Reference

NBS

Publications

NBSIR 82-2555

NAT'L INST. OF STAND & TECH

1 1 Annual Report: Technical

AlllDb ESTMET 3 Assistance for Future Insulation

Systems Research

November 1 982

Sponsored by:

Office of Eiectric Energy Systems

uC partment of Energy

j_jj ishington, DC 20585

. U56

32-2555

i doZ

NBSIR 82-2555

1981 ANNUAL REPORT: TECHNICAL

ASSISTANCE FOR FUTURE INSULATION

SYSTEMS RESEARCH

VftTIONAi BUREAU.

y STANDARDS

library

DEC G 1982

no\ QJLX-.

R. J. Van Brunt, M. Misakian, and D. A. Leep

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Electronics and Electrical Engineering

Electrosystems Division

Washington, DC 20234

E. C. Beaty

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

Quantum Physics Division

Boulder, CO 80303

J. W. Gallagher

Joint Institute for Laboratory Astrophysics

University of Colorado

Boulder, CO 80309

C. M. Cooke, K. Wyatt, and R. G. Gels

High Voltage Research Laboratory

Massachusetts Institute of Technology

Cambridge, MA 02139

November 1 982

Sponsored by:

Office of Electric Energy Systems

Department of Energy

Washington, DC 20585

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director
I
TABLE OF CONTENTS

Page

LIST OF FIGURES vi

LIST OF TABLES xi i

Abstract 1

I. INTRODUCTION 3

II. TECHNICAL PROGRESS 6

II. A. Characteristics of Corona Pulses in SFg 6

II. A. 1 Motivation 6

II. A. 2 Instrument Development 6

II. A. 3 Corona Pulse Characteristics for SFg. ..... 11

II. B. Modeling of Discharge Inception and

Electron Avalanche Growth in SFg 19

II.B.l Motivation 19

II. B. 2 Theory. 20

II. B. 2.1 Introduction. 20

II. B. 2.2 Basic Discharge Processes .... 21

II.B.2.3 Deterministic Model of Avalanche Growth .... 25

II. B. 2.4 Effect of Space Charge on Avalanche Growth. . . 27

II.B.2.5 Stochastic Model of Avalanches. ........ 35

II. B. 3 Measurement of Electron

Avalanche Distributions . 38

II. B. 4 Remaining Problems. 44
TABLE OF CONTENTS (cont.

)

Page

TECHNICAL PROGRESS

II. C. Basic Mechanisms for Corona Inception in SFg 45

II.C.l Motivation and Introduction 45

II.C.2 Definition of Corona Inception 46

II. C. 3 Calculation of Corona Inception 51

II.C.4 Discharge Initiation Mechanisms 60

II. C. 5 DC Polarity Effect 60

II.C. 6 Geometrical Effects 66

II. D. Electron Swarm Data for Electronegative Gases 70

II.D.l Motivation 70

II. D. 2 Definitions and Method of Data Handling .... 70

II. D. 3 Experimental Techniques 72

II. D. 3.1 Spatial Current Growth 72

II.D.3.2 Transverse Diffusion Coefficient 75

II.D.3.3 Temporal Current Growth 75

II. D. 3.4 Sampling Techniques 75

II.D.3.5 Errors 76

II.D.3.6 Computations Using the Boltzmann Equation. ... 76

II. D. 4 Data for Sulfur Hexafluoride 78

II. D. 4.1 Drift Velocity 79

II.D.4.2 Ratio of Diff usion-to-Mobi 1 i ty and the

Diffusion Coefficients 79

II.D.4.3 Electron Gain and Loss Processes 82
TABLE OF CONTENTS (cont. )

Page

II. TECHNICAL PROGRESS

II. E. Chemical Diagnostics Development 89

II.E.l Motivation 89

II. E. 2 Effects of Polar Contaminants on the

SFg Dielectric Constant 89

II. E. 3 Production of Oxyfluorides and Water Vapor

From Corona Discharges in SFg 93

II. F. Optical Diagnostics of Discharges 97

II.F.l Motivation 97

II. F. 2 Apparatus and Experimental Results 98

II. F. 3 Low Pressure Measurements 100

II.F.3.1 Ne and Ne + SFg 100

II.F.3.2 N 2 and N 2 + SFg 102

II.F.4 Detection of Metastable Neon at

Atmospheric Pressure. . . I 102

III. OTHER ACTIVITIES 107

IV. CONCLUSION AND SUMMARY ...................... 108

V. REFERENCES Ill

APPENDIX I ..... ................... 121

APPENDIX II ...... 126

APPENDIX III. . 130

v
LIST OF FIGURES

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Figure 7

Page

System for measuring electrical characteristics of corona

pulses. Shown also are the measured impulse responses

h i

( t ) and h 2( t ) at points A and B where the pulse

repetition rates and pulse height distributions are measured respectively 7

The measured response of the pulse counter (dashed line) and

multichannel analyzer (solid lines) to application of two narrow pulses (~5 ns) separated by a time At. The left

scale is the measured frequency and the right scale is the

recorded amplitude 9

Typical positive corona burst pulses observed in SF5 at an absolute pressure of 300 kPa and applied voltage of 32.3 kV.

These were observed with a time resolution of 0.1 ys.

Indicated are the sampling window tp of the peakholder

circuit and the minimum sampling interval t s of the

multichannel analyzer system 10

Multichannel analyzer channel number versus amplitude

(in volts) of charge calibration pulse (see fig. 10 ) 12

Measured electrical character!' sties of positive corona pulses

in SFg at an absolute pressure of 50 kPa. Shown are the corona pulse shapes, average corona current I, and pulse

height distributions at the indicated applied voltages.

The point electrode diameter is 0.1 mm and the gap spacing

i s 1 . 24 cm 13

Measured electrical characteristics of positive corona in SFg

at an absolute pressure of 200 kPa. Shown are the corona

pulse shapes, pulse repetition rates f, average corona current I, and pulse height distributions at the indicated

dc voltages. The point electrode diameter is 0.1 mm and

the gap spacing is 1.24 cm 14

Measured electrical character!' sties of positive corona in SFg

at an absolute pressure of 400 kPa. Shown are the corona

pulse shapes, pulse repetition rates f, average corona

current I, and pulse height distributions at the indicated

dc voltages. The point electrode diameter is 0.1 mm and

the gap spacing is 1.24 cm 15

V!
LIST OF FIGURES (cont.)

Page

Figure 8. Measured electrical character! sti cs of positive corona in

SFg at an absolute pressure of 500 kPa. Shown are the corona pulse shapes, pulse repetition rates f, average

corona current I, and pulse height distributions at the

indicated dc voltages. The point electrode diameter is

0.1 mm and the gap spacing is 1.24 cm 16

Figure 9. Measured electrical characteristics of negative corona pulses

in SFg at an absolute pressure of 100 kPa and applied

voltage of 14.3 k V for freshly polished stainless steel

electrodes. Shown are the average corona current I, the

pulse repetition rate f, and typical pulse shapes recorded

with a transient digitizer. The gap was not irradiated 17

Figure 10. Comparison of measured electrical characteristics of negative

corona pulses in SFg at 200 kPa for freshly polished electrodes

(upper portion). Shown are the pulse height distributions,

pulse repetition rates f, average corona current I, and

applied voltage V. The gap was not irradiated 18

Figure 11. Electron attachment cross sections for SFg

(from Asundi and Craggs) 23

Figure 12. Calculated electron avalanching in 200 kPa SFg controlled

ionization zone 26

Figure 13. Avalanche radius with 100 kPa SFg, 17 kV . . 28

Figure 14. Avalanche radius with 200 kPa SFg, 27 kV 28

Figure 15. Calculated positive ion density left by an electron

avalanche in the CIZ test cell at 100 kPa SFg 30

Figure 16. Calculated positive ion density left by an electron

avalanche in the CIZ test cell at 200 kPa SFg 30

Figure 17. Calculated negative ion density left by an electron

avalanche in the CIZ test cell at 100 kPa SFg 31
LIST OF FIGURES (cont.)

Page

Figure 18. Calculated negative ion density left by an electron

avalanche in the CIZ test cell at 200 kPa SF5 31

Figure 19. Calculated net ion density left by an electron

avalanche in the CIZ test cell at 100 kPa SFg 32

Figure 20. Calculated net ion density left by an electron

avalanche in the CIZ test cell at 200 kPa SF5 32

Figure 21. Model of avalanche used to evaluate space charge effects ... 33

Figure 22. Electron E-f iel d/ Lapl acian E-field for SFg at 100 kPa 34

Figure 23. Electron E-f i el d/ La pi acian E-field for SFg at 200 kPa 34

Figure 24. Controlled Ionization Zone Technique 39

Figure 25a. Measured electron avalanche distribution

for 100 kPa SFg, at 17.6 kV 41

Figure 25b. Measured electron avalanche distribution

for 100 kPa SFg, 17.6 kV, pulse rate = 89 41

Figure 26a. Measured electron avalanche distribution

for 100 kPa SFg, 18.6 kV, pulse rate = 41. . 42

Figure 26b. Measured electron avalanche distribution

for 100 kPa SFg, 18.8 kV, pulse rate = 50 42

Figure 27a. Measured electron avalanche distribution

for 200 kPa SFg, 29.6 kV . 43

Figure 27b. Measured electron avalanche distribution

for 200 kPa SFg, 29.6 kV, pulse rate = 11 43
LIST OF FIGURES (cont.)

Page

Figure 28. Observed pulse count rate versus applied voltage for positive

and negative point-plane dc corona in SFg at a pressure of

200 kPa. The gap spacing was 1.24 cm and the radius of

curvature of the point was 0.045 mm. The different symbols

indicate data obtained from different runs. Included are all

pulses with a charge in excess of 0.05 pC 47

Figure 29. Observed pulse count rate versus applied voltage for positive

and negative point-plane dc corona in SFg at a pressure of

400 kPa. The gap spacing was 1.24 cm and the radius of

curvature of the point was 0.045 mm. The different symbols

indicate data obtained from different runs. Included are all

pulses with charge in excess of 0.05 pC 48

Figure 30. Observed pulse count rate versus applied voltage for positive

and negative point-plane dc corona in SFg at a pressure of

200 kPa. Also shown by the solid line is the average dc

current observed prior to the inception of pulses. The gap

spacing was 1.1 cm and the point radius was 0.47 mm. The

data were obtained using uv-radiation and the different

symbols correspond to different data runs ..... 49

Figure 31. Observed pulse count rate versus applied voltage for positive

and negative point-plane dc corona in SFg at a pressure of

400 kPa. Also shown by the solid line is the average dc

current. The gap spacing was 1.1 cm and the point radius was

0.47 mm. The data were obtained using uv-radiation and the

different symbols correspond to different data runs 50

Figure 32. Calculated average-maximum electron avalanche size versus applied voltage for the different indicated gas pressures and

parameter e = f - d. The gap geometry corresponds to the

conditions of figs. 28 and 29 53

Figure 33. Collected ionization and attachment coefficients for SFg. ... 56

Figure 34. Measured and calculated ac and dc, positive and negative pointplane corona inceptions in SFg as a function of gas pressure.

The gap spacing was 1.24 cm and the radius of curvature of the

point electrode was 0.045 mm 57

ix
LIST OF FIGURES (cont.)

Page

Figure 35. Measured and calculated ac and dc, positive and negative pointplane corona inceptions in SFg as a function of gas pressure.

The gap spacing was 2.28 cm and the radius of curvature of the

point electrode was 0.045 mm .... 58

Figure 36. Calculated boundaries of the initiation volumes for SF5 positive

corona inception at the indicated applied voltages and for a gas

pressure of 100 kPa 64

Figure 37. Calculated growth in the electron initiation volume for two point

electrodes characterized by the angles n 0

= 1 1 . 575° and n 0 = 2.315°

plotted as a function of the ratio of applied voltage V to

theoretical corona inception voltage V-• 65

Figure 38. Electron drift velocity, W, for electrons in SFg

as a function of E/N 80

Figure 39. Ratio of diffusion to mobility, Dj/p,

for electrons in SFg as a function of E/N 81

Figure 40. Diffusion coefficients for electrons in SFg

as a function of E/N 83

Figure 41. Attachment coefficient for electrons in SFg

as a function of E/N 84

Figure 42. Ionization coefficient for electrons in SFg

as a function of E/N 85

Figure 43. Electron growth constant (net ionization coefficient)

for electrons in SFg as a function of E/N 86

Figure 44. Relative concentration of H2 O in SFg as a function of

energy dissipated by a positive dc corona discharge for

the indicated discharge power levels 94

x
LIST OF FIGURES (cont.)

Page

Figure 45. Measured concentrations of SOF 2 and SO2

F

2 as a function of

net energy dissipated in corona discharges operated at the

indicated power levels 96

Figure 46. Schematic view of apparatus for performing optogalvanic

measurements in a hollow cathode lamp 99

Figure 47. Optogalvanic spectra of neon and a mixture of neon with

5% SFg for comparable discharge current and gas pressure .... 101

Figure 48. Optogalvanic spectrum for N 2 showing lines from the Ledbetter

system and the (8,4) bandhead for the first positive system. . . 103

Figure 49. Measurement of neon optogalvanic spectrum at atmospheric

pressure (100 kPa) and 3.6 mA discharge current. Optogalvanic

transitions could be observed only in the negative glow region

of the discharge 104

Figure 50. Simplified energy level diagram for neon. Optogalvanic signals

are obtained when laser-induced transitions occur from the

2p 5 3s states to the 2p^3p manifold of excited states 106

Figure A.I.l Coordinates for Swarm Equilibrium Calculations

in the CIZ test cell arrangement 123

Figure A. 1.2 Normalized average electron energy for swarms

in the CIZ test cell arrangement 124

Figure A. 1.3 Average electron energies in the CIZ test

cell arrangement ......... . 124

xi
LIST OF TABLES

Page

Table I. Swarm parameters. Symbolic notation, scale factors,

and units 73

Table II. Common units conversions for swarm data 74

Table III. Dipole moments, calculated dielectric constants at 20°C

and 100 kPa, and calculated detection sensitivities for

SF 5 and contaminants commonly observed in SFg after

electric discharges 92

xi i
Abstract

A system for measuring the electrical properties of corona pulses

has been characteriz ed and is discussed. Additional data on the

pulse height distributions of positive and negative corona pulses

in pure SFg for point-plane electrode geometries are presented.

Basic mechanisms for initiation of electric discharges in S

F 5 for

highly nonuniform fields have been investigated in a collaborative

effort between NBS and the High Voltage Research Laboratory of the

Massachusetts Institute of Technology. Effects of radiation,

electrode geometry, and polarity on corona inception in SF 5 have

been measured. Corona inception voltages and discharge initiation

volumes have been calculated using the streamer criterion.

Limitations of the streamer criterion as applied to SFg in highly

nonuniform fields are discussed.

The statistics of electron avalanche growth in SFg have been

measured and compared with results of theory. While the avalanche

pulses, on average, followed expected theoretical behavior, the

distribution was not found to be regular or to follow a simple

stochastic theory. A thorough compilation and survey of electron

swarm data for electronegative gases used, and proposed for use, as components of gaseous dielectrics was completed. The parameters

considered include: electron drift velocity, attachment coefficient,

ionization coefficient, electron growth constant, diffusion coefficient,

detachment coefficient, and characteri Stic energy. These are quantities needed for prediction of breakdown and modeling of gas

discharges. Some of the important gases included in this study

are: Og, CO2, SFg, H2O, air, nitrogen oxides, halogens, and

various halogenated hydrocarbons, e.g., CF4, C2Fg, CgFg, C 4 Fiq>

CC 1 2F2 > CCIF3, C-C4FQ, c-CgFg, CHgBr, C H 2C 1 3 , CHCI3, etc. In this report we include only an example of the data collected,

namely that for SFg. Using a gas-chromatograph/mass spectrometer,

absolute concentrations of SOF2 and SO2F2 and relative concentrations

of H2O in SFg have been measured as a function of total energy

dissipated in corona discharges operated at power levels between

50 and 700 mW. The observed production rates for SOF2 and SO2F

2

appear to be proportional to power level, and the ratio of SO2F2

to SOF2 concentrations for corona is considerably higher than that

typically observed for arc discharges in SFg.

Estimates have been performed to determine the sensitivity of a technique to detect polar gas contaminants in gaseous SFg using an accurate ppm measurement of changes in the low frequency (dc)

dielectric constant of the gas. Measurements have been performed

of optogalvanic spectra from glow discharges in Ne, N2 and mixtures

of these with SFg. The effect of SFg in quenching metastables in

these gases is discussed.

1
Disci aimer:

This is a report of an ongoing research project. Therefore, some of

the results presented here, although believed to be correct, must

still be considered preliminary. The conclusions based on the data

given in this report must also be viewed as tentative and subject to

possible revisions as additional information is acquired.

2
I. INTRODUCTION

The objective for this project is to develop measurement and diagnostic

techniques for monitoring, identifying, and predicting degradation in

future compressed gas electrical insulating systems under normal operating

conditions. The focus is on providing fundamental information and data

needed to improve test design and performance evaluation criteria for

gaseous dielectrics. A basic understanding of the processes that can lead

to failure of insulation materials is required before meaningful tests can

be designed to evaluate long-time reliability of these materials. There

is also a need for reliable fundamental electron transport data that can

be used to predict electrical breakdown of gases under a variety of conditions

that can occur in practical situations. The limits of applicability and

validity of transport data, as well as the criteria used for predicting

breakdown, must also be considered and understood before being applied to

the design of insulation systems.

The emphasis of the studies reported here has been on the electrical and

chemical properties of SFq because of its recent widespread use as an insulant,

in advanced high-voltage systems. It serves as a convenient reference when

considering the performance of other gaseous dielectrics, some of which

might be considered as possible replacements for SFg. In the development

of new measurement techniques to be applied to the evaluation of gaseous

dielectrics, it is desirable to start with SFg. It is therefore important

to have reliable data on the properties of this gas which can be used as bench

marks. Although SF5 has been studied extensively, much remains to be learned

about its behavior under conditions of high electrical stress, such as the

mechanisms that are responsible for various types of electrical discharges.

Major aspects of this project have included: 1) an investigation of the

mechanisms that lead to electron avalanche formation and corona discharge

inception in SFg under highly nonuniform field conditions, 2) an examination

of the characteristics of corona discharges in SFg, 3) a compilation and

evaluation of electron swarm data needed to model electric discharge behavior

in SFg and other el ectronegati ve gases, 4) an evaluation of optical

techniques that can be used as diagnostics of gas discharges, and 5) an application of sensitive chemical analysis techniques to study corona-induced

degradation of gaseous dielectrics and to investigate the effects of low-level

gaseous contamination and decomposition on the behavior of gas discharges.

Most of the NBS-1 aboratory effort has been directed toward a study of

partial discharge (corona) phenomena in gaseous dielectrics, particularly

SFg. Corona is important in practical high-voltage insulation systems

because it can be responsible for power loss and can lead to deterioration

of the insulating qualities of the gas as well as to production of toxic

or corrosive by-products [1-3], 1 Corona is loosely defined as a localized

gas discharge in a nonuniform electric field. The degree of nonuniformity

of the field is assumed to be sufficient to limit the ionization associated

with the discharge to a region in the immediate vicinity of the most highly

stressed electrode, or electrodes. In the following discussions, the term

^Numbers in brackets refer to the literature references listed at the

end of this report.

3
corona refers to any detectable discharge phenomena in a nonuni r orm field

which gives rise to ionization in the gas resulting in a multiplication of

the number of free electrons in the gap.

Insulation systems are typically designed to minimize corona. However,

the extent to which one can limit corona depends on one's ability to define,

measure and predict corona onset (inception) as well as to understand the

basic mechanisms that can influence the initiation and development of corona discharges. Measurement of corona onset voltages can also provide

an indication of the dielectric strength of the gas since the basic theory

used to predict onset in nonuniform fields is the same as that which applies

to uniform-field breakdown [4].

Although there have been extensive studies of the properties of corona in

air and in atmospheric gases such as N

2 and O 2 [5], there have been

relatively few fundamental studies of corona in SFg. There is a need for

better understand!' ng of the basic factors that determine discharge inception

as well as the basic character!' sties of corona in this gas. In attempting

to define corona onset, it is necessary to know how the discharge develops

with applied voltage and how this development is affected by various conditions

such as, for example, the waveform of the voltage, electrode geometry, the

presence of radiation, and gas pressure and purity. Earlier investigations

[6,7] of corona activity in SFg under di rect-vol tage conditions have shown

that it appears predominately in the form of pulses or pulse bursts correspond! ng

to electron avalanches and/or streamers. This appears to be true at least

for positive corona with gas pressures above 20 kPa and for voltages from

onset to breakdown. The statistical properties of the corona pulses, however,

have not been quantitatively characteriz ed in previous work. There is

thus the need to explore new techniques to measure the electrical properties

of corona in gaseous dielectrics in a statistically meaningful way.

Instrumentation developed at MBS to study the statistical properties of corona pulses in electronegative gases is described in this report. This

technique is also discussed in a recent paper by Van Brunt and Leep [8],

together with the results of an extensive study of the pulse character!' sties

of dc-point plane corona in SFg. Here we shall present only the main

conclusions of this work, together with significant results obtained this

year and some additional details 0^ the measurement system not given previously.

The emphasis of the research at the MIT High Voltage Laboratory was on the

development and testing of a model of prebreakdown partial discharge phenomena

which can be used, for example, to understand and predict electron avalanche

statistics in highly electronegative gases. Specifically, the basic objective

of their research was twofold: (1) to develop a model which will enable a more complete fundamental understanding of inception and partial discharge

phenomena in gases, and (2) provide basic information needed to develop

new standard procedures for measurement of the insulation strength of gases.

This activity is viewed as a coll aborati ve effort which has supplemented and

strengthened the research underway at NBS on partial discharge characteristics.

A model which can be used to understand and predict discharge initiation in

nonuniform fields is needed to interpret results obtained from measurements

performed at NBS. Also, fundamental i nf ormati on obtained at NBS, e.g. , from

swarm data compilation and studies of contamination effects, should provide

useful input to the modeling effort at MIT.

4
A description of the theoretical approach taken in this investigation is

given in this report, together with results of calculations and measurements

of electron avalanche statistics. Details of this work have been presented

elsewhere [ 9 ].

Closely connected with the work at MIT was the effort at NBS to investigate

the fundamental mechanisms of corona inception in S F

5 . In addition to the

preliminary results previously reported [10] on the comparison between ac and

dc inceptions, we undertook a more thorough examination of the effects of

uv-radi ati on , electrode geometry, and electrode conditioning on the measurement

of corona inception in S F 5 . Corona inceptions were also calculated using the

streamer criterion and these were compared with our measured results. The

connection between the streamer criterion and the nature of the corona phenomena

observed near onset will be discussed, together with limitations of the streamer

criterion for predicting inceptions.

A set of preferred discharge initiation mechanisms is proposed and shown

to be consistent with the observed changes in discharge behavior with

changing gap conditions. The results of this work will be published soon

[ 11 ]. The major ideas which appear in this paper, and which were developed

during the past year, will be reiterated in this report.

At the Atomic Collisions Data Center of The Joint Institute for Laboratory

Astrophysics, a monumental survey of electron swarm data for electronegative

gases was completed in the past year.

The types of data included in this survey are: ionization, attachment,

detachment and diffusion coefficients, electron growth constants, drifty

velocities, and characteri Stic energies, all of which are relevant to

modeling of electron transport properties and electric discharges in gases.

Only electronegative gases of possible technical importance were considered,

and these included, for example, O2, CO2, SF5, H2O, nitrogen oxides, air,

the halogens, and halogenated hydrocarbons such as CF4, C2Fg, C3F3, C4Fiq>

CC 1 2F2 > CHCI3, CH3B r , C2H5B r , n-C3H7B r , n-C4HgB r , n-CgH^Bp, n-CgHjjBp, C-C4F5,

2 - c 4f 6 >

1 , 3-C4F 5 , C-C4F8, 2-C4F8, c-CsFg, c-CgF 10 s c-CgF^, C7F3, CsF 15

,

I-C7F14, C-C7F14, CCI3F, and CCIF3. This survey has been submitted for

publication in the Journal of Physical and Chemical Reference Data. The

format of the paper is similar to that of an earlier survey of swarm data

for atmospheric and rare gases by J. Dutton [ 12 ], It was not possible to

reproduce the entire manuscript in this report; however, we have included

excerpts describing the approach taken, types of data considered, and

examples of data included for SFg, these being most relevant to other

topics discussed in this report.

Estimates have been performed to determine the sensitivity of a technique to

detect polar gas contaminants in SFg using an accurate ppm measurement of

changes in the low frequency (dc) dielectric constant of the gas. Results

of calculations presented here indicate that the technique can detect the

presence of polar gases like H2O only down to the 100 ppm level.

Work has continued on the use of the gas chromatograph-mass spectrometer

(GC/MS) system to assist in determination of the effects of trace levels of

H2O on positive-corona discharges in SFg. Preliminary results of this work

5
have been reported in a paper given at the Thirty-Third Gaseous Electronics

Conference entitled "Pulse Characteristics of Positive DC Corona in SF5

: Effects of Trace Decomposition Products" by D. A. Leep and R. J. Van Brunt [13]

The GC/jMS was also used to measure the rate of SOF2 (thionylf 1 uoride)

and SO0 F

2 (sulfurylfluoride) production from dc corona in SF 5 as a function

of discharge power level. Preliminary results obtained from these measurements

will be presented in this report. Additional information about this work

has appeared in an Electric Power Research Institute Report [14] resulting

from the 1980 Workshop on Arc By-Products in Gas Insulated Systems.

The use of 1 aser- i nduced optogalvanic spectroscopy as a method for monitoring

metastable species concentrations in corona and glow discharges continued

during this year. Measurements were performed on discharges in Ne, No, and

mixtures of these with SFg for gas pressure up to 100 kPa (~1 atm). The

experimental results obtained and the observed limitations of the technique

will be discussed in this report.

II. TECHNICAL PROGRESS

II. A. Character!' sties of Corona Pulses in SFq

II.A.l Motivation

This work has been motivated by the need to develop new measurement techniques

that allow characteriz at i on of corona-discharge pulses in a quantitative

and statistically meaningful way. This is an extension of work reported

last year [15]. Some of the results presented here have also been presented

in a" recent archival publication [ 8 ]. Included in this paper are a detailed

description of the apparatus, and extensive data on the pulse characteristics

of positive and negative point-plane dc corona in pure SF5

. Additional

information can also be found in an earlier paper [16]. This report contains

some new information about the character!' sties of the i nstrumentation used

which were not given in the above publications.

1 1. A. 2 Instrument Development

A thorough analysis of the i nstrumentati on developed at NBS to study statistica

properties of corona pulses was completed in the past year. Possible

sources of error and instrumental factors which can significantly affect

the data have been carefully examined. A diagram of the instrument used

for these measurements is given in figure 1. Basic features of this system

have previously been discussed [8,15] and will not be repeated here. It

is of interest to point out, however, the measured impulse response functions

h -j ( t ) and h 2

( t ) at the critical points A and B. At point A, corona pulses

are observed with either an oscilloscope or transient digitizer. At point

B, the pulses are recorded with a multichannel analyzer (MCA), the input

to which is a peak holding circuit. If i(t) is the instantaneous current

in a corona pulse, then the signal sensed by the peak holding circuit at

point B is given by

t

( 1)

6
CORONA CELL' PRE- AMP.

0

y6 0 — o

» j._L

i—-i

CHARGE CALIB. PULSE INPUT

|

MCA PRINTER

PEAK HOLDER DELAY

\,RESET

FILTER

Figure 1. System for measuring electrical characteristics of corona

pulses. Shown also are the measured impulse responses

h-j (t) and hgU) at points A and B where the pulse repetition

rates and pulse height distributions are measured respectively.

7
It is t'ne maximum of this function which is actually recorded by the MCA.

If the width of the corona pulse At is much smaller than the half width

w of the function h

2 (t), and if the spacing between corona pulses is larger

than w, then the measured pulse height distribution (PHD) of corona pulses is

not affected by the details of ho(t). This becomes evident when the corona pulse is approximated by an impulse represented by a Dirac delta function,

i.e.

,

i (t) = QS(t-t"), (2)

where Q is the total charge contained in the pulse. Inserting this into

eq (1 ) gi ves

q m = QMt-t"), (3)

which indicates that the maximum value of q(t) will occur at the maximum

of h 2 (t-t"), and will be proportional to the scale factor Q. This property

of the measurement system has al ready been emphasized in a slightly different

way [15].

The time resolving limitations of the instrument were examined in further

detail during the past year. The results of such an investigation are illustrated in figure 2. Shown in this figure are the responses of the

counter and the MCA system to two sharp (~10 ns) pulses separated by a variable time At. The dashed curve indicates that the counter cannot resolve

pulses separated by less than 1.5 us, i.e., the maximum count rate at which

it can record individual pulses is 6.7 x 10^ Hz. The solid curve indicates

that if the pulses are separated by less than about 0.4 us, then the MCA adds

the amplitudes, i.e., it records a single pulse of amplitude 2 V for individual

pulses with an amplitude of V. Only if the pulses are more than 1.8 us apart

does the instrument record an individual event of amplitude V, and only when

the pulses are more than 8.0 us apart does it record two events of amplitude V.

Figure 3 illustrates the way in which the instrument samples a pulse burst.

The bursts shown are from positive corona in SFg, and were observed with

a circuit of higher resolution (~0.1us) than that used in figure 1. The

first pulse in the burst triggers the peakholding circuit which remains on for a time t D = 2.0 us. In this case, smaller pulses immediately following

the initial event are added to the amplitude of this event thus giving a recorded pulse amplitude which is somewhat greater than would be the case for a single isolated pulse.

While information

t

s

- t, time t,

of 6.0

- t, us

is being transferred

during which no to the MCA there exists a dead time

new information can be accepted. The

,p is controlled by the delay indicated in figure 1, but is

limited by the speed of anal og-to-digital conversion in the MCA, which

in the present system is approximately 4.0 us. After this time, if more

pulses in the burst are present and exceed a predetermined threshold, then

the cycle will be repeated. The burst will be sampled every 8.0 us as long as it persists. The effect which this method of sampling can have in

distorting the pulse height spectra of corona pulses has already been

noted [8,15].

8
At Ims|

Figure 2. The measured response of the pulse counter (dashed line) and

multichannel analyzer (solid lines) to application of two narrow

pulses (~5 ns) separated by a time At. The left scale is the

measured frequency and the right scale is the recorded amplitude.

9
ts

= 8.0 /as

tp = 2.0/as

^S^VVV.vvvvv\_Vv\_

Figure 3. Typical positive corona burst pulses observed in SFq at an absolute

pressure of 300 kPa and applied voltage of 32.3 kV. These were

observed with a time resolution of 0.1 us. Indicated are the

sampling window tp of the peakholder circuit and the minimum sampling

interval t s of the multichannel analyzer system.

10
Further tests were performed to evaluate the errors incurred in establishing

a charge scale for PHD data. As indicated in figure 1, the system is

calibrated by applying pulses of known amplitude V 0 to a standard capacitor

C' to give a known injected charge q

= C'V 0

. The level correspond! ng to

an injected charge q-j appears at a particular channel number n-j of the MCA,

where it has been found that n-j is a linear function of q-j (see fig. 4).

A least-squares straight-line fit to a set of observed calibration points

( q i , n-j, i > 3) was used to establish a charge scale from the MCA output.

The uncertainties in the charge scale were found to be less than ±10?$ for

the present method of calibration. The primary source of error appeared

to be associated with uncertainty in matching the stray capacitance of the

calibration circuit to that of the corona detection circuit. The uncertai nt ies

also appear to be greatest at the extreme low end of the charge scale where

slight deviations from linearity in the relationship between q-j and n-j were

noted (again see fig. 4).

II. A. 3 Corona Pulse Characteristics for SFg

As previously mentioned, a considerable amount of new data on the properties

of dc positive and negative corona in SFg were acquired and presented in a recent publication [8]. Examples of some of these data are shown in figures 5-10.

The results given in figures 5-8 on positive corona characteri sties support

our previously stated [15,16] conclusions concerning the voltage and pressure

dependence of the pulse burst behavior. These results will not be repeated

here.

Some new data were acquired in the past year concerning the properties of

negative corona discharges, and examples of these are displayed in figures

9 and 10. The significant fact learned about negative corona is that in

the absence of an external radiation source its characteristics near inception

are quite dependent on conditions of the point cathode surface. It was discovered that characteristics of negative corona observed using freshly

cleaned and polished stainless steel electrodes were drastically different

from those observed after the electrodes had been "conditioned" by operating

the discharge at a level of 1.0 uA or more for several minutes or by

irradiating the point with uv light. Figure 9 shows the characteristics

typically observed using "clean," unirradiated electrodes. The negative

corona appears in the form of intermittent large pulses (q > 10 pC) of low

repetition rate, even in some cases at voltages considerably in excess of

onset. Depending on gas pressure, electrode diameter, and gap spacing the

large pulses are usually followed by a long tail, or a burst of lower

level pulses, such as for positive corona, or both. The inset in figure 9

shows two typical negative corona pulses recorded with a transient digitizer.

The tails of the pulses are roughly of constant level and extend as much

as 60 ys beyond the primary event. This characteri Stic of the pulses is

reflected in the shape of the PHD, where the peak at q

= 64 pC corresponds

to the distribution of the relatively large primary events, and the sharp

peak near 14 pC results from the first sampling of the tail. Actually,

the tail, if it is longer than 16 us, is sampled more than once. Subsequent

samplings which occur on the relatively level portion of the tail give

rise to an even larger peak, not shown, at lower charge. This is more evident in the data displayed at the bottom of figure 10, which again

corresponds to clean electrodes, but at a gas pressure of 200 kPa. The

PHD peaks are broader in this case because here pulses with long tails

11
Figure 4. Multichannel analyzer channel number versus amplitude

(in volts) of charge calibration pulse (see fig. 10).

12
RELATIVE

INTENSITY

Figure 5

SF6

, P=50 kPa

9.9 kV

l=1.0x10' 6A

CORONA PULSES

20/is/DIV.

•iimnni

9.2 KV

l=2.0»10-7A

• ••».•••••*

8.9 kV ~~

I=7.0*10-«A

1,

.. '..L'E ” \ ...••**•••.

1 ® C • t) VwXjo

8.45 kV

I « 10" 10A

10 20 30 40 50 60

DISCHARGE LEVEL (pC)

Measured electrical characteristics of positive corona pulses in

SFg at an absolute pressure of 50 kPa. Shown are the corona pulse

shapes, average corona current I, and pulse height distributions at

the indicated applied voltages. The point electrode diameter is

0.1 mm and the gap spacing is 1.24 cm.

13
RELATIVE

INTENSITY

10 30 50 70

DISCHARGE LEVEL (pC)

Figure 6. Measured electrical characteristics of positive corona in SFg at an absolute pressure of 200 kPa. Shown are the corona pulse shapes,

pulse repetition rates f, average corona current I, and pulse height

distributions at the indicated dc voltages. The point electrode

diameter is 0.1 mm and the gap spacing is 1.24 cm.

14
RELATIVE

INTENSITY

SF6 , P=400 kPa CORONA PULSES - .• v.- 20/iS/DIV.

33.0 kv wammmm

~ /

*

’ ' m.o*io-6 a

: t=4.2^o3 ”

/s pni

/ : ; — •

• •*

•

• mmm

1

• •

* •

• “ * **' 29.5 kV ~ *

. I=7.0x10' 8 A

• • f=4.1 x10

2/$

v •

v.-

.

(BUB

pflflflfl Inm

lilflflBB

HBBBB

28.1 kV

l=1,2 x10'8 A

f=1.1 x10 2/s

*

IflBBB MIBB

pflflB

ftBflflfl

CTBBB

26.1 kV

I=5.0x10- 10 A

. . f=7.01/s

B9BB

Iflflflfl BBB

pBBBB

IBBflB

ILBBBB

10 30 50 70 90 110

DISCHARGE LEVEL (pC)

Figure 7. Measured electrical characteristics of positive corona in SFg at an absolute pressure of 400 kPa. Shown are the corona pulse shapes,

pulse repetition rates f, average corona current I, and pulse height

distributions at the indicated dc voltages. The point electrode

diameter is 0.1 mm and the gap spacing is 1.24 cm.

15
RELATIVE

INTENSITY

CORONA PULSES

cc /*.. 5/iS/DIV.

® * Tl? SS5*5i P=500 kPa * 37 o KV BSillllllll - . M 1xln -e . iiEJSsisii Mlxi° A

IlillBEltt

. t=5.2xio 3 /s nVBEIZ

_ : • oc n \i\i :iL-

:

•

• - :

’.

35,0

I=4.5 X

kv

10

' 7 A

BWU

o carnaltHMMieia

f=2.7><io

3/s tmlmBmaa

.•A.****' **• *• % *•

• \

33.1 1=5.0x10

kV

8 a miKinsm

- t=7.5xio 2

- /* HtaliB - imbb

31.5 kV

i=5.oxio' 9 a -

'

. f=50/s 11111 Hpnni

10 30 50 70 90 110

DISCHARGE LEVEL (pC)

Figure 8. Measured electrical characteristics of positive corona in SFg at an absolute pressure of 500 kPa. Shown are the corona pulse shapes,

pulse repetition rates f, average corona current I, and pulse height

distributions at the indicated dc voltages. The point electrode

diameter is 0.1 mm and the gap spacing is 1.24 cm.

16
CO

1.0

SF6 , P=100 kPa

•

NEG. CORONA PULSES

17

—

—

1 1 1 1 1 1 1 1 1

•

1 0/u s/DI V.

—

V=14.3 kV

c

c

i=i.o*io- 9 a

f=5.4/$

\

9

j l

0 10 20 30 40 50 60 70

DISCHARGE LEVEL (pC)

Figure 9. Measured electrical characteristics of negative corona pulses in SFg

at an absolute pressure of 100 kPa and applied voltage of 14.3 kV for

freshly polished stainless steel electrodes. Shown are the average

corona current I, the pulse repetition rate f, and typical pulse

shapes recorded with a transient digitizer. The gap was not irradiated.

17
DISCHARGE LEVEL (pC]

Figure 10. Comparison of measured electrical characteristics of negative corona

pulses in SFg at 200 kPa for freshly polished electrodes (upper

portion). Shown are the pulse height distributions, pulse repetition

rates f, average corona current I, and applied voltage V. The gap was

not irradiated.

18
were interspersed with large pulses followed by a burst of lower amplitude

pulses. It is noteworthy that the larger pulses seen for negative corona from clean stainless steel tips have a fairly narrow distribution in amplitude,

and in this sense they are similar to Trichel pulses [5] seen in negative

corona discharges of other electronegative gases. However, unlike true

Trichel pulses, their occurrence is random, i.e., they do not appear in

regular intervals with a constant repetition rate.

The upper part of figure 10 shows the observed character!' sties of negative

corona for the same gas and electrodes, after the current had been operated

at 5.0 yA for a period of 70 s. The voltage for the upper graph in

figure 10 is considerably below that for the lower graph correspond!' ng to

the clean electrodes, and yet the average corona current I is two orders

of magnitude greater. It is also seen that the repetition rate for the

pulses is considerably higher for the electrodes conditioned by prior

discharges, although the mean amplitude of the pulses is now much lower

(peaked below 1.0 pC).

Once conditioning of the electrodes had occurred, it was found that the

general features of the negative corona in SFg remained fairly unchanged,

i.e., the corona was found to "turn on" abruptly, as noted in earlier

measurements [10], and it was predominantly in the form of high-frequency,

low-amplitude pulses. Examination of the point electrode under a microscope

after conditioning showed that it was slightly discolored and microscopic

irregularities in the form of pitting had developed.

The effect of conditioning is to increase the electron emission of the

point electrode, perhaps by a combination of lowering the work function of

the surface and locally enhancing the field. It should be noted that this

effect could be achieved with "clean" electrodes by irradiating the point

with a sufficiently intense uv-source. The radiation insures electron

production via the photoelectric effect, i.e., photon-enhanced field emission.

However, once the electrodes have been conditioned by running a discharge,

the uv-radiation has only a small influence on the way in which the corona develops with voltage. This is consistent with our previously reported

observations [10,11,15].

II. B. Modeling of Discharge Inception and Electron Avalanche Growth in SFg

II.B.l Motivation

During the past year a grant was awarded by NBS to the High Voltage Research

Laboratory at the Massachusetts Institute of Technology to support their

participation in the NBS-D0E research program on gaseous dielectrics. The

emphasis of their work has been on development and testing of a model of

prebreakdown partial discharge phenomena which can be used, for example,

to understand and predict the statistics of electron avalanche growth and

the transition from avalanche to breakdown for electronegative gases in a highly localized nonuniform field region associated with a protrusion on a plane electrode. The specific motivation behind this work has been twofold:

(1) to develop a model which will provide a more complete fundamental

description of inception and partial discharge phenomena in gases, and

(2) provide basic information needed to develop new standard procedures

for measurement and evaluation of the insulation strength of gases. It

19
should be noted that this activity ties in closely with the MBS work on investigations of corona- i ncepti on mechanisms to be discussed in Sec. II. C,

and with the effort to compile and evaluate fundamental electron swarm

data to be discussed in Sec. II. D. Some results of this work have already

been reported in a thesis by Gels [9].

In this report we give a brief description of the theoretical approach

taken in this investigation and highlight some of the more significant

results. Mention will be made of the problems that have been encountered

and a proposed method for dealing with them. It is hoped that once a successful model is formulated which can predict electron avalanche size

distributions and the transition to streamers in SFg for negative points

(or protrusions), it can then be applied to the i nterpretati on of results

for positive-point discharges as given, for example, in the previous section

of this report as well as in [3] and [16]. As will become evident from

the discussions in Sec. II. C, the problem is more difficult for positive

discharges because, in addition to considering the stochastic nature of

the avalanche growth process, it is also necessary to consider the probability

of initiatory electron release as a function of location in the gas containing

gap. For negative discharges one can insure, by irradiating the point

electrode, that electrons will be released at discharge inception predominantly

from the tip of this electrode where the electric field is highest (see

Sec. II. C). Thus, for the negative point case, the statistics of the

electron release or injection process are of no concern, and the task of

calculating the statistical distribution of avalanches is simpler.

The theoretical approach taken here resembles that used by Blair, et al . [17]

in their investigation of avalanche statistics for uniform fields in SFg.

In that work it was shown that the probability that an electron avalanche

will grow to the point where it leads to streamer breakdown is vanishingly

small for E/p (field strength/pressure ) below the limiting value correspond!' ng

to the condition a-j = n a , where a-j and na are respectively the ionization

and attachment coefficients of the gas. The present work includes an attempt to extend these considerations to nonuniform field situations

where a study of avalanche inception and growth are likely to be more successful because of the highly restricted nature of the ionization region.

Moreoever, this is more likely to represent the conditions under which

breakdown occurs in practical situations. Rarely can one apply purely

uniform fields considerations to compressed gas insulated equipment in

which conducting particles may be present as well as surface irregul arities.

In practice, highly nonuniform electric fields can also appear at interfaces

with sol id i nsulators.

II. B. 2 Theory

II. B. 2.1 Introduction

The basic approach, as described here, is to use information on electron-molecule

interactions in the gas phase to predict the development of an electron

avalanche in a nonuniform electric field region, i.e., the spatial and

temporal dependence of its growth. It should be kept in mind that electron

avalanching, and for that matter breakdown, is a statistical phenomenon;

thus, it is necessary to consider it from a statistical point of view. The

20
question of practical significance is: given a set of conditions, e.g.

,

field nonuniformity, gas pressure, etc., what is the probability that an electron avalanche will grow to a sufficient size to lead to breakdown?

If electric fields are moderate, compressed gases exhibit remarkably little

electrical conductivity. The conduction is very low because there are very

few free charge carriers. The gas molecules, though mobile and constantly

moving in thermal equilibrium, are normally neutral. An occasional charged

molecule is created by background radiation effects so that a small but finite

free carrier density exists. Because there are so few carriers, the electric

current they provide is often not even measurable, typically being below

10-15 amperes.

The transition from the highly insulating to the conducting state of a gas,

i.e., breakdown, can only occur when a great number of charge carriers are introduced into the gaseous gap. Hence, the basic phenomena associated with

breakdown are the processes which influence the buildup and decay of free

charge in the gas.

II.B.2.2 Basic Discharge Processes

Gas discharges occur when conditions allow ionization to take place. The

energy needed for ionization of molecules or atoms in their ground state

is typically 10 to 20 eV. Each ionizing event results in the liberation

of at least one additional electron from a molecule, leaving behind a positive

ion. The progressive release of liberated electrons causing further ionization,

as in a chain reaction, is known as an electron avalanche.

Although ionization can occur via other mechanisms such as through photon

absorption or collisions with molecules in excited metastable states (see

Sec. II. F), it will be assumed here that ionization by electron collision

with ground state neutral molecules is by far the dominant mechanism responsible

for electron multiplication, i.e., the process

e(KE > 15.7 eV) + SF

6 - SF6 + + 2e,

where KE refers to the kinetic energy of the incident electron. Actually

for electrons with energies above 15.7 eV, the formation of a stable SFg

ion is highly improbable, and the most likely ionization process for SFg

is one that involves dissociation [18-20], namely

e + SF

6 + SF

5 +

+ F + 2e. (4)

Another process of fundamental importance in understanding electron

avalanche growth is electron attachment, examples of which are

(a)

(b)

( 5 )

21
This is the process by which electrons are removed from the gas and rendered

unavailable for ionization. The process (a) above, for the formation of a stable SFg" ion, requires a third body (molecule) to remove the excess

energy [21]. The lifetime of SFg“ exceeds 50 us; thus at high enough

pressures, it will tend to collisionally stabilize before auto-detachment

can occur. In the second process (b), referred to as dissociative attachment,

the excess energy can be consumed as kinetic energy of the dissociation

fragments, thereby insuring stability of the negative ion formed.

Given that an electron has sufficient energy to ionize (or attach), one must ask: what is the probability that such an event will occur in an electron-molecule encounter? The likelihood of an ionizing or attaching

collision between an incident electron and a target molecule can be expressed

by an "effective area," the cross section, which is the "size" of the

region in space where the two particles must be at one time for the defined

collision to occur. This formalism for describing what interactions take

place at the atomic scale has proved remarkably successful over a very wide

range of situations. In general form, the collision cross section, a, is

expressed as:

The value of cross-section information is both in the visualization of what

reactions take place and in its fundamental form which can be applied to

most situations. Its generality also is a problem, though, since a thorough

accounting of all significant reactions must be kept.

Each pair of colliding particles exhibits a specific cross-section pattern

for a given event. This pattern is typically dependent upon the relative

velocities or energies. As an illustration of the range and variation of

cross-section values, data for electron attachment in SFg gas is presented

in figure 11. These data were taken from [20].

Although one could use cross-section data directly to model electric discharge

behavior such as with a Monte Carlo-type computer calculation in which an arbitrarily large number of individual collision events are considered,

such an approach is time consuming and generally impractical. In applying

cross-section data, it is convenient to first perform an average over the

kinetic energy distribution of the electrons, and derive average quantities

(swarm parameters) known as ionization and attachment coefficients (a-j and

n a ) which give the number of ionizations (or attachments) per unit distance

in the gas. This approach may not be valid under all conditions, but it

is the approach that is commonly taken and will be useful in all cases where local equilibrium can be assumed (also see Sec. II. D).

If one knows the electron energy distribution function f(u), then one can calculate the rates of ionization v-j and attachment v

a using

0 = number of particles affected/unit time . incident intensity

1/2 oo

m

u 1/2

a.• (u)f (u)du ( 6 )

22
ATTACHMENT

CROSS-SECTION

(cm

2

Figure il. Electron attachment cross sections for SFq (from Asundi and Graggs).

23
and

1/2

v

a = N(—) f u 1/2

a

a (u)f (u)du

m J0

( 7 )

where m is electron mass, N is the gas number density and a-• and a a are the ionization and attachment cross sections. The ionization and

attachment coefficients are defined from the relationships

v-j = otjW and v

a = n a W, (8)

where W is the mean electron drift velocity. These coefficients are usually

expressed as functions of E/N, the field-to-gas density ratio (see Sec. II. D).

The electron energy distribution function can be obtained from solutions

of the Boltzmann transport equation as discussed in Sec. II. D.

If the electric field resulting from i on-space-charge can be neglected so that the electric field is solely a function of position, and if the pressure

in the gas is constant, then a-j and n a will be solely functions

of position. Thus, if ionization and attachment are the only important

processes determining avalanche growth, then we can write the following

approximate expression for the spatial dependence of the electron number

density:

dn e (x) / dx = n e (x) [a-; (x) - n a (x)] , (9)

where ne (x) is the average number of electrons in the avalanche when it

reaches position x. This equation allows for nonuniform electric fields

to exist by allowing a-j and n a to be functions of position in

accordance with the electric field. More will be said about the validity

of eq (9 ) i n Sec. 1 1 . C.

There are, of course, other processes that can affect the growth or decay

of an electron avalanche in a gas, and although these may not be important

for most conditions considered here, they are nevertheless worth mentioning.

For very high values of E/N, it may be necessary to include processes which

lead to detachment of electrons from negative ions. The possible importance

of this process in initiating electron avalanches will be considered in

Sec. II. C. This process, like ionization and attachment, is usually described

in terms of a detachment coefficient, i.e., the number of electron detachments

per unit length. Collisions involving metastable species, i.e., atoms or molecules in long-lived excited states, may also be important in some cases

as will collisions with ions. Absorption and emission of photons in the

gas can also affect the production of free electrons.

24
II.B.2.3 Deterministic Model of Avalanche Growth

The number of electrons in a given avalanche, neglecting photoionization and

ionization from ion or metastable collisions for the moment, depends on the accumulated likelihood for the various possible collision events during

the travels of all the free electrons. For a given density of particles, the

probability per unit distance of a collision event is simply proportional to

the cross section. Individual events may include electron impact ionization,

electron attachment, and detachment. As these events in the gas are not

deterministic in nature, avalanche growth is statistical. Thus, for a given

set of conditions, variations in avalanche size will occur and the result

is best described by a distribution of sizes. The size is of special

interest because it indicates when a self-sustained electrical discharge

will occur.

As a first step in modeling avalanches, however, it is useful to consider

a description in terms of average quantities as, for example, can be derived

simply from a consideration of eq (9). Modeling discharges by considering

phenomena only in terms of their average effects is sometimes referred to

as deterministic, since the underlying stochastic nature of the phenomena

is ignored. Later, when a stochastic model is formulated and the phenomena

are described in terms probability distribution functions (PDF's), it is

to be expected that averages generated from the PDF's should agree with

the average solutions generated by the deterministic model. This, in

fact, is found to be the case [9].

As a first approximation, we neglect space charges so that the electric

field is Laplacian, solely a function of position. If the electric field

is a function of position, then the ionization and attachment coefficients

for the gas are functions of position. In this case, the growth-decay

process is described by eq (9), from which the average number of free

electrons in an avalanche, ne , when it reaches position x from the cathode

is determined using swarm parameters by

It was assumed here that the avalanche was initiated by a single electron.

A numerical solution for eq (10) can be easily generated using a computer.

An example of calculated avalanching in SFg at a pressure of 200 kPa

is shown in figure 12 for the case of a nonuniform applied field. The

average number of free electrons contained by the avalanche as it moves

from the cathode surface is depicted. The field nonunif ormity in this

example was provided by a cathode protrusion comprised of a hemispherical ly

tipped metal rod, 0.2 mm radius, which protruded 2.0 mm into the gas gap

from a planar cathode surface. The values of the ionization and attachment

coefficients used are given in [9].

x

o

25
NUMBER

OF

FREE

ELECTRONS

Figure 12. Calculated electron avalanching in 200 kPa SFg controlled

ionization zone.

26
II. B. 2.4 Effect of Space Charge on Avalanche Growth

To determine the effect of space charge on the electric field, which in

turn affects the ionization and attachment coefficients, we must know not

only the space charge magnitude, but also how it is spatially distributed.

This can be determined by considering the distribution of electrons in the

head of the avalanche.

Raether [22] has shown that, in the presence of diffusion, when at time 0 we start out with n 0 electrons at the origin, the density of electrons p e at a distance r from the origin for time t > 0 is:

p e (r,t) = [n 0 /(47TDt) 3/2]exp[-r 2 /4Dt], (11)

with a mean-square radius of

oo r

2 = (l/n 0 ) f r

2 (4irr 2 p e )dr = 6Dt, (12)

Jo

where D is the diffusion constant for electrons. It can be shown [9] that even if the number of electrons is changing as a function of time in a manner dependent upon the number of electrons (this is the situation found

in an avalanche), then the electrons still maintain the distribution above.

* The avalanche can be viewed as a ball of electrons, with a density profile

in the form of p e ~ exp[-(r/R

)

2

] , where r is the distance from the

center of the ball. The center of the ball moves in the direction of the

anode, the z-direction, with expanding root-mean-square radius given by

z R = (6Dt)

1/2

= C6(D/u) f

dz7E(z')] 1/2

, (13)

Jo

where u is the electron mobility. This radius is a function of z, the

distance from the cathode. Figures 13 and 14 show calculated values of the

avalanche radius as a function of the distance from a cathode protrusion.

A value of D/y = 5 eV has been taken from the data of Naidu and Prasad [23]

(see Sec. II. D). For constant gas pressure, radii are not dramatically

different for the different terminal voltages near the discharge inception

1 evel s.

As the avalanche head moves through the gas, it leaves a trail of positive

and negative ions. Near the cathode, where the ionization coefficient

exceeds the attachment coefficient, the ions are mostly positive. Further

away from the cathode, the attachment coefficient exceeds the ionization

coefficient, and the ions are mostly negative. Here, the electrons are taken to move many times faster than ions, due to relative mobilities.

27
Figure 13. Avalanche radius with 100 kPa SFg, 17 kV.

Figure 14. Avalanche radius with 200 kPa SFg, 27 kV.

28
Thus, for any one avalanche, the ions are assumed to be stationary at

their point of creation throughout the movement of the electron "wave"

through the ionization zone. After all avalanche electrons have passed,

the ions will slowly drift out of the gap.

For the electrode arrangement used in the experiment described in [9], ion

densities (ions/mm path) were calculated at 100 and 200 kPa pressure SFg,

figures 15-18. Net ion charge is shown in figures 19 and 20. Applied

voltages which would create maximum free electron numbers just below and

above 10^ are used. Note the number of ions/mm exceeds the number of free

electrons and that, as expected, the ions create a dipole, more positives

in the growth region and more negatives in the decay region. Note also that

as gas pressure is increased, these ions (and indeed) the whole avalanche

moves closer to the cathode surface.

Taking into account electron diffusion, the avalanche leaves behind_ expanding

cylinders of positive and negative ions, having approximate radii r(z)

given by eq (13). To consider the effect of the ions on the field of the

avalanche, wejnight break the charge trail up into disks of charge AQ

having radii r = r; the space charge field at the avalanche head is then

obtained as the summed contributions of all the disks of charge. This is

shown in figure 21. The electrons in the head of the avalanche will enhance

the electric field, enhancing growth, in front of the avalanche head. On

the other hand, the electrons will diminish the field in back of the avalanche

head, diminishing growth there. Since the ionization and attachment coefficients

are nonlinear functions of electric field, the net effects of enhanced and

diminished growth do not cancel. Instead, the increased growth in front

exceeds the reduction in growth in back. If the electrons in the avalanche

head have radial distributions of the form p e ~ exp[-(r/R

)

2

] , where r is

the distance from the center of the avalanche head, then the field distortion

will be maximum at r = R.

Computer simulations were run using the assumptions and approximations

explained above. The fields due to the avalanche head electrons were found

to be several orders of magnitude greater than the fields due to the ions.

The fields due to avalanche head electrons were divided by the Laplacian

electric field, and plotted in figures 22 and 23.

Raether [24], investigating discharges in a cloud chamber, found that when

the number of electrons in the avalanche reached a certain level, a channel

formed, whose growth rate and speed suddenly increased by an order of

magnitude. Raether [25] attributed this to the enhancement of the ionization

process in front of the avalanche head, due to the space charge of the

electrons in the avalanche head. He found that this critical number of

electrons was approximately 10$. Raether was using a uniform field

configuration to investigate a non-attaching gas.

Computer simulations of the nonuniform test system of [9], filled with sulfur

hexafluoride, indicate the field due to electrons becomes roughly equal to

the Laplacian field when the number of electrons approaches 2 x 10 6 . While

this is lower than Raether' s critical value, it is encouraging that the

simple model employed shows that an avalanche growth instability can be

expected. The lower critical number resulting from the computer simulation

may be due to underestimation of the radius of the avalanche. The computer

29
Figure 15. Calculated positive ion density left by an electron

avalanche in the CIZ test cell at 100 kPa SFg.

Calculated positive ion density left by an electron

avalanche in the CIZ test cell at 200 kPa SFg.

30

Figure 16.
Figure 17. Calculated negative ion density left by an electron

avalanche in the CIZ test cell at 100 kPa SFg.

Calculated negative ion density left by an electron

avalanche in the CIZ test cell at 200 kPa SFg.

31

Figure 18.
Figure 19. Calculated net ion density left by an electron

avalanche in the CIZ test cell at 100 kPa S Fg

Figure 20. Calculated net ion density left by an electron

avalanche in the CIZ test cell at 200 kPa SFg.

32
axis of

symmetry

disk of remnant charge

AQ-[°<(x) -^(x)]n

e (x)eAX

Figure 21

.

Model of avalanche used to evaluate space charge effects.

33
5

1 atm. abs. SFCb

.* \ • •

• •*•18 KV

•

•

Figure 22. Electron E-field/Laplacian E-field for SFg at 100 kPa.

Figure 23. Electron E-field/Laplacian E-field for SFg at 200 kPa.

34
analysis considers radial motion from diffusive forces only and did not take

into account the effect of the electron space charge r ield when calculating

radial motion. This makes the computer analysis radii somewhat smaller

than may actually occur. This may explain the di screpanci es in critical

sizes, since the computed critical size is highly dependent on the radius

of the avalanche.

II.B.2.5 Stochastic Model of Avalanches

We now turn to the problem of determining the statistical variations in

electron avalanches. In 1949, Wijsman [26] examined the avalanche process

from a stochastic viewpoint for the case where there was no attachment and

Townsend's first ionization coefficient, a-j , was constant. As in all

stochastic modeling, space charge effects were considered to be negligible.

Considering one dimensional growth, he assigned a coordinate x to every

point along the discharge. He let x = 0 be the cathode, the origin for a single starting electron, and let x = d be the anode. He considered a-j(x)dx

to be the probability of an electron causing ionization when moving from

point x to x + dx. He arrived at the probability distribution p(n,x), the

probability of the avalanche containing n electrons when it reaches point x. The result is the Furry [27] distribution.

This expression can be approximated by p(n,x) = (l/n)exp(-n/n) , for large

n. It gives the same average value for the number of electrons at any

point x in the avalanche's progression as the deterministic viewpoint.

However, it shows that fluctuations from the mean are large.

If breakdown is considered from Raether's [24] streamer point of view, then

these fluctuations can be very important. As an example, suppose the

average avalanche size in a system is one half the critical avalanche

size. The deterministic viewpoint suggests that streamers will not develop

in this situation. The stochastic viewpoint, considering variations from

the mean, suggests that exp(-2) = 0.14 of all avalanches will exceed the

critical size, and develop into streamers.

Measurements of electron avalanche distributions for non-attaching gases have

yielded results which deviate from the Furry distribution in some situations.

The results of these measurements are reviewed in [9]. Modifications and

extensions of the statistical theory of avalanche formation have been made

by Legler [28] and Byrne [29] to explain the discrepancies between predicted

and measured distributions.

The statistical theory of avalanches for electron-attaching gases is somewhat

more complicated, but as will be shown here, the resulting distribution is

quite similar to the Furry distribution found for non-attaching gases.

When electron attachment is included in the stochastic model, n a (x)Ax

is considered to be the probability of an electron attaching when it moves from position x to x + Ax. If an electron avalanche starts out with exactly

p(n,x) = (l/n)[l-(l/n)] n_1

, (14)

where x (15)

35
one electron at the cathode, then the probability, p(n,x), that the avalanche

contains n electrons when it reaches point x will depend on three things:

(1) the probability that there were n electrons at point x-Ax times the

probability that none of them attached or ionized in moving the distance Ax;

(2) the probability that n-1 electrons existed at point x-Ax times the

probability that one of them ionized in moving Ax; and (3) the probability

that one of them attached in moving the distance Ax. Stated mathematically,

this means:

P(1 ,0) = 1,

p(n,x) = p(n,x-Ax)[l - n ( a-j ( x ) + n a (x))Ax]

+ p

(

n-1 ,x- Ax ) (n-1

)

a-j (x) Ax

+ p(n+l ,x- Ax) (n+1 )na (x) Ax,

(16)

where Ax is made asymptomatically small, so that no more than one population-changing collision event can occur when the avalanche moves

Ax. After some algebraic manipulation, and division by Ax, we get

the differenti al -difference equations:

= n ( x ) p ( 1 ,x),

dx (17)

j£(-n- >. x. ) = -p(n,x)n[oj (x) + n

a (x ) ] + p(n-l ,x) ( n-1 ) a- (x)

dx i a i

+ p ( n+1 , x) ( n+1 )

n

a (x)

.

The general case for this problem was solved by Kendall [30] for the case where "birth" (ionization) and "death" (attachment) were functions of time

(position). Legler [28], apparently unaware of Kendall's work, solved

this problem for the case when ionization and attachment are constants.

Kendall's solution, of which Legler's solution is a special case, is given

by:

p(o,x)

p(n,x)

where

p(x) =

1 - exp[-p(x)]/w ,

[exp[-p(x)]/w 2 ](l - l/w) n_1

,

x

na (x')]dx".

n > 1

,

(18)

(19)

and

36
X

w = 1 + exp[-p(x)]^exp[p(x")]a-j (x')dx'.

o

( 20 )

The distribution above has a mean of n = exp[-p(x)], which is identical

to the deterministic solution.

Because w is much greater than one for most cases of interest here, p(n,x)

has the asymptomatic solution

p ( n,x) - exp[-p(x)]exp[-n/w(x)]/w 2

.

This follows from taking

x f exp[p(x')]ai (x')dx' ~ 1

,

-'o

and assuming n’(x) >> 1, so that

( 21 )

( 22 )

w - n(x) J'exp[p(x")]oi(x')dx' , (23)

which is obtained from eq (20) using eq (10),

Thus we have

p(n,x) = exp[-p(x)]exp[-n/n(x) / exp[p(x')]a.j (x')dx']/w‘

(24)

For SFg under the conditions of interest here, the integral in eq (22)

above ranged from 1.1 to 1.3. A plot of the PDF versus n on a log-scale

gives a curve with a slope of

x

-l/fn(x) / exp[p(x')]a-j(x')dx'),

o

as compared t£ the case for a non-attaching gas, where by eq (14), the slope

should be -1/n. As for non-attaching gases, deviations from this modified

form for the Furry distribution are possible for very low n-values [28].

The effects of including detachment and secondary emission on the statistical

distribution of avalanches is discussed in [9], In general, the average

quantities predicted from the PDF's are the same as those given by the

deterministic model.

37
II. B. 3 Measurement of Electron Avalanche Distributions

Experimental studies of electron avalanches in SFg were conducted using a test vessel described in [9]. Details of the measurement system will not be

repeated here. The emphasis of the discussion in this report will be on the

results, and a comparison of these with predictions based on the theory given

above.

Briefly, in order to assess the avalanching model, a specific electrode

configuration was selected. The configuration employed in the experiment

is referred to here as a controlled ionization zone (CIZ). The configuration

for the CIZ is depicted in figure 24. Electrons released from the cathode

at a rate controlled by ultraviolet irradiation are exposed at first to a high-field ionization zone. Outside of this region the field quickly decays,

so that ionization products drift without further ionization to be collected

at the anode. The cathode tip employed had a 200 urn radius.

Tests of the CIZ system performance demonstrated that single avalanches

could be initiated by uv stimulation of the cathode, and that avalanche

growth in h i gh-pressure gases could be detected. The degree of experimental

stability necessary for accurate observations was also determined. The

high-voltage supply stability was approximately ±1.0 mV. A special effort

was made to insure that the entire system was electrically quiet. Partial

discharges in the al 1 -connecti ng leads were eliminated in order to achieve

the desired sensitivity for avalanche detection.

A corona detector-pulse height analyzer system was used for the measurements

because it provided the greatest sensitivity. The noise level of the

system allowed measurements of partial discharges as small as 0.05 pC. In

general, almost no partial discharges above 3 pC were measured. The noise

level of the system at each terminal voltage was determined by operating

the system at that voltage with the ultraviolet lamp off. In this state,

no avalanche initiating electrons were released from the cathode, so that

any measured pulses that occurred under this condition could be attributed

to system noise. To insure that what appeared to be discharges was not

the result of electromagnetic coupling between the ultraviolet lamp and

the system, the noise level was measured with zero terminal voltage and

the ultraviolet lamp both on and off. It was determined that any noise

that the ultraviolet lamp introduced into the system was well below the

level of the other system noise.

At all pressures, the lower bound for the range of terminal voltages was determined by the threshold at which avalanches could be measured distinctly

above the noise level. At a given pressure, as data was taken at incrementally

higher voltages, there came a point at which the pulse rate began increasing

suddenly. After this happened, the pulse rate was higher at lower voltages

than it had been previously. This showed the discharges at the higher

voltages had altered the rate of photoemission from the electrode surface.

Since it was desired to run the experiments under conditions which were as constant as possible, no measurements were taken at or above the voltages

which changed the pulse rate. This determined the upper limit of the

terminal voltages for measurements made with SFg at 100 and 200 kPa. The

upper voltage limit of the 300 kPa data was imposed by the limitations of

the power supply.

33
HIGHER-FIELD

IONIZATION ZONE

Figure 24. Controlled Ionization

ANODE

CHARGE COLLECTION

ASSEMBLY

N \ \

Zone Technique.

39
For a single test, the system was able to measure discharges over a range

of 30 dB. Separate tests were necessary to acquire data over a wider

dynamic range. The statistical distribution of avalanche sizes was measured

for many different combinations of gas pressure and applied voltage. Vie present here only a few selected examples of the results obtained. Measured

distributions obtained for the conditions indicated are shown in figures 25-27.

In these figures the horizontal axis is charge, and the vertical axis gives,

on a log scale, relative probability obtained from the number of pulses

counted within an increment of charge.

It is clear that the measured distributions deviate, in some cases rather

significantly, from the Furry distribution given by eq (24). Except for the

data in figure 25, the distributions do not show a simple exponental decay

with charge. At each gas pressure it was found that as voltage was increased,

a distinct peak appeared in the distribution, and at even higher voltages

a second well-defined peak appeared at higher charges (see figs. 26 and 27).

At some pressure, as shown in figure 27, the second peak was associated

with an isolated high charge feature well separated from the rest of the

distribution. The charge level of both the first and second peaks increases

as the terminal voltage increases, but does not increase as much as the

average charge of the total distribution.

The average charge, determined by summing all the pulse charges and dividing

by the number of pulses, was generally found to be much lower than the

theoretically predicted value. However, the dependence on terminal voltage

agreed fairly well with the theoretically predicted change. The discrepancy

between predicted and measured average charge is probably accounted for by an 11% uncertainty in determination of the peak magnitude of the applied

electric field [9].

The appearance of the lowest charge peak in the measured distributions

represents a deviation from the Furry distribution similar to that seen for non-attaching gases as discussed in [9] and [28]. Namely, it seems to

be accounted for by the fact that the likelihood of an electron causing

ionization will in general depend on its history, i.e., it will have to move a minimum distance in the gas before it has enough energy to exceed

the molecular ionization threshold. This history dependence makes it quite

reasonable to expect considerable deviations from the Furry distribution.

Nearly all the measured distributions appeared to follow a modified Furry

distribution for at least part of their ranges.

The reason for the appearance of the second, higher charge peak in the

distributions is more obscure. These peaks ranged between 1 and 3 pC. They

may have been the result of space-charge effects. Calculations show that

when the number of electrons in the avalanche approaches 3 x 1

0

5

, the

space charge field due to the electrons in the avalanche head, which is

assumed spherical and to expand only by diffusion, is equal to about 15 percent

of the Laplacian field. An avalanche of 3 x 10 5 electrons would be expected

to produce about 0.5 pC of ion charge. Measured discharges below this

level tended to follow a modified Furry type of distribution [9], Discharges

above this level tended to be larger than would have been expected if space

charges had been neglected. Furthermore, the second peak observed was

40
PICOCOULOMBS

Figure 25a. Measured electron avalanche distribution

for 100 kPa $F 6 , at 17.6 kV.

PICOCOULOMBS

Figure 25b. Measured electron avalanche distribution

for 100 kPa SFg, 17.6 kV, pulse rate = 89.

41
1.8

CQ

*=c CQocc

Q.

8.1

.01

.001

PI COCOULOMBS

Figure 26a. Measured electron avalanche distribution

for 100 kPa SF5 , 18.6 kV , pulse rate = 41.

e 12 3

PI COCOULOMBS

Figure 26b. Measured electron avalanche distribution

for 100 kPa SFg, 18.8 kV , pulse rate = 50.

42
PROBABILITY

1.0

CQ<

CQOcc

Cl.

8.1

.01

.001

PICOCOULOMBS

Figure 27a. Measured electron avalanche distribution

for 200 kPa SFg, 29.6 kV

.

PICOCOULOMBS

Figure 27b. Measured electron avalanche distribution

for 200 kPa SFg, 29.6 kV , pulse rate = 11.

43
always above the 0.5 pC level. Therefore, it is possible that the distribution

of discharges above 0.5 pC was strongly influenced by space-charge buildup

during the avalanche development. The transition to large pulses may also

be the result of el ectrohydrody namic instabilities in the gas (see appendix II).

II. B. 4 Remaining Problems

It should be clear from the preceding discussions that there are a number of

questions that remain to be answered. The relatively simple stochastic model

of avalanche formation given here for highly electronegative gases appears to

have only a limited range of applicability. Once the applied voltage exceeds

a certain value, the model breaks down and can no longer explain features

observed in the measured avalanche size distributions.

An understanding of the observed transition to "large" pulses not predicted

by the Furry distribution may be the key to understanding the transition

from electron avalanche to streamer and then to breakdown. It should be

noted here that a similar abrupt transition from avalanches to large pulses was observed in the NBS laboratory measurements of both positive and negative

corona pulses (see the previous section as well as [8] and [16]). The

appearance of the large avalanches in the experimental results points to

the need for better modeling, especially at very high values of E/N.

In attempting to improve the model of electrical discharge development in

SFg, two questions are currently being addressed. The first concerns the

range of validity of swarm parameters such as the ionization coefficient

for high E/N discharge environments where there may also be highly nonuniform

fields. The second has to do with the effect of el ectrohydrody namic (EHD)

instabilities on the development of gas discharges.

Concerning the first question, an analytical theory, described in appendix I, can be used as a first approximation to determine when and when not to

expect swarm parameters to be accurate representati ons for discharge studies.

It should be noted that this question applies to a broad spectrum of expanding

technologies where gas discharges are used. High and ultra-high power lasers;

high energy density particle-beam and projectile accelerators; stable,

high-speed mega-, giga-, and tera-watt switching and triggering systems;

and super-high (=10 9 V) voltage insulation systems are but a few areas

in which one needs to know the range of swarm parameter validity in order

to understand and predict device behavior. The approach given in appendix I provides a strai ghtf orward means of estimating the tendency of an average

electron (i.e., one characterized as having the average of a distribution

of energies) to attain and maintain equilibrium in an electric field.

Special attention is given to the case of highly nonuniform fields.

Concerning the second question, an entirely new theoretical model is under

consideration which is based on the use of perturbation analysis for the

study of EHD instabilities. These are instabilities in the discharge

parameters which may be superimposed on the developing electron avalanche.

The formalism, as described in appendix II, requires the solution of coupled

differential equations for conservation of mass, charged particles, and

momentum, as well as Maxwell's equations for the electric field. The

method appears to have broad generality in that it allows analysis of

conditions which will inhibit, or if desired, promote breakdown, and hence

44
is applicable to insulation, switching, and lasers. The primary objective

of the stability analysis in the present study is, of course, to attain an understanding of the sudden "aval anche-to-streamer" transition. Preliminary

investigations of the feasibility of this method indicate that it should

be quite promising.

II.C. Basic Mechanisms for Corona Inception in S Fq

II.C. 1 Motivation and Introduction

The purpose of this work has been to examine the basic mechanisms for the

initiation of corona discharges in highly electronegative gases such as SFg. An understanding of these mechanisms will provide a basis for

determining the effect of varying conditions on the measurement of corona inception voltage. These conditions, for example, include: gas pressure,

electrode geometry, presence or absence of radiation, voltage waveform,

electrode surface conditions, etc. The information acquired from this study

will hopefully lead to more useful and physically meaningful definitions

of corona inception which can be used in the testing of gaseous dielectrics

as well as in the design of gas-insulated systems.

This work is closely related to the NBS-supported project at MIT described

in the previous section. The emphasis in this section, however, is more on achieving an understanding of the discharge initiation processes, as opposed

to the avalanche growth processes. Also both polarities are considered

for the stressed electrode, whereas the MIT work was restricted to negative

polarities in order that the source of - i nitiating electrons could be precisely

controlled. Information presented in Sec. II. A. on character!' sties of corona pulses, together with the model of avalanche growth given in the

previous section, is taken into consideration in the following discussion

in evaluating applicability of the streamer criterion to prediction of

corona onset.

The results reported here are an extension of preliminary results previously

reported [10,16]. Most of the information presented in this section was given in a paper at the special symposium on corona and non-spark discharges

which was part of the 1981 Conference on Electrical Insulation and Dielectric

Phenomena. This paper will soon be published in archival form [11]. In addition to the comparison between ac and dc inceptions emphasized in the

earlier work [10], we report here results of a more thorough examination

of the effects of uv-radiation, electrode geometry, and electrode conditioning

on the measurement of corona inception in SFg. Corona inceptions have

also been calculated using the streamer criterion and these are compared

with our measured results. The connection between the streamer criterion

and the nature of the corona phenomena observed near onset is discussed,

and the limitations of the streamer criterion for predicting inceptions

are considered. Discharge initiation mechanisms are proposed and shown to

be consistent with the observed changes in discharge behavior with changing

gap conditions.

Since details of the techniques used to measure corona inception voltages

are covered elsewhere [10,11,16], we shall avoid discussion of the apparatus

and measurement procedures and focus here instead on interpretation of the

results.

45
II. C. 2 Definition of Corona Inception

From the measurement point of view, there is a degree of arbitrariness

associated with the definition of corona inception voltage. Corona can be

measured by a variety of techniques of differing levels of sensitivity [31].

Thus, it is to be expected that one's preferred definition of a measured

inception voltage will depend somewhat on the type of measurement method

used. If, for example, one measures discharge current as a function of

voltage, then inception is customarily defined as that voltage at which the

current equals or exceeds a certain specified level. If one is detecting

discharge pulses, then inception is usually defined as that voltage at

which the charge in a pulse exceeds a certain level. Similar definitions

would apply to optical or acoustical detection of corona. Unfortunately

,

the definition is more often determined by the sensitivity of the detection

instrument used than by any knowledge about the properties of the discharge

process itself.

If the corona discharge intensity as indicated by the current, for example,

increases abruptly with increasing voltage, then it can be argued that the

measured inception values will be relatively insensitive to the assumed

definition. For the measurements reported here for SF5 , an abrupt onset

is observed only for negative corona and then only when the point electrode

is irradiated, or conditioned so as to insure electron emission. It would

be desirable to have a phenomenological basis for defining inception, e.g.,

the voltage at which the discharge becomes completely self-sustaining. There

are, however, difficulties with this approach because the conditions that

determine the growth of the discharge, such as the microscopic nature of the

cathode surface, or the presence of trace impurities in the gas, may be too numerous or uncontrollable. There are, nevertheless, theoretical criteria

which have been successfully used in many cases to predict inception [32].

The relationship between these criteria and the measured inceptions reported

here will be examined later.

For reasons previously mentioned [10,11], we have chosen here the count rate

of corona pulses that exceed a certain level (0.05 pC) as a criterion for

defining inception. In particular, inception was defined as the intercept

of the voltage axis set at the 0.1 count/s level with a straight line fit

on a semi-log scale to the data on count-rate versus applied voltage.

Examples of such plots are shown in figures 28-31 for dc measurements

correspond!

- ng to gas pressures and electrode gap conditions indicated.

There are difficulties that arise in assuming the same definition for both

ac and dc conditions as are discussed in [10] and [11]. As a result, there

are expected to be predictable differences between measured ac and dc

inceptions based on the above definition. If the corona turns on abruptly

with increasing voltage, then these differences should be small.

It has been known from earlier studies of corona phenomena [4,32], primarily

for corona in air [33], that the initiation and development of corona discharges can depend significantly on the presence of radiation that is

of sufficient energy to enhance the release of electrons either from the

gas or from the cathode surface. The radiation reduces the formative time

lag for discharge initiation associated with random fluctuations in the

rate of initiating electron production [34], and can give rise to an increase

4 6
APPLIED VOLTAGE (kV)

Figure 28. Observed pulse count rate versus applied voltage for positive

and negative point-plane dc corona in SFg at a pressure of

200 kPa. The gap spacing was 1.24 cm and the radius of

curvature of the point was 0.045 mm. The different symbols

indicate data obtained from different runs. Included are all

pulses with a charge in excess of 0.05 pC.

47
Figure 29. Observed pulse count rate versus applied voltage for positive

and negative point-plane dc corona in SFq at a pressure of

400 kPa. The gap spacing was 1.24 cm and the radius of

curvature of the point was 0.045 mm. The different symbols

indicate data obtained from different runs. Included are all

pulses with charge in excess of 0.05 pC.

48
\/ i a—1 l i L —l_—

16.0 18.0 20.0 22.0 24.0 26.0 28J3 30.0 APPLIED VOLTAGE |kV|

Figure 30. Observed pulse count rate versus applied voltage for positive

and negative point-plane dc corona in SFg at a pressure of

200 kPa. Also shown by the solid line is the average dc

current observed prior to the inception of pulses. The gap

spacing was 1.1 cm and the point radius was 0.47 mm. The

data were obtained using uv-radiation and the different

symbols correspond to different data runs.

49
Figure 31

310

4

10 :

10

'

2

za

E

<L

10

1JI

0.1

Observed pulse count rate versus applied voltage for positive

and negative point-plane dc corona in SFg at a pressure of

400 kPa. Also shown by the solid line is the average dc

current. The gap spacing was 1.1 cm and the point radius was 0.47 mm. The data were obtained using uv-radiation and the

different symbols correspond to different data runs.

50
in the avalanche or streamer pulse rate which would therefore lead to a lowering of the apparent inception voltage. It is clear that the definition

of corona inception may also depend on the intensity and energy of the

radiation present in the gap. However, since the radiation serves only to

insure that discharge initiating electrons will be present once the proper

field conditions for inception are reached, it is expected that there will

be an upper limit above which further increase in the radiation intensity

will have no effect on the initiation of corona. For the measurements

reported here, no attempt was made to guarantee that this limit was reached.

II. C. 3 Calculation of Corona Inception

For the case of a nonuniform electric field, a net ionization which can

lead to electron avalanche formation is possible only in the region where

ct-j ( E / N ) - n a (E/N) > 0. (25)

Here a-j and na are respectively the ionization and attachment coefficients

defined in Sec. II. B. These coefficients are functions of E/N, the electric

field-to-gas density ratio. Since E is a function of location in the gap,

a-j and na will likewise be functions of location. As shown in Sec. II. B,

the growth (or decay) of the number of electrons n e (x) between positions

x and x + dx in the gap is given by

d Mx > = ne

(x)[cij (x) - n

3 (x)]. (26)

dx

In this equation, we have assumed for simplicity that all of the electrons

are located at a single point, i.e., we have neglected the effects of

electron diffusion and delayed electron emission processes. This is a reasonable approximation only if the extent of the diffusion is small

compared to the distance traveled by the avalanche where x can be associated

with the centroid of the moving electron cloud.

Solving this equation one finds an approximate expression for the average

avalanche size given by

n e U) = n e (0 ) exp[ J{

a-j(x) - n a (x))dx], (27)

o

where it is assumed that the avalanche is initiated by ne (0) electrons

which originate at the point x = 0. For the negative point discharges,

the upper limit i coincides with the critical electric field where a-j = n a. For positive point discharges, l coincides with the location of the electrode

tip and x = 0 is any point in the region where a-j > n a

. The limits of

integration have been conveniently chosen to exclude the region which does

not satisfy eq (25), i.e., where growth in avalanche size ceases and decay

begins. Equation (27) must be considered an approximate expression because

51
it is derived without consideration of the detailed stochastic nature of

avalanche formation process [9,28]. Also it does not include possible

contributions to the avalanche from secondary or delayed processes [35].

It is an average quantity in the sense that it is calculated from the swarm parameters a-j and na , which are themselves derived from averages

over the electron energy distributions as given by eqs (5) and (7).

Using eq (27) for a single initiating electron, n e (0) = 1 , we have calculated

the average-maximum electron avalanche sizes (of those that move along the

electrode axis) as a function of applied voltage for the electrode gap

conditions used in the measurements reported here. They are maximum in the

sense that the limits of integration in eq (27) are between the point of

maximum E/N and the point where a-j = n a

. The results of such calculations

are given in figure 32 for different indicated SF 5 gas pressures assuming gap

conditions like those used to acquire the data given in figures 28 and 29.

In performing these calculations, the static electric field was expressed

in terms of prolate spheroidal coordinates [36,37], so that the magnitude

of the electric field is given by

E^ = V Q [f sin n (cosh 2

? -cos 2 n)tanh _1 (cos n 0

)]

-1

, (28)

in which n and ? are the meridian coordinates related to Cartesian coordinates

by the transf ormations

x = f cosh ? cos n and y

= f sinh ? sin n ,

where x is taken to lie along the poi nt-to-pl ane axis and azimuthal symmetry

is assumed. The field is in a direction parallel to lines of constant ?. In eq (28), V 0

is the potential applied to the point electrode which has

been characterized by a surface of constant n = n 0 , i.e., a hyperboloid

of revolution for which f is the focal distance as measured from the plane

electrode. For the gap conditions used here, the value of n 0 was determined

at each gap spacing by a least squares fit of a hyperbola to a tracing of

a photograph of the point electrode made using a microscope. Deviations

of the electrode surface from these fits were generally quite small, even

in regions far removed from the active discharge volume. The greatest

uncertainty was in determining the exact shape and location of the tip,

and this could lead to significant uncertainties in the calculations of

n e , as will be noted later.

The expressions used for a-j and n a were obtained from polynomial fits

to the data of Mailer and Naidu [38] and are given by

a

i (E/P) = [-1.743 + 0 . 0269 ( E /P ) - 2.498 x 1CT 5 (E/P) 2 +

9.131 x IQ" 9 (E/P)

3 ]P, ( 29 )

for E/P > 117,

52
Figure 32. Calculated average-maximum electron avalanche size versus applied voltage for the different indicated gas pressures and

parameter e = f - d. The gap geometry corresponds to the

conditions of figs. 28 and 29.

53
( 30 )

n

a (E/P ) = [3.408 - 0.0891 (E/P ) + 5.556 x 10’ 4 (E/P) 2 -

1.017 x 10" 6 (E/P ) 3 ]P

for 250 > E/P > 117, and

n a (E/P) = 0 (31)

for E/P > 250,

where and n

a are in units of cm“~ , P is the gas pressure in torr and

(E/P) is expressed in units of V cm

-1 torr" 1

, to be consistent with the

published data. In order to obtain results consistent with the units used

in reporting our data, the calculations were performed assuming the conversion

1 torr = 0.132 kPa. The value E/P = 117 corresponds to the critical field

where a-j = na. In calculating n e , eqs (29)-(31) were used in eq (27), and

the integrations were performed numerically with a computer. The computer

code used for these calculations is listed in appendix III.

The onset of corona is presumed to occur when the avalanche reaches some critical size such as would, for example, correspond to a detectable pulse,

a streamer, or condition where the discharge is self-sustained. As we

noted earlier, there have been attempts to find phenomenological bases for

defining corona onset [32]. Perhaps the most successful and widely accepted

theoretical criterion has come about from tying the onset of corona to the

lowest voltage at which streamers are presumed to appear [39]. Although

this "streamer criterion" may exclude some of the smaller electron avalanche

pulses that were included in our measurements, it is, nevertheless, useful

and constructive to compare onsets predicted on the basis of this criterion

with our measured values. As noted in the previous section, an avalanche

can presumably become a streamer when the number of electrons it contains

is large enough that the space charge field it creates is comparable to

the applied field [34], or according to Raether [39], when the avalanche

contains on the order of 1 x 10 8 electrons. Using the streamer criterion,

one obtains inception voltages which correspond to the points of intersection

of the avalanche growth curves with a horizontal line at the 1 x 10 8 electron level as shown in figure 32.

The calculations giving the results shown in figure 32 were performed, as indicated, for different values of a parameter e defined to be the difference

between the focal length f and the gap spacing d, i.e., the distance from

the plane electrode to the tip of the point electrode. This difference can

be affected by the accuracy of the fit of a hyperboloid to the electrode

surface near the tip. The degree to which we can determine the extent of

the active region where a-j > na is determined by the uncertainty in e. This uncertainty, it should be noted, is not an indication of how accurately

we can measure the gap length but rather an indication of how accurately we

can determine the size of the small active discharge region near the tip. From

microscopic examinations of the point electrode surfaces and a consideration

of the uncertainties in fitting hyperbolae to these electrodes, we must

conclude that e cannot be known to better than ±0.002 mm. This can

54
lead to quite large uncertainties in the calculation of n e , which are due to

the fact that, especially for sharp points as considered here, a di sproportionately

large fraction of the ionization contributing to the avalanche size takes

place in the immediate vicinity of the tip. This uncertainty will, of course,

be reduced for point electrodes that are less sharp. This is evident in the

work of Sangkasaad [40], in which the good agreement between experimental

and theoretical corona inception values can be attributed, at least in part

to the rather large point electrode radius of 5.0 mm as compared to a radius

of 0.045 mm used for the calculations giving the curves in figure 32 and,

also, for obtaining that data in figures 28-31.

For highly nonuniform fields such as used in the measurements reported here,

there are likely to be additional large uncertai nties in calculated avalanche

size due to possible large uncertainties in the values of a-j at high E/N.

This is demonstrated in figure 33 where the data of Mailer and Naidu [38]

(also see Sec. II. D) used in the present calculations are compared with data

of Sangi [41] which have appeared in a thesis and conference proceedings which

are not widely available. Also shown are data from Bhalla and Craggs [42]

and Bortnik and Panov [43] for low E/N, and calculated ionization coefficients

obtained from Cooke [44]. There is obviously considerable disagreement among

the results for E/N > 500 V/cm torr, which is significant for highly nonuniform

fields where E/N of this magnitude, or greater, can be expected. Moreover,

for highly nonuniform fields at high E/N the electrons may fail to reach

local thermodynamic equilibrium over a portion of the avalanche formation

region. Therefore, use of ionization coefficients which are derived assuming

equilibrium may not be justified in all cases. As already noted in Sec. II. B,

this is a question that deserves careful consideration (also see appendix I).

In figure 34, we compare corona inceptions calculated assuming the streamer

criterion (see fig. 32) with our experimental results. The calculated

inceptions reflect the uncertainty associated with our inability to precisely

determine the electric field near the tip of the point electrode, where

rather than a single line we show a band of inception values. The measured

values were obtained from data such as shown in figures 28 and 29 and have

in fact been reported previously [10,11,15]. Results for both ac and dc

measurements are shown, and for the dc case measurements were made both with

and without uv-irradiation of the gap. For these measurements, the gap

spacing was 1.24 cm and the radius of curvature of the point electrode was 0.045 mm corresponding to the conditions indicated for figures 28 and 29.

The calculated corona inceptions appear to agree best with the results

obtained for negative corona in an irradiated gap. As will be made evident

later, this is consistent with the behavior expected on the basis of the

proposed initiation mechanisms.

We now examine the relationship between the assumed streamer criterion and

the properties of the discharge that have been observed near onset. There

remains some question about the physical basis for this criterion as it

relates to the nature of the measured phenomenon. In figure 35 are shown curves for corona inception corresponding to a critical avalanche size of

1 x 10 8 electrons for which the parameter e was adjusted, within reason,

to give a best fit to another set of data [10,11,15] for negative inceptions.

Also shown are curves for a critical avalanche of 3.3 x 10 6 electrons

from calculations performed for identical conditions. The former would

correspond to pulses of roughly 10 pC whereas the latter correspond to

55
Figure 33. Collected ionization and attachment coefficients for SFg.

56
100 200 300 400 500 600

GAS PRESSURE (kPa)

Figure 34. Measured'and calculated ac and dc, positive and negative pointplane corona inceptions in SFg as a function of gas pressure.

The gap spacing was 1.24 cm and the radius of curvature of the

point electrode was 0.045 mm.

57
GAS PRESSURE (kPa)

Figure 35. Measured and calculated ac and dc, positive and negative point

plane corona inceptions in SFg as a function of gas pressure.

The gap spacing was 2.28 cm and the radius of curvature of the

point electrode was 0.045 mm.

58
0.53 pC, which is somewhat closer to the mean value of corona pulse sizes that

we have observed for both positive and negative coronas in SFg near onset [8].

It is evident that the curve for 3.3 x 10 8 electrons lies close enough to

that for 1 x 10 8 electrons and that the differences between the two are within the expected uncertainties due to our lack of knowledge about the

fields associated with a sharp point. This is expected on the basis of the curves shown in figure 32, which indicate that near onset the size of an avalanche can typically change by several orders of magnitude within a 2-kV variation of the applied voltage. Our onset results would, therefore,

appear to be consistent with a fairly broad range of possible critical

avalanche sizes. Our pulse height distribution results, however, suggest'

a value less than 1 x 10 8

. It should further be noted that the appropriate

choice for the critical avalanche size under a given set of conditions has

been brought into question in previous discussions [45,46], and it may very

well be that this number depends significantly on the gas pressure, electrode

surface conditions, and degree of field nonunif ormity in the gap.

If one insists, in the theoretical definition of corona onset, that the

discharge should be self-sustai ni nq , then there are further complications

that arise in addition to the question of critical avalanche size. First

it should be realized that, in general, the occurrence of electron avalanches

that satisfy the streamer criterion does not automatically guarantee that

the discharge will be self-sustaining. By this it is meant that it persists

in the absence of an external ionizing agent due to the fact that processes

which occur in a given discharge pulse, e.g., ionization, excitation, or radiative emissions, supply mechanisms for the initiation of subsequent

pulses. There may, of course, exist conditions under which the discharge,

although present without irradiation, is significantly affected by the

introduction of radiation. At low pulse repetition rates, i.e., where the

time between pulses is long compared to the time required for ions and

excited species to clear the gap, it is doubtful that processes occurring

in one pulse could have significant influence on the initiation of subsequent

pulses. Therefore, although pulses of low ( <1 0/s ) repetition rate can occur without irradiation, as seen here under some conditions for positive

corona in SFg, it is unlikely that these could be considered completely

self-sustaining. Thus, as observed (see figs. 28 and 29), one can expect

radiation to have a big effect under conditions where low pulse count

rates occur without radiation.

The extent to which a discharge is self-sustai ned will depend on electrode

surface properties [32] and the degree of field nonuniformity. This is

particularly true for negative corona in SFg, evidence of which is supplied

by the results presented here and in our earlier work [8]. For positive

corona, the condition for a self-sustaining discharge will also be determined

by the availability of negative ions in the gap as will be discussed in the

next section. The experimental results given here (see figs. 28 and 29),

together with data such as given in Sec. 1 1. A, indicate that dc-positive

corona in SFg is not completely self-sustaining, i.e., independent of external

radiation, until large streamer burst-type pulses appear. The voltages at

which this happens are usually considerably above the theoretical onsets based

on the streamer criterion. As evident from the data in figures 34 and 35, even the first appearances of avalanches for positive dc corona with amplitudes

considerably below that required by the streamer criterion occur at voltages

above the theoretical onsets.

59
It thus appears from the discussion above that, at least for SFg, the

connection between measured corona inception voltages and conditions required

for streamer formation, or for the discharge to become self-sustaining, is

not always obvious. The behavior of the discharge near inception needs to

be carefully considered and, as our results show, this behavior depends

significantly on voltage and gap conditions. The reasons for these differences

can be understood in part from a consideration of the predominant discharge

initiation mechanisms for different gap conditions, as well as from a consideration of how electron avalanches grow and eventually develop into

self-propagating streamers as discussed in Sec. II. B.

II.C.4 Discharge Initiation Mechanisms

The results presented here suggest that there are certain preferred mechanisms

responsible for the initiation of corona discharges in SFg. We propose

that, in the absence of radiation, negative discharges are initiated mainly

by field emission of electrons from the cathode tip, the efficiency of

which is very much dependent on the condition of the surface, e.g., whether

or not it has been "conditioned" by prior discharges (see Sec. II. A). If

the cathode is exposed to radiation, the electron emission may be further

increased by the photoelectric effect, or more properly, field-enhanced

photoelectron emission. The presence of photons may be, in fact, essential

to discharge initiation in cases, for example, where the tip is not sharp

enough or the work function of the surface material is too high to permit

spontaneous electron emission when the field is applied. The conditioning,

as already noted, increases the spontaneous electron emission from the

surface, e.g., by chemical changes that lower the work function or by

introduction of microscopic surface i rregul ari ties that locally enhance

the electric field [8,47].

For a positive polarity applied to the point electrode, we propose that,

in the absence of radiation, colli si onal detachment of negative ions in

the gas is the most likely corona initiation mechanism. However, as will

be discussed, the probability for the occurrence of this process may be

strongly dependent on the maximum electric field strength in the gap, and

thus also on the degree of field nonuniformity. The probability will also

depend on the density of negative ions in the gap, and in the dc case, the

source of those ions for pre-corona conditions remains somewhat questionable.

They could result, for example, from attachment of electrons released by

ionization due to background cosmic radiation or by emission sites on the

cathode surface due to microscopic i rregul ari ties , impact of metastable

species, etc. No attempt was made in the present work to measure the negative

ion density in the gap. When radiation is present, photodetachment of

negative ions may become the dominant initiation mechanism for positive

corona near onset. We will now argue that these proposed mechanisms are consistent with the effects observed.

II. C. 5 DC Polarity Effect

As seen from the data presented in figures 34 and 35, the measured dc positive

corona inceptions are always higher in absolute value than the negative

inceptions. Moreover, this effect is greatest for unirradiated gaps at

the highest gas pressure used. This polarity difference in inceptions is

reduced under 60- Ffe ac conditions. For dc it can also be reduced at a

60
given pressure by: (1) decreasing the gap spacing, (2) decreasing the degree

of field nonuni formity in the gap, e.g., through the use of blunter point

electrodes (compare data in figures 28 and 29 with data in figures 30 and 31), or (3) irradiating the gap with photons of sufficient energy to photodetach

negative ions. The polarity effect observed here is consistent with that

reported by Ibrahim and Farish [7,48], who suggested that it is most likely

due to the long statistical time lags associated with the initiation of

positive corona in SFg.

In considering the reasons for this polarity difference, perhaps it should

be noted first that if the electron avalanches always achieved the maximumaverage size, then according to the streamer criteria the difference between

positive and negative corona inceptions should be small in the first approximation.

This is because the path length £ which an electron avalanche must travel

in order to attain a critical size as calculated by eq (27) is the same for

both positive and negative polarities, i.e., it is independent of the field

direction. This, of course, assumes that space charge and diffusion effects

on avalanche growth can be neglected (see Sec. II. B) and that initiatory

electrons for positive corona originate at the point in the gas where a-j = n a. Although it can be assumed that the initial electron production for negative corona always occurs with greatest probability at the point of highest

electric field, i.e., at the tip of the point electrode surface, it cannot

be assumed for positive corona that the point at which a-j = n a is

necessarily the point of most probable electron release. Thus, from this

consideration alone, there is reason to expect a polarity difference.

In order to attempt to understand this polarity effect, it is necessary to

examine the factors that determine the probabilities of discharge initiation

for each polarity. Since in the experiments reported here corona onset was defined in terms of discharge pulse repetition rate, it is appropriate to

consider the probability per unit time, p-^ for formation of a detectable

electron avalanche. According to Goldman [32], we can write this as a product,

where p^ is the probability per unit time at position r that an electron

source, e.g., a negative ion or a surface element with sufficiently low work

function will find itself in a region $-j where the necessary conditions

are satisfied for avalanche formation; P 2 is the probability of release of

an avalanche-initiating electron from the source at r; and p^ is the

probability that if the electron is released, it will then yield an avalanche

of the necessary critical size to be detected or satisfy the streamer criterion.

The size of the region ${ where the field is high enough for initiation

to occur can be expected to increase with increasing applied voltage. For

negative corona, the active region is associated with a surface area around

the tip of the point electrode, and for positive corona it corresponds to

a volume in the gas referred to here as the initiation volume .

The probability factor pi is obviously proportional to the number of electron

sources which appear per unit time at location r*. For positive

discharges, it will be assumed that this is mainly given by the rate at

(32)

61
which negative ions become available for detachment at any location in $-j,

and for negative discharges it is the number of electron emission sites

available per unit time within $-j on the cathode surface. It will be

assumed, as was the case for the experiments described here, that if

external radiation is introduced, it has insufficient energy to ionize

molecules in their ground state. Although ionization from metastable

excited species may be possible, we exclude this mechanism on the basis of

lack of information about the possible existence of long-lived excited

electronic states of SFg which are less than 4.2 eV below the ionization

limit [49]. For negative polarity, the number of emission sites will be

quite large so that we can take p-| ~ 1. However, for positive polarities,

this may not be true because the number of negative ions in the gap at any

time might be quite small unless their presence is enhanced by, for example,

irradiation of the cathode which causes release of photoelectrons that can then attach to gas molecules.

The second factor p 2 , in eq (32), is determined by the basic mechanisms

of electron release, such as, for example, the probability that a negative

ion will detach its electron in an encounter with a neutral molecule at

position r*. For negative discharges this can presumably be made

arbitrarily large, i.e., P 2 ~ 1 , by insuring field or photoelectric emission

through proper surface preparation together with sufficient field strength,

or via irradiation. It is not clear, however, that the assumption P 2 ~ 1 can be justified for positive discharges under conditions similar to those

which apply for the present measurements. This will be discussed further

in the next section.

The probability P 3 is determined by the statistical nature of the processes

by which electron avalanches are formed in a gas. Given the release of an electron under a given set of initial conditions, one can calculate the

probability that the avalanche will attain some critical size as was discussed

in Sec. II. B. Our previous considerations have indicated that if we can neglect space charge effects and assume a-j and n a are meaningfully

defined everywhere in the gap, then the mean size of the avalanches should

be nearly independent of the field direction. That is, if the field varies

in the same way over a path length l for avalanche formation, then n e , as predicted by eq (27), will be the same for both polarities. Thus, if all

initial electrons originated from comparable points for positive and

negative discharges, then P 3 should be nearly the same for both polarities.

This, however, is never the case. While avalanche initiating electrons

for negative polarities are emitted predominantly from the tip of the

point electrode, correspondi ng to the region of highest field, the electrons

for positive polarity are liberated over a broader range of fields in the

relatively lower field region of the gas. Also, the results presented in

Sec. II. B. show that, in general , P 3 depends on the value of E/N at the point

of initial electron release (also see [9]). Therefore, the positive avalanches

can be expected to have a broader distribution in size than the negative

avalanches. This implies that for the same maximum field in the gap the

positive discharge initiating electrons will have a lower average probability

for yielding avalanches of the necessary critical size as compared to the

negative case, i.e., P 3 will generally be smaller for positive polarities.

Because p] and P 2 can be made to approach unity in the negative case, the

rate of avalanche initiation should be quite high as soon as the proper

62
field conditions are met. One therefore expects a rapid development of

this kind of discharge with applied voltage as observed. For the positive

case on the other hand, p-j and p 2 may be considerably smaller than unity,

and one expects a slower development of the discharge with increasing

voltage. Even if one could assure an abundant supply of negative ions

that readily detach their electrons so that p] and p 2 approach unity,

the initiation of positive discharges is still limited by the size of the

initiation volume .

To demonstrate this, we have computed the size of $-,• as a function of

applied voltage. These volumes were defined to be regions in which the

condition

is satisfied, i.e., regions where the release of an electron could give rise

to an avalanche containing at least 1 x 10 8 electrons. The computer program

used for this calculation is listed in the appendix IV. In figure 36, we

show the calculated boundaries of the initiation volumes for the different

indicated voltages. These were calculated for gap conditions used to obtain

the data in figure 34 and for a gas pressure P = 100 kPa. The outer part

of these boundaries is determined by the requirement given in eq (25). The

boundaries closest to the electrode are determined by the minimum length l

needed to give an avalanche of the critical size. Note that at the theoretical

threshold correspondi ng to the lowest voltage at which the field conditions

are first satisfied for the formation of an avalanche of the required size,

the initiation volume is infinitesimally small, i.e., it corresponds to a single point. Therefore, <f>-j = 0 at the lowest voltage for critical avalanche

formation.

On the basis of these considerations, one is led to predict that conditions

which increase either , p] or P 2 for positive polarity will tend to

reduce the polarity difference in corona inceptions. The factor p-j can be

increased by increasing the number of available negative ions. The reduction

in the polarity difference in going from dc to 60-Hz ac conditions can be

accounted for by the effect which corona on the negative half-cycle has in

increasing the density of negative ions in the gap [10,11]. An increase

in the rate of growth of <S>-j with voltage can be achieved by using more uniform fields, i.e., by increasing the size of the point electrode. For more uniform fields the initiation volume grows more rapidly with voltage.

This is illustrated by the calculated results given in figure 37, where

the curve for n0

= 11.57° corresponds to the larger point. The size

of the volume has been plotted versus the fractional increase in the applied

voltage above inception, where V-j is the inception voltage. This trend

was verified here experimentally as can be seen by comparing the data in

figures 28 and 29 with the data in figures 30 and 31.

The factor P 2 can be increased by using radiation to photodetach negative

ions in the initiation volume, and possibly by increasing the degree of

field inhomogeneity as will be considered in the next section. The data

in figures 34 and 35 clearly indicate a reduction in the polarity difference

when uv-radiation is introduced.

I (33)

63
cm

Figure 36. Calculated boundaries of the initiation volumes for SFg positive

corona inception at the indicated applied voltages and for a gas

pressure of 100 kPa.

64
(V/Vi)

Figure 37. Calculated growth in the electron initiation volume for two point

electrodes characterized by the angles n 0

~ 11.575° and n 0

= 2.315°

plotted as a function of the ratio of applied voltage V to

theoretical corona inception voltage V-j

.

65
The reason why the polarity difference is increased in going to longer

gaps is not clear. If, for example, the ultimate source of negative ions

in the positive point case is from release of electrons from the cathode

region, then perhaps the effect is related to a reduction o^ ion densities

due to longer drift lengths which allow ions to diffuse more so that fewer

enter the initiation volume. The reason why the polarity difference is

greatest at higher pressures also remains obscure. This effect may be

related to changes in the predominant negative ions with increasing pressure,

e.g., an increase in the relative abundances of ion clusters that move

more slowly and detach less readily.

II.C.6 Geometrical Effects

In addition to the influence of electrode geometry on the magnitude of the

polarity effect described in the previous section, there are other effects

that need to be examined. The increase in corona inception voltages with

increasing gap spacing and point electrode diameter can be understood

simply from a consideration of the dependence of the electric field on gap

geometry and applied voltage. These effects are readily predicted using

the streamer criterion and need not be discussed further.

It is not immediately apparent, however, why it becomes necessary to use uv-radiation to initiate and sustain corona once the degree of field

inhomogeneity becomes too low, i.e., for larger point diameters. We

hypothesize that in the case of negative polarities the electric field at

the surface of blunter points never attains sufficient strength near onset

to permit field emission, i.e., po ~ 0 in eq (32). Photons must then be

used to insure electron production via the photoelectric effect. For

positive polarities, one can argue that if the point is not sharp enough,

then the field never reaches a value high enough to permit col 1 i sional

detachment of negative ions to occur with sufficient probability.

For uniform field gaps, Frommhold [35] has pointed out the importance of

collisional electron detachment in affecting the growth of electron avalanches

once the field is high enough that the mean life-time of a negative ion is

short compared to the time it spends traversing the gap. The probability

that discharge initiation will occur in a given time has been formulated

in terms of the life-times of negative ions by Berger and Hahn [50] and

discussed by Goldman [32,45]. It is more appropriate in the present discussion

to seek an expression for the rate of initiating electron production (dn e /dt) 0

in the initiation volume.

Given that we know: (1) the flux of negative ions incident on the initiation

volume 4>.j , i.e., the current density J 0 (a), (2) the detachment

coefficient 5^ (number of detachments per unit length) as a function

of E/N, and (3) the variation of electric field E in $-j, we ask, what

is the rate of initiating electron production, (dne /dt) 0 via collisional

detachment?

The negative ion current density at any point is related to the negative

ion density p_ and velocity v by

J = e p_v. (34)

66
where e is the electron charge. Inside the continuity equation holds,

namely

,

3p_/3t + V.p_v * -Q, (35)

where -Q is a "sink" term giving the rate of destruction of negative ions

inside the volume due to detachment. The above expression, of course,

applies specifically to a pre-avalanche condition, i.e., an initiation

volume in which electron multiplication has not yet begun. Once an initiation electron is released, it will either immediately attach again

or lead to avalanche formation, thereby altering the condition implied by

eq (35).

Assuming a steady-state condition in which the field E is constant in time, we have

(3p./3t) = 0.

It then follows from eqs ( 34 ) - ( 36 ) that

(36)

(1/e) (a) - j\(a)].da = -(1/e) (dn

e/dt) 0

. (37)

where S

Q

is the surface area enclosing and J^a) is the exiting

negative ion current density at surface area element da. The integral over

volume on the right-hand side of eq (37) is the rate of loss of negative

ions due to collisions and must therefore equal the rate of electron production,

(dne /dt) 0

. Consistent with eq (36), we can also write

dn_ dn _ o dt ^o ^dt

(38)

where the first term on the right gives the rate at which ions enter $j

and the second term the rate at which they leave.

It will now be assumed that if dn_(a) ions enter $-j at area element da,

they will all travel a distance £(a) before exiting if not destroyed.

Allowing for destruction via collisional detachment, then the number of

these ions that survive to leave the volume is given by

dnl(a) = dn_(a) exp[- )d*'].

o

(39)

67
It is preferable here to formulate the negative ion destruction in terms

of 5

(j(£) rather than the collisional detachment cross section 0^ because the incident ions do not, in general, have a well-defined velocity

and there may, in fact, be more than one type of ion involved. The

relationship between 5^ and the cross sections a^, -j for detachment of

the ions is given by

« d

= N l di

/ vad j(v)f

i (v)dv, (40)

i vi J

0

where g-j is the fraction of the total number of ions that correspond to the

ith species. In this expression f--(v) and v^ are respectively the velocity

distribution and mean velocity of the ith ion species. The background neutral

gas number density N has been assumed to be uniform throughout $•;. Although

the cross sections i appear to have fairly well-defined thresholds [51],

the extent to which one can meaningfully define correspond!' ng thresholds for

6^ depends on the width of the velocity distribution function. Only if one makes the simplifying assumption that all ions of a given species have

the same velocity can one unambiguously refer to a threshold for 6^. In

that case, f-j(v) = 5(v -j - v) , and eq (40) reduces to

s d = N I 9i °d,i (n )• < 41 )

Precluding this assumption, the terms "detachment threshold" as applied to

6^ will be taken here to mean the value of E/N at which v-j = vj j , where

v^j is the threshold value for a^-j.

Now it should be noted that eq (40) applies only to a particular point

inside , since f^(v) and Vj will vary with location as determined by

the field. Thus 5^ in eq (39) is expressed as a function of position V

.

From eqs (38), (39), and j(a).da = dn_(a)/dt, we can write

j £ (a).da

0

da.j'0(a) exp[-

4(a)

( l') dJT].

0

(42)

This, when combined with eq (37), leads to

(^e) = d/e)

dt 0

da.j'0 (a)(l

4(a)

0

(43)

68
where S 0 represents the surface of the initiation volume and £(a) is the

maximum path length along a field line that an ion could travel through the

initiation volume if it enters at a particular surface area element da.

The above equation is approximate in the sense that we have neglected ion

diffusion. From eq (43) it is clear that the rate of initiating electron

production increases as the integral over 6^

(

1 ) increases. The

dependence of the detachment coefficient on position l' is derived from

its dependence on E/N.

In the category of collisional detachment, we include not only reactions

of the form

SFg

- + SF6 SFg + SFg + e, (44)

but also detachment involving dissociation, such as

( SF6~ ) ( SF6^ n + SF6 * (" + 2)SF e + e, (45)

as well as associative detachment processes. Not included are reactions in

which the electron is merely transferred to another species, or in which

the character of the ion changes, e.g.

,

SF6

' + SF6 * SF5' + F + SF6- (46)

It is quite possible that a negative ion will change its character in

traversing the initiation volume, but that effect can, in principle, be

included in 6 d

. It is likely, especially at higher pressures, that more

than one negative ion species is involved.

The dependence of the collisional detachment coefficient on E/N is important

in determining the likelihood of this process occurring. Measurements

have been made of 5^ for collisional detachment of negative ions such as SFg", SFg", and F" in SFg [52,53]. These show that once E/N reaches a value,

usually referred to as the detachment threshold (E/N)<j, 6^ increases

abruptly with E/N. Actually, the term threshol

d

is only properly ascribed

to the dependence of the collisional detachment cross section on ion energy

or velocity and, as previously noted, the extent to which one can meaningfully

define a corresponding threshold for 6^ depends on the width of the ion

velocity distribution function. For negative ions in SFg, (E/N) ^ appears

to lie slightly below the critical value (E/N) c where a-j = n a

. Below

(E/N) d it is reported that 5^ is too small to be measured. The results of

O'Neill and Craggs [53] further indicate that the assumption 6

cj/M << n a /N

cannot be assured once E/N > 1.4 (E/N) c , and, therefore, for high enough E/N,

collisional detachment cannot be neglected in the calculation of electric

discharge current growth.

Recent measurements [51] of the total collisional detachment cross sections

of negative halogen ions by various molecular gases also show abrupt increases

69
in the detachment probability once the incident ion energy exceeds a threshold

energy which is usually about twice the electron affinity. Several reported

measurements [35, 54-56] of 0" and 0o~ detachment in 0£ show similar behavior,

i.e., abrupt increases in the detachment rate, or cross section above a certain threshold.

Thus, the limited data on collisional detachment suggest that unless E/N is

high enough, the negative ions never acquire enough kinetic energy between

collisions to permit detachment to occur. If this is the case, then po ~ 0 in

eq (32), and the probability for avalanche initiation is negligibly small. As one goes to more divergent fields, i.e., sharper point electrodes, then the

maximum value of E/N within the initiation volume $>j will increase giving

rise to a higher probability for collisional detachment. This can explain

why spontaneous positive corona initiation was observed here in unirradiated

gaps only for the sharper points.

It should finally be noted that for strong electric fields, the binding energy

of the attached electron of a negative ion in the field may be reduced sufficiently

to further enhance the collisional detachment process. In fact, Schweinler and

Chri stophorou [57] have shown that if the field is strong enough (~ 1 MV/cm),

field-induced detachment becomes possible. However, for negative ions with

electron affinities greater than 1.0 eV, it is necessary to have fields in excess of 10 MV/cm in order for field induced detachment to occur with significant

probability. For the measurements reported here, fields of this magnitude were

not attained within the initiation volume $-j. Thus, in agreement with the

suggestion of Schweinler and Chri stophorou , we must argue that field induced

detachment is unlikely to be an important discharge initiation mechanism.

II. D. Electron Swarm Data for Electronegative Gases

II.D.l Motivation

The necessity of having reliable swarm data in the modeling of electric

discharge phenomena was made clear from the discussions given in the previous

three sections. The present survey is intended to provide information

about the status of existing swarm data for gases which have application

in electrical insulation technology. In this survey, data have been compiled

from many different sources and presented with critical commentary. Major

discrepancies and gaps in the data have been pointed out.

Most of the work was performed at the Atomic Collisions Data Center of the

Joint Institute for Laboratory Astrophysics in a collaborative effort

involving Prof. J. Dutton of the University College of Swansea and scientists

at both NBS and the University of Colorado. The results of this survey

have recently been submitted for publication [58]. In the present report we give only a description of the types of data included, and an example

of the data compiled for SFg which tie in closely with the work described

in the previous sections. Reference [58] will contain information on many

other electronegative gases.

II.D.2 Definitions and Method of Data Handling ( An electron swarm is a low density cloud of electrons of density n in a gas

of much higher number density, N. The properties of the system are dependent

70
on the interactions of the electron swarm with the gas molecules (or atoms)

and ions rather than with each other or with the container walls, typically

in the presence of an electric field. The electric field increases the mean

energy of the electron swarm so it can be substantially higher than that of

the neutral gas, and electron collisions with the heavier gas molecules give

them a large random component of motion. The electron motion is described

by an energy distribution function which is dependent on the energy gain per mean free path from the electric field (see Sec. II. D. 4). For an electric

field of strength E, the latter quantity is proportional to E/N, the "reduced

field strength." For the data considered here, the gas temperature T is

relatively low and has little influence on the distribution function. The

properties of swarms studied are those relating to spatial transport, the

rates of creation and destruction of electrons, and the rates of energy

transfer to the neutral gas. The parameters included in the data review are discussed briefly below.

In an electric field the velocity of the center of mass of the electron

swarm drifts in the direction opposite to the field with a velocity known

as the drift velocity , W. The electron mobility, y, is defined as the

ratio of the drift velocity to the electric field strength and, for present

purposes, mobility is considered to be an alternate way of specifying the

drift velocity.

Diffusion is the tendency of the swarm to spread as a result of its random

motion in such a way as to make the density uniform and is characterized

by a diffusion coefficient, D. When an electric field is present, the

.diffusion is not, in general, the same in all directions. Two parameters,

the transverse diffusion coefficient, Dj, (perpendicular to the field) and

the longitudinal diffusion coefficient, D|_, (parallel to the field) then

characterize the diffuse motion. The ratio of diffusion coefficient to

mobility , D/y, has a rather special role, and data on this ratio are determined independently of the other quantities with Dy/y treated

separately. In the limit of small electric fields, this ratio tends toward

the mean energy of the electrons and, as such, it is a measure of the electron

temperature. At higher fields, the electron swarm is not in thermal equilibrium

and no temperature is defined, but D/y is a convenient measure of the energy

content of the swarm. In this context Dy/y is defined as the "character!

- Stic

energy." This terminology does not refer to DL/y.

The change in the number of the electrons in a swarm may come about as a result

of el ectron attachment (coefficient n a ) to neutral particles, electron

detachment (coefficient 6^) from negative ions in collision with other gas

molecules, and i onization (coefficient a-j) of neutrals. For some range of

values of E/N the electron density will be simultaneously influenced by all

three processes, but the spatial current growth in a Townsend discharge

(see Sec. II. D. 3.1) may be exponential over a large range of distance. It

is convenient in these circumstances to define the parameter A, the electron

growth constant, as the multiplying constant in the exponential. In the case where only ionization and attachment occur, A = a-j - n a , and is the average

net gain of free electrons per unit distance of drift. Inelastic collisions

other than those giving rise to ionization are quantified by excitation

coefficients (e). Another process which can cause a change in the number

of electrons is recombination, but because of the low electron and positive ion

densities in the swarms considered here, it is not included in the present review.

71
The swarm coefficients referred to in the previous paragraph are defined

as the average number of events occurring when one electron drifts a unit

distance in the direction of the electric field. In general, they are related to the correspond! ng two-body rate coefficients by Nko = SW, where

S is a coefficient (per unit drift distance) and l<2 the correspondi ng rate

coefficient (also see Sec. II. B). In the case of three-body processes, the

relationship is M

2

k 3 = SW, where is the three-body rate coefficient.

As the values of the parameters characterizing the swarm behavior are determined by E/N and N, it is convenient to represent them as W, D/y,

DM, S/N as a function of E/N. Thus, most of the data of this survey are presented in graphs and tables of this form. The specific parameters and

correspondi ng multiples of SI units in which they are expressed are summarized

in table I.

When the original data were published in tablul ar form, the figures and

tables were prepared directly from the original tables, and the number of

significant figures of the tabular data retained. However, in most cases,

the data were published in the form of graphs, and the graphs were enlarged

and the coordinates of the data points obtained using standard digitization

procedures. These procedures are estimated to introduce an error of no more than ±3?3 . As a recording convenience, most of the data retrieved by this

method were entered in the tables with three significant figures. In cases where experimental sources introduce higher errors, fewer significant figures

were retained.

Data are frequently published, in units other than the SI units given in table I. In these cases conversions to the SI units were made using the relationships

1 i sted i n tabl e II.

II. D. 3 Experimental Techniques

Most of the experimental data reported were obtained using variations on a small number of general methods which are briefly described below. Although

these methods are conceptually strai ghtf orward , the analysis of the measured

data to obtain accurate transport and swarm coefficients is complex.

Simplifying assumptions concerning the effects of boundaries, diffusion,

secondary ionization and, especially in the case of electronegative gases,

ion molecule reactions and detachment have frequently been made in the

analysis of data obtained by these methods. Huxley and Crompton [59] give

a comprehensive discussion of the impact of approximate' ons based on these

assumptions and the variations on experimental methods and related analyses

which have been devised to avoid them.

II. D. 3.1 Spatial Current Growth

In this technique [60], also referred to as a steady-state Townsend

discharge, a swarm of electrons is photoel ectrical ly released from the

cathode of a drift tube, and the anode current, I, is measured as a function of gas pressure, electric field strength, and electrode

separation, d. As discussed by Dutton [12], under especially simple

conditions of ionization, i.e., absence of secondary ionization,

attachment, and detachment and low E/N, the current can be expressed as

72
Table I. Swarm parameters. Symbolic notation, scale factors, and units.

Symbol

Scale Factors

Name Units

N Gas number density lO 22 m~3

P Gas pressure Pa

T Gas temperature K

W Electron drift velocity 10 2 ms'l

E/N Reduced field strength 10-21 v m

2

dtn Transverse diffusion coefficient * N 10 24 m"^ s1

d

l n Longitudinal diffusion coefficient * N 10 24 m" 1 s“*

d t/u Ratio of transverse diffusion

coefficient to mobility

V

D L /u Ratio of longitudinal diffusion

coefficient to mobility

V

n

a /N Attachment coeff icient/N 10- 22 m

2

a-j/N Ionization coeff icient/N 10 -22

m

2

«d /N Detachment coeff icient/N IQ'22 m

2

X/N Electron growth constant/N C\J E

1 CM CM o

e/N Excitation coeff icient/N 10“22 m

2

k 2 Two-body rate constant 10- 16 m

3 s1

k

3 Three-body rate constant 10'42 m

6

s"

1

73
Table II. Common units conversions for swarm data 3

.

Symbol s Conversion factor F and Conventi onal to conventional

Quanti ty SI units Units SI units

A B A = FB

Particle density N(m" 2

) N(cm" 2

) 10 6

Particle density N(m“ 2

) P (torr) 3.54 x 10 22 272 K -TTkT

Temperature T(K) T(K) i

Pressure P(Pa) P(torr) 133

Reduced Field E/N(V m

2

) E/P(V/cm torr) 2.83 x 10“ 21 J(K)

TTTK

Reduced Field E/N(V m

2

) E/N(Td) 10“ 21

Drift velocity W(m s" 1

) W(cm s" 1 ) 10- 2

Diff usi on coefficient

r—

1

1

.

CO

Ii 1 E

CM CM Q O

2 Dpccm torn

s 3.54 x 10 18 272 K iw

Diffusion/mobil ity D/u(V) D/ii(V) 1

Swarm coefficients S/N(m2

) S/P(cm torr) - ^ 28.3 x 10“ 21 T ( K ) 273 K

Pressure is incorporated into many of the units conventionally used. The related

conversions to SI units used in this paper are not a simple numerical factor, but

require incorporation of the ratio T(K)/273 K in the conversion factor F, where

T(K) is the temperature at which the measurements were made.
I “ exp(a-jd) (47)

and the ionization coefficient can be determined from measurements of the

current as a function of d. Similarly, for systems in which only attachment

occurs, i.e., no detachment or ionization and low E/N,

I « exp(-na d) , (48)

and the attachment coefficient can be determined. Of course, these special

conditions are rarely satisfied, especially for high E/N, and extensive

analysis i ncorporati ng ionization, attachment, detachment and ion-molecule

reactions is required to accurately determine swarm coefficients from these

measurements (see [12] eq (16)). Although in some cases experimental conditions

can be selected so that some parameters are negligible, measurements in

electronegative gases for a reasonable range of E/N require fitting measured

current growth curves with analytical expressions containing several swarm coefficients (e.g., a-j

, n a , 5^). The values of these coefficients

which fit the experimental data are often subject to large uncertainties.

Recently, advances in computer techniques have enabled analyses with more

sophisticated fitting procedures.

II.D.3.2 Transverse Diffusion Coefficient

In a modification of the steady-state Townsend discharge used to measure

Dj/y, the cathode emission is confined to a point source and the anode is

divided into concentric rings. Townsend's original analysis was refined by

Huxley and Bennett [61] and subsequent work, as described in [59] chapter 11.

The ionization coefficient can also be obtained from analysis of these data.

II.D.3.3 Temporal Current Growth

A pulsed Townsend discharge [62,63], which has been used since high-speed

electronics have become available, involves the production of a pulse of

photoelectrons and the observation of the time dependence of the transient

current. Because the electrons have much higher drift velocities than

ions, the related components of the current are distinguishable. Concerns

involving interpretation and analysis of results to give swarm coefficients

are similar to those for steady-state Townsend measurements.

If the energy of the electron swarm exceeds the ionization energy of the

gas molecules, an electron avalanche is initiated. Measurement of the

electron density as a function of time, either electronically or by

observation of the light emitted from the discharge, provides values of

the ionization coefficient and electron drift velocity [39].

II.D.3.4 Sampling Techniques

These techniques, also referred to as time-of-f 1

i ght and Bradbury-Niel son techniques, use a drift tube in which two or more electrical shutters are placed in the path of the drifting electrons, the first to function as a gate to admit electrons into the drift space at a known time and the second

75
to sample the density of electrons traveling the distance between the shutters

as a function of time. From these measurements , electron drift velocities

and, with more extensive analysis, longitudinal diffusion coefficients are obtained. Many variations on the construction and operation of the shutters

and on the analysis of the resulting data are included in the comprehensive

discussion of drift velocity measurements in chapter 11 of [59].

II.D.3.5 Errors

When available, the original authors' uncertainty specifications are quoted

with the data. However, because different researchers use different standards

for their uncertainty statements, the data with the smallest specified

uncertainty is not necessarily the most reliable.

There are several specific sources of error common in swarm measurements.

One is gas impurities which may have a significant influence on the quantities

observed as evidenced by measurements in intentional mixtures. A second is

the effect of surfaces in both distortion of the electric fields and the

spatial distribution of electrons and as a source of secondary electrons.

A third is the measurement of partial pressures in mixtures.

There are also error sources related to the i nterpretat ion of measured

quantities to obtain swarm coefficients, especially in electronegative

gases where the electron number density varies due to attachment and, at

higher E/N, ionization. Various aspects of the complete reaction scheme

such as detachment from negative ions and charge transfer, as well as more complex (and perhaps unidentified) reactions such as formation and attachment

to clusters, may be unidentified by the investigator or ignored in the

interest of reducing the analysis to manageable proportions. The use of mass spectrometri c techniques is essential to identification of a complete

reaction scheme, as well as to monitor impurity concentrations.

Additional sources of error in the analysis of experimental data include

the assumption of idealized geometry, the neglect of diffusion effects

(see e.g., chapter 5 of [59]) and inelastic collisions. As discussed in

Sec. II. D. 3.1, the reported transport and swarm coefficients are often

derived from curve-fitting procedures in which the parameters describing

the reaction scheme are incorporated into an analytic expression which

describes the observations. Often a range of parameters gives a satisfactory

fit, resulting in a large uncertainty.

II.D.3.6 Computations Using the Boltzmann Equation

The swarm parameters discussed so far are measures of the macroscopic

properties of an electron cloud moving through a neutral gas under the

influence of an electric field. Because there is no macroscopic theory of

electron transport (drift velocity and diffusion coefficients) or electron

excitation (here excitation is defined as reactive collisions), it is necessary

to go back to the details of the microscopic el ectron-neutral scattering cross sections to calculate swarm parameters. The Boltzmann equation provides a connection between these microscopic cross sections and the measurable

macroscopic parameters.

76
The Boltzmann equation is the equation of continuity for electrons in a sixdimensional phase space and describes the time evolution of the electron energy

distribution function, r (r,v,t). Electron transport and excitation coefficients

are calculated as averages or integrals involving f (see eqs (6)-(8)). The

electron energy distribution function contains all the information about the

electron swarm, and the calculated swarm parameters are averages in the same sense that the experiments measure average quantities. The key to a model

or theoretical calculation is then the electron energy distribution function.

The Boltzmann equation may be written as [59],

il + v.v

r

f + a. V

yf = C(f) , (49)

where J is the acceleration due to the applied field and C is the collision

operator. In order of the terms above, the time evolution of f is due to a spatial flux, a flux in velocity space, and a redistribution of electron

energy due to collisions with neutral particles. Electrons may lose recoil

energy in elastic collisions with neutrals, gain recoil energy if the electron

energy is less than the neutral energy, and gain or lose discrete amounts

of energy in exciting or de-exciting the neutrals to or from the various

rotational, vibrational, or electronic levels. For cases of interest here,

space-charge fields and Coulomb collisions are negligible.

Solutions of the Boltzmann equation are complicated because f depends on the six phase-space variables and time. An additional complication is that

the collision operator C is a combination of multiplicative and integral

operators. However, in the hydrodynamic regime, i.e., the regime of interest

in typical swarm situations where the measured parameters are free of

boundary effects and any change in current is exponential in both time and

distance, several simplifying assumptions can be made which cast the Boltzmann

equation into a form amenable to numerical solution. Even in the hydrodynamic

limit, however, much effort has been devoted to techniques for solving the

Boltzmann equation and studying the various approximations that make numerical

solutions of the equation practical.

By far the most common solution is the "two-term" approximation. Here the

spatial dependence of f is assumed small and is treated in second order.

Thus, since the current growth is exponential, 3f/3t = (constant)

x (f) and f(r,v,t) = f(v). The two-term approximation is then invoked,

i.e., the angular dependence of f (the angle being that between the electron

velocity vector and the field direction) can be approximated by the first

two terms of a spherical harmonic (or because of the cylindrical symmetry,

Legendre polynomial) expansion. This approximation leads to calculated

values of electron transport and rate coefficients (see Sec. II. B) that

agree reasonably well with the more rigorous calculations in most cases.

An alternate technique for the calculation of swarm parameters is a Monte Carlo

calculation which avoids entirely the use of the Boltzmann equation. In these

numerical simulations of the swarm motion, the trajectories of individual

electrons are followed through a large number of collisions with the exact

outcome of each collision being modeled on the basis of a random number. This

77
technique offers the advantage that boundary effects may be included, and no assumptions are made about either the r or v dependence of the distribution.

This advantage is offset by the comparatively long computational times involved.

Also, for calculations of equilibrium or steady-state swarm phenomena, the

boundary effects may be safely neglected.

There are two general categories of applications for the solution of the

Boltzmann equation:

1) Iterative extraction of low-energy electron-neutral scattering

cross sections from measured swarm data, and

2) Calculations of swarm parameters from a given set of cross sections.

These two categories differ in purpose but are the same computationally.

In the first category, the cross sections may be extracted from swarm data

in a trial and error sense by comparing calculated values of swarm parameters

with measurements using an estimate for the cross sections. Cross sections

are then adjusted using the comparison as a guide until the calculated and

measured values agree. The cross sections in He, for example, thus determined

are considered to be some of the most accurate available.

The second of the applications listed above is of more interest here. The

electron energy distribution function in a gas mixture can be very different

from those of the individual mixture components under the same experimental

conditions. In general, the distribution function for a gas mixture cannot

simply be determined from considering the separate distributions for the

gas components. It is necessary to go through the Boltzmann equation using

as input the component gas cross sections. Thus swarm parameters in mixtures

may be calculated from the constituent gas cross sections.

Calculations of swarm parameters may be made quite accurately depending on the method used to solve the Boltzmann equation. For many applications,

the "two-term" approximation yields sufficient accuracy. With few exceptions,

the theoretical values of swarm parameters reported here were calculated

using that approximation.

II. D. 4 Data for Sulphur Hexafluoride

A dominant fact of electron swarms in SFg is that low energy electrons are

very rapidly attached to form negative ions, and the rapid disappearance of

free electrons greatly complicates the measurement of other swarm parameters.

At high E/N ionization helps balance the loss by attachment. Small shifts

in the energy distribtuion function can substantially change the balance

between electron gain and loss. In two papers published in 1979, Kline,

Davies, Chen, and Chantry [64] and Yoshizawa, Sakai, Tagashira, and Sakamoto

[65] reviewed the available cross section data for collisions of electrons

in SFq. In each of these papers, the electron energy distribution function

was calculated by solving the Boltzmann equation, and the swarm parameters

were computed using the distribution function and the relevant cross sections.

The paper by Kline and co-workers also reported some new, presumably more

reliable, cross section data which are rather different from those assumed

by Yoshizawa and co-workers. On the other hand, Yoshizawa and co-workers

78
used a more accurate method of solution of the Boltzmann equation. These

papers support the conclusion that the dominant phenomena of electron

swarms in SF5 are well understood, but there are considerable uncertai nties

in the magnitudes of some of the transport coefficients.

II. D. 4.1 Drift Velocity

Naidu and Prasad [23] used sampling techniques to measure the electron drift

velocity for the E/N range 340-640 x 10 -21 V

m

2

, and the results are displayed in figure 38. These data are the only measured values available

from a direct and recognized method and are counted as the most reliable.

The authors estimate the uncertainties to be 5 percent. Teich and Sangi [41]

also reported data for the same E/N range in a conference proceedings which

is not widely available. They provide no description of experimental method

and give their results in the form of a simple equation. These data are also

displayed in figure 38. Harris and Jones [ 66 ] reported data on the drift

velocity of electrons in SFg for the range E/N = 15 - 150 x 10

" 21 Vm 2

. (The same results with less explanation were also given by Dutton, Harris, and

Jones [67].) Their method involved a detailed accounting for electrons removed

by diffusion back to the cathode. 'While this method is indirect, in other gases

it yielded data in error by only 15 percent. The results of these measurements

are given as an equation which is represented in figure 38 by a line.

Kline et al. and Yoshizawa et al . both calculated drift velocities which are displayed in figure 38. The data from Yoshizawa et al . are W^, the velocities

of the center of mass of an isolated group of electrons, which is the definition

most appropriate to the measurements of Naidu and Prasad. _ Yoshizawa et al.

considered the consequences of spatial inhomogeneity in the distribution

function and found surprisingly large effects. For instance, they report

that W v , the average velocity, is lower than by about 25 percent at

E/N = 600 x 10 ‘ 21 Vm 2

. Calculations were also performed using other

definitions of the drift velocity. Kline and co-workers, who were primarily

concerned with attachment and ionization phenomena, did not consider these

higher order effects since they used the conventional two-term approximation

and included new electrons produced by ionization.

II.D.4.2 Ratio of Diff usion-to-Mobil ity and the Diffusion Coefficients

Naidu and Prasad [23] also reported values for Dy/y. These data were

derived from measurements of the ratios of currents to concentric ring

electrodes. Taken as a whole the data set displays inconsistencies which

the authors discuss. The authors note that most of the discordant data

involved use of the outermost rings, and these data are defined to be the

result of "anomalous" diffusion. Anomalous diffusion is defended as a significant physical effect and not the result of measurement error; however,

no explanation is given for the causes. The authors suggest that data

derived from the inner rings are reliable, and these data are represented

in figure 39 as a short straight line. Mailer and Naidu [ 68 ] later reported

similar measurements which are also shown in figure 39 and are quite close

to the results of Naidu and Prasad. Kline and co-workers calculated values

of D/y along with other swarm parameters, and their results are included

in figure 39. For applicable values of E/N the experimental values are the preferred data. The calculated data represent a reasonable basis for

extrapol ation to higher and lower values of E/N.

79
Figure 38. Electron drift velocity, W, for electrons in SFg

as a function of E/N.

80
Figure 39. Ratio of diffusion to mobility, Dy/u,

for electrons in SFg as a function of E/N.

81
No direct experimental data are available on the diffusion coefficient for

electrons in SFg. Yos'nizawa et al . included diffusion coefficient calculations

as part of their Boltzmann equation analysis. As with drift velocity, data

were calculated using several definitions, but in this case the different

definitions yield data which vary only slightly (for the relatively low

values of E/N investigated). Figure 40 includes the results which they

label as D[_ and Dj values appropriate to a steady-state Townsend discharge.

Also included in figure 40 are values of DN which were calculated from the

W and D/y values reported by Kline and co-workers. What appears to be

"noise" in these data arose from reading a rather small logarithmic graph.

At low E/M these results are not significantly in disagreement with those

of Yoshizawa. At high E/N the Kline data must be considered uncertain

because of the way in which the effect of new electrons produced by ionization

was handled.

II.D.4.3 Electron Gain and Loss Processes

SFg is known to have a very large cross section at low energies for attaching

electrons to make SFg". Kline and co-workers report that this cross section

is 5.5 x 10~ 10 m

2 at 0.01 eV. They conclude that at higher energies

the cross section falls rapidly, decreasing to 3 x 10“ 12 m

2 at 0.3 eV.

Chutji an [69] reported further measurements at very low energy which offer

the possibility of being more reliable. Above about 0.3 eV dissociative

attachment is the dominant attachment process. Fehsenfeld has reported in

a conference paper [70] that the zero field attachment rate constant is

2.2 x 10“ 7 cm 3 /s at temperatures in the range 290-500 k. Crompton

et al. [71] recently gave a preliminary report of a more precise experimental

method which yields a similar conclusion. In view of the weak temperature

dependence k? can be expected to be weakly dependent on E/N for small E/N.

Fehsenfeld found the reaction rate to be proportional to gas density indicating

a two-body reaction. Actually a two-step process is involved with the

initial attachment collision producing an excited negative ion. For the

gas densities normally used in electron swarm and gas discharge work,

there is a high probability that the excited state will be col 1 i si onal ly

quenched [21]. Foster and Beauchamp [72] reported that at low densities

radiative decay is also important in stabilizing excited SFg negative ions.

Several dissociative attachment processes are known to occur in SFg, producing

a variety of negative ions. Kline et al . report that for the energy range

0.3-2. 5 eV, the dominant negative ion is SFg" and above about 2.5 eV, it

is F". Other ions formed are SF^", Fp", and SFp", none of which are dominant

at any energy. The principal reason for concern with the identity of the

ions is the impact on interpreting data relating to detachment.

Most of the available data on electron reactions in SFg have come from analysis

of spatial current growth in Townsend discharges. The first electron swarm

data on SFg were reported by Hochber and Sandberg [73], who gave values of

the ionization coefficient inferred from observations of a Townsend discharge.

However, their analysis did not recognize the possibility of electron attachment.

Data on SFg including attachment were obtained by Geballe and Harrison (as

reported by Loeb [74]) and by Bhalla and Craggs [42], and these results are given in figures 41-43. In the case of the attachment coefficient, displayed

in figure 41, some of the data points of Bhalla and Craggs fall below the

82
600

500

400

300

200

100

0

+ = K L ine

D =

D t Yoshczawa

0 = D‘ YoshtZQwo

SF

6

200 400 600 800 1000 1200 1400

E/N (10'21 Vm2

)

Figure 40. Diffusion coefficients for electrons in SFg

as a function of E/N.

1600

83
Figure 41. Attachment coefficient for electrons in SFg

as a function of E/N.

84
Figure 42. Ionization coefficient for electrons in SFg

as a function of E/N.

85
Figure 43. Electron growth constant (net ionization coefficient)

for electrons in SF 5 as a function of E/N.

86
pattern of other results. These are distinguishable from the other data

because of experimental circumstances and are considered as inferior and

rejected. We include them because they illustrate a problem with the method.

While the cathode current is not a directly desired result of the measurements,

it is needed as part of the data analysis. Cathode current is normally

assumed to be constant as the electrode separation is changed, and indirect

measurements are used to infer its value. For some of their data, Shall a and

Craggs determined the cathode current as part of the data-fitting procedure

with the result that low values of n a were derived.

Kline and co-workers [64] also reported values of a-j, na , and X derived

from an analysis of a Townsend discharge. Here n

a is the "effective

attachment coefficient" which includes the effect of detachment. These data

were obtained using the methods of Davies [75], in which the possibility of

col 1 isional detachment is considered, and probably the most reliable available

in the E/N range 200 to 600 x 10 -21 Vm 2. Special consideration was given to determination of the E/N value which yielded X = 0, because for this

case it is only necessary to distinguish whether the net electron growth is

positive or negative, and a complete quantitative analysis is unnecessary.

The reported zero-growth value of E/N is 362 x 10 21 Vm 2

. These data for

na /N, cx i / N , and X/N are displayed in figures 41-43.

In 1955 McAfee [76] reported results on electron attachment in SFg which

involved examining the transient currents following a pulse of light in a Townsend discharge. These data were described as preliminary, and as later

results from the same experimental group are significantly different, we assume that the 1955 data have been superseded. In 1963 McAfee and Edelson [77]

reported attachment coefficient data in SFg derived from a pulsed Townsend

discharge, but with no description of experimental or data analysis techniques.

In 1964 Edelson and McAfee [78] reported a detailed description of their data

analysis techniques and used the 1963 SFg attachment data as an illustration.

In this technique it is relatively easy to distinguish the electron and

negative ion components of the total current, and unlike the steady-state

situation, attachment produces an observable effect even without ionization.

More generally, the transient currents provide much more detailed information

about a variety of processes. By doing an extensive statistical analysis of

their data, Edelson and McAfee were able to provide direct evidence that

their derived coefficients are statistically significant. These attachment

data, displayed in figure 41, are the only data available at low E/N. The

maximum in n a /N must be treated with caution. Although from the point of

view of the data analysis it is statistically significant, a systematic error

which varies with E/N is possible. As E/N tends to zero the drift velocity

tends to zero, but the reaction rate constant remains non-zero. The result is

that n a /N tends to infinity as E/N tends to zero. A local maximum such as found by Edelson and McAfee must reflect an unusual behavior in either k 2 or W.

Samples of some of the other data available from steady-state Townsend

discharges are also displayed in the figures. Boyd and Crichton [79]

repeated the steady-state Townsend measurements with careful attention to

detail and report data for a-j, n a , and X. Their measurements covered a wide range of gas density and lead to the conclusion that the swarm coefficients

are proportional to gas density, a conclusion which is no longer contested.

Their reported data are not significantly different from those of Harrison

and Geballe. Their values for X/N are included in figure 43.

87
Mailer and Naidu [38] also extended the steady-state Townsend technique.

In 1975 they reported values of a-j and n a for mixtures of SFg with other

gases. In 1976 data on pure SFg were reported which are extended to higher

values of E/N than previous data. Their data on a-j/N are included in

figure 42. Figures 41 and 42 also show values calculated by Kline and

co-workers [64] and by Yoshizawa and co-workers [65]. These calculations

assume that a consistent set of cross sections can be found which give

agreement between measured and calculated swarm parameters, rather than

providing an independent theoretical confirmation of experimental values.

Some other data have been reported but not included in figures 41-43. Bortnik

and Panoff [43] reported Townsend discharge measurements , the results of which

are shown in figure 33, and seen to be similar to those displayed here in

figure 42. Dutton, Harris, and Jones [80] also reported studies of current

growth in a Townsend discharge but with a tentative conclusion that the swarm coefficients were not linear in the gas density, a conclusion which is not

supported by other data. Many investigations have been carried out on steadystate Townsend discharges in SFg and, in general, the data are remarkably

consistent. There may be, however, difficulties at large values of E/N. As was already shown in figure 33, results for X obtained by Sangi [41] depart

significantly from the results implied by the data of Mailer and Naidu [38]

at high E/N. Moreover, the calculated results of Yoshizawa and co-workers [65]

appear in figure 42 to show poorer agreement with the Mailer and Naidu data

for E/N > 1 x lO" 18 Vm 2

.

Application of the pulsed Townsend technique at high E/N requires a very rapid

light pulse. Teich and Branston [81] used this technique in SFg with a laser as

a light source, but were unable to account for all the phenomena contributing to

their transient currents. They reached a general conclusion that detachment is an important process in SFg at pressures above about 5 torr (0.67 kPa), but did

not report detachment data. In some special circumstances the observations could

be interpreted adequately to yield values of X in the range 108-130 x 10" 21 Vm 2

. The results of this measurement are not significantly different from those

obtained from the steady-state Townsend method.

Eccles et al. [52] reported detachment data, but with no identification of

the detaching ion species. The relative ion concentrations change with N and

E/N. Their principal conclusion is that for sufficiently low E/N the detachment

coefficient is so small that it is negligible in the analysis of steady-state

Townsend currents. As previously noted, however, (see Sec. II. C. 6), more recent

determinations of the detachment coefficient for SFg“ in SFg by O'Neill and

Craggs [53] indicate that the assumption 6^/N << n a /N cannot be assured once E/N > 1.4 (E/N) c , where (E/N) c corresponds to the point where n a = a-j. To

obtain detachment data, O'Neill and Craggs [53] used a double-gas drift tube

arrangement in which negative ions were formed by attachment in the first chamber

and detached in the second. Negative ions reaching the anode were identified

by mass analysis. The density dependence of the anode current implied that

either the detachment was not a two-body process or that the detaching species

were involved in some other competing process, the rate of which depended on N. The detachment coefficient for SFg“ was determined from the analysis of the

negative-ion current and the current growth curves utilizing a reaction scheme

including attachment, ionization, detachment, and charge transfer and ionconversion reactions involving SFr“ and F" as well as SFg“. It was estimated

to be 0.8 x 10

z/ m for E/N = 233 x 1Q- Zi

Vm and N = 16 x 10

zz m“ .

88
Except for the work of Kline et a 1 . , analyses of steady-state Townsend data

have included the assumption that electron detachment does not occur. In

SFg it is quite likely that more than one negative ion species is created,

and some of these may be in excited states. Following attachment, any

excitation can be expected to decay and ion-molecule reactions will produce

other ion species. Additional data on the detachment coefficients which

include specification of the ion species and the state of excitation are needed in SFg.

II.E. Chemical Diagnostics Development

II.E.l Motivation

It has been the purpose of this activity to examine and evaluate sensitive

chemical diagnostic techniques that can be applied to study the degradation

of gaseous dielectrics under conditions of high electrical stress. Of

concern here are conditions under which the rates of gaseous decomposition

are relatively slow such as might occur in the presence of a low-level corona discharge. Excluded from this study are the effects associated with

sudden, extraordinary stresses such as correspond to an arc discharge. A

number of studies of arc-induced decomposition of SFq have already been

reported in the literature [2], It is the intent of this work to provide

information that might prove useful in the design of tests to evaluate longterm chemical stability of gaseous dielectrics. The focus has been on SFg

since this serves as a kind of reference gas.

In this report we examine the feasibility of using a highly sensitive measurement

of the dielectric constant as a means of monitoring the content of polar

contaminants such as H2 O and HF in gaseous SFg. We also report on the

results of measuring the discharge power dependence of the rates of H2 O

and oxyfluoride production from corona in SFg. A gas chromatograph-mass

spectrometer (GC/MS) was used to perform the chemical analysis in these

experiments. This latter activity is an extension of work previously

reported [13-15],

II.E. 2 Effects of Polar Contaminants on the SFg Dielectric Constant

There exists within NBS the capability of measuring the low frequency

(static) dielectric constants and dielectric losses in insulating materials

subjected to high voltages to an accuracy of 1 ppm [82]. The technique has

been applied to measurements of dielectric properties of insulating materials

at cryogenic temperatures [83]. In the case of gaseous dielectrics, one is

motivated to consider the technique of accurate dielectric constant measurement

as a way of detecting the buildup of polar gaseous contaminants which might

result, for example, from corona-induced decomposition of the gas [1,15]. It may also serve as a convenient method for calibrating, or checking on the

calibration of the measurement of H2 O content using a gas chromatograph-mass

spectrometer for cases where this contaminant is introduced to study its

effects on corona characteristics, electrical breakdown, etc.

Calculations are performed here to determine the sensitivity of the method.

The question to be addressed is: given that one can detect a 1 ppm change

in the dielectric constant of the gas, what would that indicate about the

89
change in polar contaminant concentrations, e.g., the amount of H

2 O present?

Would a precision measurement of the dielectric constant be an accurate

indicator of polar contaminants?

We begin by considering the Debye expression for molar pol ariz abi 1 i ty P_ of

a pure gas, namely [34],

P =

£ - 1 4ttNci

£ + 2 V =

3

4 ttN u

2 9kT

(50)

where in this expression

e = dielectric constant

V = molar volume = 22.414 x 10 3 cm 3

a = molecular polarizability

u = permanent molecular dipole moment

N = Avogadro's number = 6.02217 x 10 23

k = Boltzmann's constant = 1.3805 x 10“ 16 erg (K"l)

T = temperature in K.

For a gas mixture consisting of several molecular species

specified number density n-j , we can write

£ - 1 _ 4tt

e + 2 3

I K a

i M)

3kT

= ^ I n i9l (T)

J i

, each with a

(51)

where g-j(T) = a-j + y-j 2 /3kT.

Solving for the dielectric constant e gives

“ (1 ln

-f 9

, )/ (1 l n^i

4tt3

(52)

Now consider a variation 6 n-j in the molecular number density of the ith

species. By taking the partial derivative of eq (52) with respect to n-j, we can find the fractional change in the dielectric constant resulting

from 6 n-j. Thus,

90
6e/e = 4Tr gi 5n

i /((l + I g i ni )(l - ^ I 9 ^-)}. (53)

3 -j 6 i

This is a general expression relating changes in dielectric constant to

changes in the concentration of a particular component in a gas mixture.

For most gases this expression can be greatly simplified by noting that

(e - 1) << 1 , e.g. , for gaseous SFg at a pressure of 100 kPa (~ 1 atm)

and at a temperature of 24°C, e - 1 = 0.00205 (see [35] and [ 86 ]). In

this approximati on eq (51) reduces to

e - 1 = 4 it l

n-j g-j (T), (54)

i

and eq (53) is replaced by — = 4 1rg

i (T)«n i> (55)

£

where again only the ith component is assumed to change.

Now if we let £-j be the known reduced dielectric constant of the ith

component of the gas at T = 300°K and at atmospheric pressure (100 kPa),

then another more convenient expression employing the above approximation is

= t p '/ p i£ , (56)

P (Ei - 1) £

where P' = 100 kPa, P is the total gas pressure given by P = £P-j, and the

ideal gas law has been assumed, i.e., 1

n-j = P-j/kT. (57)

From eq (56) above we can find the change in partial pressure SPj of the

ith species that would correspond to a measured fractional change 6 e/e

in the dielectric constant. Assuming now that existing instrumentation

allows for a sensitivity of 1 ppm, we have Se/e = 10“ 6

. It should

next be noted that the sensitivity for detection of a particular species

is proportional to the factor l/(e-j— 1 ). Therefore, the sensitivity

for detection increases as the amount by which the reduced dielectric

constant of the species differs from unity increases. As shown in table III,

species with relatively large permanent dipole moments u-j tend to have

larger values for £j ; thus, they can be detected with greater sensitivity

than species having low values for u-j. Also shown in table I are the

predicted sensitivities in ppm for detection of various species derived

from the ratio of partial pressure to an assumed total pressure of 100 kPa

found using eq (56) with 5e/e = 10“ 6

. It is seen that the highly

polar species such as H2

O, HF, and SO2 can be detected at the level of ~ 0.1%

concentration by partial pressure, whereas, nonpolar species like CF4 and

CO2 can only be detected at roughly the 1 % level.

91
Table III

Dipole moments, calculated dielectric constants at 20°C and 100 kPa, and

calculated detection sensitivities for SFg and contaminants commonly

observed in SF 5 after electric discharges.

Cal cul ated

Dipole Moment (y) Reduced Detection

Gas in debyes Dielectric Constant(e) Sensi ti vi ty

sf 6 0.1 1.00205 490

h2 o 1.85 1.00984 102

s 0

2

F

2 0.23 1 . 00023 5000

S0 2 1.63 1.00864 116

cf 4 0.0 1.00130 768

cos 0.67 1.0031 318

HF 1.91 1.01 20 a 83

C0 2 0.00 1.00092 1087

(PPm)

Possible large uncertainties due to lack of reliable data on molecular pol arizabi 1 ity

.

92
The predicted sensitivity is thus considerably below that of a gas chromatographmass spectrometer , but it is comparable, for example, to infrared absorption

spectroscopy. The other disadvantage of the technique considered here is

that it does not identify the contaminant species. It merely indicates the

change in polar gas content. Moreover, to achieve even a 0.1% sensitivity,

it would be necessary to construct a highly stable gas capacitor. The

estimates made here suggest that the technique is perhaps most useful as a supplementary way of checking on the calibration of other analytical devices

for polar gases like H2 O and HF for which there may be special problems

in achieving the desired accuracy even at relatively high concentration

levels. No specific plans exist at present to apply this method in our laboratory, although further consideration will be given to its use in

monitoring H2 O for experiments in which the effects of this gas on discharge

characteristics are studied.

II. E. 3 Production of Oxyfluorides and Water Vapor From Corona Discharges

in SF5

The rates of production of the by-products generated in a corona discharge

were measured for S

F

5 at an absolute pressure of 200 kPa (~2 atm) for

average discharge power levels in the range of 50 to 670 mW with polished

stainless steel, point-plane electrodes. The volume of the test cell was

4.0 liters and the corona was operated at constant current for a positive

dc-voltage applied to the plane electrode. The currents used were within

the range of 1.5 to 16.0 uA. A gas chromatograph-mass spectrometer

(GC/MS), details of which have previously been discussed [15], was used to

monitor the concentrations of H2 O, SOF 2 (thionylfluoride) and SO2

F 2 (sulfurylfluoride) as a function of time. The concentrations of the latter

two compounds could be determined quanti tati vely with a sensitivity of

about 1 ppm. During this year, improvements were made in the analytical

procedure which enabled us to obtain data on trace gas concentrations in

SFg. These more recent data are considered to be more reliable than those

we previously reported [15]. Nevertheless, more work is required before we

can confidently assign uncertainties to the results reported here which must,

therefore, be considered preliminary. As might be expected, the uncertainties

are greatest at the lowest concentrations but in no case do we believe they are greater than ±50% of the measured value. To assure reliability in the

quantitative analysis, the GC/MS was calibrated before and after each corona degradation experiment using several individually prepared standard samples

of SOF2 and SO2

F2 in SFg.

Thus far we have not succeeded in preparing reliable standard samples having

known amounts of H2 O in SFg. Therefore, only relative concentrations of H2 O

could be determined with the present system. It is believed that H2 O is

produced by discharge-induced desorption from the electrode surface. Its

concentration builds up rapidly with time at first and then levels off,

reaching roughly a constant value independent of discharge power. This is

illustrated by the data shown in figure 44 which shows relative concentrations

of H2 O as a function of total energy dissipated in the discharge at the

indicated power levels. There is some indication from these data that the

H2 O concentration initially builds up more rapidly at the higher discharge

power levels. The accumulated time that the discharge was maintained is,

in each case, given by the product of the energy dissipated and the reciprocal

of the power.

93
ENERGY DISSIPATED (kJ)

Figure 44. Relative concentration of H 2O in SF 5 as a function of

energy dissipated by a positive dc corona discharge for

the indicated discharge power levels.

94
It has been hypothesized [2,14,15,87] that SOF2 results primarily from hydrolysis

of the primary decomposition product SF4 , whereas, SO2

F 2 is generated within

the discharge via reactions of sulfurylf 1 uorides with free oxygen and H2

O. After

arc discharges have occurred in SF5 , the species SO2

F 2 has been observed [1,87]

to be absent, or of very low concentration compared to SOF2

.

The results of our measurements of SOF 2 and SO2

F 2 concentrations as a function

of the net energy dissipated for three different power levels are shown in

figure 45. The net energy U(t) dissipated in the discharge at time t was found using the relationship

t

U(t) = I J

V (t

1 )dt1 , (58)

0

where I is the discharge current and V(t') is the voltage across the cell.

The significant conclusions from these results are: a) the production rates

of SOF2 and SO2 F2 are nearly constant, at least up to concentrations of 200 ppm,

and roughly proportional to the power dissipated, and b) SOF2 and SO2

F 2 appear

with nearly equal concentrations. The fact that SO2 F 2 is produced with much more relative abundance in a corona discharge than in an arc is interesting,

and possible reasons for thi s important observation need to be explored. It has been suggested, for example, by Becher and Massonne [1] that in an arc the predominant reactions are with vaporized electrode metal which always

yield metal fluorides, SF4 , and subsequently SOF 2 via the reaction

SF4 + H2 0 * S0F 2 + 2HF. (59)

In a low power discharge like corona, on the other hand, free oxygen radicals

are presumed to be present to a higher degree and thus give rise to SO2

F

2 production through reactions like

SF6 + 0 SOF4 + 2F

SOF4 + H2 0 * S02 F2 + 2HF (60)

SOF4 + 0 -> SO2

F 2 + 2F .

In the present work, the presence of SOF4 could be detected, although its

absolute concent ion could not be determined due to lack of a reliable standard

sample. Methods of indirectly calibrating the GC/MS for SOF4 are being

explored. It should also be noted that no attempt was made in the present

experiments to monitor the HF concentration. It can presumably be estimated

from data on S0F2 , SO2

F

2 , and SOF4 concentrations assuming the above reactions

domi nate.

95
ENERGY DISSIPATED (kJ)

o

cm

GO

Figure 45 . Measured concentrations of SOF2 and SO2F2 as a function of

net energy dissipated in corona discharges operated at the

indicated power levels.

96
II. F Optical Diagnostics of Discharges

II.F.l Motivation

The purpose of this work has been to evaluate the possibilty of using the

laser-stimulated optogalvanic effect as a microscopic diagnostic of fundamental

processes in corona discharges. The basic idea is that by optically pumping

selected atomic or molecular species with a tunable light beam incident on the discharge region, one induces a change in the effective ionization rate

in the gas, which manifests itself as a measurable change in discharge

current. The detection of optogalvanic signals offers the possibility of

monitoring the concentrations of metastable species in the discharge. In some cases it could also provide information about the presence of contaminants

or intermediate species, such as free radicals.

The importance of metastable atoms and molecules in electrical discharges

has been recognized in the literature for many years [64,88-93]. Recent

measurements by researchers at NBS and Los Alamos have directly confirmed

the validity of earlier speculation which suggested that the presence of

metastable atoms in a hollow cathode discharge increases the level of

ionization [92]. A multitude of collision and radiative processes exist

which can affect the concentration of metastable atoms. They include, for

exampl e:

1. Production -

e + A->-A* + e- kinetic energy - colli si onal excitation

hv + A ->• A** + A* + hv' - optical pumping

e + A A** + e - kinetic energy colli si onal excitation

+ radiative decay

A** - a* + hv

e + A+ -» A** -* A* + hv - radiative recombination

e + A + + B-*A*+B + kinetic energy - three body recombination

e + a** ->• A* + e + kinetic energy - superelastic collisions

2. Quenching - A*+B-*A+B+ + e- Penning ionization

A* + e - A+ + 2e - electron impact ionization

A* + A* -> A

+ + A + e - metastable-metastable collisions

A* + e A + e + kinetic energy - superelastic collisions

A* + 2B + (AB)* + B inelastic

three-body

+ A + 2B + (hv or kinetic energy) collision

97
A* + hv -> A** > A + hv' - optical pumping

A*+B+A+B+ (hv or kinetic energy) - collisional quenching.

In the above reactions, A is assumed to be an atomic species in the ground

state, and A* is the same species in a metastable excited state. Additional

mechanisms are possible particularly if A and B are taken to be molecular

species.

Although one must consider all of these processes in attempting to predict

equilibrium concentrations of metastables in a discharge, it is clear that some are likely to be much more important than others. In the absence of

external radiation, for example, the production of metastables is most

likely dominated by processes involving collisions of electrons with ground

state atoms (or molecules). When an external radiation source is introduced,

the populations of metastables can be significantly affected by the optical

pumping processes.

Monitoring the resultant change in discharge voltage as a function of an external radiation source forms the basis of optogalvanic spectroscopy.

Earlier NBS reports [15] have described our efforts to evaluate optogalvanic

spectroscopy as a diagnostic technique for better understanding the physics

of corona discharges. Attempts were made to observe the optogalvanic effect

in a steady corona discharge in N? using coaxial electrodes and in SFg

using point-plane electrodes. Consistent with the lack of evidence for

the existence of SFg metastables (see [49]), no optogalvanic signals were

observed in the measurements using pure SFg. A change in corona current

due to the presence of the incident laser light was detected in N 2 , but an optogalvanic signal in the form of discrete lines correspond!' ng to electronic

transitions in N 2 [94] was not observed.

During the past year we have used optogalvanic spectroscopy of glow discharges

to make a preliminary examination of the possible quenching of metastable

Ne atoms and N 2 molecules in the presence of SFg. We have also used this

technique to determine if neon metastable atoms survive in high pressure

glow discharges (P ~ 100 kPa). Both measurements are relevant to gaseous

dielectric studies because they provide information about the influence of

metastables on the level of ionization in gas discharges. The effect of

metastable atoms has been shown to be important in model calculations of

breakdown in SFg/He mixtures [64] and metastable molecules appear to influence

the development of streamers in air [39,91].

II. F. 2 Apparatus and Experimental Results

The dye laser system for obtaining optogalvanic spectra is shown schematically

in figure 46. The external light source was a tunable dye laser pumped by an argon-ion laser. The laser beam was chopped with a mechanical chopper

wheel and directed into the discharge cell. A phase sensitive detector

employing a lock-in amplifier was used to observe changes in the discharge

voltage which occurred as the wavelength of the laser was varied. The output

of the phase sensitive detector was plotted on an X-Y recorder. For the

measurements reported here, the wavelength was scanned from 580 nm to 620 nm. The measurements were performed with a hollow cathode lamp which was fitted

with a valve in order to change gases and vary the gas pressure. Thus,

98
DETECTOR

Figure 46. Schematic view of apparatus for performing optogalvanic

measurements in a hollow cathode lamp.

99
all the data were obtained with static gases. Prior to the introduction

of any gas, the hollow cathode lamp and associated gas lines were evacuated

to a pressure of approximately 1.3 x 10 ^ Pa (~ 1 x 10 " 7 torr).

II. F. 3 Low Pressure Measurements

II.F.3.1 Ne and Ne + SF6

An optogalvanic spectrum obtained with research grade neon (99.999°', cylinder

purity) in a hollow cathode discharge is shown in figure 47. These measurements

were performed in part to verify proper performance of the measuring system.

"The discharge current, laser power, and gas pressure are ~ 2.5 mA, 30 mW,

and 677 Pa (5.1 torr), respect i vely . Spectroscopic lines which reveal the

presence of the 3 Po and 3 P 0 metastable states in the discharge are indicated

in figure 47. Lines which show the presence of the radiative 3 P] and 3 P]

states are also shown [95].

Spectra obtained with small amounts of SFg (1 to 5%) mixtures with neon show

no dramatic changes. For comparison, an optogalvanic spectrum of neon with

5" SF5 is also presented in figure 47 for approximately the same current,

laser power, and total gas pressure. The difference in line heights for

the two spectra is not considered significant because some changes in line

heights are observed to occur normally as a function of time due to changes

in gas and electrode conditions which can happen during operation of the

di scharge.

The fact that the neon optogalvanic spectrum is largely unaffected by SFg

is of some interest. Both metastable states of neon ( 3 P 2 , 16.62 eV

and 3 P 0 , 16.72 eV) h ave electronic energies which overlap with the band

of photoionization energies for the 3t]g orbital of SFg centered near

16.96 eV and exceed the ionization energy of the 3t] u orbital centered near 15.96 eV [96]. Penning ionization of either orbital is thus energetically

possible. In addition, there are many states in SFg with excitation

energies near those of the neon metastable atoms [49,97] and presumably

some of these states could be excited via collisions with the metastable

atoms. Our measurements suggest that both processes, as well as others [98]

which could deplete the population of metastable atoms and affect the discharge

and associated optogalvanic spectrum, do not appear to have sufficiently

large cross sections to have a measurable effect at the concentrations

studied.

While the presence of SFg does not markedly affect the appearance of the

spectra, the glow discharge was less stable and became noisier with time.

Higher voltages were also required to obtain the same discharge current

when SFg was added to the neon. A higher voltage is expected when an electronegative gas such as SFg is added to neon because the electron drift

velocity is reduced due to temporary electron attachment to SFg. This is

equivalent to having electrons make more collisions with the non-attaching

gas at some higher pressure [99]. Attempts to obtain optogalvanic spectra

with 10% SFg were not successful because of excessive noise levels associated

in part with oscillations in the discharge intensity. The cause of the noise was not investigated.

100
580 590 600 810 620 nm

Figure 47. Optogalvanic spectra of neon and a mixture of neon with

5% SFg for comparable discharge current and gas pressure.

101
II. F.3.2 N2 and N 2 + SFg

Measurements of optogalvanic spectra in nitrogen (99.9995% cylinder purity)

were more difficult than for neon. As has been noted previously in the

literature [94], the nitrogen optogalvanic spectral lines are several orders

of magnitude weaker than the neon metastable lines. Figure 43 shows a tracing

of a portion of the N 2 spectra for a gas pressure of 320 Pa (2.4 Torr),

discharge current of ~ 2.5 mA, and dye laser power near 400 mW. The results

are complicated by the overlapping of the first positive band (B 3 n + A

3 Z

U ) and the Ledbetter system (c^.

1 n

u +

) [94,100]. Indicated in f igure 43

are the (8,4) band head at 595.9 nnrfrom the first positive system and the

Q branch of the Ledbetter system at 597.7 nm. The structure to the left

and right of the Q branch is due in part to the rotational lines of the R and

P branches. The two states, A

3 Z U + and L Z +

, which are optically pumped

with the dye laser are metastable and lie y 6.4 eV and 12.3 eV, respectively,

above the ground state of N 2 [100,101].

Attempts to see the effects of SFg on the optogalvanic spectrum of N2 were

not very successful. While some indication of the Q branch of the Ledbetter

system could be observed with a 1% mixture of SFg for a discharge current

of ~ 1 mA, spectra at higher currents (e.g., ~ 2.5 mA, figure 48) could not

be obtained because of electrical noise in the discharge.

II. F. 4 Detection of Metastable Neon at Atmospheric Pressure

As noted earlier, the presence of electronically excited metastable atoms

or molecules has been considered in calculations of the dielectric strength

of gaseous insulators and the development of streamer formation in air. Becasue

gas pressures of 100 kPa or more are normally considered in such problems,

it is reasonable to examine whether metastable atoms or molecules, which

are readily detected experimentally at low pressures, can survive quenching

processes which are pressure dependent. With this question in mind, an effort

was made to obtain optogalvanic spectra of neon at atmospheric pressure. Optical

absorption measurements have revealed the presence of the 3 P 2 metastable state

of neon at pressures of ~ 40 kPa (~ 300 torr) and 53 kPA (400 torr) [102,103],

and the vacuum-uv-emission data of Leichner [104,105] have implied the

existence of the same state at pressures as high as 133 kPa (~ 1000 torr).

Figure 49 shows an optogalvanic spectrum of neon obtained with the hollow

cathode lamp at a discharge current of 3.6 mA and pressure of 100 kPa.

These results represent the first observation of the optogalvanic effect

in a neon glow discharge at atmospheric pressure and directly indicate the

presence of both Ne metastable atomic states. At such high pressures the

appearance of the discharge is significantly modified from that at low

pressure. A miniature negative glow region and a positive column of small

diameter extend from the cathode to anode as sketched in the left inset of

figure 49. The discharge was electrically very noisy and intermittant

periods of high-frequency oscillations could be observed with an oscilloscope.

The physical location of the negative glow-positive column combination

would occasionally move, disrupting the measurements. Optogalvanic spectra

were measurable only when the dye laser beam was incident on the negative-glow

region. The data in figure 49 were obtained with a dye laser power of 150 mW

for the first two lines (585.2 nm, 588.2 nm) and 110 mW for the remaining

lines. The three strongest 3 P 2 lines were truncated by the X-Y recorder.

102
597.7 nm

Q-Branch

H

Figure 48 c Optogalvanic spectrum for N2 showing lines from the Ledbetter

system and the (8,4) bandhead for the first positive system.

103
Figure 49. Measurement of neon optogalvanic spectrum at atmospheric

pressure (100 kPa) and 3.6 mA discharge current. Optogalvanic

transitions could be observed only in the negative glow

region of the discharge.

104
Shown in the right inset of figure 49 are the relative line heights at

614.3 nm ( 3 ?2) ar|d 616.4 nm ( 3 P

0

). The initially noisy signal suddenly

changed to one with hi gh-f requency oscillations. Phase-sensitive detection

permitted extraction of a relatively noise-free signal during this period

of h i gh-f requency oscillation.

Considerable information has been published in the literature regarding

col 1 isional destruction and creation processes in neon following pulsed

discharges [102-108], but little appears to be known about why certain

states are excited by a glow discharge and not others [93,107]. What

figure 49 directly shows is that one of the metastable states of neon continues to be produced at atmospheric pressure (100 kPa) and significantly

influences the degree of ionization in the discharge.

Specifically, as the number of 3 P2 metastable atoms are depleted by optical

pumping, the level of ionization in the discharge is reduced leading to an increase in the discharge cell impedance. The voltage drop across the

electrodes of the hollow cathode lamp increases and a positive optogalvanic

signal is observed [92,93].

Care must be exercised in estimating the relative equilibrium densities of

the various excited states from the optogalvanic spectra in figure 49. If

the low pressure results of Zalewski, et al. [93] regarding abundances of

the l P] and 3 P2 excited states and corresponding line heights can be carried

over to the present high pressure measurements, comparison of figures 47 and 49

suggests that at 100 kPa, a reduction in the number of atoms in the 1 P] state

has occurred relative to the 3 P2 state. This extrapolation is not without

risk [109] and ignores, for example, the likely change in electron energy

distribution that occurs at higher gas pressures and the resultant change

in efficiency of ionization of the final states (i.e., 2 p

5 3p configuration

discussed below) excited by the dye laser.

The relative line heights of the 3 P] (607.4 nm and 609.6 nm) and 3 P 0 (616.4 nm)

lines are also smaller when compared with the 3 P 2 lines, but the change

in sign at high pressure further complicates any interpretation regarding

relative abundances of these excited states. Low pressure hollow cathode

discharge measurements [95] indicate that sign changes occur for the noted

lines but at higher discharge currents (e.g. , ~ 15 mA for the 3 P 0 line versus

3.6 mA at atmospheric pressure). The apparent discrepancy may be explained

by the possible equivalence in current density for the high and low pressure

measurements. As noted earlier, a constriction in the size of the discharge

occurs at high pressure.

A model has been proposed which suggests that the gradual reduction in

spectral line height and eventual sign change as the discharge current is

increased is due to two types of competing processes following dye laser

excitation [95]. The model is briefly explained for the 3 P

2 state with

the aid of a simplified energy level diagram for neon shown in figure 50.

Optical pumping of the 3 P 2 level produces transitions to states with the

ls 2 2s 2 2p 5 3p electron configuration. At low discharge currents

these laser excited states radiate back to the ls 2 2s 2 2p 5 3s levels

with known branching ratios (optical transitions to the ground state are forbidden). Because some of the laser excited states decay to the *P] and 3 P]

states, which in turn can radiate to the ground state, the net effect is a

105
10 levels

Figure 50. Simplified energy level diagram for neon. Optogalvanic

signals are obtained when laser-induced transitions occur from the 2p^3s states to the 2p^3p manifold of excited states.

106
loss in the number of metastable atoms. As noted earlier, this reduces

the level o^ ionization and produces a positive optogalvanic signal; i.e.,

it increases the impedance of the discharge cell with a resulting increase

in voltage drop (see fig. 46). Again, a reduction in the ionization level

is expected if the metastable population declines, since not only is ionization

of metastables via electron collisions likely to be more probable than for

ground state species, but additional processes such as Penning ionization

and super elastic collisions can also enhance ionization. If ionization

of metastables by electron collisions dominates, then a decline in the

metastable population can be interpreted as giving a lower ionization

coefficient for the gas (see Sec. II. B).

At higher discharge currents, a second competing process occurs after the

1

s

2 2s ^2p 5 3p states are excited. If the current is allowed to increase,

there will be a resulting increase in the collision frequency of electrons

with atoms in these states excited by the laser. Thus the likelihood will

increase that ionization from these states will take place before they

have an opportunity to radiatively decay to lower states. The resulting

increase in ionization level reduces the voltage difference across the

hollow cathode lamp electrodes and yields a negative optogalvanic signal.

Although the change in size of the signal associated with the 3 P 0 state can be understood by this model, it is not clear that it can explain the

observed sign reversal for transitions involving the state (see fig. 49).

As shown in figure 50, this state is not considered to be metastable. In

this case collisional processes that couple the 3 P] state to the 3 P

0 and 3 P

2 states may also play a role [95]. Through coupling, population of the 3

P-|

state will indirectly affect the population of the 3 P

0 and 3 P 2 states.

Consistent with the above model, sign reversal requires successively higher

currents for the 609.6 nm, 607.4 nm, and 603.0 nm lines [95]. The data

indicate that sign reversal occurred for the first two lines and the third

line approached a near zero magnitude. Because, as shown in [95], the 3 P

2 lines require greater discharge currents than the 3 P] lines before sign

reversal occurs, the 3P 2 positive lines shown in figure 49 are also

compatible with the model, i.e., sufficient current was not achieved to

give reversal in the present experiments.

A very preliminary comparison of the optogalvanic linewidths for one of

the 3 P 2 transitions has been made for pressures of 1.2 kPa (9 torr) and

100 kPa (750 torr). The increase in linewidth due to pressure broadening

is readily observed. Because information regarding the lifetime of excited

states can be learned from linewidth measurements, possibilities of

obtaining more refined data should be explored.

III. OTHER ACTIVITIES

During this reporting period there were several other activities and

accomplishments that deserve mention. Using a photomultiplier, preliminary

measurements were made of correlation between optical emission pulses and

electrical current pulses from positi ve-dc-corona discharges in SF5

. The

temporal resolution of the measurement system was 2 ns. The results indicate

a high degree of correlation in time, i.e., no measurable average delay

107
between the optical and electrical signals. Because the results are

still considered preliminary and in need of verification, they have not

been presented in this report. More work on this is in progress.

A discussion [110] was prepared on a paper by J. M. Pelletier, et al. [111].

In this discussion, a connection was drawn between Paschen's law and Olivier's

equation [ 112 ], which was used to fit data on electrical breakdown for gas

mixtures.

In the past year the project supported the completion of one thesis [9] and

three major archival papers [8,11,58] which have been submitted for publication.

Presentations were given at the 33rd Gaseous Electronics Conference [13], the

1980 Conference on Electrical Insulation and Dielectric Phenomena [9,10], and

the 1981 NATO Advanced Study Institute on Electrical Breakdown and Discharges

in Gases. Talks and seminars were also given at the General Electric Research

and Development Center and at the Massachusetts Institute of Technology.

Visitors to NBS who were consulted concerning technical aspects of the project

included Dr. Diethard Hansen of the Hahn-Meitner Institute, Dr. David W. Tong

of the General Electric Research Laboratory, Dr. A. H. Qureshi of the

University of Windsor, Dr. John Moore of the University of Maryland, and

Dr. Andreas Kelen of ASEA. Dr. Kelen presented a seminar at NBS entitled

"Detection of Aging in Dielectric Materials." The project also supported a seminar at the MIT High Voltage Laboratory, by Dr. Eric E. Kunhardt of Texas

Tech University. Special assistance in preparing standard samples for gas

analysis was provided by Dr. George Lockyer of the Allied Chemical Corporation.

IV. CONCLUSION AND- SUMMARY

We outline here some of the more significant conclusions that can be derived

from the work described in this report. First concerning the measurement

of corona characteristics for SF5 , a new measurement scheme employing

pulse counting and pulse-height analysis has been demonstrated and shown

to yield interesting quantitative information about the statistics of

electron avalanches and streamers not obtainable by other means [ 8 ].

During the past year new data were acquired on the pulse characteristics

of positive-dc, point-plane corona in SFg which confirm tentative conclusions

previously offered [16]. Further studies were carried out on the behavior

of negative corona in SFg which showed that the nature of the phenomenon

near inception depends critically on the point electrode conditions if no external radiation is present. For clean, polished stainless steel electrodes,

the negative corona will, in the absence of radiation, appear initially as relatively large Trichel-like pulses at voltages significantly above the

theoretical onset. If radiation is introduced, or if the electrodes are conditioned by operating a discharge for a short time at currents above a microampere, then the corona will appear at onset predominantly in the

form of low level electron avalanches of high repetition rate with only an occasional "large" pulse.

Measurements of higher sensitivity carried out at the MIT High Voltage

Laboratory in connection with this project also showed that negative corona in irradiated gaps for SFg initially appears in the form of electron

avalanches which follow a modified Furry-type size distribution [9]. At

voltages above avalanche inception, significant deviations from the Furry

distribution become evident and there is often an abrupt appearance of

108
large pulses having amplitudes noticeably in excess of those of the main

body of electron avalanches. Current stochastic models of electron avalanche

formation cannot predict this behavior, and an entirely new theoretical

approach is needed which includes possible effects of el ectrohydrody namic

instabilities. This sudden transition to large pulses is similar to the

behavior observed in the NBS laboratory for positive corona in SFg, and

an understand!' ng of this transition is perhaps the key to understand!' ng

the fundamental breakdown process in SFg and other highly electronegative

gases.

A set of preferred mechanisms for initiation of corona discharges in SFg

were proposed [11]. For negative corona the predominant mechanisms appear

to be field emission of electrons from the stressed electrode surface in

the absence of radiation, and field enhanced photo-electric emission in the

presence of radiation. For positive corona the mechanisms are field-enhanced

collisional detachment of negative ions in the absence of radiation, and

photodetachment in the presence of radiation, assuming of course that the

energy of the radiation exceeds that for the electron affinity of the

negative ions. It is shown [11] that this set of mechanisms is consistent

with observed polarity, geometry, and pressure effects, and with differences

between ac and dc corona [10]. Comparisons of calculated and measured

corona inceptions for highly nonuniform fields show agreement only for

negative corona. This is expected on the basis of the assumed initiation

mechanisms. No conclusions could be drawn from this comparison about the

critical avalanche size to be used in the streamer criteria. This is due

to large uncertainties arising from lack of precise knowledge about the

electric field variation near the tip Of a sharp point electrode. Pulse

height distribution data [8,9] suggest a critical avalanche size which is

considerably below the commonly accepted value of 1 x 10 8 electrons.

Additional possible difficulties were uncovered in the modeling of corona

inception for highly nonuniform electric fields. One is the questionable

validity of swarm parameters, particularly the ionization coefficient, for

E/N in highly nonuniform situations where electrons are unable to attain

equilibrium. The other, made evident in part from the survey of electron

swarm data, is the possibility of large uncertainties in measured values

for ionization coefficients in electronegative gases at high E/N where

contributions from electron detachment processes might become important.

The survey of swarm data [58] revealed a number of gaps in the data needed

for modeling discharges in electronegative gases, and in some cases raised

questions about the reliability of the existing data. For example, in the case of SFg there is a serious lack of information about detachment of

negative ions in this gas; whereas, in the case of O2 , the available

detachment data display enormous disagreement. This survey points to areas where more measurements, or new measurement techniques, and calculations

are needed.

Concerning the measurement of discharge-generated contaminants in SFg, the

results of calculations reported here indicate that a measurement of the

low-frequency dielectric constant for SFg at a sensitivity of 1 ppm will

reveal the presence of polar contaminants such as H2 O at a level of about

100 ppm. This technique is thus seen to lack sensitivity, but might prove

useful for calibration purposes. In the use of the GC/MS to monitor buildup

109
of corona-generated stable by-products in SFg, it was found that the

oxyfluorides S OF 2 and SO2 F 2 are produced at rates directly proportional

to the discharge power for power levels between 50 and 600 mW. The production

rates are also constant, at least up to concentrations of 200 ppm. The

compounds SOFg and SO2

F

2 are produced in corona at nearly equal rates,

which is contrary to the results from arc decomposition studies that show

almost no production of S

O

2

F 2

- The reason for this difference is not yet

completely understood.

The results of optogalvanic measurements in glow discharges showed that the

presence of SF 5 in neon (at least up to the 5°' level) had little or no effect on the relative strengths of the observed signals associated with

transitions from metastable states. It can be inferred from this that SF 5 has no dramatic effect on modifying the metastable populations in the

discharge. Optogalvanic spectra were also observed for the first time in

a high pressure (100 kPa) neon discharge.

110
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112
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113
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114
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in SF6 ," J. Phys. D. , Vol. 12, pp. 1839-1852, 1979.

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Gaseous Electronics, University of California Press, Berkeley,

pp. 375-476, 1965.

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Attaching Gases," J. Appl . Phys., Vol. 47, pp. 1916-1919, 1976.

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of Formation and Mobility of Negative Ions," J. Chem. Phys.,

Vol. 23, pp. 1435-1440, 1955.

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in a Townsend Discharge by Time-Resolved Mass Spectrometry,"

Proc. Phys. Soc., London, Vol. 81, pp. 382-384, 1963.

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Experiment," Rev. Sci. Instrum., Vol. 35, pp. 187-194, 1964.

[79] H. A. Boyd and G. C. Crichton, "Measurement of Ionization and

Attachment Coefficients in SF5 ," Proc. IEE, Vol. 118,

pp. 1872-1877, 1971.

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and Breakdown in SFg," Nature, Vol. 227, pp. 702-703, 1970.

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Ionization and Electron Detachment in SFg," 3rd Int'l. Conf.

Gas Discharges, IEE Conf. Publ. No. 118, pp. 109-113, 1974.

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Capacitance Bridge with One PPM Accuracy," IEEE Trans, on Instru. and Meas., Vol. 1M-24, No. 4, pp. 336-344, 1975.

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Materials at Cryogenic Temperatures," Final Report for DoE

Contract EA-77-A-01 -6010 , National Bureau of Standards Internal

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[84] H. Frohlich, "Theory of Dielectrics," Oxford University Press,

London, 1958.

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and Electric Dipole Moments of Substances in the Gaseous State,"

NBS Circular 537, 1953.

[ 86 ] R. D. Nelson, D. R. Lide, and A. A. Maryott, "Selected Values

of Electric Dipole Moments for Molecules in the Gas Phase,"

National Bureau of Standards Report, NSRDS-NBS 10, 1967.

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[87] A. Baker, R. Dethlefsen, J. Dodds, N. Oswalt, and P. Vouros,

"Study of Arc By-Products in Gas-Insulated Equipment," EPRI

Final Report, EL-1646, 1980.

[ 88 ] K. W. Meissner and W. F. Miller, "Influence of Irradiation on the Characteristic of a Glow Discharge in Pure Rare Gases,"

Phys. Rev., Vol . 92, pp. 896-898, 1953.

[89] F. E. Acker and G. W. Penney, "Influence of Previous Positive

Streamers on Streamer Propagation and Breakdown in a Positive

Poi nt-to-Pl ane Gap," J. Appl . Phys., Vol. 39, pp. 2363-2369, 1963.

[90] E. Kuffel and M. Abdullah, High Voltage Engineering , Pergamon

Press, New York, 1970.

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Molecules on the Streamer Progression, " J. Phys. D: Appl. Phys.,

Vol. 8 , pp. 670-680, 1975.

[92] K. C. Smyth, R. A. Keller, and F. F. Crim, "Photon-Induced

Ionization Changes in a Neon Discharge," Chem. Phys. Lett.,

Vol. 55, pp. 473-477, 1978.

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Induced Impedance Changes in a Neon Hollow Cathode Discharge.

A Mechanistic Study," J. Chem. Phys., Vol. 70, pp. 1015-1026, 1979.

[94] D. Feldmann, "Opto-Gal vanic Spectroscopy of Some Molecules in

Discharges: NH2 , NO2 , H2 , and N2

," Opt. Comm., Vol. 24,

pp. 67-72 (1979).

[95] K. C. Smyth and P. K. Schenck, "Opto-Gal vanic Spectroscopy of a Neon Discharge: Mechanism Studies," Chem. Phys. Lett., Vol. 55,

pp. 466-472, 1978.

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"Photoelectron Spectra of the Halides of Elements in Groups III,

IV, V, and VI," Phil. Trans. Roy. Soc. London, Vol. A. 268,

pp. 59-76, 1970. The identities of the orbitals are those of

Potts, et al. Alternative assignments of the orbitals are given

by Hay in Ref. 97.

[97] P. J. Hay, "Excited States and Positive Ions of SF5 ," J. Am. Chem.

Soc., Vol. 99:4, pp. 1013-1019, 1977.

[98] Other processes such as neutral dissociation and neutral

dissociative excitation should also be considered. For example.

Hay's calculations (Ref. 97) predict an anti-bonding orbital

( 6a

-j g ) which is energetically accessible. For a further

discussion of processes which can lead to destruction of

metastable atoms in gas mixtures, see D. H. Stedman and

D. W. Stetser in "Prog. Reaction Kinetics," Vol. 6 , p. 75ff, 1971.

118
[99] G. Francis, "The Glow Discharge at Low Pressure" _i_n Encyclopedia

of Physics, Vol. XXII, Spri nger-Verl ag, Berlin, 1956 , p 177ff.

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and Identification of the Lowest 'z Q + Rydberg State of the

N 2 Molecule," J. Molec. Spectr., Vol. 42, pp. 100-111, 1972.

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Nitrogen," J. Phys. Chem. Ref. Data, Vol. 6 , pp. 113-307, 1977.

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Collision Coefficients for Excited Neon Atoms," Phys. Rev.,

Vol. 114, pp. 1011-1025, 1959.

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J. Phys. B: Atom. Molec. Phys., Vol. 12, pp. 4113-4129, 1979.

[104] P. K. Leichner, "Time and Pressure Dependence of the VacuumUltraviolet Radiation in Neon," Phys. Rev. A, Vol. 8 , pp. 81 5-822, 1973.

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of the Vacuum-UV Emissions from Neon, and Energy Transfers to

the Resonance States Ne( 1 P]) and Ne(^P-j) in HeliumNeon Mixtures," Phys. Rev. A, Vol. 12, pp. 2501-2513, 1975.

[106] J. R. Dixon and F. A. Grant, "Decay of the Triplet P Levels

of Neon," Phys. Rev., Vol. 107, pp. 118-124, 1957.

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Collisions Between Low-Lying Excited and Ground-State Ne

Atoms," Phys. Rev. A, Vol. 17, pp. 1343-1356, 1978.

[109] The complexities of modeling the neon discharge are discussed

in Ref. 95.

[110] R. J. Van Brunt, "Discussion on paper 81 WM 014-0 by

J. M. Pelletier, Y. Gervais, and D. Mukhedkar," IEEE Trans,

on Power App. Syst. , Vol. PAS-100, pp. 3867-3868, 1981.

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Strength of N 2 -He Mixtures and Comparison with N 2 -SF5 and

CO2 -SF5 Mixtures," IEEE Trans, on Power App. Syst.,

Vol. PAS-100, pp. 3861-3869, 1981.

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Compute Uniform Field Breakdown of Gases," IEEE Trans. Power

App. Syst., Vol. PAS-97, pp. 969-976, 1978.

119
[113] K. T. Compton, "On the Motions of Electrons in Gases,"

Phys. Rev. Vol. 22, pp. 333-346, 1923.

[114] L. Loeb, Basic Processes of Gaseous Electronics , U. of

California Press, Berkeley, pp. 211-373, 1961.
APPENDIX I.

Equilibrium Conditions - Estimation of Swarm

Parameter Applicability

In applying electron swarm parameters, such as the ionization coefficients,

to calculation of current growth, or discharge inception in gases, one needs

some assurances that these parameters are meaningfully defined over the

range of conditions to be encountered. The issue is especially significant

at high E/N where electron velocities must necessarily become greater. The

swarm parameter values are typically measured and used when the electrons

are in "equilibrium" with the driving force from the electric field. By

"equilibrium" it is meant that the average energy of the electrons has

reached the value it would have if the electrons had been traveling a long

distance; thus, also, the ionization rate which is influenced by electron

energy is in equilibrium.

We propose here a useful, simple calculation for estimating the conditions

under which the use of swarm parameters should be permissible. The technique,

which is an adaption of methods introduced by Compton [113] with extensions

suggested by Loeb [114], is believed to be applicable to regions of high

E/N and also for nonuniform fields where average electron motion might not

keep up with the rate of change of the field. While Monte Carlo methods

provide one means of determining equilibrium conditions, the technique is

proposed as an alternative and more easily used estimator. The validity

of the simplified expression given here, however, should be checked by

comparison with results of Monte Carlo calculations. Thus far this has

not been done. The expression given below is a first-order nonlinear

differential equation which can be solved by simple iteration techniques.

For convenience, the electrons in the gas are subjected to a z -directed

electric field. Their motion in one dimension is defined in accordance

with an energy balance constraint. This method equates the energy change

to energy input less energy loss, all on a per-unit-path basis. The result

is given here without proof:

= eE - ef (U - ft)U/(0.44 A

2 E), (A.I.l)

dz

where

e = electronic charge

U = average electron energy /coul omb (in eV)

E = electric field in the z -direction (in V/cm)

f = fractional energy lost/collision by an electron

X = mean free path (in cm)

ft = limiting thermal electron energy /coul omb.

If E = 0, then U = ft, corresponding to the limiting thermal energy. Generally,

f and X are U-dependent. Yet it can be shown that both f and X may be approximated

on the basis of experimental data and/or theoretical determinations of

D/y (the diffusion-mobility ratio) and W (the electron drift speed).

121
By derivation and curve fitting of published data to obtain specific values

for SFg, the following expressions were obtained for X (electron mean free

path) and for f; they apply for E/N in the range:

Equation (A.I.l) has been numerically solved for the CIZ configuration of

interest in this study. The electric field, E, was chosen as the z-component

of the Laplacian cathode tip field (see fig. A.I.l). For SFg, values of

D/p and W e were taken from the results of Kline et al. [64], The results

for various tip radii are shown in figures A. I. 2 and A. 1.3. For each figure,

the abscissa quantity is the normalized distance from the cathode surface:

where R is the tip radius and where Z/R = 1 at the very tip of the cathode.

1 x IQ" 20 < I < 3.3 x 10- 18 V

m

2

. N

Mean Free Path:

X = 2.125

(A. I. 2)

= 1.43 x 10

N

where (from [64])

,

,0.05024

8 = 1.226 x 10 10 [(JL) p \ N (A. 1.3)

Fractional Energy Loss:

3 D/p

(A.I.4)

= 2.676 x 10 15

,0.9092

XeZ- (A.I.5)

R

122
HIGHER-FIELD

IONIZATION ZONE

DRIFT ZONE

Figure A. 1.1 Coordinates for Swarm Equilibrium Calculations

in the CIZ test cell arrangement.

123
Figure A. 1.2 Normalized average electron energy for swarms

in the CIZ test cell arrangement.

124
From figure A. 1.2 the electrons are seen to remain within better than 95%

of their terminal energy values after traveling less than a micron from

the cathode tip (see the R = 0.2 mm curve). In figure A. 1.3, the average

electron energy U(X) is shown as a function of X, for R = 0.2 mm, h = 2 mm,

and P = 100 kPa, and compared with a plot of the field E

Z (X). For X > 0.01,

U(X) follows EZ (X) as expected once thermal equilibrium is attained. These

results are interpreted to provide adequate justification for the use of swarm parameters throughout more than 99% of the ionization region of the

controlled-ionization-zone electrode configuration. This means that the

avalanche calculations and studies of development of ionization discussed

in Sec. II. B. have a reasonable basis for their validity.

125
APPENDIX II.

Inception as an Instability (Electrohydrodynamic Approach)

Electron avalanche growth in and of itself does not account for the sudden

transition to discharge inception and breakdown. Additional processes which

regenerate a continuing supply of avalanches or means to enhance greatly the

gas ionization are needed. In this section, the discharge inception process

is first discussed from a classic streamer point of view and then from a new approach in which general conditions of el ectrohydrody namic events are considered.

The so-called "Raether streamer criterion" evolved from low-pressure measurements

and simple space-charge field analysis. The criterion states that an avalanche

which grows to a size of about 10 8 electrons will cause the formation of a streamer. While this has proven to be a good guide to estimating discharge

inception, it does not provide information about conditions or gases which

would alter the discharge inception values, information about expected variation,

time dependence of the process, etc.

A more general description of the electron avalanche considers the transient

electric field and pressure disturbance as a traveling electrohydrodynamic

(EHD) phenomenon. The formulation describes the time and space evolution of

the avalanche. It allows the study of possible uneven growth and hence for

instabilities in the avalanche process. If such instabilities correspond to

rapid enhanced ionization, they may also correspond to the detailed conditions

of discharge inception. Hence, EHD techniques offer an ability to probe and

search for inhomogeneous phenomena and for conditions and mechanisms of the

sudden, violent, aval anche-streamer transition.

The formalism is to produce the coupled and, in general, nonlinear differential

equations which adequately describe the avalanche. Determining which terms are needed and which may be neglected allows important simplifications to these

equations. The stability of the process is probed by introducing small

variations on desired terms, called "perturbations," then examining the system

of equations to see whether the system is unstable or stable. The mathematical

formalism is rigorous and powerful, but considerable algebra is usually involved.

A further complication arises because the discharge inception which is sought occurs as a superimposed event on an avalanche which is already dynamic in

space and time. In this new approach, then, the Townsend avalanche prior to

the appearance of a streamer is taken as the background equilibrium state

upon which a fast instability develops.

Several relationships are useful in the definition of the problem. They

i ncl ude:

° Charged particle conservat ion,

° Gauss' law and Maxwell's equations,

° Conservation of momentum,

° Conservation of mass.

126
The first two concern the el ectrody namics while the latter two concern the

pressure (i.e., density) dynamics of the neutral gas. In general, the

time scale for pressure waves to move is much longer than the expected

avalanche time scales, so that pressure waves cannot be expected to move

in front of an avalanche. However, pressure variations within and in the

wake of the avalanche front may occur. It would be necessary to evaluate

pressure effects in some examples in order to assess their influence.

This is similar to the problem associated with including the effects of

space-charge on avalanche development.

Typical expressions for the various relations are presented in order to gain

a better appreciation for the problem. The following quantities are used:

p m

= neutral mass density

V = neutral velocity vector

P = gas pressure

Wp = positive ion drift

vel ocity

Ke = electron diffusion

coefficient

3 = first coefficient of viscosity

A = second coefficient of viscosity

K

p = positive ion

diffusion

coefficient

Pp = positive ion charge density

p e

= electron charge density

E = electric field

W

e = electron drift velocity

Considering the case in which the only charged particles are electrons and

single-species positive ions and where electron impact ionization (with

coefficient a-j) is the significant charge generation mechanism, the

relating equations become:

Charged particle conservation:

jjrp e

= K

e

72 »e

- - w e>] +

“il w eK A- 11 - 1

|^p * K

p 72pp + v 'C pp('' " wpU + ai|W e |pe

. A.II.2

Gauss and Maxwell:

’•c 0

E = Pp - pe

A. 1 1.

3

V x E = 0. A. 1 1.

4

127
Conservation of momentum (Navier-Stokes equation):

+ v • Vv) + VP = gv 2 v + (A + le)v(v*v)

m

dt 3

+ (pp - P e

)E • A. 1 1.

5

Note that here the momentum change is driven by the force of the moving

charged particles.

Conservation of Mass:

A perturbation analysis is employed to probe these equations for an instability.

Specifically, the variable quantities such as charge density, ionization

coefficient, and electric field are considered to be composed of two terms:

a base-line or zero-order term which is the regular avalanche growth, and

a small variation or perturbation term, a first-order change.

The motivation for this is to see if the variation will grow faster than

the base avalanche or decay. This technique is very analogous to the method

used to study the well-known Rayl eigh-Tayl or instability in fluid systems.

The perturbation thus results in the following form for electron density:

and similar forms for the other variables of interest. The prime notation

indicates the small perturbation quantity.

By substitution of the two component variables into the governing relations

and by elimination as negligible terms with the product of two or more primed quantities and/or their derivatives, first-order equations for the

perturbation variables can be obtained. The perturbation dynamics can then

be studied by first seeing if the perturbation grows or decays in time or

space. If growth can take place, there is a possibility for instability

and the equations are further solved for the conditions to obtain the

instability. A useful technique is to assume the perturbation quantity is

a complex exponential in form. While this means that the perturbation is

of single wavelength, it can be varied and by Fourier series, in principle,

any shape can be constructed if necessary. As an example, when perturbations

are created in the y-direction for a system which has only zero-order

x-directed variations, the electron density would take the form:

A. 1 1.

6

p e (x,y,z,t) = p e (x,y,z,t) + Pe(x,y,z,t)

o

A. II.

7

p e (x,y,z,t) = p e ( x ,

t

) + Pe(x,y,t)

o A. 1 1.

8

= Pe (x,t) + R e (p

e (x)e( st “

J

' ky

)}

128
where p e

is the complex amplitude of the p e perturbati on.

The above substitution produces an n^-order differential equation in s called the "characteri st ic" equation. The value of n depends on what

processes are kept in the avalanche equations. If the equation has positive

real roots, the perturbation is an expanding instability. Thus, the problem

has been reduced to the study of the characteri stic equation.

While stability analysis is not unique to avalanching, what is proposed

here is significant for two reasons:

1) Stability analysis can be applied to a non-stationary

system where normal avalanche growth is taken as the

background;

2) The avalanche is treated in general as an EHD event, and

relevant terms may be kept as needed, according to the

situation.

This new approach to the study of discharge inception could be very powerful.

In principle, it could show not only that instabilities can occur, but also

give the specific conditions required for onset. It is proposed that studies

using this approach be continued and that typical examples be worked out.

One- or two-dimensional problems could be investigated first because they

should be simpler and would allow examination of a wider range of effects.

Then, with the experience of the simpler system, 3-D problems can be undertaken.

129
APPENDIX III.

The computer program used to calculate average maximum avalanche sizes in

terms of number of electrons for one starting electron in SFg is listed

here, together with a sample of the output printout. The program is written

in BASIC. It applies in its present form only to SFg in a point-plane gap

in which the point has the shape of a hyperboloid of revolution. In order

to apply this to another gas, one has to insert an analytical expression

for the difference between the ionization and attachment coefficients

( ai-na ) into lines 411-425 and lines 232-235. Use of the program requires

the following input: 1) the critical f iel d-to-pressure ratio v/h ere n a = a-j in units of V cm

-1 torr -1

, 2) the absolute gas pressure in kPa, 3) the

starting gap voltage, 4) the voltage increment, 5) the number of points

(voltages) desired, 6) the characteristic angle (n 0 ) of the hyperboloid in

radians, 7) the focal length of the hyperboloid in centimeters, and 8) the

poi nt-to-pl ane gap spacing in centimeters.

The output as indicated in the sample printout gives the value of the integral

given in eq (27) of the text and the corresponding value of n e (called

EXP in the printout) for each voltage requested. From a plot^of n e versus voltages one can determine the voltage at which n e attains some

critical value correspond!' ng to corona inception.

In the program listing that follows, the © sign means exponentiation (**).

130
LIST

10 DIM US(1)

12 N7=0

15 Y=0

20 ; "CRITICAL E/P"

30 INPUT El

40 ; "PRESSURE .IN KPA"

41 INPUT P 42 P=P*7.6

43 E1=E1*P

50 ; "INITIAL VOLTAGE IN KV"

51 INPUT VO

52 V0=V0*1000

60 ; "YOLTAGE INCREMENT IN VOLTS"

61 INPUT D

62 ; “NUMBER OF PTS"

63 INPUT M5

64 IF N7=0 GOTO 70

65 ; "IS ELECTRODE GAP UNCHANGED ?(Y OR N)“

66 INPUT U$

67 IF U$="Y " GOTO 120

70 ; “INFORMATION ON ELECTRODE GEOMETRY"

71 ; "FOR HYPERBOLOID PT. ELECTRODE"

72 ; “ANGLE IN RADIANS"

73 INPUT EO

74 ; “FOCAL LENGTH IN CM*"

75 INPUT F

80 ; “GAP SPACING IN CM."

81 INPUT DO

82 IF F>DO GOTO 90

83 D0=D0-.1E-4*F

90 A=COS (EO)

. 95 M=10

98 N 1=1

100 U=(A+1 )/( 1-A)

110 T=.5*L0G(U

)

111 ; "EXAMINE FIELD AND FUNC. (Y OR N)“

112 INPUT U$

115 IF U$="Y“ GOTO 700

120 Q=F*T*(1-(D0/F)®2

)

130 E=VO/Q

143 ; "PRINT DIAGNOSTICS ? {Y OR N)"

144 INPUT U$

145 IF U$="N" GOTO 150

146 PRINT E/P.Nl

150 IF E>E1 GOTO 210

160 VO=VO+D - 170 N1=N1+1

131
180 IF Nl>500 GOTO 635

200 GOTO 130

210 B=DO

215 N 2=1

220 C=1-V0/(E1*F*T)

225 IF C<0 GOTO 637

230 A=F*SQR (C

)

232 E5=P*250

233 C=l-VO/( E5*F*T

)

234 IF C<0 GOTO 637

235 A1=F*SQR(C)

236 IF U$="N" GOTO 240

237 PRINT D0-B,D0-A,D0-A1

240 T5=F*T

250 U5=V0/P

251 IF N2>1 GOTO 310

300 ; "FOR SF6 ONLY"

301 ; "FOR NEW GAS CHANGE LINES 411-425"

302 ALSO CHANGE EXPRESSION FOR LIMIT A1 , LINES 232-235"

305 K9=0

310 Y1=0

320 ; "NUMERICAL INTEGRATION"

370 N=40

375 IF U$="N" GOTO 381

380 PRINT Y,N

381 K=1

382 IF K 9=1 GOTO 391

383 IF A1>D0 GOTO 386

384 B9=A1

385 GOTO 387

386 B9=D0

387 A9=A

389 N9=N

390 GOTO 398

391 IF A1>D0 GOTO 619

392 B9=D0

393 A9=A1

394 N9=2*N

398 Z=0

399 H=(B9-A9 )/N9

400 X=A9

405 M=N9+1

410 FOR J=1 TO M

411 Q6=T5*(1- (X/F)®2

)

412 U=U5/Q6

414 IF X>A1 GOTO 421

415 Y=1 .66508-. 62 1827E-1*U

416 U1=D®2

132
417 Y=Y+.530589E-3*U1

418 U1=U*U1

419 Y=Y-. 100829E-5*U1

420 GOTO 426

421 Y=-l .74312+. 269375E-1*U

422 U1=U*U

423 Y=Y-.249789E-4*U1

424 U1=U1*U

425 Y=Y+. 91 3096E -8*1)1

426 IF Y>0 GOTO 430

4.97 ."•*-****"

428 Y=0

430 IF J=1 OR J=M GOTO 500

440 IF K=0 GOTO 530

450 K=0

460 Z=4*Y+Z

470 GOTO 600

500 Z=Z+Y

520 GOTO 600

530 Z=Z+2*Y

540 K=1

600 X=X+H

610 NEXT J

611 Y-(Z*H )/3

612 IF A1>D0 GOTO 619

614 IF K9=l GOTO 618

615 K9=l

616 Y9=Y

617 GOTO 381

618 Y=Y+Y9

619 Y7-Y*P

620 Z=(Y-Y1)/Y

621 Y1=Y

622 Zl sABS (Z)

623 N=N+2

624 IF ZK.5E-2 GOTO 628

625 IF N>42 GOTO 627

626 GOTO 375

627 ERROR > 0.5% 18 628 -/INTEGRAL =\Y7/EXP ^\EXP(Y7)

629 ; "YOLTAGE =",V0

630 IF N2=M5 GOTO 640

631 N2=N2+1

632 VO=VO+D

634 GOTO 220

635 ERROR 2"

636 GOTO 640

637 ; "ERROR 3"

133
640 GOTO 900

700 ; "FUNC ? (Y OR N)"

701 INPUT U$

702 IF US="N" GOTO 806

703 ; "INITIAL E/P"

710 INPUT U1

720 ; "FINAL E/P"

730 INPUT U2

740 U7= (U2-U1 )/50

750 ; "FUNC. OUTPUT , E/P , FUNC"

755 U=U1

760 FOR J=1 TO 50

770 IF U>250 GOTO 790

771 Y=1.66508-.621827E-1*U

772 U3=U®2

773 Y=Y+.530589E-3*U3

774 U3=U3*U

775 Y=Y-.100829E-5*U3

776 GOTO 800

790 Y=-l . 74312+.269375E-1*U

791 U3=U®2

792 Y=Y-.249789E-4*U3

793 U3=U3*U

794 Y=Y+.913096E-8*U3

800 PRINT U,Y

801 U=U+U7

805 NEXT J

806 ; "FIELD ? (Y OR N)

w 807 INPUT US

808 IF US="N" GOTO 880

810 ; "INITIAL DISTANCE"

812 INPUT XO

815 ; "FINAL DISTANCE"

817 INPUT XI

818 X2=(Xl-XQ)/50

820 ; "OUTPUT - E/P, E, X"

830 X=XO

835 FOR J=1 TO 50

840 E=V0/(F*T*(1-(X/F)®2)

)

845 U=E/P

850 PRINT U ,E,X

855 X=X+X2

860 NEXT J

870 ; "TERMINATE RUN ? (Y OR N)"

871 INPUT US

872 IF U$="Y " GOTO 950

880 GOTO 111

900 ; "MORE DATA ?(Y OR N)"

134
910 INPUT US

920 IF U$="N" GOTO 950

930 N 7=1

940 GOTO 15

950 END

BASIC 03-04

135
RUN

CRITICAL E/P

117

PRESSURE IN KPA

100

INITIAL VOLTAGE IN KV

8.2

VOLTAGE INCREMENT IN VOLTS

200

NUMBER OF PTS

5

INFORMATION ON ELECTRODE GEOMETRY

FOR HYPERBOLOID PT. ELECTRODE

ANGLE IN RADIANS

.0269

FOCAL LENGTH IN CM.

2.28007

GAP SPACING IN CM.

2.278

EXAMINE FIELD AND FUNC. (Y OR N)

N

PRINT DIAGNOSTICS ? (Y OR N)

N

FOR SF6 ONLY

FOR NEW GAS CHANGE LINES 411-425

ALSO CHANGE EXPRESSION

NUMERICAL INTEGRATION

FOR LIMIT Al, LINES 232-235

INTEGRAL = 17.538

VOLTAGE = 8200

NUMERICAL INTEGRATION

EXP = .413663E8

INTEGRAL = 18.1719

VOLTAGE = 8400

NUMERICAL INTEGRATION

EXP = .77979E8

INTEGRAL = 18.6725

VOLTAGE = 8600

NUMERICAL INTEGRATION

EXP = .12864E9

INTEGRAL = 19.3159

VOLTAGE = 8800

NUMERICAL INTEGRATION

EXP = .244776E9

INTEGRAL = 19.8195

VOLTAGE = 9000

MORE DATA ?(Y OR N)

NBASIC 03-04

EXP = .405048E9

136
APPENDIX IV.

Given here is a listing of the BASIC computer program used to

calculate corona initiation volumes according to the prescription

given in the text by Eq. (33). The restrictions that apply are the same as for the program described in Appendix III. The input

information requested is also nearly the same, with the exception

that the critical value for E/p is here assumed to be that for SF5

and one must indicate a critical electron avalanche size, e.g.,

1 x 10 8 electrons.

The output, an example of which is shown, gives the x-y coordinates

in centimeters of the boundaries of a cross section of the

initiation volume in a plane containing the electrode axis, and

also gives the calculated volume in cubic centimeters for each

voltage requested.

137
LIST

10 DIM US(1)

20 DIM X(100) ,C(100) ,S(100) ,U(100)

25 DIM Y (100) , A ( 1 00 ), B ( 1 00

)

26 DIM A1(3,3),B1(3,1),C1(3,1),D1(3,3),E1(3,1),F1(3,1)

27 ; "PRINT DIAGNOSTICS ?(Y OR N)"

28 INPUT U$

30 E 1=1 17

40 ; "PRESSURE IN KPA"

41 INPUT P 42 P=P*7 .6

43 E1=E1*P

50 ; "INITIAL VOLTAGE IN KV"

51 INPUT VO

52 Y0=V0*10OO

60 ; "VOLTAGE INCREMENT IN VOLTS"

61 INPUT D

62 ; "NUMBER OF PTS"

63 INPUT M5

70 ; "INFORMATION ON ELECTRODE GEOMETRY"

71 ; "FOR HYPERBOLOID PT. ELECTRODE"

72 ; "ANGLE IN RADIANS"

73 INPUT EO

74 ; "FOCAL LENGTH IN CM."

75 INPUT F

80 ; "MIN. AVALANCHE SIZE (NO. OF ELECTRONS)"

90 INPUT N

91 K=LOG(N)

100 REM - ANGLE INCREMENT = D1

120 N4=l

190 A=C0S (EO)

191 U=(A+1 )/(l-A)

192 T=.5*L0G (U

)

200 C(l)=l

210 S(1)=0

215 D1-.2E-1

220 X2=F*A

230 Q=1-V0/(E1*F*T)

240 IF Q<0 GOTO 1060

250 X1=F*SQR(Q

)

252 IF X1<X2 GOTO 260

253 VO=VO+D

254 GOTO 230

260 E5=P*250

270 Q=1-V0/(E5*F*T)

280 IF Q<0 GOTO 1060

290 X3=F*SQR(Q

)

292 U ( 1 )=X3

138
295 C6=C(1)

300 GOSUB 1100

301 IF U$="N" GOTO 310

302 PRINT "K=" ,K1

310 IF K1>K GOTO 340

320 VO=VO+D

330 GOTO 230

340 PRINT "VOLTAGE = \Y0

350 X(1)=X1

360 Y(1)=0

365 IF U$="N" GOTO 370

366 PRINT -X1--.X1/X2--.X2 "X3--.X3

370 PRINT " XI “ Y1

385 2=0

390 Nl=2

394 M8=0

395 M7=0

400 Z=Z+D1

410 E=EXP(Z)

420 E9=EXP ( -Z)

430 C(Nl)=(E+E9)/2

440 S(Nl)=(E“E9)/2

441 IF U$="N U GOTO 450

445 PRINT "ANGLE=",Z, COSH= ,C(N1) . 450 E=(F*C(N1) )®2

460 A1=1/(E©2)

470 B1*(C(N1)®2+1)/E

480 C1=C(N1 )®2»(V0/(E1*T*F) )®2

490 E=B1®2“4*A1*C1

500 IF E<0 GOTO 1060

510 E9=SQR(E)

520 E=(B1-E9)/(2*A1)

530 IF E<0 GOTO 1060

540 X(N1)=SQR(E)

550 X1=X(N1)

560 X2=F*A*C(N1

)

570 C1=C(N1)®2°(V0/(E5*T*F))®2

580 E=B1®2-4*A1*C1

590 IF E<0 GOTO 1060

600 E9=SQR(E)

610 E=(B1-E9)/(2*A1)

620 IF E<0 GOTO 1060

630 X3=SQR(E)

631 IF U$="N" GOTO 635

632 PRINT "X1=",X1,”X2=\X2,''X3= ,X3

635 U(N1)=X3

640 C6=C(N1)

650 GOSUB 1100
651 IF U$="N" GOTO 658

652 PRINT "K=",K1

658 IF K1>K GOTO 667

660 M7=M7+1

661 M8=l

662 Z=Z-D1

663 Dl=Dl/2

664 N1=N1-1

665 IF M7>3 GOTO 705

666 GOTO 671

667 IF M8=0 GOTO 671

668 Dl=Dl/2

669 M7=M7+1

670 IF M7>3 GOTO 705

671 N1=N1+1

680 IF N1 >100 GOTO 1040

690 GOTO 400

705 FOR N2=l TO N1

710 N3=0

730 X2=F*A*C(N2)

740 X3=U(N2)

750 D5=(X2-X(N2) )/2

760 X1=X(N2)+D5

770 C6=C(N2)

780 N3=N3+1

790 GOSUB 1100

795 IF U$="N" GOTO 800

796 PRINT N3,K1,X1

800 IF N3>20 GOTO 910

810 E9=K-K1

820 E=ABS(E9)

830 E9=E/K

840 IF E9<.1E-1 GOTO 920

850 D5=D5/2

860 IF K1>K GOTO 890

870 X1=X1-D5

880 GOTO 780

890 X1=X1+D5

900 GOTO 780

910 IF U$="N" GOTO 920

911 PRINT "ERROR>ir

920 E=l- (X (N2)®2 ) /( F*C(N2) )©2

930 IF E<0 GOTO 1060

940 Y1=F*S(N2)*SQR(E

)

950 E=l- (Xl®2 )/( F*C(N2) )©2

960 IF E<0 GOTO 1060

970 Y2=F*S(N2)*SQR(E

)

980 PRINT X(N2) ,Y1 ,X1,Y2
981 Y ( N 2

) =Y

1

982 A(N2)=X1

983 B(N2)=Y2

990 NEXT N2

995 GOSUB 1705

1000 N4=N4+1

1010 IF N4>M5 GOTO 1070

1020 V0=V0+D

1030 GOTO 200

1040 ; "ERROR-EXCEEDED ARRAY SIZE"

1050 GOTO 1070

1060 ; "SQR-NEG.ARG."

1070 GOTO 2300

1100 K9=0

1105 U5=V0/P

1110 U5aU5/{F*T)

1111 Q=F*C6

1115 N-30

1120 K4=l

1130 IF K9S1 GOTO 1210

1140 IF X3>X2 GOTO 1170

1150 B9-X3

1160 GOTO 1180

1170 B9=X2

1180 A9=X1

1190 N9=N

1200 GOTO 1250

1210 IF X3>X2 GOTO 1619

1220 B9=X2

1230 A9=X3

1240 N9=2*N

1250 Z1=0

1260 H=(B9-A9)/N9

1270 X=A9

1280 MSN9+1

1290 FOR J=1 TO M

1295 W=(X/Q )®2

1300 E=C6®2”W

1310 IF E<0 GOTO 1640

1320 E9=SQR(E

)

1330 E=l-W

1340 IF E<0 GOTO 1640

1350 E9=E9*SQR(E)

1360 U=U5/E9

1370 E=(C6®2-W)/(1-W)

1380 IF E<0 GOTO 1640

1390 L=SQR(E)/C6

1400 IF X>=X3 GOTO 1421

141
1415 Y=1.66508- .621827E-1*U

1416 U1=U®2

1417 Y=Y+. 530589E-3*U1

1418 U1=U*U1

1419 Y=Y-.100829E-5*U1

1420 GOTO 1426

1421 Y=-1.74312+.269375E-1*U

1422 ui=unj

1423 Y=Y-.249789E-4*U1

1424 U1=U1*U

1425 Y=Y+.913096E-8*U1

1426 IF Y>0 GOTO 1430

1427 •" ******"

1428 Y=0

1430 Y=Y*L

1431 IF J=1 OR J=M GOTO 1500

1440 IF K4=0 GOTO 1530

1450 K4=Q

1460 Z1=4*Y+Z1

1470 GOTO 1600

1500 Z1=Z1+Y

1520 GOTO 1600

1530 Z1=Z1+2*Y

1540 K4=l

1600 X=X+H

1610 NEXT J

1611 Y=(Zl*H)/3

1612 IF X3>X2 GOTO 1619

1614 IF K 9=1 GOTO 1618

1615 K9=l

1616 Y9=Y

1617 GOTO 1120

1618 Y=Y+Y9

1619 K1=Y*P

1630 GOTO 1650

1640 PRINT "ERROR-NEG SQR ARG”

1650 RETURN

1705 R1=0

1710 R2=0

1715 R3=0

1720 R4=0

1725 S1=0

1730 S2=0

1735 S3=0

1740 FOR Wl=l TO N1

1745 R1=R1+Y ( W1 )®2

1750 NEXT W1

1755 A1 ( 1 ,2 )=R1

142
1760 A1 (2 , 1 )=R1

1765 FOR W2 =1 TO N1

1770 R2=R2+Y (W2)®4

1775 NEXT W2

1780 A1 (1,3 )=R2

1785 A1(2,2)=R2

1790 A1(3,1)=R2

1795 FOR W3=l TO N1

1800 R3=R3+Y(W3 )®6

1805 NEXT W3

1810 A1 (2 ,3)=R3

1815 A1(3,2)=R3

1820 FOR W4=l TO N1

1825 R4=R4+Y (W4 )®8

1830 NEXT W4

1835 A1 (3,3 )=R4

1837 Al(l ,1 )=N1

1840 FOR W5=l TO N1

1845 S1=S1+X(W5)

1850 NEXT W5

1855 C1(1,1)=S1

1860 FOR W6=l TO N1

1865 S2=S2+(Y(W6)®2)*X(W6)

1870 NEXT W6

1875 Cl(2,l) sS2

1880 FOR W7=l TO N1

1885 S3=S3+(Y(W7)©4)*X(W7)

1890 NEXT W7

1895 C1(3,1) := S3

1900 MAT A1=INV(A1)

1901 IF U$ S "N" GOTO 1915

1905 ; "INVERSE MATRIX Al"

1910 MAT PRINT Al

1915 MAT B1=A1*C1

1920 IF U$= "N" GOTO 1935

1925 ; "LEAST SQR FIT COEFF, OUTER BD"

1930 MAT PRINT B1

1935 R1=0

1940 R2=0

1945 R3=0

1950 R4=0

1955 S1=0

1960 S2=0

1965 S3=0

1970 FOR Fl=l TO N1

1975 R1=R1+B(F1)®2

1980 NEXT FI

1985 Dl(l ,2 )=R1

143
1990 D1 (2 ,1 )=R1

1995 FOR F2= 1 TO N1

2000 R2=R2+B(F2)©4

2005 NEXT F2

2010 D 1 ( 1 ,3 )=R2

2015 D1 (2 ,2 )=R2

2020 D1(3,1)=R2

2025 FOR F3=l TO N1

2030 R3=R3+B (F3 )®6

2035 NEXT F3

.

2040 D1 (2 ,3 )=R3

2045 D1 (3 ,2 )=R3

2050 FOR F4=l TO N1

2055 R4=R4+B(F4)©8

2060 NEXT F4

2065 D1(3,3)=R4

2070 D 1 ( 1 ,1 )=N1

2075 FOR F 5= 1 TO N1

2080 S1=S1+A(F5

)

2085 NEXT F5

2090 FI (1 ,1 )=S1

2091 FOR F6=l TO N1

2092 S2=S2+(B(F6)©2)*A(F6)

2106 NEXT F6

2110 F1(2,1)=S2

2115 FOR F7=l TO N1

2120 S3=S3+(B(F7 )©4 )*A(F7

)

2125 NEXT F7

2130 FI ( 3 , 1

) =S3

2135 MAT D1=INV(D1

)

2136 IF U$="N" GOTO 2150

2140 ; "INVERSE MATRIX Dl"

2145 MAT PRINT Dl

2150 MAT E1=D1*F1

2151 IF U$="N" GOTO 2165

2152 -/'LEAST SQR FIT COEFF, INNER BD"

2155 MAT PRINT El

2160 REM - VOLUME DETERMINATION

2165 L5=(El(l,l)-Bl(l,l))*(Y(Nl)®2)/2

2170 L6=(El(2,l)-Bl(2,l))*(Y(Nl)©4)/4

2175 L7=(El(3,l)-Bl(3,l))*(Y(Nl)®6)/6

2180 L8=6 .283*(L5+L6+L7

)

2185 /'VOLUME =",L8

2190 RETURN

2300 END

BASIC 03-04

144
RUN

PRINT DIAGNOSTICS ?(Y OR N)

N

PRESSURE IN KPA

100

INITIAL VOLTAGE IN KV

7

VOLTAGE INCREMENT IN VOLTS

1000

NUMBER OF PTS

2

INFORMATION ON ELECTRODE GEOMETRY

FOR HYPERBOLOID PT. ELECTRODE

ANGLE IN RADIANS

.0404044

FOCAL LENGTH IN CM.

1.251

MIN. AVALANCHE

1E+8

VOLTAGE =

: SIZE (NO.

7000

OF ELECTRONS)

XI Y1 X2 Y2

1.24087 0 1.24571 0

1.24128 .315237E-2 1.24604 .228213E-2

1.24235 .620399E-2 1.24707 .443846E-2

1.24421 .900533E-2 1.24872 .638018E-2

1.24671 .115021E-1 1.25034 .862641E-2

1.24978 .136459E-1 1.2522 .112282E-1

1.25154 .145615E-1 1.25304 .129171E-1

1.25201

VOLUME = VOLTAGE

•

s

.147582E-1

.348314E-5

8000

1.25275 .139521E-1

XI Y1 X2 Y2

1.2 3942 0 1.24635 0

1.2398 .337668E-2 1.24673 .212554E-2

1.2409 .665243E-2 1.24775 .412165E-2

1.24275 •970154E-2 1.24927 .598381E-2

1.24526 .124623E-1 1.25126 .77391 IE—

2

1.24837 .148765E-1 1.25353 .964407E-2

1.25208 .168658E-1 1.25629 . 115665E —1

1.25629 .18455E-1 1.25908 .143083E-1

1.25857 . 191103E—

1

1.26063 . 158156E-1

1.25975 .194 025E-1 - 1.26107 . 172591 E-l

1.26034

VOLUME = BASIC 03-04

.195602E-1

.109686E-4

1.26099 .18515E-1

145

NBS-114A (REV. 9-781

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO. NBSIR 82-2555

2. Gov't. Accession No. 3. Recipient' s Accession No.

IS:

4. TITLE AND SUBTITLE

1981 ANNUAL REPORT: TECHNICAL ASSISTANCE FOR FUTURE

INSULATION SYSTEMS RESEARCH

5. Publication Date November 1982

6. Performing Organization Code

7‘ authoR'S*

j. y an Brunt, M. Misakian, D. A. Leep, E. C. Beat

J. W. Gallagher, C. M. Cooke, K. W.yatt, R. G. Gels

8. Performing Organ. Report No. y.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, DC 20234

10. Project/Task/Work Unit No.

11. Contract/Grant No.

12. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street, City, state, ZIP)

U.S. Department of Energy

Office of Electric Energy Systems

Washington, D.C. 20585

13. Type of Report & Period Covered Annual Report FY81

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

PI Document describes a computer program; S F- 185, FIPS Software Summary, is attached.

literature survey, mention it here.) A system for measuring'the electrical properties of corona pulses

has been characterized and is discussed. Additional data on the pulse height distributions of positive and negative corona pulses

In pure SF5 for point-plane electrode geometries are presented.

Basic mechanisms for initiation of electric discharges in SFg for highly nonuniform fields nave been investigated in a collaborative

effort between NBS and the High Voltage Research Laboratory of the Massachusetts Institute of Technology. Effects of radiation, electrode geometry, and polarity on corona inception in SFg have been measured. Corona Inception voltages and discharge Initiation

volumes have been calculated using the streamer criterion. Limitations of the streamer criterion as applmito SFg in highly nonuniform fields artdiscussed.

namely that for SFg. Using a gas-chromatograph/mass spectrometer,

absolute concentrations of SOFj and SO2F2 and relative concentrations

of H2O in SFg have been measured as a function of total energy dissipated in corona discharges operated at power levels between

50 and 700 mW. The observed production rates for SOF2 and SO2F2 appear to be proportional to power level, and the ratio of SO2F2

to SOF2 concentrations for corona is considerably higher than that typically observed for arc discharges in SFg.

The statistics of electron avalanche growth In SFg have been measured and compared with results of theory. While the avalanche

pulses, on average, followed expected theoretical behavior, the

distribution was not found to be regular or to follow a simple stochastic theory. A thorough compilation and survey of electron

swarm data for electronegative gases used, and proposed for use, as components of gaseous dielectrics was completed. The parameters

considered Include: electron drift velocity, attachment coefficient. Ionization coefficient, electron growth constant, diffusion coefficient, detachment coefficient, and characteristic energy. These are quantities needed for prediction of breakdown and model ing of gas discharges. Some of the important gases included in this study

are: O2, CO2, SFg, H2O, air, nitrogen oxides, halogens, and various halogenated hydrocarbons, e. g. , CF4, CgFg, C3F8, C4F10,

CC1 2 F2. CC1 F3 , C-C4F8, c-C5 F8 , CH3Br, CH2CI3, CHCI3, etc. In this report we include only an example of the data collected.

Estimates have been performed to determine the sensitivity of a technique to detect polar gas contaminants in gaseous SFg using an accurate ppm measurement of changes in the low frequency (dc) dielectric constant of the gas. Measurements have been performed

of optogalvanic spectra from glow discharges in Ne, N2 and mixtures

of these with SFg. The effect of SFg in quenching metastables in these gases is discussed.

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name;

separated by semicolons) corona discharges; decomposition; electronegative gases; electron avalanches;

--I..,. ’’ electron swarm data; optogalvanic spectra; oxyfluorides; SFg; sulfur hexafluoride

water vapor.

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