NBSIR 73-403

Development and Analysis of

Techniques for Calibration of

Kerr Cell Pulse- Voltage Measuring

Systems Yll

Esther Christmas Cassidy, Robert E. Hebner,

Richard J. Sojka, and Markus Zahn

High Voltage Measurements Section

Institute for Basic Standards

National Bureau of Standards

Washington, D. C. 20234

November 1, 1973

Final Report on

Sandia Corporation Order No. FAO-28-0734

Sandia Requester and Technical Consultant: S. R. Booker, 7452

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

Prepared for Sandia Corporation

Bidg. 894. Kirtland AFB

East Albuquerque. New Mexico 87115

NBSIR 73-403

DEVELOPMENT AND ANALYSIS OF

TECHNIQUES FOR CALIBRATION OF

KERR CELL PULSE-VOLTAGE MEASURING

. SYSTEMS VII

Esther Christmas Cassidy, Robert E. Hebner,

Richard J. Sojka, and Markus Zahn

High Voltage Measurements Section

Institute for Basic Standards

National Bureau of Standards

Washington, D. C. 20234

November 1, 1973

Final Report on

Sandia Corporation Order No. FAO-28-0734

Sandia Requester and Technical Consultant: S. R. Booker, 7452

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

Prepared for Sandia Corporation

BIdg. 894, Kirtland AFB

East Albuquerque, New Mexico 87115

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

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

INTRODUCTION 1

I. KERR SYSTEM DESIGN AND CONSTRUCTION 4

A. New Cell Construction 4

i

II. ELECTRIC FIELD AND SPACE CHARGE BEHAVIOR IN NITROBENZENE 8

A. Introduction 8

B. Experimental Apparatus and Techniques 11

C. Theory 17

D. Experimental Results 23

E. Summary and Conclusions 51

III. MEASUREMENT OF THE KERR CONSTANT OF NITROBENZENE 54

A. Introduction 54

B. Experimental Techniques 55

C. Results 64

IV. KERR SYSTEM PEAK- READING VOLTMETER WITH AUTOMATIC

DIGITAL DISPLAY 73

A. Instrumentation and Procedure 74

B. Kerr System Measurement Principles 82

C. Results and Conclusions 85

V. MEASUREMENT OF HIGH MEDICAL X-RAY MACHINE VOLTAGES 89

A. Introduction 89

B. Field Trip Report 90

C. Conclusions 90

D. Recommendations 92

E. Results and Benefits 93

VI. FUTURE PLANS 95

APPENDIX A: MEASUREMENT OF 60 HZ VOLTAGES USING THE

KERR EFFECT 98

APPENDIX B: RECENT REFINEMENTS AND DEVELOPMENTS IN KERR

SYSTEM ELECTRICAL MEASUREMENT TECHNIQUES 102

APPENDIX C: EXPERIMENTAL STUDY OF THE BEHAVIOR OF NITROBENZENE

UNDER VARIED HIGH VOLTAGE CONDITIONS 110

REFERENCES 119
INTRODUCTION

Previous NBS High Voltage Measurements Section research adapting

use of the Kerr electro-optical effect for purposes of electrical measurement has been presented in detail in references [l] through [6]. In

addition, several accounts covering the more important phases of this

continuing project have also been published in the open literature.

Included in these have been three papers [7-9] concerned with development,

calibration, and refinement of conventional Wunsch-type [lO] pulse-measuring

Kerr systems. Utilization of the techniques and correction methods described

has enabled measurement of pulses peaking as high as 320 kV. Pulse durations

have ranged from 5 to 15 \is, with rise times of 1-2 [is. Accuracy within

±17o is estimated for measurements of the peak magnitudes of the nearly

rectangular pulses, which were in almost all cases measured simultaneously

by a calibrated Kerr cell and a calibrated NBS pulse voltage divider.

Also included in the publications prepared under the NBS program have

been papers reporting development of Kerr electro- optical fringe-pattern

techniques for mapping and measurement of both steady-state dc [ll] and

transient [l2] electric fields between and around the Kerr cell electrodes,

and two papers reporting results from use of these methods for studies of

electric field and space-charge behavior in nitrobenzene during high voltage

operation [l3,14]. A third paper, presenting for the first time results from

electro-optical field mapping and space-charge studies under low frequency

alternating high voltage conditions, is now nearing completion. The details

of this work, which required analysis and evaluation of results from hundreds

of fringe-pattern observations, are included in Section II of this report.

1
A paper reporting use of a Kerr system for optically coupled measurements of high 60 Hz alternating voltages [l5] was also completed during this

year. In keeping with our earlier practice, its reprint and reprints of

•references [9] and [l4], also completed in FY 1973, are given in Appendices A-C.

The main body of this report, which covers FY 1973 progress on this

program in some detail, is divided into sections. As in previous years,

the first section reports on new Kerr cell construction. Section II compares

results from studies of electric field and space charge behavior in nitrobenzene

under varied high voltage conditions. Because of their novelty and promise

for ultimate attainment of an ac procedure allowing accurate (to ±0.57o or

better) high voltage calibrations of pulse measuring Kerr systems, the ac

studies are emphasized.

Results from extensive experimental measurements of the Kerr electrooptical coefficient of nitrobenzene, over a range of selected operating

temperatures and wavelengths, are given in Section III. Section IV reports

on development of a Kerr system peak-reading voltmeter which utilizes

commercially available equipment for digital display of the Kerr cell count

at the peak of a high voltage pulse, thereby yielding an immediate semiautomatic measure of the peak magnitude of [is duration high voltage pulses.

Section V describes experiments performed on a field trip to the Bureau of

Radiological Health in Rockville, Maryland. During this trip a Kerr system

was employed for measurement of medical X-ray machine voltages. As in the

short (m-s) pulse work, results are evaluated and compared with simultaneous

divider measurements.

2
Finally, this year's report concludes with a brief statement of

plans for work to be completed in FY 1974. As during past years, the

program will continue to receive partial financial support from the

Atomic Energy Commission through the Sandia Corporation of Albuquerque,

New Mexico-
I. KERR SYSTEM DESIGN AND CONSTRUCTION

A. New Cell Construction

For the most part new cell construction during FY 73 involved

attempts at fabrication of a cell virtually free of effects from the

fringing electric fields at the electrode ends. Such a cell is desirable

for two reasons: (1) its half-wave retardation voltage or cell constant,

V would be easily calculable from the cell dimensions and the Kerr

melectro-optical coefficient of the liquid, and (2) its use would allow

measurement of the Kerr coefficient without need for evaluation and

correction of dif f icult-to-predict errors introduced by the fringing

nd fields.

During this year, two cells'' were constructed which confined the

birefringent Kerr-cell liquid within a central interior volume well removed

from the electrode ends. This would appear to offer an obvious, simple

solution to the fringing end-field problem. End- and side-view photographs

of one of the cells constructed this year, that with interior liquid volume

dimensions 1 cm wide x 1 cm thick x 4 cm long, are shown in Figs. 1 and 2.

The construction of the other cell is essentially the same, except that the

length of the Kerr cell liquid path is 10 cm. In both cases the electrodes

are stainless steel with dimensions 5 cm wide x 14 cm long x 0.75 cm thick.

The surfaces of the glass cells and electrodes are ground optically flat so as

to allow glass-to-metal sealing without use of sealing gaskets or compounds. —

The special grinding and sealing processes involved in fabrication of

these cells was performed in the NBS Glassblowing Shop. The authors

are especially grateful to Edward Muth whose skill in these techniques

made construction of these cells possible.

4
5
Figure 2 Side view of "end-field-free" cell. 6
The junctions at the corners of the rectangular glass vessel are also

ground and then welded by a glass- to-glass sealing process. The entire

vessel, including its expansion and thermometer volumes, is then annealed

to relieve residual s train, especially in the end windows where the laser

beam passes during system operation. Polariscope inspection of these

windows after annealing showed that they are free of residual strain in

these areas.

After completion and cleaning of both the glass cell and the electrodes,

the glass volume was placed in a centrally located region between the electrodes

and held "finger tight" as assembled in Figs. 1 and 2 while a vacuum was

pumped through one of the outlets, the other outlet being sealed. The cell

assembly was thus drawn evenly and tightly together, effecting a dry seal

between the flat glass and steel surfaces. The bolts passing through the

external clamping assembly were then tightened lightly to maintain the seal

during later handling of the cell. Unfortunately, it was soon found that

the force exerted on the glass cell by the clamps introduced strain in the

cell windows, thereby producing an effect comparable to that resulting from

the fringing end fields. Because of this difficulty, our attempts to fabricate

a Kerr cell free of fringing end-field and strain effects were again

frustrated. The cells were, however, useful in allowing measurement of the

Kerr coefficient; a method involving use of measurements at two different

voltage levels was devised to enable experimental correction of the errors.

This method is discussed in detail in Section III.

7
II. ELECTRIC FIELD AND SPACE CHARGE BEHAVIOR IN NITROBENZENE

A. Introduction

Recent experimental work has demonstrated the usefulness of the

electro-optic Kerr effect for the determinations of various electrical parameters under the influence of high voltage. Among these are the measure1 ju- u 1 [7,8,10,16] ^ ^ . . ^ ment of pulsedhigh voltage , the determination of space charge

effects in nitrobenzene^''"^ and chlorinated biphenyl s ^ "'"^

, the measurement

of the electric field distortion caused by the insertion of a solid dielectric

in a liquid insulant ^^^"^

, the measurement of 60 Hz alternating voltages^''"^ ,

and the observation of the spatial and temporal variation of the electric

[ll 12 2l] field distribution caused by pulsed and direct voltage ' ' .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

sysl

[24]

[22] [23]

of bulk space charge and polarization waves in charged liquid systems

and the role of particulate charge carriers in electrical conductance

Realizing that further advances are predicted on a knowledge of electric

field and space charge behavior in liquid dielectrics, we have used refined

Kerr electro-optical fringe pattern techniques ^ ''"^ ~^ to measure 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 nitrobenzene 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 electro-optical fringepattern techniques to visualize electric field distributions 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 frequency

on space charge density and distribution are investigated between 0 and

±50 kV; frequencies range from 40 to 200 Hz.

Nitrobenzene is the liquid investigated, primarily because of its high

- 12 2 electro- optical 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

[25]

dielectric in prototype "high- energy" electrostatic generators to its wide-

[26] spread use in high-speed photographic shutters and laser "Q-switching"

[27] devices , to its use for precision measurements of pulsed high voltages.

In connection with the latter application, extensive studies, now underway for

more than five years, of the performance of nitrobenzene-filled Kerr cells

immersed in oil under both transient ((-ls 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

[28] charge effects , 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

[2 Its performance is also affected by other widely reported high-field phenomena

such as electrohydr odynamic 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 remains admittedly poor.

It has been our philosophy in 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 experiments 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 observed 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,

whether 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 accelerated 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. The fourth

I 10 '
section presents and discusses the data obtained under direct voltage and

under alternating voltages. The final section, Section V, presents the summary

and conclusions.

B. Experimental Apparatus and Techniques

A schematic diagram of the experimental apparatus is given in Fig. 3. The

system consists of a nitrobenzene-filled parallel-plate capacitor within a glass

vessel (Kerr cell), a triggerable pulsed argon laser, crossed polarizers oriented

at + and -45° to the interelectr ode field direction, retardation plates oriented

as indicated for elimination of field-directional fringes ^"^^"^ not pertinent in

the present work, and appropriate photographic equipment for recording of the

transmitted fringe patterns observed 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 cell electrodes.

The beam is focussed and passed through the circular aperture to exclude

extraneous reflections and, on occasion, to allow Schlieren observations of the

liquid motion invariably produced by steady-state high voltage operation. For

purposes of illustration, the diagram includes a typical fringe pattern

photographed 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 100-MQ resistive

[31] divider 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.

11
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12
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 latter '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 6 M-s) 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 output voltage pulse

for triggering of the laser pulse. The delay and synchronization of this

delayed trigger signal were adjusted. Fig. 4, so that the laser flashed in a

strobe-like 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 clock pulses during At. Two

methods were used to correlate a value for the interval At with a specific

point during a cycle of the applied voltage. The first was to detect a portion

of the laser light pulse with a photomul tiplier and display the time relationship between the laser light pulse and the applied voltage on the oscilloscope

screen. The time interval At was then adjusted until the light pulse coincided

with the peak of the positive half-cycle. The second and somewhat more

accurate method was to adjust At until the fringe pattern resulting from

the electro-optic Kerr effect indicated that the laser was pulsed at the peak

13
Figure 4. Timing 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. The center trace represents the time for one sweep of the horizontal time base of the oscilloscope. The

oscilloscope is externally 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 fxs.

14
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 |i.s, i.e., to

within ±0.87o of the shortest half-cycle used.

The present work was conducted using two specially prepared cells (see

Table 1), one with electro-polished 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 electro-polishing and glass-blasting

procedures were adopted to minimize the effects of electrode surface contamination. The electrode edges and corners were rounded to avoid premature

electrical breakdown. The nominal electrode spacing in both cases is 0.5 cm.

Glass- 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

were avoided by immersing the test vessel in transformer oil. More complete

[12] details of our cell construction technique were presented elsewhere

With regard to the test cell insulant, nitrobenzene was, as mentioned

above, selected primarily because of its high electro-optical coefficient

and relatively high electrical breakdown strength. Though the electrical

3 resistivity of commercially pure grades was inadequate (of order 10 Q*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

15
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16
long been used to remove moisture and other impurities from insulating

r 32 1 8 9

oils , increases the nitrobenzene's resistivity to the order of 10 - 10

Q m. At this level, prolonged 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 was the principal contaminant. Thus, because of the hygroscopic and toxic

properties of nitrobenzene, our entire cell-filling and sealing procedure is

performed under vacuum.

C. Theory

Comprehensive theoretical discussions of the electro-optic Kerr effect,

[33-35] including derivations of the Kerr constant , the application of the Kerr

effect to high voltage measurement, and methods for eliminating the effects

[9]

of fringing fields , are available in the literature. The purpose of this

section is to make explicit the assumptions used in the analysis of the data

presented. The governing equation for the Kerr effect is

n, - n = X B E^, (1) 11 ± ^

'

where 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. Eq. (1) can be solved for the phase shift, 0, between the components of the light beam polarized parallel to and perpendicular to the

direction of the applied field:

L

0 = 2n f E Bdje. (2)

In Eq. (2), L is the geometrical length of the optical path through the applied

field. To reduce Eq. (2) to a more convenient form it is necessary to make a

17
number of observations concerning the electric field distributions in the

cells used. To clarify this discussion, define a set of coordinate axes so

that the z-direction is the direction of propagation of the light beam, the

x-direction is perpendicular to and the y-direction is parallel to the surface of the electrodes. In this notation Eq. (2) can be rewritten

L

0(x,y,t) = 2n Jq BE^ (x,y,z,t) dz , (2a)

which also explicitly includes time dependence. The first assumption is

that B is a constant, so that

L

• 0(x,y,t) = 2nB E^ (x,y,z,t) dz. (2b)

In the present work, all field mapping is done in the x-direction. We have

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

of the electrodes. It is shown in our data and has been shown in previous

studies in cells with similar geometry that 0(y) varies only slightly near

the center of the plates so that errors in locating the exact center of

the plates are negligible in comparison to other errors in the analysis.

We can therefore rewrite Eq . (2b) as

rL 0(x,t) = 2nB Jo E (x,z,t) dz . (2c)

Because the experimental set-up is such that light polarized at an angle of

45° to the direction of the applied field passes through the Kerr cell and

18
then impinges upon an analyzer oriented perpendicular to the direction of

polarization, the light transmitted by the analyzer obeys the relation:

= sin^ [1/2 (^(x,t)]. (3)

m

In this equation we have again suppressed the y dependence and I(x,t)/I

m

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 I^, 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(x,t)/I^ = 0, i.e. the positions

of the dark fringes.

[ 9 ] It has been shown that Eq. (3) can be rewritten

m '^m

where the overbar (e.g. in A) denotes the following

(4)

and

(^) denotes

I X I m m

at a specific value of x.

19
In Eq . (4), E is the smallest effective field strength that produces a m maximum I in the amount of transmitted light. Methods have been developed m

to correct the observed values of (I(t)^I ) for variations in the x m X

[ 9 ] direction due to the fringing fields at the electrode ends . However,

these corrections were not applied to the present data because it has

been shown previously that they modify values of (E(t)/E ) measured with m X

parallel-plate electrodes greater than 10 cm in length and spaced less than

1 cm apart by less than \%.

In this study information was obtained concerning [E(t) and thus the

space charge density, at certain times during the cycle of an applied steadystate alternating 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 11"

To make explicit this situation Eq . (4) can be written

m m

where t 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.

20
The center of each dark band or fringe was assumed to indicate a relative

intensity of (I/I^)^ ^ = 0, and thus, from Eq. (5), a point where the relative

electric field intensity (E/E^)^ ^ was equal to the square root of

an even integer. In keeping with the convention established ear 1 ier ^ ''"^

,

numerical values n were assigned to each dark fringe by counting (n = 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 1) between the electrodes (see

Figs. 3 and 4). The experimental values of (x/d) and (E/E^)^ ^ obtained from each

photograph were fitted to a first degree polynominal:

(^)^ = a + b (x/d), (6)

m

or to a second degree polynominal:

(^) = A + B (x/d) + C (x/d)^ (7)

where a, b. A, B, and C were coefficients determined by a least- squares

Lb 61

best fit method . The appropriate polynominal was judged to be

sufficiently accurate whenever

(=-),. J (ir-) ±0.05 (^) (8) fitted = ^E exp exp. ^m m m

21
In order to obtain the space charge density p from the electric

field distribution, the differential form of Gauss' Law was used, i.e..

(9)

where e is the dielectric constant of the liquid medium. For the purposes

of this paper numerical values of p were not needed, and, neglecting the

effects of fringing end fields, Eq . (9) was reduced to:

m t _ Pd

S(x/d) ~ E e (10) m

Computations of the coefficients in Eqs. 6 and 7 were used to plot the

electric field distribution, i.e., (E/E ) as a function of (x/d) and to

m t allow convenient examination of space charge effects in terms of the reduced

space charge density P : "

S(E/E ) "r' 8(x/d) • (^1)

Whenever a linear electric field distribution, of which the dc pattern in

Fig. 6 is typical, was observed, Eq. (6) was fitted to the data and the

reduced space charge density was given simply by

P^ = b (12)

Whenever a parabolic field distribution was computed (see, for example, the ac

pattern in Fig. 6), the reduced space charge distribution was determined as follow'

P^ = B + 2C(x/d). (13)

22
D. Experimental Results

[9 12]

It was reported earlier ' that electric fields produced by

applying short (5 to 20 fis 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. 5. This photograph, which is a 0.3 (J-s

exposure taken at the peak of a 10 M-s 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. 6 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

interelectrode field is evident from the fringes recorded between the electrodes.

Further, plotting (see Fig. 7) of the distorted field distributions from the

fringe numbers and positions, as described in Section IM, 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 sectionsDiscussions of the reproducibility of the electrical and electro-optical

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 presented in

graphical form. A number of photographs of raw data are included to indicate

23
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to readers unfamiliar with this technique the tj^jes of observations that

can be made.

1) Measurements of Current under Direct Voltage

When the test cell is first filled with the purified nitrobenzene 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 non-reproducible.

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 electro- optical 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

electro-optic 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 reproducibility of all measurements

occurring after the brief conditioning periods. Other sealed cells have

been in use for over three years with similar results. (Because

27
nitrobenzene is hygroscopic, unsealed cells do not maintain this

reproducibility)

.

[37,38]

Other authors 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

electrodialy tic varnish. In that case, the following explanation for current

behavior was postulated^ :

". . . the oncoming residual ions are trapped within the polymer

matrix while electrical neutrality is preserved thanks to the stationary counterions; charge displacement in the reverse direction

cannot occur unless the matrix has sufficient electronic conductivity.

Of course, if voltage is reversed, the mobile ions are injected into

the liquid and the arrangement works as a very efficient injector."

However, as noted above, the same time and polarity dependent behavior

of the current was observed in our cells in which the electrodes were not

varnished. A different, equally qualitative explanation for this behavior

[39]

has been postulated . This hypothesis, which seems a plausible and perhaps

a more accurate explanation for our observations, contends that electrical

conduction is primarily the result of the motion of micrometre-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 micrometre and sub -micrometre sized particles become

trapped on insulating areas of the metallic electrodes because the

insulating areas prevent them from readily giving up their charge to

28
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

[39] current) and for the increase of current with polarity reversal

(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

)Ug

[40]

[24] one of the electrodes . The particles eventually accept enough

charge from the electrode to be repelled to the other electrode

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- induced 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

[41] greatly reduced by free particles

29
2) Electric Field Measurements and Charge Behavior with High Direct Voltag

Typical field distribution data under direct voltage are shown in Fig. 8.

This figure contains information obtained from fringe-pattern measurements

by applying 0-±30 kV direct voltage to one electrode of Cell A (see Table 1).

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. 9 shows explicitly the effects of high voltage conditioning described

earlier. The dashed lines show the electric field distribution immediately

after polarity reversal (the power supply polarity was reversed so that the

nongrounded electrode was changed from positive to negative). During one

half hour of negative high voltage operation, with sequence as shown in the

figure, the field distribution shifted to those shown by the solid lines.

[29 42 ] These results are in agreement with those reported by previous workers ' ,

in so far 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. 8 and 9. This difference is probably attributable

to differences in our electrodes; 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

30
RELATIVE DISTANCE FROM HV ELECTRODE (x/d)

Typical field distribution data under direct voltage. Photographs

from which some of the data were taken are presented in the center

of the figure. The presence of fringes behind the negative electrode

is discussed in the text.

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32
affected by the electrode material is presented 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 interelectrode field distribution, i.e., of

(E/E ) as a function of relative position (x/d) between the electrodes,

tn X , t and of the reduced space charge density 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 (Eq. 6). In this

case was independent of the relative position (x/d) between the electrodes

and its value was determined from Eq. (12).

Results calculated from the measurements of Figs. 6 and 7 with Cell A

and from similar typical experiments with Cell B are listed in Table 2.

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 high voltage 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

33
TABLE 2. Reduced space charge density in bulk of liquid during high

direct voltage operation.

CELL A

Applied

Vol tage

Reduced Charge Density

Before Conditioning After Conditioning

(kV)

+10

Pr Pr

0.87

+20 0.88

+25 0. 77

+30 0. 62

-10 2.35 2.35

-20 2.64 1.54

-25 1.43 0,90

CELL B

+15 0.64

+30 0.56 0,47 , +35 0,39 '

-30

34

0.21
work has shown that if the particles were metallic with 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, the above trends are also compatible with the postulate that

the current conduction is governed by the action of insulating particles, in

this case perhaps of sub -micrometre size alumina particles which were imperceptibly carried with the liquid in passing from the chromatographic column

during the process described in section B. If this be the case, the insulating

particles may expect 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 attached 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 removal of the applied

high voltage also tend to substantiate the particle postulate. Schlieren movies

35
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 significant intensity exists behind the negative

electrode. The fringes behind the cathode in the +20 kV pattern, for example,

indicate that fl\ < (E/E^) < ./"G in the region adjacent to the back of the

cathode surface. In this cell, for which E =9.8 kV/cm, this indicates

m

that E «i 22 kV/ cm immediately adjacent to the back surface, that E = 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 resultsfrom 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 cathode, including its

backside, and cause the observed field enhancement. The irradiance around

the cathode support 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

36
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 unforeseen 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 high-voltage 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. 6 and 10). 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 steady state operation show that the fluid motion is

jmuch 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

duration of exposure to high voltage operation: In a

continuous experiment the enhancement was observed to increase with voltage

37
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 exposure 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 minutes 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 recording the data for the -10 kV curve in

Fig. 6 (immediately after reversal of the voltage polarity), shows greater

enhancement (3 to 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 electrode 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.

3) Measurements with Alternating High Voltages

Fringe-pattern data concerning the electric field distribution, and

hence the space charge density and distrubution were taken under a variety

of alternating high voltage conditions: (1) Observations were made at the

38
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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 operation; (3) As in

the dc studies, these observations were conducted using both cell A and B so

as to bring out behavioral differences which might be attributable to the

electrode materials. Typical results from these studies are presented and

discussed in the following paragraphs.

Fig. 10 shows the fringe patterns photographed at the positive maximum

of a 22 kV rms sinusoidal voltage at various frequencies between 40-105 Hz

using Cell B. The significant observation from these photographs is that the

number of inter el ectrode 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 3. In

2 this table the relative position x/d of each transmission minimum, (E/E ) . = n, m X , t

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 frequency of the applied

voltage can be calculated (Eqs. 11 and 12). Graphs showing the reduced space

charge density as a function of the frequency of the applied voltage at

two different voltage levels are shown in Figs. 11 and 12. These data, like

those in Fig. 10 and in Table 3, are the results of observations taken at the

positive maximum of the applied voltage. Two conclusions can be seen from

the plotted vs. 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.

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(U 4-1 O M o 3 U

« OD QJ c

o •H N

c e

0) CD 3 o Qi e o

ra B •H

D. !<

<u CO J= e

QJ

dJ cu 4-1 O x; CD 3 4-1 e

-a cu •r-l

(11 00 ON X

M CD o

J-l V4

<u 1—1 60 a

J2 O •H o. > fa to

''^ *AllSN3a 39dVH0 30VdS 030003^

43
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 various times during a cycle of 15 kV rms

,

60 Hz operation using Cell B are shown in Fig. 13 . We note that the

electric field distribution is linear with positive slope throughout the

whole cycle. If we extrapolate to zero, 1/2 T, or T, the field distribution

is linear, being equally positive and negative about the center (x/d = .5).

Fig. 14 shows some of the fringe patterns from which these plots were

obtained. Note that at time 1/2 T, the applied voltage is instantaneously

zero, yet light appears near the 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 volume charge 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. 14 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 electrodes, as the field enhancement

always appears behind that electrode which is instantaneously negative.

44
Figure 13. The electr ic field distribution in Cell B at various times

during the cycle of 60 Hz, 15 kV rms applied voltage. The

period of the applied waveform is denoted T, so, for example,

the data designated as 1/4T were taken at the positive maximum

of the applied voltage.

45
60Hz

ISkVrms

5/qT

Figure 14. Photographs from which some of the data in Fig. 11 were taken.

Note that there is some light transmitted at 1/2T, i.e., when

the voltage is instantaneously zero. As explained in the text,

this indicates that the bulk space charge density is constant

throughout the cycle.

46
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. 15. From this type of observation,

the following results, showing relationship between the frequency, f , at max which the net space charge density was maximum and the applied voltage

level, were obtained:

TABLE 4 Measurements of f At max

Various Voltage Levels Using Cell B

Voltage ^max

(kV rms) (Hz)

10 45-65

12 55-65

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. 7), 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 dependent. Measurements with 20 kV rms

47

applied showed, for example, that the field distortion and charge

density were maximum at approximately 100 Hz, thereby demonstrating

good agreement with the B-cell measurements which showed f = 80-95 Hz max

at 20 kV rms (see Table IV).

There were, however, also significant differences between 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 cycle of ac operation, being periodically uniform and nonuniform

as may be seen from the field measurement data plotted in Fig. 16. 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. 7 and 16). Whereas

a linear field distribution 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 [2 8] as being indicative of charge injection at the

electrodes), was found typical of Cell A at the voltage peaks during ac

operation.

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.

49
0.2 0.4 0.6 0.8

RELATIVE DISTANCE FROM HV ELECTRODE (x/d)

Figure 16. The electric field distribution in Cell A as a function of time

with a 60 Hz, 15 kV rms applied voltage. Note that in this cell

the field distribution is no longer linear but varies periodically

during a cycle.

50
Verification of this conclusion and distinction of the relative

contributions of the material from those of the surface conditions

will, however, require further study.

E. 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 (M-s) 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 electro-polished 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 distributions 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

51
between and around the electrodes.

Observations with a cell having glass blasted nickel electrodes

showed different results. The interelectrode field 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 difference 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 distributions

observed were found to be frequency dependent; as the frequency of the exciting

voltage was increased the charge measured in the liquid bulk between the

electrodes increased. The plot of space charge density vs. frequency exhibited

a maximum, with this maximum shifting toward higher frequencies as the voltage

52
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 rules

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 high voltage operation. It is hoped that the

experimental evidence presented will stimulate the further research and

theoretical investigation needed for a more thorough understanding of

the mechanisms of breakdown in liquid-insulated high voltage equipment.

53
III. MEASUREMENT OF THE KERR CONSTANT OF NITROBENZENE

A. Introduction

The electro- optic Kerr effect was identified by John Kerr in 1875.

Since that time it has been used for a variety of purposes including high

voltage measurement, electro-optic field mapping, high speed shutter

applications, etc. Historically, the electro- optic Kerr coefficient has

been measured in an attempt to obtain information concerning either

molecular structure or molecular interactions in the liquid state. Because

the molecular systems that exhibit a large Kerr coefficient were not amenable

to convenient, accurate theoretical analysis, the accuracy requirements were

not stringent. The development of high voltage measurement systems based on

the electro-optic Kerr effect have however necessitated the accurate

determination of the Kerr coefficient to insure proper design. In addition,

it is necessary to know the temperature dependence of the Kerr coefficient

so that measurements performed at different temperatures can be compared

without loss of accuracy.

An additional significance of the present work is that most previous

determinations of Kerr constants were made before lasers became commonplace.

Most earlier determinations were not, therefore, performed at wavelengths of

interest today. Although it is recognized that a general characterization of

the Kerr constant as a function of wavelength is needed, the present study

was designed to supplement existing information at specific laser wavelengths.

The Kerr constant was defined by Eq. 2 (Sec. II-C). Making the same

assumptions that were previously discussed, we can rewrite Eq. 2c as

54
B = 0(x,t) [2n f E (x,z,t) dz]

-1

(14)

The work described here was confined to centrally located paths and the

measurements of cj and E were performed simultaneously at the peak of a

high voltage pulse of approximately 10 [is duration. We therefore suppress

the X and t dependence and rewrite Eq. 14

At this point we depart from the notation developed earlier and write

where V is the applied voltage, d is the plate spacing and L' is the

effective length of the plates. This assumes that the actual field

distribution can be represented as a uniform field of strength ^ and

extending over a length L'. Determination of the Kerr constant, therefore,

requires that the phase shift d, the applied voltage V, and the plate

spacing d be measured and that the effective length L' be determined.

B. Experimental Technique

1) Introduction

This section describes two independent pulsed voltage techniques

that were used to measure the Kerr electro-optic coefficient of liquid

nitrobenzene at various temperatures and at selected wavelengths. In

each technique, voltage pulses of 15-85 kV peak magnitude and approximately

L

(15)

B = 6 [2n (^) L']

-1

(16)

55
10 n-s in duration are used. The following discussions include a brief

description of the Kerr cell construction and the basic theory needed

in determining the Kerr electro- optic coefficient of nitrobenzene using

each technique.

2) "End-Field Free" Cell Technique

The "end-field free" cell, Fig. 1, used to make Kerr coefficient

measurements is designed specifically so that the applied electric field

is uniform over the nitrobenzene-filled segment of the light path, i.e.,

so that the fringing end field distortions are exterior to the nitrobenzene

portion of the light path. The cell was constructed with two parallel plate

electrodes overlapping a four-sided, rectangular, glass chamber used to conf

the nitrobenzene. The interior dimensions of the glass chamber were given

in Section I.

For a light path centrally located in the glass chamber and parallel

to the length of the electrodes the total phase retardation 0 is given by

^ -

,2 + ^mech

where L is the interior length of the glass chamber (the length of the

nitrobenzene portion of the light path) and ^^^^^^ is the phase retardation

resulting from mechanical strain present in the glass windows at the ends

of the chamber. Under the assumption that

0^^^^^,!,^ is a constant, the electrooptic coefficient can be determined from two separate experiments which

measure the phase retardations0^ and 0^ two different applied voltages

and V^, respectively. Using this information, both B and

0^^^^^^ can be

56
calculated from Eq. 17:

B = 2nL (V^^-V^^)

(18)

and

0.mech (19)

3) Two Cell Technique

This technique utilizes the two Kerr cells of conventional design

shown in Fig. 17. For a centrally located light path between the

electrodes in each cell the applied electric field will vary along the

length of the light path due to the fringing fields at the ends of the

electrodes. Each cell is identical except in the length of the electrodes

where the respective lengths for cell A and cell B are 24 cm and 12 cm.

From Eq. 16, the phase retardation for each cell can be written

(20)

6^ = 2nB (—) L

B (21)

The cells are constructed so that d - d and so that

57
0) 4-1

<u

g

N to C Vj

Q) CO J3 O,

(0

O -H

QJ (0 4-1 C C

r-l T3 0) E OJ T3 M C

01 00

4-1 T-l 0)

(1)m Sj o

JJ CU CO

1-1 t3 CU T3

<U S O o a) (U

y-iH -u

(U •H T3 x; > O 4J a 4-1 c C 1) 0)

00

58
(22)

L'g = (23)

where Ai is the correction that must be added to the geometric length

of the plates to obtain the effective length. The basis for the

assumption that AX is independent of the length of the plate is the

solution to the electrostatic boundary value problem first solved by

, . [43] Lemoine »

L' =X+^[1 -^logf ], (24)

[44] and later generalized by Chaumont

L' = X + Ml + ;^ log (1 + p]. (25)

In these expressions X is the electrode length, d is the spacing, and

t is the thickness of the electrodes. Eq. 25 indicates that if one

constructs two cells differing only in the length of their electrodes,

the difference between the effective lengths would be equal to the difference

between the geometrical lengths of their electrodes.

Using Eqs. 22 and 23, Eqs. 20 and 21 can be solved to yield

59
B = ^

(26)

2TTV i^-X^

4) Experimental Procedure

The experimental arrangement of Kerr cells used in making Kerr

coefficient measurements by the "end-field-free" cell and by the two-cell

method is shown in Fig. 18. A schematic diagram of the pulse voltage

generating and measurement system is also included. The basic apparatus

used in each technique is conventional in high voltage pulse measuring Kerr

[l-6]

systems, the details of which have been described previously

Additions to this apparatus and procedural changes have been included to

permit measurement of the electro-optic coefficient at selected wavelengths

and over the temperature range from 290 K to 315 K.

Electro-optic measurements are made at different wavelengths using

either a cw HeNe laser (632.8 nm) or a pulsed argon laser. A wavelength

selector at the output of the argon laser is used to obtain Kerr coefficient

measurements at a number of laser wavelengths of argon gas, specifically

514.5, 496.5, 488.0, and 476.5 nm.

The temperature of the nitrobenzene is varied using a commercially

available heater to stir and warm the oil bath in which the Kerr cell is placed

Measurements of the Kerr electro- optic coefficient are initially carried

out at room temperature. The oil bath is then heated until the mercury

thermometer sealed inside the Kerr cell indicates a temperature of

approximately 310 K. The heater is then removed but measurements are not

60
3oUO

'10 <

a.

5' < UJ o

COo

CO 0CO u O

<u e x:

<U 4-J

4-1 cn >+-( O

0)

m 73

•u

d

C CD 01S H

(U OJ -a

to >

to •!-( e

(1) 4-1

<u •H 00 U C

•H -r-l m to

0)O (U o to

^J 3 .-I ^< a. to

tu 3

fc4 (U o ^ to d O 4J CO O r-l T3 > d

tu 6

to (U -H 3 J3 to

4-1 to tu 3 m T3

4J

O to

to 6 u -u

to

d <u cx tu ^ a 6

to tu X) 3 3

4J (0

0) tM 6 to

to 3 6 cr

to 4-) .H ^ to d

to 4-1

u

•H OJ 'O O 4-1 to U 1—1 •H 1-1

4-) (U (U d

tJO

•iH

H

to

U

u tu 01 C« XI W

toe

01 J2

u

tu3

60

•1-1 [X4

61
taken until the bubbles produced from the mixing of the oil settle outj

allowing an undispersed laser beam to be transmitted through the Kerr

cell. As the nitrobenzene cools data are taken after every 1 K drop

in temperature. The cooling rate is approximately linear with a slope

of 2K/h.

Typical oscillograms used to make Kerr electro-optic coefficient

determinations from the two cell technique are shown in Fig. 19.

Included are the voltage divider "slideback" measurements showing the

peak of the applied voltage pulse and photomultiplier response to the

light transmitted through cells A and B. Each Kerr cell is situated

between a polarizer and an analyzer oriented at plus and minus 45° with

respect to the applied electric field. The light path through each cell

is aligned with a photomultiplier which provides an output voltage approximately proportional to the irradiance of the transmitted light.

The relative irradiance transmitted through a Kerr system is given

in Eq. 5,

(I/I ) = sin^ [|tt(E/E )J ] . m X , t m X , t

It is shown in Fig. 19 that as the voltage decreases the transmitted

light intensity varies through a series of maximum and minimum values

producing a series of light pulses. The maximum and minima defining each

light pulse are assigned odd and even integers respectively for counting the

first maximum before the voltage pulse falls to zero as 1, the first minimum

before the voltage falls to zero as 2, the second maximum as 3, second

62
43

Ul

:2 > :2§ 5 °- * m

Ul

U „ O < > 5)

00o

QQ II

Od < I' ^ E U o U c

(U •HO

•H

4-10)ooo

•iH u

a.oIouuo

0) co

•1-1 u

CDCeu

0) u

(U c

•H

0)Ww cr

CD

C

5-1 x:

cxo o o cu O r-l CO <u O O

!-<

O

CO 5

CJ 4-1 a 0) H -u

<7^

CU

63
minimum as 4, etc. The count is continued to the peak of the voltage

pulse, thus defining the largest integer n. The values of l/l^ and n

determined from an oscillographic record of the photomultiplier response

are used to compute 0 for a given Kerr system at the peak applied voltage.

The peak value of the applied voltage pulse is determined using

a "slideback" technique for measurement of voltage across the low side

of a 500 0 pulse divider connected in parallel with the appropriate

Kerr cell(s). This pulse measurement procedure yields a value of the peak

magnitude of the voltage pulse which is estimated to be within ±1% of its

true value.

C. Results

A comparison was made between the Kerr electro- optic coefficient

of nitrobenzene, at 632.8 nm determined by the "end field free" cell technique

and the two cell technique. Values of the electro-optic coefficient B of

nitrobenzene were determined from a series of at least ten experiments

performed using each technique at each specified temperature. The mean

values of B are compared in Table [s].

Table [5] Comparison of Kerr Coefficient Determinations

End Field Free Cell

Technique (lcmx4cm)

Two Cell Technique 3.24 x 10 296.0

9 B[m/(V) ] Temperature ( K)

3.21 X lO'-^^ 295.8

3.17 X 10"12 296.1

64
The values quoted in this table are estimated to be accurate to within

±5%. This estimate is obtained by assuming that there is a cumulative error

of not more than ±4% in the measurement of 0 and geometrical parameters involved

as there is an uncertainty of ±1% in the voltage measurement. Within each set

of at least ten measurements, no determination of B differed from the average

by more than 1.67o.

The Kerr electro-optic coefficient of nitrobenzene was measured at

different wavelengths using the "end field free" cell. As previously

explained, it is necessary to perform experiments at two different voltage

levels to correct for the birefringence due to residual strain in the glass

windows of the cell.

In Table [6], the Kerr electro-optic coefficient of nitrobenzene is

categorized according to wavelength and according to nominal values of the

peak voltages used. The Kerr coefficient is computed from Eq. 26. More

than one Kerr coefficient value entered into a given category signifies

tha t a set of experiments were taken several days apart to verify the

consistency of the measurements.

At a given wavelength, calculations (Eq. 19) indicated that the

mechanical phase retardation varied according to the pair of voltages used.

This situation is made explicit in Table 7, in which the Kerr coefficient

and phase shift due to strain birefringence in the glass window of the cell

are tabulated with wavelength and temperature as parameters. As stated

previously, at least ten observations were made at each value of temperature

and wavelength. The average and minimum and maximum value for 0 , are ° ° mech

listed. Two possible causes of the wide variation in 0 , have been mech

identified:

65
Wavelength

(nm)

Kerr electro-optic coefficient of Nitrobenzene

B(m/V^)

.632.8

a

3.20 X lO"'^^

-12

3.12 X 10

b

-12

3.19 X 10

c

-12

3.16 X 10

514.5

-12

4.20 X 10 -- -12

4.24 X 10

496.5

-12

4.43 X 10

-12

4.42 X 10

-12

4.42 X 10

488.0

-12

4.58 X 10

-12

4.54 X 10

4.66 X lO'-*"^

- 12 4.58 X 10

476.5 4.68 X lO'-^^

-12

4.72 X 10

-12

4.71 X 10

Table [6] The Kerr electro- optic coefficient of nitrobenzene B is given

for various wavelengths at a temperature of 296 K. Values of B

were computed from experimental data as prescribed for the endfield free cell technique. Columns a, b, and c indicate pairs

of nominal voltage levels (80 & 60 kV, 100 & 80 kV, and 100 &

60 kV respectively) at which experiments were performed to compute

B using this technique.

66
Wavelength (nm)

2 B(m/V )

($ , (radians) mech

T( K)

Average Minimum Maximum

632.8 3

-12

21x10 -.451 -.625 -.171 295.8

632.8 3

-12

16x10 -.457 -.878 -.079 296. 1

514.5 4.

- 12 23x10 -.565 -.740 -.322 296. 1

496.5 4

-12

44x10 -.681 -.997 -.483 296.2

488.0 4

-12

55x10 -.584 -.855 -.146 296.

1

476.5 4.

-12

70x10 -.269 -.946 -.008 296. 1

Table [7] Kerr electro- optic coefficient of nitrobenzene at different

wavelengths. Values of the mechanical strain phase retardation

'^mech ^°"^P^'^^'^ from experiments performed at the indicated

temperatures is also listed.

67
1) Slight movement of the Kerr cell with respect to the light beam

would result in a different value of 0 , as expanded beam

mech

observations showed that &> , was a function of position

mech

2) Stress caused by the coulombic attraction between the two plates,

could produce voltage dependent strain birefringence in the glass.

Although further work is being performed to identify and eliminate the

causes of the variation in , , it should be noted that the observed mech

variations, because of the large values of (^-^'^2 ^^^'^ this work,

contribute an uncertainty of less than ±3% to the value of the electro-optic

Kerr coefficient. A comparison of the present results with results of previous

measurements is given in Fig. 20. It can be seem from these plots that there

is a wide variation in the measured values for the Kerr coefficient of

nitrobenzene. In order to identify the actual magnitude of the discrepancy

an accurate method must be developed to adjust all results to the same

temperature. Our measured values of the Kerr coefficient as a function of

temperature are given in Fig. 21. Previous theoretical discussions have

indicated that the temperature dependence of the Kerr coefficient should

^ u ^ [^^5] be of the form

B = Cq + (C^/T) + (C^/T^). (25)

Fitting the data in Fig. 21 (least squares) yields the following values

for the constants

Cq = 4.44 X lO'^-^ mV'^

68
o -

ccN

UJ

UJCL X.- //

// / I I

//

2-/X -

<I ' / < / / / / / / oo

CO EcXz

LJ

_lUJ>< Om

<t

rhL.11

CDM

CD CU

to CM

CO

V

C P-<

d <l> CD N CO

?* _J 0 , M c s

CO •H Nl

d

tomm

Ij

CO

Zj ?*~> 'ti

U-l 'H

—'

It!

r! CO 1

)-i

—'

to °CM

cii XJ

__j ' 1 "'"^ CO CO

CD

}-l 1 Vj

p4

cu 1

CO

G

4-J o CO 'O

T,

CD C/J

m (11 J- ^ > O 4-J

J-i CO to M ^

•t-l 4-J 4-1 GO c c

en 0) CD

OO

nj j=:

4-J e > cn

to CN 3 4J o •H 4-t XJ 3 to to c O o d <U

CO

d tu i-i

H o OJ

)-i •H CD

to

U 4-t u to e C cn -a 4J o CD CD o 3 < Xo oXo

rd oXo

(zA/ui)

a

69
I 1 1 1 1 1 1 1 1 I-

-—

8 —

i

I

o

9

8o

E

c o

w a

cvi ro O

{£> o

n ooo

8

o

1

1 1 1 1 1 1 1 1 1 1 1-

CVJ ro

CM CVJ CVJ CM 'O 'O '2 'O •o •o

X X X X X X

o o o o o o

IP 1^ iq

lO ro rd cvi csi csi

00

o

ro

o O LU

ro ct: z>

UJ O CL

o s

ro UJ

CVI

CVJ

CVI

o c

)-l 0)

J-l CO o a

.-I0) o

Q) 4-1 U C!

14-1 <U o x:

3 o

I—

I

eg <u > u

T3 4-)

)-i l-i d <u

CO fl. CO S

cu

^400

(,A/iJU) lN3IOIdd300 nV0llcJO-Odl03n3 ad3>l

70
= -2.86 X 10

8 m K V

-2

4.85 X lo"^ m ( K)^ V

-2

From these values, the Kerr coefficient of nitrobenzene was calculated

as a function of temperature in the range between 296 K and 305 K. These

results are presented in Table 8. Because of the approximations used in

deriving Eq. 25 and because of the narrow range of temperatures investigated,

the authors are skeptical about the validity of extrapolation to temperatures

much beyond those listed in Table 8. Investigations are continuing over a

wider temperature range to accurately define the temperature dependence of

the Kerr coefficient.

71
Temperature ( K) Kerr Coefficient (m/V )

296. 0 J . z A- X iU

296. 2 J . Z J 296. 4

"i 0 T J . ZZ

296. 6 J . Z Z 296. 8 J . zu 297 . 0 J . z u 297 . 2

1 1 Q

297 .

"5 IS J . i 0

297 . 6 J . 1 / 297.8 Q 1 A 298. 0 J . i J 298.2 T 1 /, J . 298.4 J . ij

298.6 J . iZ

298. 8

"3 10 J . iz

299.0 .

"5 11 J . i J. 299.2 "3 in

299.4 no 299.6 - Q ns J . Uo

299. 8

T n7

300. 0

T n^i 300. 2

T n J . U J 300.4 1 n 1^ J . U J 300.6 T n/i 300. 8 J . UJ 301 . 0

"3 no J . uz 301 .

"3 ni

301 .

ni

301 . 6

T nn J . uu 301 .

0 Q Q

302 . 0

0 Q Q Z . Vo

302 .

0 O 7 z . y / 302 .

0 Q 7 z . y / 302.6 0 Q A z . y D 302.8 0 OK z . y J 303.0 0 Q/i 303.2 0 Q/i z . y^t

303 .

0 Q z . y J 303. 6 z

0 . QOyz

303 .

0 Q

z . y i 304. 0

0 Q

z . y i 304. 2 z

0 . anyu

304.4 2.89

304.6 2.88

304.8 2.88

305.0 2.87

Table [s] The Kerr coefficient of nitrobenzene is listed as a function

of temperature. As discussed earlier, the Kerr coefficient

values are estimated to be accurate to within ±5%.

72
IV. KERR SYSTEM PEAK-READING VOLTMETER WITH AUTOMATIC DIGITAL DISPLAY

Accurate measurement of the peak value of transient high voltages

is of considerable importance to those concerned with 1 ightning- impul se

• J - u- • ^54, 55] r , V. . and switching- surge testing of high-voltage power system equipment,

with design and reliability of pulse components used in high power radar

systems, with high power pulsed laser, particle accelerator, and fusion

^[56,57] . u 1 1 • -J . . research , with nuclear- explosive testing and weapons design, etc.

Conventionally, such measurements are made either by use of spark gap or

voltage divider methods. The procedures used in spark gap measurements

and a description of the specially constructed metal ribbon resistors used

in the National Bureau of Standards' 500Q pulse divider have previously

[58] been published . Descriptions and discussions evaluating the performance,

reliability, and errors characteristic of various types (including capacitive,

mixed, liquid-resistor, opto-electronically coupled, etc.) dividers are given

in ref erences^^^ '^^ In each of these cases the oscilloscope deflection

produced by the voltage across the low voltage arm of the divider is photographed to record the magnitude and waveform of the pulse voltage to be

measured. In cases requiring state-of-the-art accuracy (within 1-2%),

"slideback" or "suppressed zero" techniques are employed to enable higher

resolution in measurement of the pulse's peak magnitude.

In recent years, a series of ever- improving alternative approaches

employing pulse-measuring Kerr systems have been developed^^ The

technique described here, which was suggested by the authors in a previous

publication^ '"^

, is being developed in the National Bureau of Standards' High

Voltage Measurements Section as part of its pulse measurements program.

73
Though measurements with state-of-the-art accuracy (within ±1%) are easily

obtained by proper design of the Kerr system, the principle advantage of the

present approach is its facility. It provides immediate conversion of the

pulse voltage peak from analog to digital form, with digital readout and

'display of the critical data required for ready calculation of the voltage

magnitude either at the peak or at some other selected point of interest

on the waveform. Though direct and immediate display of the pulse

magnitude (in volts) has not yet been incorporated, it is evident that

this feature may easily be included with addition of straightforward

computational circuitry. Safe and reliable operation of the active electronic

circuitry incorporating the computational facility and digital display is

insured by the system's optical coupling to the main high voltage circuit.

The laser beam is easily directed to carry the measurement information to

a remote, electrically isolated and shielded location.

Finally, it is noted that the present system is regarded as only a

prototype of the more fully automated system suggested above. However,

since its fundamental operations allow significant improvement in the

facility of high voltage peak measurements and since these semi-automating

operations are easily implemented using general purpose laboratory equipment,

the present description is provided for consideration by those who might

find this approach helpful in meeting their immediate impulse measurement

and testing needs.

A. Instrumentation and Procedure

A block diagram showing the essential elements of the prototype Kerr

system peak-reading voltmeter and the standard voltage divider system used

74
in evaluating its performance is given in Fig. 22. A photograph of a

portable prototype 300-500 kV system showing a Kerr cell, submerged in an

oil-bath tank and equipped with appropriate adjustable polarizers and

mirrors for directing of the laser beam, is shown in Figs. 23 and 24. As

in conventional pulse voltage measuring Kerr systems^^ , the beam is

directed through a polarizer oriented at ±45° to the Kerr cell interelectrode

field, between and along the length of parallel plate electrodes in a

nitrobenzene-filled Kerr cell, through an analyzing polarizer oriented

at ±90° to the first polarizer, to a detecting photomul tipl ier . In the

systan shown schematically in Fig. 22, both the laser source (a 1 . 5mW He-Ne

laser) and the photomultiplier are located about 10 meters away from the

HV pulse generator, whereas the Kerr system and "standard" 500Q divider

are installed in parallel within 1 meter of an unshielded Marx-type impulse

generator. The photomultiplier and its associated equipment, as described

in the following paragraphs, are installed inside a shielded room to reduce

effects of radiated interference from the generator discharge. The laser

beam is directed as required for passage through the cell and back to the

photodetector by use of adjustable mirrors installed on the polarizer housings

on the acrylic oil-bath tank. The Kerr cell is submerged in oil to prevent

flashover on the Kerr cell surface when the HV pulses are applied.

During pulse measurement operation the instantaneous relative intensity

(I/I^) of the light transmitted by the analyzer, as modulated by the

instantaneous pulse magnitude, is detected by the photomultiplier and

displayed on an oscilloscope screen. A pulse and delay generator system

is used to synchronize triggering of the oscilloscope sweep for viewing of

75
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76
A portable prototype 300-500 kV Kerr cell. The polarizer

housing is in the foreground and the screw at the upper left

of the tank is the high voltage connection.

77 -
Figure 24. Top view of portable Kerr cell. During normal operation the

tank is filled with oil to prevent flashover.

78
the Kerr system photomul tipl ier response during the rise (or fall) of

the high voltage pulse from V = 0 to V , (or from V , to 0). At * Of peak peak

the same time, the number N of oscillations produced by the Kerr effect

during the rise (or fall) of the HV pulse is counted by a 0 - 500 MHz

universal counter /timer oscilloscope plug-in unit and displayed with the

photomul tipl ier response directly on the oscilloscope screen. The

oscilloscope's vertical (volts/div) and horizontal (ns/div) scale

sensitivities are also displayed. Photographs of typical oscilloscope

displays recorded during the fall (from ^^^^^ to 0) of several different

high voltage pulses are shown in Fig. 25. Simultaneous "standard"-

voltage-divider measurements used in evaluating the Kerr-counter system

performance were recorded on a dual-beam oscilloscope, the overall

waveform of the nearly rectangular HV pulses (risetime: 1-2 |-ls, duration:

5 to 15 M-s, peak magnitude: 20 to 320 kV) being displayed by the deflection

of one beam and the differential measurement of the magnitude of the pulse

being displayed by the other beam, as sketched schematically in Fig. 22.

To allow comparison of the Kerr-counter system result with the high

resolution divider measurements triggering of the oscilloscopes and counter

were adjusted for display and measurement of the same point on the pulse

waveform. Typical displays photographed from the screens of the two

oscilloscopes during measurements at two different voltage levels are shown

in Fig. 26.

The voltage divider slideback measurement is derived by measuring from

a photograph the oscilloscope deflection showing the relatively small

(50-100 mV) difference between the peak magnitude of the divider low-side

voltage and the fixed direct voltage (~ 20V in present work) applied to

79
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80
PULSE DIVIDER

Vd = (Bias + Vs)DR

Slideback = Vs

s M

IM

ail

Vd = 33790 volts

Vs

Vq = 50080 volts

KERR CELL

Vk = (2N - m

Digital Displays N= 38

Vk= 50070 volts

HIGH VOLTAGE PULSE MEASUREMENTS

Figure 26. Comparison of oscilloscope records from simultaneous measurements

of nearly rectangular high voltage pulses using a calibrated Kerr

system and a 500 Q pulse divider. The top beams on the divider

record are slideback measurements of the peak located on the tops

of the pulses just prior to their trailing edges; the bottom beams

display the waveform as indicated by the voltage across the

divider low side. The Kerr system records show the count and

the photomultiplier response during the trailing edge of the pulse.

81
channel B of a differential oscilloscope plug-in unit. The divider

measurement V of the voltage peak is computed as follows:

= (Bias + Vg) DR, (28)

where the direct bias voltage (Bias) is readily measured using a

calibrated digital voltmeter (accurate to better than 0.1%) and DR is

the division ratio or attenuation factor of the calibrated standard

divider

.

B. Kerr System Measurement Principles

The operation of the Kerr-counter system can be understood from

an analysis of Eq. 5:

(I/I ) ^ m X, t = sin^ [fTT (E/EmrX, Jt

Under the same assumptions as in the previous section (Eq. 16), this

[15] expression can be rewritten

I/I = sin^ [in (V/V )^], (29) m m

where V is the instantaneous value of the applied voltage and V is the m

smallest applied voltage that yields a transmission maximum, I^.

2 Whenever (V/V ) has an integral value N, (I/I ) is equal to either 0 or 1, m m

2 If one denotes the value of (V/V^) at the peak of the applied voltage as

2 (V/V^)p one can, using a counter, determine the value of the integer N

such that

82
2 N - 0.5 < (V/V ) < N + 0.5 m p

A simplified example of this is shown in Fig. 27. In this figure the

relative transmitted irradiance is shown during one half cycle of 60 Hz

alternating voltage. A simple waveform and low voltage are chosen so

that the principles of the measurement technique can be more easily

identified. To determine the peak voltage, it is necessary to measure

the value of (V/V ) for a calibrated cell, i.e., a cell in which V is m p m

2 known. In section (a) of the figure (V/V^) 8 at the peak of the applied

2 2 voltage signal, while in section (c), (V/V ) — 9. In section (b) , (V/V ) m p m p

would, of course, have some intermediate value. We note that in sections (a)

and (c) the number of peaks in the transmitted irradiance during the entire

2 pulse is equal to the appropriate value of (^^^^^^ • This is simply a

consequence of the fact that the applied voltage monotonically increases to

the peak then monotonically decreases back to zero. It can also be seen by

inspection that if the discriminator level of an electronic counter is set

at (I/I ) =0.5 a total count of 8 would insure that

m

7.5 ^ (V/V )^ ^ 8.5

m p

In this case then one can obtain the peak value of the voltage from the

expression

V = (N )^ V , (30)

p rp m

83
(q)

UJ

-Jo

>

Q

liJ

I-cr —

V = 0

I =0

(b)

UJ

< o

V =0

I =0

(c ) UJ§

o

>

QUJ

CO

a:

V =0

I =0

0 4 6

TIME (ms)

8

Figure 27 Transmitted irradiance during a half-cycle of a 60 Hz voltage

waveform. As the peak voltage increases (from top to bottom)

an additional count is added to the Kerr system response.

84
where the number of counts in a full pulse is denoted by . fp

The uncertainty introduced into the voltage measurement by rounding

the number of counts to an integral value is shown in Fig. 28. It can be

seen from this figure that the uncertainty due to rounding falls below

±1% when the total number of counts is greater than about twenty-five.

This is a consequence, of course, of the fact that the birefringence is

proportional to the square of the electric field so that the measurement

sensitivity increases with increasing voltage level.

In the present work the front of the pulse waveform was distorted.

It was, therefore, more convenient to detect only the trailing edge of the

pulse. That being the case, the value of the peak voltage was calculated

from the expression

V = (2K - 1)^ V (31)

p hp m

^

where is the number of counts during the second half of the pulse, i.e.,

during the time when the applied voltage went from its peak to zero. When

one records only the number of counts in half of a pulse, he must arbitrarily

choose to round to either an even or an odd number for . This introduces

fp

a calculable, additional uncertainty beyond that graphed in Fig. 28. For

large counts, this will be an insignificant error in many applications.

C. Results and Conclusions

Typical results obtained by recording the number of counts in the

trailing half of the voltage pulse are presented in Table [9]. These

results are compared to simultaneous divider measurements of the same pulse

85
86
to demonstrate that the results are consistent with the predictable

uncertainty limits. When the peak voltage was of order 30 kV, N^^ — 80,

and Nj_^p ~ 230 when the peak voltage was of order 84 kV.

It should be mentioned that the response of the Kerr cell tracks

[4] the entire voltage pulse so, as was previously demonstrated , one can

reconstruct the entire pulse. The present system ignores that information

so that an immediate, accurate value for the pulse peak voltage can be

obtained

.

In summary, a peak reading voltmeter based on the electro-optic Kerr

effect has been constructed. The unique feature of the device is that it

incorporates a counter which counts the number of light transmission maxima

during the voltage pulse. A straightforward arithmetic computation using this

count yields a value for the peak voltage. Tests of the device indicate that

the system operates near the theoretical minimum in measurement uncertainty.

87
V 7o Difference

P

(kV)

Divider Kerr Cell

50 10 49 97 -0. 3 50. 03 49 97 -0. 1 50. 12 49 97 -0 3

50. 08 49 66 -0 8

50. 08 49 97 -0 2 50 12 49 97 -0 3 50. 10 49 97 -0 3

84 44 84 05 -0 5 84. 37 84 23 -0 2 84. 31 84 05 -0 3

84. 27 83. 87 -0. 5 84. 33 • 84. 05 -0. 3 84. 24 83 87 -0. 4

84. 26 84 23

84. 20 84. 23

84. 20 83 87 -0 4

84. 20 83 87 -0 4

Table [9] Comparison of the results of a Kerr-counter system for the

measurement of high voltage pulses with simultaneous

measurement of the pulse using a conventional divider (the

NBS 500 0 "standard" pulse divider).

88
V. MEASUREMENT OF HIGH MEDICAL X-RAY MACHINE VOLTAGES

A. Introduction

The Bureau of Radiological Health of the HEW Public Health Service

has been given the statutory responsibility for certifying that the voltage

pulses in commercial X-ray machines are within their specified and approved

operating ranges. Having been informed of the work performed at the National

Bureau of Standards on the use of the Kerr effect for voltage measurements,

they consulted the NBS High Voltage Measurements Section for advice on

techniques of accurate pulse-voltage measurement. Immediate concern was

with the operation and performance of medical X-ray equipment at the HEW

Bureau of Radiological Health. Their current practice involves use of voltage

divider techniques for measurement of these voltages. Occasional performance

evaluations are also conducted by analysis of the X-ray spectrum produced.

However, because this procedure is lengthy and complex, there is a need for

an alternative method to check the accuracy of, or perhaps replace, dividermeasurement techniques. Some doubt about the accuracy of their divider

measurements was expressed. Such dividers are generally calibrated by measuring

their division ratios under direct voltage conditions bearing little resemblance

to those encountered in normal X-ray machine operation. Typically, medical

X-ray voltages consist of a train of one or more full-wave-rectified halfcycle 60 Hz pulses, with peak magnitudes ranging from 20 to 300 kV. The

likely possibility of significant error, due to voltage and/or frequencydependent variations in the divider ratio, in divider measurements at high

voltage was therefore indicated as an area of major concern. Accordingly,

two field trips were made to the Bureau of Radiological Health in Rockville,

Maryland Because of their pertinence to our Kerr effect studies, the

89
experiments, results, and conclusions drawn from these visits are discussed

in the following paragraphs.

B. Field Trip Report

The initial visit to BRH included a briefing by the chief and staff

of the Radiation Measurements and Calibrations Branch on their voltage

measurement problems and a tour through their laboratory. Operation of their

X-ray machine and their voltage-divider measurement procedure were demonstrated.

At the conclusion of this visit it was agreed that another field trip,

attempting adaptation of Kerr system techniques to their X-ray machine, would

be desirable. On November 15, appropriate pieces of our Kerr system apparatus,

including a calibrated 1 x 10 cm pulse-measuring Kerr cell and a small He-Ne

laser, were taken to the Radiation Measurements and Calibration Branch

laboratory in Rockville. The cell was connected to their X-ray system, in

parallel with their resistive divider, for measurement of the X-ray tube

voltage. A number of exploratory experiments were conducted. Oscilloscope

tracings comparing several of the simultaneous divider and Kerr cell measurements are given in Fig. 29. The higher resolution of the Kerr system measurements, which show sizable differences not distinguishable in the divider

measurements of the voltage peaks, is evident.

C. Conclusions

1. The experiments conducted on November 15 demonstrated the

feasibility of using Kerr-system techniques for measurement of a variety

of typical X-ray machine pulse voltages. Further experiments and testing will

be required to establish their accuracy. However, it should be noted that

similar tests and experiments are also required for calibration and evaluation

of divider performance and accuracy.

90
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91
2. Multiple voltage pulses produced by the X-ray machine (e.g., those

in Fig. 29b, c and d) vary significantly in peak magnitude and in waveform.

The X-ray dosage may be expected to vary accordingly.

D. Recommendations

In view of the above, recommendations for future action include the

following steps:

1. Complete high voltage calibration and evaluation of a divider to

be used in conjunction with the X-ray machine divider. In addition to usual

calibration under high direct voltage conditions, this should include measurement of its division ratio under pulsed and steady-state 60 Hz high voltage

conditions, and evaluation of its step response at intermediate voltages.

The purpose of this work would be to provide reliable calibration, traceable

to the NBS standard pulse divider and Kerr cell apparatus, of a BRH "standard"

divider to be used by their Radiation Measurements and Calibration Branch in

enforcement of regulations governing medical X-ray machine performance.

2. Simultaneous measurements of BRH X-ray machine voltages using the

calibrated BRH divider, a calibrated NBS Kerr cell and X-ray spectrometer.

With these three independent measurements of the voltage, the relative

accuracy and precision of the devices can be defined under X-ray machine

operating conditions.

3. If the results of Recommendation 2 indicate that Kerr system techniques

will indeed provide relatively simple, accurate, and independent (of the divider)

measurements of X-ray machine voltages, technical assistance could be provided

to BRH in the establishment of their own Kerr pulse measurement system. This

would include fabrication and calibration of a Kerr cell (or cells) designed

to provide high measurement resolution during operation at typical medical

92
x-ray machine voltages. Complete automation of Kerr system measurements,

to give digital display of the peak voltages applied to the X-ray tube,

would be most desirable. This was attempted on the field trip, but failed

due to unreliable triggering of the counting units used. Recent experiments

•at NBS have demonstrated the feasibility of this procedure, which is described

in Section IV (see Fig. 25). Since this procedure offers promise of significant

simplification in pulsed peak-voltage measurements, its development for routine

X-ray voltage measurements may be particularly helpful. The higher frequency

response afforded by use of Kerr system techniques is also foreseen as a

significant advantage; it will allow detection of transients on the X-rayvoltage waveform. Transients, with magnitude significantly greater than the

normal generator voltage, may be anticipated in X-ray machine operation

particularly during switching of the high voltage. It would seem that

detection and measurement of the magnitude of any such transient voltages

may also be important, since they may produce potentially harmful bursts

of higher energy radiation.

E. Results and Benefits

Benefits anticipated from adaption of the above recommendations include

the following:

1) accurate calibration of a BRH divider for operation under medical

X-ray- vol tage conditions,

2) a quantitative estimate of the accuracy with which the X-ray

spectrum can be predicted by voltage measurements in commercial

X-ray machines,

93
3) a publication for the technical literature outlining techniques

for measurement of voltage pulses in commercial X-ray machines,

4) increased technical expertise resulting from cooperative NBS-BRH

staff effort,

5) if determined desirable, a calibrated Kerr cell system for BRH

use in measurement of high voltages.

94
VI. FUTURE PLANS

During the fiscal year 1974, the following areas will be emphasized:

(1) Measurements of the Kerr electro-optical coefficient of nitrobenzene

will be completed, and a paper reporting results at selected laser wavelengths

and operating temperatures will be submitted for publication in the open

literature. These measurements, which were begun during FY 1973 (see

Section III) and which are the first to be reported for laser wavelengths,

are believed to be significantly improved over previous measurements which

were performed using less refined and less accurate voltage measurement

techniques

.

(2) The Kerr electro-optical coefficient of several other selected

liquids, including water, chlorinated naphalene, chlorinated biphenyls,

etc., will be measured by reference to our improved absolute measurements

for nitrobenzene. As with nitrobenzene, measurements will be made over a

range of temperatures and laser wavelengths selected for their practicality

in high voltage measurement applications. Results will therefore also include

determination of the temperature and wavelength dependence of the Kerr

coefficient and of the Kerr cell constant (for voltage measurement purposes)

for each of the liquids investigated.

(3) The Kerr effect peak-reading-voltmeter concept, which allows

immediate visual display of the count yielding a measure of the peak

magnitude of M-s duration HV pulses, will be calibrated and evaluated to the

300 kV level by reference to calibrated standard NBS Kerr cells and pulse

dividers. A paper describing the concept involved and reporting findings

95
from this work will be prepared and submitted for publication in the open

literature.

(4) A Kerr system designed for measurement of 1 ightning- type impulses

peaking as high as 1 MV will be designed, constructed and tested to the 1 MV

level. The testing will be conducted at the General Electric High Voltage

Laboratory in Pittsfield, Massachusetts. In addition to NBS participation,

this work will receive selected materials and some technical support from

A. H. Rohlfs and F. A. Fisher of the GE High Voltage Laboratory staff.

Several other portable pulse-measuring Kerr systems, constructed

during FY 1973 (see Section I) for operation to the 300 kV level, will also

be calibrated and tested under both rectangular and lightning- type impulse

conditions

.

(5) Evaluation of results from field-mapping studies under steady-state

dc and low frequency ac conditions will be continued. Included in this effort

will be preparation and presentation of a paper for the 1973 Conference on

Electrical Insulation and Dielectric Liquids to be held at the Institute for

Electrical Research in Quebec (IREQ) in October 1973. Primary responsibility

for this work will be assigned to Dr. Robert Hebner who is the principal author

of an abstract already submitted and accepted by the conference. The goal of

this work continues to be attainment of a thorough understanding of the basic

mechanism(s) contributing to space-charge distortion of the interelectrode field

in parallel plate Kerr cells during steady-state dc or ac operation, the

ultimate goal being attainment of uniform field conditions which would allow

higher accuracy in steady-state high voltage calibrations of voltage measuring

96
Kerr cells. Improvement in the accuracy of such calibrations should

allow significant improvement (from ±1% to ±0.5% or better) in the

state-of-the-art accuracy of transient high voltage measurements.

(6) Conference on Precision Electromagnetic Measurements, London

July 1974. If time and staff permit, two papers should be planned for this

conference, one being a careful evaluation of ac Kerr cell studies in

insulating liquids and the other (from results obtained in cooperation with

Stanley R. Booker of Sandia Corporation) reporting development and calibration

of a "multiple-pass" HV pulse-measuring Kerr system.

During FY 1974, the project leader and principal investigator (Esther C.

Cassidy) of the NBS Kerr Effect Studies program will be away on a U.S. Dept.

of Commerce Science and Technology fellowship assignment. Accordingly,

primary responsibility for this project will be assumed by Dr. Robert Hebner

and Richard Sojka of the NBS High Voltage Measurements Section staff, with

most of the effort carried by Richard Sojka who is planning his doctoral

thesis around his work in this area. In addition to these NBS participants,

significant contributions from Stanley R. Booker of the Sandia Corporation,

from A. H. Rohlfs and F. A. Fisher of the General Electric Pittsfield High

Voltage Laboratory, and from Esther Cassidy (in off-hours advisory capacity)

are also anticipated.

97
APPENDIX A

MEASUREMENT OF 60 HZ VOLTAGES USING THE KERR EFFECT

This material was published in the Review of Scientific Instruments,

vol. 43, pp. 1839-1841, 1972.

98
Reprinted from: THE REVIEW OF SCIENTIFIC INSTRUMENTS VOLUME 43, NUMBER 12 DECEMBER 1972 Measurement of 60 Hz Voltages Using the Kerr Effect*

Robert E. Hebner, Jr. and Esther Christmas Cassidy

National Bureau of Standards, Washington, D. C. 20234

(Received 3 August 1972)

The Kerr effect has been used to measure 60 Hz alternating voltage up to 30 kV peak. The system behaves much

as it does under the influence of a short high-voltage pulse except that in this case the frequency of the applied

voltage is sufficiently low that the space charge effects in the liquid are not negligible.

j For a number of years systems have been under development that use Kerr cells for the measurement of pulsed and

direct voltages.^"^ The purpose of this Note is to report the

use of a Kerr cell system for measuring high alternating

voltage at 60 Hz.

The Kerr cell used was conventional in that it consisted of parallel plate electrodes immersed in nitrobenzene. Laser light, linearly polarized at 45° to the electric field direction, is passed between the plates and impinges on an

analyzer that is orthogonal to the direction of the polarizer.

The nitrobenzene becomes optically birefringent when

under the influence of an electric field according to the

relationship

v»=2x5 ! mi. (1) J 0

In this expression, ^p is the phase difference produced be-

' tween the parallel and perpendicular (to the direction of the applied electric field) components of the electric vector

of the incident light beam ; B is the Kerr constant of the

liquid ; and

is the integral of the square of the electric field strength E

along the length L of the light path in the liquid. If one

jjttiakes the usual assumptions—(a) that Eq. (1) can be

iSxpressed

,p = 2TrBm', (2)

'nvhere E is the electric field in the medium, and /' is an

effective length that includes the effects of fringing fields

at the ends of the plates ; and (b) that the field between the

plates is uniform—one easily obtains the following

expression^

///TM = sin2[iT(VF„)2]. (3)

In Eq. (3), / is the irradiance of the light transmitted

through the analyzer when the applied voltage has magnitude V, Vm is the smallest applied voltage which yields a

transmission maximum, /„. If we explicitly include the time dependence of the applied voltage, we obtain

///„ = sin2[i7r(F/F^)2sin2co/.] (4)

Typical observations of the transmitted irradiance I as a fimction of time are shown in Fig. 1. To use this system

to measure voltage, the system must be calibrated by an

independent measurement of Vm- Once Vm is known for a

specific cell, one needs only to record the relative irradi- ance as a function of time to find the peak applied voltage.^

It should be noted that at the peak of the voltage signal

sin^w/=l. The relative irradiance, which corresponds to

this peak, will be maximum or minimum for {V/V^y=n, (5) where n is an integer.

To characterize the performance of the Kerr system, 37

values of V, corresponding to « = 1 to 37, were used as peak

values for the applied voltage. Each value was used in Eq.

(5) to find Vm. Because all 37 determinations should yield

identical values, the variation in the values for Vm gives an indication of the precision of the Kerr system voltage

measurements at 60 Hz. A graphical presentation of Vm vs n is shown in Fig. 2. The scatter at low values of n is characteristic of Kerr

99
1840 NOTES

cells because the Kerr cell sensitivity increases with in- creasing field strength.^ If one then neglects the first five data points because they are inherently less accurate, one

sees that there is a variation of l%-2% in the remaining

values. There also appears to be a systematic decrease in the calculated value for as n increases. Preliminary observations have indicated that this may be due to a non- uniform field between the plates similar to that observed

using direct voltage^ ''* or long (greater than 50 ;usec) pulses.'

An examination of Fig. 1 shows that for the symmetrical

waveform that exists for 60 Hz alternating voltage the number of maxima is equal to n, as defined in Eq. (5), when the applied voltage V is at an appropriate value so that the transmitted light is either maximum or minimum

at the peak of the applied voltage. This observation is significant because when V>5Vm, a l%-2% increase in V

increases {V/VmY from a value w to a value It fol- lows, therefore, that a voltmeter could be constructed with

a precision of order 2% in which data are taken by simply

counting the number of peaks in the transmitted irradiance.

It was found that commercially pure nitrobenzene was

(o)

Ulo

o

>at

z

(b)

I =0

(c)

I =0

Fig. 1. Typical response of Kerr cell system to applied voltage. The

top half of each oscilloscope tracing shows one half-cycle of the applied 60 Hz alternating voltage. The lower half shows the relative irradi- ance transmitted by the system as a function of time during the halfcycle. The applied voltage is about 6% greater in Fig. 1(c) than in

Fig. 1(a). Figure 1(b) shows the response to an intermediate value.

10 20 30 NUMBER OF LIGHT MAXIMA IN ONE HALF-CYCLE 40

Fig. 2. Determination of the voltage necessary to obtain the first transmission maximum. This value should be independent of the applied voltage, but it does show a systematic decrease which is at- tributed to a nonuniform field distribution between the plates.

unsatisfactory for use in a Kerr cell to be operated at 60 Hz

because the Kerr effect signal was strongly and randomly

amplitude modulated. Visual observations of the light

transmitted through the cell under these conditions showed

a very strong "lensing" effect. That is, shadowgraph observations showed bright and dark areas in the space be- tween the electrodes which exhibited some short term

stability.^" Around the electrodes shadowgraphs of the density gradient, apparently caused by the heating of the

liquid between the plates, could be observed. Upon further

purification^ '^ these effects disappeared and a stable Kerr

effect pattern was obtained. The apparent resistivity of the nitrobenzene that yielded stable reproducible results was of order 10'° fl-cm as measured with a current comparator bridge'^ operated at 60 Hz. The Kerr cells used in this study were used to measure

voltages up to 30 kV peak and maximvmi electric field strengths of 40 kV/cm. Caution, and not catastrophic

failure, set these upper limits, so the present study offers no

information on the voltage limitation of these cells. The major conclusion of this study is that Kerr cells using purified nitrobenzene can be used to measure high

voltages at 60 Hz. It is further expected that studies of

this low-frequency behavior will lead to improved methods

of calibration of pulse measuring systems based on the

Kerr effect. The authors would like to thank W. A. Bagley for his as- sistance with this work, S. R. Booker for suggestions for its extension, and O. Petersons for his support and careful reading of the manuscript.

* This work was supported in part by the U. S. Atomic Energy

Commission through the Sandia Corporation, Albuquerque, N. M.

87115.

1 E. C. Cassidy, Rev. Sci. Instrum. 43, 886 (1972).

2 E. C. Cassidy and H. N. Cones, J. Res. NBS 73C, 5 (1969).

3 E. C. Cassidy, H. N. Cones, and S. R. Booker, IEEE Trans In- strum. Meas. IM-19, 395 (1970).

* E. C. Cassidy, H. N. Cones, D. C. Wunsch, and S. R. Booker,

IEEE Trans. Instrum. Meas. IM-17, 313 (1968).
NOTES 1841

5 D. C. Wunsch and A. Ereteza, Rev. Sci. Instnim. 36, 816 (1964).

5 It should be noted that the Kerr effect system actually yields not

just the peak voltage, but also the entire waveform. Determination of pulse shapes from Kerr effect measurements is discussed in Ref. 3.

' G. Briere and J. Gosse, J. Chim. Phys. 65, 1341 (1968).

8 G. Briere and F. Gaspard, Chem. Phys. Lett. 1, 706 (1968). 'Z. Croitoru, Progress in Dielectrics (Academic, New York, 1965),

! Vol. 6, p. 105.

J. C. Filippini, J. P. Gosse, J. C. Lacroix, and R. Tobazeon, Conference on Dielectric Materials, Measurements and Applications,

University of Lancaster, p. 110 (1970). " F. Gaspard, Conference on Dielectric Materials, Measurements

and Applications, University of Lancaster, p. 134 (1970). " 0. Petersons, IEEE Trans. Power App. Systems PAS-87, 1354

(1968).

In--
APPENDIX B

RECENT REFINEMENTS AND DEVELOPMENTS IN KERR SYSTEM

ELECTRICAL MEASUREMENT TECHNIQUES

c

This material was presented at the 1972 Conference on Precision

Electromagnetic Measurements, Boulder, Colorado, June 26-29, 1972.

It was then selected for publication and published in IEEE Transactions

on Instrumentation and Measurement, vol. IM-21, pp. 504-510, 1972.

102
Reprinted by permission from IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT

Vol. IM-21, No. 4, November 1972, pp. 504-510 Copyright 1972, by the Institute of Electrical and Electronics Engineers, Inc. PRINTED IN THE U.S.A.

Recent Refinements and Developments in Kerr

System Electrical Measurement Techniques

ESTHER CHRISTMAS CASSIDY, WILLIAM E. ANDERSON, and STANLEY R. BOOKER

Abstract-Ken system electrical measurement techniques are im- proved by progress in two important areas: 1) in the development of

Manuscript received June 21, 1972.

E. C. Cassidy and W. E. Anderson are with the High Voltage Measure- ments Section, National Bureau of Standards, Washington, D.C. 20234.

S. R. Booker is with the Electrical Standards Division of the Sandia

Corporation, Albuquerque, N. Mex. 87115.

methods for visualizing and measuring pulsed (microsecond) electric

fields and high voltages from time-varying electrooptical fringe pat- terns recorded using high-speed photographic techniques, and 2) in the development of convenient experimental methods for evaluating and

correcting path-dependent errors in Kerr system response. Results demonstrate use of fringe-pattern measurements in achieving accurate

pulse voltage measurements and in correction of errors resulting from

sizeable end-field variations in existing 300-kV Kerr cells. 103
CASSIDY et al. : KERR SYSTEM ELECTRICAL MEASUREMENT SOS

Introduction

THE feasibility of using the Kerr electrooptical effect for measurement of pulsed high voltages has been verified by experimental research now under way for about five years. Within the context of earher progress, Kerr systems were used

to measure pulses peaking as high as 300 kV and having rise times of 1-2 with an estimated uncertainty of ±1 per- cent [1], [2]. A method was developed for observation and

mapping of high-intensity electric fields in Kerr cells under

steady-state dc conditions [3] . Knowledge of the dc field distribution, which is often distorted due to space charge ef- fects, permitted high direct-voltage calibrations of Kerr cells for pulse measurements. Kerr systems developed and constructed by the authors have been used to calibrate other pulse-measuring devices, such as resistive and capacitive di- viders, at their rated voltages, rather than at low voltages as has been the usual practice.

This paper describes recent progress in two areas: 1) in de- velopment of methods for visualizing and measuring pulsed

high voltages and electric fields from time-varying electro- optical fringe patterns, and 2) in development of convenient

methods for evaluating and correcting path-dependent errors

in Kerr system measurements. Unlike earlier approaches, the present methods apply high-speed photography for detection and recording of two-dimensional electrooptical fringe pat- terns containing the measurement data. This approach is es- pecially useful for studies of the pulsed electric field between

the Kerr cell electrodes, for evaluation and correction of pathdependent errors (due to end-field effects) in Kerr cell voltage

measurements, and for voltage measurements under high noise

or discharge conditions that make electrical isolation and

shielding extremely difficult. Results from experiments demonstrating use of fringe-pattern measurements for each of

these tasks are presented. Because of their importance in achieving accurate measurements at higher voltages (> lOOkV),

procedures devised for evaluating and correcting pathdependent Kerr cell errors are emphasized.

II. Apparatus and Methods

The basic HV pulse generating and measuring systems were

described earlier [1], [2]. Several different nitrobenzenefilled Kerr cells with parallel-plate electrodes were used in this work as follows: a 1 X 10 cm (spacing X length of electrodes)

cell for operation to 100 kV, and a 2.9 X 6 cm cell and a 3 X 30 cm cell for use to 300 kV. More complete descriptions of these and other cells with a variety of electrode structures

are given in [4]

.

The general layout of the electrooptical system with fringe

recording using a rotating mirror streak camera is shown in Fig. 1. A pulsed laser serves as a hght source. Suitable optical

components are inserted as shown to expand the beam diameter as required for illumination of the end-view area between

and around the Kerr cell electrodes. A slit aperture (width ^

1 mm, length 50-100 mm as required by Kerr cell dimensions)

is positioned perpendicular to the direction of laser beam

propagation, so that only light passing through the slit is transmitted. The inner surface of the Kerr cell electrodes are

2

where the overbar (e.g., over /I) denotes the following:

(2)

The integral is evaluated over the length L of the given light

path jc through the Kerr cell. is the effective field strength

that produces the first transmission maximum Im with a given

cell. The electric field E is understood to be the component

perpendicular to the direction of light propagation. Thus,i

(///;„) varies as a function of time and space (around the elecoriented either parallel to (as in Fig. 1) or perpendicular to the long dimension of the sHt. The cell, which is submerged in oil to prevent external HV flashover, is installed between

"crossed" polarizers so that the analyzing polarizer passes light

only during application of the HV pulses. Quarter-wave re- tardation plates are inserted as indicated to eliminate recording of "tleld-directional" fringes [4] not pertinent in these measurements. The lens directs the transmitted Hght to the rotating mirror where it is deflected to the film for continuous

time-resolved recording of space variations (over the length of

the slit) in the transmitted light intensity. The resultant fringe-pattern photographs contain information interpreted to I yield measurements of applied pulse voltage and of the electric

field distribution as functions of time. The time scale on the

film is deduced from measurement of the mirror speed or from measurement of the time between initiation and peaking of

the reproducible pulse waveform.

When equipped for instantaneous framed recordings of the

light transmitted over the entire end-view cross-sectional area, the slit aperture is removed and the streak camera is replaced

with an image-converter camera. Or more simply, the requirement for use of the image converter with its high-speed

shuttering action is avoided by use of a pulsed laser with very

short (relative to time changes in the Kerr cell field) flash duration. In either case, the rapidly changing fringe pattern is "frozen" photographically at a selected time during the pulse.

Typical exposure times in the present work were 1, 0.3, or

0.1 The recorded patterns allow probeless electrooptical

mapping and measurement of the electric field distribution be- tween and around the Kerr cell electrodes. Measurements of

the pulse magnitude at the time of the exposure are also easily

obtained (Section III). In this work, these photographs were

particularly useful because they permit convenient experimental evaluation of voltage measurement errors resulting

from Kerr cell end-field variations (Secfions V and VI).

III. Measurement Procedure and Typical Results

Kerr system operation may be summarized as follows. Whereas essentially no Hght is initially transmitted because of

the "crossed" polarizers, transmission increases when voltage is applied across the Kerr cell electrodes. At any instant the relative intensity {Illm)x of the beam emergent from a given path

X through the Kerr ceU Uquid is [1]

:

(1)
506 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, NOVEMBER 1972

Fig. 1. Kerr electrooptical system used for streak fringe-pattern measurements of high-voltage pulses.

trodes) in accordance with the effective instantaneous electric

field distribution. Transmission minima occur when (and

where) = 0, vT E^f,, 2 \/6 E^, etc. Transmission

maxima occur when (and where) E = Em, \f3 E^, \/5 E^^,, etc. When sufficiently high voltage is applied, spatial varia- tions in the transmitted light, caused by field nonuniformities,

produce fringe patterns made up of alternate bright and dark bands (see Figs. 2 and 3). The brightest or darkest points of each band delineate "equifield" hues (i.e., the effective components of the electric fields perpendicular to the light path

are identical) of effective relative electric field strength

(E/E^)=V^. (3) As in earlier work [1] , [3] , « is the numerical value assigned

to each successive dark (even integer) and bright (odd integer)

fringe by counting (« = 0. 1, 2, 3 • • •) from the outermost dark

region where « = 0 inward to the desired point in space on the image-converter photograph (see Fig. 2). When end-field varia- tions are controlled, the photograph therefore allows visualiza- tion of the pulsed electric field distribution. With a calibrated Kerr cell operating in its range of high measurement resolution,

peak voltage measurements Vj^ are quickly obtained, with ac- curacy comparable to that achieved using conventional divider and oscilloscope methods, from the following equation:

(4)

where (J'm)r - (^m<^)c> the voltage that produces the first transmission maximum for the calibrated light path c, and is

tlie numerical value assigned to the fringe most proximate to

this calibrated path. The prime over a quantity (e.g., over E)

represents the average of that quantity, taken over a centrally located perpendicular path of length d between the elec- trodes; e.g.,

„ if" Ey. dx.

Equation (4) is only valid if (E'/E^) equals (E/E^)^. It is not

valid under dc or long pulse conditions because of field nonuniformities caused by space charge effects. This will be dis- cussed in Section VI. However, for short (microsecond) pulsed

voltages where path-to-path variations in (E/E^) depend only

Fig. 2. 0.3-/is image-converter exposures of high-speed fringe patterns produced at the peaks of 135- and 166-kV pulses using the 3 X 30-cm

Kerr cell.

"SLIDEBACK' MEASUREMENT: 0. PEAK = 286.3 kVV/div

4| 5

4.3 STREAK FRINGE-PATTERN MEASUREMENT

TIME(/is) —

Fig. 3. Simultaneous time-resolved measurements of an HV pulse,

(a) With resistive divider (ratio 5140). (b) Resistive divider with

"slide back." (c) With 2.9 X 6-cm Kerr cell. Pulse divider measure- ment scales: 20 V/div, 1 ns/div.
CASSIDY et al: KERR SYSTEM ELECTRICAL MEASUREMENT 507

on the electrode geometry, (4) is valid. More accurate measurements are obtained with (E/Ef„)c determined from relative measurements of the calibrated-path interfringe intensity

il/lm)c as follows.

If «c is an even integer (dark fringe).

Hr + arc sm

1/2 1/2

If is odd (bright fringe).

.2 / /

(/?c +1) arc sin —

1/2

(5)

(6)

Though any path through the cell may be calibrated (Section VI), the central path is used in most voltage measurement

applications.

Fig. 2 shows typical image converter exposures of fringe pat- terns recorded using a 3 X 30-cm 300-kV Kerr cell. With the

side-field fringes counted inward to ^ 50 and 75, and with

(K^)c known equal to 19 140 ±150 V, v^:=V50(19 140) =

135 340 V and = V75 (19 140) = 165 750 V. Calibrated

resistive divider measurements yielded 135 130 and 165 200 V,

respectively. Repeated comparisons of similar Kerr ceU and

divider measurements showed agreement within ±1 percent

when end-field variation errors were corrected and "slide- back" or "suppressed zero" techniques [1] were employed to enhance divider measurement resolution. Measurements were made at the peaks of pulses ranging between 80 and 300 kV.

A typical streak camera record from an experiment with a 2.9 X 6-cm Kerr ceU [(F^)^ = 39 500 ±250 V] is shown with

oscilloscope traces from simultaneous pulse divider measure- ments in Fig. 3. In this experiment, the cell was oriented with

electrodes parallel to the slit aperture. Only the rising portion of the pulse was recorded. As with the imageconverter results, peak voltage may be determined by counting

the dark fringes inward to the central ("bull's eye") region,

e.g., to «£. * 53 in Fig. 3. Continuous, time-resolved measure- ments of Vfc may be derived from (4) by counting and measuring the fringe positions along a centrally located (calibrated

path position) line parallel to the time scale (Section IV). Typical streak patterns obtained with the inner electrode

surfaces of a 1 X 10-cm cell perpendicular to the sUt aperture

are given in Fig. 4. In this case the pattern consists of a series of light and dark fringes that show the relative strength of the

electric field over the central interelectrode (perpendicular to electrode surfaces) path. Under short pulse conditions, where

time is too short for space-charge distortion of the interelec- trode field, the fringes should remain perpendicular to the time scale. However, the fringing fields at the ends of the elec- trodes cause the effective fields along paths near the electrodes

to differ from the effective fields along paths nearly midway

between the electrodes. This effect produces "bending" in the

fringes, which becomes more evident as the magnitude of the voltage (and thus the measurement resolution [l]-[3]) in- creases. The "bent" fringes in Fig. 4 indicate that the effective

field along paths near the electrodes is 1 to 2 percent higher than along the central path. Finally, it was also of interest to

n=2 4 6 III- -w^V . . 0 1 2 3 4 1 5 PEAK(66.8 kV n=246 f64^ •i{!iHli}|)>l>lM»!<Cl

0 '

1 2 3 4 5 PEAK (80,3 kV) TIME(/js *-

(a)

TIME SCALE 2^5/div

(b)

Fig. 4. Comparison of noisy pulse-divider measurements with electri- cally isolated streak fringe-pattern measurements using 1 X 10-cm

Kerr cell with sUt perpendicular to electrode surfaces, (a) Streak rec- ords of fringe-pattern high-voltage pulse measurements, (b) Conventional pulse-divider measurements with noise.

compare the divider results at the bottom of the figure with

computed Kerr system measurements of the waveform (Section IV). The latter showed smooth wavefronts as in Figs. 3 and 5, thereby tracing the distortion on the divider records of

Fig. 4 to the divider-measurement circuit rather than to erratic behavior in the HV generator. This practical demonstration of

the Kerr system's freedom from electrical interference and

ground-loop currents was verified when an extraneous ground

loop inadvertently included between the main HV and divider

circuits was located and removed.

IV. Analysis of Kerr System Measurements

OF Voltage Pulses

The modulated hght output from a Kerr pulse-measuring

system may be detected and recorded continuously directly on

photographic film by use of a streak camera as described above, or it may be detected and recorded indirectly by photographing oscilloscope tracings of the output signal from an

electronic photodetector. As reported earlier [2] , the latter records are analyzed by use of a film reader, with computer

processing of the measured x-y coordinate data pairs. This

technique, which is still in use, has shown consistent agreement

to better than ±1 percent between computed divider and Kerr

cell measurements of both the peak magnitude and the time

integral of the voltage pulse waveform.

The streak fringe-pattern records of the present work are analyzed in a similar manner. Relative exposure density on

the streak photograph is scanned and measured along a path

parallel to the "writing" direction (the time scale) on the film. This is easily accomplished through use of a recording densi- tometer or film reader. Since the relative film exposure density is not directly related to the relative intensity of the light transmitted by the Kerr system, results are more readily obtained when data pairs are recorded only at the maxima and

minima exposure points. Because of the high measurement

resolution achieved with production of a multiplicity of

fringes (« > 25), this procedure proved very effective in the present work.

Pulse waveforms derived from automatic scanning and computer analyses of the typical streak camera and divider- oscilloscope records in Fig. 3 are compared in Fig. 5. The

peak values differ by less than 0.5 percent at 286 kV. The

time integrals of the pulse waveform computed over the period of streak camera recording (over approximately | of the
508 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, NOVEMBER 1972

^. , , , J • J / . J RELATIVE POSITION OF LIGHT PATH (x/d) Fig. 5. 300-kV pulse waveforms derived from automatic scanning and computer analyses of typical streak camera and divider oscilloscope Fig. 6. Factors computed (at several different voltages) for path-to-path

records. corrections of Kerr system measurements using the 2.9 X 6-cm cell.

pulse duration) were 1421 and 1433 kV-/is. Repeated comparisons over the range from 80 to 300, with cells selected for high measurement resolution, showed similar agreement.

V. Corrections for Effects of

End-Field Variations

The foregoing pulse measurements are estimated to be accurate within ±1 percent. However, it is important to note that such accuracy requires careful consideration of the effects of

the fringing fields at the ends of the Kerr cell's electrodes. These effects and methods devised for correction of resulting

path-dependent errors in pulse measurements and in direct- voltage calibrations of pulse-measuring Kerr cells are discussed

in Sections V and VI. Kerr system response depends upon , the square of the

electric field strength averaged over the length of the Hght path

in the birefringent Hquid [see (2)] . If the same effective field were imposed along all paths between the electrodes, Kerr sys- tem measurements of voltage pulses would be independent of path position. With cells of our present design, having elec- trodes immersed in the Kerr cell liquid, results have shovwi

that the fringing end fields may produce very significant (to 10 percent with existing 300-kV cells having d=3 cm) pathdependent variations in the effective field strength imposed by

an apphed voltage pulse. Accordingly, the pulse voltage re- quired to produce the first transmission maximum, which was

defined simply as the cell constant, = (Ef„d), in earlier work with smaller cells, is path dependent. This troublesome

effect has been a major source of difficulty in development of

a Kerr system for measurement of pulses peaking in excess of 100 kV.

Several alternative solutions to this problem have been considered, including the following: 1) correction by design;

2) confinement of the light path by affixing entrance and exit apertures to the Kerr cell windows; 3) multiple calibrations with determination of for all Hkely measurement paths; or 4) development of reliable procedures for correcting pathdependent errors in existing Kerr cell response. Though effective and rather simply accompHshed, the second and third

alternatives are not preferred because they require that calibra- tion of the cell be referred to pulse divider measurements.

This is not desirable, since calibrations referred to dc or low

frequency ac voltage measurements offer promise of considerable improvement in the state-of-the-art accuracy of pulse

voltage measurements—from 1 to perhaps 0.1 percent or

better. Correction by design is perhaps the most attractive solution, because it would not only eliminate path-dependent

errors in pulse voltage measurements, but because it would

also facilitate accurate Kerr constant measurements. Accordingly, a variety of techniques for constructing cells with

guarded electrodes or with the birefringent hquid confined to

a central interelectrode region weU removed from the electrode ends are under investigation. In the meantime, a convenient experimental procedure for measuring and correcting errors resulting from the effects of

end-field variations was developed. This approach employs

high-speed fringe-pattern photographs, such as those in Fig. 2, taken near the peak of a short (< 15 )us) voltage pulse. Except

for end-field effects, parallel-plate Kerr system response

should, in this case, be independent of path position because

time is too short for development of space-charge distortion

in the interelectrode field. Accordingly, the interelectrode

fringes recorded in Fig. 2 are produced by path-to-path varia- tions in the effective field along the length of the light path in the hquid. The relative positions (x/d) and n values assigned

to these fringes, therefore, yield immediate visuahzation of the

effects of path variations on the Kerr system's response. The

effective relative field intensity {EJEff,) as a function of path

position is easily determined from measurements of (x/d) ver- sus n by scanning the distance between the electrodes along a centrally located line perpendicular to the inner electrode sur- faces. A path-dependent correction factor kx is derived from

these measurements as follows:

This factor adjusts the cell constant (F;r,)c, known for a single
CASSIDY et al.\ KERR SYSTEM ELECTRICAL MEASUREMENT 509

TABLE I Comparison of Central Light Path Calibration Results

Cell (cm) \ (nm)

Direct Voltage Pulse Voltage

Calibration Voltage

Vm

(V) (V)

Calibration Voltage

(Vn,)c (V) (%)

1 X 10 514.5 27570 9970 10010 86160 10100 -0.9 30430 10030 10100 0.0 33380 10010 1 0090 -0.1 1X10 632.6 37430 11660 1 1730 88970 11790 -0.5 41100 11680 44520 11700 1 1780 -0.1

3 X 3n 514.5 18230 18750 1 '^mnn 1 0D7U +0.3 71260 18230 18800 +0.6

t Z JOU 1 OiOU 1 8860 +0.9 72560 18310 18870 +0.9 72560 18290 18870 +0.9

3 X 30 632.8 75730 20960 21640 153900 21590 +0.2 75730 20990 21670 +0.4 77400 20980 21440 -0.7 78420 20960 21640 +0.2

2.9 X 6 632.8 77280 45330 46300 101300 46170 +0.3

Direct voltage calibration before correction F^, direct voltage calibration after correction (F^)^ using ky. factors, pulse-divider cabbration (F^)^. Temperature: 25°C. A: percentage by which corrected direct voltage calibration differs from pulse- divider calibration.

calibrated light path c, for accurate voltage measurements

along any other light path x as follows

(8)

Values of ky^, derived from least-square fitting of such measurements, were computed at path intervals of (xld) = 0.05

over the entire interelectrode distance from 0 to 1.0 for several different cells with different pulse levels applied. Typical re- sults from measurements with the 2.9 X 6-cm eel! at three dif- ferent voltages are plotted by the computer in Fig. 6. It is in- teresting to note thai the curves show essentially no change in the pulsed effective field distribution to the 300-kV level, thereby verifying our assumption that space charge effects are not significant with operation under short f~ 10 ms) pulse conditions. After corrections using the appropriate values of kx, measurements along various paths of the 2.9 X. 6 cm and the 3 X 30 cm cells agreed with calibrated divider measurements

to better than ±1 percent.

VI. Correction of End -Field -Variation Errors in High Direct -Voltage Calibrations

In earlier work [3] , Kerr cells were calibrated for measure- ment of pulse voltages from steady-state fringe patterns pro- duced by application of a high direct voltage V^c- In this case, where space-charge effects produce unpredictable distortion in the interelectrode field distribution, the pulse voltage that produces the first transmission maximum was derived by use of the following [3]

:

(9)

where V^c was measured, with accuracy to better than 0. 1 per- cent using a precision resistive divider, and (E/E^)' was determined from fringe measurements along a centrally located line perpendicular to the inner electrode surfaces as follows:

F

(10)

This straightforward procedure proved effective in achieving

acceptable calibrations of cells with electrode spacing cf < I cm. However, in larger cells where end-field effects produce signifi- cant (> 1 percent) path-dependent variations in Kerr system

response {EjEm)^ the steady-state fringe pattern also includes

distortion due to end-field variations. This additional distor- tion produces errors in (9) and (10). Accordingly, accurate determinations of , which is path dependent in the larger

cells, require corrections for the effects of path-dependent

end-field variations. Since the end-field contributions to each

cell's response may be assumed fixed by its geometry, this is easily accomplished by using the appropriate k^ factor, as de- fined in (7), for correction of the n values assigned to each

interelectrode fringe measurement, as described in Section IV. Equation (9) is thus modified: Vdc

(11) iVm)c =

to yield a valid calibration (F^)^ for any selected light path c. As indicated in Section V, the required measurements of kx

versus (x/d), such as those plotted in Fig. 6, are obtained from

a single high-speed fringe-pattern photograph taken with a convenient pulse voltage. The applied pulse voltage need not be measured. Prior to development of this approach, five or more

pulse-measurement experiments with the unexpanded laser beam passed along carefully measured paths between the elec- trodes were required for correction of these end-field-variation

errors [2]

.

To check the validity of this procedure, repeated experi108
510 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. IM-21, NO. 4, NOVEMBER 1972

ments were performed using several cells at different voltage

levels. Typical results, showing direct-voltage calibrations be- fore and after correction, and comparing (F^)^

with pulse-divider cahbrations, are included in Table I. After

corrections, all tests showed acceptable agreement (A < 1 per- cent) between direct- and pulse-voltage calibrations. In conclusion, it is noted that this approach is very useful in adapting Kerr system response for accurate voltage measurements, especially since it also assures normalization of errors

resulting from construction faults, e.g., from strain in the cell's windows, from imperfections in electrode surfaces and their alignment, etc. However, development of a correction-free design allowing direct measurement of the uniform (along path

length) electric field between the electrodes remains a task considered worthy of future work.

References

[1] E. C. Cassidy, H. N. Cones, D.C. Wunsch, and S. R. Booker, "Cali- bration of a Kerr cell system for high-voltage pulse measurements," IEEE Trans. Instrum. Meas., vol. IM-17, pp. 313-320, Dec. 1968.

[2] E. C. Cassidy, H. N. Cones, and S. R. Booker, "Development and

evaluation of electrooptical high-voltage pulse measurement tech- niques," IEEE Trans. Instrum. Meas., vol. IM-19, pp. 395-402, Nov. 1970.

[3] E. C. Cassidy and H. N. Cones, "A Kerr electro-optical technique

for observation and analysis of high-intensity electric fields," /. Res. Nat. Bur. Stand., Sect. C, vol. 73, pp. 5-13, 1969.

[4] E. C. Cassidy, "Pulsed laser Kerr system polarimeter for electro- optical fringe-pattern measurement of transient electrical parameters," ^ev. Sci. Instrum. , \ol. 42, pp. 886-893, June 1972.

109
APPENDIX C

EXPERIMENTAL STUDY OF THE BEHAVIOR OF NITROBENZENE UNDER

VARIED HIGH VOLTAGE CONDITIONS

This material was presented at the 41st Annual Meeting of the

Conference on Electrical Insulation and Dielectric Phenomena, Buck

Hill Falls, Pennsylvania, October 23-25, 1972. It was subsequently

published in the 1972 Annual Report, Conference on Electrical Insulation

and Dielectric Phenomena, National Academy of Sciences, Washington, D.C., 20418,

pp. 37-44, 1973.

110
Experimental Study of the Behavior

of Nitrobenzene under

Varied High Voltage Conditions

ESTHER C. CASSIDY AND R. E. HEBNER

National Bureau of Standards

Washington, D.C.

INTRODUCTION

The present work continues the investigation of electric field behavior between parallel-plate electrodes immersed in nitrobenzene

and strives toward the realization of a Kerr cell which insures

uniformity of the interelectrode field under various HV pulse, dc,

and ac operating conditions. Our earlier direct voltage studies"'"' ^ are extended to include Kerr effect investigations of field distributions resulting from high pulsed (jUs) and 60 Hz alternating voltages.

Recently developed methods,^ employing high-speed photography

for recording of transient fringe-pattern data, are utilized for

visualizing time and space variations in the pulsed and ac fields.

Minimization of the effects from the fringing fields at the electrode

ends permits both the observation of space-charge behavior under

direct and alternating voltages and measurement of the Kerr constant of nitrobenzene. Voltages are measured simultaneously

using calibrated (with state-of-the-art accuracy) devices. Brief

descriptions of the techniques employed and some typical results

are given in the following paragraphs.

HI
APPARATUS AND TECHNIQUES

A schematic diagram of the experimental apparatus is given in

Figure 1. Basically, the system-'-"^ consists of a calibrated^ Kerr

cell, a triggerable pulsed Argon laser, and appropriate photoelectric or photographic detecting and recording equipment. The laser

is equipped with a wavelength selector enabling operation at selected

wavelengths between 514. 5 and 476. 5 nm. Data are also taken at

X = 632. 8 nm using a continuous wave He-Ne laser.

The Kerr cells are filled with nitrobenzene with purity ranging

from that of commercially available reagent grades, having apparent resistivities of 10^ to 10^ ohm-cm, to that of relatively pure

liquid (lO-'-^ to lO"'"''" ohm-cm) processed by chromatographic adsorption and sealed into the cell under vacuum. Whereas the purer

liquid may be used for prolonged steady-state dc and ac operation

without significant effects from turbulence or heating, the less pure

liquid is suitable only for short (jUs) pulse operation. Cells having

a variety of electrode materials and designs,^ including one designed to be virtually free of end-field effects for Kerr constant

measurements, are being used. Effects of varied electrode surface conditions are also being investigated, since recent results

indicate that the measured value of the resistivity depends both on

the intrinsic purity of the liquid and on the composition and surface

preparation of the electrodes. ^' ^

MEASUREMENTS DURING DC AND AC OPERATION

Figures 2 and 3 show typical results from dc and 60 Hz ac experiments with a sealed 0. 5 x 12 cm (spacing x length of electrodes)

cell. The field distribution curves of Figure 3 were computed by

fitting a second degree polynomial to fringe measurements obtained

by scanning the fringe patterns of Figure 2 along centrally located

lines perpendicular to the inner electrode surfaces. A quadratic

fit was used because it predicted all of the data points to well within

the limits of our experimental uncertainty. With knowledge of the

half-wave retardation field strength Ej^ for the calibrated cell**^ and with minimization of end-field effects, the curves showing the

interelectrode space-charge distributions were computed from the

electric field measurements using Poisson's equation. The dc

112
113
STEADY-STATE VOLTAGES APPLIED

dc 60 Hz ac

KERR-EFFECT FRINGE-PATTERN "MAPPINGS" OF

ELECTRIC FIELD DISTRIBUTIONS

FIGURE 2 Fringe patterns mapping dc and 60 Hz ac field distributions in a

0. 5 X 42 cm cell. Photographs taken at peak of negative half-cycle using

a pulsed laser (pulse width: 6 /is).

results show that the field distribution is essentially linear^ with

a uniformly distributed net positive space charge; whereas ac results with the same cell and liquid indicate the presence of nearly

equal amounts of positive charge near the anode and negative charge

near the cathode, thereby suggesting nearly equivalent charge formation or injection at both electrodes. However, conflicting results from experiments with apparently similar cells emphasize

the fact that steady-state Kerr cell behavior is dependent upon the

voltage, upon the material, design and surface condition of the

electrodes, upon the relative purity of the liquid and sealing of the

cell, etc. More comprehensive studies required for distinguishing

the effects of these parameters are in progress.

114
MEASUREMENTS DURING PULSED VOLTAGE OPERATION

In contrast to steady-state behavior, electric fields produced by

applying pulses as high as 300 kV with durations of 5 to 20 /lis showed no evidence of space-charge distortion. Figure 4 shows a

typical fringe pattern recording of the irradiance transmitted

through a Kerr system at the peak of a 65. 4 kV, 5-10 jis pulse.

The absence of space charge is indicated by the absence of fringes

between the electrodes. In higher voltage experiments, where

Kerr system measurement resolution is enhanced,"^ inter electrode

fringes are recorded in some cases. Analysis of results from

different voltage levels indicated, however, that these path

dependent irradiance variations are caused by fringing fields at the

ALTERNATING VOLTAGE DIRECT VOLTAGE +

2x10"^-

ITY IxlO"^-

1

CO

LU

0

LU

CS

or

•a -IxlO"^-

<j>

LXJ -2x10"^-

CO

0.2 0.4 0.6 0.8 X/d

0.2 0.4 0.6 0.8 X/d

E

CJ5

CO

LUa

LU

CS> oc

••a

LU

CO

2x10"

-2x10' -

CD

LU

CC

I

CO

I LU

Li_ ac

4.0

3.0

0.2 0.4 0.6 0.8 X/d

1 1

P rI I I u

0.2 0.4 0.6 0.8 X/d

FIGURE 3 Electric field and space charge distributions computed from fringe

patterns in Figure 2.

115
ends of the electrodes, residual strain in the cell windows, or

slight lack of electrode parallelism.''^ The effects of end-fields,

which produce 1-2% variations in (e/E^) in our 1 x 10 cm cell,

END-FIELD EFFECTS

Ik

ELECTRODE 5" <

; ELECTRODE f ^w

END-VIEW PHOTO AT PEAK

OF 65.4 kV PULSE

n=2 4 6 a44-\

llli:: •^;^>>:^/;.•

1

' r

0 1 ~ 1 r

1 11 2 3 4 5

PEAK(65.^

n-2f 6

iin

I

I

I

I I

I I

I

I M I

I 0 I 2 3 4 I 5

PEAK(80.3 kV)

TIME(fJs)

STREAK CAMERA RECORDINGS OF

FRONT HALF OF VOLTAGE PULSES

FIGURE 4 High-speed photographs of

fringe patterns produced by applying

microsecond high voltage pulses to a

1 X 10 cm cell. The streak camera

records are of the light transmitted

through a slit perpendicular to and

extending between the central inner

electrode surfaces.

116
PULSE VOLTAGES APPLIED

X =514.5 nm 632.8 nm

n = 7, (I/I J = 0.16 n = ll,(I/Im) = 0.9l

48.3 kV 67J kV

TIME scale: 2/i.s/div

FIGURE 5 Oscilloscope tracings of simultaneous a) slideback measurements

of pulge divider response at peaks of applied voltage pulses and b) photomultiplier records of the light transmitted by the Kerr system as a function

of time during the trailing edges of the voltage pulses.

are, for example, evident in the streak camera photographs'^ of

Figure 4. The fringes would, in the absence of end-field variations,

remain perpendicular to the time scale. Use of this procedure,^

for continuous recording of space-charge behavior during application of longer (into the ms range) pulses, is anticipated.

Measurements of the Kerr electrooptic coefficient B are also

being made under short pulse conditions. Simultaneous Kerr system and pulse divider measurements,^ Figure 5, allow measurement of both the applied voltage and the resulting phase shift. Combining this with appropriate dimensional measurements indicates a

value of B ^ 3. 2 X 10~^2 m/V^ at X = 632. 8 nm, T = 23°C and

B 4. 1 X 10-12 ni/v2 at \ = 514. 5 nm, T = 23°C.

117
REFERENCES

1. E. C. CassidyandH. N. Cones, 1969 Annu. Rep. Conf. Elec . Insul. Dielectr. Phenom. , Publ. 1764, Nat. Acad. Sci.

,

Washington, D.C. (1970), p. 77.

2. E. C. CassidyandH. N. Cones, J. Res. Nat. Bur. Stand.

73C, 5 (1969).

3. E. C. Cassidy, Rev. Sci. Instr. 43, 886 (1972).

4. E. C. Cassidy, H. N. Cones, D. C. Wiinsch, and S. R.

Booker, IEEE Trans. IM-17 , 313 (1968).

5. R. Tobazeon, "Intern, sur les Phenomenes de Conduction

dans les Liquides Isolants, " Paris (1970), p. 407.

6. N. J. Felici, Direct Current 2, 147 (1971).

7. E. C. Cassidy, W. E. Anderson, and S. R. Booker, IEEE

Trans. Instr. and Meas. , Nov. 1972, in press.

118
REFERENCES

1. E. C. Cassidy and H. N. Cones, "Development and Analysis of Techniques

for Calibration of Kerr Cell Pulse- Voltage Measuring Systems," NBS

Report 9610, or Sandia Laboratories Contract Report SC-CR- 67-2751

,

Sept. 1967.

2. E. C. Cassidy and H. N. Cones, "Calibration of a Kerr Cell System for

High Voltage Pulse Measurements," Sandia Laboratories Contract Report

SC-CR-68-3730, August 1968.

3. E. C. Cassidy and H. N. Cones, "Development and Analysis of Techniques for

Calibration of Kerr Cell Pulse-Voltage Measuring Systems III," NBS Report

10 078, August 8, 1969, or Sandia Laboratories Contract Report SC-CR-69-

3266, August 1969.

4. E. C. Cassidy and H. N. Cones, "Development and Analysis of Techniques

for Calibration of Kerr Cell Pulse- Vol tag e Measuring Systems IV," NBS

Report 10 296, August 6, 1970, or Sandia Laboratories Contract Report

SC-CR-70-6153, January 1971.

5. E. C. Cassidy, "Development and Analysis of Techniques for Calibration of

Kerr Cell Pulse-Voltage Measuring Systems V," NBS Report 10 493, October 1971.

6. E. C. Cassidy, et al, "Development and Analysis of Techniques for

Calibration of Kerr Cell Pulse- Voltage Measuring Systems VI," NBS Report

10945, November 1972,

7. E. C. Cassidy, H. N. Cones, D. C. Wunsch and S. R. Booker, "Calibration

of a Kerr Cell System for High-Voltage Pulse Measurements," IEEE Trans,

on Instr. and Meas. , vol. IM-17, pp. 313-320, 1968.

119
8. E. C. Cassidy, H. N. Cones, and S. R. Booker, "Development and

Evaluation of Electro- optical High-Voltage Pulse Measurement

Techniques," IEEE Trans, on Instr. and Meas., vol. IM-19, pp. 395-402,

1970.

9. E. C. Cassidy, W. E. Anderson, and S. R. Booker, "Recent Refinements

and Developments in Kerr System Electrical Measurement Techniques,"

IEEE Trans, on Instr. and Meas,, vol. IM-21, pp. 504-510, 1972.

10. D. C. Wunsch and A. Erteza, "Kerr Cell Measuring System for High Voltage

Pulses," Rev. Sci. Instru. , vol. 35, pp. 816-820, 1964.

11. E. C. Cassidy and H. N. Cones, "A Kerr Electro-Optical Technique for

Observation and Analysis of High- Intens ity Electric Fields," J. Research

NBS, vol. 73C, pp. 5-13, 1969.

12. E. C. Cassidy, "Pulsed Laser Kerr System Polarimeter for Electro-Optical

Fringe Pattern Measurement of Transient Electrical Parameters," Rev.

Sci. Instru., vol. 43, pp. 886-893, June 1972.

13. E. C. Cassidy and H. N. Cones, "Electro-Optical Observations and

Measurements of Distorted High- Intensity Electric Fields," 1969 Annual

Report Conf. on Electrical Insulation and Dielectric Phenomena , Buck

Hill Falls, Pa., Oct. 1969, pp. 77-86 (Nat'l. Acad, of Sci., Washington,

D.C. , 1970).

14. E. C. Cassidy and R. E. Hebner, "Experimental Study of the Behavior of

Nitrobenzene Under Varied High Voltage Conditions" 1972 Annual Report

Conf. on Electrical Insulation and Dielectric Phenomena , Buck Hill Falls,

Pa., Oct. 1972, pp. 37-44 (Nat'l. Acad, of Sci., Washington, D.C, 1973).

120
15. R. E. Hebner and E. C. Cassidy, "Measurement of 60 Hz Voltages Using

the Kerr Effect," Rev. Sci. Instru. , vol. 43, pp. 1839-41, 1972.

16. S. Y. Ettinger and A. C. Venezia, "High Voltage Pulse Measuring System

Based On Kerr Effect" Rev. Sci. Instru., vol. 34, pp. 221-224, 1963.

17. A. W. Bright, B. Makin and A. J. Pearmain, "Field Distribution in

Nitrobenzene Using the Kerr Effect" Brit. J. Appl. Phys. (J. Phys, D)

vol. 2, pp. 447-451, 1969.

18. P. Atten and J. P. Gosse, "Regime Transitoire de Conduction Lors d ' une

Injection Unipolaire dans les Liquids Isolants" Phenomenes de Conduction

dans Liquides Isolants, Editions dur Centre National de la Researche

Scientif ique, Paris, pp. 325-343, 1970.

19. E. A. Cherney and J. D. Cross, "Space Charge Effects in Chlorobiphenyls"

IEEE Trans. Elect. Insul., vol. EI-8, pp. 10-16, 1973.

20. J. D. Cross and R. Tobazeon, "Electric Field Distortions Produced By

Solid Dielectric Spacers Separating Uniform Field Electrodes in Nitrobenzene"

IEEE Trans. Elect. Insul., vol. EI-8, pp. 25-29, 1973.

21. C. E. Hill, H. House, "The Problems in Using the Kerr Electro-Optic Effect

to Measure the Field Distributions in Non-Polar Liquids" Phenomenes de

Conduction dans Liquides Isolants, Editions du Centre National de la

Research Scientif ique, Paris, pp. 465-481, 1970.

22. M. Zahn and J. R. Melcher, "Space Charge Dynamics of Liquids" Phys. Fluids,

vol. 15, pp. 1197-1205, 1972.

23. M. Zahn, "Dynamics of Stratified Liquids in the Presence of Space Charge"

Phys. Fluids, vol. 15, pp. 1408- 1417 , 1972.

121
24. W. R. L. Thomas, "The Nature of Particulate Charge Carriers in n-Hexane

and Their Role in Electrohydr odynamic Phenomena" 1972 Annual Report

Conference on Electrical Insulation and Dielectric Phenomena, National

Academy of Sciences, Washington, D.C., pp 52-59, 1972.

25. A, W. Bright and B. Makin, "Modern Electrostatic Generators" Contemp.

Phys., vol. 10, No. 4, pp. 331-353, 1969.

26. A. M. Zarem, F. R. Marshall, and F. L. Poole, "An Electro-Optical

Shutter for Photographic Purposes" AIEE Proc, vol. 68, pp. 1-8, 1949.

27. F. J. McClung and R. W. Hellwarth, "Giant Optical Pulsations from Ruby"

J. Appl. Phys., vol. 33, pp. 828-829, 1962.

28. Z. Croitoru, "Space Charges in Dielectrics" in Progress in Dielectrics ,

vol. 6, J. B. Birks and J. Hart, editors (Academic Press, Inc., New York,

1965), pp. 103-146.

29. Ibid., W. F. Pickard, "Electrical Force Effects In Dielectric Liquids"

pp. 1-39.

30. H. T. Jessop and F. C. Harris, "Photoelasticity , Principles and Methods"

Dover New York pp. 68-70.

31. J. H. Park, "Special Shielded Resistor for High-Voltage DC Measurements"

J. Res. Nat. Bur. Stds., vol. 66C, pp. 19-24, 1962.

32. J. E. Housley, "Reconditioning of Insulating Oils By Activated Alumina"

AIEE Trans., vol. 58, pp. 172-178, 1939.

33. J. D. Ramshaw, D. W. Schaefer, J. S. Waugh and J. M. Deutch, "Dielectric

Polarization and Alignment and the Structure of Polar Fluids" J. Chem.

Phys., vol, 54, pp 1239-1251, 1971,

34. G. Nienhuis and J, M, Deutch, "Structure of Dielectric Fluids II. The

Free Energy and the Kerr Effect in Polar Fluids" J. Chem. Phys., vol. 56,

pp. 235-247, 1972.
35. P. Mazur and B. J. Postma, "On the Molecular Theory of the Kerr Effect"

Physica, vol. 25, pp. 251-267, 1959.

36. Details of the fitting procedure can be found in J. Hilsenrath, et.al.,

"Omnitab, A Computer Program for Statistical and Numerical Analysis"

National Bureau of Standards Handbook 101, U.S. Government Printing

Office, Washington, D.C, pp. 124-140.

37. R. Tobazeon, "Comportement du Nitrobenzene Pur Sous Champs Intenses

Continus et Alternatifs" Phenomenes de Conduction dans Liquides Isolants,

Editions du Centre National de la Researche Scientif ique, Paris,

pp. 407-422, 1970.

38. N. J. Felici, "DC Conduction in Liquid Dielectrics" Direct Current

vol. 2, pp. 90-99, 1971.

39. Z. Krasucki, "High-Field Conduction in Liquid Dielectrics" Phenomenes

de Conduction dans Liquides Isolants, Editions du Centre National de la

Researche Scientif ique, Paris, pp. 311-323, 1970.

40. A.Y.H. Cho, "Contact Charging of Micron-Sized Particles In Intense

Electric Fields" J. Appl. Phys., vol. 35, pp. 2561-2564, 1964.

41. For a recent discussion of these effects see A. H. Cookson and 0. Farish

"Particle-Initiated Breakdown Between Coaxial Electrodes in Compressed SF^"

IEEE Trans, on Power Apparatus and Systems, vol. PAS-92, pp. 871-876, 1973.

42. G. Briere and J. Gosse, "El ectrodialyse des Solvants Polaires" Journal

de Chimie Physique, vol. 7, pp. 1341-1348, 1968.

43. J. Leraoine, "Verification de la Loi de Kerr - Measures Absolues," Compte

Rend., vol. 122, pp. 835-37, 1896.

123
44. L. Chaumont, "Recherches Experimental es sur le Phenotnene Electro-optique

de Kerr et sur les Methods Servant a 1 'Etude de la Lumiere Polarisee

Elliptiquetnent" Ann. de Phys . , vol. 5, pp. 17-78, 1916.

•45. A. D. Buckingham and R. E. Raab, "A Molecular Theory of the Electrooptical Kerr Effect In Liquids," J. Chem. Soc, pp. 2341-51, 1957.

46. Moller, R. , "Die Kerr Konstante des Nitrobenzols" Physikalische Zeitschrift,

vol. 32, pp. 697-718, 1931.

47. Piekara, A. and Konopka, R. , "Pulse Method for Measuring Kerr's Constant

Brit. J. Appl. Phys., vol. 12, pp. 50-52, 1961.

48. Ilberg, Waldemar, "Eine Methode zur Bestimraung der Kerr-Konstante Schlecht

Isolierender Stoffe mit Hilfe Elektrischer Wechself elder" Physik. Zeitschr.

,

vol. 29, pp. 670-78, 1928.

49. Zamkov, V. A. and Radkevich, V. A. , "Polarization Interferometer for

Measuring Induced Anisotropy" Opt. Spectrosc, vol. 31, pp. 437-39, 1971.

50. McComb, Harold E. , "Dispersion of Electric Double Refraction and Ordinary

Dispersion in Liquids" Phys. Rev., vol. 29, pp. 525-40, 1909.

51. Delfino, G. , "Two Beam Method for Measurements of the Kerr Constant With

Fixed Polarizers," Optics Communications , vol. 4, pp. 60-62, 1971.

52. Szivessy, G. , "Uber die Temperatura bhangigkeit der Dispersion des

Elektrooptischen Kerref f ektes" Z. Physik, vol. 2, pp. 30-49, 1920.

53. Jeppesen, Myron A., "Measurements on the Kerr Electro-Optical Effect"

Am. J. Phys., vol. 24, pp. 623-25, 1956.

54. USA and IEEE Standard Techniques for Dielectric Tests . USAS C68.1,

IEEE No. 4, Section 5 and 6, pp. 14-22 (Inst, of Electrical and

Electronic Engineers, Inc., 345 E. 47 Street, Nev? York, N. Y. 10017,

July 1968).

124
55. International Electrotechnical Commission, High- Vol tage Test Techniques ,

lEC Publication 60, pp. 51-91 (Bureau Central de la Commission

Electrotechnique Internationale, 1, rue de Varembe, Geneve, Swisse)

1962.

56. D. E. Skelton, "The Electrical Interference Problem In Fusion Research,"

in Electrical Interference in Instrumentation (lEE Conf. Publ. No. 65,

Savoy Place, London WC2R0BL) , pp. 1-3, 1970.

57. D. G. Pellinen and S. Heurlin, "A Nanosecond Risetime Megavolt Voltage

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58. J. H. Park and H. N. Cones, "Spark-Gap Flashover Measurements for Steeply

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1962.

59. A. F. Rohlfs, J. S. Kresge and F. A. Fisher, "The Response of Resistance

Voltage Dividers to Steep-Front Impulse Waves," AIEE Trans., vol. 76,

part 1, pp. 634-646, 1957.

60. A. J. Schwab and J.H.W. Pagel, "Precision Capacitive Voltage Divider for

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2382, 1972.

61. T. Harada, et_ a_l, "A High Quality Voltage Divider Using Optoelectronics

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pp. 494-500, March/April 1972.

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PAS-91, pp. 478-484, 1972.

63. F. C. Creed, M.M. C. Collins, Aa. Pedersen, and P. Lausen, "Evaluating

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125
64. F. A. Fisher, "Transient Response of Impulse Voltage Dividers," AIEE

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1958.

65. W. Zaengl, "The Impulse Voltage Divider With Lead," Bull, d I'A.S.E.

,

vol. 61, pp. 1003-1017, 1970.

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1428, 1962. -

126
U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1. PUBLK.A l'ION OR RiiPOR I' NO. 2. Gov't Accession No.

3. Recipient's Accession No.

. 11 1 I.I \Mi >iinii I I I; Development and Analysis of Techniques for Calibration of

Kerr Cell Pul s e- Vol tage Measuring Systems VII

5. 1 'uhlii ,1 1 11)11 1 >,iic November 1973

6. Performing Organization Code

. Anrn()U(s) Esther C. Cassidy, Robert E. Hebner, Jr.,

Richard J. Soika and Markus Zahn

8. l-'erfornung (;)rganization

NBSIR 7 3-403

Pl-Rl- ORMINt. ORCANl/.A riON NAMl', ANb ADDRliSS

NAIKjNAI, HUKl'.AU Ol SIAN1)AR1)S

' DKPARTMKNT OF COMMKRCH

WASHINGTON, D.C. 20234

10. ProK ct/ Task/ Work LInit No. 2110426

11. Contract/Grant No. FAO-28-0734

j. Sponsoring Organization Name and Address

Sandia Corporation

Bldg. 894, Kirtland AFB East

Albuquerque, New Mexico 87115

i

13. 1 ypc of Report & Period

Ju^yT,"^ 1972-Julyl, 1973

Final

14. Sponsoring Agency Code

. SUPPLliMliNTARY NOTF.S

|(- ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

' bibliography or literature survey, mention it here.)

To improve the accuracy of pulse voltage systems using the electro-optic Kerr

effect, it is necessary to improve the accuracy of calibration of Kerr cells.

In the past this has been attempted by calibrating the cell under direct voltage

and relying on the frequency independence of the Kerr coefficient (below 10 Hz)

to insure that the calibration was valid under high voltage pulses. Space charge

effects, however, modify the electric field distribution in the liquid under direct

high voltage. The electric field and space charge behavior in nitrobenzene have

therefore been documented as functions of the level and frequency of the applied

voltage. In addition, to improve the efficiency of cell design and to facilitate

the investigation of other liquids for use in Kerr cells, the electro- optic Kerr

coefficient of nitrobenzene has been measured as a function of temperature and

wavelength. Finally a new peak reading voltmeter based on the Kerr effect is

described and the results of using the electro-optic Kerr effect to measure the

voltage pulses in medical X-ray machines are presented.

KEY WORDS (Alphabetical order, separated by semicolons) Electric field measurement; electro-optic

Kerr effect; high voltage measurement; impulse measurement; Kerr constant; Liquid

insulants; nitrobenzene; peak reading voltmeter; space charge

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