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HIGH-POWER MICROWAVE BREAKDOWN OF
DIELECTRIC INTERFACES
by
STEVE EUGENE CALICO, B.S., M.S.E.E.
A DISSERTATION
IN
ELECTRICAL ENGINEERING
Submitted to the Graduate Faculty of Texas Tech University in
Partial Fulfillment of the Requirements for
the Degree of
DOCTOR OF PHILOSOPHY
Apjarfoved
Accepted
August, 1991
TABLE OF CONTENTS
ACKNOWLEDGEMENTS ii
ABSTRACT v
UST OF TABLES vi
LIST OF HGURES vii
CHAPTER
1. DsTTRODUCTION 1
2. EXPERIMENTAL CONHGURATION 3
2.1 High-Voltage Pulser 3
2.2 Vacuum Diode Design 6
2.3 System Diagnostics 9
3. MICROWAVE GENERATION 15
3.1 Electromagnetic Fields and Analytical Calculations 15
3.2 Microwave Generation Simulation 20
3.3 Microwave Power Calculations 27
4. EXPERIMENTAL DATA 31
4.1 Low-Power Tests 34
4.1.1 Planar Windows 36
4.1.2 Non-Planar Windows 45
4.2 High-Power Tests 55
5. DATA ANALYSIS 60
5.1 Breakdown Field Predictions 60
5.2 Window Performance Comparisons 76
6. COMPARISON TO EXISTING DATA AND THEORETICAL DEVELOPMENT 82
7. CONCLUSIONS AND RECOMMENDATIONS FOR FURTHER STUDY 90
m
•^\
LIST OF REFERENCES 93
APPENDICES
A. MICROWAVE GENERATION MAGIC SOURCE DECK 95
B. MICROWAVE POWER CALCULATION MAGIC SOURCE DECK 97
C. POWER CALCULATION DETAILS AND RADL^TION PATTERNS 99
IV
* \
ABSTRACT
A project to study the electrical breakdown of microwave windows due to
high-power pulsed microwave fields was undertaken at Texas Tech University. The
pulsed power equipment was acquired from the Air Force Weapons Laboratory
(now Phillips Laboratory) in Albuquerque, NM, refurbished and redesigned as
necessary, and serves as the high-power microwave source. The microwaves are
used to test various vacuum to atmosphere interfaces (windows) in an attempt to
isolate the mechanisms governing the electrical breakdown at the window.
Windows made of three different materials and of three basic geometrical
designs were tested in this experiment. Additionally, the surfaces of two windows
were sanded with different grit sandpapers to determine the effect the surface
texture has on the breakdown. The windows were tested in atmospheric pressure
air, argon, helium, and to a lesser extent sulfur-hexafluoride. Estimates of the
breakdown threshold in air and argon on a Lexan window were obtained as a
consequence of these tests and were found to be considerably lower than that
reported for pulsed microwave breakdown in gases. A hypothesis is presented in
an attempt to explain the lower breakdown electric field threshold. A discussion of
the comparative performance of the windows and an explanation as to the enhanced
performance of some windows is given.
UST OF TABLES
1. Zeroes of J and Cutoff Frequencies for the First Four TM Modes 17
2. Summary of Windows Tested and Test Conditions 33
3. Parameters Used In Maximum Electric Field Calculations 73
4. Maximum Power and Corresponding Maximum Electric Field 73
5. Summary of Previously Reported Breakdown Results 84
CI. Results of Method 1 Power Calculations 100
C2. Results of Method 2 Power Calculations 101
VI
UST OF HGURES
1. Overview of the High-Power Microwave Experiment 5
2. Redesigned Vacuum Diode 8
3. Uncompensated Diode Voltage Probe Waveform 10
4. Compensated Diode Voltage Probe Waveform 11
5. View of the Anechoic Chamber and the B-dot Probe Location 12
6. Calculated Frequency versus Diode Voltage 17
7. First 5 Nanoseconds of the Experimental Microwave Signal 19
8. Photograph of Fluorescent Tubes Excited by Microwaves 19
9. MAGIC Microwave Generation Simulation Region 21
10. Diode Voltage from the MAGIC Simulation 22
11. r versus z Phase-Space Plot from the MAGIC Simulation 23
12. PJ versus i Phase-Space Plot from the MAGIC Simulation 24
13. MAGIC Simulation Microwave Field in the Waveguide 25
14. FFT of the MAGIC Simulation Microwave Field 26
15. Diode Detector Calibration Curve 29
16. Non-Planar Windows: (a) Protmding Cone, (b) Inverted Cone 32
17. Marx Voltage of Low-Power Shots 35
18. Diode Voltage of Low-Power Shots 35
19. Diode Curtent of Low-Power Shots 36
20. Propagated Microwave Power through the Unfaced Planar Lucite
Window 37
21. Representative Breakdown Photogr^hs on the Planar Windows 38
22. Propagated Microwave Power through the Unfaced Lexan Window 39
23. Propagated Microwave Power through the Smooth Black Nylon Window 40
24. PMT and B-dot Signals for the Black Nylon Window in Air 41
vii
25. PMT and B-dot Signals for the Black Nylon Window in Argon 41
26. PMT and B-dot Signal for the Black Nylon Window in Helium 42
27. Propagated Microwave Power through the Lucite Window with the Small Aquadag Patch in the Center 43
28. Propagated Microwave Power through Lucite Window with the Large Aquadag Patch in the Center 43
29. Propagated Microwave Power through the Lexan Window Sanded with 1200 Grit Sandpaper 44
30. Propagated Microwave Power through the Lexan Window Sanded with 80 Grit Sandpaper 45
31. Propagated Microwave Power through the Lexan Window with Different Relative Humidities in Air 46
32. Photogr^h of the Electrical Failure of the First Non-Planar Window 47
33. Propagated Microwave Power Through the Protruding Cone in
Atmosphere Window 48
34. Breakdown Photographs on the Protmding Cone Window 49
35. Propagated Microwave Power Through the Inverted Cone in Atmosphere Window 50
36. Breakdown Photographs on the Inverted Cone in Atmosphere Window 51
37. Propagated Microwave Power Through the Inverted Cone in Vacuum Window 52
38. Propagated Microwave Power Through the Protmding Cone in Vacuum Window 52
39. Breakdown Photographs on the Inverted Cone in Vacuum Window 53
40. Breakdown Photographs on the Protruding Cone in Vacuum
Window 54
41. Marx Voltage of a High-Power Shot 56
42. Diode Voltage of a High-Power Shot 57
43. Diode Current of a High-Power Shot 57 44. Fluorescent Tubes Excited by a High-Power Shot 58
vm
45. Window Breakdown of a High-Power Shot on a Planar Lucite Window in Air 59
46. Propagated Microwave Power of the High-Power Tests Through a Planar Lucite Window 59
47. Axial Electric Field Contours for the Planar Windows 61
48. Radial Electric Field Contours for the Planar Windows 62
49. Axial Electric Field Contours for the Protmding Cone In Atmosphere 63
50. Radial Electric Field Contours for the Protmding Cone in Atmosphere 64
51. Axial Electric Field Contours for the Inverted Cone in Atmosphere 65
52. Radial Electric Field Contours for the Inverted Cone in
Atmosphere 66
53. Axial Electric Field Contours for the Inverted Cone in Vacuum 67
54. Radial Electric Field Contours for the Inverted Cone in Vacuum 68
55. Axial Electric Field Contours for the Protmding Cone in Vacuum 69
56. Radial Electric Field Contours for the Protmding Cone in
Vacuum 70
57. Breakdown Electric Field Strengths for the Different Windows 74
58. Sketch of the Breakdown Region on the Protmding Cone in
Atmosphere 75
59. Calculated Beam Energies for the Windows Tested 77
60. Device Efficiencies for the Different Microwave Windows 78
61. Theoretical Secondary Electron Emission Curves 85
62. General Insulator SEEC Curve 85
63. Ionization Efficiency of Some Gases 88
CI. Results of the B-dot Probe Calibration Calculations 101
C2. Radiation Pattern of the 1.27 cm Thick Planar Window 104
C3. Radiation Pattern of the Protmding Cone in Atmosphere 104
C4. Radiation Pattern of the Inverted Cone in Atmosphere 105 ix
C5. Radiation Pattern of the Protmding Cone in Vacuum 105
C6. Radiation Pattem of the Inverted Cone in Vacuum 106
CHAPTER 1
INTRODUCTION
In the past decade the generation of microwaves with power levels above 1
GW has been achieved and documented'. At these power levels the threshold for
air breakdown can be exceeded, resulting in the formation of a plasma. Since a
plasma is a conducting medium, some of the microwave power wiU be reflected,
refraaed, and/or absorbed upon interaction with this plasma.
The initiation of breakdown will occur in a region of highest electric field
intensity, which for unfocused waves is at the source or the antenna. If the source
operates in a vacuum, which is generally the case, the atmospheric side of the
dielectric interface (window) between the evacuated region and the atmosphere is
the place where breakdown occurs. This is the case because the electric field is
highest right at the antenna and the holdoff strength of atmospheric air is lower
than vacuum. The impedance mismatch as the wave propagates from vacuum
through the window into the atmosphere may enhance this breakdown process at
the window surface. If the breakdown at the window can be prevented, then higher
power densities can be propagated from the source into the atmosphere.
A considerable amount of experimental and theoretical work has been done
in the area of RF breakdown of various gases "*. Recentiy a report on gas break
down due to pulsed microwave fields of less than 100 ns duration has been
published . The subject of this dissertation is the phenomenon of breakdown at the
output window due to a high-power, pulsed microwave field. To this author's
knowledge no work has been documented in this specific area. In practice this
problem is overcome by flaring the wavegmde with a hom to dimensions large
enough so that the electric fields are below the breakdown threshold.
The microwaves are generated in this experiment with a virtual cathode
oscillator (vircator). An electron beam is generated in a vacuum diode and injeaed
1
into a waveguide through a transparent (screen) anode. If the electron beam
exceeds the space-charge-limit in the waveguide, then a virtual cathode that
oscillates in space and time is formed in the waveguide. Once the virtual cathode
forms and begins to oscillate microwaves can be extracted.
The vircator is driven by a typical pulsed power generator. Electrical
energy is stored in a Marx generator, transferted to a pulse forming line (PFL),
which serves as intermediate storage and pulse shaper, then switched into the
vacuum diode which is the load. A discussion of the pulser, vacuum diode,
associated support equipment, and the experimental diagnostics is given in Ch^ter
2. The microwaves that are produced and the computer simulations involved with
the experiment are discussed in C3iapter 3.
The experimental data are presented in Chapter 4. These data consist of
Marx voltages, diode voltages and currents, and microwave power signals for the
different windows tested. The data are analyzed and estimates of the breakdown
strength in air and argon are given in Chapter 5. Also, in Chapter 5 a comparative
study of the performance of the windows is carried out. Chapter 6 gives an
overview of previously reported microwave breakdown strengths in the different
gases and a theory is presented as to why the breakdown strengths obtained in this
experiment do not agree with these previously reported results. A summary of the
conclusions drawn from the experimental data is given in Chsqjter 1.
CHAPTER 2
EXPERIMENTAL CONHGURATION
To do pulsed, high-power, microwave breakdown experiments it is, of
course, necessary to have a high-power microwave source. In this case the source
is a vircator. A vircator consists of a high-voltage pulser utilized to drive a high-
power vacuum diode that produces an electron beam. The electron beam is then
injected through a transparent (screen) anode into a circular waveguide where the
space-charge-limit is exceeded, a virtual cathode forms and oscillates, producing
nucrowaves. The details of the electron beam generator have been given in a
previous M.S. thesis^ but a brief description wiU also be given here for com
pleteness.
2.1 High-Vohage Pulser
The high-voltage pulser consists of a Marx generator, oil containment tank,
charging induaor, PP^, and output switch. The Air Force Weapons Laboratory
(now Phillips Laboratory) in Albuquerque, New Mexico donated the components of
the pulser to Texas Tech University. Some of the hardware of a vacuum diode,
that has since been replaced, was included as well. Considerable refurbishment of
the device was necessary for it to become operational but these details will not be
discussed.
The principal of Marx generator operation is to charge cj^acitors in parallel,
then discharge them in series, resulting in voltage multiplication. If a Marx genera
tor is made up of n c^acitors (stages) each charged to a voltage, V , and they are
then connected in series (the Marx is erected) the output voltage will ideally be
2^roximately nV^.
The Marx generator of this experiment consists of 31, 0.2 pF capacitors,
each with a maximum voltage rating of 50 kV, therefore it can generate a maxi-
mum output of approximately 1.5 MV. The equivalent erected capacitance and
energy storage are 6.542 nF and 7.4 kJ, respectively. Switching is implemented by
gas filled spaik g£^s with breathing air as the working gas. The Marx generator is
fired upon command by applying a high-voltage pulse to field distortion planes
located in the first four switches. For high-voltage insulation purposes the entire
Marx generator is submerged in transformer oil.
It was originally planned to trigger the Marx generator with a Pacific
Atiantic PT-55 high-voltage pulser. This device can generate a 50 kV pulse of
approximately 100 ns duration with a rise time less than 10 ns under open circuit
conditions. It was found that the PT-55 did not provide reliable triggering of the
Marx bank, so a "mini-Marx" was constmcted. Four stages, each comprised of 4
"doorknob" capacitors in parallel, make up the mini-Marx and the switches are,
once again, air filled spark gaps. Upon release of the gas pressure in the mini-
Marx switches, the mini-Marx erects and a 140 kV, RC decay, pulse is delivered to
the trigger planes of the main Marx generator, initiating erection of the main Marx
bank. This has proven to be a very reliable method of triggering the experiment.
Intermediate storage and pulse shaping is provided by a coaxial, oil-filled
PFL. The electrical characteristics of the PFL are: Z^^=10 Q. and 1 ^ =12.5 ns
where Z^^ is the characteristic impedance and t ^ is the one-way transit time. A
25 pH inductor is located between the Marx generator and the PFL to provide
isolation for the Marx bank and also to determine the charging time of the PFL
(-500 ns). The inductor represents a high impedance to pulses that are refleaed
back toward the Marx generator, thus electrically isolating the Marx generator.
Charging the PFL through this charging inductor provides a ringing voltage gain, in
that, the PFL will attain a maximum voltage that is approximately 1.6 times the
output voltage of the Marx generator for this system. This also means that the
maximum energy transferted is only about 57% of the energy stored in the Marx
generator*.
The energy in the PFL is switched into the vacuum diode via a single
channel, self-breaking, oil switch. The voltage at which the switch fires is deter-
mined by the electrode separation which is adjustable from within the vacuum
diode region. The switch section is where the diode voltage and cmrent probes,
which will be discussed later, are located.
A short note about the support equipment is in order before a detailed
description of the vacuum diode is given. To fill the Marx tank, PFL, and output
switch requires close to 2500 gallons of transformer oil. An oil pumping station
was constmcted to facilitate filling and emptying the system, as well as circulating
the oil through filters for cleaning. The vacuum system consists of two mechanical
roughing pumps and a six-inch diffusion pump. The vacuum fittings, except for the
valves, are constmcted from aluminum irrigation pipe and were welded at a local
irrigation equipment dealer. This yielded considerable savings over commercial
vacuum fittings. To date the best vacuum attained has been better than 2x10"* Tort.
A A'y.Afx6' anechoic chamber was constmcted to radiate the microwaves into. All
inside surfaces of the anechoic chamber are covered with carbon impregnated foam
that absorbs microwave energy over a wide bandwidth. The foam used in this
application provides 30-40 dB attenuation at 2-3 GHz for near normal incidence.
The window that wiU be referted to repeatedly is located in the anechoic chamber.
It serves as a dielectric interface that the microwaves must pass through in going
from the evacuated waveguide to the anechoic chamber. A drawing of the overall
system is shown in Fig. 1.
Diagnostic Feedthrough
"L Mane Bank/Tank
PFl
J Oil Transfer
System
OU Switch
Diode Chamber
DUfiislon Pump
£ Waveguide
Anechoic Chamber
Roughing Pumps
Figure 1. Overview of the High-Power Microwave Experiment.
The original design of the system at Texas Tech included dielectric inter
faces on each end of the PFL. These interfaces allowed the oil switch and/or PFL
to be drained of oil without having to empty the Marx tank. Additionally, the
switch had a separate oil circulation system for more efficient filtration of the
switch oil. During the test phase of the pulser, where it was fired at relatively low
voltages, no problems with these interfaces were encountered. Upon increasing the
voltage to begin the breakdown smdies, however, both interfaces failed and have
since been removed from the system.
2.2 Vacuum Diode Design
Microwaves are produced by an oscillating virtual cathode that is formed
when the injected beam current exceeds the space-charge-limit in the waveguide.
The vacuum diode that generates this beam must, therefore, produce a beam of high
enough current to exceed this space-charge limit.
The criteria used in the design of the vacuum diode were: generate a beam
that would produce microwaves in the 2-3 GHz regime with enough power to cause
breakdown of the window. In addition it was desired to match the diode imped
ance, Z , as closely as possible to the impedance of the PFL (10 Q). Once these
parameters were established, approximate expressions for the Child-Langmuir
current and the microwave frequency were used to calculate the cathode radius and
anode-cathode (AK) gap. The relativistic Child-Langmuir current in kA is'°:
7^=8.5 K^'j
,f7-0Mll), (')
where r -r -^O.ld accounts for beam flaring, r is the cathode radius, ^ is the AK
gap, and y^ is the relativistic factor defined by:
with V, the diode voltage, in MV. The expression used for the microwave frequen
cy in GHz is** :
/ = ^4.77^
' J I^YOWYO-I^ ^ ^
where ^ is in cm. For a given operating voltage, if the frequency is known, the AK
gap, d, can be found from Eq. (3). Then, from Eq. (1) if the diode impedance is
known, the cathode radius, r , can be determined.
The PFL can be charged to a maximum voltage of ^proximately 2.4 MV,
which was found by multiplying the ringing voltage gain (1.6) by the maximum
Marx bank voltage (1.5 MV). One-half of the PFL vohage will be dehvered to a
matched load. This gives a maximum voltage of 1.2 MV across a 10 ft vacuum
diode. A diode voltage of 1 MV was chosen for the design parameter to be used in
Eqs. (l)-(3). This should generate a high current beam without over-stressing the
pulser components.
When 1 MV is substituted into Eq. (2) a relativistic faaor, y^, of 2.96 is
found. Using a frequency of 2.5 GHz, Eq. (3) can be solved to obtain a value of
3.33 cm for d. If a diode impedance, Z , of 10 Q is used then I^^ in Eq. (1) is
given by:
V IMV /_ = _ = i ^ l l = 1 0 0 kA. (4) ^ z ion
Upon rearranging Eq. (1) a quadratic equation in r can be obtained. Using the
positive solution of this quadratic equation gives a value of 10.79 cm for the
cathode radius. A beam of this radius is larger than the waveguide used in this
experiment, which has a radius of 9.84 cm. The diode impedance was increased to
15 n to reduce the cathode radius and cortespondingly the beam radius. When
this was done, r , was found to be 8.41 cm, which is the value that was used in the
diode design.
Figure 2 shows a drawing of the oil switch, redesigned vacuum diode, and a
section of the wavegmde. A radial dielectric interface made of acrylic (Lucite)
replaces the original insulator stack. The cathode is constmcted of aluminum and
hard anodized. The anodizing was then machined off the flat surface facing the
anode. The emission surface is a piece of white dress velvet cut to the desired
cathode diameter. Velvet is used because of its improved electron emission
compared to metals" and the color white was chosen because it shows the area of
intense emission by turning a brownish color. The anode is a woven stainless steel
screen with -67% transparency.
C u r r e n t S e n s o r
P r e p u l s e R e s i s t o r s
PFL
---3£-
/
/
nzs: Oil Switch-^ Cathode-I
i
Vacuum Diode
Waveguide
- - - f l
Anode
Figure 2. Redesigned Vacuum Diode.
There are six 3000 O. prepulse resistors in parallel, conneaed from the
cathode assembly to the outer conductor of the system. These serve to hold the
cathode close to ground while the PFL is being charged, otherwise capacitive
coupling wiQ cause the cathode potential to float with the PFL during charging,
thereby preventing the switch from firing and causing premature emission from the
cathode velvet. The total resistance of the prepulse resistors (500 Q) is large
compared to the diode impedance (15 ft) so that most of the current flows through
the diode, once it begins to conduct, and not through the prepulse resistors. One of
8
the prepulse resistors is configured as a resistive divider and is used to monitor the
diode voltage. Also shown in Fig. 2 is the location of the diode current probe.
2.3 System Diagnostics
The experimental diagnostics are the subject of a master's thesis that is
cuirentiy being written^ . An overview of the diagnostics wiU be given here and
the details of the constmction, calibration, and utilization will be left to the master's
thesis.
The Marx voltage and the diode voltage are monitored with resistive
dividers. The Marx voltage probe is uncompensated and has an input-to-output
voltage ratio of 6647 VA' . One of the prepulse resistors shown in Fig. 2 is
configured as the diode voltage monitor. This device consists of a 3000 Q. water
resistor in series with three, 1 ft, carbon resistors in parallel. A 50 ft carbon
resistor was soldered to the center conductor of a 50 ft coaxial cable, then this
assembly was connected across the three 1 ft resistors. The total voltage division
ratio of the probe is 18,000 to 1.
For a nanosecond rise time pulse the effects of the stray capacitance and
stray inductance associated with carbon resistors must be considered. This became
evident when the output of the diode voltage probe was recorded and the waveform
had no semblance to a pulse that might be expected from this experiment. A
waveform obtained from the probe is shown in Fig. 3. The spike at 25 ns is a
timing mark that is put on all experimental waveforms by the diagnostic system. A
computer program was developed to con^)ensate for the effects of the stray
capacitance and inductance of the carbon resistors.
The input and output of a linear system are related by:
V/CO)=//(CD)F.(CO), (5)
where Vj^co) is the Fourier transform of the output, V.((0) is the Fourier transform
of the input, H{(D) is the system ttansfer function, and co is the frequency variable.
In this case //(co) is the transfer function of the voltage probe, V.(a)) is the diode
>
40
20
0 -
-20 -
-40 -
-60
-
1 J 1
1 - i. ., . 0 50 100
Time (ns)
150 200
Figure 3. Uncompensated Diode Voltage Probe Waveform.
voltage transformed into the frequency domain, and V (co) is the probe output
transformed into the frequency domain. If //(co) can be found then:
v/0=^ //(CO)
(6)
where v.(r) is the probe input as a function of time and .?" denotes the inverse
Fourier transform operator. This means, that if //(co) is known, then the diode
voltage can be recovered from the noisy probe output. The probe transfer function
was found by recording its output due to a known input pulse. Fast Fourier Trans
forming (FFT) the input and output, and dividing the FFT of the output by the FFT
of the input. The computer code takes the output of the probe from an
10
experimental shot, takes the FFT, divides by the transfer function, then takes the
inverse FFT to obtain the diode voltage as depiaed by Eq. (6). Figure 4 shows the
waveform from Fig. 3 after application of the compensation program. The timing
mark at 25 ns is still on the waveform, it has just been smoothed by the compensa
tion process. For the complete details of the software compensation of the diode
voltage probe as well as a discussion as to the validity of this technique the reader
is referred to the M.S. thesis by Crawford .
The location of the diode current probe is also shown in Fig. 2. A transmis
sion-line Rogowski coil ^ is used to monitor the diode current. The probe is de
signed to behave as a transmission line instead of a circuit comprised of lumped
Figure 4. Compensated Diode Voltage Probe Waveform.
11
parameters as is the case in a conventional Rogowski coil. This device is capable
of very fast rise times (<1 ns) and, when homogeneously excited, the output is
proportional to the excitation cmrent for two transit times of the probe. Additional
ly, since the probe is homogeneously excited a full toroidal coil is not required to
measme the cmrent accmately. It is only necessary for the probe to have a two-
way transit time as long as the current pulse to be measmed. The probe described
here is a 60° section of a full toms. The two-way transit time is approximately 70
ns and the probe sensitivity is 2.73x10"^ V/A'^
A commercially available calibrated B-dot probe, located in the anechoic
chamber as shown in Fig. 5, is used to monitor the microwave power propagated
through the window. It is located as far from the window as possible and is
oriented to detect the H^ component of the microwave field. The output voltage,
Vp, of a B-dot probe is given by:
Waveguide
Window
1.35 m (53")
Fluorescent Tubes
Microwave Absorbing Foam
B-dot Probe
V To Oscil loscope
Figme 5. View of the Anechoic Chamber and the B-dot Probe Location.
12
v=A B O) 0 eq
where A^^ is the equivalent area of the probe (0.55xl0'^ m ) and 5 is the time
derivative of the magnetic flux density. For sinusoidally varying fields this reduces
to:
v,=coA^5=coA^^^ (8)
where co is the radian frequency of the microwave field, ji is the free space
permeability, and / / is the magnetic field intensity. This signal is sent to a micro
wave diode detector that gives an output voltage that is proportional to its input
power. The output of the diode detector is then recorded on a high speed oscillo
scope, hence the oscilloscope waveform is proportional to H^, or equivalentiy the
microwave power density.
To evaluate the total propagated power the computer code MAGIC**, a two
and one half dimensional, relativistic, self-consistent, particle-in-cell code, was
utilized. The simulation consists of a circular waveguide with the same diameter as
the experimental waveguide radiating into free space. An electromagnetic wave
representative of the experimental microwave mode was launched into the wave
guide and the magnetic flux density at a location corresponding to the B-dot probe
was calculated. From this the propagated power necessary to excite the B-dot
probe to a certain value can be found. A more detailed discussion of the MAGIC
code and the power calculations will be given in Chapter 3.
Two other diagnostic techniques are used to give qualitative information. A
grid of 4-foot long fluorescent mbes is located on the back wall of the anechoic
chamber (the wall farthest from the window). These mbes light up in areas of high
microwave power density, thus can be used to help determine the microwave mode.
The other diagnostic is a fiber optic cable, located to detect light at the window,
connected to a photo-mult^lier mbe (PMT). This is used to determine when the
breakdown of the window occurs with respect to the microwave signal. The
excitation of the fluorescent mbes is recorded by a camera located under the
13
waveguide apertme and aimed down range in the anechoic chamber. A camera is
also located to the side of the microwave window to take open-shutter photographs
of the breakdown plasma.
All of the diagnostic signals are carried by semi-rigid coaxial cables of
identical electrical lengths to a screen room where the oscilloscopes are located.
The cables were made the same length so that the signals from different locations
on the experiment could be cortelated in time. The transit time of the fiber optic
and the PMT were also adjusted to correspond to the transit time of the semi-rigid
coaxial cables. The Marx voltage is recorded on a Tektronix 7904 oscilloscope, the
dicxie current, microwave envelope signal, and the PMT output are recorded on
Tektronix 7834 storage oscilloscopes, and the uncompensated diode voltage is
recorded on a Tektronix 7104 oscilloscope. A Polaroid camera is used to save the
Marx voltage waveform and all other waveforms are digitized and saved by a
Tektronix digitizing camera system. A timing mark is added to all of the wave
forms to facilitate correlating the different waveforms in time. All oscilloscopes,
except the Marx voltage scope which is intemaUy triggered, are externally triggered
by the diode current rise. Waveforms from all of these diagnostic channels for
many experimental shots will be shown in Chapter 4.
14
CHAPTER 3
MICROWAVE GENERATION
Microwaves are generated by a vircator as a result of the conversion of the
kinetic energy in an electron beam to electromagnetic energy. The oscillation of
the virmal cathode in space and time is the mechanism of the energy conversion
process. The microwave electric and magnetic fields are determined by solving
Maxwell's equations to satisfy the boundary conditions in the circular waveguide.
These equations for the microwave fields and a discussion of the possible modes
for this system will be given. The calculated frequency value will be verified with
experimental data and a photograph of the mode pattem in the anechoic chamber
will be shown.
The two-dimensional, finite-difference time-domain computer code MAGIC
was used to simulate the microwave generation process. In addition to simulating
the nticrowave production, the code was used to calibrate the B-dot probe located
in the anechoic chamber.
3.1 Electromagnetic Fields and Analytical Calculations
In a vircator the microwaves are generated by two different and competing
processes* . In one case, the temporal and spatial oscillations of the virmal
cathode cause the axial electric field, £^, to flucmate. In the second case, electrons
reflex between the real and virmal cathodes which also causes flucmations in E . z
Regardless of which process is dominant, the time variation of E^ couples namrally
into axially symmetric transverse magnetic, TM j , modes in a circular waveguide.
The requirement that E^ 0 for a TE^ mode rules out the possibility of a TE
mode being present.
The electric and magnetic field components of a TM^ mode in cylindrical
coordinates (p ,<)) ,2) are given by:
15
£=£„MlJ, (pp)exp(- ;p .r) , (9a) cope ^
£^=0, (9b)
^.= -;^o—Jo(PpP)exp(-;-p/), (9c) cope ^
//p=0, (9d)
//,=£,lf.J,(PpP)exp(-;p^z), (9e)
//,=0, (9f)
where the following notation has been used:
Pp = xj^; Tion = n'^ zero of the zero order Bessel function of the first kind;
a = waveguide radius;
p = material permeability;
e = material permittivity;
CO = radian frequency;
P^ = propagation constant = Jpeco^-Pp ;
£(j = scaling constant;
Jp = zero order Bessel function of the first kind;
Jj = first order Bessel function of the first kind;
and the time dependence of the fields is implied. Now, for the microwaves to
propagate the frequency must be above the cutoff frequency, /^, defined by:
fr ^ - (10) 27Cflviie
Table 1 summarizes the values of Xc and f^ for the first fom TM^ modes in a
circular waveguide of 9.84 cm radius and Fig. 6 shows the frequency as a function
of diode voltage calculated using Eq. (3).
16
Table 1. Zeroes of J and Cutoff Frequencies for the First Fom TM Modes.
Mode
TM„i
™<«
™03
TM«
Xo,
2.4049
5.5201
8.6537
11.7915
/ , (GHz)
1.166
2.676
4.195
5.716
3.0
2.5
O
3
1.5 -
1.0 0.4 0.5 0.6 0.7 0.8 0,9 1.0
Diode Voltage (MV)
Figme 6. Calculated Frequency versus Diode Voltage.
17
It can be seen from Table 1 and Fig. 6 that for diode voltages in the range
0.4-1.0 MV the only mode that can propagate is a TM ,. As stated in Sec. 2.3 the
signal from the B-dot probe is usually passed through a diode detector that gives an
output voltage proportional to its input power, which is used to calculate the propa
gating microwave power in the anechoic chamber. To verify the operating frequen
cy of the vircator the diode detector was removed and the signal from the B-dot
probe was passed directiy into a high-speed oscilloscope.
The fastest available oscilloscope is a Tektronix 7104, which has a 3 dB
bandwidth of 1 GHz. It was found through experimentation, however, that this
oscilloscope will display a 2.5 GHz continuous wave (cw) signal. The magnimde
of this signal is not calibrated since the frequency is above the rated bandwidth, but
the frequency should still be accmate.
By adjusting the timing of the oscilloscope trigger it was possible to capture
the start of the microwave pulse, shown starting at approximately 15 ns in Fig. 7.
The time base of the oscilloscope must be set on 2 ns/div. to resolve the waveform,
hence only a 20 ns segment of the pulse can be captured at one time. It can be
seen from Fig. 7 that, at the beginning of the pulse at least, the frequency is around
2 GHz. For this waveform the diode voltage was approximately 550 kV which is
typical of many of the experimental shots discussed in this dissertation. This
frequency value is in good agreement with that predicted by Eq. (3). By triggering
the oscilloscope so that different 20 ns segments of the microwave pulse were
captmed it was ascertained that at no time during the pulse was the frequency
above the TM j cutoff frequency of 2.676 GHz. These data serve as further
evidence that only a TM ^ mode is present.
The fluorescent mbes located in the anechoic chamber are utilized to map
the microwave radiation pattem. The microwave field will excite the mbes in
regions of high-power density and will cause them to light up. Figme 8 shows an
open-shutter photograph of the fluorescent mbe artay being excited by a microwave
pulse. Although qualitative in natme the power null in the center, characteristic of
a TMj mode, can clearly be seen.
18
50
25 -> B
'4-1
3 o O I
CQ
-25 -
-50
' A A 1 lA r^
.
i II III A 1 II
M 1 ., .*
1
i
0 10
Time (ns)
15 20
Figure 7. First 5 Nanoseconds of the Experimental Microwave Signal.
Figure 8. Photograph of Fluorescent Tubes Excited by Microwaves.
19
3.2 Microwave Generation Simulation
The experiment was simulated with the MAGIC computer code to see if 2
GHz microwaves were produced as predicted by Eq. (3) for a diode voltage of 550
kV. The MAGIC code uses the finite-difference approach to solve the full set of
time-dependent Maxwell's equations and the Lorentz force equation at discrete time
intervals. This method provides for self-consistent solutions, in that the interaction
between charged particles and electromagnetic fields is taken into account. The
simulation is carried out in a grid of rectangles with conducting boundaries appro
priate for the experimental configuration to be simulated. For geometric configura
tions that have a symmetric coordinate, such as the (j) coordinate in this experi
ment, all three of the field components as well as the three components associated
with particle kinematics are available for output.
For the simulation of the Texas Tech vircator the grid includes a short
coaxial section (the cathode shank), the vacuum diode, and a length of the wave
guide. A transverse electromagnetic (TEM) wave is launched into the coaxial
section, it then propagates into the vacuum diode where it accelerates electrons
made available at the cathode across the A-K gap. After traversing the A-K g ^
the electtons pass through the anode foil into the waveguide where the virtual
cathode is formed. The oscillation of the virmal cathode and the reflexing of the
electrons through the anode produces microwaves that propagate down the wave
guide and are allowed to leave the simulation through a lookback boundary. A
lookback boundary provides a matched boundary through which electromagnetic
fields can leave the simulation region.
A listing of the input deck that defines the simulation is given in Appendix
A. The corresponding grid is too dense to be shown clearly on letter size paper, as
there are 196 cells in the X^ (z) coordinate and 140 cells in the X^ (p) coordinate.
A diagram of the simulation region without the grid displayed is shown in Fig. 9.
A cylindrical coordinate system is used with symmetry about the p=0 axis, i.e., <|)
is the symmetry coordinate. The voltage across the A-K gap as a function of time
20
.3905
R (m)
Input Voltage
Cathode-
Anode
Waveguide
Anode Foil
•Z ( m ) -
Lookback Boundary
8037
Center Line
Figure 9. MAGIC Microwave Generation Simulation Region.
during the simulation is shown in Fig. 10. A value of 550 kV was chosen, because
that represents the diode voltage under acmal experimental conditions much of the
time.
Two phase-space plots at a time of 20 ns are shown in Figs. 11 and 12.
Figure 11 is a p (r in the figme) versus z phase-space plot. This plot shows the
position of the macroparticles representing electrons in the A-K gap and waveguide.
Electrons are being emitted from the cathode on the left and the anode foil is
located at z«0.08 m. The virtual cathode can be seen just to the right of the anode
at z«0.12 m. To the right of the virmal cathode, in the waveguide, electron
bunching can be seen. Figme 12 is a p versus z phase-space plot which repre
sents the z component of the electron momentum as a function of z, where in
MAGIC:
P,-Yv » (11)
with y the relativistic factor and v the z component of velocity. After emission
from the cathode the electrons are accelerated by the electric field across the A-K
gap. After passing through the anode they are then decelerated and some are
reflected back through the anode (reflexing) while some propagate on down the
21
MAGIC VERSION: JANUARY 1990 DATE: 11/0/12 SIMULATION: microwove generation 3
TIME HISTORY PLOT E2 COMPONENT
INTEGRATED FROM (2.58) TO (2.140)
8.0 12.0
TIME (s) 20.0
E-9
Figure 10. Diode Vohage from the MAGIC Simulation.
waveguide and are lost to the waveguide walls. Once again electron bunching is
evident in the waveguide.
The microwaves produced, in the simulation, by this process were observed
close to the outiet end of the waveguide (far to the right in Figs. 11 and 12). Since
a TMo, mode was expected the radial electric field, £p, as a function of time at its
radial maximum was recorded. This graph is shown in Fig. 13 and the FFT of the
waveform is shown in Fig. 14. These figmes clearly show microwave radiation at
approximately 2 GHz as predicted by Eq. (3) and in good agreement with Fig. 7.
This agreement between simulation results and experimental data indicates that the
MAGIC code can be used to simulate this system to obtain reasonable results.
22
o d
MAGIC VERSION: JANUARY 1990 DATE: 11/0/12 SIMULATION: microwave generaflon 3
PHASE-SPACE PLOT OF R VS. Z AT TIME: 2.00E-08 SEC SPECIES: ELECTRON Q/M RATIO: -1.759E+11
to d
l " , * . , : N , ; - I
I / - :^->«t\v-V:' • •-•V*0V- • • ' • •Ml; -
:' : ^l^^^'i^r ':^.;^-m ••-.^^•':i.f
""'•• .-Vv,-, .•
— I
0.4
Z (m) 0.6 0.8
Figure 11. r versus z Phase-Space Plot from the MAGIC Simulation.
23
CD + Ld
E N
CL
MAGIC VERSION: JANUARY 1990 DATE: 11/0/12 SIMULATION: microwave generation 3
PHASE-SPACE PLOT OF PZ VS. Z AT TIME: 2.00E-08 SEC SPECIES: ELECTRON Q/M RATIO: -1.759E-f 11
Figure 12. p^ versus z Phase-Space Plot from the MAGIC Simulation.
24
MAGIC VERSION: JANUARY 1990 DATE: 11/0/12 SIMULATION: microwave generafion 3
TIME HISTORY PLOT E2 COMPONENT
AT COORDINATE (190.39)
TIME (s) 20.0
E-9
Figure 13. MAGIC Simulation Microwave Field in the Waveguide.
25
en LiJ
i
MAGIC VERSION: JANUARY 1990 DATE: 11/0/12 SIMULATION: microwave generaiion 3
TIME HISTORY PLOT MAGNITUDE OF FFT OF E2 COMPONENT
AT COORDINATE (190,39)
FREQUENCY (Hz) 12.0
E+9
Figure 14. FFT of the MAGIC Simulation Microwave Field.
26
3.3 Microwave Power Calculations
The MAGIC code was also used to simulate the microwave radiation in the
anechoic chamber. Through computer analysis it was found that the azimuthal
component of the magnetic flux density, B^, at the location of the B-dot probe is
directiy proportional to the radial component of the electric field strength, £ , in
the waveguide. Since the power propagated in a circular waveguide for a TM ^
mode is directiy proportional to |£ ^ p this implies that the power is also directiy
proportional to \B^\^. This relationship will be used to calculate the propagated
power in the anechoic chamber from the B-dot probe/diode detector output. In
other words the B-dot probe is being calibrated. It should be pointed out that this
calibration is frequency dependent because the radiation pattem of an antenna is
frequency dependent. The calibration was carried out at 2 GHz to cortespond with
the experimental microwave frequency. Additionally, the calibration must be done
for each of the geometrically different windows since the window geometry may
also affect the radiation pattem.
The approach was to set up a simulation grid representative of the anechoic
chamber including the end of the waveguide and the B-dot probe as shown in Fig.
5. The input deck for the MAGIC code in this simulation is given in Appendix B.
A TM(jj wave introduced into the waveguide will propagate down the waveguide,
through the window, and into the anechoic chamber, where the magnetic flux
density, B., can be observed at the location cortesponding to the B-dot probe. If
the total power can then be calculated, the B-dot probe can be calibrated. This
procedme must be repeated for each different window shs^, in case the window
affects the radiation pattem. A detailed description of the techniques used to
calculate the power and to check the validity of the results is given in Appendix C.
Also, included in Appendix C are polar plots of the calculated far field radiation
pattem for each window.
The power was calculated by finding (in spherical coordinates) the radially
directed power density, S , as a function of 9 for constant r as far from the
27
window as the simulation parameters would permit. The origin of the spherical
coordinate system used in these calculations is centered at the end of the waveguide
and the z axis points into the anechoic chamber. Once 5 was found as a function
of e it was numerically integrated from 0=0 to e=7c/2 to obtain the total power
propagated into the anechoic chamber. Usually the integration of the power density
to obtain the total power is carried out for O<0<7C but it was found that S^ makes
a negligible contribution to the integration for 7t/2<9<7C. These calculations were
carried out as far from the window as possible so that the far field ^proximation
could be used. For a TM j mode the power density is given by:
Sr-\E^;\ (12)
where E^ is the theta component of the electric field intensity and H^ is the
complex conjugate of the phi component of the magnetic field intensity. In the far
field, where the propagating wave is a transverse electromagnetic wave, this can be
approximated by:
5 ,=^ |B,P- (13) ,3
t]l'
Since 5 is a quantity directiy available from MAGIC in this simulation the power
density and then the total power can be calculated.
If the B-dot excitation at one power level is known then the power corte
sponding to some other B-dot excitation can be calculated from the relation:
P P c e
\H ^ \H 12 (14)
where P is the calibration power level, H^ is the calibration magnetic field intensi
ty, / / is an experimental magnetic field intensity, and P^ is the unknown power.
If the value of H at the B-dot probe can be found as a function of time in the
microwave pulse then the instantaneous microwave power can be calcxilated.
28
The calibration curve for the diode detector is shown in Fig. 15. In Fig. 15,
P.^ is the average power into the diode detector and V^^^ is the voltage output of
the detector and equivalentiy the voltage deteaed by the oscilloscope. For almost
all experimental shots there was a 20 dB attenuator between the B-dot probe and
the diode deteaor. When this is taken into account the calibration curve is given
by:
P^=34.6025K 1.64523 (15)
where P^ is the power out of the B-dot probe. Further, the power out of the probe
is given by:
Pr,^ V. RMS
B 50 100 (16)
10 1-1
10"
10-
10-
P * 0.346025V - 23 is out
0 Actual Data
— Curve Fit
10- 10-2 10-
V ^(V) out
Figure 15. Diode Detector Calibration Curve.
10
29
where V ^^ and V^ are the probe RMS and peak output voltages, respectively.
Substituting Eq. (16) into Eq. (15), the following relationship between the probe
voltage and the oscilloscope waveform results:
V,=58.82V:'.f^". (17)
Finally, using Eq. (8) with A =0.55x10"' m^ and co=4jtxl0' rad/sec in Eq. (17),
H^ at the probe can be found as a funaion of the oscilloscope voltage:
/ / , =677.28 vr""' . (1^)
With the use of Eq. (18) and Eq. (14) the instantaneous microwave power in the
pulse can then be calculated. The results of these calculations wiU be shown in
Chapter 4.
30
CHAPTER 4
EXPERIMENTAL DATA
Tests were done on windows made of different materials, windows of
different geometrical shapes, and windows with different surface conditions in an
attempt to isolate the dominant factors in the window breakdown. By determining
these faaors it was hoped that steps could then be taken to inhibit the breakdown
and hence, increase the propagated power density through the window. The
approach to taking data was to fire the experiment under as close as possible to
identical conditions with a variety of microwave windows on the end of the wave
guide. A clear plastic trash bag was attached to the window which allowed for
doing the breakdown tests in different gases. The gases used were bottied air,
argon, helium, and to a lesser extent sulfur-hexafluoride (SF^).
The original plan was to take at least five shots on each window and gas,
then average the data for each case. It was thought that from shot to shot the
operation of some component of the microwave generator may vary enough to
affect the produced microwaves sigruficantiy . These variable parameters include
but are not limited to the charge voltage of the Marx bank, the voltage at which the
oil switch fired, and the behavior of the vacuum diode. As experience was gained
in operating the device, it was found that in most cases it was not necessary to take
five shots to get repeatable results. If, when comparing two different shots on the
same window and same gas, the current waveforms were similar in magnitude and
shape, then the experiment was considered to have fired under identical conditions.
Under these similar current conditions, it was almost always the case that the
microwave signals deteaed at the B-dot probe were also very similar. All data
shown will be the average of at least two, and sometimes more, shots on each
window and gas.
31
The windows tested will be put into two basic categories: planar geometry
and non-planar geometry. Planar windows were made from Lucite, Lexan, and
black nylon. In addition to being of different materials some windows of the same
material had different surface preparations on the atmospheric side of the window.
Two non-planar windows, both constmcted of Lexan, were also designed for
testing. The geometry of these windows is shown in Fig. 16 and a summary of the
window parameters and test conditions is given in Table 2. The notation intro
duced in Fig. 16 for these window geometries wiU be used throughout this disserta
tion. A more detailed discussion of each of these windows and the data taken wiU
be given shortiy.
1.5 -
(a) (b)
Figure 16. Non-Planar Windows: (a) Protmding Cone, (b) Inverted Cone.
All of the windows discussed thus far were tested under what will be termed
low-power conditions. The low-power shots have calculated peak microwave
powers of slightiy greater than 100 MW. This power level was sufficient to create
a reflecting/absorbing plasma on all windows in helium, and on all windows except
one in argon. Additionally, a plasma "spike" at the center of the window was
32
Table 2. Summary of Windows Tested and Test Conditions.
Window Number
2
3
4
5
6
7
8
9
10
11
12
13
14
Description
planar Lucite, 1/2" thick, unfaced
planar Lexan, 1/2" thick, unfaced
planar nylon, 1/2" thick, faced
planar Lucite, 1/2" thick, unfaced
planar Lucite, 1/2" thick, unfaced
planar Lexan, 1/2" thick, faced
non-planar Lucite, 1" thick, faced
planar Lexan, 1/2" thick, faced
non-planar Lexan, 1/2" thick, protmding cone
non-planar Lexan, 2" thick, inverted cone
planar Lexan, 1/2" thick, unfaced
non-planar Lexan, 2" thick, inverted cone
non-planar Lexan, 1/2" thick, protmding cone
Gases Used
Air, Ar, He, SF^
Air, Ar, He, SF
Air, Ar, He
Air, Ar, He
Air, Ar, He
Air, Ar, He
Air, Ar, He
Air, Ar, He
Air, AT, He
Air, Ar, He
Air
Air, Ar, He
Air, Ar, He
Notes
black nylon (optically opaque)
2" diameter Aquadag disk painted in the window center
8" diameter Aquadag disk painted in the window center
random siuface roughening with 1200 grit sandpaper
2" diameter, 45° cone cemented in the window center
random surface roughening with 80 grit sandpaper
protmding cone on the atmospheric side
inverted cone on the atmospheric side
73% and 86% relative humidity
inverted cone on the vacuum side
protmding cone on the vacuum side
33
created in air for all windows except one. No breakdown was detected at this
power level with SF^ on the window so tests with SF were discontinued at this
power level. If, upon testing a certain window, it seemed that additional informa
tion could be gained by running a set of tests with SF , then it was done. There
was no noticeable difference in the microwave signal detected at the B-dot probe
between the shots with air and with SF . This indicates that although there is some
breakdown in air, it has a negligible effect on the propagated microwave power.
One set of data was taken on a planar Lucite window at a much higher power level
(P>1GW). The results of this test will also be given.
Light inside the waveguide is observed in the photographs of the plasma on
the transparent windows (all windows except black nylon). This is the result of a
voltage breakdown in the region of the anode screen. All attempts to prevent this
breakdown from occurring failed, so it was just allowed to happen. It is not known
what effect this has on the microwave production, but in any case, sufficient micro
wave power in a repeatable mode was generated to conduct the microwave break
down tests.
4.1 Low-Power Tests
Over 150 shots were taken to obtain the data on all the windows listed in
Table 2. These shots were all at approximately the same power level and the Marx
voltages, diode voltages, and diode currents from shot to shot were very similar.
For this reason representative waveforms for all of these quantities will be shown in
Figs. 17-19 and not repeated. As stated earlier, the Marx voltage is from an
uncompensated resistive divider, the diode voltage is from a software compensated
resistive divider, and the diode current is from the transmission line Rogowski coil.
The diode voltage in Fig. 18 shows the characteristics of a charged transmission
line being switched into an unmatched load. A series of pulses, each two transit
times of the PFL (2x^^=25 ns) in length, can be seen. The curtent waveform
given in Fig. 19 is much smoother. Referring to Fig. 2 it can be seen that the
voltage actually being measured is the voltage across the diode plus the voltage
34
400
>
00
cd
o >
Figure 17. Marx Voltage of Low-Power Shots.
Figure 18. Diode Voltage of Low-Power Shots.
35
200
Figure 19. Diode Current of Low-Power Shots.
across the inductance associated with the coaxial geometry extending from the
location of the probe to the diode load. Similarly, the cmrent probe is monitoring
the current through the diode and this induaance. This inductance is the reason for
the difference in the voltage and the current wave shapes. It should also be
remembered that the curtent sensor is only calibrated for two transit times of the
probe (-70 ns), so after approximately 120 ns, which is 70 ns after the start of the
current, the waveform shown in Fig. 19 is not representative of the experimental
current.
4.1.1 Planar Windows
Window number 1 was a 2.54 cm thick piece of Lucite. The main purpose
of this window was to be a vacuum/atmosphere interface at the waveguide output
during the constmction and testing of the project. It was not designed to be one of
the test windows so no breakdown tests were conducted on it. This explains why
the window numbering starts at two instead of one.
36
Window 2 was the first window that breakdown experiments were per
formed on. This window is a piece of unfaced Lucite, 1.27 cm thick. Unfaced,
designates that the proteaive paper used in shipping the material was just peeled
off and no machining was done to the surface. This window as well as all other
windows were cleaned with cyclohexane before the tests were done. Figure 20
shows the propagated microwave power, calculated as outlined in Section 3.3, for
air, argon, and helium. Data were also taken for SF on the window, but the
microwave powers for SF^ and air were almost identical, indicating that the small
breakdown in air is blocking a negligible amount of the microwave power.
Open shutter photographs of the breakdown for the different gases are
shown in Fig. 21, where the top photograph cortesponds to air, the middle picture
to argon and the bottom to helium. The light inside the waveguide, mentioned at
the beginning of this chapter, can be seen through the transparent window in the
top picture of Fig. 21. Using the diameter of the waveguide (19.7 cm) as a scale, it
Figure 20. Propagated Microwave Power through the Unfaced Planar Lucite Window.
37
(Air)
(Ar)
(He)
Figure 21. Representative Breakdown Photographs on the Planar Windows.
38
can be seen that the breakdown region is approximately 2.5 cm in diameter at the
window surface and extends 8-10 cm out from the window. The camera f-stop was
set at 4.5 for the air picture and at 22 for the argon and helium pictures. It can be
seen in the top of Fig. 21 that £^ (maximum at the center in a TM ^ mode)
dominates the breakdown process. Also, from Fig. 21, it appears that the helium
plasma covers the window most completely, thus blocking the microwaves most
efficientiy. The breakdown photographs for other planar windows are very similar
to Fig. 21, hence they wiQ not be repeated here.
Windows 3 and 4 were constmaed from 1.27 cm thick Lexan and black
nylon, respectively. Window 3 was unfaced, as described for window 2, whereas
window 4 had the surfaces machined smooth because it was very rough as received
from the distributor. The propagated microwave power for the different gases is
shown in Fig. 22 for the Lexan window and in Fig. 23 for the nylon window. The
propagated power, as well as the breakdown photographs for these two windows
were very similar to those obtained for the unfaced Lucite window.
^ S
g
Figure 22. Propagated Microwave Power through the Unfaced Lexan Window.
39
I
200
150 -
100 -
50 -
Figure 23. Propagated Microwave Power through the Smooth Black Nylon Window.
One reason a black nylon window was tested, was that, since it is optically
opaque, it is possible to separate the light generated inside the waveguide from that
generated by the window breakdown plasma. Figures 24-26 show the output of the
PMT and the rectified B-dot probe output. These graphs show the relationship
between plasma formation time and the microwave power for the different gases
tested. It can be seen that for similar incident microwave pulses the plasma forms
earliest in the microwave pulse for helium, then for argon, and latest for air. Since
the microwave pulses have similar rise times this implies that helium breaks down
at the lowest power level and electric field strength followed by argon, then air.
Windows 5 and 6 were of the same material and stmcture as window 2;
unfaced, 1.27 cm thick Lucite. On window 5 a 5.08 cm diameter patch of Aquadag
(gr^hite in an aqueous solution) was painted in the center of the window and on
window 6 an Aquadag patch, 20.32 cm in diameter, was painted in the center. The
20.32 cm diameter patch essentially covers the entire aperture. The secondary
electron emission coefficient (SEEC) of aquadag is much lower than that of Lucite.
40
100 150 Time (ns)
Figure 24. PMT and B-dot Signals for the Black Nylon Window in Air.
0.10 020
100 150
Time (ns)
Figure 25. PMT and B-dot Signals for the Black Nylon Window in Argon.
41
Figure 26. PMT and B-dot Signal for the Black Nylon Window in Helium.
If secondary electron emission from the window is significantly affecting the
breakdown process, then by coating the window with a material that has a low
secondary electron yield should reduce the formation of the plasma.
The breakdown in air for the window with the small Aquadag patch did
seem to decrease somewhat but the photogr^hic evidence of plasma formation in
argon and helium was inconclusive. The propagated microwave powers are shown
in Fig. 27. There is no increase in the propagated power for this window as
compared with the previously tested windows. The size of the aquadag patch was
enlarged on window 6 because it was thought that not enough of the window had
been covered to affect the breakdown in the lower threshold gases argon and
helium. Figure 28 shows the propagated power for this window. It is evident that
very litde power is making it through the window, regardless of which gas is used.
The breakdown is reduced on the Aquadag coated windows because the Aquadag
reflects the microwave power, hence less power is available to initiate plasma
formation. This fact rules out the use of Aquadag, in this form, as a component of
42
^
s
I
200
150 -
100 -
50 -
-
-
-
-
--
-
— Helium Argon
— Air
1 ; •.•• ; \
>: \ '^l\ i ;/A-/\ ... "' 1
y 1 "• 1 :
\ ' -
50 75 100
Time (ns)
125 150
Figure 27. Propagated Microwave Power through the Lucite Window with the Small Aquadag Patch in the Center.
200
150 -
^
S
I 100 -
50 -
-
--
1 1
1 I
1 1
-
^__^^
<oi^i^
— Helium Argon
— Air
50 75 100 125
Time (ns)
150
Figure 28. Propagated Microwave Power through Lucite Window with the Large Aquadag Patch in the Center.
43
a nticrowave window. A thinner carbon coating (e.g. vacuum vapor deposited) may
still work, however, this was not tried but is planned for later investigation.
It has been shown that the unipolar, pulsed surface voltage hold-off strength
of Lexan in vacuum can be affeaed by up to a factor of 2 by randomly roughening
the surface with different grit sandpapers.' The best improvement was attained
when 1200 grit sandpaper was used. Windows 7 and 9 were 1.27 cm thick, planar
Lexan with the surface on the atmosphere side randomly roughened. Twelve
hundred grit was used on window 7 and, for comparison, window 9 was sanded
with 80 grit. Once again, no dramatic increase in propagated microwave power
resulted, as illustrated in Figs. 29 and 30.
Because of the availability of planar windows already constmcted at this
stage of the experiment, a set of tests were conducted to see what effect the relative
hunudity in air has on the power propagating through the region close to the
window. What is designated as window 12 is actually window 3 with humidified
^
S V
%
Figure 29. Propagated Microwave Power through the Lexan Window Sanded with 1200 Grit Sandp^>er.
44
> s
I
200
150 -
100 -
50 -
-
-
-
-
-
• -I
--
T-
T
r J
1
— Helium Argon
— Air
/'•••• l \
I 4iv.-... 50 75 100
Time (ns)
125 150
Figure 30. Propagated Microwave Power through the Lexan Window Sanded with 80 Grit Sandpaper.
air on the atmospheric side of the window. Atmospheric air was bubbled through
water, then pumped into the trash bag enclosing the window. Measurements with a
hygrometer indicated that relative humidities of 73% and 86% were obtained. The
tests with a relative hunudity of 73% will be designated window 12a and those with
86% relative humidity window 12b. The propagated power of these two tests,
along with, for comparison, the propagated power in "dry" bottied air for the planar
Lexan window are shown in Fig. 31.
It appears that, except in the case of the Aquadag coated windows which
lowered the propagated power, the various planar windows tested demonstrated no
dramatic differences in propagated power when compared to each other. The data
taken on the planar windows will be examined in more detail in Chapter 5.
4.1.2 Non-Planar Windows
In an effort to alter more dramatically the plasma formation and microwave
power propagated, two different non-planar windows were tested. After an initial
45
—Bottled Air 73%ReL Hum.
— 86%ReLHum.
I DN
Figure 31. Propagated Microwave Power through the Lexan Window with Different Relative Humidities in Air.
test with a window made of Lucite the rest of the tests were performed on non-
planar windows fabricated from Lexan.
Window 8 was the first non-planar window to be tested. It was of the shape
designated "protmding cone" in Fig. 16a except the thickness of the bulk of the
window was 2.54 cm instead of 1.27 cm and the cone was 2.54 cm taU instead of
3.81 cm tall. The window was constmcted by taking window 1 (2.54 cm thick
planar Lucite) and cementing a 5.08 cm diameter, 45° cone in the center. It was
oriented on the end of the waveguide so that the cone was on the atmospheric side.
In all shots on this window there was electrical breakdown in the glue joint where
the cone was affixed to the planar window. A photograph illustrating this failure is
shown in Fig. 32. A full set of data was taken on this window, however, it will not
be presented because the B-dot probe was not calibrated for this particular window
as it was for the other windows discussed.
46
Figure 32. Photograph of the Electrical Failure of the First Non-Planar Window.
Since window 8 suffered catastrophic failure, another protmding cone
window was fabricated. Window 10 was fabricated from Lexan and its dimensions
are given in Fig. 16a. The propagated power graph is given in Fig. 33 and a set of
breakdown photographs are given in Fig. 34. The top, middle, and bottom pictures
in Fig. 34 correspond to air, argon, and helium, respectively. It is interesting to
note that the breakdown in air is out on the end of the cone, as shown in the top
photograph of Fig. 34. Also interesting in the middle and bottom pictures of Fig.
34 is how the shape of the plasma volume has changed in comparison to the plasma
formed on the planar windows, as depicted in Fig. 21.
A second non-planar window of the "inverted cone" design, shown in Fig.
16b and designated window 11, was constmcted of Lexan. The depression in the
5.08 cm thick material is facing toward the atmospheric side. The microwave
power is shown in Fig. 35 and a set of breakdown photographs are given in Fig.
36. Once again, the top picture is for air, the middle is for argon and the bottom is
for helium. Figure 36 has some interesting aspects, as did Fig. 34. Notably, there
47
Figure 33. Propagated Microwave Power Through the Protmding Cone in Atmosphere Window.
is no breakdown in air and much less breakdown in argon for the inverted cone
window in comparison to the other windows. Because of the qualitative nature of
the photographs it is not possible to draw conclusions about the breakdown in
helium compared to that for the planar and protmding cone windows.
Windows 13 and 14 are the inverted cone and protmding cone windows,
respectively, with the stmcture of the window oriented to face into the vacuum
instead of out into the atmosphere. In other words, the cone on window 14 is
pointing into the waveguide and the depression in window 13 is facing into the
waveguide. The propagated powers for these two windows are shown in Figs. 37
and 38. The window breakdown photographs for these two windows are shown in
Figs. 39 and 40, respectively. The sequence of the pictures on the page is the same
as for the previous breakdown figures. It can be seen that the threshold for
breakdown is barely exceeded on window 13, hence the small plasma volume,
while on window 14 there is a substantial breakdown volume.
48
(Air)
(Ar)
(He)
Figure 34. Breakdown Photographs on the Protmding Cone Window.
49
Figure 35. Propagated Microwave Power Through the Inverted Cone in Atmosphere Window.
Some observations about the data presented in this chapter will be made.
Of the three unfaced planar windows the highest power level seems to be propagat
ed through the Lucite window followed by the Lexan window, then the nylon
window. Using an Aquadag coating applied in a relatively thick layer as described
in this experiment blocks the nucrowaves. When comparing the planar windows
roughened with sandpaper the window roughened with the 1200 grit demonstrated
better performance than the one sanded with 80 grit. The relative humidity has a
negligible effect on pulsed microwave breakdown in air. For the non-planar
windows oriented with the stmctiue of the window facing into the anechoic
chamber, the protmding cone shows generally good performance in aU gases while
the inverted cone shows enhanced performance only in argon. When the windows
are turned around so that the stmcture is facing into the waveguide the inverted
cone performs poorly and the protmding cone shows just average performance in
comparison to the other windows.
50
(Air)
(Ar)
(He)
Figure 36. Breakdown Photographs on the Inverted Cone in Atmosphere Window.
51
I
Figure 37. Propagated Microwave Power Through the Inverted Cone in Vacuum Window.
200
Figure 38. Propagated Microwave Power Through the Protmding Cone in Vacuum Window.
52
(Air)
(Ar)
(He)
Figure 39. Breakdown Photographs on the Inverted Cone in Vacuum Window.
53
(Air)
(Ar)
(He)
Figure 40. Breakdown Photographs on the Protmding Cone in Vacuum Window.
54
The shape of the plasma volume in argon and helium is interesting. Two
additional "finger-like" projections can be seen in the breakdown photographs. This
phenomenon is illustrated best in the argon breakdown picture of Fig. 34. It is
thought that these projections correspond to the maxima in the radiation pattem,
i.e., peaks in the power density. An outline of the techruques used to further
analyze the data so that better conclusions can be drawn about the different
windows will be given in (Chapter 5. All of the windows mentioned so far will be
further examined except windows 5, 6, 8, and 12. Windows 5 and 6 were not
included because the Aquadag coating blocked the microwaves, and window 8 was
the protmding cone that suffered electrical breakdown in the glue joint so it was
excluded also. Since window 12 was the tests of air at different humidities, which
did not show any significant effect, it will be disregarded as well.
4.2 High-Power Tests
A few shots were taken at a much higher power level than reported so far,
in an attempt to get air to break down enough to block some of the microwave
power. To increase the power output the oil switch gap length was increased by
1.27 cm to 3.81 cm. The radius of the vacuum diode cathode was enlarged from
8.41 cm to 10.32 cm in these shots while keeping the A-K gap unchanged. This
increase in cathode radius was not a requirement for more power output, but was
done to test the diode performance with an impedance more closely matched to the
PFL. The Marx bank charge voltage was increased from 30 kV per stage to
jqjproximately 40 kV per stage as well for these shots.
The effects of the above mentioned alterations on the beam production and
microwave generation can be summarized as follows. By raising the charging
voltage of the Marx bank, the Marx output and hence the maximum PFL voltage
will increase cortespondingly. Since the oil switch gap was increased the PFL will
charge to a higher voltage before the oil switch fires. A cathode radius of 10.32
cm is very close to the theoretical value of 10.79 cm calculated for an impedance
match to the PFL, which means there should be more efficient power transfer from
55
the PFL to the vacuum diode than in the case of the low-power shots. The de
crease in the diode impedance has the effea that even though the oil switch is
firing at a higher voltage, the diode voltage may not increase much, but there
should be a large increase in the diode current. These changes should result in a
substantial increase in beam power and cortespondingly the microwave power.
Figures 41-43 show the Marx voltage, diode voltage, and diode cmrent for one of
the high-power shots. It is easy to see that the prediaions made earlier in this
paragraph are bom out in Figs. 41-43. The "spike" at -0.5 jis in the Marx voltage
waveform is the timing mark put on all signals by the diagnostic system.
It was immediately j^parent upon examination of the photographs of the
fluorescent mbes in the anechoic chamber that there was indeed a much higher
microwave power level in these shots. The null in the center of the radiation
pattem, as illustrated in Fig. 8, is almost non-existent, as shown in Fig. 44. Break
down experiments were conducted on a planar, 1.27 cm thick, Lucite window
>
s >
-1000
-1500
Figure 41. Marx Voltage of a High-Power Shot.
56
Figure 42. Diode Voltage of a High-Power Shot.
Figure 43. Diode Current of a High-Power Shot.
57
(window 2) in bottled air and SF . This was the extent of the test done at high-
power because there was a voltage breakdown in the Marx tank that rendered the
project inoperable. It is intended to repair the experiment and do more high-power
tests at a later date.
These higher power levels still did not resuh in a breakdown in SF , but did
cause considerably more breakdown in air, as shown in Fig. 45. This larger plasma
volume in air resulted in the reflection or absorption of some of the microwave
power. The propagated microwave powers from these test are shown in Fig. 46,
where it is apparent that in comparison to SF , less power propagates through the
window immersed in air. Taking the ratio of the microwave power to the beam
power (diode voltage multiplied by the diode curtent) yields a peak beam-to-RF
efficiency of over seven percent. This is higher than is reported in most vircator
experiments', but several shots showed similar results. It is believed that more
breakdown tests at these higher powers, especially for the non-planar windows, are
warranted.
Figure 44. Fluorescent Tubes Excited by a High-Power Shot.
58
Figure 45. Window Breakdown of a High-Power Shot on a Planar Lucite Window in Air.
2500
Figure 46. Propagated Microwave Power of the High-Power Tests Through a Planar Lucite Window.
59
CHAPTER 5
DATA ANALYSIS
It was desirable to somehow analyze aU of the data taken from the different
tests to explain the results obtained for the different windows. If it is strictiy
pulsed microwave breakdown of a gas, do the breakdown fields agree with values
previously reported? If disagreement is found, what other mechartism or mecha
nisms are contributing to the breakdown or lack thereof? Finally, if one window
displays improved performance with respect to the others, can this be explained?
The breakdown fields on different windows in different gases and a comparison of
the performance of the different windows will be addressed in this chapter. A
comparison to previously reported data and an attempt to explain the results of
these tests theoretically wiU be given in Chapter 6.
5.1 Breakdown Field Predictions
The breakdowns, as shown in the photographs in Chapter 4, always occur on
and near the surface of the window. To make predictions as to the electric field
breakdown strength it is necessary to quantify the electric field at the window.
This was accomplished with the use of the MAGIC code. These results are shown
in Figs. 47-56 for the five different window geometries simulated. Even though it
is the total electric field that determines breakdown, the axial electric field, £^, and
the radial electric field, E , is plotted in Figs. 47-56 since these quantities are
directiy available from MAGIC. Since E^ is 90° out of phase with E^ and always
of lesser magrumde, then the maximum value of E^ should give a good approxima
tion of the maximum value of the total electric field. These figures show contours
of constant electtic field strength for £, and E at a time step corresponding to a
maximum of the particular quantity at the window surface. All of the graphs have
the same contour level separation (200 kV/m) to facilitate direct comparisons
60
cr
MAGIC VERSION: OCTOBER 1990 DATE: 4/18/91 SIMULATION: SMOOTH LUCITE WINDOW RESTART AT 10 NS
CONTOUR PLOT AT TIME:1.04E-08 SEC OF El COMPONENT (V/M)
RANGING FROM (15,2) TO (55,44) CONTOUR WINDOW: -6.00E+05 TO 2.20E+06
CONTOUR LEVEL SEPARATION 2.000E+05
0.25
Figure 47. Axial Electric Field Contours for the Planar Windows.
61
Q:
LO
o
MAGIC VERSION: OCTOBER 1990 DATE: 4/18/91 SIMULATION: SMOOTH LUCITE WINDOW RESTART AT 10 NS
CONTOUR PLOT AT TIME:1.03E-08 SEC OF E2 COMPONENT (V/M)
RANGING FROM (15,2) TO (55,44) CONTOUR WINDOW: -4.00E+05 TO 1.60E+06
CONTOUR LEVEL SEPARATION 2.000E+05
Z (m) 0.20 0.25
Figure 48. Radial Electric Field Contours for the Planar Windows.
62
w
cr
MAGIC VERSION: OCTOBER 1990 DATE: 4/19/91 SIMULATION: LEXAN WINDOW w/ PROTRUDING CONE AT 10 NS
CONTOUR PLOT AT TIME:1.05E-08 SEC OF El COMPONENT (V/M)
RANGING FROM (15,2) TO (55,44) CONTOUR WINDOW: -4.00E+05 TO 4.00E-f06
CONTOUR LEVEL SEPARATION 2.000E+05
0.10 0.15 0.20
Z (m) 0.25
Figure 49. Axial Electric Field Contours for the Protmding Cone In Atmosphere.
63
Q :
in
MAGIC VERSION: OCTOBER 1990 DATE: 4/19/91 SIMULATION: LEXAN WINDOW w/ PROTRUDING CONE AT 10 NS
CONTOUR PLOT AT TIME:1.05E-08 SEC OF E2 COMPONENT (V/M)
RANGING FROM (15,2) TO (55,44) CONTOUR WINDOW: -4.00E+05 TO 1.40E+06
CONTOUR LEVEL SEPARATION 2.000E+05
0.25
Figure 50. Radial Electric Field Contours for the Protmding Cone in Atmosphere.
64
"i-
Ctl
to
d
o o
o
o o
•
o
MAGIC VERSION: OCTOBER 1990 DATE- 4/19/91 SIMULATION: LEXAN WINDOW w/ INVERTED CONE AT 10 NS
CONTOUR PLOT AT TIME:1.05E-08 SEC OF El COMPONENT (V/M)
RANGING FROM (15,2) TO (55,44) CONTOUR WINDOW: -1.20E+06 TO 1.80E+06
CONTOUR LEVEL SEPARATION 2.000E+05
0.10
Z (m) 0.20 0.25
Figure 51. Axial Electric Field Contours for the Inverted Cone in Atmosphere.
65
01
MAGIC VERSION: OCTOBER 1990 DATE: 4/19/91 SIMULATION: LEXAN WINDOW w/ INVERTED CONE AT 10 NS
CONTOUR PLOT AT TIME:1.05E-08 SEC OF E2 COMPONENT (V/M)
RANGING FROM (15,2) TO (55,44) CONTOUR WINDOW: -1.00E+06 TO 1.00E+06
CONTOUR LEVEL SEPARATION 2.000E+05
0.25
Figure 52. Radial Electric Field Contours for the Inverted Cone in Atmosphere.
66
ct:
MAGIC VERSION: OCTOBER 1990 DATE: 4/19/91 SIMULATION: LEXAN w/ INVERTED CONE INSIDE (10 NS)
CONTOUR PLOT AT TIME:1.01E-08 SEC OF El COMPONENT (V/M)
RANGING FROM (15,2) TO (55,44) CONTOUR WINDOW: -1.60E+06 TO 2.20E+06
CONTOUR LEVEL SEPARATION 2.000E+05
0.25
Figure 53. Axial Electric Field Contours for the Inverted Cone in Vacuum.
67
Q:
lO
d
MAGIC VERSION: OCTOBER 1990 DATE: 4/19/91 SIMULATION: LEXAN w/ INVERTED CONE INSIDE (10 NS)
CONTOUR PLOT AT TIME:9.99E-09 SEC OF E2 COMPONENT (V/M)
RANGING FROM (15,2) TO (55,44) CONTOUR WINDOW: -1.20E+06 TO 1.00E+06
CONTOUR LEVEL SEPARATION 2.000E+05
0.25
Figure 54. Radial Electric Field Contours for the Inverted Cone in Vacuum.
68
l l lMJli
ct:
lO
d
MAGIC VERSION: OCTOBER 1990 DATE: 4/19/91 SIMULATION: LEXAN w/ PROTRUDING CONE (INSIDE) ©lO NS
CONTOUR PLOT AT TIME:1.04E-08 SEC OF El COMPONENT (V/M)
RANGING FROM (35,2) TO (75,44) CONTOUR WINDOW: -6.00E+05 TO 3.00E+06
CONTOUR LEVEL SEPARATION 2.000E+05
0.25
Figure 55. Axial Electric Field Contours for the Protmding Cone in Vacuum.
69
Ql
in
MAGIC VERSION: OCTOBER 1990 DATE: 4/19/91 SIMULATION: LEXAN w/ PROTRUDING CONE (INSIDE) (glO NS
CONTOUR PLOT AT TIME:1.03E-08 SEC OF E2 COMPONENT (V/M)
RANGING FROM (35,2) TO (75,44) CONTOUR WINDOW: -1.20E+06 TO 1.40E+06
CONTOUR LEVEL SEPARATION 2.000E+05
0.10 0.15 0.20
Z (m) 0.25
Figure 56. Radial Electric Field Contours for the Protmding Cone in Vacuum.
70
between the different graphs. The soUd lines denote regions of positive field
strength values and the dashed lines denote regions of negative field strengths. The
dotted region indicates the dielectric material, i.e., the window, and the end of the
waveguide can be seen at R=0.l m.
There are interesting similarities as well as differences in Figs. 47-56. The
peak value of £^ is in all cases much greater than the peak value of £ and the
peak value of £^ always occurs in the center of the window surface. It is
especially interesting to note the dramatic differences in the peak £^ fields for what
is equivalent, to within 10%, propagated power levels. The window with the
protmding cone in atmosphere (window 10) has a maximum £^ of over 4 MV/m
while the inverted cone in atmosphere (window 11) has a peak £^ of less than 2
MV/m. Even though the peak electric field at the center for windows 10 and 11 is
so different, the radial location on the windows where the fields go to zero almost
coincide. It can be seen in Figs. 49 and 51 that the zero level contour is at
/?«0.06 m in both cases. The other simulated windows have electric field parame
ters at the window that fall between those of windows 10 and 11.
The data for Figs. 47-56 was obtained from the same MAGIC simulations
that provided the information necessary to do the B-dot probe calibration as
described in Section 3.3 and Appendix C. Given this fact, it should be possible to
get maximum electric field estimates at the window from the propagated power
waveforms in Chapter 4.
For a given experimental instantaneous power, P^^^, the magnetic field
intensity, H^^^j, at tiie B-dot probe location is:
\
P ^ exp P
sun
(19)
where H . is tht magnetic field intensity at the probe from the simulation and
P is the calculated power from the simulation. Examination of Eqs. (9) shows
that:
71
H^ocEocE , (20)
i.e., if H^ increases by a faaor of 2, so must £^ and £ . The electric field
strength, £ ^ ,, at a point in space can then be calculated from:
z,c»l ^^al z.sim (21)
where £ ^^ is the simulated £^ at a point cortesponding to £ ^ ,. Combining Eqs.
(19) and (21) gives:
z,cal
N e P £ (22)
P z.stTn sim
It should be noted that the maximum electric field at the window in relation to the
magnetic field at the probe is dependent upon the dielectric constant of the window
as well as its shape . This means that if the dielectric constant of the window is
increased, the maximum value of £^ may increase while the propagated power may
decrease. Increasing the dielectric constant increases the power reflected back
down the waveguide, hence, reducing the propagated power. At the same time, to
satisfy the boundary conditions at the interface, the normal component of the
electric field, £ , on the atmospheric side of the interface must increase.
From the preceding discussion it is concluded that given a certain propa
gated power level it should be possible to determine a peak £^ value at the
window. If the maximum power for each experimental waveform presented in
Chjroter 4 is used as this power level it should facilitate the calculation of an upper
bound for the breakdown field for each case. This calculation will provide a
maximum electric field strength at the window in the absence of breakdown. If,
upon examination of the photographs taken of the window for a certain shot,
breakdown is observed, this breakdown must have occmred at or below the
calculated electric field maximum. The values of £ . and P^^ used in these
calculations are given in Table 3 and the values of P^^ for the different windows
72
and gases as well as the calculated values of £ ^ ^ are given in Table 4. The values
of £ ^ , are presented graphically in Fig. 57. The values of £ ^ listed in Table 3
cortespond to the maximum £^ contour level in each plot of Figs. 47-56. From the
values of £ ^ , and the window breakdown photogrq)hs a value of the breakdown
field strength at the window will be estimated.
Table 3. Parameters Used In Maximum Electric Field Calculations.
Window Description
1.27 cm thick planar
protmding cone in atmosphere
inverted cone in atmosphere
protmding cone in vacuum
inverted cone in vacuum
P^(MW)
114.8
118.4
124.0
115.3
124.4
£ . (MV/m) z^m ^ ' '
1.1
4.0
1.8
3.0
2.2
Table 4. Maximum Power and Cortesponding Maximum Electric Field.
Window Number
2
3
4
7
9
10
11
13
14
Peak Power (MW)
Air
160
135
125
150
130
160
135
105
145
Argon
150
115
105
120
130
135
145
100
110
Hehum
65
75
55
95
70
80
60
70
95
£ (MV/m)
Air
2.60
2.39
2.30
2.51
2.34
4.65
1.88
2.02
3.36
Argon
2.51
2.20
2.10
2.25
2.34
4.27
1.95
1.97
2.93
Helium
1.66
1.78
1.52
2.00
1.72
3.29
1.25
1.65
2.72
73
2 3 4 7 9 10 11 13 14
Window Number
Figure 57. Breakdown Electric Field Strengths for the Different Windows.
The data of particular interest in Fig. 57 and Table 4 is that for windows 11
and 13. These windows are the inverted cone, with the cone on the atmospheric
side in window 11 and on the vacuum side for window 13. As shown in Figs. 36
and 39 there was no breakdown on window 11 and a very small region of break
down on window 13. From Table 4 it can be seen that an electric field strength of
1.88 MV/m gives no breakdown while an electric field of 2.02 MV/m does result in
breakdown. The breakdown field in air on a Lexan window has thus been bracket
ed between 1.88 MV/m and 2.02 MV/m.
The results on the other smooth Lexan windows (windows 3,10,and 14) will
be examined to check the results of the previous paragraph. To do this comparison,
the contour lines of £ , in Figs. 47-56 will be scaled to the appropriate £ , ^ level
listed in Table 4. For example, for the protmding cone in atmosphere window, the
value of £ in Table 4 is 4.65 MV/m, a 16% increase over tiie value of,
E =4 MV/m listed in Table 3. This means the contour line separation in Fig.
49 should be -233 kV/m instead of 200 kV/m for this particular discussion. Using
74
this criterion and counting in from the farthest solid contour line (the zero level)
rune contour lines toward the center gives a value of approximately 2 MV/m. From
this contour line to the center should be the region of breakdown on the surface of
the cone. Comparing this predicted breakdown extent with the top photogr^h of
Fig. 34 shows remarkable agreement. A sketch to clarify the preceding statements
is shown in Fig. 58. The boundary of the breakdown region at the window was
based on the contour lines in Fig. 49 and the boundary away from the window was
estimated from the breakdown photograph in air shown in Fig. 34. Following this
procedure on the other smooth Lexan windows shows similar agreement.
To obtain a breakdown field strength in argon was not as easy because all of
the windows tested broke down to some extent in argon. The middle picture of
Fig. 36 illustrates the case of minimum breakdown on a window in argon. Additio
nally, from this picture it can be seen that the plasma volume has a distinct bound
ary. If the breakdown is said to extend to slightiy outside the inverted cone, a
rough estimate of the breakdown field can be made. Scaling each contour line in
Fig. 51 up 8.33% and using the fifth line as the edge of the plasma volume yields a
Waveguide Flange —\
Microwaves
Window
Plasma
Figure 58. Sketch of the Breakdown Region on the Protmding Cone in Atmosphere.
75
breakdown field of -870 kV/m. It is not possible to check this argon breakdown
field against other windows because the discharge volume has no obvious cutoff on
the other windows. No estimate of the breakdown field in helium can be made for
this same reason.
It must be stated that, the calibration of the planar windows was done with a
value of 2.6 for the relative pemuttivity of the planar windows, and a value of 3.0
for the relative permittivity of the non-planar windows. A value of 2.6 was used
for the permittivity of the planar windows because the simulation was originally
done for a Lucite window. It is thought that the slight differences in the dielectric
constants of the Lucite, Lexan, and nylon windows will have a negligible effect on
the radiation pattem so the power calibration should still be vahd. The changes in
the peak £^ field caused by the different dielectric constants, however, is not taken
into account. This fact can be significant if it is desired to compare windows with
the same geometry but different dielectric constants, as is the case with the unfaced
planar windows. For this reason, caution should be exercised in making the
statement that the breakdown field on nylon (window 4) is less than on Lexan
(window 3) which are both less than on Lucite (window 2). This tendency,
illustrated in Fig. 57 on windows 2-4 in air and argon, could be a result of the
different material dielectric constants not being taken into account. The permittivity
of the non-planar windows was taken to be 3.0 because these windows are both
fabricated of Lexan and 3.0 is the value given for the permittivity of Lexan at 1
MHz ^ It was later found that 2.78 is a better value for Lexan at 2 GHz'^
5.2 Window Performance Comparisons
If a comparison is to be made between the different windows, an unbiased
method of comparison must be formulated first. One way to do this would be to
subject each window to identical microwave pulses and measure the ttansmitted
power. There are no provisions to measure the microwave power in the waveguide
on this experiment, so an altemate techruque must be used to determine the
repeatability of the incident pulse. It is known that the diode voltage and diode
76
current waveforms are very repetitive from shot to shot, varying only in magnitude.
Multiplying the diode voltage by the diode cmrent gives the beam power, which
can then be integrated with respect to time to give the beam energy. If it is
assumed that the physics of the nticrowave generation in the vircator is prediaable
and well behaved, then repeatability of the beam energy suggests repeatability of
the generated nticrowave radiation. The results of these calculations are shown in
Fig. 59. It can be seen that the last five windows of interest w re tested under very
sirrular conditions but the first four show some variance.
If the nticrowave power waveforms presented in Chapter 4 are integrated in
time one gets the energy in the nticrowave pulse. This is the nticrowave energy
that is propagated into the anechoic chamber. The ratio of the microwave energy to
beam energy yields a device efficiency, where the device is comprised of the
vircator and the window. If the vircator is assumed to behave repeatably then this
ratio can be interpreted as a measure of the relative efficiency of the different
500
400 -
SB 300
e
I 200
e
100 -
: ^ * ' ^ ^ - * * '
•
•
•
O A i i "^ Argon -^Helium
2 3 4 7 9 10 11
Window Number
13 14
Figure 59. Calculated Beam Energies for the Windows Tested.
77
windows. This method should also reduce the effect of the beam energy variations
demonstrated in Fig. 59. A graph showing these calculated device efficiencies is
shown in Fig. 60. In doing the window performance comparisons it must be
realized that there is a determirting faaor in the window performance, beside the
reflection of nticrowaves off the plasma formed on the window. In general, two
windows of identical geometry but different dielectric constant will have different
reflection coefficients. For this case, as the dielectric constant increases so does the
reflection coefficient. At equivalent incident power levels as the power reflected
increases then the power transntitted, and hence propagated must decrease.
The discussion will begin with the unfaced planar windows (windows 2, 3,
and 4). The nylon window, window 4, will be considered as unfaced even though
the surfaces were machined smooth. This is done because the tests on the different
planar windows without surface treatments were to determine the effect the material
the window is made of has on the breakdown. It was necessary to face the nylon
2.0
1.5
ee K 1.0
U
OJ
0.0 2 3 4 7 9 10 11 13 14
Window Number
Figure 60. Device Efficiencies for the Different Microwave Windows.
78
window because the surfaces were very rough as received from the distributor. It
can be seen in Fig. 60 that the Lucite window (window 2) always performed as
well as the Lexan (window 3) and nylon (window 4) windows and in many
instances performed better. Examination of the breakdown photographs for these
three windows shows that the size and shape of the plasma seems independent of
the window material and depends only on the gas type. This could very well be a
case where the dielectric constant of the window is the dominant factor in deter
mining its performance. Taking the dielectric constants of Lucite, Lexan, and nylon
at 2 GHz to be 2.6, 2.78, and 3.0, respectively, would support this idea. The values
for the permittivities were obtained from Von Hipple ^ and Rodriguez'^
The window efficiency in argon, as shown in Fig. 60, best illustrates the
notion that the lower the dielectric constant the better the window efficiency. As
mentioned earlier, increasing the dielectric constant of the window also causes the
normal component of the electric field, £^, at the window to increase. The increase
in £^ should enhance the formation of a plasma, thus further reducing the window
efficiency. Due to the qualitative nature of the breakdown photographs it is not
possible to confirm this statement for the planar windows where the difference in
dielectric constant is relatively small. The window efficiency in helium is almost
constant over the 3 windows being discussed. This is probably because the electric
field at the window far exceeds the breakdown field in helium, hence the plasma
formed at the window blocks so much of the microwave radiation that there is no
difference in propagated power for the 3 windows. It is not known at this time
why the data point in Fig. 60 for the nylon window in air does not conform to this
hypothesis.
Windows 7 and 9 are the Lexan windows randomly roughened with 1200
grit and 80 grit sandpaper, respectively. It can be seen that in all gases window 7
performs better than window 3 (unfaced Lexan) while window 9 consistentiy
performs worse. This is in agreement with the results obtained in urtipolar, vacuum
surface flashover experiments . The 1200 grit sanded window demonstrates
particularly enhanced performance in helium when compared to the other windows
79
in helium. The mechanism or mechanisms governing the behavior of the sanded
windows is not understood, but clearly tiie surface texttu-e of tiie window has an
effect on its performance. It should be pointed out that roughening the surface witii
1200 grit sandpaper may not provide optimum performance in pulsed microwave
breakdown. The selection of 80 and 1200 grit was based on experimental results
which show, for urtipolar vacuum surface breakdown, that surfaces sanded with
1200 grit have a holdoff strength up to a factor of two greater than surfaces sanded
with 80 grit.
Window 10, the protmding cone in atmosphere, shows enhanced perfor
mance in air but is consistent with the other windows in argon and helium. The
breakdown in air, as Fig. 34 illustrates, is out on the tip of the cone. By moving
the plasma volume away from the waveguide j^rture, the radiation pattem is
allowed to disperse some before interacting with the plasma. Since the radiation
pattem has "spread" some, a lesser percentage is being reflected by the plasma
volume, thus allowing more total power to propagate. In the region of the window
away from the cone, it was shown earlier in this chapter that the magrutude of the
electric field was similar to that for a planar window. This can explain why the
performance of this window in argon and helium is consistent with the planar
windows.
The inverted cone in atmosphere demonstrated poor performance in air,
enhanced performance in argon, and performance comparable to the other windows
in helium. The substandard performance in air, even in the absence of breakdown,
must be attributed to the poor transmission characteristics of the window itself.
The justification for this statement is that the reflection coefficient of windows less
than one half wavelength thick increases with window thickness. This window is
5.08 cm thick as compared to 1.27 cm thick for the other windows, hence more
reflection will result. It is interesting to note that even with plasma formation in
argon, as depicted in the middle picture of Fig. 36, the efficiency of the window is
comparable to when no breakdown is observed in air. In essence, the inverted cone
in atmosphere window has poor transmission qualities because of its thickness, but,
80
as Fig. 51 shows, its shape "grades" the field so that the maximum value of £. is
less than for any other window.
Windows 13 and 14 are the non-planar windows with the stmcture of the
window facing into the waveguide instead of into the atmosphere. The poor
performance of window 13 in air can be attributed to the poor transntission quality
of the inverted cone window combined with a lack of field grading, which was
beneficial in the case where the depression in the window is facing out into the
atmosphere. The relative good performance in argon is probably because the field
strength is not sufficient to generate a plasma in argon that blocks the ^>erture as
effectively as is the case in other windows. Window 14, the protmding cone in
vacuum, demonstrates performance comparable to a planar window.
The results of the performance comparison will be summarized. Of the
unfaced planar windows, the one with the lowest permittivity exhibited the best
performance. The Lexan window roughened with 1200 grit sandpaper gave
superior performance when compared to almost any other window in any gas, while
the Lexan window roughened with 80 grit sandp^>er gave inferior performance.
The best performance in air was by the protmding cone in atmosphere. This is
attributed to the fact that the breakdown is "pushed" out on the end of the cone,
thus blocking less of the aptituit. The inverted cone in atmosphere gave the best
performance in argon. This is probably because the poor transmission of the
window lintits the electric field strength to a value below the breakdown threshold
in argon for most of the area of the window. Since the threshold for breakdown is
not exceeded over more of the aperture, more power is allowed to propagate. This
is similar to the case for the plasma "spike" on the windows in air not effeaing the
propagated power much. The best window in helium was the planar Lexan window
roughened with 1200 grit sandpaper. An explanation as to why sanding the surface
has such an effea on breakdown in helium can not be given at this time.
81
CHAPTER 6
COMPARISON TO EXISTING DATA AND
THEORETICAL DEVELOPMENT
A comparison of the breakdown field strengths prediaed in Section 5.2 with
existing data will be made. The existing data consists of published results on
theoretically and experimentally obtained pulsed microwave breakdown. A theory
will then be put forward in an attempt to explain the disagreement between the data
in this report and the previously published results.
Some previously reported pulsed, microwave gas breakdown data will be
given. In what Byme^ terms short-pulse experiments an RMS breakdown field in
air is given to be approximately 2.5 MV/m. This is for a 2.9 GHz nticrowave pulse
with a 47 ns risetime. It is also reported that the time to breakdown after introduc
tion of the pulse was 77 ns. This value of 2.5 MV/m is also reported ^ to be the
threshold field for nticrosecond pulses. In general, as the pulse width decreases, the
breakdown field increases and, in fact, threshold fields as high as 10.0 MV/m^
have been reported for nanosecond pulses.
No experimental data for pulsed microwave breakdown in argon could be
found. A peak breakdown field strength of approximately 0.92 MV/m was obtained
from a continuous wave (cw) experiment^\ A considerable margin for ertor
should be allowed in this value because it was extrapolated from data taken at a
maximum pressure of 100 Tort. The experimental value of the breakdown strength
of helium will also be taken from Byme^ An RMS breakdown field of 1.1 MV/cm
is reported for helium due to the same pulse excitation as described earlier for air
breakdown in this reference. The time to breakdown with respea to the leading
edge of the nticrowave pulse was 44 ns. These data for helium breakdown really
calls into question the breakdown data for argon reported earlier because it was
82
found from our experiment that argon in faa has a higher breakdown threshold than
helium.
In an attempt to gain some consistency, the results of a theoretical pulsed
nticrowave breakdown smdy will be given. The effeaive field technique^ will be
used to apply dc breakdown results to pulsed nticrowave breakdown. The nanosec
ond-pulse breakdown data of Felsenthal and Proud^ will be used in the applica
tion of this techruque. The data are presented as E/p vs. px graphs where £ is the
breakdown field, p is the pressure in Tort, and T is the formative time of the
breakdown. The effeaive field, £^, is defined as:
^t'^RMS
\
v l (23)
vi+co^
where Ej^j^^ is the RMS electric field, v ^ is the collision frequency for momentum
transfer, and CO is the radian frequency of the microwaves. At atmospheric
pressure, v ^ » c o for co=47txl0^ sec"* in air, argon, and helium^ which implies
The formative time will be inferted from Figs. 24-26 and will be taken to be
the time difference between the rise of the microwave pulse and the rise of the
PMT signal. The following values of t will be used: T=20 ns for air, t = 10 ns
for argon, and T =5 ns for helium. These calculations yield approximate RMS field
strengths of 42 kV/cm, 27 kV/cm, and 17 kV/cm for air, argon, and helium
respectively. The previously reported data were converted from RMS values to
peak values and are listed in Table 5. Qearly, a wide range of experimental
conditions and cortespondingly a wide range of results are given in Table 5. Of
primary importance, however, is the faa that the breakdown threshold prediaed in
Chapter 5 for air is less than any of the results listed in Table 5. The rough
estimate of the argon breakdown threshold also ties below aU of the values for
argon in Table 5.
83
The results given in Table 5 are for bulk gas breakdown which essentially
means there are no surface effeas contributing to the breakdown process. In this
case free electton produaion is governed by ionization and electron losses are
controlled by attachment, recombination, and diffusion. The question is: which of
these processes has been altered by the experimental artangement to cause the
breakdown threshold to decrease substantially?
Table 5. Summary of Previously Reported Breakdown Results.
Reference Number
7
20
20
21
7
5,22
5,22
5,22
Gas
Air
Air
Air
Argon
Hehum
Air
Argon
Hehum
Breakdown Field (MV/m)
3.5
3.5
10.0
0.92
1.6
5.9
3.8
2.4
Notes
77 ns formative time
continuous wave
nanosecond pulse
continuous wave
44 ns formative time
theoretical, 20 ns formative time
theoretical, 10 ns formative time
theoretical, 5 ns formative time
It is thought that the nticrowave window is functioning as an additional
source of free electrons due to secondary elearon emission. Secondary electton
emission is the process by which electtons are entitted from the surface of a
material, an insulator in titis case, being irtadiated by electtons. Theoretical curves,
derived as outiined by Burke^, for tiie secondary elearon yield of Lucite, Lexan,
and nylon are shown in Fig. 61. The yield, 6 , is tiie average number of electtons
entitted from the insulator per electton impaaing the surface.
All polymer secondary electton emission curves have a shape similar to
those shown in Fig. 61. The important parameters, illusttated in Fig. 62, are the
84
^J
2.0
1.5
1.0
OJ
A n r
- I^^\ ^\\^- i - .._..
-OLudte - ^ Lexan "•" Nylon
- | ~ - ^^^^~c ; '" - lt>>*..
4- - - - - -1 - - - - IZ~~''—-^^
V , , , , . i , , i . . .
0.0 0.5 1.0
Energy (keV)
l i 2.0
Figure 61. Theoretical Secondary Elearon Entission Curves.
l i 2.0 Energy (ktV)
Figure 62. General Insulator SEEC Curve.
85
unity crossover points, Ej and £ , the maximum yield, 5^, and the energy where
6^ occurs, £^. The crossover points are where the curve crosses the 6 = 1 line.
A 6 = 1 means that for each elearon incident on the surface there is 1 electton
entitted, while for 6<1 electtons are being lost and for 6>1 there is a net electton
gain. Ej, the first crossover, occurs at about 30 eV for the curves given in Fig. 61
and Ejj has a value of approximately 1 keV. For Lucite, Lexan, and nylon 5 lies
between 2 and 2.5 and occurs for £^=250 eV. A good general discussion of
secondary electton emission and a list of references are given in an M.S. thesis by
Mary Baker^.
The fundamental processes in secondary electton emission contributing to
the breakdown at the window are viewed as follows. The equation governing the
average drift velocity, v, of an electton in a gas is given by:
m^+(mv )v=-e(E+vxB), (24)
dt ^ "'
where m is the elearon mass, v ^ is the collision frequency for momentum ttansfer,
e is the electton charge, and E and B are the electric and magnetic fields. Equa
tion (24) can be simplified if only the region near the center of the window (where
the breakdown is irtitiated) is considered. For this case, the contribution to the —> - •
force by vxB wiU be negligible since B goes to zero as the radius, p , approaches - »
zero. Additionally, the radial component of E goes to zero as p approaches zero
leaving ortiy the axial component of the electric field contributing to the right hand
side of Eq. (24). Making these simplifications, Eq. (24) reduces to:
dy , , . (25) m—i+(mvjv = - c £ e "',
where v^ is the z (axial) component of the velocity, |£ j is the magnimde of the
axial electric field, and co is the ntiaowave radian frequency. The solution to Eq.
(25) is given by:
V = -z j(om+mv
86
£ le V Z I
(26)
Now for the case where v^»co which occurs in gases at high pressure Eq. (26)
can further be reduced to:
e\E I v = - _ _ L l e ^ ' . (27)
mv m
This means that any electtons close to the window will be accelerated toward the
window for half of the microwave period and accelerated away from the window in
the other half of the period. Since this process repeats itself every 500 ps for
f-1 GHz, it could be a considerable source of electton gain. At the same time
electtons are being created by secondary emission from the window the normal
processes involved in gas breakdown, such as ionization and attachment, are also
occurring.
Figure 63 shows the ionization efficiency in some gases of interest as a
funaion of electton energy. This graph gives the number of ionizations that occur
in a gas at a pressure of 1 Tort for an electton ttaveling 1 cm in the gas and
making collisions. The curves for N2 and O^ praaically overlap on Fig. 63, so
they were represented with just one curve. Additionally, since air is mostiy N and
O2 it will be assumed that this curve is also representative of air.
It is difficult to evaluate the particular contribution made to the breakdown
formation by the processes depicted in Figs. 61 and 63. Figure 61 gives the
elearon production due to electtons incident on the window while Fig. 63 gives
electton produaion due to an electton ttaveling tiirough tiie gas and making
collisions. From tiiese graphs it is evident, however, tiiat peak electton production
occurs in both processes at about the same electton energy levels (100-200 eV).
For the sake of illusttation let the peak axial electric field have a value correspond
ing to tiiat predicted for air breakdown (-2 MV/m). The effective field given by
Eq. 23 is tiien -1.4 MV/m and EJp^\9 voh-cm"'-Tort"^ where p is tiie gas
pressure. For this value of EJp the average electton temperattire is then found to
be -1.3 eV^. Referring to Figs. 61 and 63, it is seen tiiat titis is well below tiie
87
s
1 a o
10 10 10*
Electron Energy (eV) 10
Figure 63. Ionization Efficiency of Some Gases (Adapted from von Engel).
energy necessary for ionization or to produce electton gain by secondary electton
entission from the window.
Of particular interest is some evidence^^ that the first crossover point in the
secondary electton entission curve could aaually be as low as 10 eV instead of 30
eV. This is significant because all of the gases tested have ionization energies
greater than 10 eV but less than 30 eV. Moving the first crossover point to 10 eV
would imply that via secondary emission there could be electton gain before the
electtons have sufficient energy to cause ionization. This does not mean that if the
average elearon energy is sUghtiy greater than 10 eV there will be a dramatic
increase in the free electton density because of secondary electton emission from
the window. Instead, as the average electton energy steadily increases as a result of
the ntiaowave field excitation, the average number of electtons being emitted from
the window as a consequence of electton bombardment will also steadily increase.
The free electtons produced in one ntiaowave period can then be accelerated back
into the window during the next period thereby generating even more free electtons.
88
If this process is, in fact, occurring it could have a considerable effect on the break
down at the window. Another possibility is that the electton distribution funaion
close to the window surface is different than it is out in the gaseous volume. If
processes occurring at the surface cause the distribution function to have a higher
energy "tail," a lower breakdown threshold would result. The mechanisms conttol-
ling the breakdown at the window are not well understood at this time.
89
CHAPTER 7
CONCLUSIONS AND RECOMMENDATIONS
FOR FURTHER STUDY
The data colleaed as a result of over a year of window testing has provided
information which enabled the calculation of the breakdown thresholds on Lexan
windows in air. Also, a rough estimate of the argon breakdown threshold on a
Lexan window was obtained. These tests also provided evidence to determine
which windows performed well and why. A review of these results and recommen
dations for further smdy will be given.
A breakdown threshold of - 2 MV/m was calculated for air on a Lexan
window, and a rough estimate of 870 kV/m was found for argon under the same
experimental conditions. These numbers are significant because they are less than
those reported for ntiaowave induced gas breakdown, even under continuous wave
excitation. This indicates that there must be other processes involved in the
breakdown of the window, besides those just involved in bulk gas breakdown. The
possible explanation of this points to the window as an additional source of free
electtons due to secondary electton entission. If the first crossover point on the
secondary elearon emission curve is close to 10 eV instead of 30 eV, then the
theory that secondary electton entission is enhancing the breakdown at the window
is reinforced.
The tests of the windows showed that the dielectric constant of the window,
the window shape, and the surface treatment of the window aU have effects on its
performance. For windows of the same geometrical shape, the data indicate that
the lower the dielectric constant the better the performance of the window. Not
only does the window reflea more nticrowave power as the pemtittivity increases
but the normal component of the electric field is enhanced at the window, hence
enhancing the breakdown process. The data taken on the windows that were
90
randomly roughened with sandpaper demonsttated agreement with unipolar vacuum
surface breakdown results, but this is not necessarily the optimum for pulsed
ntiaowave breakdown. The window sanded witii 1200 grit sandpaper showed
improved performance while the window sanded with 80 grit sandpaper showed
degraded performance. The prottiiding cone window perfonned weU because, even
though tiiere was breakdown, it was pushed out on tiie end of tiie cone, tiius
blocking less of tiie ntiaowave power. The inverted cone window showed substan
dard performance because even tiiough tiiere was less breakdown on tiie window
the ttansmission of tiie window itself was inferior to the other windows tested. The
inferior ttansmission of this window can be attributed to it being 5.08 cm thick
instead of 1.27 cm, which results in a higher refleaion coefficient for the window.
The air breakdown on the window in the low-power test blocked a very
small percentage of the total power incident on the window. For this reason tests
with SFg were not continued in the low-power tests. However, in the high-power
shots there was a noticeable difference between the propagated power in air and in
SFg, and also in the breakdown photographs. Argon showed minimum breakdown
conditions for the inverted cone window which is why these data were used in the
estimation of argon breakdown. The helium breakdown was such that, in all cases,
the ntiaowave radiation was severely blocked by the generated plasma.
The first recommendation for further study is to continue the high-power
tests of the windows in search of the optimum window for microwave ttansmission.
Since air is the medium of most interest for high-power nticrowave propagation the
performance of the windows in air will be more appUcable to other experimental
conditions where breakdown on the output window is being irtitiated by the normal
component of the microwave field. These tests would be conduaed in air and SF
so comparisons between the power levels propagated with and without window
breakdown could be made. Out of these tests, if breakdown in SF^ occurs, it may
be possible to estimate the breakdown sttength of SF^ which may also be of
interest.
91
It is believed that a window fabricated from Teflon would demonsttate
improved performance. The reason for this hypothesis is that the secondary
electton yield of Teflon is equal to or lower than all of the materials tested so far
and also, the energy that the maximum yield occurs at is higher; by some estimates
as high as 400 eV" compared to -250 eV for Lucite, Lexan and nylon. It is
thought that the window performance could further be enhanced by moving the
window back in the waveguide so that the incident wave from the source and the
wave reflected from the waveguide end interfere to minimize the electric field on
the atmospheric side of the window. The combination of these two effects could
enhance the performance of the window considerably .
92
LIST OF REFERENCES
1. Bamch Levush and Adam T. Drobot, "Generation of High-Power Miaowaves, Millimeter and Subntillimeter Waves: Inttoduction and Overview," in High-Power MiCTOwave Sources, ed. Victor L. Granatstein and Igor Alexeff (Artech House, Norwood, MA, 1987).
2. A. D. MacDonald, Microwave Breakdown in Gases (Wtiey, New York, 1966).
3. S. J. Tetenbaum, A. D. MacDonald, and H. W. Bandel, "Pulsed Microwave Breakdown of Air from 1 to 1000 Tort," J. Appl. Phys. 42 (13), 5871-2 (1971).
4. W. E. Scharfman, W. C. Taylor, and T. Morita, "Breakdown Lintitations on the Transntission of Microwave Power Through the Atmosphere," IEEE Trans. Antennas Propag., 709-17, (1964).
5. Peter Felsenthal, "Nanosecond-Pulse Miaowave Breakdown in Air," J. Appl. Phys. 37 (12), 4557-60 (1966).
6. Lawrence Gould and Louis W. Roberts, "Breakdown of Air at Microwave Frequencies," J. Appl. Phys. 27 (10), 1162-70 (1956).
7- Douglas Paul Byme, Ph.D. Dissertation, University of Califomia Davis, 1986.
8. Blake W- Augsburger, Master's Thesis, Texas Tech University, 1989.
9. M. O. Hagler , Circuit and Transntission Line Theory, (USAF Pulsed Power Lecture Series No. 4), Texas Tech University.
10. H. Sze, J. Benford, W. Woo, and B. Harteneck, "Dynantics of a Virtual Cathode Oscillator Driven by a Pinched Diode," Phys. Fluids 29 (11), 3873-80 (1986).
11. R. J. Adler et al., "Improved Electton Emission by Use of a Cloth Fiber Catiiode," Rev. Sci. Insttiim. 56 (5), 766-7 (1985).
12. Mark T. Crawford, Master's Thesis, Texas Tech University, 1991.
13. S. Calico, M. Crawford, M. Kristiansen, and H. Krompholz, " The design and calibration of a very fast curtent probe for the measurement of short pulses," Accepted for publication in Rev. Sci. Instmm.
93
.^BTTX
14. Bmce Goplen, Larry Ludeking, Gary Warten, and Richard Worl, "Magic User's Manual," Mission Research Corporation Technical Report, MRC/WDC-R-246, October 1990.
15. S. C. Burkhart, R. D. Scarpetti, and R. L. Lundberg, "A virtual-cathode reflex triode for high-power ntiaowave generation," J. Appl. Phys. 58 (1), 28-36 (1985).
16. John Drew Sntith, Ph.D. Dissertation, Texas Tech University, 1989.
17. The International Plastics Selector (Cordura Pubhcations, La JoUa, CA, 1977).
18. Teresa Rodriguez, General Electric Corporation, Personal Communication, 1991.
19. Arthur Von Hippie, Dielectric Materials and Applications (Wiley, New York, 1954).
20. R. A. Alvarez, P, R. Bolton, G. E. Sieger, and D. N. Fittinghoff, "Sparse Breakdown and Statistical "Sneakthrough" Effects in Low-Altitude Miaowave Propagation," Lawrence Livermore National Laboratory, UCRL-101807, 1990.
21. S. Krasik, D. Alpert, amd A. O. McCoubrey, "Breakdown and Maintenance of Microwave Discharges in Argon," Phys. Rev. 76 (6), 722-30 (1949).
22. Peter Felsenthal and Joseph M. Proud, "Nanosecond-Pulse Breakdown in Gases," Phys. Rev. 139 (6A), A1796-A1804 (1965).
23. E. A. Burke, "Secondary Emission from Polymers," IEEE Trans. Nuc. Sci. NS^ 27 (6), 1760-4 (1980).
24. Mary C. Baker, Master's Thesis, Texas Tech University, 1985.
25. A. W. Ali, "Nanosecond air breakdown parameters for electton and nticrowave beam propagation," Laser and Particle Beams 6 (1), 105-17 (1988).
26. L. L. Hatfield, Texas Tech University, Personal Communication, 1991.
27. T. S. M. Maclean, Principles of antennas: wire and aperture (Cambridge University Press, Cambridge, 1986).
94
APPENDDC A
MICROWAVE GENERATION MAGIC SOURCE DECK
TITLE " ntiaowave generation 3" / SYSTEM CYLDsTOER-THETA/ XIGRID FUNCTION 196 2 0.0 6 4.0E-3 2.4E-2 10 4.0E-3 .0254
30 1.08E-3 3.33E-2 24 1.15E-3 7.62E-2 124 5.2E-3 .6448/ X2GRID FUNCTION 140 2 0.0 46 1.2424E-3 .1016 10 4.0E-3 .0254
82 l.lE-3 .263525/ SYMMETRY AXL^L AUGN 2 2 196 2/ HELDS ALL CENTERED 8000 2.5E-12/ TAGGING 0.5/ COURANT SEARCH/ CONDUCTOR ANODE ANTI-AUGN 2 140 72 140 72 73 49 73 48 72
48 47 196 47/ DIAGONAL AUGN 48 72 49 73/ CONDUCTOR CATHODE AUGN 2 58 9 58 10 57 11 56 12 55 13 54
14 53 15 52 16 51 17 50 18 49 18 43/ DIAGONAL AUGN 9 58 18 49/ CONDUCTOR EMSURF ALIGN 18 43 18 2/ CONDUCrrOR A N O D S C FOIL 48 47 48 2/ LOOKBACK TWOD ALL 1.23 1.0 ANTI-AUGN 196 2 196 47/ VOLTAGE TWOD TM VOFT RADIAL 1.0 0.0 1.0 ALIGN 2 58 2 140/ FUNCTION "VOFT(T)=875.0E3*TANH(0.5E9*T)"/ FUNCTION RADDU- PWRTERM -1 1/ DISPLAY NO 0.0 0.804 0.0 0.402/ OBSERVE FIELD E2 2 58 2 140/ OBSERVE FIELD B3 22 58 22 58/ OBSERVE FIELD E2 190 2 190 47 FFT 5 WINDOW FREQUENCY 0.0 10.0E9/ OBSERVE FIELD El 190 2 190 2 FFT 5 WINDOW FREQUENCT 0.0 10.0E9/ OBSERVE FIELD E2 190 39 190 39 FFT 5 WINDOW FREQUENCY 0.0 10.0E9/ OBSERVE FIELD B3 190 39 190 39 FFT 5 WINDOW FREQUENCY 0.0 10.0E9/ TIMER FLTIM PERIODIC 0 99999 5/ FLUX ESURFl FLTIM ALL AUGN INDICES 20 2 20 50/ FLUX ESURF2 FLTIM ALL ANTI-AUGN INDICES 49 2 49 47/ FLUX ESURF3 FLTIM ALL AUGN INDICES 190 2 190 47/ OBSERVE FLUX ESURFl CURRENT INTERVAL 5 FFT 5 WINDOW
FREQUENCY 0.0 10.0E9/ OBSERVE FLUX ESURF2 CURRENT INTERVAL 5 FFT 5 WINDOW
FREQUENCY 0.0 10.0E9/
95
OBSERVE FLUX ESURF3 CURRENT INTERVAL 5 FFT 5 WINDOW FREQUENCY 0.0 10.0E9/
FUNCTION "JEOFT(T)=l.45E6*TANH(0.5E9*T)"/ BEAM-EMISSION ELECTRONS ELECTRON JEOFT 4 1 RANDOM l.OE-5
WEIGHTED FIXED 1.0E5 0 0 0 0/ EMIT ELECTRONS EMSURF/ KINEMATICS ELECTRON 1 YES NO YES EM 1 1/ FORCES 0.5 1.0 1.0/ CURRENTS LCC NO NO 0.0 1.0/ TIMER STTIM PERIODIC 25 99999 25/ STATISTICS STTIM/ TIMER PHTIM DISCRETE 4000 8000/ PHASESPACE PHTIM AXES XI X2
AXIS X 0.0 0.8 0.2 AXIS Y 0.0 0.2 0.05 SPECIES ELECTRON SELECT TAG/
PHASESPACE PHTIM AXES XI PI AXIS X 0.0 0.8 0.2 AXIS Y -1.0E9 1.0E9 0.5E9 SPECIES ELECTRON SELECT TAG/
TIMER RTIM PERIODIC 7900 99999 10/ RANGE RTIM 1 HELD El 190 2 190 47 2/ RANGE RTIM 1 FIELD E2 190 2 190 47 2/ RANGE RTIM 1 HELD B3 190 2 190 47 2/ TIMER CONTIM DISC31ETE 8000/ CONTOUR CONTIM HELD El 100 196 2 47/ CONTOUR CONTIM FIELD E2 100 196 2 47/ CONTOUR CONTIM FIELD B 3 100 196 2 47/ CONTOUR CONTIM FIELD El 100 196 8 47/ CONTOUR CONTIM HELD E2 100 196 8 47/ CONTOUR CONTIM HELD B3 100 196 8 47/ PERSPECTIVE CONTIM FIELD El 100 196 2 47 1 ly PERSPECTIVE CONTIM FIELD E2 100 196 2 47 1 1/ PERSPECTIVE CONTIM FIELD B3 100 196 2 47 1 1/ PERSPECTIVE CONTIM FIELD El 100 196 8 47 1 1; PERSPECTIVE CONTIM FIELD E2 100 196 8 47 1 1> PERSPECTIVE CONTIM FIELD B3 100 196 8 47 1 ly OUTPUT SYSTEM/ START/ STOP/
96
^ . kV
APPENDDCB
MICROWAVE POWER CALCULATION MAGIC
SOURCE DECK
TITLE "SMOOTH LUCITE WINDOW VERSION 4"; C DIELECTRIC CONSTANT OF LUCITE AT 3 GHZ: 2.6; C DIELECTRIC CONSTANT OF LEXAN AT 1 GHZ: 3.0; SYSTEM CYUNDER-THETA; XIGRID FUNCTION 168 2 0.0 20 9.525E-3 0.127 24 3.175E-3 0.0762
22 3.175E-3 0.1968 100 1.5E-2 1.5; X2GRID FUNCTION 162 2 0.0 32 3.175E-3 0.1016 22 3.175E-3 0.1968
106 1.5E-2 1.59; SYMMETRY AXIAL AUGN 2 2 168 2; FIELDS ALL CENTERED 2400 6.25E-12; COURANT SEARCH; CONDUCTOR WAVEGUIDE ANTI-ALIGN 2 33 22 33 22 39 19 39 19 34 2 34; LOOKBACK FIELDS ALL 1.0 1.0 ALIGN 2 34 2 162; FUNCTION "ABSORB(X) = 2.5E-1*X**2"; FREESPACE ABSORB XIANTI-AUGN 148 168 2 162; FREESPACE ABSORB X2ANTI-AUGN 2 168 142 162; DIELECTRIC ALL 2.6 22 26 2 51 -1; DISPLAY NO 0.0 2.0 0.0 2.0; DISPLAY NO 0.0 0.3 0.0 0.3; DISPLAY NO 0.05 0.2 0.0 0.15; VOLTAGE FIELDS TM VOFT VOFR 1.23 0.0 1.0 ALIGN 2 2 2 33; FUNCTION "VOFT(T)=92.28E3*SIN(1.256637E10*T)*TANH(1.0E9*T)"; FUNCTION "VOFR(X)=BESSEU1(24.43308*X)"; OBSERVE FIELD El 2 2 2 2; OBSERVE FIELD El 22 2 22 2; OBSERVE FIELD El 26 2 26 2; OBSERVE FIELD El 46 2 46 2; OBSERVE FIELD E2 2 2 2 33; OBSERVE FIELD E2 22 2 22 33; OBSERVE FIELD E2 2 26 2 26; OBSERVE FIELD E2 22 26 22 26; OBSERVE FIELD B3 2 26 2 26; OBSERVE FIELD B3 22 26 22 26; OBSERVE FIELD El 141 61 141 61; OBSERVE FIELD E2 141 61 141 61;
97
OBSERVE FIELD B3 141 61 141 61; OBSERVE FIELD El 148 2 148 2; OBSERVE FIELD El 153 2 153 2; OBSERVE FIELD El 158 2 158 2; OBSERVE FIELD El 163 2 163 2; OBSERVE FIELD El 167 2 167 2; TIMER RECl DISCRETE 1590; RECORD RECl SMLUC4.REC 10; OUTPUT SYSTEM; START; STOP;
98
j < -
APPENDIX C
POWER CALCULATION DETAILS AND
RADL^TION PATTERNS
All of the MAGIC simulations done to calculate the nticrowave power
propagated through the different windows were done in cylindrical coordinates
(p ,<|) ,z). Examination of the electtomagnetic field quantities at the window and in
the anechoic chamber shows that E^=B =B =0, just as is the case in the waveguide
(Eqs. 9). Five different simulations were run, cortesponding to the 1.27 cm thick
planar window, the protmding cone window on the atmospheric side and the
vacuum side, and the inverted cone on the atmospheric side and the vacuum side.
It should be emphasized that, since these calculations are radiation pattem depen
dent they are ortiy vahd for a TM j mode at approximately 2 GHz. —>
From the defirtition of the power density, S, in cylindrical coordinates it can
be shown:
where S and S^ are the p and z components of the power density and d^ and d^
are urtit veaors in the cylindrical coordinate system. Since £^, E^, and B^ are
avatiable from MAGIC, the power density as a function of the spatial coordinates
can be calculated. In this case S^ was found just outside the window (z^z^ for
0<p^y and 5p was found at p=p^ for z<.z<z^. These two surfaces, put
together, form a flux surface that praaically all of the propagated power must flow
through. Once S is known, the total power, P, can be obtained from:
P= rS-^= -InpjEH^dz+lnJE^H^pdp. (C2)
99
The results of the numeric integrations of Eq. C2 are summarized in Table CI. The
magnetic flux density, B^, in Table CI is the value from the simulations at a
location cortesponding to the B-dot probe.
Table CI. Results of Method 1 Power Calculations
Window Description
1.27 cm thick planar
protmding cone in atmosphere
inverted cone in atmosphere
protmding cone in vacuum
inverted cone in vacuum
B^ (Tesla)
196x10"^
192x10-^
213x10-^
188x10-*
216x10"*
Power (MW)
91.14
99.29
102.11
88.22
98.63
To verify the results shown in Table CI the power was also calculated as
outlined in Seaion 3.3. B. was obtained at r=1.4 m from the center of the
waveguide end every two degrees for 0<6<7c/2. Again the integration will only be
carried out for 0<G<7r/2 since the contribution by S^ to tiie total power is negligi
ble for n/l<Q<n . The equation for the total power:
rt/2
P^ln r5/'sin(e)^e. (C3)
was then numerically integrated to obtain the results given in Table C2. For tiie
calibration of the B-dot probe tiie quantity of interest is PI\H^ p (Eq. 14). These
values were calculated from the data given in Tables CI and C2 and are displayed
in Fig. CI. It can be seen that, although there is some disagreement in absolute
power values, there is reasonable agreement in the general trend of tiie two data
sets. The question is which data set to selea for an absolute power calibration.
100
Table C2. Results of Method 2 Power Calculations
Window Description
1.27 cm thick planar
protmding cone in atmosphere
inverted cone in atmosphere
protmding cone in vacuum
inverted cone in vacuum
B^ (Tesla)
196x10"*
192x10"*
213x10"*
188x10"*
216x10"*
Power (MW)
114.8
118.4
124.0
115.3
124.4
6000
5000
X 4000
3000
2000
ic*-Calculation 1 -•-Calculation 2
1.27 cm Protmding Inverted Protmding Thick Cone in Cone in Cone in Planar Atmosphere Atmosphere Vacuum
Inverted Cone in Vacuum
Figure CI. Results of the B-dot Probe Calibration Calculations.
101
Since the two data sets shown in Fig. CI exhibit the same tendencies, if an
absolute power value for one of the windows can be found that agrees with a value
obtained by one of the methods already used, it should justify using that data set in
the B-dot probe calibration.
A third method using the Field Equivalence Theorem and the far field
^>proximation as outiined by Maclean^^ was also used to calculate the total power
propagated. For a circular j^rture of radius A in an infirtite perfealy conduaing
plane, the far field radiation fields in spherical coordinates are given by:
a 2n
£,=^e-^*^J j{E cos^ +Esm^)e^'^''^'°^^-^ydp'di!^' (C4) 0 0
and
a 2K
E^^-J-e-J'^cosBJ fe^sincj)-Ecos^)e^"^'""^^"^^"• >'dp'd(^\ (^^) 0 0
where p and ^' are the aperture coordinates, r, 6, and ^ are the coordinates of a
point in the far field, X is the wavelength, /: is the phase constant defined by:
and, £ and £ are the components of the electric field in the aperture. For the
case of a TM j mode the fields in the aperature are approximated by:
X Or 1
( \ X„,P'
V '^ J
COS(|)' (C7)
and
y Or 1 ^0,P '
^
sincj)'. (C8)
)
102
where X^^ is the first zero of the zero order Bessel function of the first kind, Jj is
the first order Bessel function of the first kind, and E^^ is a constant. Evaluating
tiie integrals in Eqs. (C4) and (C5) gives:
and
^e=-2^^c.
Xr
/:sin6
a-X;i-(ka)hm^e
(C9) /
J,(^o.) Jfjika sinO)
-J,(^n,) JJka sinO)
r"oi^ V
-^01 -^2(^01)
"a ~ .Jj(^asin6)
(CIO)
Now, in the far field where the wave is a ttansverse electtomagnetic wave, the
power density, 5 , is given by:
5 = N
£ l£. (Cll)
The total power was found, by using eq. (C3), to be approximately 149 MW.
Comparison of this value with the values for the planar window in Tables CI and
C2 shows it to be greater than either value calculated before. The value found
using the techrtique outiined in Seaion 3.3 falls in-between the values obtained by
the other two methods which is why this data set was chosen.
From the information necessary to do the power calculations it is also
possible to plot the far field radiation patterns for the different windows, where the
magitimde of the radiation pattem as a function of G is defined as:
F(e)= S,(Q)
rjatx
(C12)
These plots are shown in Figs. C2-C6. It is apparent that the windows tested here
have littie effea on the radiation pattem in the far field.
103
270*
Figure C2. Radiation Pattem of the 1.27 cm Thick Planar Window.
90*
ISO-
Figure C3. Radiation Pattem of the Protmding Cone in Atmosphere.
104
If:
90*
180*
150" /
•
21 L0'\
\2R' ^^--^
y
' ; ' . ' •
240*^^^^^__
0 . 7 5 ^ ^
05
02SPK
/o.Vo*
60-
K ^
' • ; ; ' •
' soo*
\ 30*
0.75\
(J
-/330*
270*
Figure C4. Radiation Pattem of the Inverted Cone in Atmosphere.
Figure C5. Radiation Pattem of the Protmding Cone in Vacuum.
105
270*
Figure C6. Radiation Pattem of the Inverted Cone in Vacuum.
106
Recommended