, for similar length discharges in the four tubes oriented vertically. Absorbed power density,
, versus absorbed power, Pp, at a constant pressure of 265 torr. ..... Overall diagnostic scheme. Symbols are defined in the text and the number in each box refers to the section in this chapter which describes that part of the analysis .................. Approximation of the experimental plasma/cavity geometry with an idealized plasma/cavity geometry. Cross sectional geometry of the EM boundar value problem used in the analysis (not to scale . Unloaded cavity Q, Q , for discharges inthe four tubes oriented vertigally ............. Electron density, N , for discharges in the four tubes oriented vertically ............. Effect of adding power on electron density at a constant pressure of 265 torr ........... ix . 51 53 55 57 58 60 61 62 64 68 7O 84 85 86 Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure A-3 A-4 A-5 Effective collision frequency, v , for discharges in the four tubes oriented vertiEally ....... Radial dependence of |Er(r)| and IEZ(r)| for the average axial point in the standing wave (265 torr, 4.0 mm tube) ................. Radial dependence of IE (r)| and IE (r)| near the plasma for the same diséharge paramgters of Figure 6.5 ........................ Effect of adding power to the distribution of |Ez(r)| (265 torr, 4.0 mm tube) .......... Changes in IE (r)| with absorbed power for the l.5 mm tube at 265 torr .............. Plasma electric field strength, E , for discharges in the four tubes oriented verticglly ....... Effective electric field, E , for discharges in the four tubes oriented vergically ......... Ee/p versus p for discharges in the four tubes oriehted vertieally ................ Gas temperature, T , for discharges in the four tubes oriented vergically ............. Electron temperature, T , for discharges in the four tubes oriented vergically ........... Relationship of filament shape to measured axial distributions of IE I2 and |H¢|2 for an argon discharge at l46 to r ............... Cross sectional area of the plasma filament compared to the computed axial distribution of Absorbed power density,
, versus pressure.. . . Electron density, Ne, versus pressure ....... Changes in
and N with changes in absorbed power for argon discharges at 174 torr ....... Comparison of
for the argon surface wave discharges in a 4.0 nm tube horizontal to
for the argon cylindrical cavity discharges in a 4.0 mm tube vertical .................. 87 89 9O 92 93 94 96 97 98 99 A-5 A-8 'A49 A-lO A-ll Figure A-7 Figure A-8 Figure A-9 Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure A-lO B-l B-2 3-3 8-4 8-5 B-6 13-7 8-8 B-9 13-10 B-lli B-lZ Figure B-l3 Figure C-l Radial dependence of (E (r)| and IEr (r)|for an argon discharge at 28 orr ............ The two radial density profiles used in the comparison of surface wave propagation along an inhomogeneous plasma filament to a homogeneous plasma ....................... Ez(r) for the homogeneous and inhomogeneous cases . Er(r) for the homogeneous and inhomogeneous cases . General discharge appearance at low pressure in the TMOlZ mode .................. Plasma load line and approximate cavity resonance curves for a constant length argon plasma in the l3 mm tube at .03 torr. . . . ........... Absorbed power per unit length (P p/L) versus tube size and pressure ................. Absorbed power density,
, versus pressure and
tube size ......................
Electron density, Ne . versus pressure and tube
size .......................
Unloaded cavity Q. Qu . versus pressure and tube
size .......................
Effective collision frequency, ve’ versus pressure
and tube size ...................
Electron temperature, T , versus poR and tube size.
e
Radial dependence of IE (r)| and IE (r)| for an
argon discharge at .04 torr in the T3 mm tube . . .
Ee/poR versus poR ..... . . . . .‘ .......
Microwave coupling efficiency, Eff, versus pressure
in the 13 mm tube .................
Microwave coupling efficiency, Eff, and electron
density,"
Pp at .03 Torr
Change in discharge appearance in the TM 1 mode
for the high efficiency point in Figure 9- I2 . .
, Theoretical radial and axial distributions of E
and E2 in the THO12 mode ..............
xi
, versus absorbed power in the discharge,
A-lS
A-l7
A-lB
B-3
B-S
8-12
8-13
8-15
8-16
B-lB
B-l9
B-ZI
EM
rf
GHz
KW
ATM
ABBREVIATIONS AND NOTATION
electromagnetic
radio frequency
gigahertz (l09 cycles/sec)
megahertz (lO6 cycles/sec)
kilowatt
atmosphere
Charge on electron
mass of electron
conductivity
propagation constant
permittivity
permittivity of free space
permeability of free space
radian excitation frequency
radian plasma frequency of the electron gas
electric field
magnetic field
peak absolute value of electric field
plasma electric field (peak absolute value)
effective electric field
electron density
effective electron-neutral collision frequency
electron temperature
xii
gas temperature
microwave coupling efficiency
quality factor of a resonator
unloaded cavity 0
loaded cavity 0
incident power to cavity
reflected power from cavity
total power absorbed by cavity
power absorbed by the plasma
power absorbed by the coupling structure
absorbed power density in plasma
gas pressure
reduced pressure
average plasma diameter
resonant cavity length shift
cavity length between shorting planes
excitation probe depth
xiii
CHAPTER I
INTRODUCTION
This dissertation describes a detailed experimental investigation into
high pressure argon microwave discharges. These discharges can be charac-
terized as being steady-state, weakly ionized plasmas with contracted
diameters of l-3 mm and lengths up to l6 cm. A single cylindrical micro-
wave cavity mode was used to both couple energy into the discharges and
diagnose discharge properties. The pressure domain of the experiments was
40-l300 torr and all experimental results are for non-flowing discharges.
The main objectives were to: (I) study the formation of contracted
discharges in a microwave cavity, (2) determine the efficiency of coupling
microwave power to the discharges, and (3) generate detailed information
about argon discharge properties (such as electron density, effective
collision frequency and discharge electric field strength). To achieve
these objectives, initial experiments were performed to understand the
general behavior of the discharges in a microwave cavity and the orienta-
tion that the discharges take in different cavity modes. As the experi-
ments progressed, it became apparant that in certain cavity modes the
experimental plasma/cavity geometry could be mathematically modeled. Thus,
the main focus of the experiments became one of diagnostics; i.e. the
discharges were generated in well defined microwave fields in a single
cavity mode and the interaction of the discharges with those fields was
measured and analyzed.
Although the emphasis of this dissertation is placed on high pressure
argon discharges generated in a cylindrical cavity, two related experi-
mental investigations are described in the appendices. High pressure
standing surface wave discharges in argon, krypton and xenon were inves-
tigated using a similar diagnostic philosophy. The characteristics of
these surface wave filamentary discharges exhibited many similarities
with those generated in the cylindrical cavity. Also, low pressure argon
microwave discharges were investigated in the cylindrical cavity by extend-
ing the experimental techniques (which were independent of gas pressure)
down to pressures between .02 and l.0 torr. These low pressure results
were compared to other argon microwave discharges diagnosed with different
methods.
The overall layout of the disseration is as follows. Chapter II contains
a detailed literature review of other steady state microwave discharges
produced at atmOSpheric pressure. Chapter 111 describes the experimental
system, basic operation of a microwave cavity for sustaining a plasma and
several measurements that were made on the cavity EM fields and on the
discharges. General observations about the argon discharges are presented
in Chapter IV. These observations provide necessary background information
for understanding the EM and plasma analysis contained in Chapter V.
Discharge properties such as electron density, collision frequency, gas
temperature, electron temperature, plasma electric field and coupling
efficiency are described in Chapter VI. Overall conclusions and some
recommendations for further research are given in Chapter VII. Finally,
the appendicies contain the high pressure standing surface wave results
(Appendix A), the low pressure argon results (Appendix B) and some basic
equations related to the analysis of the discharges (Appendix C).
CHAPTER II
REVIEW OF STEADY-STATE, ATMOSPHERIC
PRESSURE MICROWAVE DISCHARGES
2.l Introduction
This chapter reviews significant work on steady-state, high
pressure microwave discharges. Emphasis is placed on discharges pro-
duced at l ATM for later comparison with experimental results of this
dissertation. General reviews of microwave discharges for other pressure
regimes are documented elsewhere [1,2].
A microwave coupling structure is a device designed to focus elec-
tromagnetic energy onto a plasma. Coupling structures can be classified
according to the principal type of EM wave phenomena used by the device
to transfer energy to the plasma [2]. These types are:
(l) radiating waves or evanescent fields (non-guided EM waves),
(2) fast EM waves (phase velocity greater than the speed of light),
and
(3) slow EM waves or surface waves (phase velocity less than the
speed of light).
The review contained in this chapter is organized according to the
classification described above. Although a given coupling structure is
usually designed for one type of electromagnetic coupling, it can often
transfer energy to a plasma through a combination of types of waves[2].
Examples of this will be pointed out in the review.
2.2 Discharges Sustained by Radiating Waves or Evanescent Fields
The most common coupling structure using this type of EM wave
phenomena has been called a coaxial microwave "torch" [3] or Vplasmatron"
[4]. Figure 2.l describes a coaxial torch showing the location of the
discharge and giving representative dimensions [5]. Microwave power
in a TEM mode propagates down the coaxial line toward the open end.
The center conductor is tapered at the end to aid in focusing the electric
field. The discharge is ignited by drawing a small spark from the center
conductor tip. Axial gas flow keeps the discharge from arcing to the
outer conductor and extends the discharge out from the end of the torch.
With higher and higher levels of absorbed power, the axial gas flow
eventually becomes insufficient to prevent arcing. Experimentally,
this limit has been put at a power level of l0 KW [6]. Discharges pro-
duced in a coaxial torch are similar to lower frequency unipolar dis-
charges [7].
In l95l, Cobine and Wilbur reported experimental results on
atmospheric pressure discharges produced in a coaxial microwave torch
[3]. Their device was coupled directly from a magnetron cavity in which
l KW tubes of varying frequency (.5 - l.l GHz) were used. Impedance
matching was accomplished with a stub tuner on the magnetron cavity
and a telescopic section in the coaxial line. Gases used in the dis-
charges were COZ’ He, He(+.3% H2) N2, 02, A and air. A discharge was
attempted in pure hydrogen but was not successful. A pyrex nozzel was
used on the end of the torch to stablize the gas flow and the discharge.
The Optimum flow rate was reported at 70 ft/min linear velocity at the
exit of the torch.
Quantitative measurements by Cobine and Wilbur were limited.
quartz tube ____
discharge
water cooled aluminum tip
center conductor (2.0 cm)
outer conductor (4.8 cm) ——-
gas inlet -—>l: :l
E‘— tefl on
support
waveguide to coax
trans1t1on VT) sliding
short
)- I. —
“Fl Hf"
c: :3
water out ———.r1 cooling
water
inlet
Figure 2.1 Coaxial microwave torch
Electrical probe characteristics were taken by inserting a small, air
cooled nickel probe into a nitrogen discharge. Using standard single
probe theory, the electron temperature was estimated at TO5 0K and the
electron density at log/cm3. Treating the probe characteristics as
3 was made for electron
conductivity data, a different estimate of l013/cm
density. Estimates of gas temperature in a nitrogen discharge were made
using a bouyant force method and resulted in a range of l900 - 3700 oK.
Cobine and Wilbur made numerous qualitative observations on the
visual appearance of the discharges, differences in the different gases,
and the effect of the discharges on center conductor tip materials.
Photographs of the discharges are included in the paper. A typical
nitrogen discharge of absorbed power approximately 350 watts was 2 cm
long and about .5 cm in diameter, looking very similar to a horizontal
flame. An important observation by Cobine and Wilbur was that discharges
in the monatomic gases (argon and helium) were cool compared to discharges
in the polyatomic gases. This difference was attributed to the molecular
dissociation - recombination mechanism, allowing the coupling of more
power per unit volume into the polyatomic gas discharges.
In l974, S. Miyake, gt _l., published a detailed investigation of
a nitrogen discharge at atmospheric pressure produced with a coaxial
torch [4]. Their power source was a 3 KW, CW magnetron operating at
2.45 GHz. Power was coupled into the torch through a rectangular wave-
guide system containing a circulator, standing wave meter, directional
couplers and a waveguide to coaxial transition. A water cooled tungsten
electrode formed the tip of the center conductor. A quartz tube extended
out of the torch in order to stablize the gas flow. Axial flow rates
were 30 - 200 liters/min.
Miyake made several types of quantitative measurements. Power
transmitted to the discharge and to radiation was measured as incident
minus reflected power using the directional couplers. Electron density
was measured in N2 + 5% H2 by spectroscopically measuring the Stark
broadening of the HB line. Radiated power from the end of the torch
was estimated with a small loop antenna. Impedance was measured using
the standing wave meter. Relative spectral intensity measurements of
the HB line were made and reported in arbitrary units. Using the electron
density measurements, electron temperature was determined from the Saha-
Eggert equation assuming local thermal equilibrium in the discharges.
A typical nitrogen plasma at 2 KW transmitted power was l0 cm long
and about .5 cm in diameter. The maximum temperature was 6700 OK and
the maximum electron density was 7 x 1013/cm3. Several graphs are
reported showing axial profiles of plasma temperature, electron density,
microwave radiation and spectral intensity. Radial distributions of
temperature and emission intensity are also reported. The functional
dependence of plasma properties on transmitted power and gas flow rate
are presented.
In l975, Batenin,__t._l., described an atmospheric pressure hydro-
gen discharge produced with a coaxial torch [8]. The power source was
a variable power, 5 KW magnetron of frequency 2.45 GHz. The trans-
mission system and method of impedance matching was similar to Miyake's,
except that no directional couplers or standing wave meter were included.
A quartz tube containing the discharges extended out of the end of the
torch. A significant difference is this coupling structure as compared
to those previously described was the placement of a resonant cavity on
the end of the torch. The power transmitted to the discharge was
reported to be enhanced by proper adjustment of the cavity length. Thus,
the actual microwave coupling to the discharges probably represented a
combination of evanescent fields and fast waves. The cavity walls and
center conductor were water cooled and all power absorbed measurements
were made calorimetrically on the cooling water.
The principal diagnostic techniques employed by Batenin were spec-
troscopic methods. The major point of the article was to generate
spectrosc0pic data on atmospheric pressure hydrogen microwave discharges
in order to compare with earlier controversial results by Kapitza [9]
(described in the next section). A detailed description of Batenin's
equipment and spectrosc0pic analysis is given in the article. The
results for a 2 KW discharge were an electron density of 3.5 x 1015/cm3,
electron temperature of 10,000 0K and a gas temperature of 8500 oK.
Batenin's conclusion was that the discharge represented a cold, weakly
ionized, nearly equilibrium plasma.
2.3 Discharges Sustained by Fast EM Waves
Coupling fast EM waves to a high pressure discharge usually involves
the use of a microwave cavity. A rectangular resonator, similar to the
one used in reference [6] is illustrated in Figure 2.2 and a cylindrical
cavity is described in detail in Chapter III. A simple description of
a cavity is that it consists of a section of waveguide (supporting fast
waves) terminated by two short circuits, forming a standing wave. Power
is coupled into the cavity through probe or loop excitation or by aperture
coupling from another waveguide. When a plasma is generated inside a
resonant cavity, the Q usually dr0ps significantly (indicating that power
is now being absorbed mainly by the discharge instead of the cavity
I/,/ A
metal cylinder
quartz tube
t",’/”l””l’ III, III I
contracted
discharge sliding short
III/I/l/III/llllll/ 'I.I/I/I//,//I II ‘/I/.
I I’ll/III,
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7 \ \\\\\\\\\‘.\\\ \\\\\\\\\\\' \\\\\' \\‘ \“‘\ \\ . x .‘ .‘ . - . . \ \\ . - \ . . .\\\\\\\\\ \ .\\\\\\\\\ . . t“ \\ x ,\ . \\ .\ .\\
II
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'
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1‘9" .
.V
v
‘ .0 O O
TEOl mode
powe r-—,
T
‘\
‘“7‘ r
s
A
‘9'9§\\ s
QO\O\‘.0.
“&L1 000009“90\0
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9‘
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_\\\\\\‘ ‘ \\A\\\\\S\'.\\\\\\\ _\‘.‘.. \\ .\\\‘ ‘ \\ t, t\\\\\\\\\\‘ \\\' \\\\\\‘ \\\\ ‘ ' \ .\\\ .\‘\\\\\\\‘.\'.\ \\\\\\\\ \\ \
inductive § §
coupling window 3 :
tapered rectangular S §
waveguide ; y side view,
g 3 rectangular resonator
-.____.—/
ll
gas flow
Figure 2.2 Retangular resonator for coupling fast EM waves to a
plasma column
10
walls) and the dispersion characteristics change (requiring frequency
tuning or cavity length tuning). In simple plasma/cavity geometries,
these effects can be modeled mathematically. Thus, the microwave
cavity can also be used as a diagnostic tool. General descriptions of
microwave plasma/cavity operation are given in references [10,11]. An
important note is that the discharges described in this section are
electrodeless as compared to those generated by a coaxial torch.
From 1950-1970, P.L. Kapitza led an investigation of hydrogen
microwave discharges at atmospheric pressure. A 1970 paper [9] summarized
his experimental system, results and conclusions; and a 1972 paper [12]
described in more detail his apparatus and measurement techniques. The
experiment consisted of a 175 KW magnetron of frequency 1.55 GHz, aper-
ture coupled to a 20 cm diameter cylindrical cavity. The cavity was
Operated in a TMOln cavity mode which has a maximum of longitudinal
electric field on the cavity axis. Length tuning of the cavity was
accomplished with a sliding short around which electrical contact was
made with a hydraulically inflatable thin walled copper tube. Cavity
walls and sliding short were water cooled and power absorbed to the
discharge was determined calorimetrically on the cooling water. The
cavity was sealed by using air cooled quartz windows over the coupling
aperture and over small observation holes on the cavity wall. Pressures
up to 5 ATM could be maintained with most of the experimental work
being done at 1-2 ATM.
Discharges were ignited by placing a small tungsten wire attached
to a quartz rod near the center of the cavity. The tungsten wire was
rapidly rotated parallel to the longitudinal electric field and then
quickly removed to prevent melting. Once ignited, the discharges tended
to float upwards due to the bouyancy force. To maintain the discharges
l]
"freely floating" in the center of the cavity, a gas circulation system
was used. Typical contracted hydrogen discharges (or “filaments") were
described as being about 1 mm in diameter and several centimeters long.
The filaments formed most easily in and were parallel to the maximum
longitudinal E-field in the center of the cavity. Plasma length in-
creased with power to a maximum of about 10 cm (1/2 the resonator wave-
length). Further increases in power caused the diameter to increase
until the filament broke up into two shorter and thinner filaments.
Discharges were obtained in absorbed power levels up to 20 KW. A large
dr0p in cavity Q due to the plasma was determined by measuring relative
strengths of electric field inside the cavity. These measurements in-
dicated that most of the power was absorbed by the discharges and little
was lost directly into the cavity metal walls.
Kapitza's diagnostics were primarily emission spectroscopy. Electron
density was measured from Stark broadening for absorbed power levels
below 10 KW and were of the order of 1015/cm3. Above 10 KW, the mag-
nitude of the Stark broadening decreased to where at 17 KW the electron
density was calculated to be only on the order of 1013/cm3. Kapitza
concluded that this phenomena was due to a masking effect by a cloud or
sheath of cold plasma surrounding a dense hot filament. To obtain density
information for power levels above 10 KW, a specially designed spectro-
meter for use in the infared region was constructed. At 12.4 KW, an
3 was determined with this method where
Stark broadening gave only 1.4 x 1013/cm3. The optics employed by'
electron density of 7.3 x 1015/cm
Kapitza were refined enough to give emission intensity distributions
transversely across the filament (where the dimension was about 1 mm).
Electron temperature was estimated in two ways and presented the
12
most controversial results. An intense continuous spectrum of radiation
0
in the wavelength range of 1050-1350 A was observed. Assuming this
radiation to be bremsstrahlung, relative emission intensities corre-
6 OK - indicating a "hot" or
sPflfidfid to an electron temperature of 10
fully ionized core of the plasma filament. Using the electron density
information and assuming the existence of a hot core of plasma surrounded
by a cold equilibrium sheath, the electron temperature was calculated to
6 7 oK for the core and 6 - 7 x 103 oK for the sheath. To
be 10 - 10
account for this large temperature discontinuity, Kapitza proposed the
existence of a double layer of charge (or space charge sheath) on the
boundary of the hot plasma core. This double layer was assumed to be
sufficiently strong to contain energetic electrons within the core.
In analyzing Kapitza's spectroscopic data, Dymshits and Koretskii
[13] reached a different conclusion regarding the electron temperature
of the hydrogen filaments. For a wavelength region of 1050 - 1250 2,
they calculated the relative contributions of recombination radiation
and bremsstrahlung for a cold, equilibrium plasma (electron temperature
of about 104 oK). It was found that the intensity of the recombination
spectrum was much greater than the intensity of the bremsstrahlung, and
that the order of magnitude of the recombination spectrum was sufficient
to explain Kapitza's experimental results. Dymshits and Koretskii also
calculated the intensity contribution of the wings of the Lyman —a line
(1216 A) for a temperature of 9000 0K and concluded that this factor
must also be considered in explaining the experimentally determined
radiation intensities. After pointing out other experimental results
of Kapitza that indicate that the temperature of the discharges was
low, Dymshits and Koretskii concluded that the hydrogen filaments were
most probably cold, equilibrium discharges.
13
Arata, _t__l,, investigated atmospheric pressure microwave discharges
in nitrogen (1976) [6] and in hydrogen (1978) [14]. Both studies used
the same experimental system and basic measurement techniques. The
power source was a 30 KW, .915 GHz magnetron. A rectangular waveguide
system containing a circulator, directional coupler and an E - H tuner
transported microwave power to a rectangular resonator, similar to the
one illustrated in Figure 2.2. Incident microwave power could be varied
continuously up to the maximum of 30 KW. The coupling structure was
water cooled in the vicinity of the discharge tube and absorbed power
to the discharges was determined by calorimetry on the cooling water.
Impedance matches were good with only a few percent of the incident power
being reflected. All powers were reported in incident power with the
understanding that the absorbed power was at least 80% of the incident
power. A helical flow of gas was necessary to keep the discharges
centered in the pyrex tube which ran transversely up through the resonator
(as indicated in Figure 2.2). The discharges were ignited by a movable
tungsten wire which was removed from the discharge tube after ignition.
At an incident power level of 5 KW, the length of the nitrogen
discharges filled the transverse section of the resonator. Upon adding
more power, the length and diameter of the discharges continued to in-
crease. At 20 KW, the length was approximately 30 cm. The size of the
pyrex discharge tube was found to have a large effect on nitrogen dis-
charge diameters. For example, in a 20 KW discharge the diameter was
1.5 cm in a 4 cm diameter pyrex tube but only .5 cm in a 2 cm pyrex
tube. Tube size also affected plasma pr0perties (diagnostics were the
same as Miyake, t al., [4]). For the 20 KW discharge in the 4 cm tube,
electron density was 1.3 x low/cm3 and plasma temperature was 6300 oK.
14
At the same power in the 2 cm tube the electron density was 3.5 x 1014/
cm3 and the temperature increased to 6800 oK.
Results of Arata in hydrogen made more extensive use of equilibrium
and nearly equilibrium plasma modeling. An extensive discussion of the
spectroscopic results was included in the paper along with a comparison
with the conclusions of Kapitza. A typical hydrogen plasma produced by
Arata was 1 mm in diameter and 20 cm in length at a power level of 20
KW. The electron density was 5 x low/cm3
and the electron temperature
was 8900 - 12,000°K depending on the plasma model. Arata reached the
same conclusion as Batenin and DymshitS'that atmospheric pressure
hydrogen filamentary discharges were cold, nearly equilibrium, weakly
ionized discharges.
The fact that Arata's hydrogen and nitrogen discharges extended
well outside the rectangular resonator (into the transverse cylinder)
indicates the presence of energy transfer from the fast wave inside the
resonator to another type of traveling wave. Arata suggested that this
traveling wave was a TEM wave with the plasma acting as the center con-
ductor of a coaxial line. However, as was pointed out by Moisan [15],
the more probable explanation is that the traveling wave was a surface
wave .
2.4 Discharges Sustained by Slow EM Waves
A surface wave launcher that has been used to produce high pressure
microwave discharges is shown in Figure 2.3 [16]. This coupler consists
of a coaxial cavity with a short gap between the center conductor and
front cavity wall. Microwave power is introduced into the cavity through
a microcoaxial line, terminated by an excitation 100p. Upon prOper
mammFa mcwcwmucoo
wasp wmcmcumwu
15
I
a a
”Waugh, . . .
o .4“. o . o . o . on... s .
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Aeoposace so em.Nv
Lopuzucou Louzo
m.~ mczmmm
Acmuosmwu Eu o.FV
Louozucoo coucou
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coop
cowumuwuxm
gooum mecwe saw:
pgozm mcwchm
QFQou mexmooocuws
16
adjustment of the cavity, intense electric fields are generated in the
gap region causing breakdown of the gas in the quartz tube (which runs
coaxially inside the center conductor). After breakdown, the microwave
electric fields launch traveling surface waves extending the plasma
column away from the gap. Since the traveling wave is transferring
energy into the plasma, it attenuates. When the wave is insufficiently
intense to maintain a high enough electron density in the plasma, the
wave is cut off and the plasma column ends.
In 1979, Hubert, _t._l., reported on properties of atmospheric
pressure surface wave discharges in argon gas [17]. Using the surface
wave launchers similar to Figure 2.3, Hubert investigated discharges
over the frequency range of .28 - 1.7 GHz. Their coupling structure
was called a "surfatron" [18]. All discharges were contained in thin
quartz tubes ranging from .5 - 5.0 mm inner diameter. Little external
cooling of the tube or internal gas flow rate was needed to prevent
melting of the quartz. A coaxial type transmission system transported
power from the oscillator to the surface wave launchers. Power absorbed
was measured using directional couplers and power meters located in the
transmission system. Absorbed powers ranged from 50 - 150 watts for
most of the experimental results reported in the paper.
A 100 watt argon discharge in a 5 mm tube was approximately 14
cm long with a contracted diameter of approximately 1 mm. Flow rate of
gas produced little change in discharge dimensions in the 5 mm tube.
Keeping the absorbed power constant, a small increase in plasma diameter
was noted with increasing frequency. Electron densities were measured
in argon + .5% H2 using Stark broadening. The addition of hydrogen did
not affect the macroscopic appearance of the argon discharges. Electron
17
densities of 2 - 5 x low/cm3 are reported depending on absorbed power.
Gas temperatures were estimated in argon + .3% N2 using a spectroscopic
measurement of a W2 rotational line. In this case, the addition of
nitrogen greatly affected the appearance of the discharge by causing its
length to decrease to about 1/2 of the length in pure argon for the same
power level. Typical rotational temperatures were 2100 - 2800 OK de-
pending on input power. Neither the electron density nor the rotational
temperatures were affected by excitation frequency.
In a 1980 paper [15], Moisan et__l,, continued the investigation
of atmospheric pressure argon surface wave discharges. Stark broadening
measurements of electron density were compared with densities obtained
with numerically generated dispersion curves. Treating the plasma as
a homogeneous, lossy dielectric, the dispersion curves were obtained by
solving the EM boundary value problem for surface wave propagation.
The electron densities obtained in this manner were about 50% lower
than those determined from the Stark broadening. Both measurements
represented an average electron density over the cross section of the
discharge and the discrepancy between the results was not explained.
2.5 Literature Review Summary
Properties of the atmospheric pressure microwave discharges reviewed
in this chapter are summarized in Table 2.1. Average power densities
were calculated from information given in the papers.
18
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CHAPTER III
EXPERIMENTAL SYSTEM, MEASUREMENTS AND PROCEDURES
3.1 Introduction
The experimental system to be described in this chapter consists
of: (l) a microwave circuit for generation, transmission and measurement
of microwave power; (2) a cylindrical cavity for transferring the micro-
wave energy to the discharges; and (3) a quartz tube for containing the
discharges in varying gas pressures and flow rates. This system is
very similar to one described in detail by Fritz [1]. Since the micro-
wave cavity is used to both generate and diagnose the discharges, a
section concerning its performance as a resonator is included. Also
described in this chapter are the basic measurements made on the plasma
and the cavity fields for use in diagnosing discharge properties.
3.2 Description of Experimental System
The microwave circuit is described in Figure 3.1. The power source
was a well filtered, 2.459 GHz, variable power (0 - 500 watts) magnetron.
When operated above approximately 30 watts, frequency drifts of the
source were less than 0.5 MHz. Microwave power from the source was
coupled into a rectangular waveguide system containing a water cooled
ferrite circulator and two 20 dB directional couplers. A 30 d8 attenuator
and a power meter were attached to each directional coupler. The inci-
dent power was isolated from the reflected power as shown in the figure.
There was no measureable attenuation or cross coupling in the circulator,
ensuring that power readings of incident and reflected power in the
19
20
cylindrical microwave cavity
7/8 inch flexible
coax
microwave source
incident
power meter
30 d8 attenuator
waveguide
to coax
transition
I k |
/ L I
circulator
reflected
power meter
30 dB attenuator
{T 4" J ‘V~Alv-
- matched
20 d8 directional coupler load
Figure 3.1 Diagram of microwave circuit
21
waveguide system were accurate.
Microwave power from the waveguide system was transported to the
cylindrical cavity through a 7/8 inch flexible coaxial cable. Attenua-
tion in this cable was measured to be approximately a .46 d8 drop (measured
through two waveguide to coax transitions). Coupling of microwave power
into the cylindrical cavity was accomplished with a coaxial transition,
shown in Figure 3.2, attached to the end of the flexible coax. Essentially,
this transition extended the center conductor of the coaxial line into
the cavity to a depth that could be manually varied. A series of fingers
machined into the outer conductor of the transition provided excellent
electrical contact with the coupling port of the cavity.
Figure 3.3 describes the microwave coupling structure. The resonant
portion (or "cavity") was formed by the 17.8 cm diameter cylindrical
brass pipe and the two transverse brass shorting planes (or "shorts").
One of the shorts was adjustable to provide a variable cavity length of
from 6 to 16 cm. Water cooling was provided by capper tubing soldered
on the brass pipe and the two shorts exterior to the cavity. The dis-
charges could be viewed and photographed through a copper screened window.
A rectangular brass piece was soldered onto the t0p of the coupling
structure and seven E-field probe diagnostic holes spaced 1.8 cm apart
were drilled through this piece and the cavity wall. A single hole was
drilled through the fixed short as indicated in the figure to allow a
shielded loop to be put into the cavity. The diagnostic probe and leap
are described later in this chapter. Figure 3.4a defines the cavity
length, Ls, and the coupling probe depth, Lp, for later use in the
dissertation.
Quartz tubes of varying diameter were located coaxially in the
22
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23
E-field probe ”9Ct3“99‘a’ 17.8 cm i.d.
diagnostic holes brass p1ece brass pipe
I O O O O O \f .
l
hole for
shielded .
100p _. common
3 11
@-
fixed
short
screened viewing
window
11‘
sliding short
coupling port
(used for cooling air)
Not shown: (1) coupling port used in all
experiments, located directly
opposite screened window 3.7
cm from inside wall of fixed
short. (2) copper cooling tubes
0n cavity exterior
Figure 3.3 Experimental cylindrical cavity
24
a. definitions of LS and L
cavity wa 1
fixed sliding
short short
11/ tile]
to flexible
coax
_' JHIAjjjjji]
I I cavity
: : coupling port .
r-Ls-a
I
b. location of brass collars
fixed short sliding short
brass collars
Figure 3.4 a. Definition of cavity length, L , and excitation
probe depth, L . b. Location of Brass collars if
used in the exBeriments.
25
coupling structure. When tubes of 1.0 cm or less outside diameter were
used, brass collars were inserted into the open holes on both the fixed
short and the sliding short as shown in Figure 3.4b. The collars aided
in maintaining the cavity mode field orientation in the region of the
open holes as long as they were motionless and did not touch the quartz
tube (which often vibrated). For quartz tubes larger than 1 cm o.d.,
the collars had little beneficial effect and were not used. For protec-
tion from microwave radiation, 5 cm diameter copper screen cylinders
were attached around the open holes exterior to the coupling structure.
The quartz tubes ran coaxially inside these screen cylinders.
The vacuum and flow systems are described in Figure 3.5. All
experiments were done using argon gas and no measureable flow rate,
although a slight amount of gas flow was actually present to ensure
purity of the gas. A mercury manometer was used to measure gas pressures
from 40 - 1300 torr. Prior to each experiment, the entire system was
evacuated to approximately .001 torr, outgassed and flushed with argon.
3.3 Performance and Operation of the Cylindrical Cavity
3.3.1 Microwave Circuit Definitions
A simple description of a microwave cavity has already been given
in Section 2.3. The basic theory of microwave circuits and cavities
is given in many EM texts [19-21] and is omitted here. However, this
dissertation makes use of some essential terminology which is described
briefly below and in more detail in references [21-23].
(1) Resonance curve - a plot of power absorbed by the cavity or
circuit as a function of frequency (for a fixed cavity length)
or as a function of cavity length (for a fixed excitation
26
rotameter
quartz ()
discharge tube‘\\\\‘
CD
argon
gas in
cylindrical
cavity TTT‘H
mercury
manometer
to vacuum .4
pump \
Figure 3.5 Vacuum and flow system
(2)
(3)
(4)
(5)
27
frequency).
Critically coupled - the.impedance looking into the cavity
is matched to the transmission line at the resonant
frequency. When this condition is met, all the incident
power to the cavity at the resonant frequency will be
absorbed and none will be reflected.
Undercoupled and overcoupled - the impedance at the
resonant frequency is not matched. When undercoupled,
the real part of the cavity impedance is greater than
that of the transmission line; and when overcoupled, the
reverse is true.
Unloaded cavity 0 (Qu) - an indication of the magnitude
of losses in the cavity walls and in the dielectric (or
plasma) contained in the cavity. Qu can also be thought
of as an indication of the frequency selectivity of
coupling power into the cavity hypothetically not con-
nected to the transmission line.
Q = an x Stored energy in cavity = :2;
u 0 Power dissipated in cavity Af
where fo is the resonant frequency and Af is the frequency
width at the half power points on the cavity resonance
curve.
Loaded Q (QL) T essentially the Q of the cavity coupled
to the external circuit. QL is normally measured and
then related to Qu'
28
QL = 2nf x Stored energy in circuit _ fo
0 Power dissipated in circuit 7 Af
where now Af is defined in terms of the circuit resonance
curve.
In definitions (4) and (5) above, the generic meaning of the word
"loaded" is referring to the cavity acting as a load on the transmission
line and is not referring to the presence or absence of dielectric
losses in the cavity. Qu will be used throughout the dissertation as the
quality factor of the cavity which contains both metal wall losses and
plasma losses and Quo will denote the unloaded cavity 0 of the cavity
without plasma present. Also, in the measurement of QL’ the stored
energy is approximately entirely in the cavity and the dissipated energy
is approximately in the parallel conductances of the cavity and the
source. When the cavity is critically coupled, Qu = 20L and when nearly
completely undercoupled Qu = QL'
3.3.2 Experimental Empty Cavity Modes and Quo of the TM012 Mode
A resonant cavity is excited in discreet cavity modes. When the
excitation frequency is fixed, the modes of a cylindrical cavity cor-
respond to distinct cavity lengths (or eigenlengths). Table 3.1 lists
the theoretical eigenlengths for an ideal empty cavity of the same
dimensions as the experimental cavity at 2.45 GHz. Since any deviations
in cavity geometry (such as the open holes or excitation probe) caused
the ideal cavity mode to be perturbed, the experimental eigenlengths of
the modes never exactly corresponded to theory. Table 3.1 also lists
the experimental eigenlengths for the empty cavity with and without the
experimental cavity experimental cavity
without collars with collars
theoretical L L L L
mode eigenlength so p0 so p0
cm cm cm cm cm
TElll 6.69 (l) 6.82 0.58
TMon 7.21 7.43 0.22 7.29 0.24
TE2H 8.24 8.37 -0.27 8.40 -0.06
TEon 11.27 11.24 1.90 (2) 11.27 1.90
10.28 0.61
TMlll 11.27 10.38 0.37}(3) 11.57 1.15
TE”2 13.39 (1) 13.55 0.81
TM012 14.41 14.56 0.00 14.47 0.12
TE3n 15.50 15.66 -0.08 15.67 -0.08
(1) could not identify mode
(2) not critically coupled
(3) two different resonances of the same dipole mode,
polarity of fields different
Table 3.1 Theoretical cylindrical cavity mode eigenlengths
compared with the experimental eigenlengths (LS
o) .
for the empty cylindrical cavity with and without
collars. Excitation frequency - 2. 45 GHz. Probe
depths (L 0) were those required for critical
coupling Bnless otherwise noted. L 0 varied
slightly depending on Quo’ p
30
brass collars in place. The coupling probe depths listed in the table
are those required for critical coupling except where otherwise noted.
These coupling probe depths are all small - indicating that the excita-
tion probe only slightly perturbed the cavity modes when critically
coupling the empty cavity.
QL of any mode was measured by sweeping the empty cavity, as shown
in Figure 3.6, and displaying the resonance curve on an oscilloscope.
This was accomplished when critically coupling the cavity so that
Q
the measured value. Several factors affected the experimental values
uo = 20L. The accuracy in measuring Quo was estimated at 1.10% of
of Quo' Although the brass collars aided in maintaining the proper mode
field patterns, they significantly lowered Quo in most modes. For
example, Q o in the TM012 mode at 2.459 GHz dropped from 12,100 to
u
6000 because of the collars. Quo in the TE011 mode, however, was
relatively unchanged. The absence of the radiation screening and the
cleanliness of the cavity also affected Quo‘ Without screening, Quo
in the TM012 mode dropped by over 1/2 indicating that unshielded large
0pen holes can cause radiated power losses which could present a sig-
nificant safety hazard. With the screen on, Quo in the TM012 mode ranged
from 8,000 to 12,100 depending on cleanliness of the cavity. The highest
value of Quo achieved in the TM mode at 2.459 GHz was 12,100 which
012
compared reasonably well with the theoretical limit of 15,500 in this
mode at the same frequency [20].
Actual experimentation with a plasma was done only in the TM012
mode for reasons explained in Chapter V, although a plasma could be
sustained in any cavity mode and in a variety of other modes not present
in an empty cavity[24]. The theoretical empty cavity field patterns
31
oscilloscope
sweep generator
O
sweep rf
out out
I
verti ca' ’t external
d.c. input" 7 horizontal input _
isolator
wavemeter directional
coupler
«rifle—G D
crystal
detector
cavity
Figure 3.6 Circuit used for the measurement of loaded Q, QL’
of the empty cavity.
32
for the TM mode are described in Appendix C for reference. Typical
012
resonance curves in this mode for the empty experimental cavity are
shown in Figure 3.7. LS was fixed at 14.48 cm for these curves and the
horizontal axis was calibrated in terms of frequency. The resonance
curves illustrate that coupling to this mode was very sensitive to probe
depth. When Lp was increased to greater than 1.0 cm, the resonance curve
became so broad that it was difficult to find precisely. It can also
be seen from Figure 3.7 that Lp affected the resonant frequency. Thus.
when operating at a specific frequency, Lp affected the eigenlength of
the cavity.
3.3.3 Basic Cavity Operation for Generating and Maintaining a Discharge
The discharges were ignited in the experimental cavity at any gas
pressure with the following procedure. A moderate amount of power (10 -
20 watts) was coupled into the empty cavity in the TM012 mode by adjust-
ing LS and L to the correct positions for critically coupling the cavity.
P
The positions were not precisely the same as those listed in Table 3.1
due to the presence of the quartz tube. Breakdown of the gas was subse-
quently easily achieved by using a Tesla coil to inject a few electrons
into the discharge zone. The discharges could be started most easily
in the pressure range of l - 10 torr. Breakdown of the gas could also
be accomplished without the use of the Tesla coil if sufficient power
was coupled into the cavity. This technique was avoided, however,
because of the increased risk of arcing elsewhere in the cavity (such
as around the brass collars) due to the high field strengths required
for breakdown.
After breakdown was achieved, the cavity was mismatched due to the
power absorbed (%)
33
100
b.
75 ._.
so A—-
a C .
25 -.
, \
0 l I “‘ih.
2.457 , 2.458 2.459
frequency (GHz)
”J
g]
:"ml
LL
.1111.
overcoupled b. critically coupled c. undercoupled
Lp = .45 cm Lp = -.09 cm Lp = f.55 cm
QL = 1637 OL = 6550 QL = 10,600
Figure 3.7 Typical resonance curves of the TM mode showing
the effects of changing L nQ aRd the resonant
frequency. (screening attgched to cavity, no collars,
empty cavity, LS = 14. 48 cm)
34
presence of the plasma. This mismatch was the result of: (1) the plasma
losses tending to undercouple the cavity (requiring an adjustment of Lp)
and (2) the dielectric nature of the plasma causing the eigenlength of
the cavity to shift away from Ls. To return the cavity to resonance
(i.e., to critically couple the cavity). both L and LS had to be adjusted.
P
In practice, these adjustments were not independent because of the dyna-
mical nature of coupling to the discharges. As one parameter was adjusted,
the plasma volume or properties changed due to increased power absorption
requiring further adjustments of the other parameter.
The basic tuning process was accomplished by observing the reflected
power meter in the rectangular waveguide system. Assuming that the pres-
sure and incident power level were set at the desired values, Ls and Lp
were varied to produce a minimum of reflected power. For a high pressure
argon discharge of length 8 cm in the center of the cavity, this minimum
could always be made zero (i.e., the cavity could always be critically
coupled for this plasma geometry). When the lengths of the discharges
extended across the entire length of the cavity (as was desired for the
analysis), critical coupling was often not achieved. In these instances,
however, the reflected powers were all small - typically 5% or less of
the incident power which is nearly critically coupled.
When a plasma is sustained by a resonant circuit, a discharge/circuit
instability can occur under high Q (i.e. low plasma loss) operation when
critically coupling the cavity [10]. This instability was not encountered
when coupling to the high pressure argon discharges due to the large
losses in the plasma, lowering Qu to less than 100. The circuit insta-
bility was encountered in lower pressure experiments (less than 1.0
torr) and is described briefly in Appendix 8.
35
3.4 Plasma and Cavity Diagnostic Measurements
3.4.1 Identification of Experimental Measurements
Once a desired geometry or length of plasma was generated and the
cavity properly tuned, four measurements were taken: (1) total power
absorbed into the cavity (Pt)’ (2) resonant cavity length shift (AL),
(3) calibrated radial E-field at a reference point at the cylindrical
cavity wall (Erw)’ and (4) average discharge diameter (d ). These
ave
measurements and definitions associated with them are described in this
section. How these measurements are utilized in the analysis to deter—
mine discharge pr0perties is described in Chapter V.
3.4.2 Total Power Absorbed by the Cavity (Pt)
Various powers in the microwave circuit can be defined as follows:
Pi - incident power at the terminal plane of the cavity
Pr - reflected power at the terminal plane of the cavity
Pt - total power absorbed by the cavity which includes
both plasma losses and cavity wall losses
Pp - power absorbed by the plasma
PC - power absorbed by the cavity walls
Obviously, Pt = P1 - Pr‘ The determination of Pi and Pr involved
correcting the actual power meter readings in the waveguide section for
the attenuation in the flexible coax and calibration factors on the
directional couplers and attenuators. The waveguide system itself was
assumed lossless.
3.4.3 Determination of Resonant Cavity Length Shift (AL)
Assuming that the cavity (with plasma and quartz tube present) was
36
properly tuned for resonance in the TM012 mode (or as near to resonance
as possible), then LS became the experimental eigenlength of the cavity.
Defining L50 as the empty cavity experimental eigenlength in the TM012
mode, AL was determined by:
Length shifts were determined on the tuning mechanism exterior to
the coupling structure and were measured with a vernier caliper. Typical
shifts were on the order of 3-4 mm and accuracy was estimated at i_.l mm.
The measurement of AL was complicated by the fact that cavity configura-
tion changes, coupling probe depths and frequency drifts of the source
all affected the experimental empty cavity eigenlength. These effects
were all accounted for in the determination of AL.
3.4.4 Determination of Erw
Small electrical probes, constructed from 2 mm o.d. microcoax,
were inserted into the diagnostic holes of the cavity to probe the
IErl and |H¢| distributions of the TM012 mode. Figures 3.8 and 3.9
describe these probes and their location in the cavity. The straight
probe (E-field probe), was inserted into one of the seven diagnostic
holes on the t0p of the cavity. This probe coupled out a small fraction
of power assumed proportional to I'Erl2 which was measured with a power
meter. A typical axial distribution of the measurements of the straight
probe is compared in Figure 3.10 to the theoretical distribution of
lErIZ. The shielded loop was sensitive to |H¢l2 and confirmed a similar
axial distribution as to that in Figure 3.10 but with maximums and
37
to power meter
slip f1t
2 mm o.d. microcoax
brass piece
cavity W31]
/
mm exposed
center conductor
\ power
\ meter
\
\
\
I".
microwave .
_. cav1ty
power
coupling
probe
Figure 3.8 E-field probe and probe circuit
38
sliding
electrical cavity wall
contact
2 mm o.d. l/J
microcoax
2 mm o.d.
solid wire
piece \
\
\
\\ shielded loop
to power .4...
meter approximately
constant. The extension of the filament in Figure 4.4b into the regions
of a null of E2 indicated some coupling to a surface mode. However, this
process was limited because further power additions caused the filament
to abruptly split into two shorter and thinner filaments as shown in
Figure 4.4c. These filaments appeared to repel each other by occupying
opposite sides of the tube as indicated in the cross sectional view of
4.4c. The transition between 1 filament and 2 filaments exhibited
hysteresis since the reverse process (when decreasing power) consistantly
took place at a lower power level than the forward process. When adding
more power (Figure 4.4d) more sections of plasma were produced in the
manner described above.
Adding power to the discharges at other pressures and in other
tube sizes had similar effects. There was. however, little tendency
for two or more filaments to form side by side in the smaller tube
sizes (4.0 mm and 1.5 mm i.d.). Instead, there was more of a tendency
for filament length to extend outside the cavity further than would be
expected from the fringing fields (indicating coupling to a surface mode).
Above 100 torr, the ability to increase plasma volume in this manner
was limited by the ability to match impedance (i.e. as incident power
was increased, increases in reflected power could not be avoided by
retuning.the cavity).
The phenomenon of a single filament splitting into two filaments
was usually very abrupt. In one case, however, the splitting appeared
gradually and is shown in Figure 4.5. In this particular case, the 12
53
filament beginning
to split into two
center of filaments
cavity 4 mm
diffuse
. a» _ '4': ° \
fixed intense
short filament
Figure 4.5 Filamentary argon discharge beginning to split into
2 filaments (1 ATM, P = 100 watts, 12 mm tube,
vertical orientation).
54
mm tube was oriented vertically and the main portion of the filament was
nearly centered in the tube when the splitting began. The spliting
occurred near the axial center of the filament (the t0p of the figure)
where the discharge radius was a.maximum.' Using approximate electron
densities from Chapter VI, the skin depth of this discharge (a quantity
defined in terms of the penetration of a plane wave into a conductor)
was about equal to the maximum radius. Another experimental observation
on the splitting phenomenon was that when discharges were oriented hor-
izontally (where there were strong asymmetric bouyant forces) filament
splitting occurred more frequently than the vertical orientation and
the transitions were always abrupt. The above observations suggest
that mechanisms important to the splitting phenomenon are: (l) the
relationship between the filament radius and the radial intensity dis-
tribution of the microwave E-field across the filament (i.e., the depth
of penetration of the E-field), and (2) asymmetric forces due to thermal
conduction and/or convection, or asymmetric EM forces.
4.5 DischargeITube Geometries and Their General Effects on the Discharges
Most of the experiments were accomplished with the specific geometry
of Figure 4.1a (i.e. filamentary discharges extending across the length
of the cavity with only a single filament in the tube cross section).
Given that geometry, varying the location of the discharge in relation
to the quartz tube wall produced noticeable changes in discharge pro-
perties. The location was varied in two different ways: (1) by orienting
the Quartz tube and cavity horizontally or vertically, and/or (2) by
changing the size of the quartz tube.
Figure 4.6 describes the two orientations of the experimental cavity
55
a. vertical cross section
of tube:
quartz tube
/
discharge
cross section
of tube:
6. horizontal
quartz ube
discharge
Figure 4.6 General effect of a change in discharge tube
orientation. a. Vertical orientation.
b. Horizontal orientation.
56
and the approximate location of the discharges. When in a horizontal
orientation, the bouyancy force tended to cause the filaments to float
up to the top of the tube. This was most noticeable above 100 torr in
the 25 mm and 12 mm tubes but was also observed in the 4 mm tube. Below
approximately 100 torr there was little noticeable effect of the bouyancy
force. In a vertical orientation, the discharges tended to remain centered
except for the ends of the filaments which curled toward the quartz wall.
In the 25 mm tube oriented vertically, upward convection currents were
visually apparent at pressures above 350 torr by a candle-like "flickering"
of the filament at the top. These currents made it difficult to keep the
discharges stable (i.e. motionless). Above 1 ATM, the discharges in this
tube shifted toward the quartz wall (asymmetric in the tube) and were
stablized by the wall.
In the horizontal orientation when discharges floated up next to
the quartz wall, two effects were noted: (1) discharge diameters were
smaller than those of vertically oriented discharges at the same absorbed
power level and in the same tube size, and (2) visual light intensity
of the discharges appeared to increase. Figure 4.7 displays the changes
in power density, , that occurred between the two orientations for
similar length discharges in the 12 mm tube. Above 100 torr, there was
a distinct difference in , with those of the horizontal discharges
being higher than those of the vertical orientation.
Similarly, changes in tube size with the discharges centered in
the tube also produced changes in discharge diameter and power density.
Figure 4.8 shows the four different tubes (vertical orientation, lengths
of discharges as in Figure 4.1a) and the approximate size and location
of the discharges. Figures 4.9 and 4.10 describe the resulting effects
103
MA
E 102
.3
:9
V
10
57
T
12 mm tube
2) horizontal
. vertical
I
\
l
D'
.__|__§11111 1 1 JJIJLJ,
102 103
p (torr)
Figure 4.7 Absorbed power density, , for similar length
discharges in the different tube orientations.
58
1.5 run inner diameter
‘llil’ 4.0 mm
discharge
12 mm
quartz tube
Figure 4.8 Discharge tube cross sections and the approximate
size and location of the discharges in the vertical
orientation.
59
on dave and . In the 25 mm tube, the pattern of Figure 4.1a could
only be maintained in a limited pressure range and is thus the reason
for the small number of data points in the figures. At any given pres-
sure, Pp was approximately the same in all tubes to produce the common
discharge length of Figure 4.1a (approximately 16 cm, which included the
ends of the filaments which curled into the region of the Open holes).
Thus, the differences in resulted primarily from the changes in
diameter which occurred in the four different discharge/tube geometries.
Figure 4.1] shows changes in with small changes in Pp for three
of the vertically oriented tubes at a pressure of approximately 265 torr.
For the 4 mm and 12 mm tubes, increases in Pp caused increases in volume
keeping approximately constant. In the 1.5 mm tube. however,
increased with Pp since volume increases were restricted.
The changes in other discharge properties for the four discharge
tubes oriented vertically are described in detail in Chapter VI. The
analysis by which those properties were determined (given in the next
chapter) depended upon the approximate rotational symmetry present in
the vertical orientation. Thus, discharges in a horizontal orientation
were not analyzed beyond the discussion in this chapter.
dave (mm)
60
,,gr I. 1.5 mm
1 || 4.0 mm
1 4‘~12.O mm
; 025.01nm
3.0 — l\t
I
4»
- \‘
\.\
\. \IS.
20 — \II o\
\ ‘\
l\ ‘
I\
I
e—e
\e.’
\
1.0 "' ‘3'-
e\.___.
11111111. 1. 1411111,
20 102 103
p (torr)
Figure 4.9 Average discharge diameter, dave’ for similar
length discharges in the four tubes oriented
vertically.
61
103 _—
__ . 1.5 mm
: r 4.0 mm ./.
: . 2: I ,/
__ ,/
_ ./
e/ '
.. /// .f///
e/. ./ /‘
102 _..- , . , / ‘ ..-_ _
C I
(w/cm3)
I I
DI \\\II
-\\>
‘1
/'
10 h———J——J.:i/:/: Ill
20 10
l l .J l I 14]] I l
2 103
p (torr)
Figure 4.10 Absorbed power density, , for similar length
discharges in the four tubes oriented vertically.
62
3 _..
10 __ II 1.5 mm
”’ || 4.0 mm
__ .A1 12 mm
.. ur—-—""""————4.
e/
./
102 —
3 .
£5
"’ A A
1—
10 J l J l J
20 30 40 50 60
Pp (watts)
Figure 4.1] Absorbed power density, , versus absorbed power.
Pp, at a constant pressure of 265 torr.
CHAPTER V
ANALYSIS OF THE EXPERIMENTAL DISCHARGES
5.1 Overall Analysis Scheme and Reasons for Using the TM012 Cavity Mode
To diagnose discharge properties such as electron density and temp-
erature, the experimental measurements were combined with an analysis
of a plasma/cavity geometry which approximated the actual experiment.
Due to the type of analysis, all discharge properties are average quanti-
ties, representing spatial averages of both radial and longitudinal
variations in the plasma. Figure 5.1 describes the overall analysis
and what information was gained in each step. The general flow of the
analysis was from the top of the figure to the bottom, with the four
experimental measurements that were defined in Section 3.4 being located
at the top. The number in each box refers to the section in this chapter
which describes that particular part of the analysis.
The power absorbed in the plasma (Pp), the power lost in the
coupling structure (Po) and the coupling efficiency (Eff) were deter-
mined from Pt and Erw using an EM perturbation solution on the TM012
mode fields. Average complex conductivity of the discharges (o) and
the electromagnetic fields (E(F) and H(F)) were determined by an EM
plasma/cavity analysis for a lossy plasma/ideal cavity geometry which
approximated the experimental geometry. The required inputs for this
determination were P , E
p rw’ AL, dave’ and the cavity and quartz tube
dimensions. Using the cold plasma conductivity model for a weakly
ionized gas discharge, average electron density (Ne) and effective
63
64
dave P1 ' Erw AL dave
5.2 EM perturbation
analysis
Eff Pp PC
5.5 Radial heat ' EM plasma/caVIIY
conduction model analys1s
‘(V 5.4 cold plasma
Tg conductivity
ve Ne
tabulated 5.6 Maxwellian
collision
cross sectio d1str1but1on funct1o
1
Te
Figure 5.1 Overall diagnostic scheme. Symbols are defined in
the text and the number in each box refers to the
section in this chapter which describes that part
of the analysis.
65
collision frequency (ve) were determined from 0. An approximate average
d and
gas temperature of the discharge (T9) was determined from Pp. ave
the quartz tube dimensions using a radial heat conduction model. Finally,
an average electron temperature (Te) was determined from v T , and gas
e’g
pressure using tabulated electron-neutral collision cross sectional data
for argon gas and assuming a Maxwellian velocity distribution function
for the electrons.
The principal reason for using the TM012 mode in the experiments
was the relatively simple geometry in which the long, thin filaments
could be generated. As can be seen in Figure 4.1a, the discharges were
basically coaxial in the cavity. In the vertical orientation (of Figure
4.8),this rotational symmetry was maintained inside each quartz tube.
8y approximating the non-uniform filaments with a homogeneous, lossy
dielectric rod, this approximate plasma/cavity problem can be mathema-
tically described. The other geometries of Figure 4.1 cannot be so
easily analyzed. Additionally, the TM cavity modes have traditionally
Oln
been used to diagnose accurate average discharge properties in plasma
columns on the axis of the cavity because of the rotational symmetry of
the fields and the strong component of E2 on the axis [24,26].
5.2 Coupling Structure Losses and Coupling Efficiency
The power lost in the coupling structure (PC) was determined with
an EM perturbational analysis. The basic assumption was that the pre-
sence of the plasma did not greatly alter the spatial distribution of
the fields from those of the empty experimental cavity in the TM012
mode. Evidence supporting this assumption was: (1) the very small
discharge volumes caused only small shifts in the eigenlengths, and (2)
66
direct measurements of the axial distribution of lErI2 at the cavity
wall always showed the presence of a similar standing wave with or with-
out the discharge present. Additionally, the numerical solutions for
the cross sectional field distributions in the modeled plasma/cavity
only deviated from those of the ideal empty cavity near the plasma in
the center of the cavity (i.e. the results were consistent with this
assumption). Examples of these numerically obtained field distributions
are given in Chapter VI.
Under the above assumption, PC with a plasma present in the cavity
was determined by using the field distributions of the empty experimental
cavity (the precise distributions of which were unknown and not needed
in the determination of Pc)‘ Since coupling structure losses at any
point are proportionaltxithe square of the field strength, Pc was deter-
mined by a measure of lErl2 at a reference point relative to similar
measurements on the empty cavity. With Erw and Pt being the measurements
described in Section 3.4, PC was determined by:
_ rw
PC — -———7 Pto (5.1)
where Erwoz and Pto were the measurements made on the empty cavity
critically coupled in the TM012 mode. As can be seen from equation
5.1, Erw did not have to be calibrated for this determination.
In a similar manner, the cavity Qu (with plasma present) was
determined by:
67
where Quo was the experimental empty cavity Qu measured at the same
time as Erwo and Pto were measured. It should be noted that the
resonance curve method of determining Qu (perhaps with a separate.
low power diagnostic circuit in a different cavity mode) was not
practical for the experiments. The reasons for this were: (1) the
plasmas brought Qu down to between 50 and 100, at which values the
resonance curve would have been completely washed out among the system
resonances; and (2) the high power excitation fields inside the cavity
would have interfered with the low power diagnostic circuit causing
filtering problems.
A coupling efficiency, Eff, to the discharges was defined as:
P
Eff = 100:prE (5.3)
t
where Pp and Pt are defined in Section 3.4 and Pp = Pt - Pc' Eff
expresses the ratio of power absorbed by the plasma to the total power
absorbed by the cavity. For a practical application, this ratio should
be high. A further discussion of the efficiency of coupling microwave
power to a weakly ionized plasma is given in reference [2].
5.3 Determination of Complex Conductivity and Plasma Electric Field
Discharge conductivity and the EM fields in the cavity were deter-
mined for an ideal plasma/cavity geometry which closely approximated
the experimental geometry of Figure 4.1a. This approximation is pic-
torially described in Figure 5.2. For the approximate problem, the
non-uniform filaments were replaced by an axially uniform, homogeneous,
lossy dielectric rod with diameter equal to dave of the filaments.
68
non-uniform
contracted d1scharge cavity
I] J’//quartz tube
‘IIn-uv”a-';:L""I~---—V
approximate
Faaznazuzuzanzgrznzunzzuln
/ \
perfectly conducting homogeneous plasma
ideal cavity column
\
quartz tube
Figure 5.2 Approximation of the experimental plasma/cavity
geometry with an idealized plasma/cavity geometry.
69
Essentially, the axial uniformity of the dielectric rod and cavity (with
ideal cavity shorts) allowed the standing wave plasma/cavity problem to
be equivalent to an axially uniform plasma/waveguide problem for the
purposes of the analysis. The amplitude of the plasma/waveguide problem
was determined by the average amplitude of the standing wave in the cavity
problem. This type of rotationally symmetric boundary value problem,
with an unmagnetized, homogeneous plasma on the waveguide axis, has been
analyzed in detail [11,24,27,28] and the method of solution is well
established [29].
Figure 5.3 describes the specific cross sectional geometry of the
plasma/waveguide problem used in the analysis. Region 2 was included
because the discharges were contracted in varying degrees away from the
quartz boundary. The quartz was assumed lossless with a relative per-
mittivity of or = 3.78. The outer metal cylinder was considered a
perfect conductor.
The solution to this boundary value problem was simplified by a
priori looking for the rotationally symmetric TM modes. Maxwell's
equations in cylindrical coordinates (e‘jmt implied) for the ith region
reduce to:
_ -jsz
Ezi(r?z) - 91(r) e
I d‘yo(r) °
_ QB __J____ -382
Er1(riz) ‘ kc, dr 9 (5-4)
jmci dvi(r) e-jBZ
H .(r,z) = Y
01 k . dr
Cl
70
region 1: homogeneous, lossy
plasma reg1on 2: free space
r §_a a §_r 5_b
region 3: quartz tube region 4: free space
b 5_rԤ_c c 5_rԤ_d
Figure 5.3 Cross sectional geometry of the EM boundar value
problem used in the analysis (not to scale .
71
where r,¢,z are the standard cylindrical coordinates and vi(r) satisfies
the modified Bessel equation of order zero:
2
d vi(r) 1 dvi(r) 2
dr2 +F dr ‘kci ii”) = 0 (5-5)
and where
2 2 2
kci 7 B 7 k1
2
2 _ cope
ki — o 1
5, = permittivity in region 1 (complex in region 1)
B = complex propagation constant (the same in all
regions)
w = radian exitation frequency
The solution to equation 5.5 is given in terms of modified Bessel
functions of the first and second kind of order zero:
Vi(r) = A, 10(kcir) + Bi Ko(kcir) (5.6)
(The choice of using modified Bessel functions or ordinary Bessel 4
functions is arbitrary since the numerics have to be typed complex in
either case. Modified Bessel functions were used due to convenience.)
When boundary conditions on tangential E and H are applied at the
interfaces, all coefficients A, and Bi can be eliminated except one
72
arbitrary coefficient. The resulting equation for a non-trivial solu-
tion is of the form:
No.51) = o (5.7)
The exact form of f(B.e]) is given as reference material in Appendix C.
The method of solving equation 5.7 is via graphical techniques or by
treating one of the parameters as known and then numerically searching
for the eigenvalues (the unknown parameter) using a complex root finding
routine. Note that the complex conductivity of the plasma, 0], is con-
tained in 6] via:
01
e] = 60 (l + jweo) (5.8)
In solving equation 5.7 for the analysis of the experiments, 8 was
treated as known (i.e. measurable) and c] was the eigenvalue. Equations
like 5.7 can have more than one eigenvalue 6] for a given 8 [28]. How-
ever, for the analysis of these experiments, 61 was unique for physically
realistic values of discharge properties. The values of effective
collision frequency, ve’ were expected to satisfy ve/w < 10. The eigen-
value c] was verified to be unique up to ve/w = 100 whereupon the
question of the existence of another eigenvalue was not pursued further.
For the analysis, the real part of 8 was determined from AL and the
theoretical empty cavity eigenlength at 2.459 GHz (Lth):
211
B = ———---—- (5.9)
73
The imaginary part of a was not measured directly, but the additional
experimental measurements of P and Erw were equivalent to a measure of
P
8.. This was accomplished by an iterative process: (1) a value for Bi
1
was assumed and 51 was computed; (2) when 61 became known, E(F) was
determined everywhere to within an arbitrary amplitude coefficient which
in turn was determined by the measure of Erw; and (3) the total power
absorbed in the plasma per unit length was calculated and compared to
Pp/L where L was the experimental plasma length (described in the previous
chapter). The above steps were iterated numerically until the calculated
absorbed power per unit length matched Pp/L.
Thus, the average plasma conductivity (0]), the E(F) and R(F) fields
in the plasma/waveguide cross section andtg were all determined from the
experimental measurements within the geometrical approximation already
described. A representative electric field in the plasma, Ep, was
defined for ease of presentation of the results since the computed
E-field cross sectional distributions were all similar. Ep was defined
as the value of |E(F)| in the cross section at the radial point where
the computed power density matched the experimental average power density
(Pp/V, where V was the measured plasma volume). E is the same as would
p
be calculated from a uniform E-field in a uniform plasma.
5.4 Determination of Average Electron Density and Effective Collision
Freguency
The simplest form of the electrical conductivity of a gas discharge
can be derived from the Langevin equation or from moments of the Boltzman
equation [30,31]. This form is called the cold plasma conductivity and
is regarded as an adequate description of the macroscopic conductivity
of a collisional, weakly ionized discharge:
74
e9 (v-szl (5-10) _
where
N electron density
C
II
electron-neutral collision frequency
The F dependence was dropped from Ne’v’ and 0 since only average
quantities were of interest in the analysis. If v is dependent upon the
electron velocity, v, (as is the case for argon) equation 5.10 is no
longer valid. However, by defining an effective collision frequency,
0e, as [31,32]:
00 3 3f
’ V 7% ‘2‘”
v = 0 vv 0) 23V (511)
ID V av dv
2 2
v(v) +01
where fO is the first term of the expansion of the velocity distribution
function of the electrons. the form of equation 5.10 remains valid with
ve replacing v.
Rewriting equation 5.10 using 0 = or + joi:
. e . w
0r + JO, = m 2 ’7’ 'J 2 '2 (5.12)
75
By separating equation 5.12 into real and imaginary parts, We and ve
were algebraically determined from o.
5.5 Determination of Gas Temperature
Approximate gas temperatures in the discharges were calculated
using a simple 2-dimensional radial heat conduction model. The geometry
of this problem was the same as that of Figure 5.3 with only regions 1
and 2 needed for the analysis. The basic assumptions for this analysis
were (1) axial uniformity; (2) power per unit length was dissipated
uniformly inside r = a through joule heating in the plasma, (3) power
was lost from the plasma only through heat conduction (convective losses
and radiative losses were neglected), and (4) the quartz boundary at
r = b was assumed to be at 3000 K (in the experiments, the quartz tubes
were cooled using forced air and did not heat up significantly). Be-
cause of the rotational symmetry, all variables were only a function
of the radial coordinate r.
The basic equation governing heat flow due to dissipated power in
a plasma is [31]:
v - (km v 10%)) = -%Re[3(_r) . 501*] (5.13)
For the geometry and assumptions of the experiment, equation 5.13
can be integrated to obtain a first order differential equation in r:
k(r) Egg _= - 2.1m P(r) (5.14)
76
where:
P(r) = total power dissipated within r for a plasma of
length L '
k(r) = thermal conductivity
T(r) = neutral gas temperature
anL = surface area (neglecting the ends of the plasma column)
The form for k(r) was taken to be [33,34]:
y
k(r) = ko T(r)2 (5.15)
Using parameters in reference [33], k0 for argon gas was calculated
to be 1.56 x 10'3 Joule/(meter-sec-OK3/2). A value of k0 used by Eden
for similar calculations on argon gas was 1.77 x 10"3 (same units)[34].
The latter value for ko was used in all calculations although it did
not make a significant difference which value was used.
The primary region of interest was r 5_a, where:
r2
P(r) = —7- P (5.16)
Solving equation 5.14 using this form for P(r) resulted in:
P 2
- 3/2 3 r 2/3
T(r) — [T(a) *W'IE (1 --—2-)1 (5.17)
0 a
where
p
_ 3/2 3 _p _b_ 2/3
T(a) - [300 + 4nk l. 1n(a)]
77
An average gas temperature was defined to be the average of the
maximum temperature at the center of the plasma and the temperature at
the plasma edge:
_.|
H
[T(o) + T(a)] (5.18)
(a
NI—l
5.6 Determination of Electron Temperature
The EM analysis described in Section 5.3 and the cold plasma theory
stated in Section 5.4 allowed the calculation of ve from experimental
measurements. By assuming a form for the distribution function, equation
5.11 can be solved numerically to obtain Te from Ve'
Defining:
p = pressure (measured)
Po = %%§_p = reduced pressure
(:(v) = collision cross section of argon (tabulated)
k = Boltzman's constant
Assuming a Maxwellian velocity distribution function [33], equation
5.11 can be simplified to:
v I: 27513, 9M d"
4'3 = .. ' (5.19)
po f0 g(v) dv
where
[11 V2
4 " 2:1
V
78
Using tabulated data for c(v) for argon gas [35,36], equation 5.19
was solved numerically to obtain Te for each data point. Similar cal-
culations have been done by Glaude et 1., on argon surface wave discharges
at low pressures [37].
5.7 Discussion of Potential Accuracy of the Results
5.7.l Accuracy of the Measurements and the Experimental Technique
The four measurements used in the EM portion of the analysis were
described in Section 3.4.) The accuracy in each measurement was estimated
to be: 1 1% in Pp and AL; and _+_10% in dave and EN. Potential errors
due to the cavity imperfections were approximately accounted for in the
measurement of AL. Frequency drifts of the source were small enough to
not present a significant source of error.
As a test on the overall accuracy of the experimental technique
(including the various cavity imperfections), the complex dielectric
constant of a homogeneous, lossy material was diagnosed. A quartz tube
filled with distilled water was placed in the cavity in the same location
as the discharges. To keep from heating the water above room tempera-
ture, the power level of about 50 watts from the source was scaled down
by a factor of 100 prior to entering the waveguide system and the measure-
ments were taken rapidly. A computed value of cr = 67-j10.5 of the
water compared reasonably well to an interpolated value from Harrington
[20] of cr = 77-j9.7. This result was well within the expected accuracy
of the technique and indicates that the experimental measurements and
analysis were adequate for diagnosing properties of a homogeneous
material.
79
5.7.2 Effect of Plasma Inhomogeneities
The analysis in Section 5.3 assumed a homogeneous plasma column
and, in effect, averaged out radial and axial variations in the dis-
charges.' The effect of radial inhomogeneities in plasma columns diag-
nosed with a TMO1n cavity mode has been investigated analytically [24].
For high density plasmas (mp > w), the average electron density deter-
mined by a homogeneous plasma model was found to be a good estimate of
the actual average electron density as long as the plasma radius was
less than or equal to the skin depth. Since all the discharges analyzed
in this dissertation met this requirement, radial variations were thus
not expected to introduce large errors into the computed averages.
For the high pressure surface wave discharges (Appendix A), the
effect of radial variations on dispersion characteristics and electric
field distributions was investigated analytically. This comparison
(on plasma filaments of the same size and electron density as the ones
generated in the TM012 mode) demonstrated that there was little change
between a radially inhomogeneous plasma and a homogeneous plasma with
an electron density equal to the average density of the radially inho-
mogeneous one. Because of the similarities in the field patterns inside
the plasma between the TM] surface wave mode and the TM01 plasma/wavequide
mode, similar results would be expected.
Thus, the major uncertainty in the effect of plasma variations is
to what extent the axial averaging process was a good approximation.
This is difficult to ascertain since solving the analytic problem for
even a simple case would be very complex.
80
5.7.3 Accuracies of the Plasma Models
As described in Section 5.4, the cold plasma conductivity model is
considered a very good description of this type of discharge and would
not be expected to introduce any significant additional error into the
results for electron density and effective collision frequency. The
models used for the calculation of gas temperature and electron tempera-
ture, however, containedmore assumptions. If any of those assumptions
were not good ones, then the results would be more open to error. For
example, in the radial heat conduction model if the quartz wall tempera-
ture was significantly higher than 3000K, Tg would be underestimated.
Also, the visible upward convection currents in the larger tubes might
play a significant role in cooling the discharges. In this case, the
gas temperatures might be overestimated. The power leaving the discharge
due to light emission might also introduce some error into the calcula-
tions. An advantage of the radial heat conduction model, however, is
that T9 was calculated directly from Pp and dave which were both of
good accuracy.
The calculation of electron temperature had all the errors from
be, T9 and the measurement of gas pressure as inputs. Thus, the combin-
ation of those errors would tend to make Te less certain. Also, the
degree that the distribution function was non-Maxwellian in the vicinity
of the Ramsaur minimum (of argon collision cross sections [31]) could
also introduce a significant error into the computed average energies
of the electrons.
5.7.4 Conclusions on the Overall Accuracy of the Results
A detailed analysis of the accuracy of the results was not part of
81
the defined work in this dissertation and is left for future research. The
results are expected to at least be within the correct order of magnitude,
and probably the accuracy is much better than that. The check on the
dielectric constant of distilled water indicates that as far as plasma
diagnostic methods go, this technique could be very accurate.
The desire to assess the accuracy of the results was one of the main
motivations for extending the experiment down to lower pressures, where
there is more experimental data on argon microwave discharges from other
diagnostic methods.' Also, there is a theory for certain discharge pro-
perties that is often used to describe microwave discharges. These low
pressure results are presented in Appendix B and generally support the
estimates of accuracy given in this section.
CHAPTER VI
ELECTRON DENSITY, ELECTRIC FIELD AND OTHER
DISCHARGE PROPERTIES
6.1 Introduction
This chapter contains results on discharge properties of the high
pressure argon filaments determined by the analysis described in Chapter
V. The order of presentation of the results basically follows the flow
of the analysis. All discharge properties represent spatial averages
over radial and longitudinal variations in the discharges. The frequency
of excitation was 2.46 GHz. All results pertain to the specific experi-
mental geometry in Figure 4.6a (i.e. vertical orientation, discharges
approximately centered in the tube cross section and a common total
discharge length of about 16 cm). The four discharge tubes were those
described in Figure 4.8. At the conclusion of the chapter is a summary
of discharge properties at 1 ATM for comparison with the literature
reviewed in Chapter II.
A common thread exists among all of the figures in this chapter
where pressure is on the horizontal axis,and Figures 4.9 and 4.10 of
Chapter IV. That common thread is that a single experiment at a
particular pressure resulted in a data point on each of the figures.
at that particular pressure. Since each discharge/tube geometry has
its own symbol which is the same in all figures, the discharge properties
of a single experiment (i.e. Ne’ v E , T . Te. etc.) can be extracted
e’ p g
from the figuresif desired.
82
83
6.2 Coupling_Efficiency, Electron Density and Effective Collision
Freguency
With a plasma present in the cavity, the power lost into the coupl-
ing structure was usually no more than 1% of the total power absorbed by
the cavity (i.e. Eff 3_99% for all experiments). This was due to the
plasma lowering Qu in the TM012 mode to values less than 100 as can be
seen in Figure 6.1. Qu generally decreased with increasing pressure -
indicating that as the plasmas became more lossy, the coupling efficiency
(Eff) increased.‘ For a common discharge length, there was little differ-
ence in Qu at a constant pressure between the different discharge/tube
geometries. Coupling efficiencies to microwave discharges are not
always as high as these efficiencies. In the low pressure experiments
(Appendix 8), values of Eff were as low as 60% at .02 torr.
Figure 6.2 displays average electron densities (Ne) versus pressure
for the different discharge/tube geometries. In each tube, Ne increased
as pressure was increased. At a constant pressure, there were distinct
differences in Ne depending upon the discharge/tube geometry (similar
to the differences in average power density described in Section 4.5).
3 for a discharge
For example, at 1 ATM Ne increased from 3.2 x 1013/cm
in the 12 mm tube to 2.7 x 1014/cm3 for a discharge in the 1.5 mm tube.
Adding power also resulted in changes in Ne similar to those of
described in Section 4.5. As can be seen in Figure 6.3, power increases
produced primarily increases in discharge volume for the 4.0 mm tube and
and larger tubes (resulting in Ne remaining approximately constant). In
the 1.5 mm tube, however, volume increases were restricted by the small
tube diameter and Ne increased with increases in Pp.
Changes in average effective collision frequency (09) with pressure
and discharge/tube geometry are shown in Figure 6.4. In all tubes, there
84
'F"""‘ll
g a _
80 -*"‘ ’ ' "- "b ' ‘ '
/'\
(I
r. A
1 —~ A- ,
‘ >785:
'/ \e\
\A-——£
Cl
60 _.. 'I ..\\p ‘\\\‘.
\-
40 r-
20 r—- II1.5 mm
||4.0 mm
a, 12 mm
d) 25 mm
1 I 1.1 I 11. J l. l .l I ll 1,
20 1o2 103
p (torr)
Figure 6.1 Unloaded cavity 0,0 for discharges in the four
tubes oriented vertiEally.
85
1o15
:r' ‘1 1.5 mm
P . 4.0m
- “‘ 12 mm
.. 1p 25 mm
(_..
“ /\.
.’.
\.,o’.
”E 1014 _-
U
.\ ..
s — ———u
e +- /'
z -
_.. /
P I
2: ./ — "/‘~‘ ‘
—-—~—- ~ ~- '74- 5/5'
—* ~ ** “~ /’
_.. ///AV"', ll , _.._.
, «I 1 3 I Q 1
_ _ /’////’f 1 l 1 ' i 1
1013 F .1, f LI 111]: . 1 Ii 11 1 11.1.1] 1
eh 83102 25. _‘ 103
p (torr)
Figure 6.2 Electron density, N , for discharges in the four
tubes oriented vert1cally.
1015 ,
1014
3
Ne (l/cm )
1013
86
- II 1.5 mm
- I. 4.0 mm
).—
.. ‘1 12 mm
1.
r- I’,//”’
,/’////’.’
— /.
o/.
)-
[— ./'\-—_.
L.
_ ‘/A \‘
\
A\‘/A
l 1 l l |
20 3O 4O 50 60
Pp (watts)
Figure 6.3 Effect of adding power on electron density at a
constant pressure of 265 torr.
ve (1/SEC)
87
11
10 __ C) 1.5 mm
L— II 4.0 mm
- a. 12 mm
b e 25 mn
P
I
e—e/‘é
— .’
. /
o 74" 1 (1
- . If] , ‘,.. '1."
I/ ,.
_.- I 5'1“ ,__.,.___,-_‘
1010 _;-—- , - - “fiwk(.\/ -_-__,._~- p...
:1 - 2444/
_ /‘ l
(L'— - ‘
f: 7 .dl-—~—-
___ -1
9 .
10 J JLJLJJI 1 -1 .1]11.~I1[ 1
102 103
p (torr)
Figure 6.4 Effective collision frequency, v , for discharges
in the four tubes oriented vertiEally.
88
was only a gradual increase in Ve with pressure - much less of an increase
than would be expected from assuming that the neutral particle density in
the discharges increased directly with pressure. This gradual increase in
”e indicates that the neutral gas temperature increased with pressure,
causing the neutral particle density in the discharges to increase more
slowly than directly with pressure. The different discharge/tube geometries
produced changes in ve, but not to as great an extent as the changes in He.
For example, at 1 ATM Ye increased from 1.2 x 1010/sec for a discharge in
the 12 mm tube to 3.0 x lO1O/sec for a discharge in the 1.5 mm tube. At
a constant pressure, 0e was approximately constant with changes in absorbed
power in all discharge/tube geometries.
6.3 Electric Field Distributions, Plasma Electric Field and Effective
Electric Field
Due to the type of analysis in Chapter V, cross sectional field dis-
tributions in and around the discharges were calculated for an axial average
point in the standing wave of the TM012 plasma/cavity mode. Figure 6.5
displays calculated distributions of |Er(r)| and lEz(r)| for this average
cross section for a 265 torr discharge in the 4.0 mm tube. The distribu-
tions of |Er(r)| and |Ez(r)| were relatively unchanged from the ideal
empty cavity distributions (described in Appendix C) for r greater than
about 1 cm.
Figure 6.6 displays the same distributions as in Figure 6.5 for the
region of the cavity (near the plasma) where the E-field distributions were
significantly changed from those of the empty cavity. lEr(r)| was relatively
high outside the plasma near the plasma boundary but was relatively small
inside the plasma as compared to lEz(r)l. Thus, the longitudinal component
of electric field (which is not discontinuous at the plasma boundary) was
peak electric field strength (v/cm)
60
50
4O
30
20
...I
C
Figure 6.5 Radial dependence of IE
89
'TT (for fields close to
'11 plasma, see Figure 6.6)
H
'1 _ 13 3
II Ne - 5.4 x 10 /cm
ll
::: ve = 1.7 x 1010/sec
TM 8 = (.429 - j.0057)/cm
[ll
Ill
111
'11
'11
1JJJ
[II
'11
'll
111
111
Ill
1).
1T1
l
'1
11
| l
' I
' 1
I
l
1
l
l
l
l
4..
I
I
l
l
1 [Fr]
.1/ I l l J J l l J
1 2 3 4 5 6 7 8
radial distance (cm) '
axis cavity
of cavity wall
(r)| and lEz(r)|for the
average axial point in the standing wave (265
torr, 4.0 mm tube).
peak electric field strength (v/cm)
90
I‘— quartz —'l
~— plasma
160 "' :
I
I
120 "’ '
I
l
I
l
I
I
80 ‘-' I
1
I
1
I
I
I
1
40 _.. I
I
I
IEZI 1
\4/%'r
I
{El '
"\ JI
r (cm)
Figure 6.6 Radial dependence of IE
plasma for the same dis
6.5
E
(r)| and lEr(r)|near the
barge parameters of Figure
91
the most important component in heating and maintaining the plasma. These
results are consistent with the observations and assumptions about the
TM012 mode made in Chapter IV. Also, Figure 6.6 shows that the radial
distribution of |Ez(r)I was reasonably uniform in the plasma, the intensity
at the plasma boundary being only about 25% higher than the intensity at
the center of the plasma.
Figure 6.7 describes the computed changes in |Ez(r)| in the cavity
with changes in power absorbed by a discharge in the 4.0 mm tube. Adding
power raised the intensity level of the fields in the cavity, as determined
by the measurement of Erw' This increase in intensity level, however, was
not in proportion to the amount of power added, i.e. doubling the absorbed
power only caused a slight increase in the field strengths inside the
cavity. Since increases in absorbed power also caused increases in plasma
diameter, the net result was that there was little change in the E-field
intensity in the discharges with increases in absorbed power. Similar
effects were noted for discharges in larger tube sizes and for other
pressures. For discharges in the 1.5 mm tube, computed strengths of
IE (r)| actually decreased in the plasma with increasing absorbed power,
2
presumeably due to the increases in Ne' This result is shown in Figure 6.8.
Since all computed E-field distributions (but not intensities) at all
pressures were similar to those shown in Figures 6.5 and 6.6, an average
electric field in the plasma (Ep) was defined in Chapter V to compare how
the intensity levels changed with pressure and discharge/tube geometry.
Figure 6.9 displays these changes, showing that in general E increased
P
with pressure. At a constant pressure, values of E were generally lower
P
in discharges having higher electron densities.
An effective electric field (E9) is often defined for microwave
92
a Pp = 38 watts
40 r-
E; b Pp = 44 watts
3 30 -
32. 56 watts
20
l0
1 2 3 4 5 6 8
r (cm)
L °-’I!l I" quartz -'I
_plasma
1?
U
\
5:
‘Th
Bi
IO "’
I I I I J
.I .2 .3 .4 .5
r (cm)
Figure 6.7 Effect of adding power to the distribution of
IEZ (r)| (265 torr, 4. 0 mm tube).
|Ez| (v/cm)
IEZI (v/cm)
)
36 watts
n,
v
II
48 watts
30
63 watts
20
i
10 "’
I 1 l I l J I
l 2 3 4 5 6 7 8
r (cm)
EH IF quartz 4
c.
40 _plasma
30— a' / \\a.
20.. / b.
10 L.—
r (cm)
Figure 6.8 Changes in IE (r)| with absorbed power for the
1.5 mm tube at 265 torr.
Ep (peak absolute value, v/cm)
ID l.5 mm
II 4.0 mm
A; 12 mm
A
30 ___ (D 25 mm 'L/////;.
/V
{5///
o/‘
/‘/ //
20 "‘ I.
1”
A/‘ :/
A/ /
II
//’
I[//fiD
/0
II
10 ._ /
II
I I I I I III I I J .1 J ILJI I
102 103
p (torr)
Figure 6.9 Plasma electric for discharges
in the four tubes oriented vertic
field strength, E ,
Em.
95
discharges to compare with the E-field strength in a d.c. discharge {38].
For these discharges, Ee was defined in terms of Ep:
2 E2 V2
= e
E. 12 TT <61)
ve+w
Figure 6.l0 plots Ee versus p0, where po was reduced pressure defined in
Section 5.6. Calculated gas temperatures to be described in the next section
were used to determine p0. As can be seen in Figure 6.10, Fe was relatively
constant at a given p0. The values of Ee at the low end of the pressure
regime appear to be approaching typical E-field values of 2-4 v/cm at l0
torr in contracted argon positive columns (i.e. d.c. discharges) [39]. Also,
the values of Ee at l ATM (i.e., po between l50 and 200 torr) agree well
with the effective electric field strength of l5 v/cm in a 34 MHz argon
discharge at atmospheric pressure [7]. Figure 6.ll displays the same
results of Ee in a different way, plotting Ee/po versus p0.
6.4 Gas Temperature and Electron Temperature
Figure 6.l2 displays T versus gas pressure for the four discharge/
9
tube geometries. In general, Tg increased with pressure, consistent with
the observations made on the dependence of ve with pressure. Also, Tg
increased at a constant pressure as the discharges were formed further from
the quartz wall (in a larger tube). Using the radial heat conduction model,
this is a result of discharges in a large tube being more insulated from
the quartz wall than discharges in a smaller tube.
Figure 6.l3 diSplays Te versus pressure and discharge/tube geometry.
A distinct difference was calculated between the two smaller tubes and the
two larger tubes which was a result of the differences observed in v (from
e
Ee (v/cm)
96
II_"‘
II 1.5 mm
II
4.0 mm II .,
A» 12 mm
l5 -- up 25 mm
l
II
II
‘I.
A
10 -—- 1.
II
1!
1|
1| III
(I
All
A A .
___ II
5
‘b I!
II I II II II II II I I I I
20 100 200 300
Po (torr)
Figure 6.10 Effective electric field, E , for discharges in
the four tubes oriented vertically.
97
‘I 1.5 mm
|| 4.0 mm
2:201—‘ AlZm
ID 25 mm
A
GI
.15 "’ 1A. ‘.
A
I IA . ‘
II
:9 . *-
-$ .10 r- || ‘1 ll
5 III 4gI1II
; C C. .
D.0
\
1.1.10)
1.
.05 --
I I I l I J I I I I I
20 100 200 300
p0 (torr)
Figure 6.ll E /p versus p for discharges in the four tubes
oFieRted vertieally.
0
T9 ( K)
98
CI l.5 mm
'1 4.0 mm
‘, 12 mm
. 25 "Ill
l500 -'
P A o
o / /
././/
A
1000 -— //
.. ‘//’ ly//”
/ /o
5.11 . -/
A!
/' ./o
3 "a /
4. |/
, o/
500 — .5 /I
,/”//’II
II
I II I I Jill I 1 I l I 1.1 II I
102 103
p (torr)
Figure 6.l2 Gas temperature, T for discharges in the four
tubes oriented ver
83c
ally.
99
II 1.5 mm
II 4.0 mm ‘.
g, 12 mm
‘. 25 mm
l5 "‘
II
. o /
/ \’
C1
0 I
I /
lI-1I--I|
lO _..
' o
22
O
m
0
I: 1.
A
\‘A\ ‘
5 -- .1 4v””
I II I l I I II I I I I I I II
102 103
p (torr)
Figure 6.l3 Electron temperature, T for discharges in the
four tubes oriented vergically.
100
which T8 was calculated). Conceivably, the distribution function could have
changed with the change in discharge/tube geometry and thus might be contri-
buting to the calculated differences in Te. In any event, the order of
magnitude of these values of Te appears to be reasonable. In a 34 MHz argon
discharge at l ATM (with the discharge not bounded by a quartz tube), Te
was spectroscopically determined to be about 6700°K [7], which agrees
reasonably well with the values of Te determined for discharges in the l2
mm tube.
6.5 Summary of Discharge Properties
Table 6.1 presents a summary of discharge properties at 1 ATM for the
l2 mm tube (representative of the two larger tubes) and the l.5 mm tube
(representative of the two smaller tubes). The differences in discharge
properties which resulted from only a difference in tube size appear to
be caused by the different rates of energy flow out of a unit volume of
the discharges (indicated directly by the absorbed power densities). These
different rates of energy flow are most probably different rates of cooling
the discharge. The presence or absence of forced flow rate of gas is
another cooling mechanism that would be expected to cause changes in
discharge properties.
The reviewed papers in Chapter II which permit the closest comparison
with the results in this section are the argon surface wave discharges of
Hubert [l7] and Moisan [l5]. Both papers concerned atmospheric pressure
microwave discharges generated in small diameter quartz tubes (but both,
however, had varying degrees of flow rate of gas). Values of Ne obtained
in the l.5 mm tube (2.7 x 1014/cm3) compared well to values obtained by
Hubert and Moisan of 3-6 x TOM/cm3 for flowing argon discharges in a 5 mm
101
12 xmm i.d. 1.5 mm i.d.
vertical vertical
orientation orientation
average diameter cm .185 .094
power density w/cm3 130 700
electron density l/cm3 3.2 x 1013 2.7 x 1014
effective collision 10 10
frequency l/sec 1.2 x 10 3.0 x 10
plasma E-field
(peak absolute value) v/cm 31 26
effective electric field v/cm 14 16.5
gas temperature 0K 1400 1100
electron temperature 0K 5500 17,000
Table 6.1 Summary of the experimental results on non-flowing,
steady-state, argon microwave discharges for a
All properties (except diameter)
are spatial averages over radial and axial discharge
pressure of 1 ATM.
variations.
102
i.e. tube (presumeably oriented horizontally) [17] and a 2 mm i.d. tube
[15]. Calculated values of T9 in the 1.5 mm tube (~ 1200 0K) were lower
than those given by Hubert of ~ 2300 oK in argon + .5% N2. The presence
of nitrogen in Hubert's discharge (which greatly affected the macroscopic
appearance of the discharge and approximately doubled the absorbed power
density) may have contributed to this difference in 19.
CHAPTER VII
CONCLUSIONS AND RECOMMENDATIONS
7.1 Introduction
The experiments described in this dissertation have extended the
knowledge of high pressure microwave discharges in three ways: (1)
these detailed results on argon discharges provide results from a
different diagnostic approach than previous investigations, (2) the
relationship between the EM fields to the orientation, size and shape
of filamentary microwave discharges is studied to a much greater extent
than previously, and (3) the overall method of generating and diagnosing
the discharges (i.e. in well defined EM fields) is viewed as a superior
approach to the study of microwave discharges than previous investigations.
The remainder of this chapter will amplify the above general conclusions.
A result of this investigation is a better understanding of how
different rates of energy transfer out of the discharge affect its size
and properties. This understanding gained in argon discharges provides
insight into the behavior of high pressure microwave discharges in other
gases .
7.2 High Pressure Argon Microwave Discharge Properties
Typical values of electron density and other discharge pr0perties
at 1 ATM determined by this investigation are listed in Table 6.1 in
the last chapter. The observations in Chapter IV and the results of
103
104
Chapter VI allow the following conclusions about pr0perties of steady-
state argon microwave discharges in the pressure range of 40-1300 torr
and for absorbed power levels up to 150 watts:
(l) The efficiency of coupling microwave power into the discharge
(2)
(3)
(4)
is high. Coupling efficiencies greater than 99% can be
expected when the discharges are generated in a high Q cavity
(i.e., Quo 3_10,000).
For a given discharge/tube geometry and power absorbed, when
gas pressure is raised: (a) discharge dimensions decrease;
(b) electric field strength, absorbed power density and gas
temperature all exhibit strong increases; and (c) electron
density and effective collision frequency exhibit small
increases.
At any given reduced pressure, the effective electric field
strength in the discharge is approximately constant - indepen-
dent of changes in discharge/tube geometry or electron density.
The values of effective electric field appear to be comparable
to the values of E-field strength in argon d.c. discharges.
Plasma properties are greatly affected by the rate of removal
of energy from the discharge. For example, at a constant
pressure and with no gas flow, changes in the relative distance
from the discharge to the quartz wall produced changes in the
rate of cooling of the discharges. Thus, changes of tube
orientation from horizontal to vertical (in a gravity environ-
ment) and/or changes in tube size greatly affect discharge
properties. Significant flow rates of gas would also be
expected to produce changes in discharge pr0perties.
105
(5) Adding power to the discharge at a constant pressure and in
a given discharge/tube geometry results primarily in increased
plasma volume with discharge properties remaining roughly
constant. When volume increases are restricted (such as by
a small diameter quartz tube) absorbed power density and
electron density increase with increases in absorbed power
and the microwave electric field strength decreases.
(6) The filament diameter at any axial point is related to the
strength of the longitudinal electric field at that axial
point (i.e., longitudinal with respect to the discharge).
This relationship appears to be that the cross sectional area
of the filament is proportional to the E-field strength.
Increases in filament diameter are limited by a maximum
diameter which is probably determined by the depth of pene-
tration of the E-field (i.e. skin depth). When this maximum
is exceeded, the filament splits into two shorter and thinner
filaments. This phenomenon should be investigated in more
detail.
7.3 Relationship of the Orientation of the Discharge to the EM fields
Contracted microwave discharges take an orientation such that the
electric field sustaining the discharge is a longitudinal electric field
with respect to the discharge. This is a consequence of the relative in-
ability of a normal component of electric field to penetrate into the
discharge (due to surface polarization). The basic arrangement of
electromagnetic fields is: (l) a longitudinal field inside the discharge,
(2) a radial component predominantly just outside the discharge, and
106
(3) a circumferential magnetic field around the filament. The microwave
fields are tied to the orientation of the filament. When bouyancy or
other forces cause a filamentary discharge to move around, it can be
inferred that the microwave fields_are also moving - maintaining the
basic field structure in and around the discharge. Direct evidence
supporting this contention is that whenever filaments were moving inside
the microwave cavity, fluctuations in the cavity fields were observed
(by the measure of Erw and the impedance match) which were related to
the motion of the discharges.
The field strengths and orientation around the surface wave
discharges (Appendix A) support the above conclusion. Also, the close
similarity of the surface wave fields with those of the TM01 plasma/
waveguide mode (near the plasma) provides insight into the efficient
coupling that often occurs between fast waves and surface waves. The
problem of excitation of electromagnetic waves on a plasma column,
including the phenomenon of one type of wave coupling to another type,
should be investigated further.
7.4 Experimental and Diagnostic Methods
Using the microwave fields to both generate and diagnose the
discharge is a useful, non-perturbing approach to the study of micro-
wave discharges. Numerical solutions to Maxwell's equations may be
required but do not represent a barrier due to the speed and availability
of modern computers; The general diagnostic method is independent of
the gas type, pressure or electron density regime of the discharges and
thus makes it a versatile diagnostic technique for simple plasma
geometries. However, the ultimate accuracy and limitations of this
107
technique should be investigated further. Specifically, the sensitivity
of the characteristic equation to changes in AL, dave’ Erw’ etc. should
by investigated. Also, the effect of axial variations in a plasma/wave-
guide of the type encountered in this dissertation should be analyzed.
Experimental results using this type of diagnostic technique should be
compared with other diagnostic methods (such as a spectrosc0pic measure
of electron density).
The study of microwave discharges from an EM point of view would
eliminate some misunderstanding that currently exists in the literature
on the type of traveling waves that are capable of sustaining a discharge.
Specifically, the notion that a high frequency TEM wave can sustain a
moderate density discharge on the axis of a hollow metal pipe [6,40] is
clearly fallacious. Analytically, if the problem of a plasma on the
axis of a metal pipe is set up as an EM boundary value problem, no roots
of the transcendental equation would be found that correspond to a TEM
wave unless the plasma were a perfect conductor. For the size of the
metal pipes, frequency of excitation and expected electron density of
the discharges in [6,40], only roots corresponding to surface waves are
possible.
Thus, the overall approach to the study of microwave discharges
described in this dissertation (both analytically and experimentally)
is a necessary starting point in understanding the mechanisms of energy
transfer to steady-state microwave discharges. Once an understanding
is attained in simple plasma/EM field geometries, it then becomes easier
to predict the behavior of similar discharges in other types of micro-
wave excitation.
APPENDIX A
APPENDIX A
HIGH PRESSURE, MICROWAVE GENERATED STANDING SURFACE
WAVE FILAMENTS
A-l Introduction and Experimental Objectives
This appendix presents results of high pressure standing surface
wave experiments in the heavy inert gases. The experiments were an
extension of a low pressure standing surface wave investigation in argon
gas [16]. A detailed description of the experimental system and general
properties of microwave standing surface wave discharges is contained
in reference [16] and will not be repeated here.
The main objectives of these high pressure experiments were to:
(1) determine properties of high pressure inert gas filaments sustained
by surface waves and (2) compare these discharges with the high pressure
argon microwave discharges described previously in this dissertation.
In this appendix, all references to sections, chapters or figures refer
to those of this dissertation.
A-2 Experimental Description, Measurements and Analysis
The experiment consisted of two contracted surface wave plasmas
generated in a common quartz tube using two surface wave launchers
identical to the one pictured in Figure 2.3 and the one used in [16].
The operation of this launcher is described briefly in Section 2.4.
Microwave power was generated by a filtered, 2.45 GHz, variable power
source. The microwave power was split by a coaxial “Tee" and equal
A-1
A-2
amounts of power were delivered to each cavity. When sufficient power
was added, the plasma columns became long enough to join together --
allowing the pr0pagating surface waves from each cavity to interact
forming standing surface waves.
Gas pressure ranged from 40-760 torr for these experiments. A 4.0
mm i.d. quartz tube oriented horizontally contained all discharges and
gas flow rate was kept to near zero flow. Pressure was measured with a
mercury manometer and the gases used were argon, krypton and xenon.
Power absorbed to the discharge, Pp, was measured as the sum of the
power absorbed by each cavity (coupling structure losses were neglected).
Discharge diameters were measured photographically in the manner described
in Section 3.4. A straight E-field probe and a shielded 100p described
in reference [16], were used to measure relative magnitudes of lErl2 and
|H¢I2 axially along the plasma just outside the discharge tube.
Electron density was diagnosed by modeling the surface wave pro-
pagation along the filament in an analogous fashion as the method de-
scribed in Section 5.3 for the plasma/cavity filaments. The axially and
radially non-uniform plasma was approximated with an axially uniform,
homogeneous, lossy dielectric rod with a diameter equal to the average
diameter of the filament. Cold plasma theory was used to describe the
electrical conductivity of the discharge. Figure 5.3 describes the
cross section of the boundary value problem used for these surface wave
discharges except that no metal waveguide was included. Because the
discharge tube was oriented horizontally, the discharge in general'
floated up in the tube (off axis). This asymmetry was neglected in
the electromagnetic analysis.
Equation55.4, 5.5 and 5.6 remained valid for this analysis since
A-3
the desired solution was again a rotationally symmetric TM mode. Applying
boundary conditions at the interfaces resulted in a transcendental equation
relating the complex propagation constant 8 to the plasma dielectric
constant -- and hence to electron density, Ne, and effective collision
frequency, Ve'
The formation of the standing surface wave allowed the determination
of Br in a similar way as in the cylindrical cavity experiments:
where Ag was the experimental surface wavelength. Since the visible
plasma diameter closely corresponded to the standing wave (as will be
described in the next section), Ag/Z was measured in the photographs as
the distance between the two minimums in diameter. 8i was not measured,
so that values of “e had to be assumed to determine Ne' The value of Ve
at any pressure was assumed to be approximately the value of ve deter-
mined by the argon cylindrical cavity experiments in the 4.0 mm tube
(Figure 6.4). These values of Ve should be a reasonable approximation
for the argon surface wave results but may be less accurate for the
results in krypton and xenon. By assuming values for ”e’ the character-
istic equation reduced to one involving Br (measured) and Ne (unknown).
For each data point, the transcendental equation was solved numerically
for Me. .
As in the analysis of Chapter V, Ne for these surface wave discharges
represented a spatial average over radial and longitudinal variations in
the plasma. The potential errors involved in determining Ne would be
similar to those discussed in Section 5.7. The sensitivity of Ne to
A-4
changes in ve was investigated to evaluate the additional source of
error by assuming values for v For values of ve up to three times
2'
those aSsumed for the analysis, Ne increased at most 30%. For values
of ”e as low as zero, Ne decreased a maximum of 20%. Thus, Ne was not
particularly sensitive to changes in v 'and.any additional error intro-
e
duced into Ne was probably not a large one.
A-3 General Discharge Characteristics, Power Density and Electron Density
The process of contraction in the surface wave discharges was
similar to the description in Chapter IV for the argon cylindrical cavity
filaments. The top of Figure A-l displays the typical appearance of a
standing surface wave filament. The visual appearance and light emission
intensity of the argon discharges were similar to the argon cylindrical
cavity filaments. Discharges in krypton were more purple in color and
discharges in xenon were more blue. Also, emission intensity was
visually less bright in these two gases than discharges in argon. Above
200 torr, discharges in krypton tended to branch out into several thin
moving surface wave filaments, making it difficult to obtain a single
standing wave filament. This was also observed in argon and xenon,
but more infrequently.
Figure A-l correlates the electromagnetic field patterns around a
standing surface wave to the visual appearance of the discharge. These
relationships were determined by the relative measure of lEr|2 and |H¢|2
using the E-field probe and shielded loop. The location of maximum
IEzI in the same region as maximum |H¢| is characteristic of a standing
TM type of wave as can be determined from Maxwell's equations. Thus, the
dominant field component in terms of sustaining the plasma appears to be
A-5
l diffus plasma bright,plasma
[E |2 max |H¢|2 max [E [2 max
r
solid line - |Er|2 (arb. units)
. n
19f? . right
cav1ty aX1al distance (cm) cav1ty
I
Figure A-l Relationship of filament shape to measured axial
d1stributions of IE [2 and [H |-2 for an argon
discharge at 146 toFr. ¢
(Sigun °que) zI¢HI - auil pausep
A-6
|Ez|. Figure A-2 correlates the filament cross sectional area at any
axial point with the computed value of lEzl at that point for an argon
discharge at 114 torr. As in the cylindrical cavity filaments described
in Chapter IV, the cross sectional area of the filament appeared to be
proportional to the strength oflEzl. Another similarity between the two
types of microwave filaments is that in these surface wave discharges,
regions of diffuse plasma generally appeared in regions of highIErl as
was observed in the cavity experiments. This effect is illustrated in
the top of Figure A-l by the dotted regions.
Figures A-3 and A-4 display power density, , and electron density,
Ne, for the discharges in argon, krypton and xenon. At a constant pres-
sure, there was little difference in Ne or , versus pressure.
1015‘ 4'
Z O argon
" II krypton
‘ xenon
_
" I
C
_ A
I
" A
- \ o
a." §
\ I
r; I '
2Q) — .
I
1013 ~—
:: II
I I I I I I II I I I I I I I II I
10 102 103
p (torr)
Figure A-4 Electron density, Ne, versus pressure.
A-1O
ZOO -
1OO ”"’ ‘1 II
5 so ...
\
5 l...
A 60 -
G.
v —
40 1-
I I I I I
1014 _—
P
F
L.
_ I
m .
g I—
Q’ r-
z
1013 I I I I I
25 3O 35 4O 45
power absorbed (watts)
Figure A-5 Changes in and Ne with changes in absorbed power
for argon discharges at 174 torr.
A-11
10 -——
0 surface wave (horizontal)
O cavity (vertical
_ /
C(/’.
E. // ./
E j/
_ . /
(D
_ /. {/0
(w/cm3)
s
N
o
/O
10 1011111I 1 1111111 I
20 102 103
p (torr)
Figure A-6 Comparison of for the argon surface wave discharges
in a 4.0 mm tube horizontal to for the argon cylindrical
cavity discharges in a 4.0 11111 tu'o'e vertical.
A-12
was larger for the surface wave discharges as expected from the
observations made in Chapter IV. Ne did not show such a clear dif-
ference - Ne for the surface wave discharges being about 50% lower than
expected. This was attributed to the fact that the sampling region for
determiningllein the surface wave discharges did not include the most
intense regions of the surface wave filament (near the cavity gaps)
whereas the determination of did include those regions.
A-4 Electric Field Distributions
Figure A-7 displays calculated cross sectional distributions of
lEr(r)| and lEz(r)| for an argon discharge at 287 torr. A point of
reminder is that the fields are rotationally symmetric and the particular
cross section represents one at an average axial position in the standing
wave. The field amplitudes were determined from , Ne and ve assuming
a uniform E-field across the plasma column. Several similarities exist
in these distributions with those of Figure 6.6 (for a cylindrical cavity
argon discharge at 265 torr). The relative distributions and field
strengths inside the plasma are very similar. This was also true for
|H¢(r)| which was not displayed in either case. Also the relative
strength and dependence of IEr(r)| just outside the plasma is similar
in both cases.
The primary difference between the two types of microwave generated
plasma columns is in the differences in field strengths and distributions
outside the quartz tube. In the cylindrical cavity excitation (Figure
6.5), the field components increase with radial distance becoming similar
to the TM01 empty waveguide field distributions. For the surface wave
excitation (Figure A-7) the fields decrease with radial distance in an
A-13
200 3: plasma L— quartz —"I
I
I
I e = 3.91 x 1013/cm3
I e = 2.14 x lOIo/sec
: r = .720 /cm
. = -.237 cm
160 — I l I
I
l
I
I
I
I
120 F- I
E 1
U
3 1
I
:~ I
—‘ I
S.
O I
_ 80 —
s. I I
LIJ
I I
| 1
1 I I\
1 : 1
40 — I I I
I | I
I E I
1 ' 1
I ====r—- ,
lErl I
\_1 I I 1
.1 .2 .3 _
r (cm)
Figure A-7 Radial dependence of [Ez(r)| and IEr(r)| for an argon
discharge at 287 torr.
A-14
exponential like fashion. Thus, the amount of wave power carried exterior
to the plasma by these types of traveling waves is strikingly different.
(In terms of standing waves these differences would be in the stored
energy of the fields). Correspondingly, the degree of coupling energy
into the plasmas by the two cases also must be different since on a per
unit length basis (for similar size and losses of the plasma), the amount
of power transferred into each plasma would be the same. For the TM01
plasma/waveguide mode, the attenuation of the wave is very small (Bi =
-.0057/cm for the case of Figure 6.5). For the TM, surface wave mode,
the degree of attenuation is much higher (81 = - .237/cm for the case of
Figure A-7). Thus, a single traveling surface wave can sustain this type
of plasma filament whereas in the T1101 plasma/waveguide mode, a resonant
cavity is required (to essentially bounce the large amount of wave power
back and forth in the cavity).
The effect of radial electron density variations on surface wave
dispersion characteristics and the EM field distributions was investigated
for a typical plasma filament (corresponding to the average diameter and
properties of the argon surface wave discharge at 287 torr). Figure A43
illustrates the two electron density profiles used in the comparison.
The homogeneous case (Figure A4k1) had an electron density equal to the
average electron density over the cross section of the inhomogeneous case.
An effective collision frequency of 2.14 x low/sec was assumed for both
cases. The particular profile in Figure A-8b was used because of its
simple analytical formula and because it resembled measured electron
density profiles in lower pressure argon contracted positive columns
[39]. An integral Operator approach developed by Sipe and Nyquist for
heterogeneous surface waveguides [41] was used to formulate the radially
A-15
a. “' plasma "I e I‘— quartz—DI £0
0
3.9 x low/cm3
\s
\\\\
1.—
0
N —-—___—_—_—_
w—————_—.———
_l
b.
15 3
1.3 x10 /cm b. plasma _.|
|-— +1
E0 quartz | so
: er = 3.78 .
I I
A cos2 ar | I
I I
a = 19.25 1 I
I I
Ne I I
I l
I I
l I
I 1
l I
I I
I I
.1 .2 .3
r (cm)
Figure A-8 The two radial density profiles used in the comparison
of surface wave propagation along an inhomogeneous
plasma filament to a homogeneous plasma.
A-16
inhomogeneous problem. This formulation allows for arbitrary variations
in the radial profile of the waveguide dielectric constant, including
jump discontinuities. A numerical moment method solution was used to
solve for the complex propagation constant and the radial electric field
distribution, Er(r). The axial field, Ez(r), was determined from Er(r)
using Maxwell's equations. .
Figure A-9 compares Ez(r) for the two cases and Figure A-10
compares Er(r). The amplitude and phase of Er(r) for the two cases
were set equal to each other at the outside wall of the quartz tube.
As can be seen from the figures, both amplitude and phase of the two
field components were nearly the same for the two surface waveguides
except near the plasma boundary where a large oscillation of the
electric field of the inhomogeneous case was observed. The propagation
constants for the two cases were also very close: 8 = (.720 - 3.237)
/cm for the homogeneous case and B = (.728 - j.218)/cm for the inho-
mogeneous case. E2 was computed to be reasonably uniform over most
of the plasma core in both cases.
A-5 Conclusions and Recommendations
For the same excitation frequency of 2.45 GHz the microwave surface
wave discharges exhibited many similarities to the filaments generated
in the cylindrical cavity. The conclusions in Chapter VII about prop-
erties of the cylindrical cavity filaments are supported by this
investigation.
Calculated average electron density in these surface wave discharges
appears to be insensitive to the radial electron density profile. Thus,
,‘ 1
E 1
:1 1 Re [E2]
> 1
V I
a.“ 0 — g
1
I
I
1
-5 ___ 1
I solid lines - homogeneous
1
: dashed - inhomogeneous
-10 F I
I
I
I
1
1
-15 '—
I I I
.1 2 .3
r (cm)
Figure A-9 Ez(r) for the homogeneous and inhomogeneous cases.
(v/cm)
E
200
150
100
50
-50
-100
Figure A-10
A-18
1
1
I
I
I
I
1
I
| Re [Er]
I
I
1
l
I
l
l
I
I \__
I
L_——— ::_“ ‘
F”
I
I
1 Im [Er]
I
1
I
1
1 solid line - homogeneous
1
1 dashed - inhomogeneous
I
I I I
.l .2 .3
r (can
Er(r) for the homogeneous and inhomogeneous cases.
A-19
the use of a homogeneous plasma model is adequate for diagnosing average
discharge properties. Depending on the actual density profile, the peak
electron density could be as high as three times the average density.
Further experimental work should be done on determining actual electron
density profiles. The integral operator technique [41] is a useful
analytical tool for the radially inhomogeneous surface waveguides. The
extension of this approach to handle a radially inhomogeneous plasma
inside a cylindrical metal waveguide should be investigated.
Similar standing surface wave discharges in other gases should be
investigated experimentally. Such eXperiments may require the construc-
tion of surface wave launchers capable of operating at high microwave
power levels.
APPENDIX B
APPENDIX B
PROPERTIES OF STEADY—STATE, LOW PRESSURE ARGON
MICROWAVE DISCHARGES
B-l Introduction and Objectives
Low pressure argon microwave discharges were investigated using the
experimental system and analysis described in the main body of this
dissertation. In contrast to the high pressure filaments, these
steady-state discharges filled the tube cross section. Electrons and
ions were probably lost by diffusion to the quartz wall and subsequent
recombination at the wall. The pressure regime of these experiments was
.02 - 1.0 torr and quartz tubes of inner diameter up to 25 mm were used
to contain the discharges. All experiments were carried out in the TM012
cavity mode using a filtered, variable power microwave source of frequency
near 2.45 GHz.
The main objectives of these experiments were to:
1. determine properties of argon microwave discharges at pressures
less than 1.0 torr for comparison with previous work on argon
microwave discharges (using Langmuir probes as the diagnostic
technique [16]) and for comparison with positive column
theories [42,43]
2. determine the microwave field distributions in the plasma and
cavity, and determine the effective electric field strength
in low pressure argon microwave discharges
3. measure the dependence of microwave coupling efficiency Defined
B-1
B-2
in Section 5.2) as a function of pressure, electron density
and discharge tube size.
Throughout this appendix, references to Chapters, sections and
figures refer to those of this dissertation.
B-2 [Experimental Considerations
Differences in experimental techniques of these experiments from
the high pressure cavity experiments will be described in this section.
Figure B-l illustrates the general appearance of the discharge in the
TM012 cavity mode. Since the discharges appeared to fill the tube cross
section, discharge diameters were assumed to be the inner diameter of
the quartz tube. As in the high pressure experiments, the discharges
were non-uniform both axially and radially as observed by variations in
light emission. The radial electron density profile for a diffusion
controlled discharge is theoretically expected to be proportional to
do (2.405 r/a), where a is the plasma radius and Jo is the Bessel
function of the first kind of order zero [31]. The axial non-uniformities
in the discharges in most cases followed the axial standing wave of
[El], i.e. the most visually intense regions of plasma were located in
regions of high IEzI' An exception to this appearance will be described
later. As in the high pressure experiments, the use of the homogeneous
plasma model means that determined plasma properties are spatial averages
over both axial and radial variations in the plasma.
Gas pressures were measured with Hastings vacuum tube gauges
located at both ends of the quartz tube. Although only a slight amount
of gas flow was present (to ensure purity of the gas), at pressures below
.1 torr there was a small pressure drop down the tube which increased
B-3
cavity
quartz tube
O . ,..'o~o\ I, ..o
s.\ \',.".‘9 ”‘ '1‘ "I. 6‘
1, o .
”A'Q‘A'
.”TTV"FVTTU
-¢.IO “‘ a A '..(
. ’O" S..‘.‘u'- .\ ’1 ' '. ,
O
‘ 0 Q Q . \
\A‘h\OA\ :'
/=
non-uniform plasma
Figure B-l General discharge appearance at low pressure in the
TM012 mode.
3-4
with decreasing pressure. In these instances, gas pressure in the dis-
charge was determined by assuming a linear pressure drop down the quartz
tube. The results on these low pressure discharges were assumed to
reflect properties of non-flowing discharges. However, this should be
investigated further.
As can be seen from Figure 6.2 (for the high pressure argon filaments)
gas temperatures appear to be approaching the quartz wall temperature in
the pressure range of l-10 torr. Thus, the gas temperature in these low
pressure discharges was assumed to be at 3000 K for use in the calculation
of electron temperatures. Because electron-ion recombination on the
quartz wall can cause the wall to heat up significantly, external air
cooling of the tube was essential for maintaining the wall near 3000 K.
As gas pressure is decreased, Oh generally increases due to lower
plasma losses. Higher values of Ou for these low pressure experiments
led to differences in the tuning process of the cavity from the high
pressure experiments. When a low pressure plasma was present in the
cavity, critical coupling was often not achieved in the TM012 mode.
This was due to the discharge/circuit instability which can occur under
high Q plasma/cavity Operation [10]. Briefly, frequency drifts or im-
perfect filtering of the microwave signal can cause a momentary non-
intersection of the plasma load line with the circuit resonance curve
or can cause a shift to an unstable intersection point. When either
happens, the plasma abruptly extinguishes. The lower the plasma losses
(i.e. the higher the Qu)’ the more likely this phenomenon occurs. 1
Figure B-2 illustrates an actual plasma load line and the approximate
cavity resonance curves associated with each operating point. Although
the proper way to display an intersection point on this type of curve is
B-5
.ggop mo. we can» as mp on» cw mammpn some» sumcmp acmamcou
a com mm>gso mucmcommg zpw>mu mumswxoeqam use mcwp weep mammpa
mum mgzmwm
m
€53 :.2 x z
c m N F
_ _ _ _
pcwoq
cppmgmno
w
I 8 m.
1
MW
D.
n
mew, umop C mv
mmem
: I 3
C o. : C 28 5
«amp momp mmmp
_ r _
m. N.
AEUV 4<
B-6
with a circuit resonance curve, Figure B-2 indicates the general graphical
approach. In this pressure regime and for the relative size of the plasma
to the caVity, there was nearly a linear relationship between cavity
length shift and electron density. Thus, both quantities are displayed
on the horizontal axis. The vertical axis represents power absorbed by
the cavity (the height of the operating point) or incident power (the
height of the resonance curve). The number above each curve is the
measured Qu at that operating point.
In each case illustrated in the figure, critical coupling could not
be achieved since either reducing the power level or increasing the
cavity length caused the plasma to abruptly extinguish. As the electron
density increased (i.e. Qu decreased), the ability to match power into
the cavity improved. For Qu less than 1000, the cavity could be nearly
critically coupled (often less than 1% of the incident power was re-
flected). As Qu increased above 1000, the ability to match power into
the cavity declined rapidly. Although the plasma/cavity could not be
critically coupled when Qu > 1000, a significant error was not intro-
duced into the results because the resonance curves were so narrow
compared to the cavity length shift.
B-3 Comparison of Discharge Properties in Different Tube Sige§_
A series of data points was taken in three different sizes of quartz
tubes (4.0, 7.0 and 13 mm i.d.) with the plasma length always approxi-
mately 16 cm as indicated in Figure B-l. Absorbed power was adjusted
to be roughly the same in all tubes at a constant pressure so that
differences in discharge properties could be attributed to the different
tube diameters. 'Figure B-3 displays the absorbed power in the plasma
Pp/L (w/cm)
I1 4.0 mm
'I 7.0 mm
A. A113.0 mm
1.5 "'
II
I.
‘ b
9 A
I.
1.0 I'-
II II
II A
‘III
-0‘
II II
II
I.
.5 "'
I IIII I I II I I I I I III II I
.02' .1 1.0
p (torr)
Figure B-3 Absorbed power per unit length (Pp /L) versus tube
size and pressure.
B-8
per unit length (Pp/L) for the data in the three tubes.
As the quartz tube diameter decreased, absorbed power density, ,
and electron density, Ne’ both increased at a constant pressure. These
results are shown in Figures B-4 and B-5. Qu’ however, changed relatively
little in the three tubes at a constant pressure as shown in Figure B-6.
These values of Ou indicate that microwave coupling efficiencies generally
decreased with pressure from about 99% at 1.0 torr to about 85% at .04
torr. Coupling efficiencies will be examined in more detail in the
next section. I
Figure B-7 displays effective collision frequency, ve, as a function
of pressure for the three tube sizes. In general, ve appeared to be
independent of the tube size and appeared to decrease nearly linearly
with pressure. Data points in the 4.02mm tube below .2 torr, however,
deviated from the above generalization. These values of Ve (which were
experimentally repeatable) were about 2-3 times higher than values of
v in the larger tubes at the same pressure. Figure B-B displays
e
electron temperatures, Te, calculated from v as a function of the
e
reduced pressure-discharge radius product, poR. Except for the four data
points in the 4.0 mm tube below .2 torr, there was good agreement as to
both order of magnitude and the general pressure dependence of Te with
positive column theories [42,43]. For the poR range of .08 - 1.0
torr-cm, there was especially good agreement with the Langmuir probe
data taken on microwave generated argon surface wave discharges [16].
Both sets of data (using different types of diagnostic techniques)
indicate a flat pressure dependence of Te in that pOR range with values
between 25,000° K and 30.000° K.
The four data points in the 4.0 mm tube below .2 torr corresponded
B-9
I0.0 w-- I'\\\\\
'_' K.
‘ \o\ ./D
1- ./
IL\\\\\\\\
.\-
IL\\‘\‘~II
‘
m; 1'0 L— \A A
.2 .. ”\A
V
_ \A
.1 4.0 mm
__ II 7.0 mm
1‘ 13.0 mm
,1 11I1I11I 1 LIIIIII
.02 .1 1.0
p (torr)
Figure B-4 Absorbed power density, , versus pressure and
tube size.
B-1O
13
10 1__- II 4.0 mm
_' II 7.0 mm
: A13.0 mm
/o
I
. /_/
" /'\ / I
I A
I ‘X
12
10 -.— 0 I
.. -/ A/
or); : ./
S ._ A
2‘” — /
_ A
A/
10” 1111111I 1 1111111I
.02 .1 1.0
p (torr)
Figure B-5 Electron density, Ne’ versus pressure and tube size.
B-11
104_
r- II 4.0 mm
F’ II 7.0 mm
" 4113.0 mm
A
A
103—
2 ° I
— A
_
_ o I
_ ' ’ I
,A II
o
- I
A
o
I
102—— ‘ I
L.
"" A
L.
r-
1111111I 11111111I
.02 .1 1.0
p (torr)
Figure B-6 Unloaded cavity Q, 0”, versus pressure and tube
size.
ve (1/SEC)
B-12
1010
_. CI 4.0 mm
" II 7.0 mm
L.
41 13.0 mm 1.
109 ,
F.
8 I
10 I I I I I II I I I I I [III
.02 .l 1.0
p (torr)
Figure B-7 Effective collision frequency, Ve’ versus pressure
and tube size.
70 51 1‘11; :1 II 4 mm
100,000 + I 7 11m
‘1 13 mm
60 --
diffusion theory
50 "" free fall theory
40 "'-
,‘ ll
8‘ ‘I ||
0')
O
CZ. 30 ‘b ‘.
l—m " _ ‘ ‘
A ‘ .1
II 1| II‘_II
20 "'
10 1-
.I l I I J I II I l I I I I IIII
10'7- 10"I . 1.0
poR (torr-cm)
Figure B-8 Electron temperature, Te’ versus poR and tube size.
B-14
to improbably high values.of TB (3105 OK) when compared with the Langmuir
probe data in [16]. These unexpected results could have been due t0: (1)
space charge sheaths or sOme other phenomenon causing elevated electron
temperatures [43], (2) large deviations in the velocity distribution
function from the Maxwellian distribution, and/or (3) heating mechanisms
other than electron-neutral collisions.
Microwave electric field strengths in the discharges behaved
similarly with pressure in all three tubes. Ep (the spatially averaged,
peak absolute value microwave field strength defined in Section 5.3)
increased from lO-20 v/cm at 1.0 torr to 90-100 v/cm at .07 torr. Typical
cross sectional distributions of (Er(r)| and lEz(r)| for a .04 torr
discharge in the 13 mm tube are displayed in Figure B-9. As in the
results of Chapter VI, this cross section represents the average axial
point in the standing wave of the TMO12 mode. A difference in these low
pressure E-field distributions is that IEr(r)| near the plasma boundary
was relatively low for these low pressure results.
Effective electric field strengths, E6, of the discharges were
relatively constant with pressure in each tube size. Over the pressure
range of .04 - 1.0 torr, Ee varied from 2.0 - 2.8 v/cm in the 13 mm
tube, 3.0 - 3.8 v/cm in the 7 mm tube and 3.8 - 8.0 v/cm in the 4.0 mm
tube. Figure B-lO displays Ee/(poR) versus poR for the data in all
three tubes.
B-4 Microwave Coupling Efficiency
The definition of microwave coupling efficiency was given in Section
5.2 and is restated here for convenience:
200
E? 150
\
E:
.C
4.1
U"
C
25
.1.»
U)
'U
15
CC
0 100
'2
4.1
U
G)
75
.2
'5
G)
D.
50
Figure B-9 Radial dependence of IE (r)| and IE
B-15
1 2 3 4 5 6 7 8 -
r (cm)
(r)| for an argon
discharge at .04 torr 16 the 13 mm "tube.
2
Ee/poR (v/cm torr)
10 __
:Z I. 4 mm
b. . 7 "III
.. 1A1 13 mm
I" I
Ob
2
10 ‘2." A
:: II
" ll
'- A
'I
II
A
10 1— '
.— ‘ '
I .
" A
1.0 II I II III_I II I I I I I I I II I
10'2 1.0
poR (torr-cm)
Figure B-lO Ee/poR versus poR
8-17
_ Power absorbed in therplasma
Eff ' 100% x Total power absorbed in the cavity
Figure B-ll displays values of Eff versus pressure for discharges
in the 13 mm tube having different values of Pp/L at a constant pressure
(but all having the same discharge length pictured in Figure B-l). In
general, Eff decreased with pressure as described in Section B—3. At a
constant pressure, Eff was higher in discharges having a higher electron
density. This variation of Eff with Ne was investigated carefully at a
pressure of .03 torr in the 13 mm tube. Figure B-12 displays Eff and Ne
as a function of power absorbed in the plasma. Except for the data point
at the lowest Pp, there appeared to be roughly a linear dependence of
Eff with Ne“ This was a consequence of other discharge properties and
the wall electric field measurement (Erw) remaining approximately con-
stant for all data points except the one at the lowest Pp:
Te = 50,000 °K
Ve z 3.2 x 108/sec
Ep 2 120 v/cm
Erw s 120 v/cm
The data point in Figure B-12 at the lowest value of PD produced
an unexpectedly high efficiency which was repeatable. For an average
density of approximately 8 x lOIolcm3'(close to mp = w), Eff was 90%
--significantly higher than would be expected by observing the dependence
of Eff with Me for the other data points. Erw for this case was 60 v/cm.
resulting in coupling structure losses of about 1/4 of those of the
Eff (%)
B-18
100 \;,—1r""r—J._—J.
10‘2/cm3
A
6 x Ion/cm3
90 -— 3.5 x 1011/cm3
_ ll 3
80 _.. Ne — 2 x 10 /cm
A
1.—
70 ._. .A
I I II I III I II II I I II III I II
10‘2 10“ 1.0
p (torr)
Figure B-ll Microwave coupling efficiency, Eff, versus pressure
in the 13 mm tube.
B-19
100
.03 torr
13 mm tube
90 F” l
3‘
A/‘/
A 80 — A/
33 ‘ ‘/
‘F \
“a: / ‘/
(t
70 -'
I l l I | l
3 _..
v3" 6 r
5
,_\
.22 ‘2;
V 4 — ‘/
z
A /
2 h- /\“A
1“
| J I l l
5 10 15 20 25
‘Pp (watts)
Figure B-IZ Microwave coupIing efficiency, Eff, and eIectron density
N8, versus absorbed power in the discharge, Pp,at .03
t rr.
B-20
other data points. In a 25 mm i.d. tube at .02 torr, a similar un-
usually high value of Eff was found near the electron density where
up = m. In this tube, the change in Eff was measured to be from 60%
for an Ne slightly lower than mp = m to 98% when Ne was increased to
about up = w (by a slight adjustment of the cavity length). In this
case, Erw dropped from llB v/cm to 27 v/cm while the power absorbed in
the cavity actually increased.
The dominant electrogmagnetic mode in the cavity when the phenomena
described above occurred was still verified to be the TM012 mode by the
measured axial distribution of IErIZ along the wall and by the start up
and tuning process. Thus. the unusually high efficiencies described
above were probably not due to a change in the cavity EM mode and were
therefore accurately measured. The high efficiencies near up = m were
attributed to a transverse resonance in the plasma column which is pre-
dicted by the type of plasma/waveguide analysis described in Chapter V
[28]. This explanation was supported by an observation on how the axial
variation of light emission changed from that of Figure B-l. As shown
in Figure B-l3, the regions of intense plasma were located near the
axial position of high IErl. This would be likely to occur if the
phenomenon was a transverse resonance.
B-5 Conclusions and Recommendations
Microwave discharge properties are affected by discharge tube size.
For a constant pressure and constant Pp/L: (1) average power density and
electron density increase as the tube diameter decreases and (2) unloaded
cavity Q and effective collision frequency remain about constant. For
small tube diameters at low pressures. values of “e can be higher than
B-21
/ cavity
./ quartz tube
plasma
Figure B-l3 Change in discharge appearance in the TM012 mode for
the high efficiency point in Figure B-l2.
B-22
expected from values in larger tube sizes at the same pressure. These
higher values may reflect heating mechanisms other than electron-neutral
collisions and should be investigated further.
Electron temperatures in low pressure argon microwave discharges
appear to be of the same order of magnitude as electron temperatures
predicted by positive column theory. Te determined by this investiga-
tion agreed well with values determined by Langmuir probes in the poR
range of .08 - l.0 torr-cm. Thus, the overall measurement technique
used in this dissertation appears to be valid, especially for pressures
higher than about .5 torr. Electron temperatures of poR less than .08
torr-cm should be investigated further by both techniques and possibly
with a third diagnostic method.
Effective electric field strengths in argon microwave discharges
also behave in a fashion similar to that predicted by positive column
theory. This should be investigated further and the values obtained in
this investigation should be compared with experimental E-field strengths
in d.c. discharges.
Microwave coupling efficiencies generally decrease with decreasing
pressure. At a constant pressure, efficiencies generally increase with
increasing electron density. A resonance phenomenon near an electron
density where q) = w appears to enhance microwave coupling efficiencies
at low pressures. An increase in efficiency from 60% to 98% was attri-
buted to this phenomenon with only a slight change in electron density.
This resonance phenomenon and coupling efficiencies at lower gas pres-
sures than those considered in this investigation need further experi-
mental and analytical work. The use of cyclotron resonance (with a d.c.
magnetic field present in the discharge) to enhance microwave coupling
B-23
efficiencies should also be investigated.
The overall system efficiency of coupling microwave power to a
discharge is limited by the coupling efficiency defined in this
dissertation. In a practical device, reflected power has to be reduced
to only a small fraction of the incident power to approach the limiting
efficiencies. For high Q plasma/cavity operation (i.e. Qu > lOOO), a
very well filtered microwave source is required to match impedance at
the resonant frequency. Experiments similar to those described in this
Appendix, but at lower gas pressures, will require a better filtered
source than was used in these experiments.
APPENDIX C
APPENDIX C
BASIC EQUATIONS
C-l Ifl0l2 Mode Fields of the Ideal Empty Cavity
Consider an axially uniform, circular waveguide of radius d
having perfectly conducting walls. The fields of the cavity mode can be
obtained by a superposition of forward and backward traveling waves.
Denote w+ as the forward wave in the TM01 waveguide mode and w" as the
backward traveling wave. Solving equations 5.4, 5.5 and 5.6 (rewritten
in terms of ordinary Bessel functions and noting that there is only one
region interior to the waveguide):
w+(r,z) ~é-tl()(kcr)e"]BZ
— A jsz
w ('32) 7 Jo(kcr)e
where A/2 is an amplitude coefficient, Jo is the ordinary Bessel function
of the first kind of order zero and kc was determined by the boundary
condition at the metal wall (r = d):
where X0] is the first zero of J0(x) and X0] = 2.405.
The fields associated with each of these waves are:
C-2
E: (r,z) = é-JE. J](kcr) e-sz
H; (r,z) = %'%$f'dl(kcr) e-jCZ
and
E; (r,z) = g-J0(kcr) 93.82
E; (r,z) = -§%§J](kcr) (3sz
H; (r,z) = %.%fif.31(kcr) ejBZ
The superposition of these two waves (i.e. E = E+ + E“ and fi = fi+
+ H") gives:
Ez (r,z) = A J0(kcr) cos Bz
Er (r,z) = AR—E- J](kcr) sin 82
H¢ (r,z)
A %§5- J](kcr) cos 82
c
The TMO12 mode can thus be formed by placing perfectly conducting
shorts at z = 0 and z = L with the requirement that:
-23;
8'L
C-3
Note that B is purely real for the ideal cavity mode. Figure C-l describes
the axial and radial distributions of Er and E2 for the TM012 mode assuming
that the excitation frequency was 2.45 GHz, d = 8.9 cm and L = 14.4 cm.
H has a radial distribution similar to Er’ an axial distribution similar
¢
to E2 and is 90° out of time phase with E.
C-2 Characteristic Equation Used in the Analysis of Chapter V
Equation 5.7 is the characteristic equation pertaining to the geometry
of Figure 5.3. The form of equation 5.7 is described in this section and
the notation is fully defined in Section 5.3. The plasma/quartz/waveguide
dimensions (i.e. a,b,c,d) are defined in Figure 5.3.
Define:
c
_ 1
A11 ‘ 10(kc2b) ' CE'Ko(kc2b)
C
_ ~3
Al2 ' ' 10(kc3b) + Cg'Ko(kc3b)
52 c1
A21 = E" [11(kc2b) * C"K1(kc2b)]
c2 2
-53 C3
A22 ’ E" [11(kc3b) + C"Ki(kc3b)1
c3 4
where:
e I (k a) E
_ l 0 c2 2
Cl ‘ k Il(kcla) TBTEETET' k 2 11(kcza)
E1 * Ko(kc23) E2
Er or E2 (arb. units)
Er or E2 (arb. units)
Figure C-l
c-4
)-
t.
axial distance
radial distance (cm)
Theoretical radial and axial distributions of Er and
E2 in the TMO12 mode.
C-5
E4 C5 I (k ) E I (k )
C = ——- c + c
3 EEZ' C5 0 c3 kc3 1 c3
6 C e
4 6 3
C = ———- ——- K (k c) - -—— K (k c)
4 kc4 C5 0 c3 kc3 1 c3
and where
10(kc4d)
C5 = 10(kc4c) ’ K0 kc4d Ko(kc4c)
10(kc4d)
C6 ' ‘ [11(kc4c) + K0 kc4d K1(kc4c)1
The characteristic equation is:
A11 A22 ' A12 A21 0
where f(8,€]) in equation 5.7 is thus:
f(8’€1) = A11 A22 ’ A12 A21
REFERENCES
10.
11.
12.
REFERENCES
R. Fritz, "An Experimental Investigation of the Characteristics of
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J. Asmussen and J. Rogers, "An Assessment of the Potential Application
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Lewis Research Center Conference on Advanced Pr0pulsion Concepts
Using Time Varying EM Fields, Michigan State University, Feb. 23- 25
1982.
J.D. Cobine and D.A. Wilbur, "The Electronic Torch and Related High
Frequency Phenomena", J. Appl. Phys. 22(6), 835-841, June 1951.
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