NBSIR 74-564

Development and Analysis of

Techniques for Calibration of Kerr Cell

Pulse-Voltage Measuring Systems YIN

Robert E. Hebner, Jr., Esther Christmas Cassidy

and Richard J. Sojka

Electricity Division

Institute for Basic Standards

National Bureau of Standards

Washington, D. C. 20234 \

August 21, 1974

Final Report on

Sandia Corporation Order No. FAO 28-0990

Sandia Requester and Technical Consultant: S. R. Booker, Org. 9532

Sandia Contracting Representative: John G. Boyes, Org. 4361

Prepared for Sandia Corporation

BIdg. 894, Kirtland AFB

East Albuquerque, New Mexico 87115

NBSIR 74-564

DEVELOPMENT AND ANALYSIS OF

TECHNIQUES FOR CALIBRATION OF KERR CELL

PULSE-VOLTAGE MEASURING SYSTEMS VIII

Robert E. Hebner, Jr., Esther Christmas Cassidy

and Richard J. Sojka

Electricity Division

Institute for Basic Standards

National Bureau of Standards

Washington, D. C. 20234

August 21, 1974

Final Report on

Sandia Corporation Order No. FAO 28-0990

Sandia Requester and Technical Consultant: S. R. Booker, Org. 9532

Sandia Contracting Representative: John G. Boyes, Org. 4361

Prepared for Sandia Corporation

Bldg. 894, Kirtland AFB

East Albuquerque, Nev/ Mexico 87115

U. S. DEPARTMENT OF COMMERCE, Frederick B. Dent, Secretary

NATIONAL BUREAU OF STANDARDS, Richard W. Roberts. Director
. . : , TABLE OF CONTENTS

I. INTRODUCTION 1

II. CALIBRATION OF PULSE VOLTAGE ^^EA£ j REMENT SYSTEMS BASED

ON THE ELECTRO-OPTIC KERR EFFECT.. 5

III. KERR COEFFICIENT DETERMINATIONS 10

A) . Int reduction 10

B) . Measurements in Halowax Oil 15

C) . Temperature Dependence of the Kerr

Coefficient of Nitrobenzene 22

:- D). Kerr Coefficient of Water 2h

IV. ELECTRIC FIELD DISTRIBUTIONS AND SPACE CHARGE BEHAVIOR IN

NITROBENZENE UNDER LOW FREQUENCY ALTERNATING VOLTAGE ,. 28

A) . Introduction 28

B) . Experimental Results 29

C) . Discussion 3^

D) . Conclusions 3^

APPENDIX A: KERR EFFECT STUDIES OF AN INSULATING

LIQUID UNDER VARIED HIGH-VOLTAGE CONDITIONS 36

REFERENCES 51
I. Introduction

This report documents recent progress in the refinement of

techniques for the accurate calibration of pulsed voltage measurement

systems based on the electro-optic Kerr effect. Previous results,

and this year's work, can be categorized into four main areas. The,,

first area, and the primary reason for this project, is the calibration

of pulsed-voltage measurement systems. Historically the Kevx system has

been used as an adjunct to a conventional resistive divider to measure

the high voltage pulse which was applied to the system under test. The

rationale for this was that the sources of error in Kerr measurements

are different from those in divider measurements. Thus if the values

obtained by the two^ methods agreed to within their combined uncertainties,

it is unlikely that there is significant error in either. Such a dual

system is, in this respect, self-checking thereby minimizing the effects

of operator error. Experience with Kerr systems used in this manner has

demonstrated the long term stability of the calibration. More recent

work has focused on the use of a Kerr system for inter-laboratory

transfer of calibration.

To gain an appreciation of the utility of a Kerr system both as an adjunct to a conventional system and as a transportable system for in situ

calibration of conventional systems, it is helpful first to examine

the difficulties that have been identified in conventional measurements.

The various sources of divider errors are included in the following

list-"-'^:

1. Residual inductance in any resistance or capacitance element.

2. Stray capacitance - (A) from any section of the divider to

ground or a grounded object, (B) from any section of the divider

to high voltage parts of the supply and test circuit, and

(C) between sections of the divider.

3. Impedance drop in the lead from the point at which the high

voltage is to be measured to the high voltage end of the

divider.

4. Impedance drop in the ground return lead from the divider due

to either extraneous ground currents flowing in this lead or

to the divider current.

5. Oscillations set up in the divider circuit caused by capacitance

from the divider high voltage terminal to ground and lead

inductance.

Although the first source of error is intrinsic to the divider,

the other four error sources depend to some extent upon the arrangement

of the experimental apparatus. The calibration of a divider in one laboratory for use in another is of value only for the identification

of intrinsic faults of the divider but does little to verify accurate

measurement, A Kerr system, being much less susceptible to stray

capacitance and ground current errors, is an attractive device for

1
in situ calibrations of resistive and c^rpacitive dividers. In Section II

of this report, the calibration of Kerr systems is discussed with

emphasis on the transportability and long-term stability of the

calibration.

There is one important facet of calibration of Kerr systems that

requires additional work. Present practice is to calibrate cells

against a carefully constructed resistive divider which has an estimated uncertainty of ±1%. Because the relative permittivity of

nitrobenzene is approximately independent of frequency over the

frequency range from 0-10 Hz, it has been postulated that the Kerr

response should also be independent of the frequency of the applied voltage

over this same range. If this be the case, it would then be possible

to calibrate a cell at a single frequency at full operating voltage.

The significance of a single frequency calibration of a Kerr system

can be seen from the following brief review of current practice for the

calibration of pulse measurement systems not using the electro-optic

Kerr effect.

In addition to the Kerr systems described in this report, there

are two other techniques for measuring pulsed high voltage. These are

the use of a carefully constructed divider to provide a lower voltage

pulse for measurement using an oscilloscope or other appropriate

measuring device and the use of the breakdown of a sphere gap.

Traceability to basic standards is maintained through the divideroscilloscope system of measurement, while the sphere gap is used to

insure consistency among various laboratories throughout the world.

The present measurement techniques permit best estimates of the measurement uncertainty of ±1% for voltage pulses having a peak value of less

than one million volts and a risetime longer than about 1 ys. Typical

uncertainties for this type of voltage pulse are ±3%. These uncertainty

estimates rapidly become larger for higher voltage levels and/or shorter

risetimes. The accepted procedure for calibration of resistive dividers

is to measure both the resistance ratio and the response of the divider

to a step voltage at low voltage in a system designed so that there is no significant voltage dependence of any component.

Against this background the significance of a single frequency

calibration can be evaluated. If a Kerr system can be calibrated at a single frequency or a number of discrete frequencies and if it can be

verified that this calibration is frequency independent over a sufficiently wide range, it will then be possible to measure pulsed high

voltage using a method which is independent of previous high voltage pulse

measurements. In addition to being independent, this approach shows

promise of being more accurate than previous measurement techniques.

The basis for the expectation of more acurate measurements is that,

at a number of discrete frequencies, it may be possible to measure

more accurately the voltage applied to the cell. At a single, low

frequency (below about 5 kHz), dividers are routinely constructed with

division ratios having uncertainties of order ±0.1% and can be constructed

with uncertainties as low as 0.001%. In addition the rms value of the

2
applied voltage can be determined with an uncertainty of order 0.01%.

Assuming that it is possible to devise a sufficiently stable voltage

source and detection system that will provide a measurement of the

waveshape of a single half cycle of the applied voltage, it may be

possible to compare the Kerr system response to a device possessing a measurement uncertainty of only ±0.1%.

Previous work has addressed itself to calibration under direct

voltage and low frequency (less than 150 Hz) alternating voltage

of nitrobenzene-filled Kerr cells. Calibrations under direct voltage

have been performed which agree with calibrations using a divideroscilloscope voltage measurement system to within the uncertainty

of the conventional system, i.e., to within ±1%. Electric field

distortion due to space charge in the liquid discourages more precise

comparison. This report contains a discussion of the frequency

dependence of the space charge dynamics in the liquid and of

measurements using a Halowax oil-filled Kerr cell under direct,

60 Hz and pulsed high voltage. It was decided to use Halowax oil

because it should not be as sensitive to the effects of impurities

as nitrobenzene. Calibrations under these three different types

of waveform disagreed by about ±1% of the average.

The second area into which the Kerr effect work can be categorized

is the measurement of the spatial and temporal behavior of the electric

field. The work is a spin-off from and serves as the basis ^og the

attempt at a single frequency calibration. Previous reports ' have

documented the measurement of the electric field distribution which is

attributable to the geometry of the cell. Appendix A of this report

contains a reprint of a journal article which summarizes the work at

NBS directed toward the measurement of electric field distributions

under direct and low frequency alternating voltage.

The third broad class of Kerr effect work deals with the development

of instrumentation based on the use of the electro-optic Kerr effect

for pulsed voltage measurements. In last year's report, NBS IR 73-403,

a measurement system based on the concept of counting the output pulses

from the Kerr system was presented. Tests of the system were described

which indicated its attainable accuracy.

In this year's report the test of a system developed by Sandia

Laboratories is discussed. The precision, accuracy and operating

characteristics are presented. In addition a novel system for more

accurate measurement of the phase shift when direct voltage is applied

to the cell is presented. Having determined its operating characteristics

refinements are being made and an improved system will be developed

during the coming fiscal year.

The final class of Kerr effect work is the determination of the

Kerr coefficients of various materials. There are three reasons for

the significance of this work. One is that accurate values of the Kerr

coefficient permit accurate voltage measurements in situations in which
calibrations of the Kerr system is impractical; the cell constant is

computed from the geometry of the cell and the Kerr coefficient.

Second, accurate values of the Kerr coefficient are necessary so that

Kerr systems with predictable response can be designed and constructed.

The final reason for the measurement of the Kerr coefficient of

various liquids is to provide a check on the accuracy of the measurement

system employed. The Kerr coefficient is given approximately by

the expression

cp = 2n Bi' V^/d^ , (1)

where cp is the phase shift between orthogonally polarized components

of the light beam, B is the Kerr coefficient, V is the applied voltage,

and a parallel plate geometry is assumed with the plates having an effective length £' and spaced a distance d apart. The determination of B

requires measurement of the optical phase shift, geometry and voltage.

Comparison of measurements of the Kerr coefficient with previous

results provides a measure of accuracy of the total measurement system.

In addition, calibration of a Kerr cell consists of determining the

magnitude of the constant of proportionality between square root of the

phase shift and the applied voltage. As can be seen from inspection of

Eq. 1, this constant of proportionality is determined by the Kerr

coefficient of the birefringent medium used and by the geometry of the

cell. The change in the Kerr coefficient per change in temperature is

about three orders of magnitude larger than the change in cell geometry

with a change in temperature. It has therefore been determined that the

temperature dependence of the cell calibration is determined by the

temperature dependence of the Kerr coefficient to within the measurement

accuracy. The metrological significance is that a given cell needs to

be calibrated at a single temperature and corrections for temperature

variations can be made through a knowledge of the properties of the

birefringent fluid.

A description of the calibration of Kerr cells provided by Sandia

Corporation is presented in Section II. Section III consists of a discussion of the Kerr coefficients of water, Halowax oil and

nitrobenzene. Section IV is a discussion of the dependence of the space

charge dynamics in nitrobenzene on the frequency of the applied voltage.

This discussion serves as an introduction to the attempt at a single

frequency calibration which will be performed during FY 75. Following

established practice, an article entitled "Kerr-Effect Studies of an Insulating Liquid Under Varied High Voltage Conditions" which was published in IEEE Transactions on Electrical Insulation and which was partially supported by this contract is included as an appendix to

this report.

4
II. Calibration of Pulse Voltage Measurement Systems Based on

the Electro-optic Kerr Effect.

During October 1973 Sandia Corporation submitted to the National

Bureau of Standards for calibration a system for the measurement of

pulsed high voltage. This system, based on the electro-optic Kerr

effect, was unique for a variety of reasons. First, it employed a double-pass optical system. That is, the polarized light beam would

pass through the Kerr cell, impinge upon a mirror and be reflected back

through the Kerr cell, effectively doubling the length of the cell.

This permits good sensitivity in a cell that is physically small and,

although cell capacitance does not usually present a problem, it too is

reduced as the plate length is reduced. The second novel characteristic

was that the entire system was packaged in a single enclosure. To use

the system one needed merely to supply power to the system, attach the

voltage to be measured to one set of terminals and an oscilloscope to

another terminal to detect the system's output. The third interesting

characteristic of this system was that it was designed to accommodate

three different Kerr cells with nominal plate spacings of 0,2, 0.5, and

1.0 cm. This permitted measurement of pulses with peak voltages

ranging from a few thousand volts to over one hundred thousand volts

.

Previous work^ has amply documented that, in Kerr cells having the

electrodes immersed in the birefringent fluid, fringing edge fields may

produce significant path dependent variations in the system's

transmittance at a given voltage level. Throughout the development of

this measurement technique several alternative solutions to this problem

have been considered including: 1) correction by design^ ; 2) confinement of the light path; 3) multiple calibration for all likely

measurement paths ; ^) development of reliable procedures for correcting

path dependent errors , In the system under test, the effect of fringing

fields was minimized using the second approach, confinement of the light

path. Definition of the position of the light path with respect to case

in which the system was housed was accomplished using a series of

aperatures between the light source and the photodetector. The Kerr cells

are then fastened to the case with screws to insure both that they do not

move during the course of a measurement and that when a cell is removed

it can be replaced in exactly the same position.

The essential features of the calibration system are shown in

Fig. 1, The trigger generator and the two delay units control the

timing of the high voltage pulse generator and the oscilloscopes used to

measure and record the response of the various measurement systems to

the applied voltage pulses. The pulse amplifier supplies a high voltage

pulse of sufficient magnitude to trigger the Marx generator. To perform

the calibration, three measurement systems are connected in parallel.

These are a 500 resistive divider, a calibrated (by reference to the

divider) Kerr cell and the Kerr cell under test. The peak of the

applied voltage pulse is determined by using a slldeback^ technique

to display the low side voltage of the divider. During the same voltage pulse, the responses of both the calibrated Kerr cell and the

Kerr cell under test are recorded,

5
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The optical coupling between the trigger generator and the pulse

amplifier is used to reduce the ground current error in the divider

measurement by eliminating the ground loop that would occur through

the interconnection of the trigger generator, pulse amplifier, Marx

generator, resistive divider, oscilloscope and delay generator. In

more than six months of operation the optical coupling system has

proven to be a cheap, effective and reliable method of transmitting

information. The optical coupler used is capable of transmitting pulses

of duration greater than approximately 1 ys and a peak input voltage

of 35 V.

The data obtained from the cell calibration is summarized in Table 1.

It should be noted that for these data the total uncertainty is

estimated to be ±2%, This estimate is larger than the ±1% which is

typically attributed to this type of calibration because the supplied

cells did not incorporate any method for measurement or control of

temperature.

The calibration of cell A required the application of voltage

pulses that were at the limit of the lowest voltage pulses that are conveniently available in the Electricity Division of the National

Bureau of Standards. Measurements were made, therefore, only at nominal

peak values of 13, 14, 15 kV. All pulses used in this calibration

had a risetime of approximately 1 \is and a duration of about 10 ys.

Table 1. Results from the calibration of Sandia Corporation Kerr cells.

This compilation of data is intended to document the variation

of the observations as the total uncertainty, both systematic

and random is ±2%.

Plate Nominal Value Number of

Cell Spacing of Applied Voltage V^^^ Observations

(cm) (kV) (volts)

0.2 13 1694 5

13-15 1686 23

0.5 15 5931 5

30 5948 5

45 5945 5

60 5949 5

1.0 45 12564 4

60 12585 5

75 12578 5

78 12608 7

101 12578 13

7
During the calibration of cell C, it was necessary to use a second

pulse generator to obtain data with an applied voltage of 100 kV.

For the measurements at 78 and 101 kV this second pulse generator was

used. In that case it was not possible to measure the waveform with

the 500 Q resistive divider. In those two sets of measurements the

applied voltage was measured only with the calibrated Kerr cell which

served as a portion of the measurement systems in the other measurements.

Fig, 2 graphically demonstrates the precision of the measurements.

This figure shows a normalized distribution of the percent deviation

from the average of each determination of the cell constant of cell A

for the set of 23 measurements listed in Table 1. It can be seen that no measurement differed from the average by more than about 0,2%, The

total width of the graph is ±2%, the total uncertainty estimated for

this measurement.

Because the cell constant changes approximately 0.5%/° C for

temperatures near room temperature, it is obvious from Fig. 2 that the

temperature remained approximately constant during this set of measurements,

In order to document the utility of the Kerr system to transfer

accurate pulsed voltage measurements between laboratories, the results

of calibrations of cells submitted by Sandia Corporation and by another

user are listed in Table 2,

Table 2, Comparison of Kerr cell calibrations by NBS and by the

cell owners in their own laboratories.

Cell

A

B

C

D

Cell Constant Determination

NBS

by

(volts)

1690

5960

12600

23640

21450 (1970)

21500 (1973)

Owner

1710

5990

12600

23640

21440

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0.7

0.0

0.0

0.3

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It should be noted that this compilation is not a result of a controlled test, but merely a tabulation of the cells calibrated by

NBS in which the owner volunteered the value that he obtained during

his tests of his cells. The results may not, therefore, reflect the

best efforts of the laboratories involved. Even granting this

qualification, there are interesting observations that can be drawn

from this limited data base. First, the largest percentage difference

observed was 1,2%, The only other method for comparing pulsed voltage

measurement accuracy between laboratories is based on the breakdown

voltage of a sphere gap. The tabulated values for sphere gap breakdown

voltages have an estimated uncertainty of ±3%. The limited data

available indicates that the Kerr system is at least no worse than the

traditional technique and holds promise of possibly being better.

The second point of emphasis concerning the results presented in

Table 2 concerns the calibration of cell E, This cell was calibrated

by NBS in 1970 and shipped to the owner. For three years it was used

by the owner and NBS had no control over nor any information concerning

its use and handling. After that three year period it was returned

for recalib ration and the value of the cell constant had changed by

about 0,2%, As indicated in Fig. 2, this change is comparable to the

precision of the measurement. Long term stability of this sort has

been observed in cells in use at J^BS, but this is the first information

NBS has obtained of similar long-term stability of cells used by others.

III, Kerr Coefficient Determinations

A). Introduction

During this contract period, the electro-optic properties of

three substances, nitrobenzene, Halowax oil, and water, were investigated.

In nitrobenzene the temperature dependence of the Kerr coefficient was

remeasured, over a wider temperature range than previously, to insure

that there was no anomalous behavior. The Kerr coefficient of Halowax

oil Was measured under direct, 60 Hz alternating, and pulsed high

voltage. The Kerr coefficient of water was measured under pulsed high

voltage.

In order to provide insight into the role these measurements play

in the development of accurate pulse voltage measurement systems, it

is necessary to review the nature of Kerr effect measurements. In the

calculation of voltage from Kerr effect data, the following relationship

is frequently used ,

I/I = sin^ [n(V/V )^/2] (2)

10
In this relationship I is the transmit tance of the optical system and

V is the lowest voltage which causes a maximum in the system's

m

transmit tance, Imm. If V is known and l/l is measured, Eq. 2 can be

m

used to determine the applied voltage from the Kerr-effect measurement.

Similarly,- the calibration of a Kerr system consists of the application

of a known voltage to the cell, measurement of l/l and calculation of

m

V from Eq. 2. In terras of more fundamental quantities.

V = d(2M')'-^^^ (3)

in

where B is the Kerr coefficient of the birefringe^t fluid and d the

spacing and £' the effective length of the plates , as parallel

plate geometry is assumed.

To obtain a serai-quantitative insight into the stability of the

calibration of the Kerr coefficient with respect to wavelength,

temperature, frequency of the applied voltage, etc., it is helpful to

examine the classical expression of the Kerr constant of a polar

fluid^.

B = np (n^ + 2)^ (e + 2)^ (9^ + e^)/27 nK (4)

In this equation, n is the index of refraction of the medium at the

wavelength of the incident light X, e is the dielectric constant of

the medium, and p is the number density of the molecules. 6^ and 9 represent expressions involving the temperature of the fluid, the

static and optical polarizabilities and the dipole moment of the

molecule. This equation is approximate and has been shown to be

inadequate for quantitative analysis, but does indicate the sources

of variation of the magnitude of the Kerr coefficient.

The first point that is to be made explicit is the temperature

9 10 dependence. From previous work *

,

+

so, suppressing all other dependencies.

11
B = Aq + A^/T + A2/T^

In the above expressions, the a's and the A's are constants and T

represents the temperature of the material. In the previous year's

cpntract report the temperature dependence of B was presented. In

this report a repetition of that work covering a wider temperature range

will be documented.

Returning to Eq. 3, it can be seen that in the absence of

dispersion, i.e., if the index of refraction is independent of wavelength,

the quantity BX should be a constant. Measurements in our laboratory?

indicate that at 296.1 K, BX = 2.171 x 10~ (m/V)^, but that over

the range of wavelength from 632.8 to 476.5 nm, the variation from

this average was of order ±3%.

The final observation to be made from Eq, 3 is that the only factor

which degends on frequency of the applied voltage, for frequencies

below 10 Hz, is the relative permittivity. The relative permittivity

of nitrobenzene and of Halowax oil are presented as functions of

11 frequency in Fig. 3. The primary characteristic of these data is

that both plots exhibit angapproximately flat frequency dependence for

frequencies below about 10 Hz. (Note that similar ^ata by ^lark-*-^

indicate that there is no change in slope between 10 and 10 Hz).

A conclusion that can be drawn from these observations is that the Kerr

coefficient should be independent of frequency over a range of six

to eight decades.

Measurements of the cell constant of a Halowax-filled cell were

performed under direct, 60 Hz alternating, and pulsed high voltage.

The motivation for these measurements was the hypothesis that Halowax

oil, being a poorer solvent than nitrobenzene, would also be less

susceptible to space charge distortion. The relationship between

its physical properties and the applicability of fluid for use in a

13 Kerr system has beem summarized by Felici and relevant portions

are presented in Table 3.

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During the course of this work, investigations were made using a type B

fluid, Halowax oil, a type C fluid, nitrobenzene, and a type D fluid,

water

.

B) . Measurements in Halowax Oil.

A schematic diagram of the apparatus used to determine the cell constant

under direct voltage of a Halowax oil-filled cell is presented in

Fig. 4. Because data were accumulated over the range in which the phase

shift between the orthogonally polarized components of the light beam

was less than it/2, it was desirable to modulate the light beam so that frequency sensitive detection could be used. The light beam

was intensity modulated upon passage through a rotating chopper

wheel. The chopped beam then impinged upon a beam splitter where

one component of the light beam passed through a conventional

polarizer—Kerr cell—analyzer system to one photodetector

while the other portion of the light beam was reflected from the beam

splitter into a second photodetector. The output from this photodetector

was then amplified and shaped so that it would provide a stable

reference frequency for the lock- in amplifier. In order to accumulate

the data, the amplified and rectified signal from the lock- in amplifier

was connected to the y-axis, while the analog output of a digital

voltmeter was connected to the x-axis of an x-y recorder. A typical

data run was retraced and is shown in Fig. 5. Determination of the cell

constant consisted of measuring the applied voltage and the corresponding

transmit tance and calculating V from Eq. 2. Typical numerical values

m

of the cell constant obtained from observations like the one presented in

Fig. 5 are listed in Table 4.

15
CO

GC

LU

CO< o

4-1 c

CO

j-i wCoo

a;c

•HBu

d)

4-1

O

01 >

cn3 -uO w at 3 1-1 4-J -H

CO T3

CO i-j &. <U a- TD

CO c

CU

4J ,—1 OB 0) CO "—I

S-i t>0 -r-l CO ^-^ r4 I r-l •H o o

•r-l

CO CO 2 g Qi O o to CO 33

16
CD

CC

I—

CO

I—

CJ

<

00c

sodu

4-1 CO

X)

r—

J

O)

•r-l M-l XI

0)

a,

03

CD>

o

c

6 M

CO -H C fa

03

^4 C

o ^

1—1

4-J CO O O

I—I -r-l a. u

CO ^ e

CD 0) u x;

•r^ a

cx, cn

CO O

x;

M-l CO O

CO C 3

u

D

O

p, cu

Pi j-i

(^I/I) 30NViillAISNVai 3AliV13y fa

17
Table 4. Determination of the cell constant of a Halowax oil-filled

cell under direct voltage.

Applied Voltage

(kV)

25.35

27.30

29.23

31.80

33.42

34.94

36.80

38.27

39.59

39.94

42.20

44.81

46.16

48.10

48.74

50.68

52.66

55.24

Cell Constant V

(kV)

20.23

20.15

20.67

20.18

20.18

20.18

20.02

20.00

19.98

19.97

20.03

20.04

19.87

19.92

19.90

19.93

19.90

19.94

AVE 20.06

It can be noted from Table 4 that there are deviations from the

average as large as 3%. A deviation of this magnitude is to be

expected for low values of the relative phase shift. To make explicit

the relationship between the fluctuation in the determination of the

cell constant V and the value of the relative phase shift 9 5 recall

V^ = V/(cp/u)^/^. (6)

Assuming all uncertainties are small.

AV

m _ I AV I 1 Acp

V

~ V~

2 cp m

(7)

18
In this discussion emphasis is placed on the contribution to the error

caused by the uncertainty in phase shift. In these measurements the phase

shift is not determined directly. The quantity measured is the

transmittance, l/l , through the entire optical system. The relationship

between an uncertainty in the^ghase shift and a measurement uncertainty

in the transmittance Al/l is

m

cos"-^{(-l)'^(l-2 [l/Imm± AI/I ])]-cos"-^[(-l)'' (1-2 I/I )] m

nn + cos"^[(-l)''(l-2 I/I )] m

(8)

In Eq. 8, n is an integer defined by the relationship ^

= n + a where

a is the appropriate positive number between 0 and 1. The response of

Eq. 8 to variations in the parameters is not intuitively obvious, but

some predictions can be made without a full numerical solution. For

example, it borders on the trivial to note that for a detection

system to exist at all it must distinguish between minimum and

maximum transmittance. That implies the numerator has a maximum

value of 71/2 while the minimum value of the denominator is nTT. The

worst case uncertainty is then

cp 2n

'

This is the basis for much of the previous work in which n was

large so that

«f = 0.01

2 cf V

If this be the case, it can be seen from Eq. 7 that the uncertainty

in the deteirmlnation of the cell constant is due to the uncertainty

in voltage measurement.

In a previous report^ a system was described in which the

transmittance maxima were counted during the high voltage pulse. This is

equivalent to saying that the numerator of Eq. 8 can be as large as tt/4.

Eq. 8 then predicts that for n > 25,

^ < 0.01 which is in good agreement

with the reported theoretical and experimental performance of that system.

In contrast with previous work, the variation in the observations

listed in Table 4 is primarily due to Acp/cp. It is estimated that for the

19
measurement of high direct voltage AV/V is no larger than 0.001. In

the course of these measurements n ranged from 1 to 7. The primary

source of error was, therefore, uncertainty in the measurement of the

transmit tance, M/l^, a quantity which was safely ignored in previous

measurements

.

Although systematic analysis of the contributions to the quantity

Al/l will be completed during the present fiscal year, the following

contributions were identified during the course of this measurement:

1) Precision of the simultaneous measurement of specific

values of V and l/l , m

2) Nonlinearit ies in the detector-amplifier system and,

3) Fluctuations in the laser output.

A discussion of the total estimated uncertainty is included after

the data taken under all three types of waveform are presented.

Typical data taken under 60 Hz alternating voltage are presented

in Table 5.

Table 5. Determination of the cell constant of a Halowax

oil-filled cell under alternating voltage.

Peak of the Applied Cell Constant V

TTl Voltage (kV) (kV)

23.57 20.25

25.55 20.25

32.36 20.23

33.08 20.42

37.37 - 20.13

37.69 20.15

42.57 20.07

42.62 19.85

42.63 20.06

43.06 20.45

46.88 19.99

46.88 19.84

50.73 20.01

50.79 19.96

54.74 19.85

AVE 20.10

20
The measurement technique employed was to use a capacitive divider

to produce a low voltage replica of the applied waveform and to use a slideback technique to measure the peak value of an individual positive

half-cycle. The Kerr response during that half-cycle was recorded in

conventional manner. Again in this case n ranged from one to seven so the errors associated with a small value of the phase shift apply to

these as well as direct voltage measurements.

Under pulsed voltages a cell constant 19.87 kV was obtained.

The calibration was performed as described in section II of this report.

Because there is a much smaller chance for self-heating or electrical

breakdown during a 10 ys pulse, the calibration was performed with a nominal applied voltage of 75 kV peak.

In summary, the average values of the cell constants were

direct voltage 20.06 kV

60 Hz , 20.10 kV

pulse 19.87 kV

It should be noted that the low frequency determinations are within

1.2% of the value determined under pulse conditions.

The variation within each of the low frequency sets of data is such

that no reading differed from the average by more than ±3%. This

consistency and the agreement among the three sets of data suggest that

the uncertainty in each of the low frequency measurements is of order

a few percent. It is therefore reasonable to refine this approach

toward a definitive determination of whether or not a Halowax oilfilled cell can be calibrated at low frequency for use in the measurement

of pulses.

The specific modifications of the apparatus that are being

developed are

1) Replacement of x-y recorder by a data acquisition system

so that more precise values of V and l/l may be recorded.

It is anticipated that this system will ^e applicable to

tests under both direct and low frequency alternating voltage.

2) Development of appropriate electronic circuitry so that

ratio of the laser's irradiance to the transmittance of

the optical system can be detected. This should minimize

the effect of fluctuations in the output of the laser.

3) Use of neutral density filters to calibrate the linearity

of detector amplifier system.

21

*
4) Incorporation of a thermocouple into the grounded electrode.

- This will reduce the thermal time constant of the temperature

measurement system and will permit accurate measurement of

the temperature in the interelectrode region.

5) Quantification of the effects of space charge in Halowax oil

by careful mapping of the interelectrode field. With the

limited sensitivity available, no effects were detected in

the reported set of measurements.

C) , Temperature Dependence of the Kerr coefficient of

Nitrobenzene,

Recall that the relationship between the cell constant and the

Kerr coefficient is given by

V = d (2Bfi,')

Taking the partial derivitive of this with respect to temperature

yields

V d ST 2B 3T " 2^' ST

* m

Note that the terms containing d and are in the form of the

coefficient of linear expansion. Because the cells are constructed of

glass and metal , these two terms would be expected to be of order

10 /°C. Previous measurements have, however, indicated that near room temperature

i M

B ST

10 ^/°C

So, to within the limit of measurement accuracy, the temperature

variation of the cell constant is reflective of the variation of

the Kerr coefficient. If the cell constant of a cell is known at one temperature, Tq, the following relationship can be used to calculate

the cell constant at another temperature, T:

22
V = (B /B )^/^ V

in,T -^0 * 0

(10)

It therefore follows that a knowledge of the temperature dependence

of the Kerr coefficient of nitrobenzene can serve to correct

observations made using any similarly constructed, nitrobenzene-filled

cell.

The temperature dependence of the Kerr coefficient of nitrobenzene

had been measured previously and the following values of the constants,

as defined by Eq. 5, were obtained:

= 4.44 X lO"-^-^ ra/V^

= -2.86 X 10"^ Kra/V^

A^ = 4.85 X 10"^ K^ra/V^

These constants were calculated from a least squares fit"''^ to the

experimental data over a temperature range from 296 K and 305 K.

Within the present contract period, data were taken over a temperature range from 286 K to 314 K, thus extending the total range

of measurement from about ten degrees to about thirty degrees. These

more recent data were fitted to the same polynomial and the following

constants determined the best fit

Aq = 2.546 X lO"-"--^ m/V^

A^ = -1.717 x lO"^ Km/V^

A^ = 3.136 X lO"^ K^m/V^

Although there was no disagreement between the two data sets as large

as 1% over the common temperature range, the change in the constants was significantly larger. The conclusion drawn from this observation

is that values of the constants are appropriate for interpolation within

the range of measured values; extrapolation beyond the range of measurements should be done only with the knowledge that there is a possibility

of introducing substantial error.

23
D) . Kerr Coefficient of Water

The data presented in this section also formed a portion of the

report NBS IR 74-544, which was prepared at the request of the U.S. Air

Force. Both the U.S. Air Force and Sandia Corporation expressed interest

in the electro-optical behavior of water and partially supported this

phase of the work,

A flow chart showing the measurement strategy and the interrelationships between the various experimental techniques is shown in

Fig. 6. The two-cell technique a^d the end-field free cell technique

were described in detail earlier. The single cell technique refers to

determination of the Kerr coefficient by a measurement of the voltage,

geometry and phase shift and using Eq. 1 to calculate the Kerr

coefficient. A modification of this approach was to measure the cell

constant rather than the geometry directly. If two different liquids are used in the same cell, the following relationship is valid

V , ^ B- _ml. _ 2 V B

m2 1

where the subscripts 1 and 2 refer to the two liquids.

This approach is convenient in that years of development have

demonstrated that V for a given cell can be determined with an uncertainty no larger than ±1%.^^ If the Kerr constant of one substance

is known, then the measurement of the cell constants of same cell

containing first the known liquid then the unknown liquid provides a measure of the Kerr constant v/ithout the associated problems of

geometrical measurement. This approach was used to determine the ratio

of the Kerr coefficient of water to the Kerr coefficient of nitrobenzene.

The cells that were used in the two cell technique^ were used to

determine the ratio of the Kerr constant of water to the Kerr constant

of nitrobenzene by this single cell technique. The measurement involved

determining the cell constant of the cell with longer electrodes when

it was filled with nitrobenzene and when it was filled with water.

Using Eq, 10, it was determined that

B(H^0)/B(C,H^NO„) = 1.058 x lO"^, at 295.6 K.

Z O D Z

As a further check, it was decided to perform measurements

of the Kerr coefficient of water using a plastic cell with electrodes

having approximately a Rogowski profile. This would yield two

different determinations of the Kerr constant. One would be from direct

24
PHASE SHIFT + GEOMETRY + VOLTAGE

( 1

»

SINGLE-CELL TWO-CELL END-FIELD FREE

TECHNIQUE TECHNIQUE TECHNIQUE \/

BfCeHsNOa)

SINGLE-CELL TECHNIQUE

I

' 1

B' BjHiO)

BICbHbNOz) BICeHsNOa)

i

B'

i

BIHzO)

BICeHsNOz)

I

BIHjO) B(H20) BIHaO)

Fig. 6 Flow chart of the various measurements made of the Kerr

coefficients of water, Halowax oil, and nitrobenzene. The

Kerr coefficient of Halowax oil is denoted by B'.

25
measurements of the phase shift and geometry. The other would be a ratio measurement of the cell constant with water to the cell constant

of nitrobenzene. Unfortunately, this latter technique could not be used

directly because nitrobenzene, a good solvent, would destroy the

structural integrity of the plastic cell. A two step procedure was

then used. First, a glass cell was filled with nitrobenzene and its

cell constant was measured. The cell was then filled with Halowax oil,

and its cell constant determined. From these observations, the following

ratio was obtained at 295,6 K,

, ^ B'/B(C^H^NO^) = 4.209 x lO"^,

where B' represents the Kerr coefficient of the Halowax oil. Halowax

oil and water could both be used in the plastic cell to determine the

ratio of their cell constants. The procedure used in this case was

to fill the cell with water (water used was the house distilled

water), seal the cell, and determine its cell constant. Through a small hole in the top of the cell, the water was then pumped out, the

cell was dried and filled with Halowax oil. This procedure was adapted to insure that the plate spacing remained unchanged during

the refilling process.

Using this technique, the following ratio was obtained at 275.6 K,

B(H20)/B' = 0.2499.

So,

B(H„0)/B(C,H,NO_) = 1.052 x lO"^

Z. D _) /

at 275.6 K.

It should be noted that the two single cell techniques yield

results differing by less than 0.6%. The Kerr constant of nitrobenzene

—12 2 at 295.6 K is 3.26 x 10 m/V . The two corresponding values of

B(H^O) are

BCH^O) 3.45 X

10~^^ m/V^

26
and

B(H20) = 3.43 X lO"-*-^ m/V^ .

From the cell constant and the geometry of the plastic cell an additional value of the Kerr coefficient of water can be derived.

For a central path, the following relationship has been predicted

IT

Inserting this into Eq. 3, yields

B =

1

2(£ + d/TT) W ^ m

-3

In this case I = 0.2998 m, d = 6.32 x 10 m and V = 44,010 V. So,

m

B = 3.42 X

10"-^^ m/V^

The close agreement among these three values is thought to be

serendipity, because the estimated uncertainty in these measurements

is ±7%.

An additional source of error was identified during the course

of these investigations. Under microsecond duration pulses the water

was occasionally in turbulent motion sufficient to modulate I , the maximum transmitted irradiance. TSiis is in marked contrast to

experience by the authors with nitrobenzene and Halowax oil in which

no turbulence is detected under high voltage pulses of this duration.

Previous results have indicated that accurate Kerr measurements

can be made even in the presence of turbulent motion. This was true

because in that case the ratio of the amount of scattered light to the

amount of transmitted light was undetectably small with the apparatus

used, A second effect occurs, however, when the scale of turbulent

motion is of order the size of the light beam. In this situation the

fluid motion causes density gradients in the fluid. The density

gradients lead to a change in the index of refraction which serves to

deflect the light beam. As a consequence, the light beam "wanders" acroas the photo- sensitive surface of the detector. Because of spatial

variations in quantum efficiency of the detectors used and/or because

27
of the fact that a portion of the light beam may miss the photosensitive

surface altogether, the photocurrent is amplitude modulated. This leads

to an envelope on the Kerr response and was first detected in this study

as an apparent voltage dependence of the cell constant. In this

study the effects of fluid motion were minimized in three ways. First

the distance between the photodetector and the Kerr cell was kept as short as possible. The other two approaches exploited the fact that

this larger scale turbulence was apparently modified by the geometry

of the cell. In the glass cell there was no detectable amplitude

modulation during the first 6 ys of the applied voltage pulse. Kerr

constant measurements were then taken only during this relatively

quiescent period. In the plastic cell the time interval between the

rise of the voltage pulse and the onset of amplitude modulation could be

varied by adjusting the water level in the cell. By a judicious choice

of water level no amplitude modulation occurred during the entire

10 ]is voltage pulse.

A final word of caution is in order concerning the electric fi^^^

dependence of the Kerr coefficient of water. There is some evidence

that the dielectric constant of water is 0.7% lower when measured at a field strength of 250 kV/cm than when measured in weak fields. The

uncertainty in the present work precluded the observation of any

corresponding saturation effect, but the possibility of saturation

cannot be ignored if the present work serves as the basis of measurement

of voltage at significantly higher field strengths.

IV. Electric Field Distributions and Space Charge Behavior

in Nitrobenzene under Low Frequency Alternating Voltage

A) . Introduction

The electro-optic Kerr effect has been used by a number of

workers over the last two decades to measure the electric field

distribution in a variety of liquids and to study the electric field

distribution around solid insulators. Measurements have typically

been either under direct or pulsed high voltage.

It has long been recognized that if one wanted to use the Kerr

effect to measure the electric field distribution due to the geometry

of his electrodes and/or insulator forms he had two choices. Either he

could perform the measurement under pulsed voltage or, alternatively,

could carefully purify his liquid, coat the electrodes with an appropriate membrane and, if he confined himself to moderate field

strengths, could be fairly certain that observed distortions were a result of geometry and not due to a property of the Kerr fluid itself.

If uncoated electrodes or higher field strengths were used the electric

field in the Kerr liquid would be distorted. Historically, depending

on the materials and their state of purity, this distortion has been

attributed to chemical or electro-chemical processes either in the bulk

or at the electrode surface or to the presence of suspended particles in

the bulk of the fluid.

28
It was judged that an understanding of the dynamics of this

distortion could lead to more accurate voltage measurement using the

electro-optic Kerr effect and to additional understanding of electrical

conductivity and breakdown phenomena in insulating liquids. We

therefore measured the electric field as a function of position and

time under direct and low frequency alternating voltage in a nitrobenzene^

filled parallel-plate capacitor.

The data presented here were taken in a cell having nickel

electrodes. The nitrobenzene was purified before it was sealed into the

cell. The measured resistivity was of order 10 -10 cm.

B). Experimental Results

The experimental apparatus consists of a nitrobenzene-filled

parallel-plate capacitor, a triggerable pulsed argon laser, crossed

polarizers oriented at + and -45° to the interelectrode field direction^

and appropriate photographic equipment for recording of the transmitted

fringe patterns observed when the laser is flashed during high voltage

operation. The laser beam is expanded and collimated to illuminate

the area between and around the test cell electrodes. During direct

voltage studies, the high voltage was connected to a parallel combination

of the test cell and a calibrated 100 Mfi resistive divider. For

current measurements a microammeter was placed in series with the Kerr

cell between the cell and ground. For ac studies, the power-amplified

output of an audio oscillator supplied a step-up transformer. The

transformer's output voltage was applied to one electrode of the cell,

the other electrode of the cell being grounded. The rms values of

the applied voltage was measured using a 1000:1 metering tap on the

transformer.

5

The governing equation for the analysis of data obtained is

In this expression I is the irradiance of the transmitted light, I is

the maximvun irradiance, E is the electric field magnitude, E is tWe

electric field necessary to produce the first maximum in theTMtransmltted

Irradiance and the overbar (e.g., in A) denotes

o

29
where L is the geometrical length of the optical path through the

applied field. It should also be noted that the subscripts x, t indicate the time and position at which the data were taken and that

we are assuming a coordinate system in which the light beam propagates in

the z-direction, and the x-direction is perpendicular to and the

y-direction parallel to the surfaces of the electrodes. We have analyzed

data only at a specific value of y, the geometric center of the

electrodes.

Fig. 7 shows the relative electric field as a function of

position under direct voltage. In order to determine the space charge

density a linear fit (least squares) was performed. From the data

presented the calculated space charge density ranges from 4 x 10

to 14 X 10 C/cm . It is noted that the space charge density observed

here agrees well with similar data obtained, using the electro-optic

Kerr effect, with a chlorobiphenyl as the insulating liquid-*-^.

In that case it was postulated "that the space charge... is due to

the dissociation of the H2O molecule and consists largely of H"*" ions."

Even though there is good agreement in both magnitude and sign it is

thought that in the present work the generation of the space charge

is dominated by electrode surface rather than fluid bulk phenomena.

This conclusion is based on the behavior under low frequency alternating

voltage which will be discussed later in the paper.

Three trends were identified from this and similar data. First,

the net charge was always positive and uniformly distributed in the

bulk. Second, the space charge density decreased as the voltage level was increased, and, third, the net charge in the liquid was slightly

greater when negative high voltages were applied.

The situation was radically different, however, when alternating

voltage was applied. In Fig. 8 is plotted the relative electric field

strength as a function of distance from the high voltage electrode at

various instants during the cycle of a 20 kV rms, 60 Hz applied voltage

waveform (plate spacing 0.5 cm). These data were taken by synchronizing

a pulsed laser (light pulse width - 6 us) with the applied voltage

waveform so that the electric field distribution was strobed at a preselected, adjustable time during the cycle. It can be seen from

Fig. 8 that as one progresses through one cycle of the applied voltage

(of period T) a field distribution indicative of homocharge is first

produced . Soon after the peak of the positive half-cycle the field

becomes uniform. The field distribution then inverts and assumes a distribution characteristic of heterocharge. Fig. 9 shows similar

observations in the same cell made at selected instants during the

cycle of 16 kV rms applied voltage at 60 and 120 Hz. In contrast with

the previous figure, there is no longer evidence of an electric field

distribution attributable to heterocharge. [Note that in this context

the words heterocharge and homocharge are used only to describe the

relationship between the polarity of the electrode and the net charge near it. They do not imply any mechanism of charge production or transport] . It was also observed in this work that the electric field

30
0 0.2 0.4 0.6 0.8 1.0

RELATIVE DISTANCE FROM HV ELECTRODE (x/d)

Fig. 7 Typical field distribution data under direct voltage.

Photographs from which some of the data were taken are presented in the center of che figure.
('"'A /A) 39VinOA QBinddV

CM ^

o d o

(P/x) 300^10313 AH lAIOdJ ISIQ

tod

00

d

lijjX

ILlJ X

ILJ

q:

I-

(/) Q

_l

UJ

|j_

o

q:

I-o

LlI _jUJUJ>

UJor

COe>

o

O

c

4-1 03 O 4-J

o

>^ J3 o o

TO U 4.)

60

•H I—

I

U <i) 3 -H

CO (U B

•H

4-1 IHO

CO3 <U O 3

4-1 M

CO COU

4-J 3 (U •H 4.)

1-1 4-1 CO

CO T-l -o - J"I—

I

(U . •H CU

M-< 00

CO U 4-) H I—* u o u >

a

.-I <u

cu -H

.—I XI a. H CO

<X3

bO

•H

32
60 Hz

4 -

3 L.'

120 Hz

T~—-I r

3/16 T

RELATIVE DISTANCE FROM HV ELECTRODE (x/d)

Fig. 9 The electric field distributions at corresponding times during

60 and 120 Hz, 15 kV rtns , applied voltage.

33
distortion was approximately constant in the range from 60-120 Hz, with

measurements being performed at 60, 80, 100, 120 Hz. At higher and lower

frequencies there was a trend toward reduction in the curvature in the

distributions with limiting cases being a uniform field under short pulse

conditions and a field which is approximately a linear function of

position under direct voltage.

C) . Discussion

There is qualitative agreement between the data and the assumption

that there are particulate impurities in the system. If particulate

impurities are present they are charged upon contacting an electrode.

Once it leaves the initial electrode, the charge on any particle can decay due to fluid ohmic conditions. The critical parameter is the

ratio of the electrical relaxation time, e/a, where e is the fluid

permittivity and a its conductivity, to the transport time d/U, where d

is the electrode spacing and U is the average particle velo^jty. The

ratio of these times is called the electric Reynolds number

\ = (e/a)/(d/U). (11)

If R ~ 1, the net charge distribution is the sum of two

exponential distributions. The predicted result is negative charge near

the cathode and positive charge near the anode. This is observed

experimentally in almost all cases. The deviations from this behavior,

shown in Fig. 8, may be attributable to the voltage dependence of

R . e If R >> 1» the observed behavior can be understood in terms of

® 13 22

the roll cell model used by Felici and Thomas . This model assumes

that the charge carriers move with the fluid, from electrode to electrode,

with a velocity U, The charge on each carrier is proportional to the

electric field strength at the electrode at the time that the carrier

is in contact with it. This predicts that as the voltage is increasing

in magnitude there will be positive charge near the positive electrode

and negative charge near the negative electrode. Sometime after the

peak the field should become uniform. The reason that this heterocharge

distribution was not observed in Fig. 3 may be that there was insufficient sensitivity at the low voltages.

D) . Conclusions

It has been shown that the electric field distribution and,

consequently, the space charge distribution, in a liquid insulant are different under direct and low frequency alternating voltage and that

both differ from ideal distribution predictable from geometry. It

has been recently shown that in commerc^^l insulating liquids the

breakdown is controlled by sg^ce charge . For lack of more substantial

information however, authors have obtained the breakdown field

34

•i
strength at 60 Hz in an insulating liquid by measuring the breakdown

voltage and calculating field from the electrode geometry. It is shown

here that even with plane parallel electrodes the field can differ

markedly from the ideal case because the electric field in a liquid

insulator is defined by both the electrode geometry and by the space

charge dynamics within the fluid.

Acknowledgements

The authors would like to acknowledge collaboration with

Dr. Markus Zahn of the University of Florida during some of the

investigations reported in Section IV of this report. In addition,

the authors would like to thank those who assisted in the experimental

investigations especially Mr. William A. Bagley for assistance in

construction and operation of the apparatus and Miss June Jones for

assistance in accumulation and analysis of the data. Finally, those

who assisted in the preparation of the manuscript should be recognized,

particularly Mrs. Mary Cutkosky who prepared the graphics and

Miss J. Cunningham for the editorial and typographical assistance

she provided.

35
APPENDIX A

KERR-EFFECT STUDIES OF AN INSULATING

LIQUID UNDER VARIED HIGH-VOLTAGE CONDITIONS

This material was published in the IEEE Transactions on

Electrical Insulation, vol. EI-9, pp. 43-56, 1974.

36
IEEE TRANSACTION'S ON ELECTRICAL INSULATION, VOL. EI-Q, NO. 2, JUNE 1974

Kerr-Effect Studies of an Insulating Liquid Under

Varied High-Voltage Conditions

ESTHER CHRISTMAS CASSIDY, senior member, ieee, ROBERT E. HEBNER, JR., member, ieee,

MARKUS ZAHN, member, ieee, and RICHARD J. SOJKA, student member, ieee

Abstract—Refined Kerr electrooptical fringe-pattern methods are used to study time and space variations in the electric field between

the electrodes of parallel-plate capacitors filled with liquid nitro- benzene. Photographs of fringe-pattern data recorded during application of high direct (both positive and negative) and sinusoidal

voltages, ranging in frequency from 40 to 200 Hz, are compiled to enable computation of space-charge distortions of the field in bulk

of the liquid during the stress of high-field (up to 85-kV/'cm) operation. The measurements reveal significant differences between the

field and charge behavior under short pulse (microsecond) voltage

conditions, during prolonged dc operation, after sudden changes in the dc voltage level and polarity, and, for the first time, at various

intervals over the course of entire cycles of sinusoidal voltage. The

results show that space-charge distortion in the interelectrode field

is influenced by the level, frequency, and duration of applied voltage. Discussions of effects believed due to particulate charge carriers, to electrohydrodynamic motion of the liquid, and to the electrode materials are also included.

I. INTRODUCTION

RECENT WORK has experimentally demonstrated

the usefulness of the electrooptic Kerr effect for the

determination of various electrical parameters under the

influence of high voltage. Among these are the measure- ment of pulsed high voltage [1]-C4], the determination

of space-charge effects in nitrobenzene [5]-[6] and

chlorinated biphenyls [7], the measurement of the

electric-field distortion caused by the insertion of a solid

dielectric in a liquid insulant [8], the measurement of 60-Hz alternating voltages [93, and the observation

of the spatial and temporal variation of the electric-field distribution caused by pulsed and direct voltage [10]-

[12]. In addition, theoretical advances in the understanding of space-charge phenomena in insulating liquids have

been made in such areas as the prediction and description

of bulk space charge [13] and polarization waves [14]

in charged-liquid systems and the role of particulate

charge carriers in electrical conductance [15].

Realizing that further advances are predicated on a knowledge of electric-field and space-charge behavior in

Maiiusciipt received September 21, 1973. This work was sup- ported ill part by the U. S. Atomic Energy Commission through the Sandia Corporation, Albuquerque, N. Max. One of the authors (M. Zahn) received partial support from the National Science Foundation under Grants GK-27S03 and GK-37594.

E. C. Cassidy, R. E. Hebner, Jr., and R. J. Sojka are with the

Electricity Division, National Bureau of Standards, Washington,

D. C. 20234. M. Zahn is with the Department of Electrical Engineering, University of Florida, Gainesville, Fla. 32601.

liquid dielectrics, we have used refined Kerr electro- optical fringe-pattern techniques [10]-[11] to mea.sure and compare electric-field and charge distributions in nitrobenzene-filled parallel-plate capacitors during pulsed,

direct, and low-frequency alternating high-voltage operation. The purpose of this work, which supplements the

substantial quantity of data published from earlier nitro- benzene studies, is the determination of, and ultimately

control of, the complex mechanisms that lead to electrical breakdown in insulating liquids. The present work was

also undertaken partly to increase the precision of 60-Hz

voltage measurements. The results demonstrate both the

feasibility' and the effectiveness of using electrooptical

fringe-pattern techniques to visualize electric-field distri- butions and space-charge behavior under steady-state

alternating high voltages. Field strengths as high as 85

kV/cm are applied. The effects of voltage level and fre- quency on space-charge density and distribution are in- vestigated between 0 and dzoO kV; frequencies range from

40 to 200 Hz. Nitrobenzene is the liquid investigated, primarily be- cause of its high electrooptical coefficient (of order 10~'* m/V-) and relatively high electrical breakdown strength

( > 100 kV/cm) . Though its powerful solvent, hygroscopic, and toxic properties make this liquid impractical

for many insulating applications, nitrobenzene is uniquely

suited to serve in this capacity for a multiplicity of diverse

specialized applications, ranging from its use as the

dielectric in prototype "high-energy" electrostatic generators [16] to its widespread use in high-speed photographic shutters [17] and laser "Q-switching" devices

[18], to its use for precision measurements of pulsed high

voltages. In connection with the latter application, ex- tensive studies, now underway for more than five years,

of the performance of nitrobenzene-filled Kerr cells immersed in oil under both transient (microsecond

pulses) and steady-state dc and ac operation have demonstrated that the physical behavior of nitrobenzene under

high-field conditions is essentially the same as that of most

insulating liquids. Its conductivity and breakdown

strength are, for example, affected by space-charge

effects [19], whether they result simply from moisture,

impurities, and particulate contaminants in the liquid, or from more complex mechanisms such as charge formation by electrochemical reaction or field emission at the

electrodes. Its performance is also affected by other widely

reported high-field phenomena [20] such as electrohydro37
IEEE TRANSACTIONS ON ELECTRICAL INSULATION, JUNE 1974

PULSED LASER

BEAM-EXPiNOlNGi COLLIMATIG OPTICSPOLARIZER X /4- PLATE AT 0

PULSEC VOLTAGE

SVSTEK

DIRECT VOLTAGE SVSTEN

Fig. 1. Schematic diagram of the apparatus used to measure the electrie-field distributions in nitrobenzene. Typical

Kerr-effect fringe pattern is shown on the right of the drawing. The systems used to supply and measure

the applied voltage are also shown.

dynamic motion, bubble formation, electrophoretic and

dielectrophoretic forces, the Sumoto effect, etc. All of these phenomena are known to be more or less pronounced

depending upon the condition of the liquid, the electrode

design, the nature and level of applied voltage, etc. Yet our understanding of electric-field and charge behavior, and

thus of breakdown, in the bulk of insulating liquids re- mains admittedly poor.

It has been our philosophy in the preparation of this paper that much is to be gained from careful analysis of

electrical stress and space-charge behavior which can be

so easily observed experimentally in nitrobenzene by use

of Kerr-effect fringe-pattern techniques. Although the

chemical composition of nitrobenzene differs significantly

from that of more commonly used insulating fluids, it is reasonable to expect that behavior attributable to physical

phenomena, such as conduction by particulate impurities

or electrohydrodynamic motion of the liquid, is similar in both cases. Accordingly, more than 600 individual ex- periments investigating such behavior were performed

with sealed nitrobenzene-filled cells under a variety of carefully monitored high-voltage conditions. The results demonstrate significant differences between the pulsed

and steady-state ac or dc field and charge behavior in the

bulk of the liquid. Whereas expected conditions were ob- served during short pulse operation, several significant

unforeseen trends were observed in the steady-state experiments, thereby pointing up the fact that extreme care should be exercised in inferring behavior at power-line

frequency from characteristics observed under dc or pulsed-voltage operation. If, for example, it is suspected

that the degradation of an insulating liquid is due to the

presence of space charge, \\-hether formed chemically or

carried by particulate impurities, the data presented here

suggest questioning of the common practice of inferring

the liquid's performance at power frequency from ac- celerated aging ( for shorter times at frequencies much

higher than 60 Hz) testing or dc testing results. The experimental techniques and methods of data

analysis employed in the present work are described in Sections II and III, respectively. Section IV presents and

discusses the data obtained under direct voltage and

under alternating voltages. The final section, Section V,

presents the summary and conclusions.

II. EXPERLMEXTAL APPARATUS AXD

TECHXIQUES

A schematic diagram of the experimental apparatus is given in Fig. 1. The system consists of a nitrobenzenefilled parallel-plate capacitor within a glass vessel (Kerr

cell), a triggerable pulsed argon laser, crossed polarizers

oriented at + and —45° to the interelectrode-field direction, retardation plates oriented as indicated for elimin- ation of field-directional fringes [21] not pertinent in the present work, and appropriate photographic equipment for recording of the transmitted fringe patterns ob- served when the laser is flashed during high-voltage

operation. The laser-beam diameter is expanded and

collimated as indicated to illuminate the area between and

around the test-call electrodes. The beam is focused and

passed through the circular aperture to exclude extraneous

reflections and, on occasion, to allow Schlieren observations

of the iicjuid motion invariably produced by steady-state

high-voltage operation. For purposes of illustration, the diagram includes a typical fringe pattern phcjtographed

38
CASSIDY it al.: KERR-EFFECT STUDIES

by flashing the laser with — 20-kV dc applied to the test

cell. During such direct voltage studies, the high voltage

(0 - ±50 kV) was connected to the parallel combination

of the test cell and a calibrated lOO-Mfi resistive divider [22] as shown. The divider was used to measure the high

voltage across the cell. For current measurements a microammeter was placed in series with the Kerr cell, between

the cell and ground.

For the ac studies, alternating high voltage was obtained

by amplifying the output of an audio oscillator. This

power-amplified signal supplied a step-up transformer, and

the letter's output voltage, as high as 40 kV rms with

frequencies over the range from 40 to 200 Hz, was applied

to one electrode of the cell, the other electrode being

grounded. The rms value of the applied voltage was measured using a 1000:1 metering tap on the transformer. In order to control the timing (during a cycle) of the

ac fringe-pattern observations, triggering of the laser pulse (flash duration ?ii 6 fis) was synchronized with the high alternating voltage applied to the cell. This was

accomplished by using the audio-oscillator output signal to trigger an oscilloscope equipped with a manually adjustable delayed-out put voltage pulse for triggering of the

laser pulse. The delay and synchronization of this delayed

trigger signal were adjusted. Fig. 2, so that the laser flashed in a strobelike manner to allow discrete observations of the fringe pattern at a selected time(s) during a

cycle. The time interval At between the triggering of the

oscilloscope and the triggering of the laser was monitored

using a conventional counter which counted its internal

\ Z'TM

im

11 tpm<

J- ., ^"piriK diagram of system used to observe the electric-field distribution at various instants of time during a cycle of alternating

voltage. The upper trace shows one cycle of the applied voltage. Ihe center trace represents the time for one sweep of the hoi izontal time base of the oscilloscope. The oscilloscope is e.vtfrnally triggered by the applied-voltage waveform. The bottom trace shows the laser trigger pulse. The delay between the start of the

oscilloscope sweep and the laser trigger pulse is manually adjustable and the duration of the laser light pulse is of order 6 ni

clock pulscis during In this way At could be very ac- curately measured. Two methods were used to correlate a value for the interval At with a specific point during a

cycle of the applied voltag(\ The first was to detect a

portion of the las(^r light pulse with a photomultiplier

and display the time relationship between the laser light

pulse and the applied voltage on the oscilloscope scre(^n. The time interval At was then adjusted until the; light pulse

coincided with the peak of the po.sitive half-cycle. The

second and somewhat more accurate m(^thod was to adjust At until the fringe pattern resulting from the elec- trooptic Kerr effect indicated that the laser was pulsed at the peak of the positive half-cycle, i.e., until the number

of fringes produced was maximum. All attempts to correlate a specific point on the applied-voltage waveform

with a value of At were reproducible to within ±20 /xs,

i.e., to within ±0.8 percent of the shortest half-cycle used. The present work was conducted using two specially

prepared cells (see Table I), one with electropolished

stainless-steel electrodes of dimensions 4 cm wide by 12 cm long, and the other with glass-blasted nickel electrodes

of dimensions 2 cm wide by 12 cm long. The electropolishing and glass-blasting procedures were ad(jpted to minimize the effects of electrod(>-surface contamination. The

electrode edges and corners are rounded to avoid pre- mature electrical breakdown. The nominal electrode spacing in both cases is O.o cm. Gla.ss-to-metal seals are used for inserting tungsten rods which provide electrical connection and support for the electrodes. An expansion

volume is included to prevent failure of the glass vessel when the test liquid expands due to heating. A thermometer is sealed into the nitrobenzene for monitoring of its temperature. (Temperature increases as large as 20°C

were encountered during prolonged high-voltage ac

operation.) External surface and air flashovers are avoided

by immersing the test vessel in transformer oil. More

complete details of our cell-construction technique were

presented elsewhere [11 J. With regard to the test-cell insulant, nitrobenzene was,

as previously mentioned, selected primarily because of its high electrooptical coefficient and relatively high electrical breakdown strength. Though the electrical resistivity of commercially pure grades is inadequate (of order lO^fl-m)

for steady-state high-voltage operation, increased resistivity is readily obtained by passing reagent-grade liquid

through a chromatographic adsorption column of activated

alumina. In the present work, this procedure, which has

long been u.sed to remove moisture and other impurities

froiTi insulating oils [23], increases the nitrobenzene's

resistivity to the order of 10*-10' n-m. At this level, pro- longed steady-state high-voltage dc and ac operation could

be maintained without excessive liquid heating or turbulence due to current leakage. Gas chromatographic

analysis of the liquid before and after processing showed

that, as is often the case with insulating oils, water is the

principal contaminant. Thus, because of the hygroscopic

and toxic properties of nitrobenzene, our entire cellfilling and sealing procedure is performed under vacuum.

39
IEEE TRANSACTIONS ON ELECTRICAL INSULATION, JUNE 1974 TABLE I Parameters for the Test Vessels Described in the Text

ELECTRODE ELECTRODE STRUCTURE CtLL CONSTANT

CELL MATERIAL 6. PREPARATION (E d)

A Nickel Parallel-plate 4900 V Glass-blasCed

B Stainless Parallel-plate 4600 V Steel Electro-polished

Xote: The cell constants listed are valid for .")14.5-nm argon laser radiation at a liquid temperature of approximately 298 K.

III. THEORY

Comprehensive theoretical discussions of the electro- optic Kerr effect, including derivations of the Kerr

constant [24]-[26], the application of the Kerr effect to high-voltage measurement, and methods for eliminating

the effects of fringing fields [27], are available in the

literature. The purpose of this section is to make explicit the assumptions used in the analj-sis of the data presented.

The governing equation for the Kerr effect is

7hi - ni = \BE^ (1) where ?hi(j.) is the index of refraction for light polarized

parallel (perpendicular) to the direction of the applied

field E. The Kerr constant of the liquid is B and X is the

wavelength of the monochromatic light traversing the

Kerr cell. Equation (1) can be solved for the phase shift,

(P, between the components of the light beam polarized

parallel to and perpendicular to the direction of the applied field

.

. ^ = 27r / E'Bdl. (2)

In (2), L is the geometrical length of the optical path

through the applied field. To reduce (2) to a more con- venient form it is necessary to make a number of observations concerning the electric-field distributions in the

cells used. To clarify this discussion, define a set of co- ordinate axes so that the z direction is the direction of propagation of the light beam, the x direction is per- pendicular to, and the y direction is parallel to the surface

of the electrodes. In this notation (2) can be rewritten

which also explicitly includes time dependence. The first assumption is that jB is a constant, so that

ip{i,y,t) -IttB ( E''{x.y,z,t) dz. (2b)

- 0 In the present work, all field mapping is dune in the x

:^ direction. We have therefore analyzed data only at a specific value of y, the geometric center of the electrodes.

It i.>; shown in our data and has been shown in previous

studies in cells with similar geometrj' that ip{y) varies only slightly near the center of the plates so that error

in locating the exact center of the plates are negligible in comparison to other errors in the analysis. We can therefore rewrite (2b) as

ip{x,t) = 2-kB f EHx,zX) (h. (2c)

•'o Because the experimental setup is such that light polarized

at an angle of 45° to the direction of the applied field passes through the Kerr cell and then impinges upon an analyzer

oriented perpendicular to the direction of polarization, the

light transmitted by the analyzer obeys the relation

= sin=[<p(/,n/2]. (3)

In this equation we have again suppressed the y de- pendence and I{x,t)/Im is the relative irradiance of the

transmitted light at a position x at any given time t, being the maximum transmitted irradiance. We have

assumed that temporal and spatial variations in /,„, which

are dependent solely on the light source and the attenuation in the media through which the light beam propagates, are negligible; especially so in the present work, as we measured only the values of x for which I{xJ) //„, = 0,

i.e., the po.sitions of the dark fringes.

It has been shown [27] that (3) can be rewritten

where the overbar (e.g., in .-1) denotes the following:

A = \- f .V dz lE Jq

and [7(0 //m]x denotes I{x,t}/Im at a specific value of x. In (4) , is the smallest effective field strength that produces a maximum /,„ in the amount of transmitted

light. Methods have been developed to correct the ob- served values of {/( 0 /Im)s for variations in the x direction due to the fringing fields at the elect r;)d(- ends [27].

However, the^e corrections were m.t applied to the presr-nt data because it has been -how:; jireviuusly that they

modify values of \R\t) ;[:„), measured with paraliel40
CASSiDY cl al.: kerr-effect studies

plate ok-ctrodos groator than 10 em in length and spaeed

less than 1 cm apart by less than 1 percent. In this study information was obtained concerning

\^K(t)2i- and thus the space-charge density, at certain times during the cycle of an applied steady-state alternat- ing high-voltage operation. These data were obtained by

illuminating the cell with a light pulse which was short compared to the observed temporal variation of the field. (Details were given in Section II.) Tf) make explicit this situation (4) can be written

(a„=-[i(i):., (5)

where ( denotes the instant at which the observation is made.

Electric-field and space-charge distribution information were obtained from photographs of the transmitted fringe

pattern at time t (see, for example, Figs. 3 and 4). The

relative positions {x/d) of the centers of the dark bands

along a centrally located path (of total length d) between

and perpendicular to the inner electrode surfaces were measured and recorded. The center of each dark band or

fringe was assumed to indicate a relative intejisity of (///„) J.,, = 0, and thus, from (.5), a point whfTe the

relative electric-field intensity {K/Em)x.i was etjual to the square root of an even integer. In keeping with the con- vention established earlier [10], [11], numerical values n were assigned to each dark fringe b}' counting (« =

0,2,4,6,- ••) successively from the outermost dark region

where n = 0 inward to the desired fringe located on the scanning path (from x/d = 0 to \ ) between the electrodes

(see Figs. 3 and 4). The experimental values of (x/d) and

{E/Em)i.i obtained from each photograph were fitted to a first-degree polynominal

or to a second-degree polynominal

^-^^ = .4 + B{x/d) + C{x/dy

(6)

(7)

where a, b, A, B, and C were coefficients determined by a

least squares best fit method [28]. The appropriate

polynominal was judged to be sufficiently accurate whenever

X-C-m/ fitted V-C'm/exp X^m/exp

In order to obtain the space-charge density p from the

electric-field distribution, the differential form of Gauss' law was used, i.e., dE

dx (9)

where e is the dielectric constant of the liquid medium.

t or the purposes of this paper numerical values of p were

Fig. 3. Fringe pattern photographed (exposure time 0.3 fis) at the peak of a 65.4-kV total-duration 10-jus pulse. The fact that the

field is uniform between the plates is demonstrated by the ab- sence of interelectrodc fringes. The side fringes are due to the

fringing field along the length of the electrodes.

STEADY-STATE VOLTAGES APPLIED

dc 60 Hz ac

CATHODE

-18 ookv -22 62 kv PEAK

Fig. 4. Typical observations of the fringe patterns resulting from

the application of direct and 60-Hz alternating voltages in ceil A. The interelectrode fringes show that the interelectrode field is not uniform under these conditions. The fringe numbering procedure

is described in Section III.

not needed, and, neglecting the effects of fringing end

fields, (9) was reduced to d{E/EJ,

d{x/d)

pd

(10)

Computations of the coefficients in (6) and (7) were used,

to plot the electric-field distribution, i.e., {E/Em)i as a

function of {x/d) and to allow convenient examination of space-charge effects in terms of the reduced space-charge

density p,:

Pt =

diElErnh

d{x/d)

(11)

Whenever a linear electric-field distribution, of which the

dc pattern in Fig. 4 is typical, was observed, (6) was

fitted to the data and the reduced space-charge density was given simply by

Pr = b. (12)

Whenever a parabolic-field distribution was computed

41
IEEE TRANSACTIONS ON ELECTRICAL INSULATION, JUNE 1974

(see, for example, the ac pattern in Fig. 4) , the reduced

space-charge distribution was determined as follows:

Pr = B + 2Cix/d). (13)

IV. EXPERIMENTAL RESULTS

It was reported earlier [11], [27] that electric fields produced by applying short (.5 -20-/iS duration) pulses as high as 300 kV show no evidence of space-charge distortion. A typical Kerr-effect fringe pattern demonstrating

this conclusion is given in Fig. 3. This photograph, which

is a 0.3-/iS exposure taken at the peak of a lO-pis-long

65.4-kV nearly rectangular pulse, shows the irradiance

transmitted through a parallel-plate cell similar to those

used in the present work. With this geometry, the field between the electrodes should be uniform. The pulsed

field's compliance with this condition is verified experimentally by the uniformity in the irradiance (the absence

of fringes) transmitted between the electrodes. In contrast. Fig. 4 shows typical records taken during

steady-state dc and 60-Hz ac experiments with the cell having parallel-plate glass-blasted nickel electrodes. The

presence of space charge and its distortion of the inter- electrode field is evident from the fringes recorded between

the electrodes. Further, plotting (see Fig. 5) of the dis- torted field distributions from the fringe numbers and

positions, as described in Section III, shows a profound

difference between the dc and 60-Hz field and charge

distributions. Observations and discussions of these and

other anomalies in steady-state dc and ac field distributions are discussed separately in the following sections. Discussions of the reproducibility of the electrical and

electrooptical measurements are included, and several alternative explanations are presented and discussed. Because the data presented typify results from over 600

individual photographs, the majority of the data are

ALTERMAT \ 'J VCLTAjE ' DIRECT VOLTAGE

Fig. 5. The relative electric-field strength and the a.^sociated space-charge density as a function of relative position between the

plates {x/d). These data were obtained from the two photographs

in Fig. 4. Although the average field strengths are appro.\imately the same in the two cases, the electric-field distribution, and

consequently the space-chaige densities, are radically different.

presented in graphical form. A number of photographs

of raw data are included to indicate to readers unfamiliar

with this technique the types of observations that can be

made.

A. Measurements of Current Under Direct Voltage

When the test cell is first filled with the purified nitro- benzene the current passed by the cell upon application of steady-state high voltage (alternating or direct) is very, high, being as much as a thousand times greater than the

steady-state current. For several minutes the conduction

and electric-field properties of the cell are not stable and

measurements, either electrical or optical, made during

this period are nonreproducible. After high voltage has

been applied for about half an hour, the current through

the cell approaches a steady-state value, and further

electrical and electrooptical measurements are reproducible. However, when there is a significant time

interval between voltage applications (e.g., overnight),

or when the type of voltage excitation is changed (e.g., from direct to alternating or even if the polarity of direct voltage is changed) , the current initially increases above

the steady-state value but within a few minutes returns

to the same steady-state value. During this period the

electrooptic fringe pattern also changes slowly indicating

changes in electric-field and space-charge distribution. Thus, whenever changes in voltage excitation are made,

reproducible measurements reoccur only after several minutes of high-voltage conditioning. The cells in this study were used over a three-month period with the re- producibility of all measurements occurring after the

brief conditioning periods. Other sealed cells have been in use for over three years with similar results. (Because

nitrobenzene is hygroscopic, unsealed cells do not maintain

this reproducibility.)

Other authors [29], [30] have noted both the decrease

in current with time during application of a constant high

voltage and the dramatic increase in current with the

decay back to a steady-state when the polarity is reversed. In their work, however, the electrodes were coated with an

electrodial5'tic varnish. In that case, the following explanation for current behavior was postulated [30]:

. . . the oncoming residual ions are trapped within

the polymer matrix while electrical neutrality is pre- served thanks to the stationary counterions; charge

displacement in the reverse direction cannot occur

unless the matrix has sufficient electrr/aic conductivity. Of course, if voltage is reversed, the mobile

ions are injected into the liquid and the arrange- ment works as a very efficient inject')r.

Howc^ver, as previously noted, the same time- and

polarity-dependent behavior of the current was observed

in our colls in which the electrodes were not varnished.

A different, equally qualitative explanatif)n for this behavior ha& been postulated [31]. This hypothesis, which

seems a plausible and perhaps a more accurate explanation

42
CASSIDY et al.: kerr-effect studies

for our observations, contends that electrical conduction

is primarily the result of the motion of micrometer-size

particles carrying charges between the electrodes. If this

is the case, two processes involving trapping of particles on the electrodes can account for the current behavior.

1) Conducting micrometer- and subniicrometer-siztd

particles become trapped on insulating areas of the metallic

electrodes because the insulating areas prevent them from

readily giving up their charge to the metal electrode. This

explanation accounts for both the decrease of current with

time (the trapping sites slowly fill, thereby reducing the

density of charge carriers and thus the current) and for the increase of current with polarity reversal [.31] (coulombic repulsion on reversal may be expected to restore the density of charge carriers temporarily to its original high value)

.

2) Fluid motion can bring small insulating particles

in contact with one of the electrodes [15]. The particles

eventually accept enough charge from the electrode to be

repelled to the other electrode [32], where the charging

and repulsive action are repeated. Under a constant

applied voltage this process continues until the charge

distribution in the liquid bulk eventually reaches a condition of steady-state current leakage and charge-induc(!d

distortion in the interelectrode field. Again, polarity

reversal, whether under dc or periodic ac conditions,

interferes with these slower processes, causing increased

repulsion and/or attraction of the particles from (or to) the electrode to which they are attached, and accordingly, an increase in current.

It should perhaps be noted that in addition to the work

presented and referenced here concerning the effects of

particles on the space-charge distribution in liquid insulators, there is a substantial body of literature concerned

with the fact that the insulation strength of compressed

gases is greatly reduced by free particles [33].

B. Electric-Field Measurements and Charge Behavior with

High Direct Voltage

Typical field distribution data under direct voltage are shown in Fig. 6. This figure contains information obtained

from fringe-pattern measurements by applying 0- to ±30-

kV direct voltage to one electrode of cell A (see Table I)

.

Several minutes of conditioning were allowed at each

voltage level to insure steady-state operation. Schlieren

observations during these experiments indicated that the

dielectric fluid was in motion. The fringe patterns were, however, stable and reproducible after the conditioning

period. This indicates that the equilibrium space-charge

distribution in the liquid was stable in the presence of and

in spite of steady-state fluid motion.

Fig. 7 shows explicitly the effects of high-voltage

conditioning described earlier. The dashed lines show the

electric-field distribution immediately after polarity re- versal (the power-supply polarity was reversed so that the

nongrounded electrode was changed from positive to negative). During 1/2 h of negative high-voltage operation, with sequence as shown in the figure, the field disE

0 0.2 0.4 0."6 0^8 1.0 RELATIVE DISTANCE FROM HV ELECTRODE (x/d) _

Fig. C. Typical field distribution data under direct voltage in cell A. Photographs from which some of the data were taken are presented in the center of the figure. The presence of fringes be- hind the negative electrode is discussed in the text.

ill 0 0.2 0.4 0,6 0.8 RELATIVE DISTANCE FROM HV ELECTRODE (x/d)

Fig. 7. This demonstrates the effects of high-voltage conditioning on the data presented in Fig. 6. The dashed lines represent the

electric-field distribution immediately after the application of negative high voltage while the distribution obtained after high

voltage was applied for about a half hour is shown by the solid line.

tribution shifted to those shown by the solid lines. These

results are in agreement with those reported by previous

workers [20], [34], insofar as all observations show that

the field distribution shifts with time when high voltage is

first applied to the plates. It is noted, however, that the

shape of the field distributions reported by earlier workers

differs from those shown in Figs. 6 and 7. This difference

is probably attributable to differences in our electrodes;

43
IEEE TRANSACTIONS ON ELECTRICAL INSULATION, JUNE 1974

they used varnished brass electrodes, while the present

results were obtained using a cell equipped with bare

nickel electrodes. Further evidence suggesting that the

field shape is affected by the electrode material is pre- sented in discussion of Figs. 11 and 14 which show the

difference between ac field-distribution results when using

stainless-steel and nickel electrodes, respectively.

Calculations of the interelectrodc field distribution,

i.e., of {E/E„i)i-,t as a function of relative position {i/d)

between the electrodes, and of the reduced space-charge

density p, were performed as described in Section III. In the dc cases the field distributions were computed and

plotted by fitting the data to a first-degree polynominal,

(6) . In this case pr was independent of the relative position

{x/d) between the electrodes and its value was determined

from (12).

Results calculated from the measurements of Figs. 4 and 5 with cell A and from similar typical experiments

with cell B are listed in Tabic II. Inspection of the results shows several trends over the range studied: 1) the net charge in the liquid was always positive and uniformly

distributed in the bulk; 2) the space-charge density in the

bulk decreased as the applied voltage (average field) increased; 3) the net charge in the liquid bulk was slightly

greater when negative high voltages were applied; 4) the

net charge in the liquid was reduced by extended highvoltage operation (conditioning) ; and 5) the net density

of space charge was greater in the cell with nickel electrodes

(cell A).

These trends lend evidence to the postulate that leakage

conduction is dominated by the motion of small particles

between the plates. Previous work [29] has shown that

if the particles were metallic with a work function smaller

than the work function of the electrodes, the particles

would receive a greater positive charge at the positive electrode than negative charge at the negative electrode. Because nickel has a very large work function it is likely

that in our case such conducting particles would have a

smaller work function and therefore that the net space- charge density would indeed be positive.

Similarly, these trends are also compatible with the

postulate that the current conduction is governed by the

action of insulating particles, in this case perhaps of submicrometer-size alumina particles which were imperceptibly carried with the liquid in passing from the

chromatographic column during the process described in Section II. If this be the case, the insulating particles may

be expected to be attracted to and form a resistive layer or

dielectric coating on the electrode surface. This layer would

be expected to increase in thickness with voltage and time,

thereby slowly reducing the net charge circulating in the

bulk and thus the leakage current through the liquid. On

removal of the voltage, the attached particles would

detach from the electrode and drift slowly back into the

bulk. Upon reapplication of voltage they would repeat

the same procedure, except that the initial current and

rate of decay may be expected to be smaller due to the

fact that some particles will undoubtedly remain atTABLE II Reduced Space-Charge Density in Bulk of Liquid During

High Diricct Voltagio Opicratiox

tached to the electrodes. On polarity reversal, similar behavior would be expected except that the electrode of attraction would change with the polarity.

Schlieren observations of the liquid behavior on re- moval of the applied high voltage also tend to substantiate

the particle postulate. Schlieren movies beginning immediately before and continuing after sudden removal of high direct voltages show development of localized changes in the index of refraction of the liquid near the

electrodes, with gradual development (over a period of several minutes) of differing refractive indices in the upper and lower regions of the test cell in a manner suggestive of gradual settling of the particles under gravity

to the lower regions of the cell. One additional discussion of the dc data is in order. The typical photographs in Fig. 6 show significant light

transmission behind the negative electrode. Some light

transmission is, of course, expected due to fringing fields behind the electrodes, but these fringing fields would be

symmetric about both electrodes and hardly evident at lower voltages. Yet Fig. 6 indicates that a field of sig- nificant intensity exists behind the negative electrode. The

fringes behind the cathode in the -|-20-kV pattern, for example, indicate that (4)"/^ < {E/Em) < (6)^'^ in the

region adjacent to the back of the cathode surface. In this

cell, for which Em = 9.8 kV/cm, this indicates that

i5 ^ 22 kV/cm immediately adjacent to the back surface,

that £ = 0 at a point located about 0.5 cm from the back

surface of the negative electrode. This enhancement of the

field behind the negative electrode probably results from

the presence of positively charged particles in the liquid bulk. Under the influence of the imposed electrostatic forces the particles would move to and collect about the

44
j CASSiDY et ah: kerr-effect studies

cathode, including its back side, and cause the observed

field enhancement. The irradiance around the cathodesupport rod in Fig. 6 supports the postulate that charged

particles also collect around this portion of the electrode. The fact that E goes to zero at a point on the electrode support could indicate that the accumulation of charged

particles in this region of the liquid is limited by the

shielding of charged particles already attached to the

electrode or by fluid motions which cause the particles to be concentrated in certain regions of the liquid.

Such observations, indicating the existence of space

charge in the bulk of the liquid behind an electrode, have

not, to the authors' knowledge, been previously reported.

Accordingly, this unforseen behavior and its contribution

to electrical stress in liquids are areas for further theoretical and experimental work. In the meantime, several trends

are noted from the present' work as characteristic of this

effect. 1) The field enhancement behind the electrode always appears behind the cathode, whether or not it is grounded, thereby ruling out the possibility that it may

result simply from stray capacitance between the highvoltage electrode and ground. 2) The field enhancement is most pronounced under steady-state direct-voltage operation; it is barely noticeable under steady-state ac conditions (see Figs. 4 and 8). Under ac conditions the rapid

variation of the electric field will not allow charged particles to collect behind an electrode; the particle does not have

enough time to travel to the back surface of an electrode before the electrode polarity is reversed. Furthermore,

Schlieren observations of the liquid during ac steadystate operation show that the fluid motion is much more

turbulent than under dc conditions. This greater turbulence would also tend to disperse any particles tending to

collect near a given electrode. 3) The magnitude of the

enhancement is affected both by the level of applied

voltage and by the duration of exposure to high-voltage

operation: in a continuous experiment the enhancement was observed to increase with voltage level, as is evident

from the -|-10- and -|-20-kV fringe patterns in Fig. 6 (one

fringe behind the electrode at 10 kV and nearly three at 20 kV) which were taken after days of intermittent ex- posure to voltage of positive polarity. In widely spaced

experiments and those performed without extensive

conditioning, the behavior of this enhancement is as yet

less predictable. For example, the -20- and -10-kV

patterns were taken in that order after about 50 min of exposure to voltage of negative polarity; the patterns show

greater enhancement at -10 kV (after longer conditioning) than at -20 kV. Another fringe pattern, that re- cording the data for the -10-kV curve in Fig. 6 (immediately after reversal of the voltage polarity), shows

greater enhancement (3-4 fringes) behind the electrode before conditioning. The cells were oriented with the

plates horizontal and it was consistently observed that

there was greater enhancement when the negative elec- trode was the lower rather than the upper electrode. It is therefore conceivable that the gravitational force might

not be negligible in this case. It is evident, however, that

further specific experimental observations are needed for a detailed and accurate explanation of the causes of field distortion and current leakage in the liquid bulk.

C. Measurements with Alternating High Voltages

Fringe-pattern data concerning the electric-field distri- bution, and hence the space-charge density and distribution, were taken under a variety of alternating highvoltage conditions. 1) Observations were made at the

positive peak of sinusoidal voltages of various levels (to

30 kV rms) and frequencies (between 40 and 200 Hz).

2) Observations were made at ( 1/16) T intervals over the

course of an entire cycle of such operations. 3) As in the

dc studies, these observations were conducted using both

cell A and B so as to bring out behavioral difTerences which might be attributable to the electrode materials.

Typical results from these studies are presented and

discussed in the following paragraphs.

Fig. 8 shows the fringe patterns photographed at the

positive maximum of a 22-kV-rms sinusoidal voltage at various frequencies between 40-10") Hz using cell B. The

significant observation from those photographs is that the

number of interelectrode fringes is frequency dependent,

with a maximum at approximately 80 Hz. Typical data

from frequency studies at 25 kV rms, obtained from twenty

different fringe-pattern photographs, are compiled in Table III. In this table the relative position x/d of each

transmission minimum, {E/En,)i,r = «, is tabulated with

the frequency of the applied voltage as a parameter. It is immediately obvious that the number of interelectrode

fringes is frequency dependent, with a broad maximum

in the vicinity of 80-105 Hz. From these data, the space- charge density as a function of the frequencj^ of the

applied voltage can be calculated [(11) and (12)].

Graphs showing the reduced space-charge den.sity as a function of the frequency of the applied voltage at two different voltage levels are shown in Figs. 9 and 10. These data, like those in Fig. 8 and in Table III, are the

results of observations taken at the positive maximum of the applied voltage. Two conclusions can be seen from the

plotted pr versus frequency curves: as the magnitude of the alternating voltage is increased, the frequency at which the maximum space charge occurs shifts toward

higher frequencies and the magnitude of the maximum

space charge increases. During the course of this study, data were taken not

only at the positive maximum of the applied voltage but

also at selected points during the cycle of the applied

voltage. Field distributions plotted from typical observations at v^arious times during a cycle of 15-kV-rms 60-Hz

operation using cell B are shown in Fig. 11. We note that

the electric-field distribution is linear with positive slope

throughout the whole cycle. If we extrapolate to zero,

( 1/2)7", or T, the field distribution is linear, being equally

positive and negative about the center (x/r/ = 0.5).

Fig. 12 shows some of the fringe patterns from which these

plots were obtained. Note that at time (1/2)7", the applied

voltage is instantant;ously zero, yet light appears near the

45
IEEE TRANSACTIONS ON ELECTRICAL INSULATION, JUNE 1974 22 kV rms, Positive Maximum

Fig. 8. Photographs showing the fringe patterns taken at the positive peak of a 22-kV-rms sinusoidal voltage at various frequencies between 40-105. It can be seen that the number of interelectrode fringes is frequency

dependent with a maximum at approximately 80 Hz.

TABLE III Fringe Position x/d as a Function of Frequency with 2.5 kV RMS Applied to Cell B

Frequency

130 135

Hz 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125

Fringe

No. n

Ub .06 .02 .02

48 .02 .01 .06 .07 .11 .08 .08 .05 .02

50 .02 . 10 .09 . 12 .13 . 15 . 13 . 13 .09 .08

52 . 10 . 18 . 16 .17 . 18 .20 . 18 . 17 . 13 . 12

54 .08 .13 . 11 .20 . 25 .22 .23 .23 .26 .22 .22 . 18 .17 .02

56 .35 . 31 .29 .25 .30 .32 .29 .29 .28 .32 .28 .28 .23 .22 .07 .05

58 .59 .47 .43 .39 .40 .40 .38 .35 .34 .38 .34 .34 . 30 .29 .13 . 11 .08 .04 . 03

60 .77 .62 .58 .54 .50 .49 .45 .43 .41 .45 .41 .40 .37 .35 .21 . 18 . 15 .09 .08 .05

62 .91 .75 .72 .71 .62 .58 . 55 . 51 .49 . 52 .47 .47 .44 .42 .29 .27 .23 . 16 . Ih .11

64 .88 .85 .88 .75 .68 .65 . 59 .56 .59 . 54 . 54 .51 . 50 .37 .36 .32 .25 .2"; .19

66 .97 .96 .98 .88 .79 .75 .67 .64 .65 .61 . 60 .58 . 57 .47 .46 .41 .34 .38 .30

68 .98 .88 .85 . 75 . 71 . 72 . 68 .68 . 64 . 63 .56 . 55 . 52 .47 ,5: .45

70 .97 .91 .84 .79 . 79 .74 .74 . 71 .68 .63 .64 .60 . 57 .6: .59

72 .91 .86 .85 .81 .81 . 78 . 75 .70 . 72 .68 .67 .72 .72

74 .98 .93 .91 .87 .87 .85 . 81 . 77 . 79 . 75 . 75 , 80 .80

76 .98 .97 .93 .93 .91 .87 .83 .86 .81 .83 .3/ .88

78 .98 .98 .96 .92 .90 .92 .97 .89 .93 .94

80 .97 .97 .98 .93 .95 x/d

46
CASSiDY et al.: kerb-effect studies

T

1 1 r

• - 5

5 i

FREQUENCY (Hz) Fig. 9. The reduced space-charge density pr in cell £ as a function

of the frequency of an applied 15-kV-rms voltage. Each data point was determined from the electric-field distribution observed at the positive peak of the applied sinusoidal voltage. The error bars

indicate the standard deviation of the coefficient pr as determined from a linear least squares fit of the electric field between the

electrodes. Note that the reduced space-charge density has a maximum at a frequency of approximately 60 Hz.

ill o

<

Xo

CJ

O

UJo

o

FREQUENCY (Hz)

Fig. 10. The reduced space-charge density as a function of the frequency of an applied 25-kV-rms voltage. The meaning of each data point is the same as in Fig. 9. In comparison with Fig. 9

the maximum reduced space-charge density has shifted to a

higher frequency of approximately 90 Hz.

60Hz

Fig. 11. The electric field distribution in cell B at various times Fig. 12. Photographs from which some of the data in Fig. 11 were

during the cycle of 60-Hz 15-kV-rms applied voltage. The period taken. Note that there is some light transmitted at 1/2T, i.e., of the applied waveform is denoted T, so, for example, the data when the voltage is instantaneously zero. As explained in the

designated as 1/4T were taken at the positive maximum of the text, thi:, indicates that the bulk .space-charge density is con.stant applied voltage. throughout the cycle.

47
IEEE TRANSACTIONS ON ELECTRICAL INSULATION, JUNE 1974

Fig. 13. The electric-field distribution at selected frequencies and voltage levels in cell B. All of the data in this figure were taken at the positive maximum of the applied voltage.

electrodes. When the voltage is instantaneously zero, the

total surface charges on each electrode are negative and

equal in magnitude, while the total volume bulk charge is double in magnitude and positive, keeping the system

neutral. ( The surface charge per unit area on the electrodes can be computed by the discontinuity of the normal

component of eE.) At other times in the cycle, the volumecharge density remains constant (independent of voltage

polarity) , while the surface charge on the electrodes varies sinusoidally with time.

It is also interesting to note from Fig. 12 that again some

light, although over a much smaller area than was found

with dc voltages, is also transmitted behind the cathode

during ac operation. Further measurements over the

complete cycle show this anomalous field enhancement

follows the sinusoidal cycle, alternating between elec- trodes, as the field enhancement always appears behind

that electrode which is instantaneously negative.

Measurements of the electric field as a function of

position at the positive maximum of the applied voltage

at various voltage levels and selected frequencies are plotted in Fig. 13. From this type of observation, the

following results, showing relationship between the fre- quency /max at which the net space-charge density was maximum and the applied-voltage level, were obtained:

Measurements of /mai at Various Voltage Levels Using Cell B

Voltage /max (kV rms) (Hz)

10 45-65

12 5.5-65 15 60-85

20 80-95

22 80-95

25 90-105

Similar measurements with cell A showed many of the same features. The dc field was observed to be a linear function of position between the electrodes (see Fig. 5),

again indicating a uniformly distributed net positive

charge in the liquid bulk. In addition, observations at the

peak voltages during ac operation at various frequencies

indicated that the distortion in the ac field, and thus the

density of charge in the liquid, was again frequency de- pendent. Measurements with 20 kV rms applied showed,

for example, that the field distortion and charge density were maximum at approximately 100 Hz, thereby demonstrating good agreement with the B-ce\\ measurements

which showed /max = 80-95 Hz at 20 kV rms (see previous

table)

There were, however, also significant differences be- tween the A and B observations. The A-cell fringe-pattern

measurements consistently showed that the A-cell ac

electric field is not a linear function of position, and that

the field distribution varies periodically with time during

each cj'cle of ac operation, being periodically uniform and

nonuniform as may be seen from the field measurement

data plotted in Fig. 14. The curves show that maximum

distortion occurs near the positive and negative peaks of the alternating voltage waveform. Moreover, observations

at these times showed that the interelectrode field in this

cell has an inverted "U-shaped" distribution (see the ac

results in Figs. 5 and 14). Whereas a linear field distribu- tion was found typical in cell B, this inverted U-shaped

distribution, which implies the presence of positive space charge near the anode and negative charge near the

cathode (a situation noted by Croitoru [19] as being

indicative of charge injection at the electrodes) , was found

typical of cell A at the voltage peaks during ac operation.

48
CASSiDY el al.: kerr-effect studies

(1/4) T

-5 —

0 2 0.4 06 08

RELATIVE DISTANCE FROM HV ELECTRODE (x/d)

Fig. 14. The electric-field distribution in cell A as a function of time with a 60-Hz 1.5-kV-rms applied voltage. Note that in this

cell the field distribution is no longer linear, but varies periodically

during a cycle.

Finally, since the field-distributions characteristic of each cell were found to be reproducible for substantial

periods of time, in spite of repeated refillings of the cells with nitrobenzene, we have felt it reasonable to attribute

the differences between their ac field distributions to the

differences in their electrode materials and/or surface

preparations. Verification of this conclusion and distinc- tion of the relative contributions of the material from those

of the surface conditions will, however, require further study.

V. SUMMARY AND CONCLUSIONS

Our purpose has been to document, from examination

of results from' extensive Kerr-effect fringe-pattern observations in nitrobenzene, several space-charge-induced

trends in the behavior of an insulating liquid under the

stress of high-voltage operation. We have demonstrated

experimentally that electric-field distributions in the

bulk of the liquid are predictable only during operation

under short (microsecond) pulse conditions. Results from

observations during dc and low-frequency ac operation

have shown that the interelectrode electric-field and space- charge distributions are dependent upon the level and

frequency of the applied voltage, the electrode material

and their surface condition, and the immediate previous

history of the system. In a cell with electropolished stainless-steel electrodes,

the interelectrode-field distribution was approximately

linear and the net space-charge density was positive

during operation under high dc and low-frequency voltages. Further, the net charge measured during operation

at a given ac voltage (i.e., at a constant rms level) was

found to be independent of the instantaneous voltage.

The net charge in the liquid bulk between the electrodes remained constant throughout the entire course of the

ac cycle, even when the instantaneous voltage was zero, thereby suggesting that the field and charge distribu- tions in this cell are governed primarily by a steady-state

arrangement of charged particles uniformly distributed

and suspended in the bulk by the steady streaming motion

of the liquid between and around the electrodes. Observations with a cell having glass-blasted nickel electrodes showed different results. The interelectrodefield distribution was linear under direct voltage, but

parabolic under alternating voltages. The observed ac

fields were weaker near the electrodes and stronger in the

region midway between them, thereby implying the formation of positive space charge near the anode and negative

charge near the cathode. As might be expected in a charge

injection process, the electric-field distribution and charge

density in the bulk also varied as a function of time (and

thus voltage) during each cycle of ac operation. The dif- ference between the field and charge behavior in the two

cells is attributed to their differences in electrode materials

and surface conditions. Except for these features, essentially the same behavior was observed in both cells. Their dc fields were both

linear functions of position between the electrodes, and

both showed space-charge enhancement of the field behind

the negative electrode. This latter effect is maximum for direct voltages and decreases with excitation voltage

frequency, whereas electrohydrodynamic motion of the

liquid (always observed during steady-state high-voltage

operation), distortion of the interelectrode field, and

charge density in the liquid are much more pronounced

during low-frequency ac operation.

With regard to the distortions in the ac fields, the dis- tributions observed were found to be frequency de- pendent; as the frequency of the exciting voltage was in- creased the charge measured in the liquid bulk between

the electrodes increased. The plot of space-charge density

versus frequency exhibited a maximum, with this max- imum shifting toward higher frequencies as the voltage

level is increased. As the frequency of excitation was

further increased, the field distribution became uniform

and the space-charge density in the liquid approached

zero, as would be expected when the time between polarity

reversals was too short for charge collection in the liquid near and around the electrodes.

Finally, though these observations still offer no conclusive results for reliable prediction of steady-state field and charge behavior (and thus of the onset of breakdown)

in an insulating liquid, they do demonstrate several important, as yet undocumented trends to be expected in the bulk of the liquid when under the stress of liighvoltage operation. It is hoped that the experimenta

evidence presented will stimulate the further research and

theoretical investigation needed for a more thorough

understanding of the mechanisms of breakdown in liquidinsulated high-voltage equipment.

49
IEEE TRANSACTIONS ON ELECTRICAL INSULATION, JUNE 1974 REFERENCES

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50
Ref erences

1. J. H. Park and H. N. Cones, "Sphere-Gap Volt-Time Curves--Ref erence

Standards for Steep Front Measurements" Am. Inst. Elec. Engrs.

Conference Paper, Reprint No. 57-215, 1957.

2. E. Kuffel and M. Abdullah, "High Voltage Engineering" Pergamon

Press, New York, p. 273, 1970.

3. D. C. Wunsch and A. Erteza, "Kerr Cell Measuring System for High

Voltage Pulses" Rev. Sci. Instru. , vol. 37, pp. 816-820, 1964.

4. International Electrotechnical Commission, "High Voltage Test

Techniques" lEC Publication 60, 1962.

5. E. C. Cassidy, W, E. Anderson, S. R. Booker, "Recent Refinements

and Developments in Kerr System Electrical Measurement Techniques"

IEEE Trans. Instru. and Meas., vol. IM-21, pp. 504-510, 1972.

6. E. C. Cassidy, R. E. Hebner, Jr., M. Zahn, and R. J. Sojka, "KerrEffect Studies of an Insulating Liquid under Varied High Voltage

Conditions" IEEE Trans. Elec. Insul., vol. EI-9, pp. 43-56, 1974.

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November 1973.

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for Calibration of Kerr Cell Pulse-Voltage Measuring Systems IV"

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vol. 2, pp. 90-99, 1971.

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of Nitrobenzene and Water" NBS IR 74-554, August 1974.

51
15. Details of the fitting procedure can be found in J. Hilsenrath,

et.al., "OMNITAB, A Computer Program for Statistical and Numerical

Analysis" NBS Handbook 101, U.S. Government Printing Office,

Washington, D.C., pp. 124-140.

16. E.G. Cassidy, "Development and Analysis of Techniques for Galibration

of Kerr Cell Pulse Voltage Measurement Systems V" NBS Report 1-493,

October 1971.

17. P. D. Thacher, private communication.

18. J. B. Hasted, "Liquid Water: Dielectric Properties" Water A

Comprehensive Treatise . F. Franks, ed. , Plenum Press, New York,

vol. 1, p. 262, 1972.

19. E. A. Cherney and J. D. Gross, "Space Charge Effects in Ghlorobiphenyls" IEEE Trans. Elec. Insul., vol. EI-8, pp. 25-29, 1973.

20. Z. Groitoru, "Space Charges in Dielectrics" in Progress in Dielectrics , vol. 6, J. B. Birks and J. Hart, ed. , Academic Press, Inc.,

New York, pp. 103-146, 1965.

21. H. H. Woodson and J. R. Melcher, Electromechanical Dynamics , vol. II,

J. Wiley and Sons, Inc., New York, p. 383, 1968.

22. W.R. L. Thomas, "The Nature of Particulate Charge Carriers in

n-Hexane and Their Role in Electrohydrodynamic Phenomena" 1972

Annual Report Conference on Electrical Insulation and Dielectric

Phenomena, National Academy of Sciences, Washington, D.C.,

pp. 52-59, 1972.

23. Y. Hawaguchi, H. Murata and M. Ikeda, "Breakdown of Transformer

Oil" IEEE Trans. Power Appar. Sys. PAS-91, pp. 9-23, 1972.

52
N1S-1UA (REV. 7-73)

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION Ok REPORT NO.

NBSIR 74-564

2. Gov't Accession

No.

3. Recipient's Accession No.

i TITI F AND SURTITI K Development and Analysis of Techniques for Calibration

of Kerr Cell Pulse-Voltage Measuring Systems VIII

5. Publication Date August 1974

6. Performing Organization Code

7. AUTHOR(S)

Robert E. Hebner, Jr., Esther C. Cassldy, and Richard J. Sojka

8. Performing Organ. Report No. NBSIR 74-564

0 PKRPORUIKir^ riPr, AN 17 ATION NAMF AND AHHR F*^<\ NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/Work Unit No. 2110426

11. Contract/Grant No. Sandla Order No.

FAO 28-0990

19 wL/Ull3L'i Sr\nncrtrino Ml o <ir» i af i nn NafTi/* finn C r*fnrt1^*tf* A<'lHr*»QQ ^StfAf*t CZitx/ StJitf^ ^.JP\ ft, h£ alt I £. al I KJH i^d lilt. dll U l.'lllL'ilClvr '•UVJIC>>0 ^•-'Kv^l, V-' J'Xr ^lalCT, A> i t } Sandla Corporation

Bldg. 894, Klrtland AFB

East Albuquerque, New Mexico 87115

13. Type of Report & Period Covered Final

7/1/73 - 6/30/74

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

16. ABSTRACT (,A 200-word or less {actual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here.)

This report documents recent progress In the refinement of techniques for accurate

calibration of pulsed voltage measurement based on the electro-optic Kerr effect.

The work Includes a discussion of calibration techniques and a comparison of

calibrations performed In various laboratories. In addition the Kerr coefficients

of water, nitrobenzene and Halowax oil were determined. The measurements In

Halcfwax oil were performed under direct, 60 Hz alternating, and pulsed high

voltage. The measurements of the Kerr coefficient of nitrobenzene and water were

performed under pulsed high voltage, but measurements of the space charge dynamics

In nitrobenzene under low frequency alternating voltage are discussed.

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only tfie first letter of the first key word unless a proper name; separated by semicolons)

Calibration; electrical measurements; high voltage measurements; Insulating fluids;

Kerr coefficient; nitrobenzene; pulse voltage measurement; space charge; water

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