HIGH POWER MICROWAVE WINDOW FLASHOVER

AT ATMOSPHERIC PRESSURES

by

GREGORY FORD EDMISTON, B.S.E.E.

A THESIS

IN

ELECTRICAL ENGINEERING

Submitted to the Graduate Faculty of Texas Tech University in

Partial Fulfillment of the Requirements for

the Degree of

MASTER OF SCIENCE

IN

ELECTRICAL ENGINEERING

Approved

Andreas Alfred Neuber Chairperson of the Committee

James C. Dickens

Accepted

John Borrelli Dean of the Graduate School

December, 2005

c©2005

GREGORY EDMISTON

All Rights Reserved

ACKNOWLEDGEMENTS

I would like to thank my committee for their continuous support and guidance

throughout this project. Special thanks to Dr. Neuber for serving as chairman of my

committee, his continual support and input were pivotal to the success of the project.

I would also like to thank Dr. Dickens for serving as co-chair of my committee

and for always keeping the project on track. Additionally, I would like to thank

Dr. Krompholz for his valuable input and contributions to the analysis of the data

collected on the project.

Special thanks are also owed to the staff of The Center for Pulsed Power and Power

Electronics at Texas Tech. Specifically, I would like to thank Dino Castro, Danny

Garcia, Shannon Gray, Marie Byrd and all of the undergraduates who assisted me

on this project. I would also like to thank John Krile for the numerous hours he

sacrificed to chase leaks, machine “ideas”, test theories, or simply attempt to explain

the unexplainable. A very special thanks to all of my colleagues in the lab for their

suggestions, contributions, and friendship.

Last of all, I wish to express supreme gratitude to my Abby, for her encouragement,

support, companionship and unconditional love. I never would have made it this far

without her.

ii

CONTENTS

ACKNOWLEDGEMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . ii

ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi

LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii

LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii

CHAPTER

I INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

II BACKGROUND THEORY . . . . . . . . . . . . . . . . . . . . . . . 3

2.1 Electron Emission Mechanisms . . . . . . . . . . . . . . . . . . 3

2.1.1 Field Emission of Electrons . . . . . . . . . . . . . . . . . 3

2.1.2 Photoelectric Emission . . . . . . . . . . . . . . . . . . . . 5

2.1.3 Secondary Electron Emission . . . . . . . . . . . . . . . . . 6

2.1.3.1 Secondary Electron Production . . . . . . . . . . . . 6

2.1.3.2 Yield of Secondary Electron Emission . . . . . . . . 7

2.2 Ionization Processes . . . . . . . . . . . . . . . . . . . . . . . . 9

2.2.1 Ionization by Collision . . . . . . . . . . . . . . . . . . . . 9

2.2.2 Coefficient of Ionization by Electron Collision . . . . . . . 10

2.2.3 Ionization Coefficient in A/C Fields . . . . . . . . . . . . . 10

2.2.4 Photoionization . . . . . . . . . . . . . . . . . . . . . . . . 11

2.3 Loss Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.3.1 Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.3.2 Recombination . . . . . . . . . . . . . . . . . . . . . . . . 13

2.3.3 Electron Attachment . . . . . . . . . . . . . . . . . . . . . 15

2.4 Electrical Breakdown Mechanisms . . . . . . . . . . . . . . . . 15

2.4.1 The Electron Avalanche . . . . . . . . . . . . . . . . . . . 16

2.4.2 The Townsend Discharge . . . . . . . . . . . . . . . . . . . 16

2.4.3 Streamer Formation . . . . . . . . . . . . . . . . . . . . . . 17

2.4.4 Paschen’s Law . . . . . . . . . . . . . . . . . . . . . . . . . 19

iii

2.5 Previous Research . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.5.1 Surface Flashover in Vacuum . . . . . . . . . . . . . . . . . 20

2.5.2 Single Surface Multipactor on Dielectric Surface . . . . . . 21

2.5.3 Volume Breakdown at Microwave Frequencies . . . . . . . 22

III EXPERIMENTAL SETUP . . . . . . . . . . . . . . . . . . . . . . . 27

3.1 Experimental Test Chamber . . . . . . . . . . . . . . . . . . . 28

3.1.1 Environmental Control . . . . . . . . . . . . . . . . . . . . 31

3.1.2 Exit Flange Geometry . . . . . . . . . . . . . . . . . . . . 33

3.2 Diagnostics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.2.1 Power Measurement . . . . . . . . . . . . . . . . . . . . . . 38

3.2.2 Luminosity Diagnostics . . . . . . . . . . . . . . . . . . . . 40

3.2.3 ICCD Cameras . . . . . . . . . . . . . . . . . . . . . . . . 40

3.2.4 Spectrograph . . . . . . . . . . . . . . . . . . . . . . . . . 41

3.3 Data Manipulation . . . . . . . . . . . . . . . . . . . . . . . . 44

IV EXPERIMENTAL RESULTS AND DISCUSSION . . . . . . . . . . 46

4.1 Breakdown Waveforms . . . . . . . . . . . . . . . . . . . . . . 46

4.1.1 Breakdown at High Pressure . . . . . . . . . . . . . . . . . 46

4.1.2 Breakdown at Low Pressure . . . . . . . . . . . . . . . . . 47

4.2 Delay Times . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

4.2.1 Effect of Power Levels . . . . . . . . . . . . . . . . . . . . 48

4.2.2 Effect of UV Illumination . . . . . . . . . . . . . . . . . . . 49

4.2.3 Effect of Gas Humidity . . . . . . . . . . . . . . . . . . . . 51

4.2.4 Comparison with data from Volume Breakdown . . . . . . 52

4.2.5 Holdoff Time Estimation . . . . . . . . . . . . . . . . . . . 53

4.2.6 Comparison with High Field Enhancement Studies . . . . . 54

4.3 Optical Emission Spectroscopy . . . . . . . . . . . . . . . . . . 57

4.3.1 Synthesis Program . . . . . . . . . . . . . . . . . . . . . . 58

4.3.2 Experimental Spectra . . . . . . . . . . . . . . . . . . . . . 63

4.4 Imaging of Flashover Formation . . . . . . . . . . . . . . . . . 64

iv

4.4.1 Surface Flashover Liftoff . . . . . . . . . . . . . . . . . . . 77

4.4.2 Pulsed UV Illumination of Surface . . . . . . . . . . . . . . 77

V CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

APPENDICIES

A MOLECULAR SPECTRA SYNTHESIS PROGRAM . . . . . . . . 90

B ENERGY LEVELS AND POTENTIAL CURVES OF N2 . . . . . . 108

v

ABSTRACT

One of the major limiting factors to the transportation of high power microwave

(HPM) radiation is the interface between dielectric-vacuum or even more severely be-

tween dielectric-air if HPM is to be radiated into the atmosphere. Surface flashover

phenomena which occur at these transitions severely limit the power levels which can

be transmitted. It is of major technical importance to predict surface flashover events

for a given window geometry, material and power level. When considering an aircraft

based high power microwave platform, variances in the operational environment cor-

responding to altitudes from sea level to 50,000 feet (760 torr to 90 torr) are also

important. The test setup is carefully designed to study the influence of each atmo-

spheric variable without the influence of high field enhancement or electron injecting

metallic electrodes. Diagnostic equipment allow for the measurement of power lev-

els, luminosity and optical emission spectra with resolution in the nanosecond time

regime.

Experimental results on HPM surface flashover are presented, including the im-

pact of gas pressure and humidity, and the presence of UV illumination, along with

temperature analysis of the developing discharge plasma and temporally resolved im-

ages of the flashover formation in air and nitrogen environments. These results are

compared with literature data for volume breakdown in air, with discussion of the

similarities and differences between the data.

vi

LIST OF TABLES

2.1 Selected Ionization Coefficient Constants and ranges of applicabilityfor Atmospheric gases from Raizer [3] . . . . . . . . . . . . . . . . . . 11

3.1 MS 257 Grating Properties . . . . . . . . . . . . . . . . . . . . . . . . 43

4.1 Values of constants used in spectra synthesis program . . . . . . . . . 59

4.2 Other Prominent Systems in Air Discharges . . . . . . . . . . . . . . 81

vii

LIST OF FIGURES

2.1 The lowering of the potential barrier by an external field: curve 1–energy curve with no external field, −W = e2/16πε0x; curve 2–energydue to applied field, −Wf = eEx; curve 3–total energy curve Wt =We + Wf [2] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.2 The energy distribuition of secondary electrons emitted by silver ac-cording to Rudberg [12, 13] . . . . . . . . . . . . . . . . . . . . . . . 7

2.3 Universal curve of secondary electron emission (δ/δmax as a function ofEp/Emax). Crossover points one, Ep1, and two, Ep2, which correspondto δ = 1 are indicated for a specific material with δmax = 3, Emax =420eV [6] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.4 Recombination coefficient for ions in air [16] . . . . . . . . . . . . . . 13

2.5 Temperature variation of the recombination coefficient for ions in oxy-gen at 1 atm [16, 17] . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.6 Diagram of the stages of streamer formation from Nasser [2] . . . . . 18

2.7 Breakdown potentials in various gases over a wide range of pd values(Paschen curves) [3] . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.8 Secondary Electron Emission Avalanche [20] . . . . . . . . . . . . . . 21

2.9 Model of a single-surface multipactor in a parallel rf and normal dcelectric fields from Kishek [22] . . . . . . . . . . . . . . . . . . . . . . 22

2.10 Variation of Dp with E/p in air [1, 24] . . . . . . . . . . . . . . . . . 24

2.11 Comparison of different experimental results for the breakdown thresh-old of short high power microwave pulses [25] . . . . . . . . . . . . . 25

2.12 Comparison between theoretical and experimental results for air break-down by short intense microwave pulses [27] . . . . . . . . . . . . . . 26

3.1 HPM Surface Flashover Experimental Setup Overview . . . . . . . . 27

3.2 Isometric view of HPM Surface Flashover Experimental Setup . . . . 28

3.3 The electric and magnetic field configurations for a TE10 mode in arectangular waveguide [28] . . . . . . . . . . . . . . . . . . . . . . . . 29

3.4 Scattering parameters of atmospheric test section from HFSS simula-tions and low-power measurements . . . . . . . . . . . . . . . . . . . 30

viii

3.5 Attenuation of Atmospheric Test Section (S21) vs. Incident Power . . 31

3.6 Atmospheric Divisions of HPM Surface Flashover Experimental Setup 32

3.7 Environmental Control System . . . . . . . . . . . . . . . . . . . . . 33

3.8 Close up view of the exit flange geometry utilized to eliminate metallicconductors from the flashover location . . . . . . . . . . . . . . . . . 34

3.9 Intermediary Gasket Design A . . . . . . . . . . . . . . . . . . . . . . 35

3.10 Intermediary Gasket Design B . . . . . . . . . . . . . . . . . . . . . . 35

3.11 Field profiles of intermediary gaskets A and B along the A-A cut lineof Figs. 3.9 and 3.10 respectively, from Ansoft HFSS simulations . . . 36

3.12 E-field components along the polycarbonate window surface as a func-tion of vertical location along the A-A cut line of intermediary gasketB (c.f. Fig. 3.10) from Ansoft HFSS simulations, 3.25MW incidentpower . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.13 E-field components along the polycarbonate window surface as a func-tion of horizontal location along the B-B cut line of intermediary gasketB (c.f. Fig. 3.10) from Ansoft HFSS simulations, 3.25MW incident power 38

3.14 Location of diode detectors for power measurement . . . . . . . . . . 39

3.15 Port designations for directional coupler . . . . . . . . . . . . . . . . 40

3.16 Spectrographic setup for HPM surface flashover experiments . . . . . 42

3.17 Multitrack Operation of Spectrograph from Oriel . . . . . . . . . . . 43

3.18 Exaggerated collection area of optical emission spectra (actual collec-tion area much narrower) . . . . . . . . . . . . . . . . . . . . . . . . . 44

3.19 Calibration curve for HP 8474B diodes . . . . . . . . . . . . . . . . . 45

4.1 Typical waveforms for HPM surface flashover at high pressure (285torr). Top Graph: Black-Incident power, Medium Grey-Reflected power,Light Grey-Transmitted power, Bottom Graph: Black-Absorbed Power,Medium Gray-Luminosity, Light Gray-Luminosity * 100 . . . . . . . 47

4.2 Typical waveforms from HPM surface flashover at low pressure (90torr). Top Graph: Black-Incident power, Medium Grey-Reflected power,Light Grey-Transmitted power, Bottom Graph: Black-Absorbed Power,Medium Gray-Luminosity, Light Gray-Luminosity * 100 . . . . . . . 48

ix

4.3 Effect of Incident Power on delay time, Squares-3.0 MW, Circles-4.5MW 49

4.4 Effect of UV Illumination of sample, Triangles-No UV illumination,Circles-UV illumination . . . . . . . . . . . . . . . . . . . . . . . . . 50

4.5 Effect of Gas Humidity on delay time, Squares-Low Humidity (< 15%RH), Triangles-High Humidity (> 85% RH) . . . . . . . . . . . . . . 51

4.6 Effective electric field/pressure (E/p) vs. pressure times pulse width(pτ), Dotted Line-Gould and Roberts for volume breakdown, Triangle-3MW surface flashover, Circle-4.5MW surface flashover, Square-3MWwith UV illumination . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

4.7 Estimated pulse duration vs. transmitted power resulting in surfaceflashover event for a polycarbonate window . . . . . . . . . . . . . . . 54

4.8 HPM surface flashover experimental setup involving high field enhance-ment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

4.9 Peak electric field strength at breakdown for various dielectric materialsand volume vs. pressure in a high field enhancement geometry, curvesrepresent breakdown field strengths extrapolated from the electrode-less geometry experiments . . . . . . . . . . . . . . . . . . . . . . . . 56

4.10 Peak electric field vs. vertical coordinate for high field enhancement(with electrodes) and electrode-less (without electrodes) geometries,3.25MW incident power . . . . . . . . . . . . . . . . . . . . . . . . . 57

4.11 Optical emission spectrum collected from HPM surface flashover (250nm-500nm); dotted vertical lines represent spectral components expectedif brass electrode material was present [32, 34] . . . . . . . . . . . . . 58

4.12 N2 C3Πu → B3Πg Spectrum from synthesis program, same conditionsas in Fig. 4.13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

4.13 N2 C3Πu → B3Πg Spectrum from Nassar [37] . . . . . . . . . . . . . . 62

4.14 Experimentally gathered optical emission spectrum in air (Top) vs.Synthesized Spectra (Bottom); convolution profile: combination ofsquare, gaussian and lorentz profiles with δλ = 0.23nm . . . . . . . . 63

4.15 Relative error between experimental and synthesized spectra vs. tem-perature variation from the optimal temperature value obtained fromparametric analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

4.16 Front reference image . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

x

4.17 Flashover formation in air at 90torr; 17ns camera gate, 33ns beforeluminosity rise; Frame 1 of 5; Intensity ×4 . . . . . . . . . . . . . . . 66

4.18 Flashover formation in air at 90torr; 17ns camera gate, 20ns beforeluminosity rise; Frame 2 of 5; Intensity ×1 . . . . . . . . . . . . . . . 67

4.19 Flashover formation in air at 90torr; 17ns camera gate, 14ns beforeluminosity rise; Frame 3 of 5; Intensity ×1 . . . . . . . . . . . . . . . 68

4.20 Flashover formation in air at 90torr; 17ns camera gate, 29ns after lu-minosity rise; Frame 4 of 5; Intensity ×1 . . . . . . . . . . . . . . . . 69

4.21 Flashover formation in air at 90torr; 17ns camera gate, 68ns after lu-minosity rise; Frame 5 of 5; Intensity ×1 . . . . . . . . . . . . . . . . 70

4.22 Flashover formation in air at 155torr; 17ns camera gate, 24ns beforeluminosity rise; Frame 1 of 5; Intensity ×4 . . . . . . . . . . . . . . . 71

4.23 Flashover formation in air at 155torr; 17ns camera gate, 16ns beforeluminosity rise; Frame 2 of 5; Intensity ×1 . . . . . . . . . . . . . . . 72

4.24 Flashover formation in air at 155torr; 17ns camera gate, 33ns afterluminosity rise; Frame 3 of 5; Intensity ×1 . . . . . . . . . . . . . . . 73

4.25 Flashover formation in air at 155torr; 17ns camera gate, 54ns afterluminosity rise; Frame 4 of 5; Intensity ×1 . . . . . . . . . . . . . . . 74

4.26 Flashover formation in air at 155torr; 17ns camera gate, 67ns afterluminosity rise; Frame 5 of 5; Intensity ×1 . . . . . . . . . . . . . . . 75

4.27 Pseudo color image of flashover formation along the polycarbonatewindow at 90 torr in air; 17ns optical gate . . . . . . . . . . . . . . . 77

4.28 Left- E-field Lines; Right-Comparison of flashover path in air and N2 . 78

4.29 Temporal spectrum of Oriel Model 60963 5-Joule Flashlamp Illuminator 79

4.30 Application of UV illumination pulse (at time tp) prior to HPM pulse(time t = 0) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

4.31 Liftoff of surface flashover vs. application of UV pulse . . . . . . . . . 81

B.1 Potential Energy Curves for N2 and N+2 [47] . . . . . . . . . . . . . . 108

B.2 Energy level schemes for N2 [40] . . . . . . . . . . . . . . . . . . . . . 109

xi

CHAPTER 1

INTRODUCTION

Microwave breakdown phenomena have been an area of interest in many areas

of applied physics for some time. Since the need to transmit high power microwave

(HPM) radiation is paramount in communication systems as well as the development

of technologies such as directed-energy systems and high power radar applications,

the breakdown phenomena which limit the generation and transportation of this

radiation deserve considerable attention. The term “high power microwaves” is often

used to refer to power levels on the order of one megawatt for X-band systems, or

tens of megawatts for an S-band system. These power levels correspond to electric

field strengths of around 20 to 30kV/cm, which is roughly the volume breakdown

threshold of air at atmospheric pressures. The desire for the next generation of high

power microwave systems compels research to develop models capable of describing

each of the limiting factors associated with the development of these technologies.

The limitations of RF pulsed applications associated with air-volume breakdown

have been extensively studied and the mechanisms contributing to the development

of this phenomena are thoroughly discussed in literature [1, 2, 3, 4]. However, sur-

face flashover phenomena occurring at dielectric/vacuum or dielectric/air interfaces

in a high power microwave system have recently emerged as the major limiting factor

in the transportation of this radiation. Extensive studies have identified the phys-

ical mechanisms associated with vacuum-dielectric flashover [5], but relatively few

attempts have been made to study the mechanisms of RF flashover of a dielectric

surface in atmospheric pressures [6, 7]. The study of RF surface flashover in atmo-

spheric pressures is complex compared to surface flashover in vacuum due to the added

effects associated with presence of a gas. Variations in the constituents comprising

atmospheric gases, such as dust or humidity, combine with standard gas parameters

such as pressure and temperature to complicate the analysis and modeling of surface

flashover events. Available data for this type of surface flashover involving high field

1

enhancement due to the presence of a triple point have shown that the volume break-

down threshold (dielectric removed) is approximately 50% higher than the flashover

threshold with a dielectric interface over the 90-760 torr range [5].

In order to examine the mechanisms contributing to the surface flashover process

associated with dielectric surface independent from the effects of an electron injecting

metallic surfaces, the effects of the triple point must be minimized or eliminated

entirely. Mechanisms investigated include surface effects such as secondary electron

emission, emission of photoelectrons, and electron capture by the surface in addition

to gaseous ionization and electron emission from the high field region. Successful

development of a theory for HPM surface flashover requires a clear understanding of

which processes are involved and to what extent.

The following chapters of this document contain an overview of the physical mech-

anisms related to HPM surface flashover, including emission and ionization, followed

by a summary of research performed in the areas of RF volume breakdown and surface

flashover in vacuum. Understanding the models behind these phenomena is impor-

tant due to the fact that any theory developed for HPM surface flashover is expected

to evolve from a combination of the same processes and mechanisms associated with

these previously studied fields. Following the theoretical overview sections, a detailed

explanation of the experimental setup is provided. Information on the diagnostic

equipment used to monitor surface flashover development is located in that section.

The presentation of data collected from surface flashover events is found in the second

half of this document with analysis and comparison to the previously studied fields.

The results of this analysis are briefly summarized at the end of the document.

2

CHAPTER 2

BACKGROUND THEORY

In order to adequately study high power microwave surface flashover, it is nec-

essary to understand the processes which define electrical breakdown. Once these

processes are understood, it is possible to determine which processes are relevant,

and which processes are dominant in surface flashover events. A detailed discus-

sion of virtually all of these processes is available in literature [2, 3], and is briefly

summarized here.

2.1 Electron Emission Mechanisms

Electron emission mechanisms play a primary role in the formation of electrical

breakdown events. This is due to the fact that “free” electrons contribute to the

number of charged particles in a discharge gap, increasing the conductivity of the

gap, and have the potential to liberate additional charged particles by ionization and

secondary emission processes. While electron emission may be discussed as a whole,

it is easier to discuss the various types of electron emission categorically, with each

category dealing with the method by which an electron is liberated.

2.1.1 Field Emission of Electrons

Field Emission of electrons deals with the liberation of an electron from a surface

due to the presence of an electric field. This process is accomplished by overcoming

the work function of the surface material via the lowering of the potential barrier

by an external electric field. As an electron leaves a surface, its electric field can be

considered that of a point charge at some distance from an equipotential surface. The

force on the emerging electron at a distance x from the surface can be calculated by

Coulomb’s law. By integrating from over the distance x, the potential energy of the

electron, We, is determined by the equation

3

We =−e2

16πε0x(2.1)

The potential energy of the electron with an external electric field E perpendicular

to the surface is

Wf = −eEx (2.2)

Figure 2.1: The lowering of the potential barrier by an external field: curve 1–energycurve with no external field, −W = e2/16πε0x; curve 2–energy due to applied field,−Wf = eEx; curve 3–total energy curve Wt = We + Wf [2]

The combined effect of these two potential curves is Wt = We + Wf , a lowered

potential energy curve represented by Fig. 2.1. The effective value of the work

function in the presence of the field E is

W = e

[φ−

(eE

4πε0

)1/2]

(2.3)

The process of electrons leaving the surface can be represented by an equivalent

current density j per unit area. Using quantum mechanics, Fowler and Nordheim

examined this phenomena and described it as the tunnel effect, where electrons in

the Fermi level of a solid without sufficient energy to overcome the potential barrier

4

can tunnel through [8]. This is accomplished by solving the wave equation of an

electron and finding that in cases of a sufficiently thin potential barrier (<1nm),

there is a finite, although small, probability of finding the electron on the other side

of the barrier [9]. The equation describing the probability of electrons penetrating

the potential barrier per unit of time is referred to as the Fowler-Nordheim equation

and is defined as the current density

j = fE2

φε−gφ3/2u/E A/m2 (2.4)

where f = 1.54× 10−6, g = 6.83× 109 and u2 = 1− 1.4× 10−9E/φ2 with E in V/m

[2]. However, evaluation of Eqn. 2.5 requires fields on the order of 109 to 1011 V/m

in order to achieve measurable currents, where as experimental data yields similar

currents at electric fields several orders of magnitude weaker [2]. In order to account

for this difference, the Fowler-Nordheim equation was modified to include the field

enhancement factor, β, of micro-protrusions on the electrode surface. The modified

Fowler-Nordheim equation given by

j = fβE2

φε−gβφ3/2u/E A/m2 (2.5)

with values of β ranging from around 10 to several 100 [10].

2.1.2 Photoelectric Emission

Photoelectric emission is process by which electrons are liberated from a surface

illuminated by incident photons. The energy of the incident photons, hν, must be

sufficient to overcome the work function of the surface material. If the energy hν

is greater than the work required to liberate an electron, eφ, the remaining energy

is found in the form of kinetic energy of the liberated electron. This relationship is

expressed by

hν = eφ +1

2mv2 (2.6)

5

where eφ is the work function of the surface, h = 6.626× 10−34m2kg/s and m and v

are the mass and velocity of the liberated electron.

2.1.3 Secondary Electron Emission

In the event that electrically charged particles bombard a solid surface with suf-

ficient energy, emission of electrons from the surface may occur. This phenomena

was originally observed by Austin and Starke in 1902 [11]. The bombarding charged

particles incident to the surface are commonly referred to as primaries whereas the

electrons liberated from the surface are referred to as secondaries. The incident

particles may either be electrons or ions, however, the theories of secondary electron

emission under electron bombardment and ion bombardment vary considerably. Elec-

tron bombardment of a surface consists of electrons of varying energies penetrating

into the surface of a solid and producing a bulk effect, whereas ion bombardment

of a surface produces only a surface effect [12]. Unless otherwise noted, discussions

involving secondary electron emission here will assume electron bombardment.

2.1.3.1 Secondary Electron Production

Given primary electrons incident upon a solid surface, some of the primaries will

be elastically reflected from the surface while the others penetrate into the solid. The

penetrating primaries will lose energy by exciting lattice electrons into higher energy

levels. Once excited to higher energy levels, some electrons will move towards the

surface and eventually escape. Some incident penetrating primaries will return to the

surface and escape after losing some of their initial energy through inelastic collisions

inside the solid in a process known as Rutherford scattering [12]. Therefore, rather

than referring to all emitted electrons from a surface as secondaries, these electrons

can be classified into three categories:

(a) Elastically reflected primaries

(b) Inelastically reflected primaries (Rutherford scattering)

(c) “True” secondaries

6

Figure 2.2: The energy distribuition of secondary electrons emitted by silver accordingto Rudberg [12, 13]

Observation of the energy distribution of electrons emitted by silver bombarded

by primary electrons shown in Fig. 2.2 from Dekker [12] and Rudberg [13] shows

local maxima denoting the three categories of secondary electrons.

2.1.3.2 Yield of Secondary Electron Emission

The yield of secondary electron emission, δ, is defined as the total emitted sec-

ondary electron current as a proportion of the primary electron current [14]. This can

also be interpreted as the number of emitted electrons per incident primary electron.

For quantities of δ < 1, the net flow of current is into the surface where δ > 1 indicates

multiplication and a net current out of the surface. When quantifying the secondary

yield for various materials (metal, insulator, semiconductor), it is of importance to

note the relationship between δ and the energy of the incident primary, Ep. It can be

shown that over a variety of materials, this relationship is clustered about a universal

curve [15] shown in Fig. 2.3. Observation of the curve shows that for a certain value

Emax there is a maximum yield δmax on the curve, followed by a decline in δ. To

7

explain this shape, it is necessary to divide the process of electron emission into two

stages. The first stage of electron emission involves the impact of a primary electron

and the subsequent excitation and liberation of lattice electrons at a depth x within

the surface. The second stage involves the newly created secondaries and the proba-

bility that each will survive movement from the creation depth x, to the surface and

escape. Considering these two stages, the shape of the universal curve is defined. The

left section of the curve is dominated by the “stage one” production of secondaries

indicated by an increase in δ with increasing Ep. This relationship continues until

the “stage two” mechanism becomes dominate, indicated by the maximum, δmax, at

the energy Emax. Primary electrons with energies increasing above Emax have an

increased impact depth and as a result yield fewer and fewer secondary electrons due

to the reduced probability of a produced secondary escaping from those depths.

Figure 2.3: Universal curve of secondary electron emission (δ/δmax as a function ofEp/Emax). Crossover points one, Ep1, and two, Ep2, which correspond to δ = 1 areindicated for a specific material with δmax = 3, Emax = 420eV [6]

8

2.2 Ionization Processes

When an atom or molecule absorbs enough energy to lose an electron, it becomes a

positively charged particle and is said to be ionized. The number of charged particles

in a volume of gas is an important factor for electrical breakdown because this value

is directly related to the current density in the volume by the equation

j = e(n+v+ + n−v−) A/m2 (2.7)

where e is the elementary charge, n+ and n− are the densities of ions and free electrons

in the volume, and v+ and v− are the corresponding drift velocities defined by

v =2

3

eE

mλυ−1 (2.8)

where E is the applied field, m is the mass of the particle, and the term λυ−1 represents

the averaged product of the mean free path λ and the inverse of the rms thermal

velocity, υ [2]. To successfully determine the number of charged particles in a volume

it is necessary to understand the processes which produce charged particles.

2.2.1 Ionization by Collision

One of the most common ionization processes in a volume breakdown event is

ionization by collision. Ionization by collision involves the impact of an electron with

energy exceeding the ionization potential of a gas molecule. The direct products of

this collision include a secondary electron and a positive ion. This type of ionization

by collision, caused by the exchange of kinetic energy, is an example of a first order

electron ionization process [2]. When an excited impacting particle transfers a fraction

of its internal energy resulting in ionization, this is known as a second order ionization

process. The following equations represent two of the first order processes [9]:

XY + e → XY + + 2e (Direct Ionization)

XY + e → X + Y + + 2e (Dissociative Ionization)

9

X, Y gas atoms or molecules

Y + = positive ion

e =electron

The Penning effect is a second order ionization process represented by the equation

[2]

A∗ + B = A + B+ + e

2.2.2 Coefficient of Ionization by Electron Collision

It is of great importance when investigating breakdown phenomena to quantify

the number of ionizations each electron produces while traveling from cathode to

anode. The number of electrons produced per unit length in the field direction, α, is

known as the ionization coefficient by electron collision or Townsend’s first ionization

coefficient[2]. The first ionization coefficient, α, is also the number ions produced

due to the fact that each ionization event produces a secondary electron and positive

ion. For high values of E/p and moderate energy levels, Townsend’s first ionization

coefficient can be approximated by the equation

α = Ap · e−Bp/E (2.9)

where p is the pressure, E is the applied electric field, A is a temperature dependent

gas constant in ionizations/cm-torr, and B is a gas constant in V/cm-torr [2]. Table

2.1 gives values from Raizer [3] for A and B for several gases and the corresponding

regions of applicability.

2.2.3 Ionization Coefficient in A/C Fields

As the frequency of an E-field applied to a gas increases above a few kilohertz,

the electron motion remains similar to dc field motion with the addition of the field

alternating directions every half cycle. A/C fields in the microwave range have very

10

Table 2.1: Selected Ionization Coefficient Constants and ranges of applicability for

Atmospheric gases from Raizer [3]

Gas A [cm−1torr−1] B [V/cm−1torr−1] E/p Range

N2 12 342 100-600

N2 8.8 275 27-200

Air 15 365 100-800

CO2 20 466 500-1000

H2O 13 290 150-1000

short time periods restricting free electrons only to an oscillatory motion in between

gas particles. The inability of free electrons to gain sufficient energy to ionize gas

particles before experiencing field reversal, and the corresponding reduction in the

effective value of the ionization coefficient α, demonstrate the need to evaluate the

coefficient for high-frequency ionization, ζ, in microwave fields. This coefficient is

defined as

ζ =νi

DE2(2.10)

with νi as the ionization frequency and D as the diffusion coefficient. The impor-

tance of diffusion in the microwave region is prominent [2], constituting the primary

deionization process and is thus included in the evaluation of ζ. Further discussion

of diffusion processes is found later in this chapter.

2.2.4 Photoionization

Ionization may also occur due to absorbtion of energy from either an external

radiation source or background radiation gas. In the case of an incident photon on

a gas molecule, ionization occurs if hν ≥ Wi, where Wi is the ionization energy of

the gas molecule and hν is the energy of the photon. This relationship can also be

expressed in the form

ch

λ≥ Wi (2.11)

11

where c is the speed of light, h is Planck’s constant, and λ is the wavelength of the

incident photon. Photoionization is described by the equation

Y + hν = Y + + e (Photoionization)

2.3 Loss Mechanisms

Since the ionization processes which create and multiply charged particles in a

gas must be considered when studying electrical breakdown, it is equally important

to study the processes which remove charged particles from a gas. These processes

are referred to as deionization processes.

2.3.1 Diffusion

Diffusion is a process by which the particles of one type (in this case charged

particles) spread throughout a volume of particles of a second type (neutral particles)

until the concentration gradient of both particle densities in the volume in the absence

of any external forces present, goes to zero. The primary factor contributing to

diffusion is the natural thermal chaotic motion of all particles in a gas. The process

of diffusion removes charge carrying particles from a potential breakdown channel,

and is a primary loss mechanism. When considering a three dimensional space filled

with n0 charged particles, the current due to diffusion is defined as

J = −D∇n (2.12)

with ∇n as the concentration gradient of charged particles and D as the constant

of proportionality between the rate of flow and the concentration gradient. D is

commonly referred to as the diffusion coefficient and is given by

D =1

3λυ m2/sec (2.13)

with υ as the average velocity and λ as the mean free path of the charged particles

[2]. It is of importance to note that D ∝ p−1.

12

2.3.2 Recombination

A common loss mechanism for ions is the recombination of negative ions or more

importantly electrons, with positive ions. The recombination is directly proportional

to the ion concentration and is given by the equation

dn+

dt=

dn−

dt= −ρn−n+ (2.14)

The proportionality constant ρ is referred to as the recombination coefficient[16].

Using the assumption that the number of positively charged particles, n+, is equiva-

lent to the number of electrons, n−, solving Eq. 2.14 for n yields

1

n=

1

n0

+ ρt (2.15)

where n0 is the initial ion concentration at t = 0. This linear dependance of 1n

on t

is commonly recognized in experiments as a recombination process [16]. Fig 2.4 from

Brown [16] shows the recombination coefficient in air up to 1500 torr.

Figure 2.4: Recombination coefficient for ions in air [16]

13

In addition to being pressure dependent, the recombination coefficient is also

dependent on gas temperature. Empirical data of the recombination coefficient found

in Gardner shows that ρ exhibits a 1/T 2 dependence [17]. This temperature variation

is shown in Fig. 2.5.

Figure 2.5: Temperature variation of the recombination coefficient for ions in oxygenat 1 atm [16, 17]

When a negative ion strikes a positive ion, and the involved energy transfer results

in the deionization of both ions, this is called ion-ion recombination and is given by

the formula

A− + B+ → A + B∗ (Ion-Ion Recombination)

Other paths of recombination are shown by the formulas [3]:

A+2 + e → A + A∗ (Dissociative Recombination)

A+ + e → A + hν (Radiative Recombination)

A+ + e + e → A + e (Radiative Recombination in Three-Body Collisions)

14

2.3.3 Electron Attachment

In electronegative gases (gases with unfilled outer electron shells) such as SF6 or

02, the attachment of electrons to gas particles is a common deionization process. If

the collision frequency of an electron is νc, and the drift velocity in the applied field

E is given by the equation

υ =

(−e/m

jω + νc

)E = µE (2.16)

then the number of electrons lost to attachment in a distance x is given by

dn

dx= −hn

νc

µE(2.17)

where h is a proportionality constant referred to as the probability of attachment[16].

The probability of attachment h is sometimes shown as β, which is analogous to the

first ionization coefficient α and is given by

β =νa

µE(2.18)

with νa as the frequency of attachment [16].

2.4 Electrical Breakdown Mechanisms

Electrical breakdown is the common term used to describe the process by which a

nonconducting medium becomes a conductive through the application of a sufficiently

strong electric field. The study of the mechanisms leading to electrical breakdown be-

gan with experiments by Townsend in the early 1900’s and has expanded greatly since

the 1920’s. There exist many comprehensive literature sources describing the char-

acteristics of electrical breakdown mechanisms, including books by Nasser, Raizer,

Brown and Papoular [2, 3, 16, 18]. The following sections give a brief overview of the

basic processes intrinsic to the study of electrical breakdown mechanisms.

15

2.4.1 The Electron Avalanche

When considering a parallel plate geometry, separated by a distance d filled with

a gas, it has been shown that with the application of an electric field E, any electrons

(n0) in the gap will experience a number of ionization events while transiting from

cathode to anode. These ionization events have been shown to produce a population

of charged particles given by

n = n0eαd (2.19)

To visualize the effects of this “charge multiplication”, an example of this phe-

nomena given in Nasser [2] is as follows:

At moderate E/p of less than 100 V/cm-torr, α/p of some 10−1 ionizations

per cm-torr is reached. Considering a parallel-plate electrode arrangement

in atmospheric air having a 1.0cm spacing, αd will be in the order of 7.6

and eαd = 2 ∗ 103 electrons. Thus one electron starting at the cathode

brings about 2000 electrons to the anode.

As shown in the excerpt, extreme multiplication of electrons bridging the gap is

possible. This multiplication is typically referred to as the electron avalanche.

2.4.2 The Townsend Discharge

When neglecting positive ion contributions, a simple electron avalanche model

can be considered a nonselfsustaining discharge. The lack of any feedback process in

the mechanism shows that once the eαd electrons arrive at the anode the “discharge”

is completed. However, when considering positive ions produced by the electron

avalanche, a feedback mechanism presents itself. The positive ions produced by the

head of the electron avalanche experience an acceleration towards the cathode in

the same manner that the electron cloud experiences an acceleration towards the

cathode. Although heavier than their counterpart electrons, the positive ions can

gain enough energy to ionize other particles through collision or liberate secondary

16

electrons through collisions with the cathode [16, 9] although this is rarely observed

experimentally. More likely methods of producing secondary electrons at the cathode

include photoemission provided by photons emitted from ion-electron recombinations

or excited molecules, or transferred energy from impacting metastable particles on

the cathode providing for the release of secondary electrons. The combined effect of

all of these processes is represented by γ, known as the second Townsend coefficient.

These γ processes allow for a discharge to become selfsustaining and are known as a

Townsend Discharges. This is represented by

γ(eαd − 1

)= 1 (2.20)

meaning that each initial electron must produce at least one secondary electron to

make the discharge selfsustaining.

2.4.3 Streamer Formation

Investigations into spark formation show that electron avalanches predicted by

the Townsend mechanism are not the only form of ionization which developes [2]. If

the density of electrons in the head of an avalanche reaches the critical avalanche size

(108 electrons [19]), the space charge field of the avalanche head must be considered.

At densities above this critical avalanche size, avalanches can transition to “stream-

ers”, a distinctly different ionization channel named for its filamentary nature [2].

Streamer formation can occur in very short time periods on the order of 10−8s and is

represented visually in Fig. 2.6 from Nasser [2]. Explanation from Nasser [2] of the

streamer development associated with the Fig. 2.6 follows. In part (a) of Fig. 2.6, the

developing avalanche develops a space charge on the order of the externally applied

electric field. The associated high amplitude fields allow the electrons in the head

of the avalanche to acquire higher energy, leading to increased UV emission. In part

(b), absorption of the UV radiation by neutrals leads to seed electrons for a second

generation of avalanches. As the positive space charge bridges the gap as shown in

(c), the secondary avalanches are attracted to the positive space charge trunk. In part

17

(d), the accumulation of positive ions at the cathode has increased by the addition

of two auxiliary streamers, and an ionization channel is forming between the anode

and cathode. Two subsequent streamer branches grow into incoming avalanches in

(e) whereas one dies out due to the lack of incoming avalanches in (f). If the process

continues the streamer will eventually bridge the gap as shown in part (g), and the

ionization channel becomes the breakdown path.

Figure 2.6: Diagram of the stages of streamer formation from Nasser [2]

18

2.4.4 Paschen’s Law

When discussing the Townsend Discharge, it can be shown that the αd shown in

Eq. 2.20 is equivalent to ηVb [16, 18]. The value η is a ionization proportionality

constant related to the applied electric field and is given by the equation

η =α

E(2.21)

Substituting these values in Eq. 2.20 and rearranging, the breakdown criterion

(breakdown voltage, Vb) for a gas can be shown as the formula [2]

Vb =Bpd

ln Apdln(1+1/γ)

(2.22)

with values of A and B shown in Table 2.1. This method of relating the breakdown

voltage as a function of pd is known as Paschen’s Law. The value of pd determines

the number of free paths that exist in the field direction between the electrodes,

and Eq. 2.22 shows that there is unique relationship between this product and the

breakdown voltage. This relationship can be shown in the Fig. 2.7. The shape of the

Paschen curve is explained by examining the two regions of the product pd. For very

small pd’s, there is insufficient gap distance for an electron to ionize the very few gas

particles that exist. This regime is often referred to as mean-free path dominated. For

pd very large, E/p is reduced in addition to a smaller free path between particles,

thus a larger voltage is required for breakdown. This region is commonly referred to

as collision dominated. The minimum on the curve represents the transition between

these two regions.

19

Figure 2.7: Breakdown potentials in various gases over a wide range of pd values(Paschen curves) [3]

2.5 Previous Research

2.5.1 Surface Flashover in Vacuum

Surface flashover of insulators in vacuum has been studied rather extensively and

the processes involved are well known and agreed upon. The prevalent model divides

this type of surface flashover into three stages: (a) initiation, (b) growth, and (c)

gaseous ionization along the surface of the insulator [20]. There is general agreement

that the initiation stage is triggered by the field emission of electrons from the cathode

triple point [20, 21]. The triple point is defined as the area where the metal, dielectric

and vacuum intersect. While the factors influencing the growth stage of surface

flashover in vacuum are less agreed upon than the first stage, the most commonly

accepted mechanism for the second stage is a secondary electron emission avalanche

or SEEA [20]. The SEEA process is depicted graphically in Fig. 2.8.

In an SEEA, electrons are emitted from the surface of a dielectric via secondary

emission due to the impact of some primary ion or electron incident to the surface.

Once free from the surface, the electrons experience an acceleration parallel to the

surface in the direction of the applied electric field. However, the process of liberating

electrons from the dielectric surface leaves a net positive charge on the surface, and

20

Figure 2.8: Secondary Electron Emission Avalanche [20]

thus a DC restoring field appears. This restoring field accelerates the “freed” electrons

back towards the surface. If the applied electric field is large enough, the liberated

electrons will impact the surface of the dielectric with sufficient energy to liberate

more electrons, having gained this energy from the applied electric field in the time of

flight between departing from and returning to the surface. As previously mentioned,

the final stage of surface flashover is generally agreed upon and involves gaseous

ionization near the surface due to atoms or molecules desorbed by the SEEA [20].

2.5.2 Single Surface Multipactor on Dielectric Surface

The multipactor discharge is a resonant discharge often observed in microwave

systems at low pressures [6, 22]. The term “multipactor” comes from “AC Electron

Multiplier” and was coined by P. T. Farnsworth, the original identifier of the phe-

nomenon, in the early 1930’s [22]. The multipactor discharge is essentially caused

by the secondary electron emission avalanche previously discussed, with slight mod-

ifications. In the secondary emission avalanche discussed above, the field imparting

energy upon the liberated electrons is DC. In the multipactor discharge, this imparta-

tion of energy is accomplished by the rf electric field. Due to the oscillating nature of

the rf field, any electron liberated from the surface experiences opposite acceleration

forces during each half cycle of rf excitation, and thus placing a dependence on the

21

development of any secondary emission avalanches at frequencies above 20GHz [6].

Fig. 2.9 from Kishek depicts graphically the single-surface multipactor in a configu-

ration with the rf electric field parallel to the dielectric surface, and is reasonable for

rf window applications.

Figure 2.9: Model of a single-surface multipactor in a parallel rf and normal dc electricfields from Kishek [22]

2.5.3 Volume Breakdown at Microwave Frequencies

Although the Townsend discharge criterion was originally developed for DC dis-

charges, the underlying theory has proven valuable for discharges produced by any

frequency, including those in the microwave range [1]. The criteria for breakdown

as described by Townsend states that if the number of the electrons produced by

ionization events is equal to the number lost due to processes including diffusion,

recombination and attachment, then a steady state discharge will occur. If the pro-

duction rate of electrons and ions is slightly larger than the loss rate, the gas quickly

becomes ionized and breakdown occurs. Herlin and Brown [23] were the first to prove

the applicability of the Townsend ionization processes to electric fields in the mi-

crowave frequency range. In electric fields at microwave frequencies, free electrons

in a gap experience an oscillating force such that very little distance is traversed in

22

one-half cycle. This oscillatory motion prevents ionized particles from being “swept”

out of the gap merely by the electric field. Therefore, the only loss mechanisms

dominating rf-breakdown are diffusion, recombination and attachment. Due to the

complexity of the collision properties of air, most early breakdown experiments dealt

with noble gases and hydrogen. It was not until Gould and Roberts [4] in 1956 and

MacDonald [1] in the 1960’s , that a firm theory of microwave breakdown in air was

developed. The first pulsed breakdown data was measured by Gould and Roberts

at 2.8GHz [4], and by MacDonald, Gaskell and Gitterman at 0.99, 9.4, and 24 GHz

[24]. Unlike CW excitation, where the density of charged particles slowly rises with

the electric field until ion production outweighs loss mechanisms, pulsed applications

require this state be reached before the power is turned off at the end of the pulse.

Consequently, pulsed breakdown fields are higher than those of CW fields, and expe-

rience a dependence on both the pulse length and the rate of repetition [1]. With this

in mind, modifications must be made to CW volume breakdown theory to make it

applicable to pulsed applications. A detailed theory of pulsed rf-volume breakdown

in air can be found in literature sources [4, 1, 25] and is summarized here. It can be

shown that the continuity equation for electrons in a volume is

∂n

∂t= νin− νan +∇2(Dn) (2.23)

where n is the electron density, νi is the ionization rate, νa is the attachment rate,

and D is the electron diffusion coefficient. Approximating the diffusion coefficient by

∇2(Dn) ∼= n(−D/Λ2) (2.24)

where Λ is the characteristic diffusion length. In most experimental arrangements

involving large parallel plates, the value Λ is equal to the plate separation divided by

π [1]. Continuing from Eqn. 2.23, a solution for the continuity is as follows

n = n0e(νin−νan−D/Λ2)t (2.25)

23

where n0 is the initial electron density. MacDonald has shown that in air D follows

the relation [1]

Dp = [29 + 0.9(E/p)]× 104 [cm2torr/sec] (2.26)

where p is pressure in torr and E is the amplitude of the electric field in kV/cm. This

variation of Dp with respect to E/p is shown graphically in Fig. 2.10.

Figure 2.10: Variation of Dp with E/p in air [1, 24]

For pulsed microwave breakdown, the electron density growth rate is expressed

by ν, and is given by the expression

ν = νi − νa −D/Λ2 (2.27)

Breakdown takes place for pulsed conditions if the electron concentration reaches

the plasma concentration value by the end of a given pulse [25, 24]. This calculation

assumes that the time between successive pulses is sufficiently long such that there

are no electrons left over from a previous pulse. The critical plasma density is defined

as

24

nc = ε0meω2

q2e

≈ 1013/λ2[cm−3] (2.28)

where ω is the angular frequency of the electromagnetic field and λ is defined as the

free space wavelength of the EM field in cm [26]. It follows that the pulse duration,

τ , for breakdown to occur can then be determined approximately from the equation

nc = n0eντ (2.29)

Considerable research has been conducted in recent years on the relationship be-

tween the power level and pulse width combinations leading to rf-volume breakdown.

A comparison of these recent studies on microwave volume breakdown is shown nor-

malized against pressure in the form of breakdown plots of Ee/p vs. pτ in Fig. 2.11

from Sullivan at the University of Maryland and Fig. 2.12 from Yee at Lawrence

Livermore National Laboratory.

Figure 2.11: Comparison of different experimental results for the breakdown thresholdof short high power microwave pulses [25]

25

Figure 2.12: Comparison between theoretical and experimental results for air break-down by short intense microwave pulses [27]

26

CHAPTER 3

EXPERIMENTAL SETUP

In order to develop a theory of HPM surface flashover, it is necessary to analyze

any environmental factors which may contribute to HPM surface flashover initiation

and development. It is of primary interest of this study to investigate all parameters

affecting HPM surface flashover associated with atmospheric changes corresponding

to altitudes from sea level to 50,000 feet. Included in these atmospheric parameters

are considerations for pressure (760 torr to 90 torr), humidity, gas composition, and

the presence of solar UV radiation. The experimental setup described in the following

sections provides a means to control each of these variables, and through an array

of diagnostic equipment, determine to what extent each may contribute to the HPM

surface flashover phenomena. Fig. 3.1 shows an overview of the experimental setup

used for HPM surface flashover studies.

Figure 3.1: HPM Surface Flashover Experimental Setup Overview

27

3.1 Experimental Test Chamber

The HPM surface flashover experiments were conducted utilizing a setup consist-

ing of both WR284 and WR650 waveguide standards. A representation of the setup

is shown in Fig. 3.2. Polycarbonate samples used in testing were placed at one end

of a WR284 S-Band waveguide section. The “upstream” end of the waveguide is

connected to the HPM source, a US Air Force AW/PFS-6 radar set modified for sin-

gle pulse operation. A Varian VMS1143B coaxial magnetron, capable of producing

2.85GHz, 2.5-3.5µs pulses in excess of 5 MW, is the main component of the radar set.

Figure 3.2: Isometric view of HPM Surface Flashover Experimental Setup

The experiment utilizes propagation of the dominant TE10 mode of the S-band

(WR284) waveguide. The electric and magnetic field configurations of this mode are

shown in Fig. 3.3 from Inan [28] with x and y as the major and minor axes of the

waveguide, and z as the axis of propagation.

Placed around the polycarbonate sample is a specially designed section of WR650

waveguide allowing for propagation traveling waves while creating a sealed environ-

ment for atmospheric testing. The design properties of this section are not optimized

for ideal transmission parameters, but rather provide a simple geometry to study the

development and effects of HPM surface flashover. The walls of the WR650 testing

chamber are lined with ECCOSORB FDS broad frequency high-loss silicone rubber

sheets (30 mil thickness). These non-conductive silicone sheets prevent breakdown

28

Figure 3.3: The electric and magnetic field configurations for a TE10 mode in arectangular waveguide [28]

in both the WR650 and tapered WR650-WR284 transition sections. In addition,

the high magnetic and dielectric loss properties of the ECCOSORB FDS material

offer a means to simulate an “open-air” radiating structure while maintaining the

ability to direct transmitted power for measurement. Scattering parameters of the

ECCOSORB equipped atmospheric test chamber were calculated via Ansoft HFSS

simulations and experimentally measured for low power levels (< 5 dBm) using a

Hewlett-Packard HP 8719C network analyzer (50 MHz - 13.5 GHz). The results of

these calculations and measurements are shown in Fig. 3.4.

As depicted in Fig. 3.4, the calculated and measured transmission loss (S21) of

the section are around 5dB. However, due to the saturation characteristics of the

ferrite materials in the ECCOSORB, the measured transmission loss of the section

for high power levels was somewhat lower. The transmission loss of the atmospheric

test chamber for high power levels is shown in Fig. 3.5 as a function of incident

power. The dotted line at the bottom of Fig. 3.5 represents the losses of the section

due to the geometry without the ECCOSORB material. The vertical gap between

the predicted S21 values from HFSS and low power measurements and the bold line

representing the measured S21 is an indicator of the saturation of the ECCOSORB

29

Figure 3.4: Scattering parameters of atmospheric test section from HFSS simulationsand low-power measurements

material.

Other design features of the testing chamber include four optical viewing ports

consisting of two H-plane ports with side viewing access, and two ports with 45o view-

ing access (see Fig. 3.1). The 45o viewing ports are primarily utilized for either CW

or pulsed UV illumination of the polycarbonate sample, or for photomultiplier tube

diagnostics. Two additional viewing ports are affixed to the test chamber allowing

for full view of both the front and the back of the polycarbonate sample.

30

Figure 3.5: Attenuation of Atmospheric Test Section (S21) vs. Incident Power

3.1.1 Environmental Control

In order to accurately test HPM surface flashover in conditions approximating

that of the atmosphere from sea level to 50,000 ft., variables such as pressure, hu-

midity and gas composition must be controllable. For this reason, the atmospheric

testing section shown in the center of Fig. 3.2 can be evacuated to these pressures.

Atmospheric pressure is monitored utilizing MKS Baratron transducers with a 1-

1000 torr operating range. Fresh gas enters the atmospheric test section and flows

across the sample to evacuate the system of byproducts and contaminants caused

by previous breakdown events eliminating any effects they may have and providing

for a “pure” gas mixture in the section. This controllable atmospheric zone of the

experimental setup is shown in blue in Fig. 3.6. All waveguide sections between the

polycarbonate sample and the magnetron are either kept at high vacuum or filled with

sulfur-hexafluoride. Keeping this area of the experiment in such conditions reduces

the probability of breakdown events occurring away from the area of study. The areas

filled with SF6 or evacuated to high vacuum are shown as green in Fig. 3.6.

31

Figure 3.6: Atmospheric Divisions of HPM Surface Flashover Experimental Setup

The atmospheric test chamber can also be affixed with a humidification system

to control the moisture content of any gases introduced to the chamber. In the

absence of humidity requirements, the humidification system components may be

used for mixing relative compositions of gases, a process completed by disabling the

ultrasonic humidifier in the system. The environmental control and humidification

system is shown in Fig. 3.7.

32

Figure 3.7: Environmental Control System

3.1.2 Exit Flange Geometry

In an effort to focus primarily on the impact of the dielectric window in the

initiation and growth stages of HPM surface flashover, it is necessary to isolate the

flashover location from other potential catalysts to these processes. For these reasons,

the dominant design goal for the test sample area of the experimental setup was to

remove all metallic conductors from areas around the flashover location. The removal

of these objects constitutes the removal of any metallic electron-injecting sources

which if present, would most likely dominate flashover development when compared

to processes attributed to the presence of the dielectric surface. Fig. 3.8 shows the exit

flange geometry utilized to satisfy this design requirement. Eight nylon bolts are used

to secure the polycarbonate test sample to the open-ended waveguide. The absence

of bolts near the high field regions of the TE10 mode are deliberate, as to minimize

any effect the presence of the bolt may have on flashover development. Noticeably

33

also is the absence of nylon bolts near the sample’s vertical axis of symmetry. The

omission of bolts in this location allows for an unobstructed side view of flashover

events on the surface of the dielectric.

Figure 3.8: Close up view of the exit flange geometry utilized to eliminate metallicconductors from the flashover location

As shown in Fig. 3.8, the polycarbonate sample is attached to the WR284 waveg-

uide flange with an intermediary gasket. The purpose of the intermediary gasket is

to reduce the field enhancement at the polycarbonate/metal/SF6 triple point inside

the waveguide, specifically in the center of the waveguide as this corresponds to the

location of the highest E-fields in the TE10 mode. Without this design modification,

flashover events tend to initiate from this location. Proper reduction in the field

enhancement caused by this triple point results in flashover initiating only on the

atmospheric side of the sample. A variety of gaskets were designed to satisfy this

requirement, two of which are shown in Figs. 3.9 and 3.10.

34

Figure 3.9: Intermediary Gasket Design A

Figure 3.10: Intermediary Gasket Design B

35

Simulations of the two gaskets performed in Ansoft HFSS determined that the

high field area of gasket B was approximately 50% lower than the high field area of

gasket A. To ensure accuracy, the simulations included the geometry of the entire test

section, with all appropriate material properties. Field profiles of the two intermediary

gaskets are shown in Fig. 3.11. The gaskets had minor effects on the system reflection

S-parameter (S11), with values of 0.49 and 0.50 for gaskets A and B respectively.

Incident power for the simulations was 3.25MW yielding an E-field magnitude at the

outside surface of the sample of 14.1 kV/cm with 10 kV/cm normal and 10 kV/cm

tangential field components.

Figure 3.11: Field profiles of intermediary gaskets A and B along the A-A cut line ofFigs. 3.9 and 3.10 respectively, from Ansoft HFSS simulations

The simulations in Ansoft HFSS also provided valuable insight into the peak elec-

tric field components related to location on the window surface. Figs. 3.12 and 3.13

show the maximum electric field components on the polycarbonate window surface as

functions of location. The ETangental component is comprised of the electric field along

the surface in the vertical direction due to the fact that there is no horizontal com-

ponent of the electric field present in the TE10 mode. HFSS simulations confirm the

lack of appreciable magnitude in the horizontal direction, therefore this magnitude is

not shown in Figs. 3.12 and 3.13.

Testing of the intermediary gaskets with comprehensive luminosity diagnostics on

either side of the polycarbonate sample verified that flashover events on the atmo-

36

Figure 3.12: E-field components along the polycarbonate window surface as a functionof vertical location along the A-A cut line of intermediary gasket B (c.f. Fig. 3.10)from Ansoft HFSS simulations, 3.25MW incident power

spheric side prior to any flashover events originating from the polycarbonate/metal/SF6

triple point on the inside of the sample, if any such event should occur. Therefore, the

design modifications to the intermediary gaskets accomplished the goal of reducing

breakdown initiation from the triple point on the SF6 side of the window.

3.2 Diagnostics

Since the temporal development of a HPM surface flashover event is typically on

the order of nanoseconds, all diagnostic equipment used to record this phenomena

must have a temporal resolution of no more than a few nanoseconds. In an attempt

to obtain as complete an analysis as possible of the development of an HPM sur-

37

Figure 3.13: E-field components along the polycarbonate window surface as a functionof horizontal location along the B-B cut line of intermediary gasket B (c.f. Fig. 3.10)from Ansoft HFSS simulations, 3.25MW incident power

face flashover all relevant data to a flashover event is collected; these include the

power levels (incident, reflected, transmitted) associated with the dielectric window,

luminosity, spectroscopic data and temporally resolved imaging of the developing

discharge.

3.2.1 Power Measurement

Power levels in the experimental setup are measured via HP 8474B planar-doped

barrier diode detectors. Advantages of this diode model include an extremely flat

frequency response and very good frequency response stability versus operating tem-

perature. The diodes have a temporal response of 2ns and a maximum operating input

38

power of 100mW (20dBm). Diodes are placed on the directional couplers shown in

Fig. 3.14 to measure the incident, reflected and transmitted power with respect to

the dielectric window.

Figure 3.14: Location of diode detectors for power measurement

S-parameters for both directional couplers were measured utilizing the previously

mentioned Hewlett-Packard HP 8719C network analyzer (50 MHz - 13.5 GHz). If

port designations of the couplers are defined as in Fig. 3.15, then the scattering ma-

trices of the couplers are

Coupler1 =

X 0dB X X

0dB X X X

−38dB −56.4dB X X

−58.9dB −38.2 X X

Coupler2 =

X 0dB X X

0dB X X X

−38dB −56.4dB X X

−58.9dB −38.2 X X

with X representing values for which no measurement was taken (needed). All mea-

surement ports required additional attenuation in order to prevent exceeding the

20dBm maximum input power of the diode detectors. In most cases, this additional

attenuation was between 40 to 50dB.

39

Figure 3.15: Port designations for directional coupler

3.2.2 Luminosity Diagnostics

Since surface flashover events inherently involve some light production, luminosity

diagnostics were included in the experimental setup to identify the spatial and tempo-

ral origin of any such events. Two Hamamatsu H6780-04 Photosensor modules were

used for these luminosity diagnostics. Data sheets for these photomultipliers list a

time response of 0.78ns with a spectral response over the 185nm to 850nm range. The

two PMT’s are enclosed in a small Faraday cage to reduce interference from outside

sources. Fiber optic cables are used to direct light to the PMT’s from the rear and

45o viewports shown in Fig. 3.2. Temporal delay tests on the PMT’s yielded total

system response times of 32ns and 25ns for the front and rear PMT’s respectively.

With this configuration, it is possible to determine which side of the polycarbonate

sample experiences surface flashover first. Due to variances in surface flashover delay

times, these diagnostics play a pivotal role in developing temporally resolved image

sequences of surface flashover development.

3.2.3 ICCD Cameras

An Andor Istar DH734-25U-03 intensified CCD camera equipped with a UV-

Nikkor f/2.8 105mm Micro lens is used to acquire images of HPM surface flashover

40

events. This Andor camera model is equipped with a Marconi CCD47-10 ICCD unit

(φ25mm) with a 1024x1024 resolution [19.5µm2 effective pixel size]. The camera setup

is small enough to allow for relocation at any one of the viewports shown in Fig. 3.2

with ease. Relocation to these ports allows for imaging of surface flashover from the

front, 45o, or from the back of the polycarbonate sample. The adjustable gain onboard

the camera, in addition to a logarithmic display mode allow for the captured images

of the luminous events to span several orders of magnitude in intensity. Although

the camera and corresponding controlling computer system support an internal delay

generator and gating device, the majority of the operational time was spent in the

“direct gate” mode, where the gating of the micro-channel plate is controlled via an

external trigger source. When operating in the “direct gate” mode, it is important to

consider the 12ns delay between the rising edge of an applied external trigger signal

and the beginning of the exposure. Other considerations include the 20ns minimum

external gate required to successfully trigger the camera. It is possible to monitor

the actual exposure gate via a “monitor” connection on the camera. When affixed

to a spectrograph, the Andor IStar camera is also utilized as the recording media for

temporally resolved optical emission spectroscopy.

3.2.4 Spectrograph

A spectrographic setup is included in the HPM surface flashover setup to provide

insight into the characteristics of the developing discharge plasma. Proper analysis

of this optical emission spectrographic data can provide information on the plasma

temperature and density. Fig. 3.16 shows the spectrographic equipment setup.

The spectrograph used is an Oriel Instruments MS 257 14

meter imaging spectro-

graph. The MS 257 utilizes specially shaped mirrors that correct for the astigmatism

associated with spherically shaped mirrors normally found on spectrographs. The

result of this modification allows the MS 257 to be categorized as a “multi-track”

spectrograph, allowing for data collection from multiple sources. When coupled with

the two-dimensional ICCD device found on the Andor Istar camera, the multi-track

41

Figure 3.16: Spectrographic setup for HPM surface flashover experiments

feature allows for data collection with both spatial and spectral resolution. An exam-

ple of this multi-track operation is provided with the spectrograph product literature

and is shown in Fig. 3.17.

While the light path from only one source is shown in the Fig., it is understood that

light entering the spectrograph at different points on the vertical axis will be recorded

on separate rows on the CCD (i.e. A, B, or C). This multitrack operation allows for

spatial resolution (∼= 0.2mm/pixel) along the discharge axis of the polycarbonate

sample. Armed with this resolution, it is possible to resolve the emission spectra at

the origin of the discharge (TE10 mode high field region) separate from the spectra

in the middle of the discharge plasma. The area of the polycarbonate sample from

which spatially resolved optical emission spectra can be collected is exaggerated by

the area shown in Fig. 3.18.

42

Figure 3.17: Multitrack Operation of Spectrograph from Oriel

The MS 257 also features a four grating turret with automatic grating switching.

This feature allows for spectral resolution over a variety of wavelength ranges and

is convenient due to the fact that proper spectral analysis often requires resolutions

ranging from several hundreds of nanometers for molecular transition identification,

to several tens of nanometers for vibrational and rotational temperature analysis.

Table 3.1 shows characteristics of the four gratings equipped on the MS 257.

Table 3.1: MS 257 Grating Properties

Grating # Blaze Wavelength Lines/mm λ Range

Grating 1 350nm 1200 62nm

Grating 2 400nm 600 110nm

Grating 3 300nm 150 510nm

Grating 4 413nm 121.6 N/A

43

Figure 3.18: Exaggerated collection area of optical emission spectra (actual collectionarea much narrower)

3.3 Data Manipulation

All data collected by the oscilloscopes, camera and spectrograph must undergo

some manipulation to “balance out” the physical parameters of the system setup. One

of the primary tasks in the data manipulation process involves time shifting signals to

account for differing transit times between sensors and the oscilloscope. Typical times

associated with these shifts are on the order of a few nanoseconds, but some cases

such as the delay between the luminosity diagnostics and the camera gate monitor

can run as high as 50ns. Once time shifted, signals from the diode detectors must be

transformed to power levels. This process is completed by applying the calibration

curve shown in Fig. 3.19, along with all the associated coupling and attenuation losses,

to the recorded voltage signal. All of these operations are performed in a program

written in MathCad. Luminosity signals are typically given in terms of arbitrary units

and thus have no scaling function applied to them. When processing images taken

of surface flashover development, all files are tagged with a scalar value to allow for

luminosity comparisons. Processing of spectrographic data is slightly more complex,

often involving integration of several rows of the ICCD array per spatial origin via a

program written in Andor MCD code.

44

Figure 3.19: Calibration curve for HP 8474B diodes

45

CHAPTER 4

EXPERIMENTAL RESULTS AND DISCUSSION

4.1 Breakdown Waveforms

4.1.1 Breakdown at High Pressure

The waveforms from a typical flashover event in an air environment at 285 torr

are shown in Fig. 4.1 (5 MW, 3.5 µs HPM pulse). The surface flashover event is

marked by a rise in luminosity about 1.6µs after the beginning of the HPM pulse.

This is indicated in both the small scale and large scale luminosity signals shown in

the bottom of Fig. 4.1. This luminosity “spike” is followed by a significant drop in

the incident, transmitted and reflected power waveforms. The reflected power signal

drops upon initiation of the flashover before rising several 100ns later. This drop

in reflected power with a corresponding drop in transmitted power suggests power

consumption by the developing discharge plasma. This absorbed power is shown by

the black waveform in the bottom of Fig. 4.1 and is calculated by subtracting the

transmitted and reflected power signals from the incident power. The peak power

consumption, which occurs slightly before the rise in reflected power, is shown to be

in excess of 80% of the incident power. The rise in reflected power indicates a plasma

density sufficient to reflect the incident microwave energy.

46

Figure 4.1: Typical waveforms for HPM surface flashover at high pressure (285torr). Top Graph: Black-Incident power, Medium Grey-Reflected power, LightGrey-Transmitted power, Bottom Graph: Black-Absorbed Power, Medium Gray-Luminosity, Light Gray-Luminosity * 100

4.1.2 Breakdown at Low Pressure

Fig. 4.2 shows the typical waveforms from an HPM surface flashover event at

lower pressures. In contrast to Fig. 4.1, the HPM pulse in Fig. 4.2 is somewhat

less powerful (3MW) and shorter (2.5 µs) in duration. Important to note in the

figure is the location of the flashover event in the HPM pulse. For pressures lower

than 90 torr, or for power levels increasing above 3MW, the flashover event occurs

more and more on the rising edge of the HPM pulse. Flashover events occurring

on the rising edge of the HPM pulse are undesirable due to the rapidly changing

power levels, and consequently make quantitative calculations on the corresponding

breakdown field thresholds more difficult. For these reasons, the experimental validity

of flashover events occurring in the first 400ns (approximate rise time) of the HPM

47

Figure 4.2: Typical waveforms from HPM surface flashover at low pressure (90torr). Top Graph: Black-Incident power, Medium Grey-Reflected power, LightGrey-Transmitted power, Bottom Graph: Black-Absorbed Power, Medium Gray-Luminosity, Light Gray-Luminosity * 100

pulse is questionable, and any analysis of such events will either be discarded or

included only as speculation.

4.2 Delay Times

4.2.1 Effect of Power Levels

Surface flashover experiments were performed with HPM pulses of 4.5 MW and 3

MW over a range of pressures. The flashover delay times, cf. Fig. 4.3, are determined

by the time between the application of the HPM pulse and the subsequent flashover

event, defined by a luminosity spike at the sample and the sudden drop in reflected

and transmitted power shown in Fig. 4.1.

48

Figure 4.3: Effect of Incident Power on delay time, Squares-3.0 MW, Circles-4.5MW

As expected, at a given pressure, the 3 MW tests resulted in substantially longer

delay times than that of the 4.5 MW tests at the same pressure. The pressure range

that can be tested is ultimately limited by the length of the HPM pulse, which

decreases with pulse amplitude. For this reason, the lower power tests cannot yield

as wide of a pressure range as the higher power tests.

4.2.2 Effect of UV Illumination

Surface flashover delay times were also measured utilizing illumination from a UV

light source, with motivation for these tests stemming from the increasing presence

of solar UV radiation at higher altitudes. The total flashover delay time is com-

prised of both the statistical delay time, the time for an electron to appear above the

polycarbonate surface, and the formative delay time, the time for that electron to

develop an avalanche and subsequent flashover event. The presence of UV radiation

49

Figure 4.4: Effect of UV Illumination of sample, Triangles-No UV illumination,Circles-UV illumination

incident to a polycarbonate sample has been shown to induce photoelectric emission

from the sample, effectively reducing the statistical delay time [29]. DC tests have

also shown that a dielectric illuminated with UV will exhibit a lower flashover voltage

than without UV illumination. Consequently, tests performed with UV illumination

should have a lower total delay time for any given pressure. Tests were performed

with an illumination intensity on the sample of about 6-8 mW/cm2 over the 250-400

nm range. This intensity is roughly equivalent to that of normal incident solar radi-

ation on a sunny day and varies about 50% over a 0-12 km altitude range [30]. The

total delay times for HPM surface flashover experiments performed with and without

UV illumination are also shown in Fig. 4.4. As expected, the total delay times as well

as the standard deviation are significantly lower for those tests involving a surface

with UV illumination, than for those without UV illumination at the same pressure.

50

Figure 4.5: Effect of Gas Humidity on delay time, Squares-Low Humidity (< 15%RH), Triangles-High Humidity (> 85% RH)

4.2.3 Effect of Gas Humidity

In order to determine the effect of gas humidity on HPM surface flashover, the

atmospheric test chamber was filled with high (> 85%R.H.) and low (< 15%R.H.)

humidity air. The flashover delay times at these two humidity levels are shown in

Fig. 4.5.

The effect of humidity on surface flashover events has been studied for DC and

pulsed conditions. For those conditions, it is believed that the relative humidity of

the gas creates a thin layer of water on the surface with a thickness related to the

relative humidity level, which can more easily be ionized. With this thin layer of

water present at the surface, electrons field emitted from the surface can more easily

produce secondary electrons through ionization. The net effect of this process has

been shown to lower flashover field amplitude for DC and unipolar flashover cases

[31, 32, 33]. Since higher humidity levels appear to lower the overall flashover delay

51

time as shown in Fig. 4.5, it is believed that this process is also present in window

flashover resulting from HPM excitation.

4.2.4 Comparison with data from Volume Breakdown

In an attempt to a compare volume breakdown data involving different power lev-

els and pressures, Gould and Roberts [4] showed that a relatively simple theory can

be developed and applied to estimate the relationship of several parameters includ-

ing delay time, microwave frequency, pulse amplitude and pressure. This theoretical

relationship can then be used to develop a single-pulse breakdown curve for the nor-

malized effective field (E/p) as a function of pressure times pulse width (pτ). This

model is based on an analytical solution of the electron continuity equation and a

numerical evaluation of the net ionization frequency over a wide range of effective

fields. Applying similar normalization procedures to data collected from HPM sur-

face flashover events, it can be shown that the E/p vs. pτ values of these events

also lie about a single curve. This empirical curve derived from the HPM surface

flashover tests is shown in Fig. 4.6 along with the unified curve developed for volume

breakdown in air described by Gould and Roberts.

Examination of this plot reveals that the surface flashover tests occur at a higher

E/p than the curve developed for volume breakdown in air. Possible explanations

for this observation include the fact that the surface flashover tests were conducted

without the influence of an electron injecting structure such as a metallic electrode.

Also, the experiments performed by Gould and Roberts were conducted in homoge-

neous electric fields with geometry dependence in only one direction, whereas this

experimental setup produces strongly inhomogeneous fields with a geometry depen-

dence in three dimensions. The consideration of geometry differences between the

two setups affects the extent any loss mechanisms may have on breakdown develop-

ment. Gould and Roberts showed that over the 90 torr to 760 torr range, attachment

was the dominant loss mechanism in volume breakdown. For surface flashover, the

additional effects of diffusion must be included due to the proximity of the window

52

Figure 4.6: Effective electric field/pressure (E/p) vs. pressure times pulse width(pτ), Dotted Line-Gould and Roberts for volume breakdown, Triangle-3MW surfaceflashover, Circle-4.5MW surface flashover, Square-3MW with UV illumination

surface. Since the average electron energy is low due to the high collision frequency

at atmospheric pressures, the window surface likely acts as a “sink”, capturing slow

electrons. The combination of all of these factors is believed to be responsible for the

vertical shift of the curve.

4.2.5 Holdoff Time Estimation

With the extrapolation of a unified curve (c.f. Fig. 4.6) on which the E/p vs.

pτ values of HPM surface flashover occur, it is possible to estimate the relationship

between the transmitted power of a microwave system utilizing polycarbonate win-

dows and the pulse duration which will result in a surface flashover event. This is

accomplished by taking the equation of the extrapolated line and inserting different

values of p. The corresponding breakdown estimation curves are shown in Fig. 4.7

53

Figure 4.7: Estimated pulse duration vs. transmitted power resulting in surfaceflashover event for a polycarbonate window

for various operational altitudes. For example, the figure estimates that at 16,000ft.

above sea level, an 8MW pulse for 1µs will not result in a flashover event. The area

shaded below 400ns indicates an area of speculation. This is due to the fact that the

microwave source described earlier in the experimental setup is not capable of pro-

ducing HPM pulses with a rise time less than 400ns, thus preventing data collection

in this region.

4.2.6 Comparison with High Field Enhancement Studies

As previously mentioned, this experimental setup has the advantage studying the

factors influencing surface flashover separate from the influence of metallic electrodes.

It is of importance to compare the data collected from this experimental setup to

data collected on setups involving high field enhancement. Fig. 4.8 shows the “slab

in waveguide” setup which was utilized for previous studies of HPM surface flashover.

54

Figure 4.8: HPM surface flashover experimental setup involving high field enhance-ment

The setup consists of a dielectric sample placed in the high field region (TE10 mode)

of an S-band waveguide. Two triangular metal electrodes serve as field enhancement

devices. Breakdown events initiate from this high field enhancement area allowing

for straightforward, repeatable observations.

Fig 4.9 shows the macroscopic peak electric field at breakdown for various dielec-

tric materials and volume breakdown for various pressures for the experimental setup

shown in Fig. 4.8. As shown in the figure, the breakdown field strengths increase

with pressure similar to the right hand side of a Paschen curve. Lexan samples tested

in this geometry displayed holdoff times at 90 torr and 200 torr of 130ns and 175ns,

respectively. Included in the figure are two curves representing the breakdown field

strengths for the pulse widths of 130ns and 175ns derived from the extrapolated E/p

vs. pτ curve from HPM surface flashover events without the influence of electrodes

or field enhancement points. Examination of these curves versus the collected data

from the high field enhancement setup shows that the high field enhancement data

experienced surface flashover events at electric fields of about 1/2 the magnitude of

those predicted by the electrode-less setup data.

With these factors in mind, it is evident that direct comparison of experimental

results between these two different setups is difficult for several reasons. While the

55

Figure 4.9: Peak electric field strength at breakdown for various dielectric materialsand volume vs. pressure in a high field enhancement geometry, curves representbreakdown field strengths extrapolated from the electrode-less geometry experiments

macroscopic field enhancement provided by the triangular electrodes is around 30-

35%, the localized field near the tips is much larger, see Fig. 4.10.

When considering the effects of these tips, two cases must be considered. In the

first case the tip field enhancement point is the triple point of the geometry. The

enhanced field, although strongly inhomogeneous, combines with the presence of a

metallic electrode to flood the surface with field emitted electrons. In the second case,

it is assumed that some area of the field enhancement point other than the tip makes

direct contact with the dielectric surface. In this case, even though the tip is not in

direct contact with the dielectric surface, the extremely high field near the tip may

accelerate electrons toward the surface leading to other processes such as secondary

electron emission or photoemission from the surface which may serve as a catalyst

process for the entire surface flashover event. Clearly, both cases present factors in

the flashover process which are decisively different than the factors associated with

56

Figure 4.10: Peak electric field vs. vertical coordinate for high field enhancement(with electrodes) and electrode-less (without electrodes) geometries, 3.25MW incidentpower

HPM surface flashover in an electrode-less setup. Therefore, a prediction of electric

field strength at breakdown determined from this experimental setup cannot not take

into account all of the processes and factors associated with a high field enhancement

setup, and any generalized comparison between the two setups must be taken at face

value as an area of speculation.

4.3 Optical Emission Spectroscopy

Optical emission spectroscopic data was collected from the discharge plasma. Fig.

4.11 shows an experimental spectrum collected using a grating with 150 lines/mm

with a blaze angle of 300nm. The vertical dashed lines in Fig. 4.11 are the spectral

lines Zn I&II, Mg II, and Cu I observed in DC flashover tests due to the presence

of brass electrodes [32]. The absence of these spectral lines in spectra taken with

both transparent and opaque polycarbonate windows is evidence that the discharge

57

Figure 4.11: Optical emission spectrum collected from HPM surface flashover (250nm-500nm); dotted vertical lines represent spectral components expected if brass elec-trode material was present [32, 34]

developed apart from any brass components and on the air-side of the polycarbonate

window. Identification of the spectral peaks in Fig. 4.11 suggested that the dominant

transition in the discharge plasma was the N2 C3Πu → B3Πg transition, also known

as the N2 second positive system. In order to determine the vibrational and rotational

temperatures of the plasma, a detailed simulation was developed to synthesize the

N2 C3Πu → B3Πg transition for a wide range of plasma characteristics.

4.3.1 Synthesis Program

Proper simulation of the N2 second positive system required a number of pa-

rameters for the N2 C3Πu → B3Πg transition. General parameters for the system,

including rotational, vibrational, centrifugal distortion and anharmonicity constants

were found in literature sources by Herzberg [35] and Gardet [36]. These values used

in the simulation are summarized below in Table 4.1.

58

Table 4.1: Values of constants used in spectra synthesis program

Constant Symbol Value

C3Πu State

Level

Upper-level electronic energy Te 89147.3 cm−1

Vibration

Upper-level oscillation frequency ωe 2035.1 cm−1

First anharmonicity constant ωeχe 17.08 cm−1

Second anharmonicity constant ωeγe -2.15 cm−1

Rotation

Upper Level Rotation Constant B′e 1.8259 cm−1

Second coefficient for rotational constant α′e 0.0197 cm−1

Upper-level centrifugal distortion constant D′e 5.879× 10−6 cm−1

B3Πg State

Level

Lower-level electronic energy Te 59626.3 cm−1

Vibration

Lower-level oscillation frequency ωe 1734.11 cm−1

First anharmonicity constant ωeχe 14.47 cm−1

Second anharmonicity constant ωeγe 0 cm−1

Rotation

Lower Level Rotation Constant B′′e 1.6380 cm−1

Second coefficient for rotational constant α′′e 0.0184 cm−1

Upper-level centrifugal distortion constant D′′e 5.846× 10−6 cm−1

59

The Born-Oppenheimer formulas for approximation of total energy were found in

Nassar [37], and are given by

E = En + Eν + EJ = hc(Tn + G + F ) (4.1)

with

G(ν) = (ν +1

2)ωe − (ν +

1

2)2ωeχe + (ν +

1

2)3ωeγe + · · · (4.2)

F (J) = BνJ(J + 1)−DνJ2(J + 1)2 + · · · (4.3)

with h and c being physical constants; ωe, ωeχe, ωeγe, Bν and Dν are constants for a

given electronic state; En, Eν , and EJ are the electronic, vibrational and rotational

energies, respectively; and Tn, G(ν) and F (J) are spectral terms given in units of

cm−1. Utilizing these values, the wave number σ (in cm−1), corresponding to a

transition from an upper state E ′ to a lower state E ′′ is given by [37]

σul = (T ′n + G′(ν ′) + F ′(J ′))− (T ′′

n + G′′(ν ′′) + F ′′(J ′′)) (4.4)

Given these equations, it is possible to calculate the Einstein coefficient for spon-

taneous transition given by the equation

Aul =64π4σ3

ul

3h

R2eqν′ν′′

(2− δ0,Λ′)(2S ′ + 1)

SJ ′J ′′

(2J ′ + 1)[s−1] (4.5)

where Re is the electronic transition moment, qν′ν′ is the Franck-Condon factor, σul

is the transition wave number given by Eqn. 4.4, δ0,Λ′ accounts for electron spin

degeneracy, S ′ = 1 because C3Πu denotes a triplet, and SJ ′J ′′ represents the branching

variable. Tables for Re and qν′ν′ values were found in literature from Gilmore [38]

and Laux [39]. Using these values, the emission coefficient εul of a given transition

from an upper level, E ′(n′, ν ′, J ′), to a lower level, E ′′(n′′, ν ′′, J ′′), is given by

εul =1

4πNuhcσulAul [W m−3 St−1] (4.6)

60

where Nu is a the number of molecules in the upper level as defined by the Boltzmann

distribution. Spectral synthesis is accomplished by adjusting the temperatures of

the electronic, vibrational, and rotational Boltzmann distributions. To validate the

synthesis program, a synthesized spectrum is shown in Fig. 4.12 vs. literature spectra

shown in Fig. 4.13.

61

Figure 4.12: N2 C3Πu → B3Πg Spectrum from synthesis program, same conditions asin Fig. 4.13

Figure 4.13: N2 C3Πu → B3Πg Spectrum from Nassar [37]

62

4.3.2 Experimental Spectra

With the availability of a detailed spectra synthesis program, identification of the

band heads appearing in emission spectra from the developing HPM surface flashover

is possible. Additionally, modification of the plasma variables in the synthesis pro-

gram provide for a means to identify the vibrational and rotational temperatures of

the surface flashover discharge plasma. Fig. 4.14 shows a comparison between the

experimentally gathered spectrum and the synthesized spectrum.

Figure 4.14: Experimentally gathered optical emission spectrum in air (Top) vs.Synthesized Spectra (Bottom); convolution profile: combination of square, gaussianand lorentz profiles with δλ = 0.23nm

The experimental spectrum shown in Fig. 4.14 was collected with a 500ns gate

time using a grating with 1200 lines/mm and a 350nm blaze angle, with data collec-

tion over the 350nm to 412nm range. The band heads of the synthesized spectrum

shown in the bottom of Fig. 4.14 are identified above by their vibrational transitions.

A parametric analysis performed with a sweep of the temperature variables in the

63

Figure 4.15: Relative error between experimental and synthesized spectra vs. tem-perature variation from the optimal temperature value obtained from parametricanalysis

synthesis program yielded minimum error signals between the experimental and syn-

thesized spectra at the vibrational and rotational temperatures of 2675◦K and 325◦K

respectively. These results of this analysis, shown in Fig. 4.15., in conjunction with

the similarity of the spectra in Fig. 4.14 suggest that these values are reasonable

estimates of the vibrational and rotational temperatures of the discharge plasma.

4.4 Imaging of Flashover Formation

In an effort to investigate the origin of a flashover event and the subsequent

flashover path, high speed imaging was used to create an image sequence of this

event. Typically, a 20ns gate time was used to acquire these images. Figs. 4.17-

4.21 and Figs. 4.22-4.26 show the respective flashover sequences for 90 torr and 155

torr. A reference image is provided in Fig. 4.16. Included in each figure are the

64

Figure 4.16: Front reference image

incident, transmitted and reflected power signals in addition to the luminosity signal

and camera gate. Notable in both image sets are luminous areas near the high field

region of the WR284 waveguide corresponding to TE10 mode excitation. It is evident

from the pictures that without the presence of metallic electrodes, the flashover will

form from the area of highest electric field, cf. Fig. 3.11, and then spread across

the sample. As the discharge plasma spreads across the sample, this effectively forms

a short that reflects the power incident on the sample, as seen by the drop in the

transmitted power waveform. Note that in the following images, the optical gate for

the ICCD camera is shorter than the electrical pulse shown by approximately 8 to

12ns. Additionally, the temporal error of this gating pulse is ± a few nanoseconds.

65

Figure 4.17: Flashover formation in air at 90torr; 17ns camera gate, 33ns beforeluminosity rise; Frame 1 of 5; Intensity ×4

66

Figure 4.18: Flashover formation in air at 90torr; 17ns camera gate, 20ns beforeluminosity rise; Frame 2 of 5; Intensity ×1

67

Figure 4.19: Flashover formation in air at 90torr; 17ns camera gate, 14ns beforeluminosity rise; Frame 3 of 5; Intensity ×1

68

Figure 4.20: Flashover formation in air at 90torr; 17ns camera gate, 29ns after lumi-nosity rise; Frame 4 of 5; Intensity ×1

69

Figure 4.21: Flashover formation in air at 90torr; 17ns camera gate, 68ns after lumi-nosity rise; Frame 5 of 5; Intensity ×1

70

Figure 4.22: Flashover formation in air at 155torr; 17ns camera gate, 24ns beforeluminosity rise; Frame 1 of 5; Intensity ×4

71

Figure 4.23: Flashover formation in air at 155torr; 17ns camera gate, 16ns beforeluminosity rise; Frame 2 of 5; Intensity ×1

72

Figure 4.24: Flashover formation in air at 155torr; 17ns camera gate, 33ns afterluminosity rise; Frame 3 of 5; Intensity ×1

73

Figure 4.25: Flashover formation in air at 155torr; 17ns camera gate, 54ns afterluminosity rise; Frame 4 of 5; Intensity ×1

74

Figure 4.26: Flashover formation in air at 155torr; 17ns camera gate, 67ns afterluminosity rise; Frame 5 of 5; Intensity ×1

75

When comparing the flashover image sequence at 90 torr shown in Figs. 4.17-

4.21 with the image sequence at 155 torr in Figs. 4.22-4.26, it is clear that the

lower pressure flashover events exhibit a more diffuse path while the higher pressure

flashovers experience a more tightly constricted path. This behavior is consistent

with previous breakdown studies involving high field enhancement geometry and the

presence of metallic electrodes [5], and also with volume breakdown studies. Both

pressures exhibit a discharge path which forms and tracks near the polycarbonate

surface. An image of this developing discharge along the surface is shown in Fig.

4.27, obtained from side-on imaging of the polycarbonate window.

76

Figure 4.27: Pseudo color image of flashover formation along the polycarbonate win-dow at 90 torr in air; 17ns optical gate

4.4.1 Surface Flashover Liftoff

As shown in Fig. 4.27, in an air environment the flashover discharge path forms

near the surface of the window. However, in a purely nitrogen environment, parts of

the discharge path lift away from the surface of the window and follow the electric

field lines. The discharge path in nitrogen is shown vs. the discharge path in air in

the images in Fig. 4.28 along with a vector plot of the E-field lines at the window

location.

4.4.2 Pulsed UV Illumination of Surface

To explain the differences in the discharge path shown (c.f. Fig. 4.28) in an

purely nitrogen environment as opposed to an air environment, the effect of the oxy-

77

Figure 4.28: Left- E-field Lines; Right-Comparison of flashover path in air and N2

gen component of air must be considered. Photons emitted from an O2 molecule

decaying from an excited state lie primarily in the ultraviolet range less than 190nm

[40]. Since the work function of polycarbonate material has been shown to be around

4.26eV [41], photoelectric effects should occur on a polycarbonate surface for photons

of wavelength less than about 290nm. Therefore, UV illumination of the polycarbon-

ate window should produce photoelectrons near the surface influencing the subsequent

discharge to form near the surface where there is a large population of free electrons.

Furthermore, due to the electronegative nature of O2, electrons away from the win-

dow surface are more likely to be “scavenged” by the gas, effectively increasing the

mass of the charge carrier and decreasing further contributions to the breakdown

development. Although the “scavenging” effect cannot be simulated without the ac-

tual presence of an electronegative gas, UV illumination can be added to a purely N2

environment to simulate the photoelectric effects of O2. UV illumination is provided

78

Figure 4.29: Temporal spectrum of Oriel Model 60963 5-Joule Flashlamp Illuminator

via an Oriel Model 60963 5-Joule flashlamp. Temporally resolved emission spectra

of this flashlamp is shown in Fig. 4.29 at 4µs, 10µs, and25µs, into the illumination

pulse.

As shown in Fig. 4.29, the main UV components of the flash illumination occur

in the first few microseconds of the pulse. To determine the effects of ultra-violet

radiation incident on the window surface, a UV illumination pulse is applied to the

polycarbonate surface at some time, tp, prior to the application of the HPM pulse.

This process is depicted graphically in Fig. 4.30. If the HPM pulse is applied at

time t = 0, then as tp approaches zero, the effects of UV illumination should become

more evident. Fig. 4.31 shows developed surface flashover discharges for decreasing

values of tp. When the illumination pulse is applied 77µs prior to the HPM pulse,

liftoff occurs as in the nitrogen environment with no UV illumination shown in Fig.

4.28. As the illumination pulse is applied closer and closer to the HPM pulse, the

discharge develops in closer proximity to the window surface. Through analysis of

79

these images, it is believed that UV photoemission from the O2 molecules is the

primary contributor to arc development near the window surface, along with some

supplemental contribution from the electronegative nature of the gas.

Figure 4.30: Application of UV illumination pulse (at time tp) prior to HPM pulse(time t = 0)

While the effects of the O2 molecule are considered the primary contributor to the

behavior of the arc path in air, the effects of other species which may exist in an air

flashover event must be considered. Studies involving transverse cw dc arc discharges

in air showed that in addition to the N2 first positive system, spectral lines were

noticeable from NO γ system, the hydroxyl OH UV system, the O2 Shumann-Range

system, and the N2 first positive system [42]. Table 4.2 shows a summary of these

systems with wavelengths of the most intense bands.

80

Figure 4.31: Liftoff of surface flashover vs. application of UV pulse

Table 4.2: Other Prominent Systems in Air Discharges

Name System Transition λ (nm)

NO γ A2Π+ → X2Π (0,0) 226.9

(0,1) 236.3

(0,2) 247.1

hydroxyl OH UV A2Σ → X2Π (0,0) 306.4-308.9

O2 Shumann-Range B3Σ−u → X3Σ−

g (0,14) 337.0

N2 First Positive B3Π → A3Π (7,4) 654.5

(8,5) 646.9

(11,7) 580.4

81

In addition to these systems, the effects of any ozone (O3) produced in a discharge

event must be considered due to the molecules strong absorption in the UV region.

Production of ozone in electrical discharges is accomplished through the two step

process

e + O2

k1

GGGGGGA e + O + O

O + O2 + O2

k3

GGGGGGA O2 + O3

and simultaneously destroyed by the processes

O + O3

k4

GGGGGGA O2 + O2

O2 + O3

k5

GGGGGGA O + O2 + O2

with the rate constants [43] as

k1 = 2× 10−9 cm3 s−1

k3 = 6.9× 10−34 × (300/T )1.25 cm6 s−1

k4 = 1.8× 10−11 × e(−2300/T ) cm3 s−1

k5 = 7.3× 10−10 × e(−11400/T ) cm3 s−1

where T is the temperature in ◦K. However, production of ozone is a slow process

when compared to the length of the HPM pulse. Studies have shown that for single

discharge event in air 10% of the total ozone produced occurs in the first 15µs after

the discharge, whereas 90µs is required to produce 60% of the total ozone [44]. Fur-

thermore, at low pressures (100 torr) maximum ozone concentrations will not occur

until around 0.9ms after the discharge event [45]. Regardless of the formation charac-

teristics, the presence of ozone in the system may help to increase holdoff delay times

82

and likewise affect the arc path by preventing high energy UV photons from reaching

the polycarbonate surface.

The effects of all of these systems (see Table 4.2) are believed to be minor when

compared to that of the O2 molecule due to their lack of intensity in the collected

discharge spectrum and their formation time. However, in order to develop a complete

theory behind the discharge characteristics of HPM surface flashover, the contributing

effects of each of these systems should be further considered.

83

CHAPTER 5

CONCLUSIONS

The purpose of this experiment was to investigate the contributing factors to high

power microwave (HPM) surface flashover on dielectric windows. The test setup

constructed enables investigation of the many parameters associated with an atmo-

spheric transmission medium at operational altitudes from sea level to 50,000 feet.

Furthermore, the geometry used in this experimental setup allows for the study of

contributing mechanisms to the surface flashover process isolated from the effects of

metallic electrodes.

Flashover Delay Time

Examination of the data collected from the surface flashover studies shows a

relationship between pressure, pulse amplitude, microwave frequency, and surface

flashover delay time over a wide range of experimental parameters. The empirical

data collected show that a reduction in pressure or an increase in power levels will

result in a reduction in flashover delay time. In addition, the presence of solar UV

illumination reduces the overall flashover delay time for a given set of parameters by

providing seed photoelectrons and reducing the statistical delay time. Through the

extrapolation of an E/p vs. pτ curve on which all of the surface flashover events

tend to occur, and the subsequent evaluation of that curve at increasing pressures, it

is possible to estimate the power levels and pulse lengths which will lead to surface

flashover on a microwave system utilizing polycarbonate windows for various opera-

tional altitudes.

Discharge Plasma Characteristics

Optical emission spectroscopic data collected from the HPM surface flashover

events identifies the dominant molecular transition for an electrode-less microwave

surface flashover event along a polycarbonate window as that of the N2 C3Πu → B3Πg

84

transition, with exact vibrational and rotational temperatures estimated by synthe-

sized spectra. Differences in the emission spectra of discharge plasmas developing in

N2 and air environments are expected, but not apparent over the 300nm to 650nm

range. However, with the most intense band heads of the O2 system lying in the deep

ultraviolet range, coupled with the decreasing efficiency and sensitivity of the spectra

collection equipment in that range, comparative spectra showing differences in surface

flashover discharge plasmas developed in air and N2 is not currently available.

Discharge Paths in Air and Nitrogen

Utilizing a field shaping gasket between a dielectric window and the exit flange

of a waveguide, it is possible to create a significant normal component to the electric

field on the external surface (air-side) of the dielectric window. In air environments, a

developing surface flashover event will tend to form in close proximity to the window

surface, whereas formation in nitrogen environments tends to occur away from the

surface along the electric field lines. The possible explanation of this phenomenon lies

in both the photoemission properties of the O2 molecule producing a large number of

photoelectrons near the window surface, and the “scavenging” of electrons away from

the surface due to its electronegative nature. While other species present in the gas,

including ozone, can have an effect on both the flashover delay time and arc path,

the contributions of these systems are believed to be minor when compared with the

contributions of the O2 molecule.

Future Research

To further understand the many processes in action at the gas-dielectric interface

which lead to HPM surface flashover, additional studies are required to investigate

the effects of other atmospheric variables for which little experimental data is avail-

able. These variables include material variations and temperature considerations, as

well as high-speed turbulent gas flow across the interface.

85

REFERENCES

[1] A. D. MacDonald, Microwave Breakdown in Gases, John Wiley & Sons, NewYork, 1966.

[2] Nasser, Essam. Fundamentals of Gaseous Ionization and Plasma Electronics,Wiley-Interscience, New York, 1971.

[3] Raizer, Yuri P. Gas Discharge Physics, Springer-Verlag, New York, 1991.

[4] L. Gould and L. Roberts, “Breakdown of Air at Microwave Frequencies,” Journalof Applied Physics, Vol. 27, No. 10, October, 1956.

[5] A. Neuber, D. Hemmert, J. Dickens, H. Krompholz, L. Hatfield, and M. Kris-tiansen, “High Power Microwave Window Breakdown under Vacuum and Atmo-spheric Conditions,” Proceedins of the SPIE Conference, Aerosense 2000, 24-28April 2000, Orlando, Florida.

[6] A. Neuber, L. Laurent, Y. Lau, H. Krompholz, “Windows and RF Breakdown,”High-Power Microwave Sources and Technologies, IEEE Press, New York, 2001.

[7] S. Calico, “High Power Microwave Breakdown of Dielectric Interfaces,” Disser-tation for the Degree of Doctor of Philosophy in Electrical Engineering, TexasTech University, Lubbock, Texas, 1991.

[8] Fowler, R. H. and Nordheim, L. W., “The effeect of the image force on theemission and reflexion of electrons by metals,” Proc. Roy. London Soc., A-121,626, 1928.

[9] Raju, G., Dielectrics in Electric Fields, Marcel Dekker, New York, 2003.

[10] D. Alpert, D. A. Lee, E. M. Lyman, and H. E. Tomaschke, “Initiation of Elec-trical Breakdown in Ultrahigh Vacuum,” Jour. Vac. Sci. & Tech., Vol. 1, Iss. 2,pp.35-50, November 1964.

[11] Austin, L. and Starke, H. “Uber die Reflexion der Kathodenstrahlen und einedamit verbundene neue Erscheinung sekundarer Emission,” Ann. Phys. Lpz., 9,271, 1902.

[12] Dekker, A. J., Solid State Physics, Prentice-Hall, Englewood Cliffs, 1957.

[13] Rudberg, E., Proc. Roy. Soc. (London), A127, 111, 1930.

[14] Bruining, H. Physics and Applications of Secondary Electron Emission, McGraw-Hill, New York, 1954.

[15] Vaughan, J. R. M. “A New Formula for Secondary Emission Yield.” IEEE Trans.Electron Dev. 1989.

86

[16] Brown, Sanborn C., Introduction to Electrical Discharges in Gases, John Wiley& Sons Inc., New York, 1966.

[17] M. E. Gardner, “The Recombination of Ions in Pure Oxygen as a Function ofTemperature and Pressure,” Phys. Rev., Vol. 53, p.75-83, 1938.

[18] Papoular, R., Electrical Phenomena in Gases, American Elsevier Pub. Co. Inc.,New York, 1965.

[19] Raether, H. Electron Avalanches and Breakdown in Gases, Butterworths, Lon-don, 1964.

[20] Miller, H., “Surface Flashover of Insulators,” IEEE Transactions on ElectricalInsulation, Vol. 24, No. 5, pp. 765-786, October 1989.

[21] A. Neuber, M. Butcher, L. L. Hatfield, and H. Krompholz, “Electric currentin dc surface flashover in vacuum,” Journal of Applied Physics, Vol. 85, No. 6,pp.3084-3091, 15 March 1999.

[22] R. A. Kishek, Y. Y. Lau, L. K. Ang, A. Vafells, and R. M. Gilgenbach, “Multi-pactor discharge on metals and dielectrics: Historical review and recent theories,”Physics of Plasmas, Vol. 5, No. 5, pp. 2120-2126, May, 1998.

[23] M. A. Herlin and S. C. Brown, Phys. Rev., 74, p.291, 1948.

[24] A. D. MacDonald, D. U. Gaskell, and H. N. Gitterman, Phys. Rev., 130, p.1841,1963.

[25] C. A. Sullivan, W. W. Delstler, J. Rodgers, and Z. Segalov, “Short-pulsehigh power microwave propagation in the atmosphere,” J. Appl. Phys., 63,11,pp.5228-5232, June 1988.

[26] J. E. Drummond, Plasma Physics, McGraw-Hill Inc., New York, 1961.

[27] J. H. Yee, R. A. Alvarez, D. J. Mayhall, D. P. Byrne, and J. DeGroot, “Theoryof intense electromagnetic pulse propagation through the atmosphere,” Phys.Fluids, 29, 4, pp.1238-1244, April 1986.

[28] U. S. Inan and A. S. Inan, Electromagnetic Waves, Pretence Hall, Upper SaddleRiver, N. J., p.340, 2000.

[29] K. P. Morales, J. T. Krile, A. A. Neuber, and H. G. Krompholz, “Pulsed Dielec-tric Surface Flashover in Atmospheric Conditions,” submitted to IEEE Transac-tions on Dielectrics and Electrical Insulation, Sept. 2005.

[30] A. Y. Dvorkin, and E. H. Steinberger, “Modeling the Altitude Effect on SolarUV Radiation,” Solar Energy, Vol. 65, No. 3, pp. 181-187, 1999.

87

[31] J. Krile, A. Neuber, J. Dickens, H. Krompholz, “DC and Pulsed Dielectric Sur-face Flashover at Atmospheric Pressure,” IEEE Trans. Plasma Sci., vol. 33, no.4, pp. 1149-1154, Aug. 2005.

[32] J. T. Krile, A. A. Neuber, J. C. Dickens, H. G. Krompholz, “DC Flashover ofa Dielectric Surface in Atmospheric Conditions,” IEEE Trans. Plasma Sci., vol.32, no. 5, Oct. 2004.

[33] M. Fujihira and H. Inokuchi, “Photoemission from Polyethylene,” ChemicalPhysics Letters, vol. 17, no. 4, December 1972, pp. 554-556.

[34] A. R. Striganov and N. S. Sventitskii, Tables of Spectral Lines of Neutral andIonized Atoms, IFI/Plenum, New York, 1968.

[35] Herzberg, G. Spectra of Diatomic Molecules. 2nd Ed. D. Van Nostrand Co. 1965.

[36] G. Gardet, G. Moulard, M. Courbon, F. Rogemond, and M. Druetta, “Evalu-ation of the rotational temperature in N2 discharges using low-resolution spec-torscopy,” Meas. Sci. Technol., No. 11, pp. 333-341, 2000.

[37] Nassar, H., Pellerin, S., Musiol, K., Martinie, O., Pellerin, N., Cormier, J.,“N+

2 /N2 ratio and temperature measurements based on the first negative N+2

and second positive N2 overlapped molecular emission spectra”, J. Phys. D:Appl. Phys. Vol. 37, 2004, pg 1904-1916.

[38] Gilmore, Forrest R., Laher, Russ R., Espy, Patrick, J., “Franck-Condon Factors,Centroids, Electric Transition Moments, and Einstein Coefficients for Many Ni-trogen and Oxygen Band Systems.” J. Phys. Chem. Ref. Data, Vol. 21, No. 5,1992.

[39] Laux, C., and Kruger, C., “Arrays of Radiative Transition Probabilities for theN2 First and Second Positive, NO Beta and Gamma, N+

2 First Negative, andO2 Schumann-Runge Band Systems,” J. Quant. Spectrosc. Radiat. Transfer, Vol.48, No. 1, pp. 9-24, 1992.

[40] R. W. B. Pearse and A. G. Gaydon, The Identification of Molecular Spectra,Chapman & Hall Ltd., London, 1963.

[41] D. K. Davies, “Charge generation on dielectric surfaces,” Brit. J. Appl. Phys.,Ser. 2, Vol. 2, 1969.

[42] V. Chernyak, V. Naumov, V. Yukhimenko, “Spectroscopy of atmospheric pres-sure air jet plasma in transverse arc discharge,” 12th International Congress onPlasma Physics, 25-29 October 2004, Nice (France).

[43] P. Pignolet, S. Hadj-Ziane, B. Held, R. Peyrous, J. M. Benas, and C. Coste,“Ozone generation by point to plane corona discharge,” J. Phys. D., No. 23, pp.1069-1072, 1990.

88

[44] F. Hegeler, H. Akiyama, “Spatial and Temporal Distributions of Ozone After aWire-to-Plate Streamer Discharge,” IEEE Trans. Plas. Sci., Vol. 25, No. 5, pp.1158-1165, Oct. 1997.

[45] C. Guitierrez-Tapia, E. Camps, and O. Olea-Cardoso, “Perturbative Method forOzone Synthesis From Oxygen in a Single Discharge,” IEEE Trans. Plas. Sci.,Vol. 22, No. 5, pp.979-985, Oct. 1994.

[46] Spitzer, Lyman. Physics of Fully Ionized Gases, John Wiley & Sons, New York,1962.

[47] A. Lofthus and P. H. Krupenie, “The spectrum of molecular nitrogen,” J. Phys.Chem. Ref. Data, Vol. 6, No. 1, 1977.

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APPENDIX AMOLECULAR SPECTRA SYNTHESIS PROGRAM

90

91

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100

101

102

103

104

105

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107

APPENDIX BENERGY LEVELS AND POTENTIAL CURVES OF N2

Figure B.1: Potential Energy Curves for N2 and N+2 [47]

108

Figure B.2: Energy level schemes for N2 [40]

109

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