Ministry of Higher Education and Scientific Research University of Technology Laser and Optoelectronics Engineering Department

Republic of Iraq Ministry of Higher Education and Scientific Research University of Technology Laser and Optoelectronics Engineering Department

DESIGN AND IMPLEMENTATION OF MARX GENERATOR FOR LASER APPLICATIONS

A Thesis Submitted to The Laser and Optoelectronics Engineering Department, University of Technology in Partial Fulfillment of the Requirements for the Degree of Master of Science in Laser Engineering

By Eng. Sarmad Fawzi Hamza

B. Sc. Electrical and Electronic Eng. / Laser Eng. 2003

Supervised by Dr. Naseer Mahdi Hadi Dr. Kadhim Abid Hubeatir

February 2008 A. D. Safer 1429 A. H.

جمھورية العراق وزارة التعليم العالي والبحث العلمي الجامعة التكنولوجية قسم ھندسة الليزر والبصريات االلكترونية

ﺘﺼﻤﻴﻡ ﻭﺒﻨﺎﺀ ﻤﺠﻬﺯﻤﺎﺭﻜﺱ ﻟﺘﻁﺒﻴﻘﺎﺕ ﺍﻟﻠﻴﺯﺭ

رسالة مقدمة إلى قسـم ھندسـة الليـزر والبصـريات االلكترونيـة الجامعة التكنـولوجيـة كجزء من متطلبات نيل درجة الماجستير علوم في ھندسة الليزر

تقدم بھا المھندس

سرمد فوزي حمزة

الھندسة الكھربائية واأللكترونية / ھندسة الليزر2003 بإشراف د. نصير مھدي ھادي د. كاظم عبد حبيتر

شباط 2008 م صفر 1429ھ الخالصة

إن منظومات الليزر الغازية ذات عرض نبضة خرج قصير . وقمة . طاقة عالية تحتاج إلى نبضات تفريغ كھربائي بمواصفات خاصة مثل محاثة واطئة, معدل تكرارية للنبضة وزمن نھوض سريع . وان مجھز قدرة نوع ماركس واطئ المحاثة ممكن أن يوفر ھذا النوع من نبضات التفريغ لتشغيل الليزرات الغازية بكامل مواصفاتھا . تم تصميم وبناء وتشغيل نوعين من مجھز قدرة ماركس . األول مجھز قدرة ماركس ذو ثمانية مراحل تضخيم يمكن أن يوفر فولتية خرج لغاية 64 كيلو فولت كحد أقصى . تم شحن فولتية أولية 2 كيلو فولت وحصلنا على فولتية خرج فعلية 12 كيلو فولت بنبضة ذات زمن نھوض 666 666 نانوثانية ومحاثة 11 مايكرو ھنري وكفاءته %75 , أما المجھز الثاني فكان مجھز قدرة ماركس ذو عشرة مراحل تضخيم ممكن أن يوفر 400 كيلو فولت كحد أقصى , تم شحنه بفولتية أولية 4 كيلو فولت وحصلنا على فولتية خرج فعلية بحدود 38 كيلو فولت بنبضة ذات زمن نھوض 50 نانوثانية ومحاثة 4.2 مايكرو ھنري وكفاءته 95% . تم تصميم نوعين من دوائر القدح لنوعي مجھز ماركس , األولى , دائرة قدح باستخدام مصباح وميضي مع محولة قدح لمجھز ماركس ذو ثمانية مراحل والثانية باستخدام محولة قدح (ملف إشعال) مع دائرة ترانزستور نوع (MOSFET) لمجھز ماركس ذو عشرة مراحل . . تم الحصول على نبضة فولتية من دائرة المصباح الوميضي حوالي 4.5 كيلو فولت وعرض نبضة حوالي 2 مايكروثانية , بينما دائرة القدح الثانية حوالي 7.5 كيلو فولت وعرض نبضة حوالي 40 مايكرو ثانية . II

Abstract

Gas laser systems with high peak power and short pulse duration requires special properties of high voltage discharge pulses; i.e. low inductance, high pulse repetition rate and fast rise time. Low inductance Marx generator power supply can offer this kind of discharge pulses for the gas lasers optimum operation. Two types of Marx generators have been designed, built and tested. The first Marx generator with eight stages, can deliver 64 kV maximum output, is charged up to 2 kV and the high voltage output was 12 kV with pulse rise time of 666 ns and inductance 11 µH and efficiency of 75% . The second Marx generator with ten stages, can deliver 400 kV maximum output, is charged up to 4kV and the high voltage output is 38 kV with pulse rise time 50 ns, inductance 4.2 µH and efficiency of 95%. Many types of trigger circuits have been designed and implemented for triggering of two Marx generator systems. The first trigger is built circuit using Xenon flash lamp with a trigger transformer. The second trigger has been built using automobile ignition coil as a trigger transformer with a MOSFET driver .The Xenon flash trigger circuit of high voltage output pulse (4.5 kV) and pulse width of 2µs while the automobile ignition coil high voltage output pulse is 7.5 kV and pulse width of 40 µs.

Appendices

APPENDIX (A)

no+ n+ = total electrons from cathode . αd Electron Multiplication equation. a = 0enn

αd ………… ……………………………………….(1) oa += + )( ennn

n …………………………………………… . ..(2) nnn )( =+− + oa + γ where γ : cathode yield in electrons per incident ion.

αd oa + o + o +−+=+− nnennnnn + )()()(

n n + = a eαd − )1( γ eαd

en α d n = a ……………………………..………………….(3) a γ e α d − )1( from eq.(2):

n + oa )( nnn + +=− γ ⎡ 1 + γ ⎤ ( a o ) =− nnn + ⎢ ⎥ ⎣ γ ⎦

γ − nn (oa ) ………………………………………...……..….(4) ∴n+ = 1+ γ substitute eq.(4)to eq.(3): αd ()− oa enn na = ()1 γ ()eαd −+ 1

en αd en αd o = a − n ()1 γ ()e αd −+ ()11 γ ()e αd −+ 1 a

αd αd αd o a a ()1 γ (enenen −+−= 1)

αd αd αd αd o a a −+−= aa γ (ennenenen − 1)

Appendices

e αd = nn oa 1 γ ()e αd −− 1

e αd = II oa 1 γ ()e αd −− 1

Appendices

APPENDIX (B)

L1 G R1

1 C1 R2 C2

Circuit arrangement

1/C s Ls V(s) 1 1 R1

R2 V/s V/s 1/C2s

Transform circuit

V z sV = .)( 2 s + zz 21 Where;

1 Z1 ++= RsL 11 1sC

1 R * 2 sC Z = 2 2 1 R2 + 2 sC

Appendices

V 22 sCR +1. sV = .)( s R2 1 +++ RsL 11 +1. sCsCR 22 1

V 22 sCR +1. sV = .)( 2 s 12 22 +++ 11 22 ++ 2211 sCRsCRsCRsCLsCRsCR + )1()1(.1

22 + )1( 1sCsCR

V = C2 1 3 2 L1 2 R1 ss 21 sCLs 21 ++++++ sCRs CRC 121 R2 R2

1 = V. 23 ⎡ 1 R1 ⎤ ⎡⎡ 1 R1 1 ⎤⎤ 1 + DD ⎢ + ⎥ + D⎢⎢ ++ ⎥⎥ + ⎣ RC 22 L1 ⎦ ⎣⎣ CL 11 21221 ⎦⎦ LRCCCLRCL 1221

Appendices

APPENDEX (C)

− α 1t − ee − α 2 t = EV T ()− αα 122

Differential equation for found maximum time:

−α t E −α 2t 1 0 = []2 _ αα 1ee T − αα 122 )(

− α 2 t − α 1 t α 2 e = α 1 e

− α 2 t − α 1 t ln( α 2 e = ln() α 1 e )

ln α − α 22 t = ln α − α 11 t

α 2 )ln( α 1 t .max = ( 2 − αα 1 )

Appendices

APPENDIX (D)

1 = V. 23 ⎡ 1 R1 ⎤ ⎡ 1 R1 1 ⎤ 1 + DD ⎢ + ⎥ D⎢ +++ ⎥ + ⎣ RC 22 L1 ⎦ ⎣ CL 11 21221 ⎦ LCCRCLRCL 1122

1 V(s) = V. 3 2 ⎡ L1 ⎤ ⎡⎡ 1 R1 ⎤⎤ 11 1 + DLD ⎢ + 1 ⎥ DR ⎢⎢ +++ ⎥⎥ + ⎣ RC 22 ⎦ ⎣⎣C1 222 ⎦⎦ RCCCRC 221

Where inductance L1=zero, D =s

1 = V. 2 1 R1 1 1 1 sRs ( ) ++++ C1 RCCCRC 221122

1 R 1 ++ CRCRCR R ( 1 ++ () 121122 2 − 4) 1 C CRC m RCC RCC s −= 1 122 212 212 2R1

Therefore

RC 12 ++ CRCRCR RC ( 22 11 12 −± [411){ 21 ]} RCC C R 212 ( 2 1 ++ )1 2 C R s = − 1 2 2 R 1

RC 12 C R RC ( 2 1 −±++− 411){1 21 } C R C R 1 2 ( 2 1 ++ )1 2 C1 R2 S 2,1 = 2 CR 21

Where s is α

Appendices

APPENDIX (E)

s 1/C1s Ls R V(s) =Vo

Vi/s 1/C2s

1 V sC , V = i 2 ° 11 111 4L s LsR +++ where: += , R = 12 sCsC CCC 21 C

1 CV = i Cs C 2 1 2 LsRs ++ sC

CV 1 + LssR 2 i [ −= ] sC 2 1 2 ( LsRss ++ ) C

R R 2 s + s 2 = C 4 Rs R 2 1 s( s 2 ++ ) C 4 C 2

4 s + = RC 2 (s + ) 2 CR

A B ⇒ + 2 ⎛ 2 ⎞ ⎛ 2 ⎞ ⎜ s + ⎟ ⎜ s + ⎟ ⎝ RC ⎠ ⎝ RC ⎠

Appendices

A = 1 4 2 s s ++=+ B RC RC

2 B = RC

i CV 1 A B V° [ −= ( + )] sC 2 2 2 2 s + (s + ) RC RC

2 2 t − t − i CV 2 t = − (1[ e RC + e RC )] C 2 RC

2 − t i CV 2 RC = 1(1[ +− et ]) C 2 RC

Appendices

Appendix (F)

When L =zero

1/C1s R

1/C2s Vi/s

1 Vi 2 sC Vo ×= s R ++ 11 1 2 sCsC

1 V sC = i × 2 s R + 1 Cs

1 2 sRC =Vi × s + 1 CR

1 V C = i × CRs C s + 1 2 CR

⎡⎛ 1 ⎞ ⎤ ⎜ ⎟ +1 CV ⎢ CRs 1 ⎥ i ⎢⎝ ⎠ − ⎥ = C 1 1 2 ⎢ s + s + ⎥ ⎢ CR ⎥ ⎣ CR ⎦

CV ⎡ 11 ⎤ = i ⎢ − ⎥ ⎢sC s + 1 ⎥ 2 ⎣ CR ⎦

⎡ −t ⎤ iCV CR = ⎢1− e ⎥ C2 ⎣ ⎦

Appendices

Appendix (G)

G 2 = B − VVV G

G −= VV

G B += VVV

⎡ ⎤ ⎢ + CC 31 ⎥ V = V ⎢ ⎥ BH ⎣ ++ CCC 321 ⎦

⎡ + CC 31 ⎤ G 2 = VV ⎢ ⎥ + V ⎣ 1 2 ++ CCC 3 ⎦

⎡ ⎤ 1 + CC 3 VV ⎢1 += ⎥ ++ CCC 3 ⎣⎢ 1 2 ⎦⎥

Chapter One General Introduction 1

Chapter One General Introduction

1.1 Marx Generator Power Supply: A Marx Generator is a clever way of charging a number of capacitors in parallel, then discharging them in series. Originally it was described by Erwin Marx in 1924. Marx generators offer a common way of generating high voltage impulses that are higher than the available supply charging voltage. Discharge capacitors can also be kept at relatively lower voltages, usually less then 200 kV, to avoid bulky and very expensive capacitors as well as engineering problems associated with extremely high DC voltages. A charging circuit diagram of simple 3-stage Marx generator during charging state is shown in figure (1-1). When the charging voltage is applied to the system, each stage capacitor is eventually charged to the same applied voltage through the charging resistors [1].

Fig. (1-1) Simple Marx generator charging circuit [2].

With fully charged of the system (capacitors), either the lowest gap is allowed to breakdown from overvoltage or it is triggered by an external source, if the gap spacing is greater than the charging voltage breakdown spacing. The erected capacitance, a common specification, is the stage Chapter One General Introduction 2

capacitance divided by N-stages. After (erecting) the Marx bank, the capacitors are momentarily switched to a series configuration refer to figure (1-2). This allows the Marx to produce a voltage pulse that is theoretically N-stages times the charging voltage. The output switches in figure (1-1) and figure (1-2) are used to isolate the load while the Marx is charging, and to insure full Marx erection before the energy is transferred to the load [1].

Fig. (1-2) Simple Marx generator discharging circuit [2]. Chapter One General Introduction 3

Charging resistors are chosen to provide a typical charging time constant of several seconds. The charging resistors also provide a current path to keep the arc in the spark gaps alive. The discharge through the charging resistors sets an upper bound on the impulse fall time, although the impulse fall time is set by external resistors in parallel with the load or the load itself. If the gaps in the Marx generator don't fire at exactly the same time, the leading edge of the impulse will have steps and glitches as the gaps fire. These delays also result in an overall longer rise time for the impulse [1]. Jitter is the variation of time delay between shots given similar electrical stimulus. If the jitter in the gaps is reduced, the overall performance is improved. The traditional Marx generator operating in air has all gaps in a line with the electrodes operating horizontally opposed. This allows the Ultra Violet (UV) from bottom gap to irradiate the upper gaps, and due to photoelectric effects, reducing the jitter [1]. Various Marx generator designs are available in the open literature. A selection are shown in table (1-1). Table (1-1) shows a selection of these generators, also the specification of these generators as, the designer and year of production, maximum voltage, relative size, storage energy, rep- rate frequency of the system, and the load. Some basic analysis of the energy density (J/kg) is conducted with the resulting graph of the design for each generator shown in figure (1-3). The weights of the systems are approximated using a density of 1000 kg/m3 if the weight is not given. The graph shows a large range of energy density for the various designs mainly due to the diverse overall sizes and the uses for each system by using Excel programer. However, the graph separates systems that marking the repetitive systems.

Chapter One General Introduction 4

Table (1-1) Comparison of Various Marx Generators

V Joules Rep- Author/Year max size(m3) Load (Ω) (J) rate(Hz) (kV) M.T. Buttram 1988 [3] 440 0.634× 10-3 6000 1-10 10 Ω soap water

J. D. Sethian 1989 [4] 840 7. 56× 10+1 350000 No 100 nH pinch load Yu.A.Kotov 1995 [5] 200 9. 82 ×10-2 25 50 100 J. Hammon 1997 [6] 1000 1. 58× 10-1 62. 5 10 800 F. E. Peterkin 1999 [7] 1000 2. 9× 10-2 80 20 100 A. J. Dragt 2001 [8] 400 3. 22× 10-3 40 1 100 M.B.Lara,et.al.2005[9] 40 0.0135 33 200 50 -2 Laura K.Heffernan 2005 [10] 1000 12. 82 × 10 7200 No 300 Ω dummy load Kirk Slenes, et.al. 2006 [11] 500 0.4823 150 10 50 J.R.Mayes, et.al. 2006 [12] 40 3.37×10-2 100 100 267 nH Jong-Hyun Kim,et.al 2007[13 120 0.59796 10800 1000 1000

10 J/Kg 5

1988 1989 1995 1997 1999 2001 2005 .2005 2006 2006 2007 n t m n etl . im a ian o rag yes ttr Kotov D ra K u eth . eterki . a etl B S .A J L s .Ma . . amm . P . effernan . R yun T D Y H A .H .B . -H . . . . E J M J J K M F ong J Kirk Slene Laura Autho r and ye ars

Fig. (1.3) The ratio J/kg of various Marx designs.

Recent work with compact Marx generators is moving this technology from the traditional energy storage, pulse charging supply to a Chapter One General Introduction 5

direct microwave generation device. With voltage pulse rise times decreasing down to hundreds of picoseconds and peak powers reaching several gigawatts, these compact generators are finding their niche [14]. Typical applications of the Marx generator have been used with pulse charging circuits. In essence, the generator is used as an energy storage element, at relatively low voltages, and when fired, the pulse charges the transmission line to a high voltage. Typical applications are seen in high power microwave and accelerators. Generators in this role tend to be large, as well as slow devices. Smaller versions of the Marx generator have filled the role of trigger generator for larger systems. These generators are typically characterized by their low pulse energies with several hundreds of kV. The main attraction to these pulses lies in their rise time and compact geometry [2]. Improvements have made Marx generator an essential part of todays pulsed power systems. Their capabilities have been improved dramatically by developments in Marx circuit that allow low prefire rates and low –jitter triggering. These improvements, which are the main subject of this chapter, allow for construction and reliable operation of large, multimodule, synchronized Marx systems [15].

1.2 Spark Gaps: The spark gap is a conceptually simple device. It consists of two electrodes separated by an insulating material. The insulating material may be a gas, liquid, or solid, but a gas is the most commonly used material. So this research will consider only gas-filled spark gaps. A voltage is applied across the spark gap, lower than the breakdown voltage for the gas. Then a trigger pulse is applied and the gas breaks down. The trigger often consists simply of applying a momentary over voltage between the electrodes. Then the gas breaks down and a current flows across the gap. Chapter One General Introduction 6

The required breakdown voltage depends on the nature of the gas, its pressure, the shape and separation of the electrodes. For plane electrodes spaced one centimeter apart with gas pressure of one atmosphere, the breakdown voltage is 1.3 kV for neon, 3.4 kV for argon, 12 kV for hydrogen, 22.8 kV for nitrogen and 23 kV for air. These values are reduced for pointed electrodes [16].

1.3 Trigger Circuits: External triggering uses a high voltage trigger pulse to create a thin ionized streamer between the anode and cathode within the spark gap. Ionization starts when gas adjacent to the gap is excited by the voltage gradient induced by the high voltage pulse from the trigger device. The trigger pulse width is important because a finite amount of time is required for the ionized streamer to propagate down the space of the spark gap. The trigger rise time has a decisive effect on the commutation time of the tube; fast rising pulses of high peak amplitudes cause the device ( spark gap, krytron or thyratron) to break down in a shorter time due to the over voltage function. Three major driver features will strongly affect the switching performance [17]. They are (1) trigger jitter (2) trigger output delay time and (3) trigger rise time. Where; Delay time: is the time taken between the application of a trigger pulse and the commencement of conduction between the primary electrodes. Jitter time: is the variation of time delay between shots which gives similar electrical stimulus [18]. Four types of trigger circuits have been used in triggering the discharge circuit as illustrated bellow [17]:

Chapter One General Introduction 7

1.3.1 Switching By Using Thyristor Trigger Circuit: The circuit consists of a trigger transformer with a capacitor and a Silicon Control Rectifier (SCR) (Thyristor) in the primary. When the capacitor is charged, a high voltage is generated at the secondary which breaks down the switch as shown in figure (1-4) [17].

Fig. (1-4) Thyristor trigger diagram [17].

1.3.2 Switching Using Krytron Trigger Circuit: In this circuit a Krytron type KRP-20 (Krytron Pac; A Krytron have been associated with trigger transformer into one miniature package, from EG&G). Figure (1-5) shows the Krytron circuit diagram, the Krytron will be triggered by the SCR (Thyristor) when it is discharging the capacitor CGS into the grid making the Krytron in the on case, this will discharge the capacitor CPS into the trigger, the thyratron or the spark gap [18] as shown in Figure (1-5). Chapter One General Introduction 8

Fig. (1-5) Krytron circuit diagram [17].

1.3.3 Switching By Using Thyratron Trigger Circuit:

The major requirements of the thyratron circuit are to deliver high quality trigger pulse with adequate voltage and current to turn on the switch (thyratron or spark gap). To meet these requirements, selection of fast switching to trigger the thyratron must be done. The circuit diagram is shown in Figure (1-6) [17]. The Thyratron is triggered by two ways; first by using Thyristor and pulse transformer as in figure (1-4) and second by using krytron and pulse transformer as in figure (1-5).

Fig. (1-6) Schematic diagram for thyratron trigger diagram [17].

Chapter One General Introduction 9

1.3.4 Switching by using Commercial Trigger Module: Instead of the three trigger circuits, there is a commercial trigger module type (TM-11A, EG&G) which have been used. It is a compact versatile laboratory instruments designed to produce a high voltage trigger pulse of fast rise time. It provides a trigger pulse of 30 kV that can be utilized for initiating commutation in trigger spark gaps and to provide an ignition type pulse for fast triggering. A control voltage provides variable output pulse from 20 kV to 30 kV; figure (1-7) shows the trigger module. The output voltage pulse rise time is about 70 ns [17].

Fig. (1-7) EG&G trigger circuit module [17].

Chapter One General Introduction 10

1.4 Gas Laser Discharge: The power supplies for continuous-wave gas lasers are similar in design to those used in direct-current power supplies. Gas laser power supplies tend to be current-limited regulated DC power supplies. The designs are basically the same for all gas-discharge devices. The details depend on the particular voltage-current characteristics of the gas and the configuration of the laser. Three essential elements are used in the design of all gas laser power supplies these are the starter or ignition circuit, the operating supply and a current-limiting element. Many gas lasers such as

CO2, metal vapor, and excimer are operated in a pulsed mode. These lasers pose great problems in power-supply design because the impedance of the gas is changing rapidly during the laser pulse [16].

1.4.1 Electrical Characteristics of Gas Discharge: In pulsed lasers, the impedance of the gas is changing over a very large range. As the gas breaks down and begins to conduct, the impedance drops rapidly. This makes the design of power supplies difficult. It becomes hard to control the current rapidly enough. This section explains power supply requirements for several types of gas lasers, beginning with the common He-Ne laser, and also describing power supplies for carbon dioxide lasers, metal vapor lasers and excimer lasers. Most gas lasers are pumped by an electrical discharge that flows through the gas mixture between electrodes. Collisions between electrons in the electric discharge and the molecules in the gas transfer energy from the electrons to the energy levels of the molecules. In this process, the upper levels of the laser transition become populated. To describe the requirements of the power supplies needed to drive the gas discharge, the present study begins with a discussion of the nature of the discharge and its initiation [16]. Chapter One General Introduction 11

Electrical discharge in gases is characterized by current-voltage characteristics as shown in Figure (1-8). The exact characteristics of course, depend on the nature of the gas, its pressure, length and diameter of the discharge. At low values of applied voltage to the gas, there is no current flow. As the voltage is increased, the current remains essentially zero until some relatively high voltage is reached. This is denoted as point (A) in the figure. At this point a very small current begins to flow because of a small amount of ionization that is always present. This small amount of ionization is provided by the presence of natural radioactivity and cosmic rays. The small current is referred to as the pre-breakdown current. The value of the current in this region may be a few nanoamperes.

Fig. (1- 8) Relation between current-voltage and gas discharge [16].

The pre-breakdown current increases slowly until a point called the breakdown voltage is reached point B in the figure (1-8). This is the value at which a large number of gas molecules become ionized. The conductivity of the gas is increased and the electrons are accelerated to velocities at which they can transfer enough energy to ionize more molecules through collisions. Thus as the current increases, the resistance of the gas decreases and the voltage required to sustain the discharge Chapter One General Introduction 12

actually decreases with increasing current (region C in the figure). This condition called negative resistance. It is the behavior that would be predicted by Ohm’s law with a value of resistance less than zero. The current would continue to increase, through region D (amperes) to thousands of amperes (region E), with less and less voltage required to sustain it. Figure (1-8) shows ranges of current, from nanoamperes to kiloamperes, along the abscissa. Devices operating at various valves of current are indicated above the curve. The requirements for power supplies for gas lasers will be derive from the characteristics curve in Figure (1-8).The exact design for a particular gas laser power supply will depend on the specific current- voltage curve for the gas mixture that is being excited, but three essential elements for any gas laser power supply are [16]: i. A starter circuit. This portion of the power supply provides an initial voltage pulse. The peak value of the voltage pulse must exceed the breakdown voltage of the gas. The pulse drives the gas past point B i.e. reach region C. ii. Operating supply. This part of the power supply provides a steady current flow through the gas mix, after the gas has reached region C. It must operate at the appropriate voltage and current levels to sustain the current in the particular gas. iii. Current limiter. This limits the current through the gas to a desired value and prohibits the unbounded increase of current. It usually takes the form of a ballast resistor in series with the discharge. The characteristics of the gas discharge as shown in Figure (1-8) lead to challenges in the design of power supplies to drive gas lasers. It becomes difficult to control the voltage across the gas because the voltage depends on the current after the discharge begins [16].

Chapter One General Introduction 13

1.5 Aim of the Work: The aim of this project is to design and implement a pulsed power supply type Marx generator with its triggering circuits, which is suitable for pumping gas lasers and also to achieve the following characteristics: 1- Fast discharge pulse durations ns to µs. 2- Pulse rise time of few ns. 3- High discharge voltage about 40 kV DC. 4 - Output energy of Marx generator is suitable for any application.

Chapter Two Theoretical Concepts 14

Chapter Two Theoretical Concepts 2.1 Gas Breakdown: The details of gas-insulated gaps depend strongly upon the breakdown mechanisms of the gas involved. There are typically two stages, avalanche and streamer formation, although a thorough analysis includes more complex stages. J.S. Townsend (Electricity in Gases, 1914) did the basic work in this area. A sidelight to his work was the discovery of cosmic rays in order to account for the observed condition in gases. When an electric field exists in a gaseous medium, a small current will be observed due to available free electrons resulting from ionizing radiation. As the field is increased, electrons begin to acquire enough energy between collisions with gas molecules to produce secondary ionization upon impact [19], as shows in figure (2-1).

Fig. (2-1) Discharge characteristic in Townsend region [20].

Chapter Two Theoretical Concepts 15

Townsend defined α as the number of ionizing collisions per centimeter in the field direction produced by a single initiating electron [15]. Thus leads to [20]:

αd = oa enn ………………………………………………………..... (2.1) as the description of the current reaching the anode. As the field is further increased, a second mechanism takes effect; generation of electrons at the cathode due to positive ion bombardment. This has a coefficient that relates ion current to electron generation. When this term added to the upper relation [19], then we get: [21] [Appendix A] e α d = II ………..……………………….……………… (2.2) 0 1 γ (e α d −− 1) when n related to I by taking into account the electronic charge of each electron. At some point, the denominator approaches zero so that:

αd 1 γ (e ) =−− 01 , or approximately when e α d 〉〉 1 then:

αd γe = 1. When the term eαd is about the order of 20, transition from avalanche to streamer takes place [22]. One consequence of this is that the dielectric strength for small (less than 1 centimeter) spacing is greater than for larger gaps. Figure (2-2) is a typical voltage-current relationship for a gas in a uniform field. The behavior, after reaching breakdown, depends upon the gas. In general, a sharp drop in voltage occurs. Figure (2-3) represents the growth of a single electron in avalanche mode with transition to streamer mode. Note that a negative space charge builds up due to the relatively immobile ions. Eventually, a virtual cathode forms out in space, and it tends to produce secondary structures. A physical difference between avalanche and streamer mode is that avalanche is invisible, but streamers Chapter Two Theoretical Concepts 16

marked by photoionization and photoemission and are brightly luminous. In addition, the velocity of propagation is different. A velocity of ( 107 cm / s) is accepted for avalanche, (108 cm / s) or greater is a typical velocity of streamers [19].

Fig. (2-2) V-I characteristic for a gas in a uniform electric field [19]. Chapter Two Theoretical Concepts 17

Fig. (2-3) Breakdown in avalanche to streamer [19].

There are two other mechanisms of importance to consider in gas breakdown: electro-negativity and the Penning effect. Some monovalent gases, such as fluorine, and some more complex gaseous molecules, such as SF6, have outer rings deficient in one or two electrons. These tend to capture or attach free electrons to form negative ions. The low mobility of such ions effectively removes the electron from the avalanche process and reduces the first Townsend coefficient (α ). If this attachment coefficient given by n, the breakdown criterion becomes [20]: γα [e ()α −n d ]=− 11 ……………..…………………..……………… (2.3) α − n)( The Penning effect, on the other hand, reduces breakdown strength. If, for example, trace (1 percent) of argon added to neon, a large reduction in breakdown strength occurs. Several mixtures exhibit this effect including helium-argon, neon-argon, helium-mercury, and argon-iodine. The Paschen curve for several gases is shown in figure (2-4). Note the Penning effect on neon, also the minimum point. For a given spacing, Chapter Two Theoretical Concepts 18

as pressure drops, so does the probability of an electron-gas molecule collision. A point is reached where mean free paths correspond to electrode separation, and the drops. At this point, the apparent dielectric strength increases again [19].

Fig. (2-4) Paschen curve- typical breakdown voltage curves for different gases between parallel–plate electrodes [19]. 2.2 Transient Voltage:

An impulse voltage is a unidirectional voltage, which rises rapidly to a maximum value and then decays slowly to zero. The wave shape is generally defined in terms of the times t1 and t2 in microseconds, where t1 is the time taken by the voltage wave to reach its peak value and t2 is the total time from the start of wave to the instant when it has declined to one-half of the peak value. The wave then referred to as t1/t2 wave. The exact method of defining the impulse voltage, however, is specified by various international standard specification which define the impulse voltage in terms of nominal wave front and wave tail durations. Figure (2-5) shows Chapter Two Theoretical Concepts 19

the shape of an impulse wave where the nominal wave front duration t1 specified as [23]:

1 = 25.1 TTt 21 ……………………………………………..………….. (2.4)

Where: OT1 = time for the voltage to reach 10% of the peak voltage,

OT2 = time for the voltage to reach 90% of the peak voltage.

The point O1 where the line CD intersects the time axis defined as the nominal starting-point of the wave. The nominal wave tail t2 is the time between O1 and the point on the wave tail where the voltage is one-half the peak value, i.e. = TOt 412 .The wave is then referred to as a t1/t2 wave according to the standard specified in B.S. 923 (British Standard) A 1/50 μs wave is then standard wave. The specification permits a tolerance of up to ± 50% on the duration of the wave front and ± 20% on the duration of the wave tail [23].

Fig. (2- 5) General shape of an impulse voltage [23].

Chapter Two Theoretical Concepts 20

In the corresponding American specification, the nominal wave front is defined as 1 5. TT 21 and the standard wave is a 1.5/40 μs. The tolerances allowed on the wave front and the wave tail is ±0.5 μs and ±10 μs respectively [23].

2.2.1 Single- Stage Impulse Generator Circuit: An impulse generator essentially consists of a capacitor, which is charged to the required voltage and discharged through a circuit, the constants of which can be adjusted to give an impulse voltage of the desired shape. The basic circuit of a single- stage impulse generator is shown in fig (2-6(a)) where the capacitor C1 is charged from a direct current source until the spark gap G breaks down. A voltage is then impressed upon object under test of capacitance C2 [23].

The wave shaping resistors R1 and R2 control respectively the front and the tail of the impulse voltage available across C2 [23].

The resistor R1 will primarily damp the circuit and control the front time T1. The resistor R2 will discharge the capacitors and therefore essentially controls the wave tail. The capacitance C2 represents the full load, i.e. the object under test as well as all other capacitive elements, which are in parallel to the test object (measuring devices; additional load capacitor to avoid large variations of t1/t2, if the test objects are changed). No inductances are assumed so far, and are neglected in the first fundamental analysis, which is also necessary to understand multi-stage generators. This approximation is in general permissible, as the inductance of all elements has kept as low as possible [24].

It is important to mention the most significant parameter of impulse

2 generators. Which is the maximum stored energy: EMarx = 21 (VC o max1 ) Chapter Two Theoretical Concepts 21

within the discharge capacitance C1. As C1 is always much larger than C2, this figure determines mainly the cost of a generator [24].

An analysis of the simple circuit, presented by Draper [23] is as follows. Figure (2-6(b)) represents the Laplace transform circuit of the impulse generator of fig. (2-6(a)) and the output voltage given by the expression:

(a) Circuit arrangement

(b) Transform circuit

Fig. (2-6) Single-stage impulse generator [23].

Chapter Two Theoretical Concepts 22

R2 V Z 1 sC v(s) = 2 Where Z += R , Z = 2 s + ZZ 1 sC 1 2 1 21 1 R2 + 2 sC

By substitution:

R 2 V ( sCR + )1 v(s) = 22 s 1 R 2 R 1 ++ 1 sC ( 22 sCR + )1

V R = 2 s ⎛ 1 ⎞ ⎜ R 1 + ⎟ × ()22 1 ++ RsCR 2 ⎝ 1 sC ⎠

V R = 2 CR s sCRR 1 22 ++++ RR 221 sC C 21 1 1 V 1 = CR 2 ⎛ ⎞ ⎛ ⎞ 21 s ⎜ +++ 111 ⎟s + ⎜ 1 ⎟ ⎝ 11 22 CRCRCR 21 ⎠ ⎝ CCRR 2121 ⎠

V 1 ⎛ 111 ⎞ or v(s) = where a ⎜ ++= ⎟ and 2 ⎜ ⎟ CR 21 ++ bass ⎝ CRCRCR 212211 ⎠

⎛ 1 ⎞ b = ⎜ ⎟ ⎝ CCRR 2121 ⎠

V ⎡ 111 ⎤ v(s) = ⎢ − ⎥ 2121 ⎣ −− 1 − ssssssCR 2 ⎦

s s 2 Where 1 and 2 are the roots of the equation s + as + b = 0 and both will be negative. From the transform tables:

V υ t)( = []1 − 2tsts )exp()exp( − ssCR 2121 )( Chapter Two Theoretical Concepts 23

In a practice R2 is much greater than R1 and C1 much greater than

C2 and an approximate solution is obtained by examining the auxiliary

2 ⎛ 111 ⎞ ⎛ 1 ⎞ equation: s ⎜ +++ ⎟s + ⎜ ⎟ = 0 ⎝ CRCRCR 212211 ⎠ ⎝ CCRR 2121 ⎠

Where the value of (1/R1C1+1/R2C2) is much smaller than 1/R1C2.

2 ⎛ 1 ⎞ ⎛ 1 ⎞ The equation then becomes: s + ⎜ ⎟s + ⎜ ⎟ = 0 ⎝ CR 21 ⎠ ⎝ CCRR 2121 ⎠

1 1 And the roots are: s1 −≈ , s2 −≈ and s 〉〉 s21 CR 21 CR 12

The equation for the output voltage then becomes [19]

⎡ ⎛ t ⎞ ⎛ t ⎞⎤ υ Vt ⎢exp)( ⎜−= ⎟ exp⎜−− ⎟⎥ …………………………………….(2.5) ⎣ ⎝ CR 12 ⎠ ⎝ CR 21 ⎠⎦

And the graph of the expression is shown in figure (2-7).

Fig. (2-7) The impulse voltage and its components [23]. Chapter Two Theoretical Concepts 24

The above analysis shows that the wave shape depends upon the values of the generator and the load capacitances and the wave-control resistances. The exact wave shape will be affected by the inductance in the circuit and the stray capacitances. The inductance depends upon the physical dimensions of the circuit and is kept as small as possible [23].

A theoretical analysis have presented for the single-stage impulse generator and the load circuit. The simplified circuit is shown in figure

(2-8(a)) [23].It shows that, after the discharge of the condenser C1, the variation in the voltage V, across the load, capacitance C2 can be analyzed by extremely tedious methods involving a quartic differential equation. If

L2 is neglected or in effect combined with L1, the equation reduces to one involving only the third and lower powers and it takes the form,[23] [Appendix B] ,

⎡ 23 ⎛ R1 1 ⎞ ⎛ R1 ⎞ 111 ⎤ ⎢ DDV ⎜ ++ ⎟ + D⎜ ++ ⎟ + ⎥ = 0 ….….….(2.6) ⎣ ⎝ RCL 221 ⎠ ⎝ ⎠ RCCLCLCLCLR 22111121212 ⎦

Chapter Two Theoretical Concepts 25

(a)

(b)

Fig. (2-8) Simplified circuit of impulse generator and load. (a) Circuit showing alternative positions of the wave-tail control resistance, (b) Circuit for calculation of wave front [23].

The wave-tail resistance can be either on the load side or on the

' generator side. If the wave-tail resistance is in position R2 , the parameters are slightly different but the equation remains in the same form. An expression of this form is of little more than mathematical interest as the stray capacitances, inductances distributed throughout the circuit, and no precise values can be assigned to them. Chapter Two Theoretical Concepts 26

In most cases, it is desirable to simplify the calculations by assuming that the circuit of figure (2-8(a)) is non-inductive. Taking the case where R2 is on the generator side of R1, it can be shown that the roots

−α1 and −α 2 of the differential equation for V are

⎧ ⎫ 1 ++ / TTX 12 ⎪ /4 TT 12 ⎪ 1 or αα 2 = ⎨ 11 −± ⎬ 2 T ⎪ ()1 ++ / TTX 2 ⎪ 2 ⎩ 12 ⎭

− α 1t − ee − α 2 t and = VV C 1 ……..………………………….………….(2.7) T − αα 122 )(

where : X=C2/C1, T1=C1R2, T2=C2R1

The actual time for the voltage V to rise to its peak value given by: [Appendix C]

loge ()α α12 tactual = ………………………………..……………………..(2.8) −αα 12

The efficiency (η) of the generator is given by V /VC1, i.e.

− α t11 − ee − α t12 η = ……………………………...……………………(2.9) T − αα 122 )(

If R 2is on the load side of R1, the roots of the equation are: [Appendix D]

⎧ ⎫ ++ /1 12 XTTX ⎪ /4 TT 12 ⎪ orαα 21 = ⎨ 11 −± ⎬ 2T ⎪ ()++ /1 XTTX 2 ⎪ 2 ⎩ 12 ⎭

The position of R2 greatly affects the voltage efficiency of the system and it will be apparent from figure (2-8(a)) that when R2 is on the load side of R1, the resistors R1 and R2 from a potential divider and the output voltage is reduced. No such reduction in voltage takes place when

R2 is on the generator side of R1. Edwards et al [23] had shown how the efficiencies of the two arrangements vary with the ratioC2/C1. Chapter Two Theoretical Concepts 27

Figure (2-9) shows the effect of position of R2 on voltage efficiency of the generator. For low values of C2/C1 the efficiency is very low when R2 is on the load side of R1 , but when the circuit is arranged so that R2 is on the generator side , the efficiency is highest when the load is zero and decreases gradually with increase in the ratio C2 /C1. For any value of the ratio C2 /C1, the voltage efficiency is higher when the resistance R2 is on the generator side of R1 [23]. In the simplified arrangement of figure (2-8(b)), the critical resistance R for the circuit to be non-oscillatory is given by:

4L 111 R = where += C CCC 21

The voltage V across the load capacitance C2 is then given by: [Appendix E]

CV C 1 ⎡ ⎛ 2 t ⎞ − /2 CRt ⎤ V = ⎢ ⎜11 +− ⎟ e ⎥ ……….……….……..………..…..(2.10) C 2 ⎣ ⎝ CR ⎠ ⎦

If the inductance is reduced to zero, then: [Appendix F]

CV V = C 1 (1 − e − /2 CRt )………….…….………………………..……(2.11) C 2 Chapter Two Theoretical Concepts 28

Fig. (2-9) Effect of position of wave-tail resistance on voltage

efficiency, (a) Resistor R 2on generator side of R1, (b) Resistor R 2on load

side of R1 [23].

The “nominal wave front “as defined in B.S. 923 (1940) is equal to 2.75 CR when L is zero and to 2.1CR when the circuit is critically damped. Neglecting the inductance, the nominal wave tail is approximately equal to

0.72 R1 (C1 + C2). The resistance values calculated in the following sequence.

The value of R1 required to make the circuit shown in fig (2-8(a)) non-oscillatory is first calculated ignoring R2. Then the value of R1

(> 4 CL ) required to give the desired wave front is computed. Finally, the value of R2 is calculated to give the required wave tail when R2 is on the generator side of the R1 in the arrangement shown in the figure (2-8(a)).The efficiency of the generator can then be approximately estimated when [C1/

(C1+C2)] multiplied by factor which is about 0.95 for a 1/50 μsec wave [23]. Chapter Two Theoretical Concepts 29

The maximum value of (I) the current in the undamped discharge circuit of a generator into a short circuit can be calculated from the energy 2 2 equation: 1/2LI =1/2C1V i.e. [23]

C = VI 1 ……………………………….……………………………..(2.12) L

If the circuit is critically damped, the current will be given by an expression [23]:

V C I = 1 ………………………………………….………………… (2.13) e L

An analysis have been made of impulse generator circuits of various types and presented the values of the constants corresponding to the most commonly used waveforms. This treatment may be extended to evaluate the constants for any desired wave shape. [23]

The analysis showed that, the wave shape of the impulse generator is largely affected by the circuit parameters. Has analyzed the influence of wave front resistance, the series inductance and the load capacitance in modifying the shape; the results are shown in figure (2-10). These relations show that for values of the series resistance higher than a critical value,

(i.e. 4 CL ) the wave front duration increases with increasing values of the resistance and the magnitude of the peak voltage decreases. With increasing the series inductance and load capacitance the wave front increases but the magnitude of the peak value varies little for the chosen range of inductance and capacitance.

The lengthening of the wave front by increasing these parameters provides a convenient method of generation of long-front impulse voltages suitable for carrying out tests [23]. Chapter Two Theoretical Concepts 30

Fig. (2-10) Effect of varying circuit parameters on voltage wave shape [23].

2.2.2 Multistage Impulse Generator Circuit:

The one-stage circuit is not suitable for higher voltages because of the difficulties in obtaining high direct current voltages. In order to Chapter Two Theoretical Concepts 31

overcome these difficulties, Marx suggested an arrangement, which is described below [23].

2.3 Marx Generator: A Marx generator is a clever way of charging a number of capacitors in parallel through resistances, then discharging them in series through spark gaps [23] as show in figure (2-11).

Fig. (2-11) Marx Generator (a) Charging (b) Discharging.

The essence of the Marx principle is the transient series connection of a number of electrostatic energy stores. The eponymous Erwin Marx described his original generator [25].Marx generators are probably the most common way of generating high voltage impulses for testing of insulations Chapter Two Theoretical Concepts 32

when the voltage level required is higher than available charging supply voltages. A typical circuit presented in figure (2-12) which shows the connections for a five-stage generator. The stage capacitors C charged in parallel through high-value charging resistors R. At the end of the charging period, the points A,B,…,E will be at the potential of the D.C sources, e.g. +V with respect to earth, and the points F,G,…,M will remain at the earth potential. The discharge of the generator initiated by the breakdown in the spark gap AF, which followed by simultaneous breakdown of all the remaining gaps. When the gap AF breaks down, the potential on the point A changes from +V to zero and that on point G swings from zero to -V owing to the charge on the condenser A.G. If for the time being the stray capacitance C` is neglected, the potential on B remains +V during the interval of the gap AF sparks over. A voltage 2V, therefore, appears across the gap BG that immediately leads to its breakdown. This breakdown creates a potential difference of 3V across CH; the breakdown process, therefore, continues and finally the potential on M attains a value of -5V. In effect, the low voltage plates of the stage capacitors are successively raised to -V, - 2V…,-NV, if there are N stages. This arrangement gives an output with polarity opposite to that of the charging voltage.

Chapter Two Theoretical Concepts 33

Fig. (2-12) Basic circuit of a five-stage impulse generator [23].

The above considerations suggested that a multistage impulse generator should operate consistently irrespective of the number of stages.

In practice for a consistent operation it is essential to set the first gap (G1 ) for breakdown only slightly below the second gap (G2 ). A more complete analysis shows that voltage distribution across the second and higher gaps immediately after the breakdown of the lowest gap (G1 ) is governed by the Chapter Two Theoretical Concepts 34

stray capacitances and gap capacitances shown in dotted lines in figure

(2-12). The effect of stray capacitances on voltage across G2 immediately after breakdown of G1 which may be estimated as follows: Assume the resistors as open circuits and stray capacitances negligible in comparison with the stage capacitors. Let (A) in figure (2-12) be charged to (+V). After breakdown of G1 the point G initially at earth will assume a potential –V, but the potential of B is fixed by the relative magnitudes of ,CC 21 and C3 and is given by [24]:

⎛ + CC ⎞ ⎜ 31 ⎟ BH = VV ⎜ ⎟ ………………………………………………….(2.14) ⎝ ++ CCC 321 ⎠ hence the voltage across the gap (G2 ):

⎛ + CC ⎞ ⎜ 31 ⎟ G2 VV ⎜1+= ⎟ ………………………………………………..(2.15) ⎝ CC 21 ++ C3 ⎠ [Appendix G].

If C 2 = 0, VG2 reaches its maximum value of 2V. If both C1 and C3 are zero, V will equal to V, i.e. its minimum value. G2 It is apparent, therefore, that the most favorable conditions for the operation of the generator occur when the gap capacitance C2 is small and the stray capacitances C1 and C3 are large. The conditions set by the above expression are transient, as the stray capacitors start discharging. The practical stray capacitors are of low values, consequently the time constants are relatively short ≈ 10−1 μsec or less. For consistent breakdown of all gaps, the axes of the gaps should be in same vertical plane so that the ultraviolet illumination from spark gap in the first gap irradiates the other gaps. This ensures a supply of electrons in the gaps to initiate breakdown during the short period when the gaps are subjected to the over voltage. The consistency in the firing of the first stage spark gap improved by providing trigger circuits [23]. Chapter Two Theoretical Concepts 35

The wave-front control resistors, in a multistage generator, can be connected either externally to the generator or distributed within the generator, also it may partly connected in or outside it. In the best arrangement, about half of the resistance is outside the generator. An advantage of distributing the wave-front resistors within the generator is that, it reduces the need for an external resistor capable of withstanding the impulse voltage. If all the series resistances distributed within the generator, the inductance and capacitance of the external leads and the load form an oscillatory circuit [23]. An external resistance, therefore, becomes necessary to damp out these oscillations. The method of placing part of the wave-front control resistance in series with each gap serves to protect against disruptive discharge as well as to damp out any generator internal oscillation. Wave- tail control resistances generally used as the charging resistors within the generator. The circuit shown in figure (2-13) commonly used to obtain high efficiency with distributed series resistors. The value of R3 is made large compared with R1 and R2 which are made as small as is necessary to obtain the required length of the wave tail. Under some conditions the current through R2 does not flow through R1 and so does not reduce the initial generator output voltage, no matter how small R2 or how large R1 may be. In a practical generator employing this circuit, the voltage drop in R1 is made less than 1% of the output voltage by selecting suitable values of the parameters. The stage capacitance was 0.2 μF, R1 is about 40 Ω and the wave-tail resistance R2 required for a 5 μsec wave tail is about 25 Ω. R3 is made nearly 10 k Ω [23]. Chapter Two Theoretical Concepts 36

Fig. (2-13) Multi-stage generator with distributed series resistors [23].

2.3.1 Charging Of the Marx Generator: In N-stages Marx bank, the output voltage available at any instant is theoretically the sum of the individual stage voltages. Thus, there is an RC line in each, except for the first stage, all forcing functions are time and position dependent. Two solutions are conveniently available. One relationship, according to Fitch as in figure (2-14) [19], is:

2 CH = oo NCRT ………………………………………………….……… (2.16)

Fig. (2-14) Marx bank charging performance [19]. Chapter Two Theoretical Concepts 37

The second relationship is shown in figure (2-14), presents a power series analysis that he takes to the limit as N goes to infinity. In an LC circuit, recourse can be taken to the PFN a characteristic .ideally, such a network has characteristic time is given by:

τ CH = MARX CL MARX ………………………….…….………………...... (2.17)

The discharging into matched impedance requires a time 2τ . In mismatched cases, oscillations occur that extend this time. More commonly, some command charge system employed in which an external inductor, large with respect to the Marx inductors, is resonated against the total network capacitance. Charging usually accomplished in a half cycle of the resonant frequency, leading to [19]:

CH = πτ TOTALCL MARX …………………………….……………….…… (2.18)

2.3.2 Discharging of the Marx Generator: The inefficiencies of charging have a matching set of inefficiencies associated with the discharge. Figure (2-15) reveals that, in general, a stage capacitor is paralleled by two charging impedances, Z o . In the resistive case, the self-time constant is just: CR τ = oo ………………………….……………………………… (2.19) DISCH 2

Fig. (2-15) Marx bank discharge relationships [19].

This time must be long compared to the output pulse for good efficiency. When inductances used as charging impedances, the behavior is Chapter Two Theoretical Concepts 38

similar except for the appearance of resonance in place of the simpler RC case. The analysis in is straightforward and summarized here. A given mesh will attempt to resonate with a current given by[19]:

C t = Vi NLC sin …………..………….………………..…………..(2.20) L LC For good efficiency the self-ring period, T chosen much greater than the discharge period, τ. Thus, the sine of the angle can be replaced with the angle and:

C t N tV LC ≅ Vi N = ……………………..…………………….. (2.21) L LC L Because the process terminates when the bank is discharged. If the Marx discharges into matched impedance, the Marx current is:

NVN I1 = …………………………………….……………………….. (2.22) 2Z N

and the efficiency can be related by the ratio of (iLC I/ 1 ). When the first gap fires, all voltages around the loop must add up as before, and equal zero, by Kirchhoff``s Law. (Gaps are opposite in sense to capacitors.)

i = NVNV gap Initially …………………………..………………………(2.23)

i ()−= 1 VNNV gap One gap fired ……………..…………………………(2.24)

i ()−= 2 VNNV gap Two gaps fired ……………….……………………(2.25) or, alternatively, the voltage across an unfired gap should be: NVi V Gap = .…………………….……….…………..………(2.26) − nN 1

2.4 Trigger Spark Gap: The trigger spark gap was invented in the early 1940`s to serve as a switch in high-power modulators for radar [26]. The spark gap consists of three electrodes in a hermetically sealed pressurized envelope. Specific Chapter Two Theoretical Concepts 39

applications fall into two general areas, both involving capacitor switching at low impedance levels follows: (i) Protective device, where the gap is used to crowbar energy storage elements such as filter capacitors and PFN`s, providing shunt protection of RF tubes and other circuitry. (ii) Series switch, where energy is discharged rapidly into loads include, Marx Generators, Kerr Cells, Pockel Cells, flash tubes for pumping gas, liquid and solid lasers and also gas lasers, such as UV Nitrogen, TEA-CO2 and metal vapors [27].

2.4.1 Electrical Operation: The triggered spark gap is a unique switch, able to change quickly from a near-perfect insulator to a low impedance conductor in response to voltage applied to the electrodes. The two main electrodes carry the load current after trigger electrode initiates conduction. Triggered spark gaps generally characterized by peak current capability of tens of thousands of amperes, delay times of tens of nanoseconds, arc resistance of tens of milliohms, inductance of 5 to 30 nanohenries and life of thousands to millions of shots depending on the application. Typical current pulse widths are in the range of one to tens of microseconds [27]. Different spark gaps designed to employ one particular method to create the main anode to cathode discharge, figure (2-16) shows spark gap types. The different methods are following the triggered spark gap electrode configurations: 1- Field distortion: three electrodes; employs the point discharge (actually sharp edge) effect in the creation a conducting path. 2- Irradiated (laser trigger switches): three electrodes; spark source creates illuminating plasma that excites electrons between the anode and cathode. 3- Swinging cascade: three electrodes; trigger electrode nearer to one of the main electrodes than the other. Chapter Two Theoretical Concepts 40

4- Mid plane three electrodes, basic triggered spark gap with trigger electrode centrally positioned. 5- Trigatron: trigger to one electrode current forms plasma that spreads to encompass a path between anode and cathode. The triggered Spark gap may be filled with a wide variety of materials, the most common are: (1) Air (2) SF6 (3) Argon (4) Oxygen. Often a mixture of the above materials is employed. However, a few spark gaps actually employ liquid or even solid media fillings. Solid filled devices are often designed for single shot use (they are only used once- then they are destroyed) Some solid filled devices are designed to switch powers of 10 TWatts such as are encountered in extremely powerful capacitor bank discharges, except (obviously) in the case of solid filled devices, the media is usually pumped through the spark gap. Spark gaps often designed for use in a certain external environment (e.g., they might be immersed in oil). A system for transmitting the media to the appropriate part of the device may sometimes be included. Common environments used are: (a) Air (b) SF6 (c) Oil. Make miniature triggered spark gaps specially designed for defense applications. These devices are physically much smaller than normal spark gaps (few cm typical dimensions) and designed for use with exploding foil Slapper type detonators. Laser switching of spark gaps, the fastest way to switch a triggered spark gap is with an intense pulse of Laser light, which creates plasma between the electrodes with extreme rapidity. There have been quite a few designs employing this method, chiefly in the plasma research area. Triggered spark gaps tend to have long delay times than Thyratrons (their chief competitor, at least at lower energies) However once conduction has started it reaches a peak value exceptionally rapidly (couple of nanoseconds commutation). Chapter Two Theoretical Concepts 41

Fig. (2-16) Trigger spark gap types, (a) the trigatron gap, (b) the laser triggered gap, and (c) the field distortion gap [28].

Chapter Two Theoretical Concepts 42

2.4.2 Ratings and Operating Characteristics: The transfer characteristic curve in figure (2-17) and the voltage- current waveform in figure (2-18) show the ratings and behavior of a triggered spark transfer to the main electrode, or more correctly, to cause the trigger spark to initiate complete gap breakdown and condition of current between the main electrodes. When minimum trigger voltage required to initiate a complete breakdown is plotted versus main electrode (E-O-E) voltage, a typical curve of all triggered spark gaps shown in figure (2-17). This curve defines a region on the left where firing does not ordinary occur, called the cut-off- region, a central region called the normal operating region and a region on the right above the point marked static breakdown voltage where the gap self-fires simply form over-voltage on the main electrodes. Triggered spark gaps should always operate well above the minimum trigger voltage and above the cut-off voltage portions of the curve to avoid the possibility of a random misfire and they should always operate well below the static breakdown voltage point to avoid the chance of prefire [27]. The important parts of the transfer characteristic curve are:

V T (min)-Minimum Trigger Voltage The minimum open circuit triggers voltage for reliable triggering. Spark Gaps should operate well above minimum trigger voltage, if possible. E-E (co)-Cut-Off Voltage The main electrode (E-E) voltage marked by a sudden rise in minimum trigger voltage as E-E voltage reduced. Operating near cut-off should always avoid, particularly near the knee of the transfer characteristics curve.

Chapter Two Theoretical Concepts 43

E-E (min)-Minimum Operating Voltage The minimum main electrode voltage for reliable operation represents approximately 1/3 of maximum operating voltage. E-E (max)-Maximum Operating Voltage Typically represents 80% of self-breakdown voltage (SBV), and it is a value chosen to prevent random prefires. SBV- Static Breakdown Voltage The point where the gap will self-fire with no trigger voltage applied. Pressure fill and electrode spacing determine this point [27].

Fig. (2-17) Transfer characteristics for spark gap [27]. Chapter Two Theoretical Concepts 44

Fig.(2-18) Typical-current waveform characteristics [27].

2.4.3 Range: It is the area between minimum and maximum operating voltages. Normal gap operating range typically has a 3:1 ratio (i.e. maximum to minimum operating voltage). For the most reliable operation with minimum delay time and jitter, triggered spark gaps should usually operated at the high end of the range, between 60% and 80% of SBV. Operation at 50% to 70% of SBV may give longer useable life at high energy, if delay time is not critical [27].

Chapter Two Theoretical Concepts 45

Fig. (2-19) Paschen curves for triggered spark gaps [29].

Figure (2-19) shows the preferable operating range of a 3- electrode spark gap. The operating range is in the middle distance (A) between the voltage of automatic breakthrough and a lower limit where no spontaneous breakthrough can be enforced, even by a triggering spark of extremely high energy. This operating point indicated in figure (2-19), which even in the case of fluctuations offers sufficient space on both sides [29].

2.4.4 Trigger Mode: There are actually four transfer characteristics curves for any given trigger spark gap, depending on the trigger mode, a term applied to the relative polarities of the opposite, adjacent, and trigger electrodes, these mode designations shown in figure (2-20). Chapter Two Theoretical Concepts 46

Fig.(2-20) Gap mode designations [27].

Generally, with the large gaps, the widest operating range and shortest delay times are obtained with mode (A) operation, that is, with the opposite electrode negative and the trigger electrode positive with respect to the adjacent electrode. When mode of operation is not possible or practical, usually voltage range is reduced severely with an increase in delay time. The smaller gaps, with smaller electrode spacing, often have the widest operating range in Mode C. In this mode both the opposite electrode and trigger electrode are positive with respect to the adjacent electrode [27].

Chapter Two Theoretical Concepts 47

2.4.5 Delay Time and Jitter:

Delay time (tad) is measured between trigger voltage breakdown and main gap conduction as shown in figure (2-18). Delay time is a function of E-E voltage, trigger wave shape, and trigger mode. Minimum delay time achieved at the upper end of the E-E range with a fast trigger applied with the suitable mode polarity shown in figure (2-20). Delay time of the gap will generally be much less than that due to rise time and delay in the trigger circuitry [27].

Total jitter (tj) is the shot-to-shot variation in delay time plus the shot-to- shot variation in trigger breakdown time. Jitter may be minimized by using a fast-rising trigger pulse with trigger voltage in excess of minimum specified trigger voltage.

2.4.6 Recovery Time: Recovery time of gas-filled gaps is about several milliseconds depending on peak current, current reversal, and voltage recharge rate. To achieve proper turnoff of the gap, the discharge circuit should slightly under damped, with voltage reversal of 5% or less. For a gap to properly recover after discharge the gap current go to zero and the voltage across the gap must be reduced to less than 30 volts. Recharging of the energy storage capacitor must take place slowly, preferably from an inductive, resonant LC, or command triode charging source. RC charging, for example, is not conductive to short recovery time, but may be used if charging currents are less than 5 mA DC [27].

2.5 Inductor:

The role of an inductor in the Marx generator is to charge high voltage capacitors (C1 - Cn) in charging mode and isolate DC input voltage and high voltage pulse in high voltage pulse generation mode .The charging time (TCH) in charging mode can be calculated as : Chapter Two Theoretical Concepts 48

T 2π CL π CL T == tCh = tCh ….…….………………..……….(2.27) CH 4 4 2

To meet maximum pulse repetition rates (fmax.), the charging time should be less than Tmax. (=1/fmax.). So maximum inductance of LCh is obtained as follows;

π L C 1 Ch .max t ≤ ………….…………………………(2.28) 2 f max

The current of an inductor LCh has a maximum value in high voltage pulse generation mode. To limit maximum current of an inductor

LCh, the minimum inductance of LCh is calculated as follows [30]:

Δ T .max L .min ≥ ν L .max, …………………………...………………….(2.29) Δ I L .max,

2.6 Power Supply of Gas Lasers: A gas laser is a laser in which an electric current is discharged through a gas to produce light. The first gas laser, the Helium –neon, was invented by an Iranian physicist Ali Javan 1960 [31].

[

2.6.1 Power Supply for TEA CO2: A common variety of pulsed carbon dioxide laser is the TEA laser (Transversely Excited at Atmospheric pressure). This is inherently a pulsed device rather than a continuous laser. In contrast to most carbon dioxide lasers that operate at total gas pressures much less than one atmosphere, the TEA laser operates near one atmosphere gas pressure. This allows extraction of relatively large amounts of energy per pulse. The energy in a pulse from a carbon dioxide laser that is pulsed in the microsecond regime increases as the square of the gas pressure (E ά P2). Thus it became desirable to increase the gas pressure and operate at a pressure near one atmosphere, a convenient value. But at these pressures, the uniform electrical discharge tends to transform into an arc discharge. The discharge voltage pulse range from (~ 300 ns - 500 ns) and the discharge current Chapter Two Theoretical Concepts 49

pulse (~ 150 – 300 ns) while the output laser pulse ~ 100 ns ( main pulse) plus ~ 200- 400 ns ( pulse tail). The electrical discharge breaks down into a narrow streamer, similar to a lightning bolt. This does not excite the whole gas volume uniformly. To avoid this undesirable effect, the devices are operated in a relatively short pulse regime, and a number of other measures are used, including preionization and special shaping of the electrodes [16].

2.6.2 Power Supply for Metal Vapor Laser: Pulsed metal vapor lasers first were developed around 1966 but were slow. The technology of these lasers has been difficult, primarily because of the high temperature at which the laser tube must be operated to keep the metal in vapor form at a reasonable pressure (around 1500 C in the case of gold). Because these lasers offer desirable wavelengths, they have been developed to commercial status and are now reliable, robust commercial products. A metal vapor laser may consist of a ceramic tube with pellets of metal (such as gold or copper) positioned inside. The tube is surrounded by a cooling water jacket. An electrical discharge through a gas (neon) in the tube heats the metal and produces a low-pressure vapor. The laser is essentially a pulsed device with a high pulse repetition rate (0.5 - 5 kHz) so that the beam appears continuous to the eye. The applied voltage depends on the dimensions of the active medium (~ 5-20 kV for copper vapor laser). The beam diameters are typically 1 cm or more, larger than those of most familiar visible lasers. Commercial pulsed metal vapor lasers are copper (511- and 578- nm wavelengths) and gold (628 nm). Experimental demonstrations have included lead (723 nm), manganese (534 nm), and barium (1500 nm). The availability of these wavelengths from small devices with short pulse duration has allowed development of a number of novel applications, such Chapter Two Theoretical Concepts 50

as photodynamic therapy in medicine and high-speed photography. Although such lasers are still not common, they are beginning to be used for industrial material processing. The short wavelength and high peak power allow high irradiance to be delivered to a small area on a work piece. Of the metal vapor lasers, copper is the most highly developed [16].

2.6.3 Power Supply for Excimer Laser: Excimer lasers have used two main methods of excitation: pulsed electric discharges or high-energy electron beams. Development of excimer lasers has branched into two channels that represent the two excitation methods. Electron-beam-excited devices are capable of producing very high energy pulses. Electron-beam excitation involves large, expensive sources of high-energy electrons. Such devices can be scaled to very large size and are capable of reasonably high efficiency, potentially in the 5- to 10-percent range. Devices have been constructed with energy in the kilo joules range, and amplifiers with energy-extraction capability in the hundred-kilo joule range appear possible. Electric-discharge Excimer lasers may be much smaller and less expensive. Their energy-extraction capabilities are much lower than those of the electron-beam devices. Typical characteristics for commercial models are pulse energy of from a few tenths of a joule to a few joules per pulse and pulse repetition rates of tens to hundreds of hertz, with average power in the range of one hundred watts. Because of the unstable nature of the chemical species in an excimer laser, it is available only as a pulsed device with short pulses, typically in the 200-nanosecond regime. The problems with the changing impedance of the gas during the discharge become more severe. The change is much faster and covers a greater range than is the case for carbon dioxide laser gas mixtures. Chapter Two Theoretical Concepts 51

Excimer lasers require short excitation pulses with half widths less than 100 ns with rise time less than 50 ns and currents in the range of kiloamperes. Also some means for preionizing the gas between the electrodes is required. The usual approach has been a two-stage circuit in which charge is stored on a storage capacitor, and then transferred by a thyratron switch to an array of secondary capacitors, called peaking capacitors. The basic idea is to be able to store the charge in one portion of the circuit, where the process can be relatively slow, and then to perform the discharge in another portion of the circuit, which can be much faster. The charge is transferred across preionization spark gaps that introduce some charge into the gap between the electrodes and prepare the gas for the main discharge [16].

Chapter Three Experimental Work 52

Chapter Three Experimental Work

3.1 Introduction: A homemade high voltage DC power supply up to 4 kV, two trigger circuits (one with camera flash igniter and the other with MOSFET transistor) where designed and implemented, two Marx generators (eight stages and ten stages) have been designed and tested as a high voltage pulse generator devices.

3.2 Design Principles:

The major requirements of the project are shown in the following block diagram figure (3-1).

Fig. (3-1) Block diagram for the major requirements.

Chapter Three Experimental Work 53

3.3 Variable High Voltage Supply: A homemade variable 4kVDC power supply is developed for charging the Marx capacitors as shown in figure(3-2), it is consist of a variac (0-220VAC, 5Amp), high voltage transformer (220V/4kV), current limiter resistor 330 Ω, high voltage diodes 6kVDC for rectification (it works as a half wave rectifier), capacitor (0.1µF-25kV) and 100kΩ charging resistor.

Fig. (3-2) A homemade high voltage power supply.

3.4 External Trigger Generator Circuits: In order to trigger the spark gap for first stage of the Marx generator two trigger circuits were developed for this purpose, first camera flash lamp trigger circuit figure (3-3), it consists of a relaxation oscillator to generate a high voltage trigger impulse to initiate the spark at the first gap and the second trigger circuit is the ignition coil driver circuit figure (3-4).

Chapter Three Experimental Work 54

Fig. (3-3) Camera flash lamp trigger circuit.

Fig. (3-4) Ignition coil driver circuit.

Chapter Three Experimental Work 55

3.4.1 Xenon Camera Flash lamp Triggering Circuit: A small xenon camera flash lamp liner (300V max. applied voltage) with commercial trigger transformer (TR) 200V max. input and 20 kV max output. The resistor (Rt ) and capacitor (Ct) are used to form the trigger generator circuit as shown in figure(3-5). The breakdown action in the xenon flash lamp occurs when the voltage across the lamp is 256 VDC. The (10nF) capacitor (Ct) is charged through (Rt) as the flash lamp breaks down discharging (Ct) into the primary coil of the trigger transformer to produce an output high voltage pulse on the secondary (~8 kV DC) which is used to trigger the first gap of the Marx generator (8-stage).

Fig. (3-5) Xenon flash lamp trigger circuit.

Chapter Three Experimental Work 56

3.4.2 Ignition Coil Switching Trigger Circuit: The car coil circuit consists of two parts, first the dc power supply circuit and second the ignition coil driver circuit as in figure (3-6).

12V

15V

Fig.(3- 6) Ignition coil switching trigger circiut.

A variable DC power supply is used to get an input voltage to supply the primary ignition coil with a 12 volt DC, also a 15 volt DC is used to supply the IC 555 trigger circuit which is used as a stable oscillator. The IC 555 oscillates at frequency up to 4 Hz depending on the variable resistors VR, R3 and capacitor C4.The calculations for IC 555 time on (Ton ) and time off (Toff ) and the duty cycle are :

TON = 0.7x VR x C4 = 0.7 x 50 x 103 x 0.1 x 10-6 =3.5msec

Chapter Three Experimental Work 57

TOFF = 0.7 x R3 x C4 = 0.7 x 70 x 103 x 0.1 x 10-6 = 4.9 msec

Duty Cycle with Diode = TON/ ( TOFF + TON ) = 416 msec The output from the IC 555 directly drives a high current switching power MOSFET transistor which switches the current through the primary coil of the coil transformer and the output at the secondary coil is approximately (20kVDC). The IC 555 is a in stable operation with the output high (pin3) the capacitor C4 is Charged by current flowing through VR and R3 . The threshold (pin6) and trigger (pin2) inputs monitor the capacitor voltage and when it reaches 2/3 Vs (threshold voltage ) the output becomes low and the discharged (pin7) is connected to 0 V, when the voltage falls to 1/3 Vs ( trigger voltage ) the output becomes high again and the discharge (pin7) is disconnected allowing the capacitor to start charging again a pushbutton switch is connected between (pin2) and capacitor C4 to control the trigger pulse, also to achieve a duty cycle of less than 50% .A diode

(D1) is added in parallel with R3 as shown in the diagram, this will bypasses

R3 during the charging part of the cycle so that the space time or off time depending only on VR and C4. An ignition coil is essentially an autotransformer with a high ratio of secondary to primary windings. "Autotransformer", means that the primary and secondary windings are not actually separated but they share a few of the windings. The ratio of secondary to primary turns in an ignition coil is somewhere around 100:1. However, the ignition coil does not work like an ordinary transformer. An ordinary transformer will produce output current at the same time of input current is applied. An ignition coil actually does most of its work as an inductor. When the ignition coil is connected to the

Chapter Three Experimental Work 58

supply, the inductor is 'charged' with current. It takes a few milliseconds for the current to build up the magnetic field; this on account of reverse voltage caused by the increase in magnetic field. An output high voltage trigger pulse (12kV) is produced to trigger the first gap. 3.5 Marx Generators: A typical Marx generator consists of (N) number of stages (eight and ten stages), each stage consisting of resistors, capacitor and spark gap which is the switching device. All modules are connected together such that the capacitors are charged in parallel with spark gaps. The Marx generator is a capacitive energy storage circuit which is charged to a given voltage level and then quickly discharged delivering its energy quickly to a load at very high voltage levels. Two Marx generators were designed and implemented in this work. A variable (4kVDC) power supply is used for this purpose when all the capacitors are charged up to the desired voltage, first spark gap is triggered by trigger generator circuit this makes the rest of the gaps to be overvoltage and causing self break down, all the capacitors are thus connected in series resulting an output voltage N times the charging voltage, two trigger generators circuits were developed one for an eight stages Marx generator and another for a ten stages Marx generator.

3.5.1 Marx generator (8 – stage): A compact repetitive Marx generator has been designed, built and tested. The generator of 8 stages is an R-C ring that consists of 8 capacitors (4.7 nF per capacitor) and 14 resistors (2 MΩ per resistor). The generator is charged quickly to 2kV within a charging time less than 0.52 second by a DC charging source. The trigger system is constructed for repetitively triggering the first discharging spark gap (There are 8 discharging spark gaps in the generator). Due to the limited capacity of the DC charging source the generator is tested at single pulse discharge with an output

Chapter Three Experimental Work 59

voltage about 12 kV (efficiency 75%). The outlook of Marx generator is shown in the figure (3-7).

Fig. (3-7) Marx generator (8-stage).

The Marx generator consists of an array of Resistances, Capacitances & Spark Gaps (R, C & S.G.). The elements of Marx Generator are; C= 4.7 nF, R = 2MΩ and the input power supply voltage = 0 - 4 kVDC, as shown in figure (3-8).

Fig. (3-8) Circuit diagram for Marx generator (8-stage).

The spark gap is formed with a tinned copper wire with a diameter of 1.5 mm and the gaps should be initially set to about 1.5mm as shown in figure (3-9).

Chapter Three Experimental Work 60

Fig. (3-9) Copper wire spark gap.

The distance between the spark gaps depend on input voltage and number of stages. The measured output voltage pulse of Marx generator (8- stage) is (12kVDC) for an input voltage 2kV high voltage probe also the trigger pulses and the current pulses were measured, figure (3-10) shows the gaps glow discharge.

Chapter Three Experimental Work 61

Fig. (3-10) Gaps glow discharge.

3.5.2 Marx Generator (10 - Stage): A ten-stage Marx generator is built with the following parameters; ten homemade spark gaps, (18) resisters each (100kΩ), ten ceramic capacitors (2400 pF, 40kV), twenty wiring copper sheets , two Perspex rulers, one Bakelite base and base holder as shown in figure (3-11).

Chapter Three Experimental Work 62

(a) Front view. (b) Side view. Fig. (3-11) Marx generator (ten stages).

The spark gaps are designed and machined from brass metal depending on commercial spark gap which is produced from lumenics corporation arranged as shown in figure (3-12) with the following dimensions, Diameter = 2.5 cm and Length = 4cm.

Chapter Three Experimental Work 63

Fig. (3-12) Spark gap arrangements.

The curvature of the gap is the most important parameter which governed the uniformity of the discharge between the two electrodes. The spark gap electrodes are designed using Chang profile, Chang showed that the gradient (i.e. the E field strength) between the electrodes is greater than

Chapter Three Experimental Work 64

the gradient outside the plane portion. The equations for the uniform field electrode (Chang`s family of profiles) are [32]:

+= o uvKux )sinh()cos(

+= o uvKvy )cosh()sin( x and y are space coordinates and Ko(<<1) is a parameter controlling the electrode width (chang 1973). For the π/2 profile the electrode surface is defined by

x = u ; y π += O uK )cosh()2/( The field is greatest in the center region between the plates and less everywhere else. If the making of the electrode follow the calculated contour, the breakdown voltage between the electrodes will be the same as if the field is infinitely uniform. The ten- stage Marx generator was tested for an input voltage 4 kV. The obtained output voltage was 38 kV, the circuit is operated using ignition coil trigger circuit to obtain a trigger pulse on the first stage spark gap as shown in figure (3-13).

Chapter Three Experimental Work 65

Fig. (3- 13) First trigger spark gap.

Figures (3-14) and (3-15) show the system arrangement for the Marx generator with measuring instruments during testing operation.

Chapter Three Experimental Work 66

Fig. (3-14) Marx generator system (10- stage) experiment.

Fig. (3-15) Marx spark gaps discharge operation test.

Chapter Four Result & Discussion 67

Chapter Four Results and Discussion 4.1 Introduction:

The output results for the Marx generator eight stages and the Marx generator ten stages are the voltage pulse, current pulses and trigger pulse for the trigger circuit. Theoretical and experimental inductance calculations were achieved for the two Marx systems.

4.2 Marx Generator (8-stage): 4.2.1 Xenon Flash Lamp Trigger Circuit:

Output voltage pulse from camera xenon flash lamp trigger circuit is measured by using high voltage probe (P6015, 1000X, 3pF, 100mega ohms DC, 20kV max. DC cont., 40kV peak pulse, Tektronix Inc) and a 100 MHz oscilloscope (Oscillation Tektronix 2221A, 100 MHz Digital Storage Oscilloscope). Figure (4-1) shows the output trigger pulse delivered from the circuit shown in figure (3- 3).

Scale (1V, 5µs) Fig.(4-1) Output voltage trigger pulse 4.5kV.

Chapter Four Result & Discussion 68

4.2.2 Current Pulse for Marx Generator (8-stage):

Marx generator (8-stage) current pulse was measured using current probe (Termination for P6021 AC Current Probe, Tektronix ® 011-0105- 00, LP3db ≈ 450Hz, Tc ≈ 0.35ms). Figure (4-2) shows the current pulse for variable input voltages.

Scale (5V, 0.2 µs) Fig. (4-2) Marx generator (8-stage) current pulse.

The Xenon trigger circuit shown in figure (3-5) was tested with different voltage from zero volt up to its maximum which is found to be ~ (256 volts). This voltage pulse has been used to trigger the first stage of Marx generator. Eight stages Marx generator current pulse is measured using current probe directly mounted to the output section of the generator, the current probe signals are shown in figures (4-2). The current calculations are:

Chapter Four Result & Discussion 69

I Max. = 225 mA

IR = 140 mA= 0.14 A

I Min. = 85 mA= 0.085 A T = 300 ns

The Marx is charged up to (2 kV), the energy is:

2 EMarx = 1/2 C V = 75.2 mJoule.

The eight stages Marx generator charged about (2kV) using the homemade variable power supply and then triggered by the xenon flash lamp, the output voltage pulses shown in figures (4-4) and (4-5).

Scale (1V, 2µs) Scale (1V, 10 µs) (a) Full voltage pulse. (b) Selected voltage pulse (first)

Figure (4-4) Voltage pulse for Marx generator - third stage 4.5 kV.

Chapter Four Result & Discussion 70

Scale (1V, 10 µs) Scale (2V, 10 µs) (a) Full voltage pulse (fifth stage). (b) Full voltage pulse (eight stages). t r ≅ 666 ns , Pulse width ≅ 4.5µs Figure (4-5) Voltage pulse for Marx generator stages.

4.3 Marx Generators (10-stage): Marx generator ten stages charged from variable high voltage power supply up to 4 kVDC. The Marx output voltage pulse shown in figure (4-6) is (38 kV). Figure (4-7) shows the voltage pulse for trigger circuit with car ignition coil shown in figure (3-6).

Chapter Four Result & Discussion 71

Scale (5V, 0.2 µs) Fig. (4-6) Marx generator (ten stages) voltage pulse. Pulse width = 450 ns, rise time = 50 ns.

(a) 5.9 kV (b) 7.5 kV Scale (1V, 0.1 ms) Fig. (4-7) Trigger circuit high voltage output pulse about 7.5 kV (ignition coil).

Chapter Four Result & Discussion 72

4.4 Measurements and Calculations: One of the most important parameters affecting the Marx output pulse is the inductance. Calculations have been done using two methods, first by measuring it with LCR meter device (PM 6303 RLC meter Philips) for the whole components of the Marx generator, second by direct calculations from the Marx generator output pulses.

4.4.1 LCR meter measurements method:

Inductance: L S.G.s = 2.6 µH L Stripes = 2.5 µ H L Capacitor = 20 nH

Then, Marx generator ten stages: L Marx = L S.G.s + L Stripes + L Capacitances

= 2.6 µ H + 2.5 µ H + 200 n H

= 5.4 × 10 -6

= 5.4 µ H.

4.4.2 Marx generator (10-stage) output pulse calculation method:

For ten stage Marx generator the inductance calculations depending on the Marx output pulse is done depending on the measurements from figure (4-6).

⇒ Rise time t r ≅ 50 ns

1 1 ⇒ f = = = 2× 107 Hz. T 50ns

1 1 f = 2π LCT

1 1 2× 10 7 = 2π ×10CL

Chapter Four Result & Discussion 73

L = 2.64 nH.

−6 ⇒ Decay time t de ≅ 2×10 s

1 ⇒ f = = 5×105 Hz T

⇒ L = 4.2 µ H.

⇒ Pulse width ≅ 450 ns

1 ⇒ f = = 2.1×106 Hz. T

L=2.3×10 -7 H.

∴L Total = L Rise Time + L Decay Time

= 2.64 nH +4.2 µ H

= 4.2 µH.

-7 L Pulse Width = 2.3×10 H.

4.4.3 Marx generator (8-stage) output pulse calculation method:

For eight stages Marx generator the inductance measured from the measurements from figure (4-5 (b)):

-7 ⇒ Rise time t r ≅ 6.66 ×10 s

1 6 ⇒ f = = 1.5 ×10 Hz. T ⇒ L = 2.99 × 10 -7 H.

- 6 ⇒ Decay time t de ≅ 4 × 10 s

1 ⇒ f = = 2.5 ×105 Hz. T ⇒ L = 1.07897×10-5 H.

Chapter Four Result & Discussion 74

⇒ Pulse width ≅ 4.5×10 -6s

1 ⇒ f = = 2.222× 105 Hz T

⇒ L = 1.3658×10-5 H.

∴L Total = L Rise Time + L Decay Time

= 11.0887µH -5 L Pulse Width = 1.3658×10 H.

Table (4-1) shows the inductance results for the eight and ten stage Marx generators. Table (4-1)

Lrise Ldeca y L Pulse width -7 -5 -5 8 - stage 2.99 × 10 H 1.07 ×10 H 1.36×10 H 10 - stage 2.64 nH 4.2 µ H 2.3×10 -7 H

Chapter Four Result & Discussion 75

4.5 Characteristic Marx generator (10-stage):

The calculated results are listed in table (4-2) for the 10-stage Marx to show the all parameters which affected the Marx output pulse width. Table (4-2) Parameter Description Value Unit

V Open Open circuit voltage 400 kV N Number of stage 10 stage Stage capacitance max. C Stage 2400 pF voltage 40 kV -10 C eq. or C Marx Erected capacitance 2.4 10 F

VMax. Ch Maximum charging voltage 40 kV

VCh Real charging voltage 4 kV

L Marx or L eq. Erected series inductance 4.2026 Hµ -7 L Stage Stage inductance 4.2026 10 H

Z Marx Marx impedance 132.328505 ohm 8 P Peak Power peak 3.03 10 watt

E Marx Energy stored in marx 192 mJ

T Ch Charging time 0.0216 s

f RR Maximum Repetition rate 46 Hz

t r Rise time 50 ns

t de Decay time 2 µs

P ave Average power 8.8 watt η Efficiency into a load 95 %

ICharge Charging current 40 mA

From table (4-2) the first important parameter is the output pulse rise which is 50 ns; this result is close to the aim for the designed Marx which is around 10 nsec. The second parameter is the pulse repetition

Chapter Four Result & Discussion 76 frequency which is 46 Hz, this parameter is very important for the gas laser which work with high repetition frequency like Excimer and nitrogen laser. Table (4 -3) Dimensions of the Marx generator (`10- stage) Parameter Diameter Value Unit

L Marx Marx length 75 cm

W Marx Marx width 7.5 cm

H Marx Marx hight 11 cm

Chapter Four Result & Discussion 77

4.6 Characteristic Marx Generator (8-stage): The calculated results are listed in table (4-4) for the 8-stage Marx to show the all parameters which affected the Marx output pulse width. Table (4 -4) Parameter Description Value Unit

V Open Open circuit voltage (typical) 64 kV

N N Number of stage 8 stage

C Stage Stage capacitance, max. 4.7 nF voltage 8kVDC -10 Ceq. or C Marx Erected capacitance 5.875 10 F

VMax.Ch Maximum charging voltage 8 kV

VCh Real charging voltage 2 kV

L Marx or L eq. Erected series inductance 11.0887 Hµ

L Stage Stage inductance 1.3860875 Hµ

Z Marx Marx impedance 137.38407 ohm

P Peak Peak power 7.453 MW

E Marx Energy stored in marx 75.2 mJ

T Ch Charging time 0.5264 s

f RR Maximum repetition rate 1.8996 Hz

t r Rise time 666 ns

t de Decay time 4 sµ

P ave. Average power 0.1428 watt η Efficiency into a load 75 %

ICharge Charging current 1 mA

From table (4-4) the first important parameter is the output pulse rise which is 666 nsec; this result is far from the aim of the designed Marx which is around 10 nsec. The second parameter is the pulse repetition

Chapter Four Result & Discussion 78 frequency which is 1.8996 Hz; this parameter was less than the expected which is about 10 Hz. Table (4-5) Dimensions of the Marx generator (8- stage) Parameters Diameters Value Unit

L Marx Marx length 38 cm

W Marx Marx width 5.5 cm

H Marx Marx height 4 cm

Chapter Five Conclusions And Recommendations For Future Work 79

Chapter Five Conclusions And Recommendations For Future Work 5-1 Conclusions: From the present work, we can conclude the following: 1- The spark gap design imposes great effect on the discharge output pulse width and rise time. Spark gap also affected the Marx generator inductance and impedance because it adds an imaginary stray capacitance which causes increasing in the inductance of whole system. 2- The components of the Marx generator (capacitors, resistors and wiring connections type) play an important role in determining the impedance and inductance of the whole system. To design and build Marx generator with low inductance and fast rise time pulse, it must use low inductance capacitors and special resistors (e.g. silicon carbide type). 3- The trigger circuit is affecting the discharge properties for the first spark gap of the Marx, which will in parallel affect the whole gaps discharge too, so one must determine the trigger pulse properties such as; pulse width, rise time, fall time and peak power depending on the Marx generator spark gap design and properties. 4- High voltage pulses with short pulse width and fast rise time depends greatly on the earthing system used in the laboratory, because bad earthing system will increase the pulse duration and change all the signal properties even if the system is well designed and implemented. 5- The open circuit voltage for 8 stage Marx generator is 64 kV but the real measured output voltage was 12 kV because the primary charging voltage is 2 kV and it is possible to reach the Marx maximum output voltage if the laboratory earthing system is well designed and implemented. 6- The open circuit voltage for 10 stage Marx generator is 400kV but the real Measured output voltage was 38 kV because the primary charging

Chapter Five Conclusions And Recommendations For Future Work 80 voltage is 4 kV and it is possible to reach the Marx maximum output voltage if the laboratory earthing system is well designed and implemented. 7- The inductance for the two Marx supplies from table (4-1) is 13.6 µH for the 8-stage and 0.23 µH for the 10-stage, the inductance difference between the two systems is duo to the kind of capacitors, resistors, spark gaps design and wiring. For the 8-stage, capacitors was commercial type (cheap) and the spark gaps were made from curved copper wire, but for the 10- stage the capacitors were ceramic type (low inductance ~ 20 nH) and the spark gaps were well designed (Chang profile), which decreases the inductance for the 10-stage system.

5-2 Recommendations for Future Work: The suggested future work to improve the present research and to obtain more advanced results is the following: 1-Decreasing the jitter time and pulse width by enhancement of the Marx generator components (low inductance materials). 2- Design and construction of Marx generator with different spark gaps design. 3- Design and construction of solid state Marx generator using solid-state switches. 4- Design and construction of circuit for a pair of Marx stages. 5- Design and construction of a compact, low inductance repetitive Marx generator. 6- Design and construction of an atmospheric and pressurized spark gap filled with N2 or SF6 gas for Marx generator operation.

III Contents

Acknowledgment I Abstract II Contents III List Of Abbreviation VI List Of Symbols VII

1. Chapter One: General Introduction 1 1.1 Marx Generator Power Supply. 1 1.2 Spark Gaps. 5 1.3 Trigger Circuits. 6 1.3.1 Switching By Using Thyristor Trigger Circuit. 7 1.3.2 Switching By Using Krytron Trigger Circuit. 7 1.3.3 Switching By Using Thyratron Trigger Circuit. 8 1.3.4 Switching By Using Commercial Trigger Module. 9 1.4 Gas Laser Discharge. 10 1.4.1 Electrical Characteristics Of Gas Discharges. 10 1.5 Aim Of The Work. 13

2. Chapter Two: Theoretical Concepts 14 2.1. Gas Breakdown 14 2.2. Transient Voltage 18 2.2.1 Single -Stage Impulse Generator Circuit 20 2.2.2 Multistage Impulse Generator Circuit 30 2.3 Marx Generator 31 2.3.1 Charging of Marx Generator 36 2.3.2 Discharging of the Marx Generator 37 2.4 Trigger Spark Gap 38 2.4.1 Electrical Operation 39 IV 2.4.2 Ratings and Operating Characteristics 42 2.4.3 Range 44 2.4.4 Trigger Mode 45 2.4.5 Delay Time and Jitter 47 2.4.6 Recovery Time 47 2.5 Inductor 47 2.6 Power Supply of Gas Lasers 48

2.6.1 Power Supply for TEA CO2 48 2.6.2 Power Supply for Metal Vapor Laser 49 2.6.3 Power Supply for Excimer Laser 50

3. Chapter Three: Experimental Work 52 3.1 Introduction 52 3.2 Design Principles 52 3.3 Variable High Voltage Supply 53 3.4 External Trigger Generator Circuits 53 3.4.1 Xenon Camera Flash lamp Triggering Circuit 55 3.4.2 Car Coil Switching Trigger Circuit 56 3-5 Marx Generator 58 3-5-1 Marx generator (8 – stage) 58 3-5-2 Marx Generator (10 – Stage) 61

4. Chapter Four: Results and Discussion 67 4-1 Introduction 67 4-2 Marx generator (8-stage) 67 4-2-1 Xenon Flash Lamp Trigger Circuit 67 4-2-2 Current Pulse For Marx Generator 68 4.3 Marx Generator (10-stage) 70 4-4 Measurements and Calculations 72 V 4-4-1 LCR meter calculation method 72 4-4-2 Marx generator (10-stage)output pulse calculation 72 method 4-4-3 Marx generator (8-stage) output pulse calculation 73 method 4.5 Characteristic Marx generator (10-stage) 75 4.6 Characteristic Marx Generator (8-stage) 77

5.Chapter Five: Conclusions And Recommendations For Future 79 Work 5-1 Conclusion 79 5-2 Recommendations For Future Work 80

6. References 81

7. Appendices i Appendix(A) i Appendix(B) iii Appendix(C) v Appendix(D) vi Appendix(E) vii Appendix (F) ix x Appendix (G)

VI List of Abbreviations

Symbol CGS Grid storage capacitance.

CPS Anode storage capacitance.

EPS Anode supply voltage. PFN Pulse forming network.

RGC Grid charging resistor.

RKA Keep alive resistor.

RPC Anode charging resistor. SBV Self- breakdown voltage. SBV Static. Breakdown voltage. SCR Silicon controlled rectifier. U.V. Ultra violet.

VII List of Symbols

Symbol Unit

C Capacitance for LC circuit. F

C1 Discharge Capacitance of generation. F

C2 Capacitance of the load. F

Co Charge capacitance. F

Ceq. , C Marx Erected capacitance. F

C Stage Stage capacitance. F

Ct Total capacitance. F d Distance between electrodes. cm e Damping factor.

E Marx Energy stored in Marx. J E-E(CO) Cut off voltage. V E-E(max.) Maximum operating voltage. V E-E(min.) Minimum operating voltage. V f Max. Maximum pulse repetition rate. Hz G Spark gap.

H Marx Marx height. cm I Current arrive to anode. A

I1 Marx current. A

ICharge Charging of current. A iLC Current for LC circuit. A

IMax. Maximum current pulse. A

IMin. Minimum current pulse. A

Io Current arrive to cathode. A

IR Next peak current pulse. A

K o Aspect ratio. %

L Inductance for LC circuit. H VIII

L1 Internal inductance of generation. H

L2 External inductance of load or connection. H

LCh Charge inductor. H

L Marx , L eq. Erected series inductance. H

Lmin. Minimum inductance. H

L Stage Stage inductance. H n Attachment coefficient. cm-1 N Number of stage. stage -1 n a Numbers of electron arrive to anode. cm -1 n o Number of elec. incident to cathode due to external cm radiation . -1 n+ Number of elec. incident to cathode by secondary cm emission n1 Number of fired gaps.

P Peak Peak power. W

P ave. Average power. W

R1 Resistance controlling the wave front. Ω

' R2 , R2 Resistance controlling the wave tail. Ω

Ro Charge resistance. Ω t Maximum of time. sec. T Period. sec. t ad Delay time. sec. t J Jitter time. sec. t1 Nominal wave front duration. sec. t2 Nominal wave tail duration. sec. tactual Actual time. sec. t r Rise time. sec. t dec Decay time. sec.

TCH Time of charge. sec. u Flux function. ν Potential function. IX

VC1 Voltage to which C1 is charged. V

VCh Maximum charge voltage. V

VGap Voltage across the gap. V

Vi Initial voltage. V

VL max. Maximum high voltage. V

VN Stage voltage. V

V Open Open circuit voltage. V

VT(min.) Minimum trigger voltage. V

W Marx Marx width. cm x Space coordinates of x-axis. y Space coordinates of y- axis.

Z Marx Marx impedance. Ω

ZN Stage impedance. Ω

Zo Impedance. Ω α Townsend coefficient. cm-1 γ Cathode yield in electrons per incident ion. cm-1

ΔILMax Maximum current of an inductor. A η Efficiency. %

τ DISCH Discharge period. sec.

References 81

References

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