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IMBSIR 80-2177

Generation and Measurement of

DC Electric Fields With Space

Charge

Martin Misakian

Electrosystems Division

Center for Electronics

and Electrical Engineering

National Bureau of Standards

U.S. Department of Commerce

Washington, DC 20234

November 1980

Issued January 1 981

Under Department of Energy Contract No. EA-77-01-6010

Task No. A018-EES

H)(?*iH«i«aM*pared for: 100 3ctric Energy Systems Division

y ^0

ipartment of Energy

80-2177

1980

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3AT10NAL UUUAU

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NBSIR 80-2177 3 0 1981

m fioi dec - < GENERATION AND MEASUREMENT OF

DC ELECTRIC FIELDS WITH SPACE

CHARGE

Martin Misakian

Electrosystems Division

Center for Electronics

and Electrical Engineering

National Bureau of Standards

U.S. Department of Commerce

Washington, DC 20234

November 1980

Issued January 1981

Under Department of Energy Contract No. EA-77-01-6010

Task No. A018-EES

Prepared for: Electric Energy Systems Division

Department of Energy

U.S. DEPARTMENT OF COMMERCE, Philip M. Klutznick, Secretary

Jordan J. Baruch, Assistant Secretary for Productivity, Technology, and Innovation

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director
. tiM. / -ACH/"

•

*

-v e i'.
1

ABSTRACT

Characterization of the electrical environment in the vicinity

of high voltage dc transmission lines requires measurement of a number of

electrical parameters associated with the lines. These parameters include

the electric field strength with significant space charge contributions.

This report describes an experimental effort to generate known dc electric

fields containing controlled amounts of space charge. An apparatus which

has been built for this purpose is described and two types of field probes

currently used for transmission line field measurements are examined with

the apparatus. Limitations on the operation of one type of probe in the

presence of very large current densities are identified and discussed.
TABLE OF CONTENTS

Abstract i

I. Introduction 1

II. Apparatus and Theory 2

III. Experimental Results and Discussion 10

A. Current Density Profile Measurement 10

B. Current Density and Mobility Measurements Under Space Charge

Limited Conditions 12

C. Comparisons of Calculated and Measured Electric Field

Strengths 23

C.l Negative Space Charge 24

C.2 Positive Space Charge 26

IV. Summary and Conclusions ’. 34

V. Acknowledgements 35

VI. References and Notes 36
GENERATION AND MEASUREMENT OF DC ELECTRIC FIELDS

WITH SPACE CHARGE

I. INTRODUCTION

With the gradual growth of dc transmission of electrical energy

has also come an interest for a full characterization of the electrical

environment in the vicinity of high voltage dc (HVDC) transmission lines.

Because some corona is usually associated with normal operation of HVDC

lines this environment is complicated by the presence of space charge. The

electrical parameters of primary interest are currently thought to include^

the electric field strength t, with significant space charge contributions,

the current density J, and the space charge density p. At the present time

probes used for the measurement of HVDC transmission line electric fields at

ground level are calibrated with space-charge-free (p=o) fields produced

between parallel plates. The probes are subsequently used to measure electric

fields which may exceed 30 kV/m in the presence of space charge current

12 2

densities ’ as large as 0.1 yA/m . It is noteworthy that future dc transmission systems, as well as biological exposure systems presently under

consideration, may produce fields and current densities which are greater

than the above values.

This paper describes an experimental effort to generate known dc

electric fields with space charge. Experimental uncertainties are noted

and are used to estimate the possible error in calculated values of electric

field strength produced by a parallel plate apparatus. The apparatus has

been used to examine the performance of two types of commonly used electric

3 field probes, namely, an electric field mill and two commercial vibrating-plate
- 2 -

3

probes . While there have been earlier reports of laboratory apparatus which

2 4

generate dc electric fields with space charge ’

, this work focuses more

on the problems associated with producing an electric field of known magnitude.

II. APPARATUS AND THEORY

In deciding on the design for an apparatus, several electrode geometries

were examined. The electric field in each case satisfies Poisson's equation,

V*t = p/e

Q

, (1

)

and the constitutive relation for the conduction current density

. 3 = pkE , (2)

where is the permittivity of free space and k is the ion mobility.

5 6

Because corona in air will generate several ion species ’, Eq. (2)

must be modified to

3 = (Ep^pt (3)

t h

where p. and k.. are the charge density and mobility of the l charge

carrier species respectively . Expressing

( 4 )
-3-

where is the fraction of the total charge density attributable to

L. the i tn charge carrier, Eq. (3) can be written

= p(Ea.jk.j)E = pKf: ( 5 )

where K is the weighted average of the individual mobilities. The quantity

K will be referred to below as simply the "mobility." It is assumed that

K is constant throughout the interelectrode region and there are no ion losses

as the ions traverse the distance between the electrodes, i.e., J is conserved.

The concentric wire-and-cyl inder electrode geometry was considered as

a candidate design for an apparatus because it had been extensively studied;

a theoretical relationship between corona current and applied voltage was

first given by Townsend^. Employing pure gases, the current-vol tage data

obtained with coaxial electrodes can be fitted to a theoretical expression

O

using the mobility as a fitting parameter . With the mobility so determined,

the electric field at the surface of the cylinder, where an electric field

8 9

probe would be positioned, could be calculated from an expression ’ derivable

from Eqs. (1 ) and (5)

E 2 ^l2E 2(r

l) +

I (R

2

- i-, 2

)]

2lre oK

(6)

where R is the radial distance of the cylinder from the center of the

wire, r-j is the radial distance where E begins to decrease from the

breakdown value, E(r-j), and I is the measured corona current per unit

length of wire.
-4-

In examining the above theory and procedure, however, the following

points suggest that an alternative approach be sought.

(1) No direct measurement of the electric field profile near the

wire has ever been performed and, consequently, it is not clear what

value r-j should actually have. In the case of positive corona, the wire is

surrounded by a glowing sheath, but there is no reliable quantitative

theory describing this region. The glowing region is believed to be the

source of positive ions. The outer edge of the visible sheath has sometimes

been taken to be r-j , but the validity of this assumption is not known.

The situation appears to be significantly different for the case of

negative corona because the sheath is now replaced by many individual glow

points on the wire's surface. The wire is now an emitting surface for

electrons which can subsequently attach to electronegative molecules. The

negative molecules formed near the wire then drift to the outer electrode.

Once again, the value to be taken for r-j is not clear; from the above

description, however, it appears that rj would be different for opposite

polarity corona.

(2) In deriving Eq. (6), it was assumed that the mobility of the

charge carrier was independent of the electric field strength. The

assumption breaks down, however, if the energy gained by the ion from

the field between successive collisions is comparable to the average

thermal energy of the host gas^. This condition does, in fact, exist

in the high field region near the wire. It is, therefore, not clear that

the determination of the fitting parameter, K, described earlier can

yield a number that can be treated as an "effective mobility".
-5-

(3) Use of a cylindrical field generating apparatus to evaluate an

electric field probe will also be made difficult because a good geometrical

match between the curved cylindrical surface and the typically flat

electric field probe will not be possible- Measurements in our laboratory

have shown that a M mm displacement of a vi brat ing-pl ate type probe

above or below the surface of the ground plane of a parallel plate electric

field apparatus (space charge free) affects the electric field reading

by several percent- Thus, some error will be introduced with an apparatus

having a circular geometry.

The difficulty posed by the last point can be eliminated by use of

a square coaxial geometry, but the uncertainties associated with calculation

of the electric field strength, i-e-, items (1) and (2), remain a problem.

Another design for an apparatus which was examined and finally adopted

is a parallel plate electrode system similar, in principle, to one

1

1

reported by Withers et al., and employed for charging aerosols. A

schematic view of our apparatus, which is much larger than the Withers

system, is shown in Fig. 1. Corona wires instead of points for producing

space charge and an additional ion control grid are other differences.

Ions generated by thirty 0.0057 cm diameter stainless steel corona

wires are directed both upward (to the cap) and downward 8 cm to the

first screen. Charge carriers not collected on the first screen

continue downward another 8 cm to the second screen which is the top "plate"

of a parallel plate system. The charge carriers which pass through the

top plate travel a distance d to the bottom plate and form the current density J.

The first screen consists of crossed 0.03 cm diameter tinned copper

wire mounted on an aluminum frame 1.6 m x 1.6 m. The square openings

are 1 cm x 1 cm. The second screen is an aluminum window screen with
CAP

Figure 1. Schematic view of apparatus. The configuration shown is

appropriate for generating an electric field with positive

space charge. The top and bottom plates of the parallel

plate structure are located in the planes z=0 and z=d. The corona wires are oriented parallel to one another and are perpendicular to the plane of the figure.
- 7 -

0.02 cm diameter wire and square openings of approximately 0.12 cm x 0.12 cm.

This screen was also mounted on a 1.6 m x 1.6m aluminum frame and

stretched to provide a nearly flat surface. The bottom plate consisted

of nine aluminum plates 0.2 cm thick mounted on a 1.6 m x 1.6 m aluminum

frame and electrically grounded. The electrodes above the ground plane

were energized using dc power supplies and biasing resistor networks as

shown schematically in Fig. 1. The total corona current as well as

currents to the cap and screens were monitored. Three electrically

2

isolated current sensing elements, having areas of approximately 100 cm

were mounted on the bottom plate for measurements of J. The current sensing

elements were within 0.01 cm of the plane defined by the bottom plate. An

electrometer was used for the current measurements in the ground plane. The

current density profile was measured with a moveable circular probe 6 cm in

diameter with a 2 cm wide guard band. The voltages were measured with

uncertainties of less than 0.5% using electrostatic voltmeters. Because

the ions are produced in a region external to the parallel plates, the

uncertainties associated with the choice of r-j and the influence of excessively

high electric fields on the ion mobility are avoided. The flat surface of

the bottom plate also permits a good geometrical match between the ground

plane and an electric field probe.

Tv/o holes near the center of the bottom plate permitted the placement

of two field probes in the ground plane for comparisons of simultaneous

measurements. Each vibrating plate probe was compared with the field mill.

The field mill used in this study has two signal outputs, a linear ac signal

and a logarithmic dc signal which is obtained with phase sensitive circuitry.

Phase sensitive detection circuits are also employed in both vibrating-plate probes.
- 8 -

The electric field between the parallel plates must still satisfy Eqs. (1)

and (5). Solving for p in Eq. (5) and substituting into Eq. (1), yields for

the one dimensional case.

dE _ J dz -

e 0

KE

•

Solution of this differential equation gives

(7)

( 8 )

where E

Q

is the electric field at the top plate, z=0. With the

planes z=0 and z=d at potentials Vy and 0 respectively, Eq. (8) can

be integrated, using £=-VV, to give a useful relation between E Q

, K

and J,

3JV

T , p 2 . 2Jd->3/2 r 3

Ke

[t

o Ke

" L o

' o o (9)

Other useful relations are found from Eqs (8) and (9) when the current

density in the parallel plate region is limited by space charge. Then

E q

=0 so that

K

- 8 ^s d^_

9 e, ,, 2

'o V

T

( 10 )

and

(ID
-9-

where is the space charge limited current density. When K

[Eq. (11)] is substituted into Eq. (10) we have that the field

at the bottom plate is

( 12 )

and independent of value.

That the problem can be characterized as one-dimensional in Eqs. (7)-(12)

can be justified if the current density profile is made sufficiently uniform

in the region of interest. Then, because of the initially uniform spacecharge-free field, no field component orthogonal to the z-axis will

exist (except in the area of fringing fields far from the site of the

* o measurements) and the electric potential will change throughout the region

according to

Thus, a field probe within this region will view an electric field

with a perimeter boundary condition characteristic of an infinite parallel

plate system. Experimental results which indicate that this condition has

been reasonably approximated are presented in the next section. It is

noted that on the scale of the closely spaced holes in the top plate,

it can be shown that the individual ion "beams" will overlap because of

1

2

diffusion as the ions traverse the distance to the bottom plate .

The strategy originally adopted for generation of a calculable dc

electric field with space charge involved several steps: (1) The quantity K

(13)
- 10 -

was to be determined in situ by measuring^ for a specific Vy and

employing Eq. (11). An in situ measurement of K is required because small

amounts of gases such as CC^ and H^O can cause significant changes in the

predominant charge carrier species *

. (2) Witn K determined, the

quantity EQ

would be obtained for arbitrary J and Vy using Eq. (9). (3) Finally,

the electric field would be calculated with Eq. (8) using the values of

E q

, J and Vy from step 2. How this approach had to be modified is discussed

in the next section.

III. EXPERIMENTAL RESULTS AND DISCUSSION

A. Current Density Profile Measurements

Typical measurements of the current density for positive space charge

as a function of position at the bottom of the parallel plates are shown in

Fig. 2. The measurements were performed at 56 locations with the moveable

circular probe. Forty-four values within a circular area of 0.7 m radius

were averaged and the J values shown are normalized with respect to this

average. An electrostatic field of 8 kV/m (i.e., Vy ^ 800 volts and d = 0.10 m)

existed prior to the introduction of the space charge; the average current

i -6 2 density was near 0.2 x 10 A/m and the total corona current, I , was

l near 0.6 mA. Temporal fluctuations of J were typically less than ±2%.

Ignoring these fluctuations, it can be seen that within a radius of 0.7 m,

the current density does not deviate from the average value by more than ±6.5%.

Within a radius of 30 cm the spread in J values is less than ±3%. Current density

profiles measured at other voltages and current densities with parallel

plate spacings near 10 and 15 cm were similar to those shown in Fig. 2.

Comparable results were obtained with negative space charge.
-lion

Figure 2. Measurements of the current density on the surface of the

bottom plate. The results were obtained with a movable

circular probe 6 cm in diameter with a 2 cm wide guard

band and normalized with respect to the average of 44 measurements

within a distance of 0.7 m from the center. The average J

-fi 7 value is near 0.2 x 10 A/m .
- 12 -

B. Current Density and Mobility Measurements Under Space Charge

Limited Conditions

Figure 3 shows measurements of with positive space charge for

values of Vy ranging from 400 V to 1000 V. All current density measurements

were performed near the center of the bottom plate as the current

incident on the top plate, Iy, was increased. This was accomplished by

increasing V

A

while keeping (V

CQ

-V

A

) nearly constant (see Fig. 1).

Also shown in Fig. 3 are values of the mobility determined from Eq. (11).

Evident from the values in Fig. 3 and confirmed by additional measurements

at higher values of Vy is a downward trend in K as Vy is increased. At

2000 V, for example, K is calculated to be near 1.4 x 10~ 4

m^/V-s. An

explanation of this downward trend would seem to exclude a mechanism involving

the actual change in the value of K barring a change in air composition.

That is, growth in the size of the charge carriers with an associated decrease

in mobility is believed to occur in some cases as the time-of-fl ight is

1

3

increased . The trend observed here, however, is just the opposite. Much

of the noted trend can be explained by more careful consideration of the

potentials encountered by a charge carrier as it passes through the top plate.

It is recalled that when Eq. (11) is determined from Eq. (8), the

boundary conditions invoked are that the top plate (screen) is at potential

Vy and the bottom plate is at zero potential. While the potential at the

bottom plate is well defined, the experimental conditions necessary to

achieve a space-charge-limited current density in the parallel plate region

leads to a significant perturbation of the potential experienced by the

charge carrier as it passes through the screen forming the top plate. For

example, when Vy is equal to 800 V, V^ must be increased to near 9 kV in

order for J to become space charge limited.
-13-

Current Incident on Top Plate (><106 A)

Figure 3. Measurements of space charge limited current density. The current

density near the center of the bottom plate was monitored as the

current incident to the top plate (screen) was increased. Also

shown are values of mobility calculated from Eq. (11).
-14-

An expression which has been used to obtain an approximate^ 4 graphical view

of conditions near the screen for this situation is one that is used for

obtaining the equipotential s for a triode tube in the absence of space

1

5

charge. The equipotential s are determined from the equation for

the potential 5 V(z,y)

V(z,y) = V

T

F

1 + v A

F

2

( 14 )

where

F

1 = y

d

1 + z -(P/47rd

2

) (d

2 + d-j ) ln{e 4lTZ/P + 1 - 2e

2uz/P cos(^)}

di + d^ + yd-j

F

2 ’

d

1 + z +(P/4ird2

) yd-j ln{e4ltz/P + 1 - 2e 2¥z/P cos(^)}

di + d

2 + yd-j

-2nd,

y

=

P ln{2sin(^-)}

d-j is the parallel plate spacing, d

2

is the distance to the screen above

z=0, P is the spacing of the grid wires, R is the radius of the grid wire

and y is the coordinate orthogonal to z. Equation (14) has been derived

assuming that the positive z direction is opposite to that shown in Fig. 1,

the grid wires are parallel, infinitely long and R <_ P/20. The actual screen

has a square mesh with spacing, P, equal to 0.14 cm and a value of R equal

to 0.014 cm, i.e., R = P/10. Consequently, the amount of field penetration

predicted by Eq. (14) may be somewhat excessive.
-15-

Shown in Fig. 4 are plots of equipotential s when is 8 kV and the

potential of the grid is 800 V. For this model calculation an ion passing

through the plane of the screen experiences a space potential near 835 V which

is significantly greater than the measured potential of 800 V. The 800 V

1 fi equipotential plane is now 0.285 cm below the grid. If the assumption is

made that E=0 within ^0.1 cm below z=0 when J=J

s the results in Fig. 4

suggest that a value of Vy larger than that measured with the electrostatic

voltmeter should be used in Eq. (11). Calculations with Eq. (14) show,

however, that the relative perturbation of Vy will diminish as Vy is increased.

Use of such modified values of potential in Eq. (11) could yield a value for

mobility which is independent of the voltage applied to the top plate.

The model was tested experimentally for a range of applied voltages

with negative and positive charge carriers. Monitoring the dc signal, the

field mill was first employed to measure E when J was space-charge-limited.

Then from Eq. (12),

3

V

,n

E(z-d) - §-|& (15)

the effective space potential, designated V

sp

, encountered by the

charge carriers as they passed through the top plate was calculated. When

mobilities are determined with V

sp

instead of the potential Vy applied to

the grid of the top plate, the downward trend in K is eliminated. Values

of mobility calculated with Eq. (11) for applied potentials Vy and corresponding

space potential V

$p

are listed as K’ and K respectively in Table I. The

results represent two sets of measurements obtained on different days.
z

(cm)

-16-

0.14 cm

©

Figure 4. Two dimensional plot of equipotential s near a screen of

parallel wires. The field is assumed to be Laplacian (i.e.,

space charge free). Nominal fields of 100 kV/m and 8 kV/m are assumed in the regions above and below the screen (top plate)

respectively. The potential of the screen is taken to be

800 V.
-17-

TABLE I SPACE CHARGE MOBILITIES

d

= 0. 099 m T = 25.2 °C Rel. Humidity ^ 50%

Negative Space Charge

J

s (A/m

2

) V

T

(V) K'(m

2 /V s)

V

sp

< V > K(m

2 /V s)

0.725 x 10“ 6

- 595 2.01 x 10" 4

- 648 1.70 x 10“4

1.90 -1003 1.85 -1036 1.73

2.66 -1209 1.79 -1238 1.71

3.86 -1497 1.69 -1491 1.71

6.33 -2013 1.54 -1939 1.66

Positive Space Charge

J

s (A/m

2

)

0.569 x 10" 6

1.59

2.29

3.40

vT

(v) K'(m

2

/V s)

595 1.58 x 10" 4

1003 1.56

1209 1.54

1497 1.49

2013 1.41

' (v)

sp

v ' K(m

2 /V s)

658 1.29 x 10“4

1070 1.37

1269 1.40

1514 1.46

5.83 1974 1.47
-18-

The negative mobilities, K, are independent of applied voltage from

approximately -600 V to -1500 V where V has a value slightly less than

^ r' the applied potential. The calculated values of V sp are less than Vy when

Vy exceeds -1500 V because the measured field values show less than 50%

enchancement [Eq. (15)]. In terms of the above discussion on space potentials,

the condition V

sp

<Vy must be considered as physically not possible. The

difficulty, however, appears not to be in the functioning of the field probe

but in the operation of the apparatus. For constant mobilities, it can be

shown from Eq. (11) that

W , v

i 2

W' V

(16)

where the V's are now taken to be values of space potential. For there to

be a 50% field enhancement when V

$p

= -2013 V, for example,

2 J

s (-2013 V) = J

s (-1238 V)(^I|) .

Using the J (-1238 V) value from Table I, we have that J (-2013 V) should

be near 7.0 x 10"° A/iti . The experimental value is 6.33 x 10 A/m and as

a result a smaller electric field is produced. Why the value of J saturates

before acquiring the theoretical ly expected magnitude is not clear. Evidently the
-19-

1

6

assumption that a diffusion mechanism can provide sufficient space charge

between the parallel plates so that J is space charge limited is no longer valid.

Measurements of the negative space charge mobility were also

made with a parallel plate spacing near 0.15 m for applied voltages between

-807 V and -1086 V and were found to be in good agreement with the values

in Table I. The mobility values are also in good agreement with average

1

7

negative air ion mobilities reported by other investigators .

Because of uncertainties in the measurement of J , d, and E [Eq. (15)],

the tabulated values of negative space charge mobility between applied

voltages of -595 V and % -1497 V are estimated to be accurate within ±1°L

This estimate includes the uncertainty in the correct choice for within

a central circular region of radius 0.4 m on the bottom plate. The precision

of the results is estimated to be near ±3%.

Table I shows that while the downward trend with applied voltage of

positive space charge mobility has been eliminated, an upward trend has taken

its place. The condition V

S p<V-p also occurs with positive space charge, but

at a higher applied voltage between 1500 V and 2000 V. Additional

measurements have shown that V

S p<Vy first occurs near an applied voltage

~6 2

of 1750 V with a corresponding current density of ^4.4 x 10 A/m .

In light of the constant negative space charge mobility measurements, the

upward trend in K for positive space charge does not appear to be an

artifact of the apparatus. An "aging" mechanism in which the size of the

charge carrier grows as the time-of-fl ight between the plates increases is

consistent with the data. The resulting decrease in K is compatible with the

view that the predominant charge carriers produced by positive corona in

laboratory air are hydrated protons, i.e., (I^O^'H which can grow in
- 20-

size as a function of time-of-fl ight or distance travelled.

Measurements of positive space charge mobility were also made with a

parallel plate spacing near 0.15 m for applied voltages between 907 V and

1806 volts. The upward trend in the measured mobility again occurred and

the mobility values corresponding to the same ratios (Vy/d) in Table I were

slightly smaller in each case. The value of K was also measured when (Vy/d) ^ 10 kV/m and d = 0.3 m and was found to be near 1.28 x 10" 4

m^/Vs.

The comparisons cannot be considered conclusive evidence for the

aging model suggested above, but are supportive. Because the moisture

content in the room air could not be controlled, a systematic study of the

model could not be made. A 20 percent decrease in air moisture did not

measurably affect the values of the mobility.

The values of positive space charge mobility in Table I compare well

with average mobilities in air reported by other investigators 17. The

earlier comments regarding accuracy of the negative space charge mobility

measurements apply again for the positive space charge case.

Attempts to determine mobilities with the two vibrating-plate field

probes were not successful. The calculated values of V

$p were found to be

less than Vy for most of the voltages examined. Because the response of each

vibrating-plate probe to the electric field is similar, only results for one of

the probes are presented.

Several simultaneous measurements of the normalized electric field, with

negative space charge, made with the field mill (dc signal) and a vibrating

plate probe are shown in Table II; the corresponding values of V are also

b \J given. According to the simple qualitative model depicted in Fig. 4, field
- 21 -

TABLE II SPACE POTENTIAL MEASUREMENTS

d = 0.099 m T = 25.2 °C Rel . Humidity^ 50%

Negative Space Charge

Field Mill Vibrating-pl ate Probe

J

s (A/mc

) vT

(v) [E(J=J

s )/E(J=0)]

m Vv > [E(J=Js )/E(J=0)]

m yv >

0.725 x 10" 6

- 595 1.63 - 648 1 .47 - 585

1.90 1 —

j

oo CO 1.56 -1036 1.39 - 932

2.66 -1209 1.53 -1238 1.37 -1103

3.86 -1497 1.49 -1491 1.34 -1338
- 22 -

enhancements in excess of 50 percent are expected when J=J

s

. In no

case does the vibrating-plate probe indicate as much as 50% enhancement

for the field strengths and current densities shown. It should be noted

here, however, that the current densities reported under HVDC transmission

lines are much smaller than the values presently being considered. Electric

fields with less space charge are considered in the next section. The

vibrating-plate probes show similar discrepancies from 50% field enhancement

when electric fields with positive space charge are examined.

Simultaneously monitored with the field measurements listed in Table II

was the ac signal of the field mill. For each applied voltage, the normalized

field determined with the ac signal exceeded the corresponding field

determined with the dc signal which is produced with phase sensitive circuitry.

The difference in probe response results in higher values of V sp

. The higher

normalized electric field and associated space potentials are considered to

be an instrumental artifact. When J^O, contributions from the space charge

conduction current will add to the charge induced in the field mill sensing

element by the electric field. The artifact interpretation is also supported

by an examination of the higher V

$p

values. Knowledge of V^, Vy, and J impinging

on the top plate permit an estimate of the electric field in the region above

the top plate (Fig. 1). Approximate calculations of V using Eq. (14)

j p indicate that the space potential values determined from the ac signal are

q f h l too high. Because the conduction current signal is in quadrature with

respect to the induced signal, the phase sensitive detection circuitry eliminates

the above source of error from the dc signal of the field mill.

-
-23-

Final ly, in closing this section it is noted that the use of the

field mill to determine K means that the goal of calculating the electric

field from "first principles" has been abandoned. The parallel plate apparatus

can still be used, however, for the evaluation of electric field probes. The

use of a probe to determine physically reasonable values of K (or V

sp

) can

be regarded as one test of the instrumentation. A comparison between calculated

[Eqs. (8) and (9)] and measured field values when the current density is not

space charge limited represents another test. Such comparisons are described

in the next section for the two types of probes.

C. Comparisons of Calculated and Measured Electric Field Strengths

Calculations of electric field strength with negative and positive space

charge were performed for arbitrary values of J and Vy and compared with

measurements obtained simultaneously with the a field mill and vibrating plate

probes. The values of K were determined using the field mill (dc signal); E Q

and E were found from Eqs. (9) and (8) respectively. As noted in the previous

section, the positive space charge mobility appears to change with charge

carrier time-of-fl ight or applied voltage. The change in K as a function of

applied voltage is not rapid, however, and its use for field calculations is

permitted if a greater uncertainty can be tolerated in the calculation (see

Sec. C.2). Only mobility values determined when V

sp

>Vy are used in the

calculations for both polarity space charge. The electric potential in Eq. (9)

is taken to be the applied voltage Vy in all cases because the fields above

and below the top plate are comparable in magnitude when J is less than J .

It is noted that calculations of the electric field with space charge

of either polarity are somewhat "forgiving." Uncertainties in J, d, and

K tend to cancel one another during the determination of E Q

[Eq. (9)]. Two
-24-

uncertainties associated with J, i.e., its relation to the average J value

and the area of the sensing element, are decreased because of division by K

in Eqs. (8) and (9). When the electric field is determined from Eq. (8), the

square root operation further reduces the uncertainties.

The calculated normalized field values with negative space charge presented

below are estimated to be accurate to within ±2%. The calculated normalized

field values with positive space charge have an added uncertainty because of

the upward trend in the mobility values. The accuracy of the calculation

is related to the choice of K value and is discussed later. All normalized

field measurements have been performed with uncertainties of less than ±1.5%.

C.l Negative Space Charge

Comparisons between the calculated normalized field values, [E(J?*0)/E(J=0)] ,

and the corresponding measured values using the field mill and a vibratingplate probe are shown in Figs. 5 and 6. The mobility values used for field

calculations in each case were determined when \Jj = -1003 V. The field mill

data in Fig. 6 show very good agreement with the calculations but appear to be

systematical ly higher than the calculated values in Fig. 5. For the current

densities shown there is poor agreement between the calculations and the vibrating

plate probe measurements in each case.

A possible explanation for the slightly high field mill values in

Fig. 5 may be related to an effect not previously discussed, but initially

observed as a "zero drift" in the instrumentation when the space charge was

turned off after mobility measurements. It was later learned that the "zero

drift" was actually due to the presence of a residual charge on the aluminum

screen forming the top plate. The magnitude of this surface charge decayed

1

8

very slowly, even when the top plate was directly connected to ground .
-25-

Figure 5. Comparisons between calculated and measured normalized

electric field strengths when (Vy/d) ^

-10 kV/m. The

solid line corresponds to exact agreement and the shaded

area represents the uncertainty in the calculation. Typical

error bars for the measurements are also shown.

[E[J*0)/E[J=0]]

c

Figure 6. Comparisons between calculated and measured normalized

electric field strengths when (Vy/d) is increased to -18 kV/m.

The solid line corresponds to exact agreement and the shaded

area represents the uncertainty in the calculation. Typical

error bars for the measurements are also shown.
- 26-

Surface charging of the top plate may be the source of a small

perturbation of Vy not detectable with the electrostatic voltmeter

which monitors the potential of the aluminum frame. An increase in the

value of Vy would result in a larger value of E q

[Eq. (9)] and E [Eq. (8)],

and better agreement with the measurements in Fig. 5. At higher applied

voltages, the relative perturbation is apparently smaller and has less

influence on the calculation.

The values of current density considered in Fig. 5 and 6 are much

greater than those observed in the vicinity of HVDC transmission lines. Fields

with less current density but with comparable magnitudes can be generated by

increasing the plate spacing and maintaining the same ratio (Vy/d). It can

be seen from Eq. (11) that the current density then scales as (1/d) if the

mobility is constant and J=J . Measurements of normalized electric field with

the two types of probes are given in Table III for three plate spacings with

(Vy/d) ^

10 kV/m.

The results in Table III show improved agreement between the field mill

and vibrating-plate probe measurements as the current density is decreased.

An estimate of how small J must be before the vibrating-plate probe agrees

with the field mill is obtained from a plot of J

s

~^ versus [E( J/0)/E( J=0)

]

m for each probe; the appropriate entries from Table III are plotted in Fig. 7.

The measurements appear to agree when the space charge limited current, J , is

-6 2 approximately 0.3 x 10 A/m . This conclusion is appropriate only for the

vibrating-plate probe under consideration and for (Vy/d) ^

10 kV/m. This last

point is discussed further when similar data for positive space charge is

considered.

C.2 Positive Space Charge

Using a single value of K determined when V y

= 1003 V, calculated

normalized field strengths are compared with experimental values obtained
-27-

TABLE III FIELD MEASUREMENTS WITH DIFFERENT PARALLEL PLATE SPACING

Negative Space Charge (Vy/d) VI 0 kV/m

V i bra ting

Field Mill Plate Probe

J(A/m

2

) [E(J^0)/E(J=0)]

c [E(W)/E(J*0)]

m [E(J*0)/E( J=0) ] m

d=0. 3 m

0.188 x 10" G 1.18 1.19 1.15

0.292 1.26 1.28 1.24

0.355 1.32 1.34 1.28

0.481 1.42 1.45 1.37

0.616* eo — 1.55 1.47

d=0. 15 m

0.284 x 10‘ b

1.13 1.14 1.10

0.537 1.24 1.26 1.19

0.668 1.30 1.32 1.23

0.876 1.38 1.41 1.30

1.25* -- 1.56 1.42

d=0.099 m

0.391 x 10" 6 1.12 1.13 1.08

0.775 1.23 1.25 1.14

0.958 1.28 1.30 1.19

1.32 1.38 1.39 1.26

1.90* — —

>

1.55 1.39

* J=J

s
[E|i/0!/E|M))]ni

-28-

Figure 7.

J S"1

( x10“5m2 /A)

Intercept of two lines provides estimate of space charge limited

current density for which there will be agreement between field

mill and vibrating-plate probe measurements when (Vy/d) ^

TO kV/m.

Typical error bars are shown.
-29-

simul taneously with the field mill and vibrating-plate probe in Fig. 8; the

ratio (Vy/d) is near 10 kV/m and d=0.099 m. The poor agreement between the

vibrating-plate probe measurements and the field mill results is again

seen. The calculated values of the normalized field are, as in the case

with negative space charge, systematically lower than the field mill data.

In addition to the possible perturbation of Vy discussed previously, the

use of a constant value of mobility should introduce some error in the calculations

since K apparently is changing as a function of charge carrier position

between the plates. This added uncertainty leads to small changes in the

calculated values of E, however. If, for example, K is varied by ±2.5% from

19

the value determined at (Vy/d) = 10 kV/m, the change in E is less than

-fi 7

±0.6% when J is equal to 1 x 10 A/m ; smaller changes occur in E for lower

J values. Thus, use of a single value of K determined at the same applied

voltage for the field calculations and measurements does not introduce

large error.

Comparisons between calculated and measured normalized field values

when Vy is increased to 1497 V are shown in Fig. 9; the mobility has been

determined with an applied voltage of 1497 V. The improved agreement between

the calculations and field mill measurements may again be indicative of a

relatively smaller perturbation of Vy due to charging of the top plate

(Section C. 1

)

.

As in the case with negative space charge, comparisons between measurements

obtained with the two types of probes improved as J was decreased. Table IV

shows simultaneous field measurement data for three different parallel plate

spacings.
-30-

Figure 8. Comparisons between calculated and measured normalized electric

field strengths when (Vy/d) ^ 10 kV/m. The shaded area above

the solid line has been increased to 2.6 percent to show effect

on calculation if K is reduced by 2.5 percent.

POSITIVE SPACE CHARGE

Figure 9. Comparisons between calculated and measured normalized electric

field strengths when (Vy/d) ^ 15 kV/m. Improved agreement

between the field mill and calculated values is observed as (V,/d) is increased.
-31-

TABLE IV FIELD MEASUREMENTS WITH DIFFERENT PARALLEL PLATE SPACING

Positive Space Charge (Vy/d) ^10 kV/m

Field Mill

V i bra ting

Plate Probe

J(A/m2

) [E(J^0)/E(J=0)]

m

[E(J/0)/E(J=0)]

d=0. 3 m

0.0580 x 10" 6 1.07 1.06

0.135 1.18 1.14

0.313 1.38 1.32

0.469* 1.57 1.50

d=0.15 m

0.080 x 10“ 6

.1.06 1.03

0.218 1 .14 1.09

0.521 1.31 1.24

0.618 1.38 1.28

1.00* 1.59 1.45

d=0.099 m

0.149 x 10' 6 1.08 1.03

0.432 1.19 1.11

0.758 1.31 1.20

0.984 1.39 1.25

1.58* 1.59 1 .40
-32-

Plotting the field measurements as a function of J

s ~^, as was done

in Fig. 7 indicates that for positive space charge the vibrating-plate probe

c 7 will agree with the field mill when is approximately 0.26 x 10 A/m and

(V

T

/d) ^

10 kV/m.

Similar measurements using the second vibrating-plate probe indicate

-fi 7

that agreement with the field mill occurs when J

s is about 0.290 x 10 A/m .

Using an older sensing head with the second field probe, measurements of

the electric field revealed a greater difference from the field mill results

( J=J

S

, Vy = 1003 V, d = 0.099 m) than did the new sensing head or the first

vibrating-plate probe.

A possible explanation for the low field readings observed with the

vibrating-plate probes, in the presence of a space-charge current, is now

20 briefly described . Shown in Fig. 10 is a simplified schematic view of a

vibrating-plate probe exposed to a dc field produced with a positive voltage,

Vy. In the absence of space charge, a negative charge is induced in the

vibrating plate and the operation of the probe is such that a negative feedback

3(c) potential is applied to the face plate to null v ' the signal V

g

; the field

reading is proportional to the feedback signal, Vy. .

If a flow of positive ions is also present, as in our measurements, V

$

will acquire a positive dc component due to the voltage drop across the

resistor R shown in Fig. 10. Because of the motion of the vibrating-olate,

some positive voltage will be added to the feedback signal to null V . The

smaller negative feedback voltage results in a lower field reading.

Differences in the value of R due to the circuit components employed, or

the surface condition of the vibrating plate could explain, in part, the

differences in response of the various vibrating-plate probes.
-33-

Figure 10. Simplified schematic view of vibrating-plate probe with electric

field containing positive space charge. The probe responds to a field-induced negative charge on the vibrating plate by generating

a negative feedback voltage and to a positive ion current

incident on the vibrating plate by generating a positive feedback

voltage.
- 34 -

IV. SUMMARY AND CONCLUSIONS

A parallel plate apparatus has been developed for generation of known

dc fields with space charge and has been used to examine the performance of two

types of electric field probes. Use of the probes to determine the space

charge mobility provides information on the performance of the instrumentation

as well as operation of the apparatus. The data indicate that a field mill

with phase sensitive signal detection functions well in the presence of

high current densities, but under the same conditions field probes with a

vibrating-plate design give erroneous results.

With a valid in situ determination of mobility, known fields of arbitrary

strength and controllable amounts of space charge can be produced. The

data show that, for a given field strength, the performance of the vibratingplate probes improves as the current density is reduced. Only examples where

the space charge contribution to the total electric field strength is

significant have been considered.

The laboratory measurements of electric fields described in this study

must be considered as somewhat ideal because of the absence of wind, charged

aerosols, and dust which are frequently encountered during outdoor measurements.

The presence of wind significantly perturbs the value of J and leads to large

temporal fluctuations in the field valued If charging of a field probe can

result in measurement errors, charged dust and aerosols will aggravate the

problem . In closing, we note that the results presented above appear to be

the first reported comparison between calculated electric field values (J^O)

in a parallel plate apparatus -- with estimates of accuracy -- and measured field

values.
- 35 -

V. ACKNOWLEDGEMENTS

The author is pleased to acknowledge useful conversations with

Jo R. Melcher, R. S. Withers, W. E. Feero and co-workers at NBS. The

assistance of S. B. Kelley during the preparation of the manuscript is

also greatly appreciated . This work has been supported by the Department

of Energy.
-36-

VI. REFERENCES AND NOTES

1. T. D. Bracken, A. S. Capon, and D. V. Montgomery, "Ground Level

Electric Fields and Ion Currents on the Cel ilo-Sylmar ±400 kV DC

Intertie During Fair Weather," IEEE Trans. Pow. App. and Syst., Vol

PAS-97, pp. 370-378, 1978.

2. T. D. Bracken and B. C. Furumasu, "Fields and Ion Current Measurements

In Regions of High Charge Density Near Direct Current Transmission Lines,"

in Proceedings of the Conference on Cloud Physics and Atmospheric

Electricity (American Meteorological Society, Boston, 1978) d. 544.

3. For discussions of the operation of field mills see (a) W. W. Mapleson

and W. S. Whitlock, "Apparatus for the accurate and continuous measurement

of the earth's electric field," J. Atmosph. Terr. Phys., Vol. 7, pp. 61-72,

1955 and the references cited therein. The effect of an incident ion

current on a field mill is described in (b) P. J. L. Wildman, "A device

for measuring electric field in the presence of ionisation," J. Atmosph.

Terr. Phys., Vol. 27, pp. 417-423, 1965. The principle of operation of

the vibrating-plate field probes used during this study is found in (c)

R. E. Vosteen, "D.C. Electrostatic Voltmeters and Fieldmeters, " Conf.

Record of 9th Ann. Meeting of IEEE Indust. Appl . Soc., October 1974.

4. 0. J. Tassicker, "Boundary probe for the measurement of current density

and electric field strength - with special reference to ionized gases,"

Proc. IEE, Vol. 121, pp. 213-220, March 1974.

I
-37-

5. M. M. Shahin, "Mass-Spectrometric Studies of Corona Discharge in Air

at Atmospheric Pressures," J. Chem. Phys., Vol . 45, pp. 2600-2605, 1966.

6. M. M. Shahin, "Nature of Charge Carriers in Negative Coronas,"

Appl . Optics, Supple. No. 3 on Electrophotography, pp. 106-110, 1969.

7. J. S. Townsend, Electricity in Gases (Oxford Univ. Press, New York, 1915).

8. H. Albrecht and E. Wagner, "Measurements and Calculations In A Cylindrical

Corona Discharge," 11th International Conference on Phenomena in Ionized

Gases, Prague 1973, p. 192; H. Albrecht, E. Wagner, and W. H. Bloss,

"Berechnung und Messung der Entladung scharakteristi k einer positiven

Korona," Elektrotechnische Zeitschrift, Vol. 94, pp. 599=603, 1973.

© 9. J. D. Cobine, Gaseous Conductors , (New York: Dover Publications, 1958),

p. 258 ff. The cgs units in this reference have been replaced by SI units.

10. E. W. McDaniel and E. A. Mason, The Mobility and Diffusion of Ions in

Gases , (John Wiley & Sons, New York, 1973) pp. 4-5.

11. R. S. Withers, J. R. Melcher, and J. W. Richmann, "Charging, Migration,

and Electrohydrodynamic Transport of Aerosols," J. Electrostatics

Vol. 5, pp. 225-239, 1978.

12. See Ref. 10, pp. 10-12 and Ref. 11.
-38-

13. M. Cabane, P. Krien, G. Madelaine, and J. Bricard, "Mobility

Spectra of Ions Created in Gases Under Atmospheric Pressure," in

Electrical Processes in Atmospheres , Eds. H. Dolezalek and R. Reiter

(Steinkopff, Darmstadt 1977), pp. 30-39.

14. Only an approximate treatment of the problem near the screen can be

made because the charge density p is unknown in this region.

15. J. W. Gewartowski and H. A. Watson, Principles of Electron Tubes

(Van Nostrand, Princeton, NJ, 1965), p. 150 ff.

16. When J=J

s

, the electric field theoretically vanishes in a region plane)

near z=0. Most of the arriving space charge follow field lines that

terminate on the top plate (screen); these field lines must lie above

the region where E=0. Diffusional effects are believed to be adequate

to provide sufficient space charge below z=0 to maintain the saturated

current, J

s [R. S. Withers, "Transport of Charged Aerosols," Sc.D.

dissertation Dept, of Elect. Eng. and Comp. Sci., Massachusetts Institute

of Technology, 1978 (unpublished) p. 132]. Given the values of V« and Vy,

it is difficult to conceive of field lines (Fig. 4) from above the screen

penetrating to a depth greater than the grid spacing before terminating on

a grid wire. This suggests that the region where E vanishes should lie

within ^0.1 cm below z=0.

17. V. A. Mohnen, "Formation, Nature, and Mobility of Ions of Atmospheric

Importance," in Electrical Processes in Atmospheres , Eds. H. Dolezalek

and R. Reiter (Steinkopff, Darmstadt 1977), pp. 1-17. Average values
-39-

of mobility for small air ions generated with corona and various

-4 2 radiation sources reported in this reference range from 1.23 x 10 m /Vs

to 1.40 x 10~ 4 m

2 /Vs for positive ions and 1.70 x 10~ 4

m'VVs to

-4 2 2.0 x 10 m /Vs for negative ions.

18. A number of tests confirmed the existence of the surface charge on

the top plate. The "zero drift" in the field mill could be eliminated

by shielding the probe with a grounded plate, producing space charge

of opposite polarity with the corona wires for a short time interval,

or by applying a voltage (M0 - 20 V) to the top plate with opposite

polarity. The presence of charge on an aluminum surface should

not be unexpected (with hindsight) because the normally present aluminum

oxide surface is a good insulator.

19. Values of K determined when Vy = 803 V and Vy = 1209 V differ from

the value of K when Vy is 1003 V by less than 2.5 percent.

20. We thank Mr. Bruce Williams for providing this explanation and

Mr. Robert Vosteen for additional useful remarks.

21. Both manufacturers of the vibrating-plate field probes recommend

periodic cleaning of the sensing heads.
.
U.S. DEPT. OF COMM. 1. BIBLIOGRAPHIC DATA

SHEET (See instructions) \

PUBLICATION OR 2 REPORT NO.. Performing Organ. Report NoJ 3. Publication Date

4. TITLE AND SUBTITLE

Generation and Measurement of DC Electric Fields with Space Charge.

5. AUTHOR(S)

Martin Misakian

6. PERFORMING ORGANIZATION (If joint or other than NBS, see instructions) 7, Contract/Grant No. NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE S. Type of Report & Period Covered

WASHINGTON, D.C. 20234

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. State, ZIP)

Department of Energy

Office of Electric Energy Systems

12th Street & Pennsylvania Ave. , N.W., Mail Stop 3344

Washington, D.C. 20461

10. SUPPLEMENTARY NOTES

TM

| | Document describes a computer program; SF-185, FIPS Software Summary, is attached.

11.

ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bi bliography or literature su.rvey, mention it here)

Characterization of the electrical environment in the vicinity of

high voltage dc transmission lines requires measurement of a number

of electrical parameters associated with the lines. These parameters

include the electric field strength with significant space charge

contributions. This report describes an experimental effort to

generate known dc electric fields containing controlled amounts of

space charge. An apparatus which has been built for this purpose

is described and two types of field probes currently used for

transmission line field measurements are examined with the apparatus.

Limitations on the operation of one type of probe in the presence

of very large current densities are identified and discussed.

12.

KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons)

Calibration; dc transmission lines; electric field; electric field meters; electric

field strength; electric power transmission; measurements; space charge.

13.

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