NEGATIVE DIFFERENTIAL CONDUCTIVITY IN E-BEAM SUSTAINED

DIFFUSE DISCHARGES FOR SWITCHING APPLICATIONS

by

BRYAN EDWARD STRICKLAND, B.S. in E.E.

A THESIS

IN

ELECTRICAL ENGINEERING

Submitted to the Graduate Faculty of Texas Tech University in Partial Fulfillment of the Requirements for

the Degree of

MASTER OF SCIENCE

IN

ELECTRICAL ENGINEERING

Approyed

May, 1986

ACKNOWLEDGMENTS

I would like to express my sincere appreciation to Dr.

Karl Schoenbach for serving as advisor of my graduate work

and co-chairman of my committee. His advice, guidance, and

technical assistance throughout the course of these exper­

iments and during the preparation of this manuscript has

been invaluable. I would also like to thank Dr. Gerhard

Schaefer for serving as co-chairman of my committee and

providing invaluable support and guidance for the prepara­

tion of this manuscript. I am also deeply indebted to the

other members of my committee: Dr. Osamu Ishihara who was

instrumental in the development of a computer code and Dr.

Clyde Martin.

I would also like to express my gratitude to those I

have worked with in the laboratory on the project. I en­

joyed working with and have been greatly assisted by Chuck

Harjes, Doug Skaggs, Kim Zinsmeyer, Ken Rathbun, Rick

Korzekwa and other students in the Plasma and Switching

Laboratory at Texas Tech.

I must also extend a special thanks to Paul Vanderford

who has been very helpful in the preparation of this manu­

script. Finally, I owe my deepest appreciation to my par­

ents, who have stood by me with unwaving support and en­

couragement.

11

TABLE OF CONTENTS

ACKNOWLEDGMENTS ii

ABSTRACT v

LIST OF FIGURES vi

I. INTRODUCTION 1

II. BACKGROUND AND THEORY 5

2.1 Attachment Instability 6

2.2 One-Dimensional Model of the Discharge 9

2.3 Formation of Domains in E-beam Controlled Diffuse Discharges . . 11

III. ELECTRICAL MEASUREMENTS 15

3.1 Experimental Set-up 15

3.1.1 E-beam System 15

3.1.2 Switch System 17

3.1.3 Diagnostics 18

3.2 Experimental Results 18

3.2.1 C2F6:Ar Results 19

3.2.2 N2:Ar Results 22

IV. OPTICAL MEASUREMENTS 24

4.1 Optical Set-up 24

4.2 C2F6:Ar Results 25

4.2.1 Region of Positive Differential Conductivity . 25

4.2.2 Region of Negative Differential Conductivity . 28

111

4.2.3 Region of Approximately Zero Differential Conductivity . 28

4.2.4 Effect of Applied Voltage

on Position of Striation . . 32

4.3 N2:Ar Results 35

V. CONCLUSIONS 37

LIST OF REFERENCES 39

IV

ABSTRACT

In e-beam sustained diffuse discharges in gas mixtures

which contain small additives of electronegative gases, the

discharge characteristic (current density versus reduced

field strength) may exhibit negative differential conduc­

tivity (NDC) depending on the source function and the con­

centration of attacher gas. In discharges exhibiting nega­

tive differential conductivity, electron depleted domains

of high electric field intensity are formed in the dis­

charge.

The results of electrical and optical measurements

performed on an e-beam sustained diffuse discharge in a gas

mixture of 2% C2F6 in 1 atm Ar are presented and compared

with theoretical predictions. The steady state current

density (J) versus reduced field strength (E/N) exhibits a

strong negative differential conductivity in an E/N range

of 2.5 Td < E/N < 5 Td. Time resolved photographs taken in

this E/N range show distinct luminous layers perpendicular

to the discharge axis.

LIST OF FIGURES

1. Electron mobility and attachment rate as a function of E/N for gases in diffuse discharge opening switches 3

2. Regions of operation corresponding to an I-V characteristic exhibiting negative differential conductivity 7

3. Distribution of E/N (curves a - e) and n+ (a) in • cm^ discharge gap with E/N = 4.8 • lO"-'- V

(Problem 1, VQ = 6 • 10^ cm/sec); current density at times: a) 0; b) 2 ysec; c) 4[1) (E/N) • 10" ^ = 3.3 V • cm2; 2) 3.9; 3) 4.8]; d) 5; e) 6 [12] . 13

4. Cross sectional view of e-beam and switch systems 16

5. Steady state current density, J, versus E/N for a discharge in 2% C2F5:Ar at 1 atm 20

6. Discharge resistivity, p, versus E/N for a discharge in 2% C2F6:Ar at 1 atm 21

7. Steady state current density, J, versus E/N for a discharge in 5% N2:Ar at 1 atm 23

8. Experimental set-up for optical measurements of the discharge 26

9. Photograph of discharge at 2 Td in the positive differential conductivity region . . . 27

10. Photographs taken at 100 ns intervals in a discharge at 5 Td in the negative differential conductivity region 29

11. Photodensitometer curves of the discharge along the discharge axis at 5 Td 30

12. Photographs taken at 100 ns intervals in a discharge at 9 Td in the zero differential conductivity region 31

13. Photodensitometer curves of the discharge along the discharge axis at 9 Td 33

VI

14. Position of striation as a function of reduced field strength, E/N 34

15. The effect of reversing the polarity on the position of the striation 36

vii

CHAPTER I

INTRODUCTION

In recent years interest has grown in the use of in­

ductive energy storage devices in pulsed power systems be­

cause with inductive devices it is possible to achieve sig­

nificantly higher energy densities than with capacitors.

In order to use an inductive energy storage device in a

pulsed power system, an opening switch is required to

switch the energy from the inductor to the load. In a re­

petitive pulsed power system the opening switch should op­

erate in a controlled mode, have a high current carrying

ability (kA), have a high voltage stand off capability

(kV), have low losses in the conduction phase, and endure a

long lifetime. Electron-beam (e-beam) controlled diffuse

discharges show promise for use as repetitively operated

switches in inductive energy storage systems.

In order for a diffuse discharge switch to have the

previously mentioned properties, it is necessary to prop­

erly engineer the gas mixture used in the switch. To ob­

tain low losses in the conduction phase, it is necessary

for the gas to have a high electron mobility and a low

electron loss rate (recombination and attachment) at low

reduced field strength (E/N) which corresponds to the con­

duction phase. Furthermore, to improve the opening and

stand off capabilities of the switch, it is desirable to

have a gas that has a low electron mobility and a high

electron loss rate at higher values of E/N that correspond

to the opening and hold off phases. For the switch to

achieve fast opening times, electronegative gases or at-

tachers must be in the switch gas mixture. To satisfy the

conditions listed above, it has been suggested to use an

attacher that has a low attachment rate at low E/N and a

high attachment rate at high E/N [1,2,3]. The desired

electron mobility and attachment rate relationship as a

function of E/N is illustrated in Fig. 1.

Hunter [4], Kovalchuk, et al. [5], Fernsler, et

al. [6], Hallada, et al. [7], Harjes, et al. [8], and

Schoenbach, et al. [9] have investigated e-beam controlled

diffuse discharge switches in various modes of operation.

An e-beam controlled diffuse discharge switch facility has

been constructed at Texas Tech University to investigate

promising switch gas combinations in a repetitive mode of

operation [8,9].

Christophourou, et al. [10] has investigated the prop­

erties of some promising gases for use in diffuse discharge

opening switches. Fluorocarbons in combinations of Ar or

CH4 buffer gas exhibit an electron mobility and attachment

rate similar to the idealized relationship shown in Fig. 1

[10].

ATTACHMENT RATE

(E/N) (E/N)

Fig. 1. Electron mobility and attachment rate as a function of E/N for gases in diffuse discharge opening switches.

The use of attachers in e-beam controlled diffuse dis­

charge switches and their subsequent effect on the current-

voltage (I-V) characteristics of the switch has been

theoretically investigated by Schaefer, et al. [3]. The

results show that a switch that utilizes attachers with a

strongly increasing attachment rate as a function of E/N

will have an I-V characteristic which exhibits negative

differential conductivity (NDC) depending on the magnitude

and energy of the ionization source and the concentration

of the attacher.

CHAPTER II

BACKGROUND AND THEORY

In an externally sustained diffuse discharge for

switching applications, the primary processes in the dis­

charge which must be considered in order to describe the

electrical behavior of the discharge are ionization by the

external source, given by the source function, S; the ioni­

zation due to the applied electric field (E), described by

the ionization rate coefficient, ki(E); the electron at­

tachment depicted by the attachment rate coefficient,

ka(E); and the recombination of electrons and ions,

described by the electron-ion recombination rate coeffic­

ient, 3ei« ^or the switch gas combination of C2F5:Ar, the

recombination rate and the source function are independent

of the applied electric field while the attachment rate,

the ionization rate, and the electron drift velocity, v^,

are strongly dependent on the applied field or reduced

field strength.

As predicted by Schaefer et al. [3], the discharge is

recombination dominated at low E/N where the attachment

rate coefficient, k^iE), is very small. With increasing

E/N, ka(E) increases and the discharge becomes attachment

dominated. As E/N increases further, ionization through

discharge electrons becomes significant and finally the

discharge becomes self sustained. It is within the attach­

ment dominated stage of operation that the attachment rate,

ka(E), is a strongly increasing function of E/N and, conse­

quently, the discharge may exhibit NDC [3]. The previously

mentioned stages of operation are illustrated in a typical

I-V characteristic exhibiting NDC, as shown in Fig. 2.

2.1 Attachment Instability

Electron-neutral dissociative attachment generally has

a threshold electron energy corresponding to the dissocia­

tive energy of the unstable intermediate negative ion [11].

Therefore, over a certain E/N range in which the mean elec­

tron energy approaches the negative ion dissociation en­

ergy, the dissociative attachment rate is a strongly in­

creasing function of E/N. Under steady state conditions, a

small increase in the local electric field results in an

increase in the attachment rate which causes a reduction of

the electron density and a further increase in the electric

field. Therefore, an instability occurs [11].

Ultimately, electron depleted domains of high electric

field are formed in the discharge. These domains can be

static or moving across the discharge, which results in

oscillations in the discharge current and voltage

[12,13,14,15]. A further consequence of attachment insta­

bility in a diffuse discharge is that the high local

z UJ a

z u oc tr =3 U

RECOMBINATION

DOMINATED

ATTACHMENT

DOMINATED

SELF SUSTAINED

REDUCED FIELD STRENGTH E/N

Fig. 2. Regions of operation corresponding to an I-V characteristic exhibiting negative differential conductivity.

8

fields produced by the electron attachment loss will

greatly increase the local heating and, therefore, the ion­

ization rate, until streamers are initiated which grow to­

ward both electrodes resulting in a glow-to-arc transition.

As previously mentioned, a diffuse discharge which

contains attachers may exhibit a NDC characteristic. Nega­

tive differential conductivity is also a characteristic of

semiconductors exhibiting the Gunn Effect. In each case,

the reason for the NDC characteristic is a decrease in

electron drift velocity due to an increase in the effective

mass of an electron with increasing energy. In semiconduc­

tors the increase in effective mass is caused by the scat­

tering of the electrons into the satellite or higher val­

leys [16,17], while in gas discharges the increase in

effective mass is due to the attachment of the electrons by

the heavier electronegative gas molecules. In bulk semi­

conductors that exhibit a NDC characteristic, the homogene­

ous bulk material can become electrically heterogeneous

with a high field dipole domain forming and propagating

through the semiconductor under d.c. bias conditions

[16,17]. Therefore, it is of interest to determine if the

domains present in a diffuse discharge [12,13,14,15] which

exhibits NDC have similar properties as the domains in

semiconductors.

2.2 One-Dimensional Model of the Discharge

The spatial dependence of the fields and particle den­

sities in a diffuse discharge can be described by the space

dependent, one dimensional continuity equations for elec­

trons (1), positive ions (2), and negative ions (3):

3n e + -— Me' e = S + kiN^ne

3t 3x

- kaNane - 6eiJ en+ (^

8n+ a it i^ \i+^+^ = S + kiNane

- Biin+n_ - Beirier + ^2)

9n_ 3 + —- u_n_E = kaNanp

3t 3x a a e

- Biin+n_ (3)

and Poisson's equation

3E —e — = — (n+ - n_ - ne) , E > 0 , (4) 3x e

0

where UQ, n_, and n+ are the densities of electrons, nega­

tive ions, and positive ions; Ue^ ^-' ^^^ ^+ ^^^ ^^® corre­

sponding mobilities; the source function, S, is the rate at

which electrons are produced by the external source; Bei

and 3ii are the electron-ion and ion-ion recombination rate

coefficients, respectively; Ng is the number density of

10

attacher molecules; and e is the charge of an electron. We

must adjoint to the system of equations (l)-(4) the bound­

ary conditions at the electrode surfaces and the equations

governing the external circuit. With the cathode at x = 0

and the anode at x = L, the boundary conditions are

Uene(0,t) = YM+n+(0,t) , (5)

n _ ( 0 , t ) = 0 , (6)

and

n+(L,t) = 0 , (7)

where y is the secondary-emission coefficient at the cath­

ode which relates the emission of electrons from the cath­

ode due to bombardment of the cathode by positive ions.

The secondary-emission coefficient, y is defined by the

ratio of electron current at the cathode to positive ion

current at the cathode [18],

le Y = — . (8)

••• +

The boundary condition in equation (5) can be obtained from

the definition of the secondary-emission coefficient and

consideration of the electron and positive ion currents in

a high pressure (dense) plasma. Equation (6) says that

there are no negative ions at the cathode for any time, t.

This condition can be physically visualized since there are

11

no mechanisms for creating negative ions at the cathode.

Furthermore, any negative ions which are created in the

discharge region will move toward the anode due to the

electric field. Similar reasoning for positive ions re­

sults in equation (7). The equations governing the ex­

ternal circuit are

L Q

j(t) = - J iUe^e •*• M+n+ + p_n-)Edx ^ 0 (9)

and

L J* Edx = UQ = constant , (10) 0

where UQ is the supply voltage and L is the interelectrode

gap length.

2.3 Formation of Domains in E-beam Controlled Diffuse Discharges

In order to investigate the formation of domains in a

diffuse discharge of interest for pumping CO2 lasers,

Barkalov and Gladush [12] used the mathematical model pre­

viously discussed to describe a discharge containing a mix­

ture of N2 + O2 which exhibited NDC. When a voltage UQ,

corresponding to the electric field E in the region

Ei< E <E2 of Fig. 2, is applied to the discharge, a domain

is formed at the cathode and moves with constant velocity.

12

amplitude, and shape along the interelectrode gap, as shown

in Fig. 3. The sloping line of Fig. 3(a-c) indicates that

the domain moves at a constant velocity, VQ = 6 x 10^

cm/sec. Upon reaching the anode, the domain merges with

the anode. The voltage released by the merging process is

redistributed between a new domain growing at the cathode

and the discharge column as shown in Fig. 3d. This merging

process causes the current in the external circuit to in­

crease until the new domain is completely formed. The new

domain picks off voltage from the discharge column which

causes the current to fall to its minimum value. The cur­

rent remains constant while the domain is moving along the

interelectrode gap.

These calculations [12] revealed that as the applied

voltage is further increased there is a proportional in­

crease in the width of the domain, as shown in Fig. 3b.

Furthermore, the domain velocity is independent of applied

voltage. Since the domain width increases with increasing

voltage, the period of the current oscillation becomes

smaller with increasing voltage [12].

A computer code was developed that reproduced the re­

sults of Barkalov and Gladush [12] by implementing the im­

plicit finite difference methods to solve numerically the

system of equations (l)-(4). This computer code is cur­

rently being modified in order to solve the system of

equations (l)-(4) for a discharge in a gas mixture of 2%

13

(E/N) 10? V-cnr

/Z

n^'JO , cm

Fig. 3. Distribution of E/N (curves a - e) and n+ (a) in discharge gap with E/N = 4.8 • 10 -^ V • cm^ (Problem 1, VQ = 6 • 10^ cm/sec); current density at times: a) 0; b) 2 usee; c) 4[1) (E/N) • 10^^ = 3 3 V • cm^; 2) 3.9; 3) 4.8]; d) 5; e) 6 [12].

14

C2F6 in Ar at a total pressure of 1 atm. The basic gas

data for this gas mixture were obtained from Christophourou

et al. [10]. The results obtained from this calculation at

this time do not agree with the experimental observations.

This discrepancy may be due to the uncertainty of parame­

ters such as the positive and negative ion mobility or the

electron-ion and ion-ion recombination rate for gas mix­

tures of C2F5:Ar.

CHAPTER III

ELECTRICAL MEASUREMENTS

In order to study the electron-beam controlled conduc­

tivity in a high pressure diffuse discharge containing

small amounts of electronegative gases, a repetitive

electron-beam controlled diffuse discharge switch exper­

iment has been constructed and used to investigate promis­

ing gases for opening switches [8].

3.1 Experimental Set-up

The e-beam system consists of an e-beam gun inside of

a Pyrex chamber that is located between the two parallel

plates of the e-beam pulser's transmission line. The

stainless steel switch chamber is located above the e-beam

system. Figure 4 is a cross-sectional view of the e-beam

and switch systems [8].

3.1.1 E-beam System

The e-beam gun is a tetrode that consists of a dispen­

ser cathode, a control grid, a screen grid, and the anode.

The electron source or cathode is a Ba02 dispenser cathode

capable of emitting 4 A/cm^ uniformly over the 100 cm^

area of the cathode at a temperature of SSO^K. The e-beam

15

16

CURRENT SENSOR

DISCHARGE VOLUME

PFN CONNECTION

E-BEAM PULSER

/f,//,/n

CURRENT SENSOR

VACUUM PUMP

Fig. 4- Cross sectional view of e-beam and switch systems.

17

gun is operated in a vacuum of 10"^ torr. The temporal

structure of the e-beam is controlled by a control grid

that is driven by a transmission line pulser capable of

generating a pulse train with a variable pulse duration and

separation. In addition, a d.c. biased screen grid shields

the control grid from the effects of induced voltage by the

anode or e-beam pulser.

The e-beam pulser consists of a two-stage Marx genera­

tor that is capable of delivering a maximum output voltage

of 250 kV with a risetime of 5 ns and a decay time of

2.5 ijs into a 300-ohm load.

3.1.2 Switch System

The diffuse discharge is generated in a stainless

steel chamber that has been tested up to 4 atmospheres. A

25 um titanium foil serves as the interface between the

high pressure switch chamber and the high vacuum, e-beam

chamber. A 12 urn aluminum foil functions as the lower

electrode while the upper electrode is made of stainless

steel. After traveling through each of the foils, the

e-beam ionizes the gas between the switch electrodes and

creates a plasma. The plasma continues to conduct until

the ionizing e-beam is turned off, which allows recombina­

tion and attachment processes to remove the remaining free

electrons, thus creating an insulating medium or opening

the switch. A 2-ohm pulse forming network with a maximum

18

output voltage of 60 kV supplies the current through the

discharge plasma.

3.1.3 Diagnostics

Transmission line current transformers [19,20] and

fast resistive current probes were used to measure the

e-beam current and switch current, respectively. Fast re­

sistive voltage dividers were utilized as voltage probes.

All current and voltage waveforms were recorded with Tek­

tronix 7834 storage oscilloscopes. Since the anode of the

e-beam gun is at the same potential as both the lower elec­

trode and the switch chamber, ail diagnostic probes for the

switch system were referenced to the high voltage of the

e-beam pulser. Consequently, the storage oscilloscopes

that recorded the data for the switch system were placed in

a floating screen box.

3.2 Experimental Results

While operating the e-beam gun as a cold cathode di­

ode, which relies only on field emission for electron pro­

duction, electrical investigations were performed on a high

pressure diffuse discharge in a gas mixture of 2% C2F6 in 1

atm Ar. The impedance of the switch system was held con­

stant at 4 ohms. In the cold cathode diode mode the source

term, which is the number of electrons produced per

19

cm- • second, was in the range of 2-3 x lO' cm' s"-'-. The

electrode gap spacing was maintained at a constant 3.9 cm

while the applied voltage was varied from 0 to 15 kV.

3.2.1 C2F6:Ar Results

The steady state current density (J) versus the re­

duced field strength characteristic for a gas mixture of 2%

C2F6 in 1 atm Ar is shown in Fig. 5. This characteristic

contains a region with a pronounced negative differential

conductivity in the reduced field strength range of 2.5 Td

< E/N < 5 Td. This range of reduced J corresponds to the

range of E/N where the attachment rate for the gas mixture

of 2% C2F6:Ar is strongly increasing.

In previous experiments performed under the same con­

ditions, using various mixtures of CO2, SO2, or N2O in 1

atm N2, the steady state J versus reduced E/N character­

istic did not yield a region of NDC [21]. In order to ob­

tain a high pressure diffuse discharge whose steady state J

versus E/N characteristic exhibits a strong NDC character­

istic, it is necessary to use a gas mixture with an attach­

ment rate that increases strongly with E/N, such as C2F6:Ar

and C3F6:Ar mixtures [22].

The experimentally obtained resistivity (p) versus E/N

characteristic for this gas mixture is shown in Fig. 6.

This result shows an increase in resistivity by a factor of

20

1 Atm. Argon •*• 2% C2^Q

E U \ <

(A

2 UJ Q

u

3. 0

2.5

2.0 -

1.5

1. 0 -

0. 5

0. G

• I I I I 1 1 r T 1 1 r

' • ' ' ' • L.

10 15

REDUCED FIELD STRENGTH E/N / C Td 3

Fig- 5. Steady state current density, J, versus E/N for a discharge in 2% C2F6:Ar at 1 atm.

21

10'

E O I E

r. 10^

a Q:

1—4

—

»—t

ULI

T 1 r

•ooo-

10'

1 Atm. A r g o n + 2% ^ 2 ^ 5

T 1 1 1 1 1 1 1 1 r

J I L.

10 15

REDUCED FIELD STRENGTH E/N/ C Td ]

Fig. 6. Discharge resistivity, p, versus E/N for a discharge in 2% C2F6:Ar at 1 atm.

22

50 in a reduced field strength range of 2 Td < E/N < 12 Td.

The change in resistivity for this gas mixture is an order

of magnitude greater than that found for a gas mixture of

0.7% N2O in 1 atm N2 [23]. The opening times for the gas

mixture of 2% C2F6:Ar at 1 atm were below 100 ns.

The mixture seems to be relatively stable since repro­

ducible results were obtained for 200 shots without chang­

ing the gas; therefore, this mixture may be a reasonable

switch gas candidate for use in a repetitively operated,

closed system.

3.2.2 N2:Ar Results

Other work done by Long, et al. [24], Haddad [25], and

Petrovic' [26], suggest that it may be possible to obtain a

NDC characteristic by using a mixture of a molecular gas,

such as N2 in a buffer gas such as Ar, which exhibits a

Ramsauer minimum in the momentum transfer cross-section.

Therefore, investigations were performed in mixtures of 2%

N2 in 1 atm Ar and 5% N2 in 1 atm Ar. The current density

(J) versus E/N characteristic for a gas mixture of 5% N2:Ar

is shown in Fig. 7. It shows that under our operating con­

ditions this discharge did not exhibit a NDC characteris­

tic. A similar result was obtained for the gas mixture of

2% N2 in 1 atm Ar.

23

I E U

(0

tn LU

a z: UJ on cr ID U

IQ T 1 1 I 1 1 1 1 1 1 T I I

J I i I I I i I I I t i _ _

5 10 15

REDUCED FIELD STRENGTH < E/N )/Id

Fig. 7. Steady state current density, J, versus E/N for a discharge in 5% N2:Ar at 1 atm

CHAPTER IV

OPTICAL MEASUREMENTS

The formation of high field domains can be expected in

e-beam sustained diffuse discharges that exhibit a NDC

characteristic [27,28,12]. In regions of high field inten­

sity, the number of excited atoms or molecules is in­

creased, causing an increased level of emission processes.

In order to investigate the possible formation of such do­

mains in our discharge, time resolved photographs were

taken at various times during the discharge while using

various bias conditions.

4.1 Optical Set-up

Time resolved photographs of the discharge were taken

using a high speed, high resolution, image converter camera

that consisted of a proximity focusing diode manufactured

by ITT with a Tektronix roll film back mounted on the rear

of the diode [29]. A krytron-switched Blumlein pulser was

used to deliver a 10 kV, 10 ns rectangular pulse to the di­

ode; consequently, the camera has a shutter speed of 10 ns.

The diode has a high resolution of 45 Ip/mm.

The experimental arrangement for the optical investi­

gations performed on the discharge is schematically

24

25

illustrated in Fig. 8. Optical investigations were per­

formed on discharges containing gas mixtures of 2% C2F5:Ar

and 5% N2:Ar.

4.2 C?Ffi;Ar Results

The diffuse discharge containing 2% C2F5:Ar was inves­

tigated in three operation regions: the region of positive

differential conductivity (PDC), corresponding to the E/N

range 0 < E/N < 2 Td as shown in Fig. 5; the region of neg­

ative differential conductivity (NDC), corresponding to the

E/N range 2.5 < E/N < 5 Td; and the region of approximately

zero differential conductivity (ZDC), corresponding to the

E/N range 5 < E/N < 9 Td.

4.2.1 Region of Positive Differential

Conductivity

A time resolved photograph of the discharge biased at

2 Td so that it would operate in the PDC region is shown in

Fig. 9. This photograph illustrates that the discharge is

homogeneous or has no field domains other than the cathode

fall for bias points to the left of the current density

maximum. The discharge is homogeneous throughout the dura­

tion of the 500 ns discharge current pulse.

26

ins I

10 kv i_

A

DISCHARGE IMAGE CONVERTER CAMERA

Fig. 8. Experimental set-up for optical measurements of the discharge.

27

Fig. 9. Photograph of discharge at 2 Td in the positive differential conductivity region.

28 4.2.2 Region of Negative Differential

Conductivity

The discharge was biased at 5 Td so that it would op­

erate in the region of NDC. Time resolved photographs

taken at 100 ns intervals throughout the duration of the

discharge current are shown in Fig. 10. At any point of

operation in this region, the discharge is not homogeneous.

These photographs show a distinct luminous layer perpendic­

ular to the discharge axis.

In order to obtain qualitative information about the

position of these luminous layers or striations as a func­

tion of time, photodensitometer plots were made from the

negative of each photograph. The normalized photodensito­

meter plots along the discharge axis corresponding to the

photographs in Fig. 10 are shown in Fig. 11.

These curves show that the domain forms at the cathode

and propagates toward the anode with constant velocity and

shape, as predicted by Barkalov and Gladush [12], As shown

by Douglas-Hamilton [11] and Barkalov and Gladush [12], the

domain velocity, VQ - 1.95 x 10^ cm/sec, is approximately

equal to the electron drift velocity.

4.2.3 Region of Approximately Zero Differential Conductivity

Time resolved pictures of the discharge biased at 9 Td

(ZDC region) are shown in Fig. 12. Discharges in this

29

^^^^^^S^^ - i i

~<';-y c -

i i i t i i

E-BEAv

1 a t m At- 2 Z C 2 ^ 5

3 0 0

4 0 0 n s

5 0 0 n s

E / N ° 5 T d 5 c m

T£:-'PORAL DEVELOPMENT OF STRIATIONS I

DIFFERENTIAL CO iDUCTIVITY

THE E/N RANGE WITH NEGATIVE

Fig. 10. Photographs taken at 100 ns intervals in a discharge at 5 Td in the negative differential conductivity region.

30

1.0

CO z: LLI

0.5

0.0 L 0

300 ns

400 ns

— • 5 0 0 ns

ANODE DISTANCE [cm]

CATHODE

Fig. 11. Photodensitometer curves of the discharge along the discharge axis at 5 Td.

31

i •

2 0 0

i k k i k k k

h-BEAM

1 a t m A r - 2 Z ^.^^Q

E/N = 9 Td

lEMPORAL DEVELOPf'iENT OF SIRIATIONS

IN THE E/N RAf GE WITH APFROXIf;AIELY

ZERO DIFFEREKTIAL CONDUCTIVITY

3 0 0

4 0 0 n s

5 0 0 n s

F i g . 12 . Photographs taken at 100 ns intervals in a discharge at 9 Td in the zero differential conductivity region.

32

operating region showed the occurrence of striations simi­

lar to those observed in the NDC region. The normalized

photodensitometer plots shown in Fig. 13 correspond to the

photographs in Fig. 12.

These results are similar to the curves obtained for 5

Td and they illustrate that the domain velocity,

v-Q ^ 1.95 X 10° cm/sec, is independent of applied voltage.

These curves also show that with increasing voltage the

domain width increases proportionally as predicted by

Barkalov and Gladush [12]. Similar results were obtained

for any bias point in the attachment dominated stage of

operation.

4.2.4 Effect of Applied Voltage on Position of Striation

From the photographs shown previously, it is evident

that the shape and position of the striations vary with ap­

plied voltage; therefore, the discharge was photographed at

a constant time of 400 ns in the discharge current in the

reduced field strength range of 2 Td < E/N < 15 Td. The

position of the striation with respect to the anode, as a

function of applied voltage, is shown in Fig. 14.

The effect of reversing the polarity of the applied

voltage, with respect to the direction of the e-beam, on

the position of the striation was also investigated op­

tically. The normalized photodensitometer plots of two

33

E/N= 3 Td

1.0

0.8

>-

CO

LU I -•-H 0 . 4

0. 5

0. 2

0. 0

t - 200 na

t-300 ns

. . t-400 ns

ANODE

1 2

DISTANCE Ccm] CATHODE

Fig. 13. Photodensitometer curves of the discharge along the discharge axis at 9 Td.

E U

3 . 0 T I I 1 1 1 1 1 1 1 1 1 1 1 1 r

LU a a 2 . 0

a en LL

LU U z <

Lf)

1.0

0. 0 I I ' ' ' ' ' 1 I I I . I I I I I I -

8 10 12 14 16 18

REDUCED FIELD STRENGTH CTd]

34

Fig. 14. Position of striation as a function of reduced field strength, E/N.

35

photographs of the discharge biased in the NDC region with

opposite polarities are shown in Fig. 15. For a fixed

anode and cathode, the effect of reversing the polarity is

obtained by reversing the direction of the e-beam. In Fig.

15, -• corresponds to negative polarity and -^ corresponds to

positive polarity. In the negatively and the positively

biased cases, moving domains form in the discharge when the

magnitude of the applied voltage is such that the discharge

operates in the E/N range where the discharge is attachment

dominated.

4.3 N^iAr Results

Time resolved photographs were taken of a discharge

containing a mixture of 5% N2 in 1 atm Ar. These pictures

revealed a homogeneous discharge like that shown in Fig. 9

for the gas mixture of 2% C2F6 in 1 atm Ar in a region of

PDC. Since the I-V characteristic of this discharge, shown

in Fig. 7, did not exhibit NDC and the photographs of the

discharge revealed a homogeneous discharge, one can con­

clude that it is necessary for a discharge to exhibit NDC

in order to observe striations in the discharge.

E/N=7 Td

36

1.0

0 . 8

cn 0.5

z LLI I -Z H-t 0 . 4

0 . 2 -

0 . 0 0

ANODE

- Q-bQam " ^

o-baam ^-"

v-"--

1 2 DISTANCE Ccm]

CATHODE

Fig. 15. The effect of reversing the polarity on the position of the striation.

CHAPTER V

CONCLUSIONS

Electron-beam controlled diffuse discharges used as

fast opening switches were operated in gas mixtures con­

taining small additives of attachers. Attachers which have

a strongly increasing attachment rate will cause the dis­

charge to exhibit a NDC characteristic depending on the

magnitude of the source function and the concentration of

attacher gas. Gas mixtures which cause a NDC character­

istic in an intermediate E/N range are most suitable for

diffuse discharge opening switches which are operated in a

single shot mode where the inductor is recharged after each

shot. For a repetitive mode of operation, the closing pro­

cess is obstructed and the maximum possible current can not

be utilized [30].

If an e-beam sustained diffuse discharge which exhib­

its NDC is operated in an E/N range where the discharge is

attachment dominated, moving domains of high field inten­

sity will be formed in the discharge. The velocity of

these domains is independent of applied voltage while the

amplitude and width are dependent on the applied field.

Oscillations in the current and voltage can be expected in

applications where the discharge conducts longer than the

transit time of a domain moving across the discharge. This

37

38

might open up the possibility of using diffuse discharges

which exhibit NDC as high power oscillators.

LIST OF REFERENCES

1. Schoenbach, K.H., Schaefer, G., Kristiansen, M., Hatfield, L.L., andGuenther, A.H., "Concepts for Optical Control of Diffuse Discharge Opening Switches," IEEE Trans. Plasma Sci., Vol. PS-10, pp. 246-251, (1982).

2. Christophourou, L., Hunter, S., Carter, J., and Mathis, R.,"Gases for Possible Use in Diffuse Discharge Switches," Appl. Phys. Lett., Vol. 41, pp. 147-149, (1982).

3. Schaefer, G., Schoenbach, K., Krompholz, H., Kristiansen, M., and Guenther, A.H.,"The use of attachers in electron-beam sustained discharge switches - theoretical considerations," Laser and Particle Beams, Vol. 2, pp. 273-291, (1984).

4. Hunter, R.,"Electron Beam Controlled Switch," IEEE Int. Pulsed Power Conf., Lubbock, Tx., pp. IC8:l-6, (1976).

5. Kovalchuk, B., and Meysats, G.,"Current Breaker with Space Discharge Controlled by Electron Beam," Sov. Tech-Phys. Lett., Vol. 2(7), pp. IC7:l-5, (1976).

6. Fernsler, R., Conte, D., and Vitkovitsky, I.,"Repetetive Electron-beam Controlled Switching," IEEE Trans. Plasma Sci., Vol. PS-10, pp. 176-180, (1982).

7. Hallada, M., Bletzinger, P., and Bailey, W.,"Application of Electron-beam Ionized Discharges to Switches - A Comparison of Experiment with Theory," IEEE Trans. Plasma Sci., Vol. PS-10, pp. 218-224, (1982).

8. Harjes, C.H., Schoenbach, K.H., Schaefer, G., Kristiansen, M., Krompholz, H., and Skaggs, D., "Electron-Beam Tetrode For Multiple, Submicrosecond Pulse Operation," Rev. Sci. Instrum., Vol. 55, pp. 1684-1686, (1984).

9. Schoenbach, K.H., Schaefer, G., Kristiansen, M., Krompholz, H., Skaggs, D., and Strickland, E.,"An Electron Beam Controlled Diffuse Discharge Switch," Proc. 5th IEEE Int. Pulsed Power Conf., Washington, D.C, To be published, (1985).

10. Christophourou, L., Hunter, S., Carter, J., Spyrou, S., and Lakdawla, V.,"Basic Studies of Gases for Diffuse Discharge Switching Applications," U.S.-F.R.G. Joint Seminar on Externally Controlled Diffuse Discharges, pp. 103-132, (1983).

39

40

11. Douglas-Hamilton, D.H., andMani, S.A., "Attachment instability in an externally ionized discharge," J. Appl. Phys., Vol. 45, pp. 4406-4415, (1974).

12. Barkalov, A.D., and Gladush, G.G.,"Domain Instability of a Non-self-sustaining Discharge in Electronegative Gases," Translated from Teplofizika Vysokikh Temperatur, Vol. 20, pp. 19-24, (1982).

13. Barkalov, A.D., and Gladush, G.G.,"Domain Instability of a Non-self-sustaining Discharge in Electronegative Gases," Translated from Teplofizika Vysokikh Temperatur, Vol. 20, pp. 201-206, (1982).

14. Barkalov, A.D., and Gladush, G.G.,"Spontaneous Oscillations in a Discharge in an Electronegative Gas," Sov. Phys. Tech. Phys., Vol. 24, pp. 1203-1206, (1979).

15. Bekefi, G., Editor, Principles of Laser Plasmas, New York: John Wiley and Sons, p. 283, (1976).

16. Bar-Lev, A., Semiconductors and Electronic Devices, Englewood Cliffs: Prentice-Hall Inc., pp. 329-334, (1979).

17. Gunn, J.B.,"Microwave Oscillations of Current in III-V Semiconductors," Solid State Communications, Vol. 37, pp. 88, (1963).

18. Kaminsky, M., Atomic and Ionic Impact Phenomena on Metal Surfaces, New York: Springer-Verlag, p. 239, (1965).

19. Krompholz, H., Doggett, J., Schoenbach, K.H., Gahl, J., Harjes, C., Schaefer, G., and Kristiansen, M., "Nanosecond Current Probe for High-Voltage Experiments," Rev. Sci. Instrum., Vol. 55, pp. 127-128, (1984).

20. Krompholz, H., Schoenbach, K., and Schaefer, G., "Transmission Line Current Sensor," Proc. IMTC-IEEE Instrum. and Meas. Tech. Conf., pp. 224-227, (1985).

21. Schoenbach, K.H., Schaefer, G., Kristiansen, M., Krompholz, H., Harjes, H.C., and Skaggs, D.,"An electron-beam controlled diffuse discharge switch," J. Appl. Phys., Vol. 57, pp. 1618-1622, (1985).

41 22. Hunter, S.R., Carter, J.G., Christophourou, L.G.,

and Lakdawala, V.K.,"Transport Properties and Dielectric Strengths of Gas Mixtures for use in Diffuse Discharge Opening Switches," Proc. 4th Gaseous Dielectrics Conf., pp. 224-237, (1984).

23. Schoenbach, K., Schaefer, G., Kristiansen, M., Krompholz, H., Harjes, H., and Skaggs, D., "Investigations of E-beam Controlled Diffuse Discharges," Proc. 4th Gaseous Dielectrics Conf., pp. 246-253, (1984).

24. Long, W.H., Jr., Bailey, W.F., and Garscadden, A., "Electron drift velocities in molecular-gas - rare-gas mixtures," Phys. Rev., Vol. A-13, pp. 471-475, (1976).

25. Haddad, G.N.,"Drift Velocities of Electrons in Nitrogen-Argon Mixtures," Aust. J. Phys., Vol. 36, pp. 297-303, (1983).

26. Petrovic', Z.Lj., Crompton, R.W., and Haddad, G.N., "Model Calculations of Negative Differential Conductivity in Gases," Aust. J. Phys., Vol. 37, pp. 23-24, (1984).

27. Lopantseva, G.B., Pal*, A.F., Persiantsev, I.G., Polushkin, V.M., Starostin, A.N., Timofeev, M.A., and Treneva, E.G.,"Instability of an externally sustained discharge in mixtures of argon with molecular gases," Sov. J. Plasma Phys., Vol. 5, pp. 767-773, (1979).

28. Petrushevich, Yu.V., and Starostin, A.N.,"Domain instability in mixtures of inert and molecular gases," Sov. J. Plasma Phys., Vol. 7, pp. 463-468, (1981).

29. The image converter camera was designed and constructed by M. Michel, Technische Hochschule Darmstadt, FRG.

30. Schaefer, G., Schoenbach, K.H., Kristiansen, M., Strickland, B.E., Korzekwa, R.A., and Hutcheson, G.Z.,"The Influence of the Circuit Impedance on an Electron-Beam Controlled Diffuse Discharge with a Negative Differential Conductivity," Submitted to Appl. Phys. Lett.

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