i ( I * J > / D M X 2 ( I + l » J ) - X ? ( I - l , J ) ) / ( 2 . 0 + A 6 )
CONTINUE
A L O N G THE R - A X I S ( Z = C )
D =0.0
D O 31 J = 2 , N
D s D * 1•0
EZ(1.J) =C1(1,J)/0MX2(1,J+1)-X2(1,J-1))/(2.*A6 )
ER(1,J)=0.
CONTINUE
ALONG THE Z - A X I S ( R x O )
D O 32 1 = 1 , M l
E Z ( I , 1 ) = 2 . * C 1 U , 1 M ( X 2 ( I , 2 ) ) / ( A 6 )
E R ( I » 1 ) 3C .0
-U1-
SPACE.
32
CONTINUE
C
C
METAL
? GUN DA F Y
DC
33
J 5 *N 1
along
T HE
SIDE
WAL L
ALONG
T HE
BOTTOM
1 * 1 , Ml
D-FLOAT(JD)
E Z ( I , N 1 ) * 0« C
E R (I,N 1 )» 0 .
CGNTINUE
33
C
C
MET AL BOUNDARY
D * 0 .0
DC 3 A J = 2 , N
WAL L
D=D+1.0
E Z ( M 1 , J ) = C 1 ( M 1 , J ) * ( X 2 ( M1 , J + l ) - X 2 ( M l , J - l ) ) / < 0 * 2 . 0 * A 6 >
'
ER(Ml,J)=C.C
3 A
• CONTINUE
C
EZ(M1,N1)=0.G
ER(M1,N1)=0.0
C
c
c
C
U
SQUARE
C.
0 0 AC 1 = 1 , M l
DO AO J = 1 , M 1
U S C d , J )= ( E f t d , J ) * E R ( I , J
AO
)
+
E Z d , J )* E Z (I, J M / 2 . 0
CONTINUE
C
C
NORMALIZE
U
SQUARE
TO
THE
INPUT
MI CROWAVE
P04ER
C
F * 0 .0
DO A 7 1 = 2 , M , 2
DC A 7 J = 2 , N‘» 2
• F6"US0(I,J > *C K (I,J)*J
F 7 = ( U 3 0 d + l , J + l)*f.>K (I+l,J + l ) * ( J + l ) +U S 0 ( I + ] , J - l ) * D M 1+1, J - l ) * ( J - l )
# + U S C ( 1 - 1 , J + l ) * D K ( 1 - 1 , J + l ) * ( J + 1 ) + U S O ( 1 - 1 , J - l ) * CK ( 1 - 1 , J - l ) ♦ ( J - l ) )
F 8 = ( U S G ( I + i » J ) + rX ( I +• 1 , J ) ♦ J +■ U S O ( J - l , J ) * D K ( I - l . J ) * J
+
•
A7
HfUSQd, J + l )* 0 K ( I »J + l ) ♦ ( J +l )
F=F + A . * a s * * 3 * ( A . / 9 . * F 6
+
CONTINUE
+ U S Q d ,j'-U *r > K d . J - i ) * ( J - l ) )
F7/36.
+ F 8/9 .)
C
UG=a*P/(F*to*EPSlLGN)
DC AA 1 = 1 , M l
DO AA J = 1 , N 1
AA
BUSQ(I ,J )= U C * !J S O (I,J )
CONTI NUE"
C
c
C
C
NORMALIZATION
F OR
THE
DENSITY
G»0.0
DO A 5 I = 2 , M > 2
DO A 5 J = 2 , N * 2
C5 = C H A R G E * C H A R GE / ( A . + ' W * W * E M A S S * A K B * T )
C
G6=EXP(-C5*BUSQ(I,J) )*J
G 7 * E X P ( - C D + j US 3 ( 1 + 1 , J + l ) ) * ( J + l ) + E X P ( - C 5 * B U S Q ( I + l , J - l ) ) * ( J - l )
* + E X P ( - C t ’> e j S Q d - l , J + l ) ) i : ( J + l ) + E X P ( - C S v 3 U S C ( I - l , J - l ) ) * ( J - l )
G 8 = E X P ( - C 5 + > i u S 3 ( I + 1 , J ) ) •> J + x P ( - C 5 ♦ E U S 0 ( 1 - 1 » J ) ) * J
K + - E X P I —C 5 * B U 5 w ( I , j + - l ) ) * ( J + l )" + c x ? ( - C b * *i •; S 5 ( I , J — 1 ) ) * ( J - 1 )
G = G + A . * A f c * * i * ( A./V*Gfc + G 7 / 3 ' j . + G R / 9 , )
A5
CONTINUE
-H2-
C
DO 4 6
I«1,M1
DO 4 6 J = 1 , N 1 ■
G N C * E M A S S * E PS l L G N * v . * W / { C H A p G E * O H A P G E )
ON«TGTAL/(G)
DEN ( I , J ) * U f « * E < P ( - C 5 * E U S Q ( I » J I I
CONTINUE
oonn
46
CALCULATE
DIELECTRIC
CONSTANTS
DO 3 1 5 I « l , M l
DO 3 1 5
J=1,N1
B K ( I , J ) = 1 • C— D E N ( I , J ) / QNC
CONTINUE
oooo
315
DERIVATIVES
OF
E K • S ( D I E L E C T . CONST . )
DO. 3 5 I * 2 , M
• •
DO 3 5 J = 2 , N
B K Z ( I , J ) = ( d < ( 1 + 1 , J ) —« K ( 1 - 1 , J ) ) / ( 2 . 0 * A 6 )
'
35
BKP ( I » J ) = ( 6 K ( I , J + 1 ) - 5 K ( I > J —1 ) . ) / C 2 • 0 * A6 )
CONTINUE
36
AL ONG T H E Z - A X I S
DO 3 6 I = 2 , M
B K 2 ( I / 1 ) = ( E M I + i , 1 ) - BK ( 1 - 1 , 1 ) ) / ( 2 • 0 * A6 )
BKP(I,1)=0.C
CONTINUE
C
C
C
BKP( 1 » i ) = 0 . G
BKZ(1,1)=0.0
C
C
•
37
ALONG THE
THE R - A X I S
DO 3 7 J = 2 , N
BKZ(1,J)=0.0
BKP ( 1 » J ) = ( P. K( 1 , J + l ) - 3 K ( 1 , J - l ) ) / ( 2 . 0 * A 6 )
CONTINUE
C
BKZ( 1 , N i )=0 .0
B K R (l,N l)= C » .*D K (l,M )-4 .*B t< (lfN > +4 . * B i < ( l f N - l ) ) / ( 2 . * A t )
C
C
38
A L O N G T H E oOTTO. N M E T A L
EJLNOARY
DO 3 0 J = 2 > N
BKR( M l , J ) = ( B K( M1 , J +l ) - B K ( M l , J - l ) ) / ( 2 . * A 6 )
BK Z ( M l f J ) = ( 3 . 0 « p < ( M l f J ) - a . C * B . < ( M 1 - 1 , J ) + e K ( M l - 2 , J ) ) / ( 2 . * A 6 )
CONTINUE
C
6K M N lf
BKZ ( M l ,
BKP ( M l ,
BKZ ( . 1 1 ,
C
C
l)=G.O
i ) = ( 2 . * B K ( M l , 1 ) - 4 . - M K ( M, 1 ) + o K ( + - 1 , 1 ) ) / <2 . * A 6 )
N1 ) = ( 3 . 0 * 3 K ( M l f N l ) - 4 . 0 * i l K ( M l f M) + 3 K ( M l » N - 1 } ) / ( 2 . * A6 )
f l l ) = ( 3 . * 5 * ( M l , M l ) - 4 . * B K ( M , N 1 ) + 6 K ( M . - l , N l J) / ( 2 . + A 6 )
AL ONG THE S I C E ME T A L
WAL L
DO 3 9 1 = 2 , M
B K Z ( I f N l ) = ( 2 K ( I + l , N l ) - < K { I - 1 , N 1 ) ) / ( 2 . * Af c)
39
BKR( I , N l 1= I 3 . * R K( I . N l ) - 4 . *BK( I , N ) + B K ( I , N - l ) ) / ( 2 . * A 6 )
CONTINUE
C
IF
(A 6 S (D K (2 ,2 )-o K (2 ,2 ) J
DC
DO
199
199
. L E . EPS 5 )
C
1 = 1 . Ml
J«lf'.l
-H3-
GO
TO
330
OK C I , J ) = 3 < ( I , J >
DKZ<IfJ) = i*Z( I,J )
DKP( I f J ) =3*P( I f J )
199
CONTINUE
200
CONTINUE
W R I T E ( 6 , 69)
WRlTEtfcf69)
WRI TE
(6,96 )
330
WR I T E ( 6 f 9 6 )
H R I T E C 6 / 9 3)
I CQUNT
C
W R I T E ( 6 , 9 4 ) Kl
WRITE(6, 113)
C
W R IT E (6 f69)
WRITE(6fE9)
C
410
DO 4 1 0 1 = 1 , M l
W R I T E ( 6 f 8 3)
( £ Z( I f J ) fJ =l f N l )
W RITE(6fll4)
C
420
DG 4 2 0 1 = 1 f Ml
WRI TE
( 6f 83)
( ER( I fJ )
>J = 1
, N l )
C
400
WR I T E ( 6 , 1 1 2 )
DO 4 0 0
1 = 1 , Ml
WRITE(6f93)
( 3 US 3 ( I , J ) , J = 1 f N 1 )
C
440
•WRITE(6f 115)
CO 4 4 0
1 = 1 ,.'1 1
WP. I TE ( 6 , £ 3 ) ( D 2 N ( I ,
450
WP. I T E ( 6 f l l l )
DO 4 5 0
1 = 1 , HI
WRI TE ( 6 , 9 3 )
( 3K ( I , J ) , J = 1 , N l )
J
),
J
= 1 , N1)
C
C
•
W R I T E ( 6 , 69)
WRlTE(6,f9)
WRITE(6,117)
6.0
W R I T E ( t f 11=)
PI
WRITE(6,119)
T
WR1TE(6,94)
wl
64
63
WRITE(6,97)
C
F GRMAT ( / / / / " * * * * * * 9
CF
F O R M A T ( / / 1 2 ( I X , h l C . 4»)
92
94
95
96
97
98
93
111
112
FORMAT( / / / / 1 0 X , 17)
FORMAT!//"
RESONANT F PEOL ENCY I S } " , E 1 9 . 6 , " H Z " )
FO P M A T(////"***N J
I N N E R S O L U T I O N F OUND A F T E R
100
I T E E AT 1 O N S * * ♦ " )
F O R M A T ( / / / / " * * * M0 C U T E R S G L U T I u N F O U N D A F T E R
100
I T E R A T I O N * 1* " )
FORMAT( / / "
CUALITY FACTDP= " , F 2 0 . 5 )
F 0 R M . A T ( / / l l H f ;IG£NVALUE = , F i 0 . 5 J
F ORMAT ( / / / / / "
* * ■ > • > * n c-r O U T E R I T E R A T I O N
IS * * * * * * J" , I I 0)
FORMAT!////" ***OIElECTRIC
C O N S T A N T AT E A C H ME S H P O I N T * * * " )
F O R M A T ! / / / / " * * * S O L A h' E QF E - F I E L O
I N MKS A T E A C H M E S H P O I N T * * * " )
113
114
115
117
FORMA T (
F O R MA T (
F ORMAT
"FOPMAT(
INNER
ITERATIONS
I S* * * * * * ", 1 1 0 )
/ / / " * * ' F Z - C L M ‘ p r . N E f . T OF F - r I F. LO ( N O T NOR M A L I Z E D ) * * * * " )
/ / / " * * * J . - C ' 1 M P L . jL M S
O f E - F I E L D ( N j T N U * M AL U E D ) * * * + " )
( / / / / ' ,Jl + * v D E N S I T Y
I n C U L I C MET ER * < • * • * « )
/ / / / "
AfcFAGE
PL ASMA O E f o I T Y
IS;
" . E29.6,"PER
CUBIC CM")
-1H-
' "
"
118
119
FOPMAT( / / / / "
M I C R O W A V E P 0 <i £ P I S
:"»F2C.b,"
F OP MAT ( / / / / • •
P L A S M A T E MP E ft A TlJP £ } " , F 2 D . 2 » "
WATTS")
DEGREE I N
KELVIN")
C
107
STOP
C
END
C
SUBROUTI NE M A T I N V { APRAY, NOPOES, DET )
I N V E R T A S Y MM £ T R I C M A T R I X AMI)
CALCULATE
C
C
C
C
C
C
10
11
21
23
24
30
31
32
41
43
50
51
53
60
61
63
70
71
74
75
80
64
83
DETERMINANT
IK(K ) = I
J K CK ) = J
CONTINUE
IF
(AMAX)
4 1 , 3 2 , A1
DET=0.
GC T O 1 4 0
I = IK CK)
IF
(1-K)
21,51,43
DO 5 0 J = 1 , NCR 0 E R
SAVE=ARRAY(K,J)
. A RP A Y ( K » J ) = A R ft A Y ( I , J )
ARR6Y(l,J)*r-SAVE
•
J =JK(K )
IF
(J-K)
21,61,53
DO 6 0 1 = 1 , N O R D E R
SAVE = A R R A Y ( I , K )
A RP A Y ( I , K ) = £ r ft A Y ( I , J )
A R P A Y ( I , J ) = —S A V E
DO 7 0 I = l , N 0 9 O E t
IF
( I —K ) 6 ? , 7 0 , 4 3
A R R A Y ( I , K ) = - A - « f t A M I , K ) / AMAX
CONTINUE
DO 8 0 1 = 1 , N OR D E R
DO e o J = 1 , N C R 0 £ R
IF
(I-K )
74,60,74
IF
(J-K)
76,60,76
A R R A Y ( ) , J ) = A p ft A Y ( I , J ) ♦ A R R A Y ( 1 , K ) * A R R A Y ( K » J )
CONTINUE
DC 9 0 J = l , N O R D E R
IF
(J-K)
8 3 , 9 0 , e3
ARRAY(K,J)=AftftAY(K,J)/AMAX
90
CONTINUE
APRAY ( R , K ) = 1 . / A M A X
100
101
DET=OET4AMAX
DO 1 3 0 L « l , N O S O E K
K=NQPD£P L +1
J = I K ( K)
105
ITS
USAGE
CALL M A T I N V ( A R P A Y , N C R D E P . O E T )
ARRAY INPUT MATRIX
hHICH
I S R E P L A C E D SY I T S I N V E R S E
NCR DE R D E G R E E O f M A T R I X ( G R D t f t OF D E T E R M I N A N T )
DET D E T E R M I N A N T OF I N P U T M A T R I X
REAL A R R A Y , A M a X , S A V E
DIMENSION A R R A Y ( 1 2 1 , 1 2 1 ) , I K ( 1 2 1 ) , J K ( 1 2 1 )
. DET=1.
DO 1 0 0 K = l , N O R D E R
AMAX=0.
DO 3 0 I = K , N G ft D E R
DC 3 0 J = K , N C R ' D E R
IF
(AP. S( AMAX) ARS(ARRAY(I,J))>
24, 24,30
A MA X = A P. R A Y ( 1 > J >
IF
(J-K)
i l l , 111,105
DO 1 1 0
I ■ 1 » ! i C ft 0 L ft
S A V (' s A K r A Y ( I , .< )
A P P A Y ( I , K ) = -/.= ■ » AY ( I , J )
"
-H5-
110
111
113
120
130
140
A R P A Y ( I » J ) * S AVE
I * JK( K )
IF
(I-K )
1j C » 120#1 13
DC 1 2 C J = l # N i V < D t K
SAVE= » ARS A Y ( « # J J
A R R A Y ( K# J ) > - A i J » ' A r ( I # J )
ARP A Y ( I # J ) = S A V E
CONTINUE
RETURN
E ND
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