design and implementation of marx …...the first marx generator with eight stages, can deliver 64...

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

مي لوزارة التعليم العالي والبحث الع الجامعة التكنولوجية

قسم ھندسة الليزر والبصريات االلكترونية

مجهزماركس لتطبيقات بناءتصميم و

الليزر

إلىرسالة مقدمة ةـولوجيـالجامعة التكن ةـريات االلكترونيـزر والبصـة الليـم ھندسـقس

علوم فيمن متطلبات نيل درجة الماجستير كجزء الليزرھندسة

تقدم بھا

المھندس

سرمد فوزي حمزة 2003ھندسة الليزر/ لكترونيةاألوالھندسة الكھربائية

بإشراف

كاظم عبد حبيتر. د نصير مھدي ھادي . د

ھ1429صفر م 2008شباط

الخالصة

وقمة .منظومات الليزر الغازية ذات عرض نبضة خرج قصير إن

طاقة عالية تحتاج إلى نبضات تفريغ كھربائي بمواصفات خاصة مثل محاثة

مجھز قدرة نوع وان .معدل تكرارية للنبضة وزمن نھوض سريع , واطئة

ماركس واطئ المحاثة ممكن أن يوفر ھذا النوع من نبضات التفريغ لتشغيل

. الليزرات الغازية بكامل مواصفاتھا

األول . تم تصميم وبناء وتشغيل نوعين من مجھز قدرة ماركس

ذو ثمانية مراحل تضخيم يمكن أن يوفر فولتية خرج مجھز قدرة ماركس

كيلو فولت وحصلنا 2تم شحن فولتية أولية . كيلو فولت كحد أقصى 64لغاية

666كيلو فولت بنبضة ذات زمن نھوض 12على فولتية خرج فعلية

أما المجھز الثاني فكان , %75وكفاءته مايكرو ھنري 11اثة نانوثانية ومح

كيلو فولت 400مجھز قدرة ماركس ذو عشرة مراحل تضخيم ممكن أن يوفر

كيلو فولت وحصلنا على فولتية خرج 4 تم شحنه بفولتية أولية , كحد أقصى

نانوثانية ومحاثة 50كيلو فولت بنبضة ذات زمن نھوض 38فعلية بحدود

. %95وكفاءته يكرو ھنريما 4.2

األولى , تم تصميم نوعين من دوائر القدح لنوعي مجھز ماركس

ذو دائرة قدح باستخدام مصباح وميضي مع محولة قدح لمجھز ماركس

دائرة مع) إشعال ملف(والثانية باستخدام محولة قدح ثمانية مراحل

.ذو عشرة مراحل لمجھز ماركس ) MOSFET(ترانزستور نوع

لوميضي حوالي اتم الحصول على نبضة فولتية من دائرة المصباح

بينما دائرة القدح , ثانية مايكرو 2 كيلو فولت وعرض نبضة حوالي 4.5

. مايكرو ثانية 40 وعرض نبضة حوالي تكيلو فول 7.5الثانية حوالي

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 .

Electron Multiplication equation. d

a enn α0=

………… ……………………………………….(1 )d

oa ennn α)( ++=

…………………………………………… . ..(2)

where γ : cathode yield in electrons per incident ion. γ+

+ =+−nnnn oa )(

)()()( +++ +−+=+− nnennnnn o

dooa

α

)1( −=+ dda e

enn ααγ

……………………………..………………….(3)

from eq.(2): )1( −

= d

da

a eenn α

α

γ

γ+

+ +=−n

nnn oa )(

⎥⎦

⎤⎢⎣

⎡ +=− + γ

γ1)( nnn oa

……

( )( )( )

( …………………………………...……..….(4)

substitute eq.(4)to eq.(3):

)γ

γ+−

=∴ + 1oa nnn

11 −+−

= d

doa

a eenn

n α

α

γ

( )( )

( )( ) ad

da

d

do n

een

een

−−+

=−+ 1111 α

α

α

α

γγ

( )

( )11 −+−= d

ad

ad

o enenen ααα γ

( )1−−+−= daa

da

da

do ennenenen αααα γ

Appendices

( )11 −−= d

d

oa eenn α

α

γ

( )

11 −−= d

d

oa eeII α

α

γ

Appendices

APPENDIX (B)

L1 R1G

C2 C1 R2

Circuit arrangement

V/s

1/C1s L1s R1

R2 1/C2s

V(s)

Transform circuit

21

2.)(zz

zsVsV

+=

Where;

111

11 RsLsC

Z ++=

sCR

sCR

Z

22

22

2 1

1*

+=

Appendices

11122

2

22

2

11.

1..)(RsL

sCsCRR

sCRR

sVsV

++++

+=

sCsCRsCRsCRsCRsCLsCRsCR

sCRR

sVsV

122

2211222

112212

22

2

)1()1()1(.1

1..)(

+

+++++++

=

2

121

2

2

1221

3

121

2 1RRsCRs

RLsCLs

CRCCss

V

++++++=

122121221

1

111

1

22

23 1111LRCCCLRCL

RCL

DLR

RCDD +⎥

⎦

⎤⎢⎣

⎡⎥⎦

⎤⎢⎣

⎡+++⎥

⎦

⎤⎢⎣

⎡++

1.V=

Appendices

APPENDEX (C)

( )122

21

αα

αα

−−

=−−

TeeEV

tt

Differential equation for found maximum time:

[ ]tt eeT

E12

12122

_)(

0 αα αααα

−−

−=

tt 1122 lnln

tt ee 12

12αα αα −− =

)ln()ln( 1212

tt ee αα αα −− =

α − α = α − α

)(

)ln(

12

1

2

.max αααα

−=t

Appendices

APPENDIX (D)

112221221

1

111

1

22

23 11111.

LCCRCLRCLR

CLD

LR

RCDD

V+⎥

⎦

⎤⎢⎣

⎡+++⎥

⎦

⎤⎢⎣

⎡++

=

221222

1

11

22

121

3 1111.

RCCCRCR

CDR

RCL

DLDV

+⎥⎦

⎤⎢⎣

⎡⎥⎦

⎤⎢⎣

⎡+++⎥

⎦

⎤⎢⎣

⎡++

= V(s)

Where inductance L1=zero, D =s

221122

1

11

2 1)11(

1.

RCCCRCR

CsRs

V++++

=

1

212

12

212

121122

122

1

1

2

4)()11(

RRCC

RRCC

CRCRCRCRC

RC

s−

++++

−=m

Therefore

1

2

2

1

1

2

21

12

212

121122

2

])1(

[411)(

RRR

CC

RCRC

RCCCRCRCR

++−±

++

−s =

21

2

2

1

1

2

21

12

2

1

1

2

2,1 2

)1(

411)1(

CRRR

CC

RCRC

RR

CC

S

++−±++−

=

Where s is α

Appendices

APPENDIX (E)

1/C1s Ls R

1/C2s

V(s) =Vo

Vi/s

,

where: 21

111CCC

+= ,CLR 4

=

sCsC

LsR

sCs

VV i

12

2

11

1

+++=°

sCLsRs

CsC

CVi

1

1

22 ++=

])1(

1[2

2

2

CLsRss

LssRsC

CVi

++

+−=

)1

4(

4

22

2

22

sRC CRss

sRCRs

++

+=

2)2(

4

CRs

RCs

+

+=

222⎟⎠⎞

⎜⎝⎛ +

+⎟⎠⎞

⎜⎝⎛ +

⇒

RCs

B

RCs

A

Appendices

1=A

BRC

sRC

s ++=+24

RCB 2=

)])2(2

(1[22

RCs

B

RCs

AsC

CVV i

++

+−=°

)]2(1[22

2

RCtt

RCi eRC

teC

CV −−+−=

])21(1[2

2

tRCi et

RCCCV −

+−=

Appendices

Appendix (F)

When L =zero

1/C1s

1/C s

R

2Vi/s

sCsCRsC

sV

V io

21

2

11

1

++×=

CsRsC

sVi

1

12

+× =

CRssRC

i 1

12

+×V =

CRsCRs

CCi

1

1

2 +×

V =

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

+−

+

+⎟⎠⎞

⎜⎝⎛

CRsCRs

CRsC

CVi

11

1

11

2

=

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡

+−

CRssCCVi

111

2

=

⎥⎦

⎤⎢⎣

⎡−

−CR

ti e

CCV

12

=

Appendices

Appendix (G)

GBG VVV −=2

VV G −=

VVV BG +=

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡

+++

=321

31CCC

CCVBH

V

VCCC

CCVV G +⎥⎦

⎤⎢⎣

⎡++

+=

321

312

⎥⎥⎦

⎤

⎢⎢⎣

⎡

+++

+=32

31

1

1CCC

CCVV

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


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].


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.


Table (1-1) Comparison of Various Marx Generators

Author/Year

V

max

(kV)

size(m3) Joules

(J)

Rep-

rate(Hz) Load (Ω)

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

Laura K.Heffernan 2005 [10] 1000 12. 82 ×10-2 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

0

5

10

15

20

M.T. Buttra

m 1988

J. D. S

ethian 1989

Y.A.Kotov 1995

J. Hammon 1

997

F. E. P

eterk in 1999

A. J. D

ragt 2

001

Laura K.He ffe

rnan 2005

M.B.La ra etl.2005

Kirk S lenes etl

. 2006

J.R.M

ayes 2006

Jong-Hyun K im

2007

J/Kg

Author and years

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


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.


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]:


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 into the grid making the Krytron in the on case, this will

discharge the capacitor into the trigger, the thyratron or the spark gap

[18] as shown in Figure (1-5).

GSC

PSC


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].


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].


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].


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


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].


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]:

………………………………………………………..... (2.1) doa enn α=

)

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]

( 110 −−= d

d

eeII α

α

γ………..……………………….……………… (2.2)

when n related to I by taking into account the electronic charge of each

electron. At some point, the denominator approaches zero so that:

( ) 011 =−− deαγ , or approximately

when then: 1⟩⟩de α

1=deαγ .

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].


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]:

( )[ 11)(

n =−−

− den

α

α]γα ……………..…………………..……………… (2.3)

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]:

211 25.1 TTt = ……………………………………………..………….. (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 is the time

between O1 and the point on the wave tail where the voltage is one-half the

peak value, i.e. .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].

2t

412 TOt =

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


In the corresponding American specification, the nominal wave

front is defined as 1 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].

215. TT

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

generators. Which is the maximum stored energy: ( )2max121 oMarx VCE =

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].


v(s)21

2

ZZZ

sV

+= Where 1

11

1 RsC

Z += , sCR

sCZ

22

2

2

2 1+=

R

By substitution:

v(s) )1(

1)1(

22

2

11

22

2

+++

+=

sCRR

sCR

sCRR

sV

( ) 2221

1

2

11 RsCRsCR

Rs

V

++×⎟⎠⎞⎜

⎝⎛ +

=

⎟⎠⎞⎜

⎝⎛+⎟

⎠⎞⎜

⎝⎛ +++

=

++++=

2121212211

221

211

22

1221

2

11111

1

CCRRsCRCRCRsCRV

RRCCR

sCsCRR

RsV

or v(s)bassCR

V++

= 221

1 where ⎟⎟⎠

⎞⎜⎜⎝

⎛++=

212211

111CRCRCR

a and

⎟⎟⎠

⎞⎜⎜⎝

⎛=

2121

1CCRR

b

v(s) ⎥⎦

⎤⎢⎣

⎡−

−−−

=212121

111ssssssCR

V

Where and are the roots of the equation s2+ as + b = 0 and both

will be negative. From the transform tables:

1s 2s

[ ])exp()exp()(

)( 212121

tstsssCR

Vt −−

=υ


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

equation: 01111

2121212211

2 =⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛+++

CCRRs

CRCRCRs

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

The equation then becomes: 011

212121

2 =⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛+

CCRRs

CRs

And the roots are: 21

11CR

−≈s , 12

21CR

−≈s and 21 s⟩⟩s

The equation for the output voltage then becomes [19]

⎥⎦

⎤⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛−−⎟⎟

⎠

⎞⎜⎜⎝

⎛−=

2112

expexp)(CRt

CRtVtυ …………………………………….(2.5)

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

Fig. (2-7) The impulse voltage and its components [23].


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] ,

01111

22111121212

1

221

123 =⎥⎦

⎤⎢⎣

⎡+⎟⎟

⎠

⎞⎜⎜⎝

⎛+++⎟⎟

⎠

⎞⎜⎜⎝

⎛++

RCCLCLCLCLRR

DRCL

RDDV ….….….(2.6)


(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 , 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.

'2R


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

1α− and 2α− of the differential equation for V are

( ) ⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

++−±

++= 2

12

12

2

1221 /1

/4112

/1TTX

TTT

TTXor αα

and )( 122

1

21

αα

αα

−−

=−−

TeeVV

tt

C ……..………………………….………….(2.7)

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]

( )12

12logαααα

−= e

actualt ………………………………..……………………..(2.8)

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

)( 122

1211

ααη

αα

−−

=−−

Tee tt

……………………………...……………………(2.9)

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

( ) ⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

++−±

++= 2

12

12

2

1221 /1

/4112

/1XTTX

TTT

XTTXorαα

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.


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:

CLR 4

= where 21

111CCC

+=

The voltage V across the load capacitance is then given by:

[Appendix E]

2C

⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ +−= − CRtC e

CRt

CCVV /2

2

1 211 ……….……….……..………..…..(2.10)

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

( )CRtC eC

CVV /2

2

1 1 −−= ………….…….………………………..……(2.11)


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

(> CL4 ) 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].


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

equation: 1/2LI2 =1/2C1V2 i.e. [23]

LCVI 1= ……………………………….……………………………..(2.12)

If the circuit is critically damped, the current will be given by an

expression [23]:

LC

eVI 1= ………………………………………….………………… (2.13)

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. CL4 ) 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].


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.


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 ( )

for breakdown only slightly below the second gap ( ). A more complete

analysis shows that voltage distribution across the second and higher gaps

immediately after the breakdown of the lowest gap ( ) is governed by the

1G

2G

1G

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 immediately

after breakdown of which may be estimated as follows:

2G

1G

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 the point G initially at earth will

assume a potential –V, but the potential of B is fixed by the relative

magnitudes of and and is given by [24]:

1G

21 ,CC 3C

⎜⎜⎝

⎛++

+=

321

31

CCCCC

VVBH ⎟⎟⎠

⎞………………………………………………….(2.14)

hence the voltage across the gap (G ): 2

⎟⎟⎠

⎞

3C

3C

⎜⎜⎝

⎛++

++=

21

312 1

CCCC

VVG

≈

………………………………………………..(2.15)

[Appendix G].

If C 2 = 0, VG2 reaches its maximum value of 2V. If both and

are zero, will equal to V, i.e. its minimum value.

1C 3C

2GV

It is apparent, therefore, that the most favorable conditions for the operation

of the generator occur when the gap capacitance is small and the stray

capacitances and are large. The conditions set by the above expression

are transient, as the stray capacitors start discharging.

2C

1C

The practical stray capacitors are of low values, consequently the time

constants are relatively short μsec or less. 110−

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].


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 is made large

compared with and which are made as small as is necessary to obtain

the required length of the wave tail. Under some conditions the current

through does not flow through and so does not reduce the initial

generator output voltage, no matter how small or how large may be. In

a practical generator employing this circuit, the voltage drop in is made

less than 1% of the output voltage by selecting suitable values of the

parameters. The stage capacitance was 0.2 μF, is about 40 Ω and the

wave-tail resistance required for a 5 μsec wave tail is about 25 Ω. is

made nearly 10 k Ω [23].

3R

1R 2R

2

2R 1R

2R 1R

1R

1R

R 3R


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: 2NCRT ooCH = ………………………………………………….……… (2.16)

Fig. (2-14) Marx bank charging performance [19].


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:

………………………….…….………………...... (2.17) MARXMARXCH CL=τ

The discharging into matched impedance requires a time τ2 . 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]:

MARXTOTALCH CLπτ = …………………………….……………….…… (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, . In the resistive

case, the self-time constant is just:

oZ

2oo

DISCHCR

=τ ………………………….……………………………… (2.19)

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]:

LCt

LCVi NLC sin= …………..………….………………..…………..(2.20)

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:

LCt

LCVi NLC ≅

LtVN= ……………………..…………………….. (2.21)

Because the process terminates when the bank is discharged. If the

Marx discharges into matched impedance, the Marx current is:

N

N

ZNV2

I1 = …………………………………….……………………….. (2.22)

and the efficiency can be related by the ratio of ( i ). 1I/LC

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.)

gapi NVNV = Initially …………………………..………………………(2.23)

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

( ) gapi VNNV 2−= Two gaps fired ……………….……………………(2.25)

or, alternatively, the voltage across an unfired gap should be:

1nNNViVGap −

= .…………………….……….…………..………(2.26)

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).


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].


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].


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).


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 :


242

4tChtCh

CH

CLCLTTππ

=== ….…….………………..……….(2.27)

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;

max

.max 12 f

CL tCh ≤π ………….…………………………(2.28)

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]:

.max,

.max.max,.min

LL I

TLΔΔ

≥ ν …………………………...………………….(2.29)

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).


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

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


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).

Ω

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


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


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


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


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).


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.


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).


(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.


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


the gradient outside the plane portion. The equations for the uniform field

electrode (Chang`s family of profiles) are [32]:

)sinh()cos( uvKux o+=

)cosh()sin( uvKvy o+=

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

ux = ; )cosh()2/( uKy O+= π

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).


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:


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:

EMarx = 1/2 C V2

= 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.


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).


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 ≅ ⇒ f =

T1 =

ns501 = 2× 107 Hz.

f = TLC

121π

2× 10 7 =CL 10

121

×π


L = 2.64 nH. Decay time t de ⇒ ≅ 2 s 610−× ⇒ f =

T1 = 5×105 Hz

⇒ L = 4.2 µ H.

⇒ Pulse width ≅ 450 ns ⇒ f =

T1 = 2.1×106 Hz.

L=2.3×10 -7 H. ∴L Total = L Rise Time + L Decay Time

= 2.64 nH +4.2 µ H = 4.2 µH. L Pulse Width = 2.3×10 -7 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)):

Rise time t r 6.66 ⇒ ≅ ×10 -7s

⇒ T

f 1= = 1.5 ×106 Hz.

⇒ L = 2.99 × 10 -7 H. ⇒ Decay time t de ≅ 4 × 10- 6 s ⇒ f =

T1 = 2.5 ×105 Hz.

⇒L = 1.07897×10-5 H.

Chapter Four Result & Discussion 74 ⇒ Pulse width ≅ 4.5×10 -6s ⇒ f =

T1 = 2.222× 105 Hz

⇒ L = 1.3658×10-5 H.

∴L Total = L Rise Time + L Decay Time

= 11.0887µH

L Pulse Width = 1.3658×10-5 H.

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

Marx generators.

Table (4-1)

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

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)

Unit Value Description Parameter

kV 400 Open circuit voltage V Open

stage 10 Number of stage N

pF 2400 Stage capacitance max.

voltage 40 kV C Stage

10-10 F 2.4 Erected capacitance C eq. or C Marx

kV 40 Maximum charging voltage VMax. Ch

kV 4 Real charging voltage VCh

Hµ 4.2026 Erected series inductance L Marx or L eq.

10-7H 4.2026 Stage inductance L Stage

ohm 132.328505Marx impedance Z Marx

10 8watt3.03 Power peak P Peak

mJ 192 Energy stored in marx E Marx

s 0.0216 Charging time T Ch

Hz 46 Maximum Repetition rate f RR

ns 50 Rise time t r

µs 2 Decay time t de

watt 8.8 Average power P ave

% 95 Efficiency into a load η

mA 40 Charging current ICharge

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)

Unit Value Diameter Parameter

cm 75 Marx length L Marx

cm 7.5 Marx width W Marx

cm 11 Marx hight H Marx


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)

Unit Value Description Parameter

kV 64 Open circuit voltage (typical) V Open

stage 8 Number of stage N

nF 4.7 Stage capacitance, max.

voltage 8kVDC

C Stage

10-10F 5.875 Erected capacitance Ceq. or C Marx

kV 8 Maximum charging voltage VMax.Ch

kV 2 Real charging voltage VCh

Hµ 11.0887 Erected series inductance L Marx or L eq.

Hµ 1.3860875Stage inductance L Stage

ohm 137.38407Marx impedance Z Marx

MW 7.453 Peak power P Peak

mJ 75.2 Energy stored in marx E Marx

s 0.5264 Charging time T Ch

Hz 1.8996 Maximum repetition rate f RR

ns 666 Rise time t r

sµ 4 Decay time t de

watt 0.1428 Average power P ave.

% 75 Efficiency into a load η

mA 1 Charging current ICharge

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)

Unit Value Diameters Parameters

cm 38 Marx length L Marx

cm 5.5 Marx width W Marx

cm 4 Marx height H Marx

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

method 72

4-4-3 Marx generator (8-stage) output pulse calculation

method 73

4.5 Characteristic Marx generator (10-stage) 75

4.6 Characteristic Marx Generator (8-stage) 77

5.Chapter Five: Conclusions And Recommendations For Future

Work 79

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)

Appendix (G)

ix x

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

VIIIL1 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

n a Numbers of electron arrive to anode. cm-1

n o Number of elec. incident to cathode due to external radiation .

cm-1

n+ Number of elec. incident to cathode by secondary emission

cm-1

n1 Number of fired gaps.

P Peak Peak power. W

P ave. Average power. W

R1 Resistance controlling the wave front. Ω

R2 , '2R 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.

IXVC1 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

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design and implementation of marx …...the first marx generator with eight stages, can deliver 64...

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