PULSED BREAKDOWN PHENOMENA  
IN PARTIAL VACUUM 
 
by 
 
Zhenhong Li 
 
 
 
 
A thesis submitted to the Graduate Faculty of 
Auburn University 
in partial fulfillment of the 
requirements for the Degree of 
Master of Science 
 
Auburn, Alabama 
December 8, 2012 
 
 
 
 
 
 
Copyright 2012 by Zhenhong Li 
 
 
Approved by 
 
Hulya Kirkici, Chair, Professor of Electrical and Computer Engineering 
Thaddeus Roppel, Associate Professor of Electrical and Computer Engineering 
Michael Baginski, Associate Professor of Electrical and Computer Engineering 
 
 
  
ii 
 
 
 
 
Abstract 
 
In this thesis, the pulse generation and pulsed breakdown phenomena have been studied 
in detail.  Pulsed power is widely used in food processing, biotechnology, military defense, and 
industrial applications.  The first part of this work covers the simulation and analysis of common 
high voltage DC and pulse generator circuits.  Then high power switching techniques which are 
essential to the generation of pulsed power are also explored.  Due to the rapid development of 
high energy laser and accelerator, high power switches capable of handling powers up to 
terawatts are in great demand in industry.  Pseudospark switch using the hollow cathode effect is 
an example for these applications.  Pseudospark discharge is triggered by many means and is 
challenging. Carbon Nanotubes (CNTs) triggering is achieved in pseudospark switches operated 
in helium and tested in the laboratory.  The delay time of the triggered breakdown with several 
CNTs samples under different trigger voltages is summarized.   
As the second part of this research, the pulsed breakdown phenomena in partial vacuum 
are investigated thoroughly.  Solid insulators are widely employed in power systems operating in 
atmospheric pressure and partial vacuum.  However, the hold-off capability of an insulator in 
vacuum is limited by the surface flashover problem due to the cathode ?triple-junction? effect.  
This is a common problem for space power and aerospace power systems.  In this work, the 
surface flashover characteristics of nanodielectric materials composed of cast epoxy resin mixed 
with nano-dielectric particles in partial vacuum are studied.  The samples except the control 
samples are made by adding nanoscale Al2O3 or TiO2 powder with predetermined ratios into the 
iii 
 
epoxy resin with known properties.  The samples are cylindrical in shape (2.5 cm in diameter and 
1 cm in thickness) and varying electrode configurations and spacing are used in this study.  The 
surface flashover characteristics of the samples are investigated using both DC and 20 kHz 
pulsed-unipolar signals separately.  The frequency and duty cycle of the pulsed signal are also 
varied in the experiments in order to obtain a clearer understanding of pulsed surface flashover in 
partial vacuum.  Initially the cylindrical samples are sandwiched between two parallel plate 
electrodes, and the voltage, current, and light emission waveforms during the flashover events 
are recorded and analyzed.  As a second test set, the electrodes laterally placed on the samples? 
flat surface and surface breakdown experiments conducted and comparisons to the parallel plate 
case are made.   
 
 
 
 
 
 
 
 
 
 
 
 
 
 
iv 
 
 
 
 
Acknowledgments 
 
 
The author would like to thank his advisor Dr. Hulya Kirkici for her patience and 
guidance on this research work during the past two years.  Without her support this work would 
be impossible to achieve.  The author would like to thank Dr. Baginski and Dr. Roppel for 
serving as the committee members.  The author also would like to express appreciation to Ms. 
Linda Barresi and Mr. Calvin Cutshaw for their material assistance during this work.  Thanks are 
also due to his group members, especially Rujun Bai, Haitao Zhao and Huirong Li who help him 
run the experiments over and over again.  Finally, the author wishes to thank his mother and 
sisters, for their unfailing support and understanding.   
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ? Work partially sponsored by AFOSR grant # AF-FA9550-08-10051 
 
v 
 
 
 
 
Style manual or journal used Graduate School's Thesis and Dissertation Guide 
 
Computer software used Microsoft Office 2007  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
vi 
 
 
 
 
Table of Contents 
 
 
Abstract ......................................................................................................................................... ii 
Acknowledgments ....................................................................................................................... iv 
List of Tables ............................................................................................................................... ix 
List of Figures ............................................................................................................................... x 
Chapter I INTRODUCTION & BACKGROUND ....................................................................... 1 
1.1 Introduction  ................................................................................................................ 1 
1.2 Electrical Breakdown of Gases ................................................................................... 4 
1.2.1 Townsend Mechanism ....................................................................................... 4 
1.2.2 Paschen?s Law ................................................................................................... 6 
1.2.3 High Frequency Breakdown .............................................................................. 9 
1.2.4 Pulsed Breakdown ........................................................................................... 11 
1.2.5 Glow Discharge ............................................................................................... 13 
1.2.6 Hollow Cathode Discharge .............................................................................. 14 
1.3 Pulsed Power ............................................................................................................. 15 
1.3.1 Pulsed Power Generation ................................................................................. 15 
1.3.2 Power Switches ................................................................................................ 17 
1.4 Surface Flashover...................................................................................................... 20 
1.4.1 Space Environment & Spacecraft .................................................................... 20 
1.4.2 Surface Flashover in Vacuum & Partial Vacuum ............................................ 22 
vii 
 
Chapter II HIGH VOLTAGE GENERATOR SIMULATION & APPLICATION ................... 24 
2.1 High Voltage DC Power Supply  .............................................................................. 24 
2.2 High Voltage Pulse Generator  ................................................................................. 27 
2.3 Application: CNTs Initiated Hollow Cathode Discharge ......................................... 31 
2.3.1 Experiments Setup ........................................................................................... 33 
2.3.2 Experiment Results & Discussions .................................................................. 33 
Chapter III SURFACE FLASHOVER IN PARTIAL VACUUM ............................................. 36 
3.1 Sample Preparation  .................................................................................................. 36 
3.2 Experimental Setup ................................................................................................... 38 
3.3 Experimental Procedure ............................................................................................ 40 
3.4 Breakdown Voltage versus Pressure ......................................................................... 41 
3.4.1 DC Breakdown Voltage versus Pressure ......................................................... 43 
3.4.2 Pulsed Breakdown Voltage versus Pressure .................................................... 46 
3.5 Electrode Configurations Effect on Breakdown Voltage ......................................... 49 
3.6 Breakdown Voltage versus Pulse Parameters ........................................................... 51 
3.6.1 Breakdown Voltage versus Frequency ............................................................ 52 
3.6.2 Breakdown Voltage versus Duty Cycle ........................................................... 54 
3.7 Surface Effect on Breakdown Voltage ..................................................................... 54 
3.8 Conclusions ............................................................................................................... 57 
Chapter IV CONCLUSIONS ...................................................................................................... 59 
References ................................................................................................................................... 61 
Appendix A SPICE Listing for Pulse Generator Circuit .......................................................... A-1 
Appendix B Surface Breakdown Voltages vs. Pressure (Sandwiched Electrode) .................... B-1 
viii 
 
Appendix C Surface Breakdown Voltages vs. Pressure (Lateral Electrode) ............................ C-1 
Appendix D Surface Breakdown Voltages vs. Pressure (Machined Samples) ......................... D-1 
Appendix E Surface Breakdown Voltages vs. Frequency ........................................................ E-1 
Appendix F Surface Breakdown Voltages vs. Duty Cycle ........................................................ F-1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
ix 
 
 
 
 
List of Tables 
 
 
Table 2.1 CNTs sample list ......................................................................................................... 34 
Table 3.1 Nanodielectric sample list in the experiment .............................................................. 37 
Table 3.2 Test conditions in surface flashover experiments ....................................................... 41 
Table 3.3 ((pd),Vmin) comparison between sandwiched & lateral electrode configurations ....... 51 
Table 3.4 Breakdown voltages comparison between sandwiched & lateral electrode 
configurations at pd of 1200 and 400 mTorr?cm ........................................................................ 51 
 
Table 3.5 ((pd),Vmin) comparison between untreated and machined surface samples ................ 57 
Table 3.6 Breakdown voltages comparison between untreated and machined surface samples at 
pd of 1000 and 400 mTorr?cm .................................................................................................... 57 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
x 
 
 
 
 
List of Figures 
 
 
Figure 1.1 Schematic of simple gas breakdown test ..................................................................... 5 
Figure 1.2 Variation of current as a function of applied voltage .................................................. 6 
Figure 1.3 Paschen curves for different gases under DC .............................................................. 8 
Figure 1.4 Paschen curves for various gases under 400 Hz AC ................................................... 8 
Figure 1.5 Paschen curves for various gases under 20 kHz unipolar sinusoid signal .................. 9 
Figure 1.6 Ratio of high-frequency breakdown voltage to static breakdown voltage as a function 
of frequency for a uniform air gap .............................................................................................. 11 
 
Figure 1.7 Time lags determining the dynamics of breakdown in a gas-insulated gap. ............. 12 
Figure 1.8 General structure of a glow discharge ....................................................................... 14 
Figure 1.9 Pulsed power train diagram ....................................................................................... 16 
Figure 1.10 (a) Simple capacitive storage discharge circuit (b) output voltage with RC decay . 17 
Figure 1.11 (a) PFL circuit (b) square output pulse voltage ....................................................... 17 
Figure 1.12 Range of gas pressure and operating voltages for different types of gas switches . 18 
Figure 1.13 Typical schematic and electric field configuration in pseudospark system ............ 20 
Figure 1.14 Schematic of vacuum flashover initiation from triple junction ............................... 23 
Figure 2.1 3-stage 10 kV voltage multiplier circuit .................................................................... 25 
 
Figure 2.2 Spice simulation of output voltage from different tapping points ............................. 26 
Figure 2.3 Spice simulation of output current at full load .......................................................... 26 
Figure 2.4 In-house made voltage-regulated 1 kV pulse generator (a) prototype (b) output pulse
..................................................................................................................................................... 27 
xi 
 
 
Figure 2.5 High voltage pulse circuit. ......................................................................................... 29 
Figure 2.6 Waveform of control signal from Node 17, 22, and 27 ............................................. 29 
Figure 2.7 Output voltage waveform from Spice simulation ..................................................... 30 
Figure 2.8 Short-circuited output current waveform .................................................................. 30 
Figure 2.9 Electrodes setup in CNTs initiated hollow cathode discharge .................................. 32 
Figure 2.10 Schematic of the experimental setup ....................................................................... 32 
Figure 2.11 Image of CNTs initiated hollow cathode discharge with sample R-40 ................... 34 
Figure 2.12 Typical hold-off voltage and trigger pulse waveforms when breakdown event occurs
..................................................................................................................................................... 35 
 
Figure 2.13 Delay time as a function of trigger voltage for different samples ........................... 35 
Figure 3.1 Nanodielectric samples preparation processes .......................................................... 37 
Figure 3.2 Schematic of surface machined samples ................................................................... 37 
Figure 3.3 Schematics of the electrodes setups (a) sandwiched; (b) lateral ............................... 39 
Figure 3.4 The experimental setup employed in the surface flashover study ............................. 40 
Figure 3.5 Voltage, light intensity and current waveforms of control sample with sandwiched 
electrode configuration during flashover at 500 mTorr under DC voltage ................................ 42 
 
Figure 3.6 Images of the fully developed plasma after a surface breakdown event ................... 42 
Figure 3.7 Voltage, light intensity and current waveforms of control sample with sandwiched 
electrode configuration during flashover at 500 mTorr under pulsed voltage ............................ 43 
 
Figure 3.8 DC surface breakdown voltage vs.  (pd) for different samples (a) for the sandwiched 
electrode configuration (b) for the lateral electrode configuration ............................................. 45 
 
Figure 3.9 Pulsed surface breakdown voltage vs.  (pd) for different samples (a) for the 
sandwiched electrode configuration (b) for the lateral electrode configuration ......................... 47 
 
Figure 3.10 Surface breakdown curves of the control sample and S-T2 sample under dc and 
pulsed applied fields ................................................................................................................... 48 
 
xii 
 
Figure 3.11 Pulsed surface breakdown curves for both the sandwiched and lateral configuration 
of (a) control sample (b) S-T2 sample ........................................................................................ 50 
 
Figure 3.12 Typical schematics of surface breakdown voltage as a function of frequency for  
(a) sandwiched (b) lateral configuration ..................................................................................... 53 
 
Figure 3.13 Typical surface breakdown curves for smooth untreated and machined surface of (a) 
control sample (b) S-A6 sample ................................................................................................. 56 
 
 
 
 
 
 
 
1 
 
 
 
CHAPTER I  
INTRODUCTION & BACKGROUND 
 
1.1 Introduction 
Pulsed power technology is widely employed in biotechnology, food processing and 
preservation, military defense, and other industrial applications [1-5].  Pulsed power is a scheme 
where energy is stored for a long time, and then discharged into a load as electrical energy in a 
single short pulse or as short pulses with a controllable repetition rate [6].  Generally the pulsed 
power generation system consists of high voltage power supply, energy storage component, 
pulse compression stages, impedance matching network, switches, and discharge load [4].  
Pulsed power generators are classified as either inductive or capacitive where energy is stored 
respectively.  Although lacking of stored energy density, high voltage energy storage capacitors 
are still used in most pulsed power systems, because it is much easier to build reliable system, 
and can be made repetitive.  Power switches are essential to the pulsed power generation system.  
Also fast closing switches for capacitive storage systems are more developed than the counter 
partners of opening switches for induction storage systems [6].  Gas switches and solid-state 
switches are two types of commonly used closing switches.  Because of the compactness, light 
weight, high operation speed, low cost, and high frequency, in recent years semiconductor 
switches are extensively used to generate high voltage pulses [5].  However, their performance 
on power capability is usually limited because of the relatively low mobility and density of 
 
2 
 
charge carriers and low operating temperature [6].  Conventional gas switches such as spark gap, 
vacuum gap, and pseudospark switch are more powerful and can handle very large currents and 
charges.  Pseudospark switch taking advantage of the hollow cathode effect stands out because 
of its high power capability, less electrode erosion, and higher lifetime.  In this thesis, as a 
preliminary study of pseudospark switch, the helium hollow cathode discharge initiated by 
carbon nanotubes (CNTs) cold cathodes is tested in the lab.  With the properties of low turn-on 
voltage and excellent field emission, CNTs are promising cold cathode emitters as innovative 
trigger methods for pseudospark switches.  In this work, a pulse generator used as the power 
source to trigger CNTs cold cathode as trigger electrode is also analyzed, simulated, and built. 
In the second part of this thesis, the pulsed breakdown phenomena of nanodielectrics are 
investigated.  The insulation of space power system has been a serious issue since the beginning 
of the space exploration program.  Continual advances in space systems have increased the 
demand for higher power requirements and the operation voltage has changed from traditional 28 
V standards to much higher levels.  For the International Space Station requiring 100 kW level 
electric power, operation voltage at 160 V is used.  But for the solar power satellite (SPS), in 
which gigawatt power is generated by large solar arrays, it is typically operated at 1000 V in the 
power generation and transmission system [7].  However, this adds severe weight constraint on 
space power systems.  It has been shown that two methods can be employed to fulfill the critical 
demand on weight reduction [8-9].  One method is to operate the magnetic circuitry at much 
higher frequencies; the other is to use more compact components.  Thus the working frequency 
of modern high voltage switching mode power supplies in space system is increased from low 
frequency range of 60 Hz ~ 400 Hz to radio frequency range of 100 kHz ~ 1 MHz or even higher 
[7].  More compact systems means, spacing between the differently biased components is 
 
3 
 
drastically reduced.  Thus stringent electrical insulation of these components and sub-systems are 
required.  Meanwhile, in order to satisfy the increasing power demand in spacecraft, power 
generation at higher voltage and lower current is a commonly employed method from the point 
of view of reducing power loss in the transmission lines [10].  However, the reduced spacing 
between the components (effective electrode gap), the operation at higher frequency than 
traditional 400 Hz, and higher voltage than 28 V in space power systems increase the stress on 
electrical insulation.  It has been shown that many compact designs have failed because of 
insulation design overstress, incompatible coordination, and improper insulation testing during 
and following final packaging [7].   
 Partial discharges and coronas enhanced by high frequency and high voltage is more 
likely to occur in these systems, resulting in power loss and leading to degradation, aging or 
thermal breakdown of the insulation and components.  They also generate undesirable noise as 
electromagnetic interference (EMI) which can disturb the signal transmitted in the space power 
systems.  As in the case of ground based systems, insulation already experienced short circuiting, 
power losses, and spurious signals in communication systems and sensitive sensors [11] due to 
arcing discharge.  In space and aerospace systems, other environmental factors such as electrical 
degradation and decrease in breakdown strength are due to molecular particulate contaminants 
[12].  Consequently studies on electrical breakdown of dielectrics in space environment are still 
meaningful.   
 Although significant work has been made on gas breakdown in partial vacuum [13-14], 
most of the data on maintenance and protection in literature only deals with ground based power 
systems operating at 50/60 Hz at atmospheric pressure.  Furthermore, there are only a few 
reports available on high frequency breakdown in partial vacuum [13], and breakdown 
 
4 
 
characteristics of dielectrics in partial vacuum under kHz range pulses still need more 
investigation.   
 Nanodielectrics are a group of filled-polymers where sub-micrometer or nanometer sized 
ceramic or metal-oxide insulating particles are added to polymeric dielectric materials.  They are 
widely used in the photonics and electronics areas currently and are also promising materials in 
electrical insulation (high power density and high voltage) [15].  In general, the hold-off 
capability of an insulator in vacuum is limited by the surface flashover problem due to the 
cathode ?triple-junction? effect [16].  This is also true for nanodielectrics.  This thesis focuses on 
the study of nanodielectrics surface flashover under DC and kHz range pulses in partial vacuum.   
 
1.2 Electrical Breakdown of Gases 
Air is commonly used as insulating medium in electrical installation because of its 
abundance and excellent self-restoring capability after breakdown.  On the other hand, solids and 
liquids usually contain gas voids and contamination leading more frequent breakdown and partial 
discharges.  Therefore the gaseous breakdown research is significant for designers and operators 
who are working on electrical and electronic equipment insulation.   
 
1.2.1 Townsend Mechanism  
A simple gas breakdown test system is illustrated in Figure 1.1.  It consists of a pair of 
parallel plates enclosed in a gas chamber and separated by a distance d.  The electric field 
between the electrodes is assumed to be uniformly distributed when a high voltage is applied 
between the electrodes.  When electrons are emitted from the cathode by any means, they are 
accelerated toward the anode under the strong applied electric field.  If the electrons acquire 
 
5 
 
enough energy, they can ionize the gas molecules through collisions.  The generated new 
electrons propagate along the field as the primary ones, and then ionize other gas molecules.  The 
primary avalanche ends after the ions enter the cathode region.  If the amplification and electron 
avalanche is increased, more electrons are liberated in the gap by secondary ionization from 
positive ions, excited atoms, photons, and metastables.  These secondary electrons initiate new 
avalanches, resulting in a space charge formation in the gap.  The space charge formation 
enhances the electric field somewhere between the electrodes, with a subsequent fast current 
increase, leading to the breakdown of the gas ultimately.  This is the classical Townsend 
mechanism.   
 
Figure 1.1 Schematic of simple gas breakdown test 
 
The relationship between the current and applied voltage was explained by Townsend as 
shown in Figure 1.2 [18].  He determined that the current at first increases proportionally as the 
voltage increases, and then reaches a saturation current I0 and remains steady for a while.  The 
current I0 results through photoelectric effect produced at the cathode by external irradiation.  If 
the voltage is increased further, current increases exponentially.  This reveals the eventual spark 
breakdown of the gap.   
 
6 
 
In the steady state, the circuit current is given by 
? = ?0???1??(??? ?1)              (1.1) 
where ? is Townsend first ionization coefficient, ? is Townsend secondary ionization 
coefficient, d is distance between electrodes,  I0 is saturation current, I is current flowing in the 
circuit. 
Neglecting the power supply internal resistance, the current becomes infinite if  
? ??? ? 1 = 1               (1.2) 
Normally, ???  >> 1, and Equation 1.2 is simply expressed as 
???? = 1                         (1.3) 
Equation 1.2 defines the onset condition of spark and is known as the Townsend criterion 
for spark breakdown.   
 
Figure 1.2 Variation of current as a function of applied voltage [12] 
 
1.2.2 Paschen?s Law 
 Paschen?s law is a fundamental but most important principle in gas breakdown 
phenomena.  It describes the relationship between the breakdown voltage V and the product of 
pressure p and electrode distance d in a gaseous environment.  By investigating the ionization 
 
7 
 
process by electron impact, we can determine the coefficients of ? and ? both functions of the gas 
pressure and the electric field.  Namely, ? = ? ? ?1(??) and ? = ? ? ?2(??).  Since ? = ??  for 
parallel plate electrodes, Equation 1.2 can be revised as  
 ?2  ????  ?????1 
?
??? ? 1 = 1                (1.4) 
or V = F(pd). 
 This is the well-known Paschen?s law [19].  The experimental data of Paschen curves for 
different gases under uniform dc field are shown in Figure 1.3 [20].  The ?V? shape Paschen 
curve has a minimum breakdown voltage at a specific product of pd.  If we assume the electrode 
spacing d is fixed, then there are two regions namely high pressure and low pressure in this plot.  
As the pressure reduces from atmospheric pressure on the right-hand side to the paschen 
minimum, the electron free path increases as the gas density decreases.  Therefore, when the 
electrons travel toward the anode, they have fewer collisions with the gas molecules and gain 
more energy from the electric field with less collision loss.  Thus a lower electric field is strong 
enough to provide electrons with sufficient energy for ionization collision and electrons are 
accelerated further leading breakdown at lower voltage.  When the minimum point of the curve 
is reached, the density is even lower and fewer collisions occur.  If the pressure is further 
lowered, then the breakdown takes place at a higher level.  This region is called the left-hand 
side of Paschen curve, and electron mean free path is relatively large with less density of 
background gas.  Because there are a few molecules, fewer collisions take place, and this is the 
reason for higher breakdown voltage. 
Empirical formula has been proposed to calculate the dc breakdown voltage of uniform-
field gaps at atmospheric pressure air as following: 
? = 2440? + 61 ?   kV             (1.5) 
 
8 
 
where d is the gap length in meters.  However, for the space power systems, this may not be used 
because of the operation in low pressure. Also traditionally space power systems operate at low 
frequency AC, however, recently they have operated at kHz frequency. The breakdown curves in 
this case are still similar to the Paschen curve as shown in Figure 1.4 [21] and Figure 1.5 [22].   
 
Figure 1.3 Paschen curves for different gases under DC [20] 
 
Figure 1.4 Paschen curves for various gases under 400 Hz AC [21] 
 
9 
 
 
Figure 1.5 Paschen curves for various gases under 20 kHz unipolar sinusoid signal [22] 
 
1.2.3 High Frequency Breakdown 
 In uniform-field gaps, electrical breakdown starts with the avalanche process as 
described above for DC and low-frequency AC cases.  If the frequency of the applied field is 
increased to kHz and beyond, the discharge behavior begins to change.  For a given electrodes 
spacing d, there is a critical frequency fc at which positive ions can just be cleared from the gap 
during one half-cycle of the AC applied voltage, 
 ?? = ?+??2 ?            (1.6) 
where k+ is the mobility of positive ions and V is the applied voltage.   
If the applied AC frequency is smaller than fc, the breakdown conditions are similar to 
those of static fields.  If the AC frequency is larger than fc, the cloud of positive ions will 
oscillate between the electrodes.  As the continuous generation of new avalanches, the density 
and size of the positive cloud will keep increasing until stability and breakdown occur.  The 
 
10 
 
electric field distribution in the gap is distorted by the accumulating positive space charges, 
leading to the AC breakdown with voltages lower than that under DC case.  The high frequency 
voltage breakdown behavior is illustrated in Figure 1.5 [19]. 
 Likewise, there is a critical frequency fce above which electrons cannot reach the 
opposite electrode in one half-cycle,  
 ??? = ????2 ?             (1.7) 
where ke is the mobility of electrons and V is the applied voltage.   
If the applied AC frequency is between fc and fce, the oscillating positive ion space 
charges in the gap still dominate the electrical breakdown behavior.  At even higher frequencies, 
electrons in the gap begin to oscillate between the electrodes.  If some of them cannot reach the 
anode during one half-cycle, they will neutralize the positive-ion space charges, reduce the 
distortion of electric field in the gap, and lead to higher breakdown voltages ultimately.  If the 
AC frequency keeps increasing to a certain frequency fco at which the breakdown mechanism is 
controlled by diffusion, the electrodes will not play any role and make any contribution to the 
ionization process.  The breakdown voltage under this condition usually drops sharply since the 
breakdown is mainly controlled by diffusion.   
 
11 
 
 
Figure 1.6 Ratio of high-frequency breakdown voltage to static breakdown voltage as a function 
of frequency for a uniform air gap [19] 
 
1.2.4 Pulsed Breakdown 
Pulsed breakdown is another consideration in electrical and electronic equipment 
insulation design.  In power systems and electrical components, impulse overvoltages leading to 
breakdowns are frequently imposed due to lightning and switching surges.  Under pulsed applied 
fields, a time lag is observed between the moment the voltage is applied and the breakdown 
occurs.  In detail, the time lags involved in the pulsed breakdown process are shown in Figure 
1.6. The symbols in this figure are described as: 
t0 ? the time until the applied voltage exceeds the static breakdown voltage Ub; 
ts ? the statistical delay time until a seed electron able to create an avalanche occurs; 
 
12 
 
ta ? the avalanche build-up time until the critical charge density is reached;  
tarc ? the time required to establish a low resistance arc across the gap.   
The statistical delay time ts results from the statistics of electron appearance in the gap.  
Not every electron emitted into the gap is able to initiate an avalanche even though the applied 
voltage is higher than the static breakdown value.  Nevertheless, after the first seed electron 
avalanche is initiated, pulsed breakdown is well developed in two different ways, namely, 
Townsend breakdown and streamer mechanism [6].  In the Townsend breakdown mechanism, 
several generations of avalanches can be developed till a glow-to-spark transition or a quasi-
stable glow discharge occurs.  During the streamer breakdown, a single avalanche is strong 
enough to produce a critical number of electrons before the anode is reached. Electrons that 
escape from the avalanche head can cause a field distortion, which drives the self-propagation of 
the avalanche ultimately.  Therefore, the build-up time ta is very different for these two cases.   
 
Figure 1.7 Time lags determining the dynamics of breakdown in a gas-insulated gap [6] 
 
 
13 
 
1.2.5 Glow Discharge 
Glow discharge is a kind of luminous low pressure discharge which has widespread 
industrial applications such as analytical chemistry, micro-electronics fabrication, and lasers 
[23].  Glow discharge is the self-sustained continuous DC discharge consisting of a cold cathode, 
which emits electrons as a result of secondary emission mostly induced by positive ions [20].  
Figure 1.7 is the schematic of typical normal glow discharge.  Immediately next to the cathode is 
a dark layer known as the Aston dark space and then a relatively thin layer of the cathode glow.  
It is a bright region close to the cathode with high ion number density.  Adjacent to cathode glow 
zone is the cathode dark space followed by the negative glow which is the brightest region with 
intense excitation and ionization of atoms.  Electrons accelerated in the cathode region collide 
with the background gas and cause light emitting processes.  The negative glow gradually 
decreases in brightness toward the anode, becoming the Faraday dark space.  The positive 
column emerging after that is uniform, bright (though not as bright as the negative glow), and 
relatively long if the length of the discharge tube is sufficiently large.  At constant pressure, if the 
length of the discharge tube is increased, the positive column will lengthen while the cathode 
region will remain constant.  In the area of the anode layer, the positive column is evolved first 
into the anode dark space and then into the narrow anode glow zone and finally the anode dark 
space area.  A special feature of a glow discharge is the cathode layer with dense positive space 
charges and the strong electric field with a large voltage drop almost equal to the applied voltage 
level. 
 
14 
 
 
Figure 1.8 General structure of a glow discharge [20] 
 
1.2.6 Hollow Cathode Discharge 
If a single planar cathode in glow discharge is replaced by a cathode with hollow 
structure, the current will be orders of magnitude larger than that in the plannar structures.  The 
negative glow region of the discharge moves into the hollow structure of the cathode, leading to 
higher ionization and excitation processes.  This effect is called the hollow cathode effect which 
is mainly caused by pendulum electrons [24-25].  Electrons emitted from the internal hollow 
cathode surface are found to be reflected on the opposite cathode surface when they go through 
the negative glow without significant energy loss.  These reflected electrons regarded as 
pendulum electrons and they greatly increase the ionization collisions in the hollow cathode.  
Because of the larger weight of positive ions compared to the electrons, the cloud of ions 
remains in the cathode cavity after collisions and form a virtual anode.  The electric field in the 
cathode is enhanced by this virtual anode and more electrons are emitted which further 
strengthen the ionization collisions with the background gas and contribute to the increase of the 
positive ion density.  The cathode fall, referred as the distance between the virtual anode and the 
cathode sheaths, can be significantly thinner in hollow cathode configurations, resulting in an 
 
15 
 
extremely high electric field and the succeeding higher secondary electrons emission rate.  In this 
way, the hollow cathode structure increases the probabilities of multiple processes and collisions 
for all particles and is able to generate very high density plasma inside the hollow cathode.   
In general, the hollow cathode discharge range for rare gases is given as 1 torr?cm < pD < 
10 torr?cm, where p is pressure and D is the diameter of the hollow cavity [26].  Due to this pD 
restriction, most of the hollow cathode discharge devices are operated at low pressure and on the 
left-hand side of the well-known Paschen curve.   
 
1.3 PULSED POWER 
Pulsed power engineering is the technology of storing energy in capacitive or inductive 
form over a relatively long period of time (usually seconds to minutes) and then discharging it 
into a load over a much shorter time period (usually nanoseconds to microseconds) as electrical 
energy by closing or opening power switches.  Power generation, power switches, pulse forming 
network, and the load are the major components of a pulsed power system. 
 
1.3.1 Pulsed Power Generation 
Many types of high voltage and nanosecond pulse generators are commercially available 
currently.  However, the performance of these generators varies broadly and they should be 
chosen according to load requirements, such as output voltage, pulse width, rise time, repetition 
rate, and peak power.   
The fundamental purpose of all pulsed power system is to convert a low-power, long-
time input into a high-power short-time output.  A general pulsed power system diagram is 
shown as Figure 1.8 [4].  The high voltage power supply fed from wall power by full-wave 
 
16 
 
rectifiers is the power source to the pulsed power system.  It determines the charging time of the 
energy storage section, which normally ranges from microseconds to minutes.  The pulse energy 
is stored in the energy storage section for an amount of time which depends upon the output 
requirements.  When the energy in the storage section is transferred into the first pulse 
compression or pulse forming stage, pulse compression section starts to run.  The number of 
pulse compression stages can vary from one to many, which depends on the application.  Each of 
these stages usually requires a switch.  The impedance match section, for instance, a transformer 
or transmission line, is necessary to discharge the maximum power to load with the minimum 
reflections.  The final section before the discharge load, the primary power switch, delivers all of 
the pulsed power into the load. 
 
Figure 1.9 Pulsed power train diagram [4] 
 
Generally all pulse generation circuits are classified as either capacitive or inductive 
storage.  The simple capacitive storage discharge circuit and pulse forming line (PFL) are two 
elemental methods to generate short pulses.  Other pulse generators such as Marx generator and 
Blumlein PFL are mostly adapted from them. 
 An RC circuit shown in Figure 1.9 can be easily used to generate double-exponential 
high voltage pulses by charging the capacitor C and then discharging its energy into the load by 
simply closing the switch S1.  Transmission line or PFL in Figure 1.10 is another good 
alternative to generate high voltage rectangular pulses.  When the switch S1 is closed at t = t0, a 
 
17 
 
pulse of amplitude (?V0/2) propagates down the line toward line length d.  It then reflects at d 
and returns to the switch and the load at 
t = t0 + 2d ?rc  (sec)                (1.8) 
where ?r is the relative permittivity of the transmission line, d is the length of the transmission 
line in meters, c is the speed of light. 
 
Figure 1.10 (a) Simple capacitive storage discharge circuit (b) output voltage with RC decay [4] 
 
Figure 1.11 (a) PFL circuit (b) square output pulse voltage [4] 
 
 
 
18 
 
1.3.2 Power Switches 
Power switches, between the storage devices and the loads, play an indispensable role in 
the generation of pulsed power.  The shape, rise time, and magnitude of the generator output 
pulse depend strongly on the properties of the power switches.  Moreover, the maximum power 
capacity and power density that the power switches could handle also limit the performance of 
pulse generators.  Switches are generally categorized into closing switches for capacitive storage 
devices and opening switches for discharging inductive storage devices.   
Gas switches and semiconductor switches are two common types of closing switches.  
Gas switches are highly employed in high power pulse generators.  They are easy to use, can 
handle relatively large currents, and can be also triggered accurately.  Several kinds of gas 
switches such as ignitron, krytron, thyratron, pseudospark switch, and spark gap are reported in 
literature [6].  Their operating gas pressure and hold-off voltage ranges are shown in Figure 1.11.   
 
Figure 1.12 Range of gas pressure and operating voltages for different types of gas switches [6] 
 
19 
 
  
Among these, pseudospark switch taking advantage of hollow cathode effect, stands out 
because of its reduced electrode erosion, high power capability, and long lifetime.  Figure 1.12 
shows the typical schematic and electric field configuration in a two-electrode pseudospark 
switch.  Generally the operation of pseudospark switch is described in four different periods: pre-
discharge, hollow cathode discharge, high current super-emissive discharge, and the decay of the 
discharge plasma [27].  In order to make use of the pseudospark discharge, a precise triggering 
system is required for the switch.  For reliable triggering, about 109 to 1010 electrons are needed 
inside the hollow cathode [28].  A lower number of electrons results in higher delay and jitter 
time values, or cannot initiate the discharge at all.  Several triggering methods have been 
researched, such as surface flashover, low current glow discharge, optical triggering, and 
electrons injection.  Each of the methods has its pros and cons [27] with regard to the lifetime, 
operating frequency, construction complexity, and delay time.  As a preliminary study of 
pseudospark switch, the helium hollow cathode discharge initiated by carbon nanotubes (CNTs) 
cold cathode is tested [27].  With the properties of low turn-on voltage and excellent field 
emission, CNTs are highly potential to be employed as an innovative trigger method.  In this 
thesis the pulse generator used to trigger CNTs is developed and constructed. 
 
20 
 
 
Figure 1.13 Typical schematic and electric field configuration in pseudospark system 
 
1.4 SURFACE FLASHOVER 
Surface flashover is a very common phenomenon in atmosphere pressure.  When the 
insulator surface is wetted by fog or rain, the pollution layer becomes conductive and final 
flashover occurs after a serial of events such as conduction layer build-up, dry band formation, 
partial arcing, arc elongation, and eventual arc spanning the whole insulator [32].  In vacuum, the 
surface flashover is caused by another mechanism called ?triple-junction? effect [16], where the 
electrons are emitted from the cathode at the cathode-vacuum-insulator intersection where field 
is enhanced, and propagate along the insulator surface causing breakdown.  However, for 
aerospace power system operating in partial vacuum environment, the surface flashover has not 
been fully explained and is expected to be similar to the one in the case of surface flashover in 
vacuum [33].   
 
 
 
21 
 
1.4.1 Space Environment & Spacecraft 
Space is often mistakenly considered as a vast, empty vacuum.  In reality, space is a 
dynamic place filled with energetic particles, radiation, and trillions of objects.  Specifically, 
space environment is a low-pressure gas consisted of a small quantity of weakly ionized gas 
from solar interactions, abundant neutral atoms and molecules, and other charged particles as 
electrons [12].   
Spacecraft orbiting in the space suffers from the radiation, space debris and meteoroid 
impact, and electrostatic charging.  Space debris and meteoroids can cause serious mechanical or 
electrical damage to the spacecraft if they collide at very high speeds.  The average speed of 
space debris is 10 km/s while the meteoroids move at even higher speeds.  Tragedy occurred 
from the electrical malfunction related to this kind of collision.  ESA?s (European Space 
Agency) Olympus -1 satellite lost altitude control and was severely damaged during the 1993 
Perseid meteor shower.  Spacecraft also suffers from electrostatic differential charging by the hot 
plasma environment around the Earth.  This high potential, resulted from the continuous 
accumulation of static charges, can be of the order of several kilovolts.  If discharged improperly, 
this differential discharging may cause direct or indirect damages to semiconductor devices and 
electronic systems on the spacecraft.   
Furthermore, the space environment is influenced by the presence of spacecraft also.  The 
local pressure around the spacecraft is altered by a few orders of magnitude due to outgassing, 
gas leaks, or exhausts.  Data from several early STS flights are presented in [17] with regard to 
the gaseous envelope surrounding the shuttle, the particle population orbiting with the shuttle, 
and the optical interference from the local sources.  Neutral species are tested in the bay area of 
the spacecraft, such as H2O, NO, He, Freon, Ar, O2, CO2, N2/CO and other heavy molecules.  
 
22 
 
The major contaminants were water and helium.  This is reasonable because the materials used in 
the mechanical and electrical equipments rang from liquids to solids.  The continuous outgassing 
processes contaminate the space environment and change the space pressure to some extent.  The 
wide range of pressure and temperature variations during the spacecraft orbiting process will 
enhance the chance of spacecraft anomalies.  From Paschen?s law, when the electrode distance is 
fixed, electrical breakdown property is very sensitive to the local pressure in the spacecraft.  At 
the pressures of 1 to 2 Torr, the breakdown of helium for 1 cm electrode gap is in the range of 
200 Volts, which is relatively high compared with the operating voltage level in the space power 
systems [12].  Therefore, electrical insulation in the spacecraft should be carefully considered 
and never be overstressed.   
 
1.4.2 Surface Flashover in Vacuum & Partial Vacuum 
Different from the case in atmospheric pressure, the voltage hold-off capability of solid 
insulator in vacuum is limited by its surface breakdown voltage and is lower than that of a 
vacuum gap with the same dimensions [16].  Several reviews concerning the electrical behavior 
of insulators in vacuum have been published [16, 29-31].  In general, surface flashover of an 
insulator may be divided into three stages: the initiation stage, the development stage, and the 
final stage.   
The initiation of a surface flashover is widely assumed to start with the emission of 
electrons from the triple junction since the equipotential lines normally concentrate in the 
interface among insulator, metal cathode and vacuum where small voids are unavoidable.  
However, there are considerable disagreements on the development stage of the discharge.  
Probably the most generally accepted mechanism for this stage is an electron cascade along the 
 
23 
 
surface of the insulator as illustrated in Figure 1.13.  Some of the electrons emitted from the 
triple junction bombard the surface of the insulator, producing additional electrons by secondary 
emission.  Some of these secondary electrons will again impact upon the insulator surface, 
generating tertiary electrons.  Continuous development of this process leads to an electron 
cascade along the insulator surface and later evolves into a secondary electron emission 
avalanche (SEEA).  This SEEA, in turn, can finally result in a complete surface breakdown.  For 
the final stages of surface flashover, it is generally considered to occur in the desorbed surface 
gas or the vaporized insulator materials.   
 
Figure 1.14 Schematic of vacuum flashover initiation from triple junction 
 
 In partial vacuum, significant work has been done on the research of surface flashover 
[13-14].  Based on a large amount of experiments, surface breakdown curves in partial vacuum 
are very similar to the well-known Paschen curve.  However, more theoretical research should be 
conducted in this area in order to clearly explain its breakdown mechanism.  This thesis focuses 
on surface flashover of nanodielectrics under high frequency pulsed electric fields. 
 
24 
 
 
 
 
CHAPTER II  
HIGH VOLTAGE GENERATOR SIMULATION & APPLICATION 
 
2.1 High Voltage DC Power Supply 
High voltage DC power supply is widely employed in research work and in industry, 
such as electron microscope, particles accelerator, and dielectric testing.  In dielectric test, the 
voltages are increased up to several million volts while currents are decreased to several 
milliamps.  In our experiments, DC power supplies are necessary for the gas breakdown tests and 
capacitive storage charging.  Therefore a 10 kV 0.1 ?A DC power supply is designed for lab use.   
The design employs the classic Cockroft-Walton voltage multiplier circuit, which is 
probably the most popular method of generating high voltages at low currents at low cost.  It is 
highly reliable, portable and simple while useful for the research.  Similar to Marx generator, a 
set of capacitors are charged to 2Vs(max) separately, and then provide (2n* Vs(max)) at the output 
when they are connected in series.  All of the capacitors and diodes only need to stand a voltage 
of 2Vs(max), which greatly decreases the costs on components and insulation.  In addition, the 
different voltage levels can be taken out through tapping at every stage of the multiplier circuit.  
However, this circuit has the disadvantage of having very poor voltage regulation, that is, the 
voltage drops rapidly as a function the output current.  Therefore voltage multipliers are usually 
used in special applications where load is constant and has high impedance or where input 
voltage stability is not very critical, such as dielectric strength test, particle acceleration, and X-
 
25 
 
Rays machines.  Figure 2.1 is the circuit of a 3-stage 10 kV voltage multiplier.  The operating 
principle is as follows: on the negative half-cycle of Vs, C1 charges through rectifier D1 to 
Vs(max).  On the positive half-cycle of Vs, rectifier D2 conducts and the peak voltage is Vs(max) from 
the source and Vs(max) from C1; that is, the capacitor C2 is charged to 2Vs(max).  During the next 
negative half-cycle, rectifier D3 conducts and voltage which is applied to C2 is the sum of Vs(max) 
from the source and 2Vs(max) from C2 less the voltage on C1; namely, C3 is charged to 2Vs(max).  
For higher output voltages of C4 and C6, the circuit is repeated with a cascade connection.  
Therefore the total output voltage reaches 2n*Vs(max) above the earth potential.  But the voltage 
across any individual capacitor or rectifier is 2Vs(max), except for C1, which is only charged to 
Vs(max).  In the circuit, the AC wall power (120 V RMS, 60 Hz) is used as the input and it is 
boosted to 1200 V RMS by a step-up transformer.  So the output voltage in this circuit is 
2n*Vs(max) = 2*3*1697 = 10.18 kV.   
 
Figure 2.1 3-stage 10 kV voltage multiplier circuit 
 
26 
 
Figure 2.2 is the Spice simulation of the output voltage from different tapping points of 
this circuit.  Figure 2.3 is the output current at full load.  From the simulation, we see that the 
output voltage is 9.92 kV and output current is 99.2 nA at full load, both of which are consistent 
with the calculation.  The voltage ripple, around 136 mV, is also very small.   
 
Figure 2.2 Spice simulation of output voltage from different tapping points 
 
Figure 2.3 Spice simulation of output current at full load 
 
27 
 
 
2.2 High Voltage Pulse Generator  
In our experiments, a negative pulse voltage is needed to trigger the CNT samples to emit 
electrons.  Therefore a voltage-regulated 1 kV pulse generator is developed and constructed in 
the lab as shown in Figure 2.4a.  Figure 2.4b is the typical waveform of its output pulse voltage, 
in which the magnitude of the pulse is 400 V and the delay time is approximately 1 ms.  The 
internal circuit of this generator is adapted from [34] as illustrated in Figure 2.5. 
            
                          (a)                                                                           (b) 
Figure 2.4 In-house made voltage-regulated 1 kV pulse generator (a) prototype (b) output pulse 
 
This circuit consists of two parts, pulse generator circuit and control circuit.  For the 
pulse generation part, when the PowerFET Q1 is in the off state, C1 is charged to a voltage +HV 
via R8, R9, R10, and D1.  If the PowerFET Q1 is turned on, the output of the circuit becomes 
?HV volts as the positive terminal of C1 is now grounded.  Then the capacitor C1 discharge to 
the output load through Q1 and R1 immediately.  For the control part, a 0/+5V signal on the 
input port operates the driver IC2 MAX 626, from which a 0/+12V signal is presented on the 
 
28 
 
gate of the PowerFET Q1, turning it off or bringing it into conductance.  In the circuit, C2, R5, 
R6, R7 form a snubber network to protect the PowerFET against voltage spikes and consume the 
remaining current when the PowerFET is turned off.  R11, R12, R13, and R14 consist of a 
resistor divider for the output voltage measuring, which is 1 mV/V.  The short circuit and 
overload protection is achieved based on R1.  When the output current increases, the gate-source 
voltage of the PowerFET decreases because of the increase of voltage drop on R2, increasing the 
on-resistance of the PowerFET.  In this circuit, the output peak current is limited to around 40 A.  
IC2 TC4426 is the PowerFET driver designed to convert TTL inputs (0/+5V) to higher voltage 
outputs (0/+12V) to drive the gate of the PowerFET.  IC1 4N25 is an optocoupler used to isolate 
the control circuit from the high voltage pulse circuit.  The TTL signal 0/+5V is achieved by 
common 555 Timer circuits.  The duty cycle and period of the timer circuits are determined by 
the time constants of the capacitor charging and discharging circuit.  In our design, two timer 
circuits are employed to generate continuous or single TTL pulse signals.  In continuous 
operation mode, we set the signal period of 7 s and duty cycle of 50% in order to let the capacitor 
fully charged to the desired high voltage level.  Figure 2.6, 2.7 and 2.8 are the results from 
LTSpice simulation.  The detailed list of the circuit file is described in Appendix A.  The spice 
models of IC2 TC4426 and MOSFET are downloaded from the manufactures? website.  Figure 
2.6 is the voltage waveform of control signal from Nodes 17, 22, and 27.  Figure 2.7 is the 
waveform of the output voltage when the output is open-circuited and the HV DC power supply 
is 400 V.  The simulation result, -400 V pulse and 1 ms delay time, is very consistent with our 
in-house made pulse generator as illustrated in Figure 2.3b.  Figure 2.8 is the output current 
waveform when the output is short-circuited.  With the protection from resistor R1, the current is 
clapped around 38 A.   
 
29 
 
 
Figure 2.5 High voltage pulse circuit [34] 
 
Figure 2.6 Waveform of control signal from Nodes 17, 22, and 27 
 
30 
 
 
Figure 2.7 Output voltage waveform from Spice simulation 
 
Figure 2.8 Short-circuited output current waveform from Spice simulation 
 
31 
 
 
2.3 Application: CNTs Initiated Hollow Cathode Discharge 
This voltage-regulated 1 kV pulse generator is employed to trigger the field emission of 
CNTs cold cathode, which can initiate hollow cathode discharge in helium.  It is a promising and 
practical trigger method for pseudospark switches.  Hollow cathode discharge is operating on the 
left-hand side of the well-know Paschen curve and the hold-off voltage is significantly high, 
which is suitable for the high voltage and high power switching applications.   
 
2.3.1 Experiments Setup 
The CNTs initiated hollow cathode discharge setup consists of four main parts, a plane 
anode, a hollow cathode, a trigger electrode, and the external circuit as illustrated in Figure 2.9.   
Figure 2.10 is a schematic of the experimental setup. The anode is a circular plate with a 
diameter of 1.8 cm while the cathode is in cylindrical shape with a hollow cavity.  A hole with a 
diameter of 2 cm machined on the cathode front surface which is placed opposite to the plate 
anode with a spacing of 3 mm.  Both of the cathode and anode electrodes are made from copper 
and well polished.  The trigger electrode holder is aluminum with CNTs attached on the top and 
is inserted into the hollow cathode cavity.  The whole electrodes setup is enclosed in an 8 cm 
long and 2 cm diameter quartz tube, serving as the vacuum chamber sustaining 10-6 Torr for 
several days. In addition, the anode is connected to an adjustable 35 kV DC power supply and 
the hollow cathode is grounded.  The trigger electrode is connected to a voltage-regulated 
negative pulse generator described in the previous section (see Figure 2.4a).  The maximum 
magnitude of the output pulse voltage is 1 kV.  In the experiment, helium is fed into the well-
sealed chamber and the operating pressure is kept from a few mTorr to 150 mTorr.   
 
32 
 
The acquisition system is consisted with oscilloscope, current probe, high voltage probe, 
and high speed camera.  The voltage between anode and hollow cathode and the pulse voltage 
between the trigger electrode and ground are monitored.  The first voltage is attenuated by 2000 
and the second one is attenuated by 1000 for oscilloscope measurements.  The current waveform 
is also recorded from a current probe.  The high-speed camera on the top of the chamber is 
installed to capture the plasma formation process of helium hollow cathode breakdown. 
Comprehensive discussion of this work is given in [26], and only a summary of the work 
outlined in the following section.  
 
Figure 2.9 Electrodes setup in CNTs initiated hollow cathode discharge [26] 
 
Figure 2.10 Schematic of the experimental setup  
 
33 
 
2.3.2 Experiment Results & Discussions 
Delay time is one of the most important parameters in terms of how efficiently the energy 
is transferred to the load by the high voltage and high power switches.  In this work, we will 
concentrate on the study of time delay under different trigger voltages and different CNTs 
samples.  From the static self-breakdown (hold-off voltage) test in [26], 100 mTorr is selected as 
the operating pressure and 12 kV is set as the hold-off voltage between the anode and hollow 
cathode in our delay time test.  At the fixed chamber pressure and hold-off voltage, several 
randomly oriented CNTs samples with different growth time are employed to initiate the hollow 
cathode breakdown.  The waveforms of the negative trigger pulse and hold-off voltage are 
recorded when the breakdown events occur.  Table 2.1 is a list of samples studied in our 
experiments.  Figure 2.11 is the image of CNTs initiated helium hollow cathode discharge with 
sample R-40.  Similar to the hold-off test, the plasma filled out the hollow cathode cavity and 
went through the cathode towards the anode immediately.  Figure 2.12 is the typical waveforms 
of hold-off voltage (top) and trigger pulse voltage (bottom) when breakdown event occurs.  The 
hold-off voltage drops in a few microseconds when the trigger pulse is applied.  The delay time 
is defined as the time difference between the initial drop points between the trigger and hold-off 
voltage.   
In our experiments, for a particular CNTs sample, five trigger pulse voltages, 200V, 400 
V, 600 V, 700 V, and 800V, are used to initiate the hollow cathode breakdown.  However, only 
the sample R-120 can initiate the breakdown at trigger pulse voltage of 200V.  Figure 2.13 shows 
the delay time as a function of trigger pulse voltage for different CNTs samples [26].  The delay 
time of different samples ranges from 2 to 10 microseconds.  It is clearly shown that the delay 
time decreases with the increasing trigger voltage for each sample.  It may be because as the 
 
34 
 
applied trigger pulse voltage becomes higher, more intense electron emission from the CNTs 
samples takes place which is able to initiate the hollow cathode discharge much faster.  From the 
figure, we could also see that the delay time becomes smaller when the growth time of the CNTs 
samples increases.  This is expected since compared to the CNTs samples with shorter growth 
time, the samples with longer growth time are much denser and longer and have much lower 
turn-on electric field, which is much easier for these CNTs samples to emit enough electrons in 
relatively shorter time and initiate the final breakdown.   
Table 2.1 CNTs sample list 
Samples Name Grow Time 
R-20 Randomly oriented CNTs with 20 min growth time 
R-40 Randomly oriented CNTs with 40 min growth time 
R-80 Randomly oriented CNTs with 80 min growth time 
R-120 Randomly oriented CNTs with 120 min growth time 
 
 
Figure 2.11 Image of CNTs initiated hollow cathode discharge with sample R-40 [26] 
 
 
35 
 
 
Figure 2.12 Typical hold-off voltage and trigger pulse waveforms when breakdown event occurs 
 
 
Figure 2.13 Delay time as a function of trigger voltage for different samples [26] 
 
36 
 
 
 
 
CHAPTER III 
SURFACE FLASHOVER IN PARTIAL VACUUM 
This chapter mainly describes the experiments on surface flashover in partial vacuum.  
The chapter is organized from the samples and electrodes preparation and experimental setup to 
experiment results and discussions.  Several experimental conditions influencing surface 
flashover are taken into consideration in this work. 
 
3.1 Samples Preparation & Electrode Geometries 
The samples except the control samples are produced by adding nanoscale Al2O3 or TiO2 
powder into the epoxy resin with specific weight ratios.  The epoxy resin is prepared by mixing 
the EPO-THIN resin (20-8140-032) and EPO-THIN hardener (20-8140-016) with 5:2 ratio first, 
then either Al2O3 or TiO2 dielectric particles (powder from Alfa Aesar) are added to the mixture 
and set to cure according to the manufacturers specification.  The aluminum-oxide (Al2O3) is 
99.98% pure with 850 to 1000 nm sized particles and the titanium dioxide (TiO2) is 99.9% pure 
with 32 nm sized particles.  The weight ratios between the powder and epoxy are 1:50 (2%) and 
1:16.6 (6%) separately.  For the control sample, no nano-particles are added into the epoxy resin.  
All of the mixtures are kept in the small cylindrical containers and cured at room temperature for 
24 hours.  The final samples are cut into 1-cm length and surfaces are machined.  Figure 3.1 
shows the preparation procedures of the nanodielectric samples.  The final samples are 
cylindrical shaped with the diameter of 3 cm and thickness of 1 cm.  In addition, in order to 
 
37 
 
study the surface effect on the surface flashover, the top surfaces of those samples used in the 
lateral electrode configuration test are machined as shown in Figure 3.2.  Table 3.1 is a list of all 
the samples prepared in our experiments. 
 
Figure 3.1 Nanodielectric samples preparation processes 
 
Figure 3.2 Schematic of surface machined samples  
Table 3.1 Nanodielectric samples list in the experiment 
Sample Name Nano-particle additives Weight ratio between additives  and epoxy resin 
* Total two 
samples for 
each (flat 
surface and 
textured 
surface) 
CS (Control Sample) N/A N/A 
S-A2 
Al2O3 
1:50 (2%) 
S-A6 1:16.6 (6%) 
S-T2 
TiO2 
1:50 (2%) 
S-T6 1:16.6 (6%) 
 
38 
 
 Two different kinds of electrode architectures are studied in this research; the sandwiched 
and the lateral as shown in Figure 3.3.  The sandwiched configuration is achieved by holding the 
samples firmly between two parallel plate electrodes and the lateral configuration is realized by 
placing a pair of electrodes on the surface of the samples.  For the sandwiched setup, although 
the sample thickness is 1 cm, the path across the two electrodes on the surface of the sample is 
1.6 cm.  Therefore, the electrode spacing for this configuration is 1.6 cm while the electrode 
spacing for the lateral configuration is 0.7 cm.  The electrodes for the sandwiched configuration 
are made of aluminum and for the lateral configuration they are copper.   
 
3.2 Experimental Setup 
 The test fixture (the electrodes and the sample) is placed in a high vacuum chamber and 
the electrodes are connected to an adjustable high voltage power supply (either DC or pulse 
generator).  For each sample, a DC applied field is used initially, and then a high frequency 
pulsed field is applied.  A pulsed high voltage source which can generate a unipolar square pulse 
train with frequencies from 15 kHz to 220 kHz with varying duty cycle is used for the high 
frequency tests.  The pulse generator is fed from a function generator and a high voltage DC 
power supply.  The magnitude, frequency, and duty cycle of the output pulses are adjusted 
according to the test sequence.  Nitrogen is selected as the working gas and the pressure in the 
chamber is varied from 100 mTorr to 900 mTorr or 3000 mTorr throughout the experiments.  
The current probe, oscilloscope, photomultiplier (PMT) and pico-ampere-meter are used as part 
of the data acquisition system as shown in Figure 3.4.  The high-speed camera on the top of the 
chamber is employed to capture the plasma formation process of surface flashover events.   
 
39 
 
 
(a) 
 
(b) 
Figure 3.3 Schematics of the electrodes setups (a) sandwiched; (b) lateral 
 
 
40 
 
 
Figure 3.4 The experimental setup employed in the surface flashover study 
 
3.3 Experimental Procedure 
Surface flashover voltage as a function of pressure (pressure sweep), as a function of 
frequency (frequency sweep), and as a function of duty cycle (duty cycle sweep) are recorded 
and plotted in sequence.  In the pressure sweep experiment, for each pressure data point a 
constant pressure value is set and a DC or 20 kHz unipolar square pulse voltage is applied by 
gradually increasing the voltage (approximate rate of 100 V/s) until a breakdown event occurred 
and the light emission from the breakdown triggered the data acquisition system with the 
assistance of the PMT.  For the pressure sweep experiments with the high frequency pulsed field, 
the frequency of the field is set to 20 kHz with 50% duty cycle, then the voltage is increased until 
a breakdown event occurred.  The waveforms of voltage, current and light intensity during the 
surface flashover are recorded.  Between three to five breakdown voltages are recorded for each 
 
41 
 
fixed pressure and then averaged to generate a data point for this particular pressure.  In this way, 
the surface breakdown voltage is obtained for the pressure range specified in the study.  For the 
frequency sweep experiments, the pressure value at which the breakdown voltage has a 
minimum is determined first then this value is set as the constant pressure.  Based on the pressure 
sweep data, we selected the fixed pressure to be 300 mTorr in the sandwiched configuration and 
900 mTorr in the lateral one.  In the frequency sweep experiment, we keep the pulse duty cycle 
to be 50%, but changed the frequency from 20 kHz to 220 kHz.  The same experimental 
procedures are used in this case also and the breakdown events are recorded for each particular 
frequency at this fixed pressure then plotted as a function of frequency.  For the duty cycle sweep 
test, all procedures are the same as frequency test except the frequency is fixed at 20 kHz and the 
duty cycle is varied from 10% to 90%.  The breakdown events are recorded for each particular 
pulse duty cycle at the predetermined fixed pressure then plotted as a function of duty cycle.  
Table 3.2 is a detailed list of the test conditions specified in different experiments. 
Table 3.2 Test conditions in surface flashover experiments 
Tests Configurations Pressure (mTorr) Frequency (kHz) Duty Cycle (%) 
Pressure 
Sweep 
Lateral 100 ~ 3,000 DC DC 20 50 
Sandwiched 100 ~ 900 DC DC 20  50 
Frequency 
Sweep 
Lateral 900 15 ~ 220 50 
Sandwiched 300 15 ~ 220 50 
Duty cycle 
Sweep 
Lateral 900 20 10 ~ 90 
Sandwiched 300 20 10 ~ 90 
 
3.4 Breakdown Voltage versus Pressure 
Figure 3.5 shows a representative voltage, current and light emission waveforms for a DC 
surface flashover event.  From this figure we clearly see the voltage drops with a sudden increase 
 
42 
 
of light intensity and current increases when the surface flashover occurs across the sample.  The 
surface breakdown voltage is defined as the point at which the voltage across the sample 
collapses as marked on the figure.  Figure 3.6 are the images of the fully developed plasma after 
a surface breakdown event for both the lateral and sandwiched electrode configurations.  The 
plasma bridges the anode and cathode across the surface of the sample.  Figure 3.7 shows the 
voltage, current and light emission data for pulsed applied field at 20 kHz frequency with 50% 
duty cycle.   
 
Figure 3.5 Voltage, light intensity and current waveforms of control sample with sandwiched 
electrode configuration during flashover at 500 mTorr under DC voltage 
 
Figure 3.6 Images of the fully developed plasma after a surface breakdown event 
 
43 
 
 
Figure 3.7 Voltage, light intensity and current waveforms of control sample with sandwiched 
electrode configuration during flashover at 500 mTorr under pulsed voltage 
 
3.4.1 DC Breakdown Voltage versus Pressure 
The breakdown voltages of different samples under varying pressure are collected and 
analyzed.  In the experiment of sandwiched setup, the pressure in the chamber was changed from 
100 mTorr to 900 mTorr with steps of 50 mTorr and several breakdown data for each pressure 
are recorded as described in Chapter 3.3.  For the lateral configuration, the pressure range was 
from 100 mTorr to 3,000 mTorr.   
Figure 3.8 shows the DC surface breakdown voltages of different samples as a function 
of the product of pressure and electrodes gap distance (pd).  As expected for all samples, the 
 
44 
 
breakdown curve resembles the well-known Paschen curve.  There is always a minimum surface 
breakdown voltage occurring in our tested pressure range.  This corresponds to an approximate 
pd value of 700-800 mTorr?cm for the sandwiched electrode configuration as shown in Figure 
3.8a.  The minimum DC surface breakdown voltage is approximately 525 V for the sandwiched 
configuration.  A representative curve showing the trend is included in the plot.   
It was observed that in the sandwiched electrode configuration, in some cases the 
breakdown occurred between the wires instead of across the electrodes over the sample.  
Although these data points are not included in the plot, there is little correlation between the 
surface breakdown data of loaded samples.  On the other hand it is clear that the surface 
breakdown of the control sample (with no loading) has the lowest value among all other samples.   
For the lateral electrode configuration, the surface breakdown voltage has the same trend 
as the sandwiched electrode configuration as shown in Figure 3.8b.  The minimum breakdown 
voltage corresponds to a pd value of approximately 600 to 700 mTorr?cm in this case.  This is 
about 100 mTorr-cm shift to the lower pressure range compared to the sandwiched electrode 
configuration.  The minimum DC surface breakdown voltage is approximately 535 V for the 
lateral configuration.   
In the lateral case, the breakdown voltage is more predictable in the lower pressure range 
than the sandwiched case.  Contrary to the sandwiched electrode configuration, the sample S-T6 
(the 6% TiO2 filled) has the lowest surface breakdown data.  Closer examination shows that at 
lower pressures, the breakdown data does not follow the expected shape.  Therefore, we 
speculate that there may be an experimental or instrumental irregularity with the data collection 
set.  Furthermore, the sample S-A6 (the 6% Al2O3 filled) has the highest surface breakdown 
characteristics only under sandwiched electrode configuration as seen in Figure 3.8a.   
 
45 
 
 
(a) 
 
(b) 
Figure 3.8 DC surface breakdown voltage vs.  (pd) for different samples (a) for the sandwiched 
electrode configuration (b) for the lateral electrode configuration 
 
46 
 
3.4.2 Pulsed Breakdown Voltage versus Pressure 
Similar to the dc experiments, the breakdown voltages of different samples under varying 
pressure and 20 kHz 50% duty cycle applied pulsed field are collected and analyzed.  Figure 3.9 
shows the pulsed surface breakdown voltages of different samples as a function of pd.  Similar to 
the dc data, the breakdown curves have a minimum breakdown voltage at a certain pd range 
occurring at around 450 mTorr?cm for sandwiched electrode configuration and 700 mTorr?cm 
for the lateral configuration.   
Furthermore, although the difference is small, the dc surface breakdown seems to be 
slightly higher than the pulsed case.  Figure 3.10 shows the surface breakdown curves of the 
control sample and S-T2 (the 2% TiO2 filled) sample under dc and pulsed applied fields.  It is 
clear that high frequency surface breakdown is relatively lower than the dc case for these 
samples.  This is in agreement with the literature data where the breakdown strength of 
dielectrics decrease as frequency of applied field is increased.  Similar observation is made for 
the other filled samples also; however, in general, the current data is relatively scattered and no a 
clear observation can be made at this time.   
In addition, with the limited data, the trend does not seem to be proportional to the 
loading percentage.  We expect that different loading ratios of nano-particles play a role on the 
electrical properties of these samples.  Specifically, there may be a different critical loading ratio 
for different nano-particles in improving the insulation properties of dielectric materials.  In our 
experiments, the samples S-T6 (the 6% TiO2 filled) performed better, with higher surface 
breakdown voltage compared to non-filled samples, whereas for the Al2O3 loaded samples, 2% 
seems to be an optimum loading ratio.  However, further studies are needed for explaining this 
critical loading ratio. 
 
47 
 
 
(a) 
 
(b) 
Figure 3.9 Pulsed surface breakdown voltage vs.  (pd) for different samples (a) for the 
sandwiched electrode configuration (b) for the lateral electrode configuration 
 
48 
 
 
(a) 
 
(b) 
Figure 3.10 Surface breakdown curves of the control sample and S-T2 sample under dc and 
pulsed applied fields 
 
49 
 
3.5 Electrode Configurations Effect on Breakdown Voltage 
We also observed some differences in surface breakdown voltages between the 
sandwiched and lateral electrode configuration.  As stated earlier, the electrode gaps are different 
for these two configurations.  Therefore, we plotted the surface breakdown voltages as a function 
of the product of the pressure and the gap distance (pd) to allow better understanding of the data.  
Figure 3.11 shows the comparison of the pulsed surface breakdown curves of the control and S-
T2 (the 2% TiO2 filled) samples for both the sandwiched and lateral configuration.  From Figure 
3.11a, we see that the minimum breakdown voltage corresponds to a pd value of 400 mTorr?cm 
and 800 mTorr?cm respectively.  The corresponding minimum surface breakdown value is 570 V 
for sandwiched configuration and 520 V for the lateral case.  On the other hand, we see relatively 
different behaviors for the pulsed surface breakdown voltage.  In this case, the surface 
breakdown voltage is substantially lower than sandwiched electrode configuration with pd 
minimum shift to higher values for the control sample.  Table 3.3 shows the differences of 
((pd),Vmin) between the sandwiched and lateral electrode configurations.  Normally a shift around 
100-300 mTorr?cm between two different configurations could be found.  Table 3.4 is a detailed 
surface breakdown voltage comparison between sandwiched & lateral electrode configurations at 
pd of 1200 and 300 mTorr?cm.  It clearly shows that at higher pd, the surface breakdown voltage 
in sandwiched configuration, whether DC or pulsed electric field, is significantly greater than 
that in lateral configuration.  The difference could even reach a couple of hundred volts.  With 
the pd decreasing, the difference between the surface breakdown voltages under two 
configurations becomes smaller, which is normally less than 50 V.  However, there is an 
exception for the sample S-A2 (the 2% Al2O3 filled) whose DC breakdown voltage under the 
sandwiched configuration is 30 V lower than the lateral case.   
 
50 
 
 
(a) 
 
(b) 
Fig 3.11 Pulsed surface breakdown curves for both the sandwiched and lateral configuration of 
(a) control sample (b) S-T2 sample 
 
51 
 
Table 3.3 ((pd),Vmin) comparison between sandwiched & lateral electrode configurations 
Samples dc pulse Sandwiched Lateral Sandwiched Lateral 
CS (650,525 V) (500, 540 V) (350, 570 V) (550, 514 V) 
S-A2 (400,535 V) (650, 550 V) (400, 570 V) (700, 565 V) 
S-A6 (450, 605 V) (650, 525 V) (500, 595 V) (500, 540 V) 
S-T2 (500, 555 V) (600, 525 V) (350, 580 V) (650, 500 V) 
S-T6 (470, 526 V) (550, 480 V) (400, 560 V) (500, 520 V) 
                                                                                           (Unit: pd - mTorr?cm) 
Table 3.4 Breakdown voltages comparison between sandwiched & lateral  
electrode configurations at pd of 1200 and 300 mTorr?cm 
Voltage 
Types Samples 
pd=1200 mTorr?cm pd=300 mTorr?cm 
Sandwiched Lateral ?Vb Sandwiched Lateral ?Vb 
dc 
CS 580 V 560 V 20 V 610 V 570 V 40 V 
S-A2 640 V 560 V 80 V 540 V 570 V -30 V 
S-A6 725 V 550 V 175 V 640 V 590 V 50 V 
S-T2 800 V 555 V 245 V 590 V 580 V 10 V 
S-T6 630 V 515 V 115 V 560 V 520 V 40 V 
pulse 
CS 700 V 540 V 160 V 570 V 540 V 30 V 
S-A2 635 V 590 V 45 V 585 V 575 V 10 V 
S-A6 705 V 565 V 140 V 605 V 560 V 45 V 
S-T2 740 V 525 V 215 V 580 V 555 V 25 V 
S-T6 720 V 540 V 180 V 570 V 530 V 40 V 
 
3.6 Breakdown Voltage versus Varying Pulse Parameters 
The pulsed surface breakdown is affected by the pulse parameters, such as pulse 
frequency and duty cycle.  In our experiment, unipolar pulsed electric field is employed, that is, 
the electric field between the electrodes varies between ?on? and ?off? state.  Therefore the 
electrical charges around the dielectrics and electrodes will be accelerated and drifting 
alternatively till the surface breakdown events occurred.  The period and duty cycle are two 
major parameters of pulses, determining the movements of the electrical charges in the 
 
52 
 
electrodes gap.  Therefore we also conducted experiments with varying frequency at fixed 
pressure and duty cycle and varying duty cycle at fixed pressure and frequency.  
 
3.6.1 Breakdown Voltage versus Frequency 
The surface breakdown voltages of the samples under varying pulse frequency are 
investigated in the experiment.  In order to see the frequency effects on breakdown voltages, we 
fixed the pressure in the chamber at 300 mTorr for sandwiched electrode configuration and 900 
mTorr for lateral configuration which are both approximately where the minimum breakdown 
occurs, and the pulse duty cycle to be 50%.  Then the pulse frequency is varied from 15 kHz to 
220 kHz and data is recorded as outlined in Chapter 3.3.  Appendix E are the plots for the surface 
flashover voltages of all samples as a function of pulse frequency.  Figure 3.12 is the typical 
surface breakdown voltage as a function of frequency for the sandwiched and lateral electrode 
configurations.  As seen, the surface breakdown voltage decreases at first and then maintains in a 
stable value as the frequency increases.  The voltage drop is around 100 V in the sandwiched 
electrode configuration and about 50 V in the lateral case.  This data is in agreement with the 
literature data where breakdown voltage of solids and gaseous media decrease as frequency 
increases [13].  We can speculate that for the surface flashover case under unipolar pulsed 
voltages, the relationship between breakdown voltage and pulse frequency is the same.  
Generally in high frequency ranges, more ionization collisions are caused by electrons, leading 
to the lower surface breakdown voltage.   
 
53 
 
 
(a) 
 
(b) 
Figure 3.12 Typical schematics of surface breakdown voltage as a function of frequency for  
(a) sandwiched (b) lateral configuration 
 
 
54 
 
3.6.2 Breakdown Voltage versus Duty Cycle 
The breakdown voltages of the samples under varying duty cycle are also measured.  In 
order to see the duty cycle effects on breakdown voltages, we fixed the pressure in the chamber 
at 300 mTorr for sandwiched electrode configuration and 900 mTorr for lateral configuration and 
pulse frequency of 20 kHz.  Then the pulse duty cycle is varied from 10% to 90% in a step of 10% 
and data is recorded as illustrated in Chapter 3.3.  Appendix F is the plots for the surface 
flashover voltages of the samples as a function of pulse duty cycle.  As seen, the variation of 
duty cycle plays a greater effect in the surface breakdown voltages for sandwiched configuration 
compared with lateral setup.  Meanwhile, the surface breakdown voltage for sandwiched 
configuration is generally higher than the lateral one.  However, it is hard to get a consistent 
conclusion on the effects of duty cycle played on the surface breakdown voltage because of the 
limited data points at this time.   
 
3.7 Surface Effect on Breakdown Voltage  
The surface effects on surface breakdown voltage are investigated.  The top surface of the 
samples are machined as describe in Chapter 3.1.  Lateral electrode configuration as shown in 
Figure 3.2a is employed in this study.  All of the experiment sets including the pressure sweep, 
frequency sweep, and duty cycle sweep are conducted.  The experimental procedure is the same 
as stated in Chapter 3.3.  Although the electrodes spacing is 0.7 cm, the discharge path across the 
surface of the sample in this case is approximately 0.9 cm because of the saw-shaped surface.  In 
order to observe the surface effect on the breakdown voltage, the surface breakdown voltage as a 
function of the product of the pressure and the gap distance (pd) is plotted.   
 
55 
 
Figure 3.13 shows the comparison of the surface breakdown curves for the untreated and 
machined surface under lateral electrode configuration.  It is clearly that the pd value at which 
the breakdown voltage reaches the minimum is about 500-600 mTorr?cm, demonstrating that the 
surface flashover occurred across the sample surface.  The minimum surface breakdown voltage 
for untreated surface is 540 V and 520 V for the machined surface in Figure 3.12 (a).  Table 3.5 
gives the specific differences of ((pd), Vmin) for the untreated surface samples and machined 
surface samples.  There is only a minor shift between the breakdown curves for the samples with 
different surface conditions, which is very consistent with the Paschen?s law.   
Furthermore, we also observed that the surface breakdown voltage for the untreated 
surface, whether DC or pulsed field, is generally higher than the machined surface except for the 
sample S-T6 (the 6% TiO2 filled).  Table 3.6 is the comparison of the breakdown voltages 
between the untreated and machined surface samples at pd of 1000 mTorr?cm and 400 mTorr?cm.  
The difference of the breakdown voltages ranges from 0 to 80 V.  However, it is expected since 
the machined surface is very coarse compared with the untreated surface and the electric field 
and ionization will be enhanced around the protrusions and voids, and the space charges may 
accumulate in the machined channels beyond the sample surface between the electrodes, both of 
which lead to the surface breakdown at lower voltage.   
Finally, as shown in Appendix F, the behavior of surface breakdown voltage as a function 
of frequency for untreated and machined surface samples is very similar.  The breakdown 
voltage decreases first and then maintains at a stable value in the higher frequency range.   
 
 
56 
 
  
(a) 
 
(b) 
Figure 3.13 Typical surface breakdown curves for untreated and machined surface of  
(a) control sample (b) S-A6 sample 
 
57 
 
Table 3.5 ((pd),Vmin) comparison between untreated and machined surface samples 
Samples dc pulse Untreated Machined Untreated Machined 
CS (500, 540 V) (600, 524 V) (550, 514 V) (650, 520 V) 
S-A2 (650, 550 V) (700, 532 V) (700, 565 V) (700, 464 V) 
S-A6 (650, 525 V) (700, 524 V) (500, 540 V) (600, 500 V) 
S-T2 (600, 525 V) (650, 530 V) (650, 500 V) (650, 504 V) 
S-T6 (550, 480 V) (650, 520 V) (500, 520 V) (600, 504 V) 
                                                                                           (Unit: pd - mTorr?cm) 
Table 3.6 Breakdown voltages comparison between untreated and machined  
surface samples at pd of 1000 and 400 mTorr?cm 
Voltage 
Types Samples 
pd=1000 mTorr?cm pd=400 mTorr?cm 
Untreated Machined ?Vb Untreated Machined ?Vb 
dc 
CS 560 V 540 V 20 V 547 V 528 V 19 V 
S-A2 554 V 515 V 39 V 564 V 528 V 36 V 
S-A6 540 V 526 V 14 V 562 V 544 V 18 V 
S-T2 555 V 540 V 15 V 556 V 540 V 16 V 
S-T6 505 V 525 V -20 V 492 V 540 V -48 V 
pulse 
CS 536 V 528 V 8 V 530 V 530 V 0 V 
S-A2 575 V 495 V 80 V 575 V 505 V 70 V 
S-A6 556 V 514 V 42 V 546 V 516 V 30 V 
S-T2 520 V 516 V 4 V 535 V 520 V 15 V 
S-T6 530 V 512 V 18 V 526 V 514 V 12 V 
 
3.8 Conclusions 
This study experimentally confirms that nanoscale powder additives play an effect on the 
surface flashover of the dielectrics in the partial vacuum of nitrogen gas under either DC or 
pulsed electric field.  For different samples, the DC and pulsed surface breakdown curves under 
different electrode architectures resemble the well-known Paschen curve.  Although the 
difference is small, the dc surface breakdown generally seems to be slightly higher than the 
pulsed case.  For different nano-particles, there might be a different critical loading ratio in 
improving the insulation properties of dielectric materials.   
 
58 
 
The surface breakdown voltage depends on the test electrode configurations.  In most 
cases, sandwiched electrode configuration exhibits better surface flashover characteristics than 
the lateral electrode configuration.  In the normalized surface flashover breakdown curves, there 
is usually a pd shift under sandwiched and lateral electrode architectures.   
Furthermore, the breakdown voltage is a function of the pulse frequency.  In all of the 
samples, the surface breakdown voltages decrease first and then are maintained in a stable value 
as the frequency increases.  For duty cycle sweep test, the variations in breakdown voltage for 
sandwiched configuration are greater than that for the lateral case.   
In addition, the surface condition of the dielectric samples also affects both the discharge 
path of surface flashover and the surface breakdown voltage.  The surface flashover always 
bridges the electrodes across the surface of the samples in partial vacuum environment.  
Meanwhile, as expected, because of the roughness of the machined surface, the breakdown 
voltage for theses samples is relatively lower than that for untreated surface samples.  All of the 
discoveries in this work shed light on the further understanding of the surface flashover 
phenomena in partial vacuum.   
  
 
59 
 
 
 
 
CHAPTER IV 
CONCLUSIONS 
 
In this theis, two major parts related to pulsed breakdown phenomena have been studied 
and presented, namely, pulse generators including an application, and surface flashover in partial 
vacuum under pulsed applied field.   
The voltage-regulated 1 kV pulse generator based on a simple RC circuit is designed and 
developed in the lab in order to trigger the CNTs cold cathode.  The pulse generator is capable of 
providing a maximum output of a negative 1kV pulse.  The simulation results including output 
voltage and delay time are a good match with those of in-house constructed pulse generator.  The 
CNTs initiated hollow cathode discharge is achieved with this pulse generator.  The negative 
pulse from the pulse generator applied to CNTs generated sufficient field emitted electrons to 
trigger a breakdown in plasma chamber. Finally the hollow cathode discharge in helium is 
initiated.  As it is a promising and practical trigger method for pseudospark switches, the delay 
time of the switch is investigated in our work.  Randomly oriented CNTs samples are proven to 
be a very good trigger material to initiate the hollow cathode breakdown in helium.  It has a very 
small delay time of several microseconds with relatively low trigger voltage levels of several 
hundred volts.  The delay time of the CNTs samples decreases with the trigger voltage 
increasing.  CNTs samples with longer growth time have relatively lower delay time in the 
experiments compared with samples with shorter growth time.  The excellent field emission 
 
60 
 
property and low turn-on electric field enable the CNTs samples to be an effective and efficient 
cold cathode trigger material.   
As the second part of this thesis work, an attempt was also made to better understand the 
surface flashover phenomena of nanodielctrics in partial vacuum.  Most of the experimental 
conditions including samples, electrode configurations, surface conditions, and applied pulse 
parameters are taken into consideration in our work.  This study confirms that nanoscale powder 
additives influence the surface flashover phenomena of the dielectrics in the partial vacuum of 
nitrogen gas under either DC or pulsed electric field.  The DC and pulsed surface breakdown 
curves under different electrode architectures for different samples resemble the well-known 
Paschen curve.  Although the difference is small, the dc surface breakdown normally seems to be 
slightly higher than the pulsed case.  Furthermore, the surface breakdown voltage greatly 
depends on the test electrode configurations.  In most cases, sandwiched electrode configuration 
exhibits better surface flashover characteristics than the lateral electrode configuration.  In the 
normalized surface flashover breakdown curves, there is usually a pd shift under sandwiched and 
lateral electrode architectures.  Moreover, the breakdown voltage is a function of the pulse 
frequency and pulse duty cycle. Finally, it is also observed that the surface condition of the 
dielectric samples affects both the discharge path of surface flashover and the surface breakdown 
voltage.  The surface flashover always bridges the electrodes across the surface of the samples in 
partial vacuum environment.  All of the discoveries in this work provide useful information on 
the further understanding of the surface flashover phenomena in partial vacuum.   
 
 
 
 
61 
 
 
 
 
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December 1, 1997.  
 
 
 
 
 
A-1 
 
 
 
 
Appendix A SPICE Listing for Pulse Generator Circuit 
 
 
The list of circuit file of the pulse generator for LTSpice simulation is attached as 
following. 
Netlist: 
* 1 kV Pulse Generator Design 
XIC1 16 0 22 0 15 4N25 
R16 16 17 200 
D2 0 16 1N4148 
R18 0 15 10MEG 
R17 26 22 5.6k 
C6 26 0 100n 
V1 17 0 PULSE(0 5 10m 1n 1n 20m) 
C4 26 0 4.7? 
C5 26 0 0.1? 
V2 26 0 12 
V3 0 24 5 
R8 1 6 2k 
R9 6 5 2k 
R10 5 4 2k 
R22 4 0 10meg 
V5 4 0 400 
R1 0 3 0.1 
C2 1 9 10n 
R5 9 8 33 
R6 8 7 33 
R7 7 0 33 
C9 1 Vout1 1? 
D1 Vout1 0 DMOD 
.MODEL DMOD D (IS=2.2E-15 BV=1000V TT=0) 
R2 Vout2 0 0.02 
R11 Vout1 10 330 
R12 10 11 330 
R13 11 12 330 
R14 12 0 2.2 
R3 Vout2 13 4.7k 
C3 13 0 22n 
RL Vout1 Vout2 1e11 
.model D D 
.lib C:\PROGRA~2\LTC\LTSPIC~1\lib\cmp\standard.dio 
XIC2 22 27 26 24 TC4426_I2D_B 
.SUBCKT TC4426_I2D_B 1 2 3 4 
* Input Impedance/Clamp 
 
A-2 
 
R1  4    1    100MEG 
C1  4    1    12.0P 
G3  3    1    TABLE { V(3, 1) } ((-770M,-1.00)(-700M,-10.0M)(-630M,-
1.00N)(0,0)(20.0,1.00N)) 
G4  1    4    TABLE { V(1, 4) } ((-5.94,-1.00)(-5.4,-10.0M)(-4.86,-
1.00N)(0,0)(20.0,1.00N)) 
* Threshold 
G11 0    30   TABLE { V(1, 11) } ( (-1m,10n)(0,0)(0.78,-.1)(1.25,-1)(2,-1) ) 
G12 0    30   TABLE {V(1,12)} ( (-2,1)(-1.2,1)(-0.6,.1)(0,0)(1,-10n)) 
G21 0    11   TABLE { V(3, 4) } 
((0,1.35)(4.00,1.35)(6.00,1.5)(10.0,1.48)(13.0,1.49)(16.0,1.5)) 
G22 0    12   TABLE { V(3, 4) } 
((0,1.35)(4.00,1.16)(6.00,1.25)(10.0,1.24)(13.0,1.24)(16.0,1.25)) 
R21 0    11   1 TC 504U  2.33U 
R22 0    12   1 TC 231U  -103N 
C30 30   0    1n   
* HL Circuit 
G31 0    31   TABLE { V(3, 4) } 
((0,146)(4.0,63.3)(6.00,43.4)(10.0,34.8)(14.0,32.6)(18.0,28.4)) 
R31 31   0    1 TC 1.93M  -1.89U 
G33 0    30   TABLE { V(31, 30) } ( (-1M,-10)(0,0)(1,10N) ) 
S31 31   30 31 30 SS31 
* LH Circuit 
G32 32   0    TABLE { V(3, 4) } 
((0,104)(4.0,36.8)(6.00,19.7)(10.0,12.1)(14.0,10.2)(18.0,9.5)) 
R32 0    32   1 TC 2.26M  2.88U 
G34 30   0    TABLE { V(30, 32) } ( (-1M,-10)(0,0)(1,10N) ) 
R30 32   30   1MEG   
* DRIVE 
G51 0    50   TABLE { V(30, 0) } ( (-5,-1U)(-3,-1U)(0,0)(6,1.00)(18,1.020) ) 
G52 50   0    TABLE { V(0, 30) } ( (-5,-1U)(-3,-1U)(0,0)(6,1.20)(18,1.220) ) 
R53 0    50   1   
G50 51   60   VALUE {V(50,0)*300M/(-700M+18/(V(3,4) + 1M))} 
R51 51    0   1   
G53  3    0   TABLE {V(51,0)} ((-100,100)(0,0)(1,1n))   
G54  0    4   TABLE {V(0,51)} ((-100,100)(0,0)(1,1n))   
R60 0    60   100MEG   
H67 0    69   V67 1 
V67 60   59   0V 
C60 561  60   200P 
R59 59   2    8.19 
L59 59   2    10.0N 
* Shoot-through adjustment 
VC60 56 0 0V 
RC60 56 561 1m 
H60 58 0 VC60 56 
G60P 0 3 TABLE { V(58, 0) } ((-1,-1u)(0,0)(25,10.0m)(40,0)) 
G60N 4 0 TABLE { V(0, 58) } ((-1,-1u)(0,0)(25,10.0m)(40,0)) 
* Source Output 
E67 67   0    TABLE { V(69, 0) } ( (-1.3,-1.3)(0,0)(1,2.00) ) 
G63 0    63   POLY(1) 3 4 22.9 -1.86 54.4M 
R63 0    63   1 TC 4.29M 11.7U 
E61 61   65   VALUE {V(67,0)*V(63,0)} 
V63 65   3    100U 
G61 61   60   TABLE { V(61, 60) } (-20.0M,-130)(-15.0M,-65.0)(-10.0M,-
13.0)(0,0)(10,1N)) 
* Sink Output 
 
A-3 
 
E68 68   0    TABLE { V(69, 0) }  ( (-1,-2.00)(0,0)(1.5,1.5) ) 
G64 0    64   POLY(1) 3 4 22.9 -1.86 54.4M 
R64 0    64   1 TC 4.29M 11.7U 
E62 62   66   VALUE {V(68,0)*V(64,0)} 
V64 66   4    100U 
G62 60   62   TABLE { V(60, 62) } (-20.0M,-150)(-15.0M,-75.0)(-10.0M,-
15.0)(0,0)(10,1N)) 
* Bias Current 
G55 0    55   TABLE { V(3, 4) } 
((0,0)(4.5,530U)(10.0,770U)(14.0,910U)(18.0,1.38M)) 
G56 3    4    55 0 1 
R55 55   0    1 TC  -1.53M -407N 
G57 0    57   TABLE { V(3, 4) } 
((0,0)(4.5,70.0U)(10.0,80.0U)(14.0,90.0U)(18.0,120U)) 
G58 3    4    57 0 1 
R57 57   0    1 TC  -1.53M -407N 
S59 55   0    1 0 SS59 
* Models 
.MODEL SS59 VSWITCH Roff=1m Ron=100Meg Voff=1.2V Von=1.5V 
.MODEL SS31 VSWITCH Roff=100MEG Ron=800 Voff=0.2V Von=0.1V 
.ENDS TC4426_I2D_B 
XMOS 1 27 3 102N21A 
.SUBCKT 102N21A   10 20 30 
*  TERMINALS:  D  G  S 
*  1000 Volt  21 Amp  0.52 ohm  N-Channel Power MOSFET 
*  REV.A  01-09-02 
M1   1  2  3  3  DMOS L=1U W=1U 
RON   5  6  0.3 
DON   6  2  D1 
ROF   5  7 .1 
DOF   2  7  D1 
D1CRS 2  8  D2 
D2CRS 1  8  D2 
CGS   2  3  5.5N 
RD    4  1  0.5 
DCOS  3  1  D3 
RDS   1  3  5.0MEG 
LS    3  30 .5N 
LD   10  4  1N 
LG   20  5  1N 
.MODEL DMOS NMOS (LEVEL=3 VTO=3.0 KP=3.8) 
.MODEL D1 D (IS=.5F CJO=1P BV=100 M=.5 VJ=.6 TT=1N) 
.MODEL D2 D (IS=.5F CJO=400P BV=1000 M=.4 VJ=.6 TT=400N RS=10M)  
.MODEL D3 D (IS=.5F CJO=900P BV=1000 M=.3 VJ=.4 TT=400N RS=10M) 
.ENDS 102N21A 
.lib 4N25.sub 
.tran 0 50m 0 1u 
.backanno 
.end
 
B-1 
 
 
 
 
Appendix B Surface Breakdown Voltages vs. Pressure (Sandwiched Electrode) 
 
 
Complete set of figures for every test set, the surface flashover breakdown voltages are plotted as 
the function of pressure for the sandwiched configuration.  For one test set plot, DC and unipolar 
pulse signal (20 kHz, 50% duty cycle) breakdown voltages are compared.   
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
B-2 
 
 
Figure B-1 
 
Figure B-2 
 
B-3 
 
 
Figure B-3 
 
Figure B-4 
 
B-4 
 
 
Figure B-5 
 
 
 
 
 
 
 
C-1 
 
 
 
 
Appendix C Surface Breakdown Voltages vs. Pressure (Lateral Electrode) 
 
 
Complete set of figures for every test set, the surface flashover breakdown voltages are plotted as 
the function of pressure for the untreated surface samples under the lateral configuration.  For 
one test set plot, DC and unipolar pulse signal (20 kHz, 50% duty cycle) breakdown voltages are 
compared.   
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
C-2 
 
 
 
Figure C-1 
 
Figure C-2 
 
C-3 
 
 
Figure C-3 
 
Figure C-4 
 
C-4 
 
 
Figure C-5 
 
 
 
 
 
D-1 
 
 
 
 
Appendix D Surface Breakdown Voltages vs. Pressure (Machined Samples) 
 
 
Complete set of figures for every test set, the surface flashover breakdown voltages are plotted as 
the function of pressure for the machined surface samples under the lateral configuration.  For 
one test set plot, DC and unipolar pulse signal (20 kHz, 50% duty cycle) breakdown voltages are 
compared.   
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
D-2 
 
 
Figure D-1 
 
Figure D-2 
 
D-3 
 
 
Figure D-3 
 
Figure D-4 
 
D-4 
 
 
Figure D-5 
 
 
 
E-1 
 
 
 
 
Appendix E Surface Breakdown Voltages vs. Frequency  
 
 
 
Complete set of figures for every test set, the surface flashover breakdown voltages are plotted as 
the function of frequency under different electrode configurations and surface conditions.  In all 
of the tests, the duty cycle of the unipolar pulse signal is set at 50%.  Figure E-1 is the 
corresponding plot under sandwiched configuration at 300 mTorr.  Figure E-2 is the 
corresponding plot for the untreated surface samples under the lateral configuration at 900 mTorr.  
Figure E-3 is the corresponding plot for the machined surface samples under the lateral 
configuration at 800 mTorr.  
 
 
 
 
 
 
 
 
E-2 
 
Figu
re 
E-
1 
 
 
E-3 
 
Figu
re 
E-
2 
 
 
E-4 
 
Figu
re 
E-
3 
 
 
F-1 
 
 
 
 
Appendix F Surface Breakdown Voltages vs. Duty Cycle 
 
 
Complete set of figures for every test set, the surface flashover breakdown voltages are plotted as 
the function of frequency under different electrode configurations and surface conditions.  In all 
of the tests, the frequency of the unipolar pulse signal is 20 kHz.  Figure F-1 is the corresponding 
plot under sandwiched configuration at 300 mTorr.  Figure F-2 is the corresponding plot for the 
untreated surface samples under the lateral configuration at 900 mTorr.  Figure F-3 is the 
corresponding plot for the machined surface samples under the lateral configuration at 800 
mTorr.  
 
 
 
 
 
 
 
 
 
 
 
 
F-2 
 
Figu
re 
F-
1 
 
 
F-3 
 
Figu
re 
F-
2 
 
 
F-4 
 
 
Figu
re 
F-
3