HIGH-POWER MICROWAVE BREAKDOWN OF IN ELECTRICAL ENGINEERING the

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 cjâcitors in parallel,

then discharge them in series, resulting in voltage multiplication. If a Marx genera

tor is made up of n câcitors (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 -Ô.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)

^.= -;ô—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 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

-

^__^^

<oiî^

— 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)



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


RANGING FROM (15,2) TO (55,44) CONTOUR WINDOW: -4.00E+05 TO 4.00E-f06


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




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




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




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)




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)




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




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




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

HôcEocE , (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 ^âl 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



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






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)ê. (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






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

£,=ê-^*^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

ê=-2^^c.

Xr

/:sin6

a-X;i-(ka)hmê

(C9) /

J,(ô.) Jfjika sinO)

-J,(^n,) JJka sinO)

r"oi^ V

-^01 -^2(^01)

"a ~ .Jj(âsin6)

(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

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