A11100 =^4534

PUBLICATIONS

IMBSIR 81-2267

1980 Annual Report: Electric and

Magnetic Field Measurements

R. H. McKnight, F. R. Kotter, M. Misakian, and P. Ortiz

Electrosystems Division

U.S. Department of Commerce

National Bureau of Standards

Washington, DC 20234

February 1981

Issued May 1981

-QC—

10G

. U56

81-2267

1981

c.2

sponsored by:

)ffice of Electric Energy Systems

>epartment of Energy
I

I
ratiohal bursau

OF »TAKDARD8

L1BRART

JUL 2 0 1981

NBSIR 81-2267

K-«. 1980 ANNUAL REPORT: ELECTRIC AND

MAGNETIC FIELD MEASUREMENTS

R. H. McKnight, F. R. Kotter, M. Misakian, and P. Ortiz

Electrosystems Division

U.S. Department of Commerce

National Bureau of Standards

Washington, DC 20234

February 1981

Issued May 1981

Sponsored by:

Office of Electric Energy Systems

Department of Energy

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

NATIONAL BUREAU OF STANDARDS, Ernest Ambler. Director
j ,. ol, ,

'» s JUl

’ ' : - J

‘

. .

'

. !

-

* •

. —
TABLE OF CONTENTS

Page

Summary i

Abstract iii

1. Introduction 1

2. Parallel Plate Apparatus 3

3. Errors Associated with Wilson Plate Measurements 3

A. Introduction 3

B. Approach 4

C. Results 4

D. Discussions and Conclusions 13

4. Off -Ground Field Measurements 13

A. Introduction 13

B. Approach 13

C. Results 14

D. Discussion and Conclusions 18

5. Development of a Facility for Producing Space Charge

for Use in Evaluating Ion Measuring Instruments 19

A. Introduction 19

B. Approach 21

C. Results 24

D. Discussion and Conclusions 33

6. Ion Density Measurements 36

A. Introduction 36

B. Approach and Results 38

Bl. Ion Counters 38

B2. Net Space Charge Measurements 47

C. Discussion and Conclusions 52

7. Discussions and Conclusions 53

8. References 55

Appendix I - Model Calculations of Perturbations to Ambient

Fields Caused by Instrument Support Structure 57
.

'
i

Summary

The NBS program is concerned with developing methods for evaluating and

calibrating instrumentation for use in measuring the electric field and various

ion-related electrical quantities in the vicinity of high-voltage direct

current (HVDC) transmission lines and in apparatus designed to simulate the

transmission line environment.

A parallel plate apparatus designed to produce electric fields in the

presence of space charge has been evaluated and used to determine the response

of two vibrating plate electric field meters and a field mill to electric

fields greater than ^6 kV/m with attendant current densities up to

^3.5 yA/m2

. The original one-dimensional model used to predict the operation

of the system has been modified to take account of field penetration into the

parallel plate region of the apparatus. A field mill, the operation of which

is theoretically predicted to be free of significant errors associated with

incident current, has been used to verify predictions of the modified theory.

The response of the field mill to various field and current density conditions

shows that there is no significant error due to incident current. Both

vibrating plate meters display errors in indicated field which are a function

of the magnitude of the incident current. In this work, both positive and

negative fields were used.

Errors associated with lack of coplanarity of Wilson plate sensors with

the ground plane have been investigated using both ac electric fields and dc

electric fields with space charge in a parallel plate apparatus. The ac

results would be expected to produce enhancement factors which would be the
n

same as those for the dc electric fields with space charge if the ions which

make up the incident current follow the electric field lines. Substantial

errors were observed when the Wilson plate sensors were operated above the

ground plane. The magnitude of the errors depended on the sensor geometry and

distance above the ground plane with the largest errors being associated with

unguarded sensors. Agreement between ac and dc results was good for conditions

like those expected under a HVDC transmission line.

Model calculations to estimate errors associated with self-charge of offground field measuring instruments were completed as were estimates of errors

contributed by support structures. For symmetrical systems located 1 - 2 m

from the ground plane, errors due to self-charge appear to be small.

A low-speed air-flow facility has been constructed to produce a volume

containing space charge which can be used as a source of ions for evaluating

and comparing instruments designed to measure various ion related properties.

Net space charge densities in the systems can be made temporally smooth and

spatially uniform over a given plane in the test volume. Studies have been

completed showing the dependence on the net space charge density of air flow,

source configuration, and corona-source discharge voltage. In these studies,

net space charge density was determined by using a high efficiency particulate

air (HEPA) filter, sometimes called an absolute filter.

Studies have been made of small-ion losses at the inlet structure of

parallel plate ion counters. Two systems were evaluated; one had substantial

losses. An assembly in which the geometry was variable was constructed to be

used in studies to determine the loss mechanism involved, which appears to be

due to fringing fields.
Abstract

The NBS program is concerned with developing methods for evaluating and

calibrating instrumentation for use in measuring the electric field and various

ion-related electrical quantities in the vicinity of high-voltage direct

current (HVDC) transmission lines and in apparatus designed to simulate the

transmission line environment.

A parallel plate apparatus designed to produce electric fields in the

presence of space charge has been evaluated and used to determine the response

of two vibrating plate electric field meters and a field mill to electric

fields greater than ^6 kV/m with attendant ion current densities up to

<3.5 yA/m2

. While the field mill appears to be free of significant errors

associated with incident ion current, both vibrating plate meters display

errors associated with the presence of sufficiently large ion current incident

on the sensing element.

Errors associated with lack of coplanarity of Wilson plate sensors with

the ground plane have been investigated using both ac electric fields and dc

electric fields with space charge in a parallel plate apparatus. Agreement

between ac and dc measurements was good for conditions like those expected

under a HVDC transmission line.

A low-speed air-flow facility has been constructed to produce a volume

containing space charge which can be used as a source of ions for evaluating

and comparing instruments designed to measure various ion-related properties.

Studies were made of losses at the inlet structure of two commercial parallelplate ion counters.

Model calculations to estimate errors associated with self-charge of offground field measuring instruments indicate errors are small for appropriate

geometries
, : ' l|/
1. Introduction

The objectives of the investigation are to develop methods for evaluation

and calibration of instrumentation which is used in characterizing the

electrical environment in the vicinity of high voltage direct current (HVDC)

transmission lines and in apparatus designed to simulate the transmission line

environment. The motivation for the effort is concern that the electrical

environment in the vicinity of high voltage transmission lines, both ac and dc,

may prove hazardous to living organisms. Suitable instrumentation exists for

measurements near ac lines, and there are recommended procedures for making

such measurements [1]. In addition to electric fields near dc lines,

significant ion concentrations are produced, since the lines are continuously

in corona discharge. Electrical parameters of interest near HVDC lines include

the electric field, vertical current density, positive and negative charge

densities, and net space charge. Related parameters, more difficult to

determine, are ion mobilities and species. The production and dispersion of

charged aerosols may also be of importance. Measurements of electric field and

ion densities are required at or near ground level.

Measurement techniques presently available for determination of these

electrical quantities were historically developed to investigate electrical

parameters of the atmosphere [2]. The use of these techniques under the

conditions existing near HVDC transmission lines requires considerable

extension beyond original design considerations. The performance of these

devices must be systematically evaluated over the full measurement range

expected in the field and, where possible, calibrated using facilities which

produce experimentally known or calculable fields and space charge.
2

By evaluating the performance of various instruments under different

electrical conditions, estimates can be made of errors associated with

corresponding measurements. In this way, the optimum operation of the

instrument in the laboratory can be determined. Use of the instrument in the

field will result in additional uncertainties because of varying climatic

conditions and the requirement for long term operation. These types of

uncertainties are not addressed in the present study.

The approach to the general measurement problem has been to consider

separately the measurement requi rements for each of the individual electrical

parameters. As a result, the effort described in this report was divided into

a number of individual subtasks and is reported as such.

Much of our effort has been directed toward the development of facilities

which can be used to simulate certain aspects of the transmission line

environment in the laboratory. While the primary function of these facilities

is to allow the evaluation of instruments and measurement techniques, their

ultimate usefulness in calibration schemes is also of interest. Two facilities

have been designed and constructed. One, which produces a dc field with

accompanying space charge, has been extensively investigated and used to

evaluate the operation of two different types of electric field meters. A

second system, designed to produce a region of spatially uniform and temporally

smooth space charge, is in a more rudimentary state. Studies done with these

facilities and other accomplishments during this year are described in the

following sections.
3

2. Parallel Plate Apparatus

The development of a parallel plate apparatus for generation of dc fields

with space charge was completed and used to examine the performance of two

types of electric field probes employed for measurements of electric fields

near high voltage dc transmission lines. Use of field probes to determine the

space charge mobility provided information on the performance of the

instrumentation as well as operation of the apparatus. These data indicated

that a field mill with phase-sensitive signal detection can function well in

the presence of high current densities, but, under the same conditions, field

probes with a vibrating-plate design would give erroneous results.

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

strength, with controllable amounts of space charge, are produced. The data

showed that, for a given field strength, the performance of the vibrating-plate

probes improved as the current density was reduced. Only examples where the

space charge contribution to the total electric field strength is significant

were considered. A separate manuscript describing the apparatus and results of

the study was prepared and forwarded to DoE in 1980 [3].

3. Errors Associated with Wilson Plate Measurements

A. Introduction

Measurements of vertical currents to ground near a HVDC transmission line

are normally made using a Wilson plate, which was invented for use in

atmospheric electricity research. In the simplest implementation, the Wilson

plate is a conducting sensor, located in or near the ground plane, which is
4

connected to ground through a current measuring device. Frequently a guard

ring structure surrounds the sensing element. If the Wilson plate is not

coplanar with the ground plane, errors in indicated current may arise as a

result of the enhancement of the field at the surface of the sensing element.

B. Approach

In an effort to determine errors from lack of coplanarity, initial studies

were made with ac electric fields using the parallel plate apparatus briefly

discussed in Section 2. These measurements determined the field enhancement

factors associated with a series of small square Wilson plate assemblies.

For the situation where there are ions and a nearly uniform dc field,

these enhancement factors would be expected to apply if the ions are

precipitated to ground along field lines. Some preliminary measurements using

the parallel plate apparatus to generate an electric field with space charge

were made which confirm this thesis.

C. Results

Eight small square "Wilson plates" were constructed from 0.157 cm thick

copper-clad fiber glass sheet. On six of them a central section of the copper

was isolated from an outer ring by a narrow slot (about 0.5 mm wide) milled

through the copper as indicated in Figure 1. The nominal dimensions were as

tabulated in the figure. Metal spacers, 7.5 x 7.5 x 0.160 cm, were used

to elevate the plate above the ground plane. The "in-ground-plane" value was

obtained by plotting the current readings as a function of elevation above the

ground plane and extrapolating to zero elevation. Using 4 kV, 60-Hz excitation

of the parallel -plate structure with a plate separation of approximately
Nominal

Dimensions

5

|ID O IOq LDOID

I 10 csi no c\i oo

co in in irj if)

go go go go

CO O

V V V

00 O Q

< CO >

1 00

03

COo

00

CO X o CO

o

o

+-*

o

03

3

CO "to

E

Figure

1.

Dimensions

of

"Wilson

plates"

used

in

the

present

study.

The

material

thickness

is

0.157

cm.
6

0.5 meter, several series of data were taken with each of the plates listed in

Figure 1. Figure 2 is representative of the data obtained with one set (A-D)

of plates. The maximum uncertainty in these results is less than five percent,

due in part to the fact that with the separation used for the parallel plate

facility, the perturbing effects of nearby objects are not negligible.

However, relative values are considered correct within a few tenths of one

percent.

A theoretical estimate of the error to be expected from a Wilson plate not

in the ground plane can be obtained from a consideration of the field

perturbation produced by an oblate spheroidal boss on the surface of a plane on

which a uniform electric field is incident. The enhancement of the field at

the center of the surface of such a boss is tabulated in [4] as a function of

the ellipsoidal parameters. Figure 3 is a plot of the values given in [4], and

Figure 4 provides a comparison of the experimental results obtained using the

small Wilson plates with calculations for two rather arbitrarily chosen

spheroids used as approximations to the actual geometry. The geometry of the

boss relative to the Wilson plate is as indicated in the figure. These results

are considered of value in that they provide confirmation that the experimental

results obtained are in agreement with those which can be expected from

theoretical considerations.

The value of a guard ring in reducing the error resulting from a departure

from coplanarity is indicated in Figure 2. The results obtained with all six

plates are shown in normalized form in Figure 5, which might be used in

designing a Wilson plate as follows. The value of a/d is determined by a

decision as to the minimum elevation above the ground plane and the maximum

lateral plate dimensions which are practical. The guard ring width required to
7

Figure 2 . Percentage current density increase for plates A-D

l i g • 1). Straight lines have been drawn throuqh data points to indicate related data.
8

Figure

3.

Field

enhancement

factor

E/E0

at

the

top

of

an

oblate

spheroidal

boss

ona

plane

surface

with

an

incident

uni

formfi

eld

E«.
9

to ai c 4-> o CO r— co O to

4-> 3 a»

co <L>

x c 1

ai 3 3 •>- 3 x: JZ X r— O 4-> 3 +-> <u 

4J oj

x

CO 3 <4-

C CO 3 4-> <J >—i O •r— f— CO O 3 O 1

to “O OWE

<o • ai <u r- 44 </> X «

• 3 IO 3 • o CO r— 03 U I— to E co O CO * 4-> • > •r— ai > E 3

-X CDO JX o -p— +> •!— o c 4-4 O O

•i— <4- 3 •I— 3 O CL 5

44

4-> to

tO 4-> r—

4-4 ( to <v x fO C S- II CO

a> to 3 a> o 4-4 CO to t(_ ro 3 

a* 44 co to -a s. w s. E > to 03 CL +-> O •i— o n CO ai <4- 3

r— jQ 3 3 44 CO ca II to 9 Cl

+-> r— CO <0

X

C <o

A - 3 3 X 44

<u

xx <3 •(- 3 £ •r— 44 1— 1— CO 44

•r- o 4->

X CO £1 3 3 3 c X 4-> e 4-> <U at <u fO 41 3 U

Q-x: to x: oj x: X a <u cm to £ LC CD

4) to s- \ CO *|— • 3

Q. COx tco

O

<4- a; 44 3 O +-> to II 44 O- II x:

cO 3 £ X 4-4 3 i

o 8 1— UJ IO o o •r— 3

to 3 4-> 3 3

•r— CL CO • • • • o CO 3 i

3 44 tO 4- 3

<0 CO 3 <v 3 4)

X

CL

O to 3 3 0 E 3 r— o CDr— 44 o o CO x: •i— CO tO 3 o M— U o 4- > CO <o

4>33

cn
10

m

co

CM

CO

mmi iN30M3d

Figure

5.

Errors

determined

by

present

measurements

as

a

function

of

guard

ring

width

and

elevation

above

ground

plane.
11

reduce the error resulting from the non-zero value of d to a value considered

acceptable can then be estimated by interpolation between the curves given.

It should be noted that the results obtained to date are for the

capacitive current in an ion-free ac system. Except in the case of the plate

with no guard ring (see below) they are expected to apply to the ion current in

a dc system if ion motion occurs along the field lines, an assumption expected

to be valid in the absence of winds. This is equivalent to assuming that the

current to the sensing element will be increased in proportion to the

geometrical enhancement of the field.

The effect of fringing at the edge of the unguarded Wilson plate will be

different for the ac and dc cases as can be seen from Figure 6. Field lines

which terminate on the underside of the sensing plate will contribute to the

induced current (the ac case) but ions which traverse these field lines (the dc

case) are prevented from reaching the sensing plate by the insulating support.

If the resistivity of the insulation is sufficiently high, presumably a charge

will accumulate on the surface of the insulation and distort the field. If the

resistivity is not so high as to permit significant charge accumulation, the

ion current associated with this fringing field will divide between the sensing

plate and the ground plane. In either case the results for the unguarded plate

with ac (the c/d = 0 curve in Figure 5) cannot be expected to apply when the

plate is used for measurement of ion current.

While only preliminary results of the dc experiment are available, they

indicate significantly better agreement with corresponding ac measurements when

the sensing plate is guarded than when it is not. The c/d = 0 dc values for

I
Figure 6 

Schematic of flux lines terminating on

a sensor plate

located above the ground plane.
13

enhancement fall below the c/d = 0 curve of Figure 5 by about 10 percent for

values of a/d in the neighborhood of 12.

D. Discussions and Conclusions

Field enhancement factors for eight different Wilson plates raised above

the ground plane have been determined using ac techniques. These enhancement

factors, when extended to vertical current density measurements, indicate that

substantial errors may result if guard rings are not utilized and if the plates

are operated above the ground plane. A limited number of preliminary

measurements made using a parallel plate apparatus to generate a dc field

accompanied by space charge show reasonable agreement with the ac results for

all but the unguarded Wilson plates.

4. Off-Ground Field Measurements

A. Introduction

Measurements of the electric field at the surface of the ground are

accomplished with rotating vane (field-mill-type) or vibrating plate field

meters mounted with their sensing surfaces in or near, and parallel to, the

ground plane. Measurements at significant distances above the ground plane are

complicated by field distortions introduced by the field meter itself, by the

structure used to support it, and by the self-charge which will exist on the

meter in the event its potential is not precisely the same as the ambient space

potential

B. Approach

The field enhancement resulting from the introduction of the conducting

body (the field meter) into the field may be determined by full scale or model
14

experiments In the laboratory using pa ral lei -plate "uniform-field" calibration

structure.

Field meters which are claimed to be free from self-charge errors [5] have

been developed for use in atmospheric electricity research. Theoretical

analysis of the performance of these meters [5] confirms the validity of those

claims; however, only when the instrument is in a "free space" environment,

i.e., very remote from other conducting or dielectric bodies. The calculations

in the following section show how far from a ground plane such a device must be

to insure that the error from this cause will not exceed a specified value.

C. Results

Consider a sphere, divided into two hemispheres insulated from each other,

rotating about a horizontal axis passing through the center of the sphere in

the insulating plane. If an electric field exists normal to the axis of

rotation, an ammeter which joins the hemispheres will indicate an alternating

current resulting from flow of the charges induced on the hemispheres by the

f i el d.

The signal current, which is a measure of the field, results from the

charge separation between the two hemispheres produced by the field E 0

. That

charge difference, obtained by integrating the induced surface charge density

over the two hemispheres and subtracting (Ref. 4, p. 226), is

q lower " q upper

“ 67TE 0ea2. (1)

The sphere itself may be charged. If the sphere is in free space, this

self charge will be uniformly distributed over the sphere and will produce no
15

error signal. However, If there are other objects present which disturb the

uniformity of the charge distribution, the net charge may introduce an error.

Consider the case of a grounded plane near the sphere as in Figure 7. The

problem of the charge distribution on a conducting sphere in the vicinity of a

conducting plane is treated by Weber [6]. An approximate solution, which

appears valid to better than 1 percent if the radius of the sphere is less than

10 times the distance of the sphere center from the plane, gives for the

surface charge density distribution (see Figure 7):

2

% — [1 - 3(t^-) cos 6] . 4iTa‘

:

( 2 )

Integration of this equation gives for the division of the total charge

between the hemispheres

q upper

=

2 ^ "I

^ ^

q lower I ^ +

2

^ ^ and (3)

q' _ q

* = 3Q (_a_\

Slower ^upper 2 '2h'

This charge difference constitutes an error signal as the sphere is caused to
16

</> i~ «3 o

S- CD

s- c I a> to <4- 3 o

4-> = C o a>

4-> <D

ra t. 3 tO O <o r- <u

«5 E U

"O

a> r-

.c: <u

+-> -r- O T3

**- c3

T3

O

0) S- CO CT> 3 I

<L)O

©o c E fO

a> sz -c +j

+J -rtt-o -a

a> >> +-> S- fO +J -i- a> o E o O «/l at to cu <a

r^.

<L) t-3

CD

Lispherical

field

meter.
17

rotate about a horizontal axis and the current between hemispheres used as a

measure of the electric field normal to the axis of rotation.

For the case of a grounded sphere a distance h above a ground plane which

bounds a uniform field E 0 , the charge Q is given by Q

= CV where C is the

capacitance between the sphere and the plane and V is the space potential at

the location of the sphere. With the ratio of sphere radius to distance from

the ground plane 1:10, the self-capacitance of the sphere is equal to the

free-space value, 4-rrea, to within 5 percent [7]. Then

The proportional error for this case (obtained by dividing (1) by (5)) is then

Q

= 4-rrea E 0

h (4)

and the error signal is

(5)

2 h

)/(q] - q ower ^upper ( 6 )
18

With a/h % 1/10, the error is approximately 2.5 percent. It may be reduced by

decreasing the ratio, a/h, or by biasing the sphere near the potential of the

space adjacent to it.

On the assumption that a field meter of this type could be suspended on a

cord or wire between two poles and rotated by means of an internal battery

driven motor, with data being recorded on a self-contained battery driven unit,

the principal field distortion resulting from the support structure would be

caused by the poles. The question as to how far apart the poles would have to

be to reduce the distortion at the location of the meter to an acceptable level

has also been explored theoretically (see Appendix I). It has been concluded

that pole separations equal to or greater than four times the pole heights will

be sufficient to reduce the error from this cause to less than 1 percent.

D. Discussion and Conclusions

Model calculations of the errors associated with off-ground electric field

measurements made by a rotating, split-sphere field meter indicate negligible

error due to self charging effects. An analysis of errors due to attendant

support structures for such a meter also show only a small perturbation of the

field at the measuring position. While such an instrument with either

spherical or cylindrical geometry would appear to be ideally suited for

off-ground field measurements, the errors introduced in the measurement due to

ion currents to the device if it were electrically grounded are unknown. A

more detailed analysis of the rotating field mill is needed to determine

whether its operation either grounded or biased relative to ground is

feasible.
19

5. Development of a Facility for Producing Space Charge for Use in Evaluating

Ion Measuring Instruments.

A. Introduction

Some of the small ions continually produced by a high voltage dc

transmission line are precipitated along field lines to ground near the

transmission line. Particulates and aerosols which may be charged by passing

near the line have much smaller electrical mobilities than do the small ions

and may be widely dispersed by ambient winds. The net space charge at a point

near a high voltage dc line may be highly variable, presenting a difficult

measurement problem. In addition to this, the presence of the electric field

produced by the line itself means that the measurements of ion related

quantities made above ground level may be influenced.

Clearly, it would be difficult to evaluate basic instrument operation

under a transmission line. A less extensive and more controllable system

suitable for laboratory investigations is required.

Investigations of instruments designed to measure ion-related properties

require a source of space charge which is well characterized, stable,

reproducible and controllable. This space charge should be confined to a test

volume within which measurements may be made or from which an air sample

containing ions may be drawn.

The design philosophy for our effort to develop a standard ion source is

based on the requirements listed above. A brief historical description will

provide needed background for the present report. Two useful means of

producing ionization are the use of corona discharges and radioactive sources.

For health physics reasons, radioactive sources which are easily handled and
20

shielded are used, i.e., alpha, beta, or low energy x-ray sources. Each of

these sources produces intense ionization in the region of the source, where

positive and negative charges are produced in equal abundance. If ions of only

one polarity are required, the source may be biased producing an electric field

the direction of which is chosen to inhibit the motion of ions of the unwanted

polarity away from the source.

Corona sources differ from radioactive sources in that the source is

intrinsically biased so that in the volume surrounding the source, the space

charge is predominately of one sign. In addition, these ions are transported

away from the source electrode by the electric fields that exist in the space

surrounding the source. The number of ions produced in the corona discharge

can be controlled to some extent by varying the electrical potential of the

source electrode. Either source of ionization may be used to produce ion

densities in volumes of a few cubic meters comparable to those found near high

voltage direct current transmission lines.

The second problem to be solved in developing a standard ion source is

that of removing the ions produced by corona discharges or radioactive sources

from the region of the sources and dispersing them in the test volume. Having

accomplished this, the performance of instruments such as ion counters, Gerdien

tubes or net space charge measurement devices may be investigated by either

immersing the instruments in the region containing space charge or aspirating

ion-laden air from the test volume. The test region, ideally, would have

several characteristics - uniform ion density, both spatially and temporally;

minimal external electric field penetration; good stability and day-to-day
21

reproducibility; variable ion density; and a well characterized ion

composition.

The design of the space charge facility should be such to keep the

perturbation produced by the measuring instrument to a minimum. In the air

flow facility to be described, the volumetric flow rate is much larger than the

flow rate through a typical aspiration instrument.

B. Approach

Initial efforts to produce a standard ion source involved the use of small

fans to carry ions away from the region of ionization near an alpha particle or

corona discharge source into a closed test volume. Aspiration instruments such

as absolute filters or Gerdien conductivity tubes extracted air from this test

volume and the exhaust from these instruments was returned to the test volume

so as to maintain a closed system. By using several mixing fans, it was felt

that through diffusion and air motion within the test volume, a more or less

uniform mixture of ions would be achieved. What was observed was an ion

distribution which was temporally very uneven. The system could be made fairly

reproducible and to some extent spatially uniform but various attempts to

remove the temporal fluctuations in the observed ion density were unsuccessful.

Several experiments suggested that these fluctuations were related to the lack

of smoothness of the air stream carrying ions away from the region of

ionization. Because of these results, a different approach was adopted. We

decided to concentrate on developing a facility to produce a uniform air stream

into which a source of ionization could be placed. The ions could be carried

downstream from the source and at some point the ion-air mixture would

constitute a "test volume".
22

The approach taken was to borrow from the design principles applied to

I wind tunnel fabrication where low turbulence and uniform air flow are

mandatory. A low speed air flow facility was assembled and is illustrated

schematically in Fig. 8. The facility is of the open flow type with a fan

pulling air through the structure and the return air path through the space

surrounding the facility. An inlet structure conditions the air stream by

reducing both swirl and turbulence to a low level. The use of flow

straighteners and a series of screens to reduce turbulence are standard

techniques in wind tunnel design. This first system was not optimized but was

intended to serve as a developmental facility to aid in the design of a future

system.

An ionization source (in this case, a corona discharge) was located

downstream from the turbulence screens. At this point a fairly uniform, low

turbulence air stream flows by the wires thus transporting ions into the test

section.

Two types of measurements are necessary in investigations of the

suitability of this facility for use as a standard ion source. The first

involves measurements related to the air stream of such things as the velocity

profile and the degree of turbulence. The second is of the uniformity of the

ion density produced in the test volume. A hot film anemometer was used for

the air flow measurements. For the ion density measurements, an absolute

filter assembly was used to measure the ion density at a selected location in

the test volume. A sampling tube connected to the inlet of the filter assembly

was scanned across the test volume at a selected height above the floor of the

flow facility. The current from the filter is proportional to the ion density
Inlet

Flow

Straightener

23

''E

todE

in

<N

Figure

8.

Low

speed

air

flow

facility.
24

at a given location of the probe. The corona discharge source was designed so

that the ground plane and wire configurations could be varied. By studying the

ion distributions produced by different configurations, the ionization source

design can be optimized.

C. Results

Because of the developmental nature and the less than ideal design of the

first air flow facility, air flow characteristics far from optimum were

expected. Flow characteristics obtained using a hot film anemometer confirmed

this expectation. The average speed was uniform to ±3 percent over the central

two-thirds of the structure. Turbulence levels were substantial over

approximately the outer half of the air stream. Measurements made at different

locations in the flow facility indicated the turbulence was generated by screen

and ion source support structures protruding into the inlet air stream. Also,

no attempt was made to design a satisfactory transition section. Since design

and construction of a new, more substantial system was planned in the future,

no attempts were made to optimize the existing structure.

Initial source development was concentrated on the use of a corona

discharge to produce ions. The space charge produced by the corona-discharge

ion sources depends primarily on (i) corona voltage, (ii) speed of the air

stream flowing by the source, and (ill) source configuration. For the coronadischarge ion source experiments, simple one- and three-wire configurations

were used with ground planes represented by arrays of five parallel wires.

These configurations as well as a seven-wire source using a screen ground plane

are shown in Figure 9. The ground planes for the one and three wire sources
25

Figure

X X X X X XX

X

(b)

Air flow

xxx

• ••• • •••••

Id)

X X X

*

1 m

(Top view)

9 . Corona ion source configurations, drawn to scale. Not shown are support frames, insulators, etc., x - corona wires, ---- - grounded screens; - ground wires The corona wires are 64 in diameter.
26

are much more transparent than source 9a, and represent extremes of electric

field orientation relative to air flow.

The screen material was al uminum window screen while the individual ground

wires were 254~ym diameter copper wires. The corona wires were 64-ym diameter

stainless steel. Scans across the test volume using the absolute filter at a

fixed distance above the floor of the enclosure for source configuration [a]

(Fig. 9) with 7 wires are shown in Fig. 10. Distances above the floor and

across the test volume are indicated. The curves, which are proportional to

the ion density at a given point in the test volume, are all plotted to the

same scale and the error bars represent a ±5 percent deviation from the

reference value. The fluctuations indicated are representative of the temporal

smoothness of the ion density. The fall off in ion density near the right hand

side of the volume is an artifact of the scanning technique. A comparison of

the ion distribution produced by source configuration 9a with 3 and 7 wires is

shown in Fig. 11. The traces shown are for scans across the test volume at 3

different distances above the floor of the flow facility and are plotted to the

same scale as in Fig. 10. There is substantial improvement in the uniformity

of the ion density for the greater number of source wires.

Despite the turbulence and lack of uniformity observed in the air flow,

the ion density is remarkably uniform in the plane scanned. A proposed

explanation for this observation is that the uniformity is due to the dispersal

and mixing of the space charge by internal Couloumb forces during transit from

the source region to the region of observation. The turbulence itself could be

expected to be responsible for some mixing.
27

(s^ufi |9d) A^jsuaa uo|

Figure

10.

Isometric

presentation

of

measurements

of

the

ion

density

in

the

test

volume

determined

by

using

an

absolute

filter.

Scans

were

made

at

different

distances

above

the

floor

of

the

test

volume

as

indicated.

Corona

source

voltage

was

10

kV

and

the

air

speed

in

the

system

was

1.1

m/s.
28

1.0 0.60

w l.o

a.- cc

</) c

CD

o

1.0

7 Wires

0) E

2

0.39 -S

</> 0)

o

o

E

o

0

0.19 «

<o

"35 SB

o

0.70

Distance from Edge of Test Volume (m)

Figure 11 . Comparison of ion densities produced by two different corona

sources with 3 and 7 wires respectively. Scans across the test

volume were made at selected distances above the floor of the

test volume. For each set of measurements the corona voltage

was 10 kV and the air speed 1.1 m/s.
29

For sources b-e, the space charge density, produced as a function of

corona voltage and air speed, was determined at the midplane of a given

location in the test volume using the absolute filter probe. As expected, the

spatial uniformity varied considerably from source to source and even more

strongly with increasing corona voltage. Rather than present all of the space

charge density profiles obtained, some representative data for source

configurations (b) and (d) are summarized in Figure 12. The space charge

density shown in Figure 12 represents an average over the middle one third of

the test volume. Similar results were obtained for sources (c) and (e),

although for these particular configurations the space charge density profiles

were very nonuniform at higher voltages. This nonuniformity, seen above 20 kV,

may be associated with observed, large-amplitude mechanical oscillations of the

source wires and with the onset of negative corona from the ground wires. The

space charge produced in these experiments ranged from 3-10 x 10_ 8 c/nr*

(corresponding to a singly charged ion density of 2-6 x 10*1 ions/m^),

which is comparable to that found near the ground in the vicinity of an HVDC

transmission line.

While there appear to be no technical barriers associated with producing

large values of space charge density, the problem of reducing the space charge

below the minimum generated at corona onset has not been solved. Although the

measured space charge density is a function of air flow, it is desirable to

develop a system in which this is an independent variable. Therefore, as

described below, both electrical and mechanical techniques have been used to

control the space charge.
NET

SPACE

CHARGE

DENSITY,

(x

10

_/

C/m

30

Figure 12. Space charge density produced by 1 wire (source (b), fig. 9)

and 3 wire (source (d), fig. 9) source configurations. Air

speeds shown are at the source. Errors associated with space charge measurements are estimated to be ±10%.
31

Initially, a number of grounded screens (ordinary al uminum window screen

mesh) were placed downstream from the ion source. This resulted in an

attenuation of approximately 6-8 percent per screen. Since control over orders

of magnitude is required, an electrical filter has been constructed. The

filter consists of a 3-screen sandwich, in which the center screen can be

energized and the outer screens grounded. The attenuation curve obtained for

this filter is shown in Figure 13. As previously, the reported space charge

density is an average over the central region of the test volume normalized to

the initial value. These measurements were made using source (a) (Figure 9)

operated at 10 kV. There is an initial rapid drop in ion density, but above

300 volts, there is little attenuation with increasing voltage. This is not

understood, but is not inconsistent with the hypothesis that a fraction of the

space charge is due to charged aerosols or particulates, the motion of which

would be dominated by aerodynamic, not electrical, forces for the present

conditions.

These charged particles may result from the circulation of room air into

the system with subsequent charging of particulates in the corona region, or

from charging of particulates in the laboratory. Since the air flow facility

is an open return system, this is unavoidable. In a future system, absolute

filters will be used at the inlet to insure the air entering the system will be

clean and free of charge.

The previous discussion has focused on corona discharge ion sources. In

our initial work, however, a-particle sources were used to produce ionization.

Radioactive sources have been used by others in earlier ion effects research

and their employment as sources of space charge in exposure chambers for
32

V (-VOLTS)

Figure 13. Attenuation of space charge density by an electrical

filter. Screen spacing is 0.025 m. The f i 1 ter-to-source

spacing was appoximately 0.15 m.
33

biological experiments has been recently suggested, since, in contrast to a

corona source, there is no ozone production. In an effort to provide some

comparison between space charge produced by a-particle and corona discharge ion

sources, a limited number of measurements were made using a-particle sources.

In these measurements, five a-particle sources were equally spaced along a

vertical wire located at the position of the corona wire in source (b) of

Figure 9. The wire was biased to a potential of +1 kV and space charge density

measurements made as a function of source location and air flow using the

absolute filter. A comparison between the space charge density produced by the

a- sources and a single-wire corona source is indicated in Figure 14. The

differences in the dispersal of ions is striking. In other measurements, using

more sources with different source-ground plane configurations, very nonuniform

distributions were consistently observed.

Further investigations using radioactive sources and the general question

of the distribution of ions in the flow facility will be deferred until a new

air flow system is constructed.

D. Discussions and Conclusions

Much of the work presented above is considered exploratory, since a

cursory literature examination revealed little previous work which could be

related to the task of producing a volume of space charge with characteristics

suitable for use in evaluating ion measuring instruments. The broad dispersal

of ions from the various sources studied was not expected. It was found that a

single-wire corona source is almost as effective at filling the flow system

with charge as is a seven-wire source. The amount of space charge produced is

not strongly dependent on total corona current. The speed of the air flowing
Figure 14. Space charge density produced by an a-particle source

(described in the text) maintained at +1 kV bias and by

corona source (b) (fig. 9) at 10 kV . Air flow was 0.56 m/s

for both measurements. The space charge produced by the

corona source is divided by 3 for presentation. The

horizontal axis is the distance from the edge of the test

volume.
35

across the source region most significantly influences the charge density.

More "open" ground planes produce higher ion densities, but care must be taken

to insure there is no corona discharge from the ground plane. Based on the

results of experience with the developmental flow system, a new flow system has

been designed and is being constructed. This new system, which will be

described in future communications, incorporates a number of improvements

including a more substantial mode of construction, a continuously variable

speed fan, a new flow-straightener section with absolute filters, a larger area

ratio between the flow-conditioning section and test volume, turbulence screens

with frames which do not protrude into the air stream and a new transition

section design. Some of these changes will substantially improve the quality

of the air flow while others will make the facility more suitable for use in

instrument comparison and calibration.

It has been shown that this approach can produce a volume containing a

spatially uniform and temporally smooth space charge, with maximum ion

densities equal to or greater than those found under a dc transmission line.

For purposes of instrument evaluation, this space charge is made up essentially

of ions of one sign, so that the net space charge density and homopolar charge

densities are the same.

A number of important questions have been left unanswered and will be

addressed in future work. These include, among others, interactions of the

measuring instrument with the space charge system, schemes for calibration of

instruments, mobility spectrum of the ions making up the space charge and

control of the ion density.
36

6. Ion Density Measurements

A. Introduction

The continual production of ions by the corona discharge associated with a

high voltage dc transmission line results in the presence of space charge which

modifies the nominal electric field near the line and causes a vertical current

to ground in the vicinity of the line. These ion-related effects are discussed

in other sections of this report. Other ion related electrical quantities

include the homopolar charge density, the net space charge (which is the

algebraic sum of the positive and negative homopolar charge densities), the

conductivity, and the ion mobility spectrum. Measurements of these quantities

have been of interest to the atmospheric electricity community for many decades

and various instruments and measurement techniques are described in the

literature [2].

However, in the absence of severe thunderstorms, the electrical

environment encountered in atmospheric electricity research is much less

hostile than that encountered near a high voltage dc transmission line. As a

result, demands are placed on instruments which far exceed those for which they

were originally designed. This requires that the operation of the instruments

under conditions like those near a line must be characterized. In addition,

there is concern about absolute calibration of instruments and assessment of

errors associated with various measurement techniques.

Emphasis in the effort described here has been placed on measurements of

space charge density and homopolar charge density. Knowledge of conductivity

provides a useful correlation between other measurements, but no information
37

about quantities of direct interest. Mobility measurements are of concern, but

have been deferred to the future.

The measurement of the homopolar charge density in air at atmospheric

pressure has traditionally been done using instruments called ion counters.

These aspiration-type devices do not actually count ions, but measure charge

per unit volume.

Ion counting involves the use of instruments which, in the simplest form,

continuously draw ion-laden air from the atmosphere. The ions in the air are

subjected to electrical forces in the ion counters which cause them to

precipitate out on collecting electrodes. A measurement of the ion current to

these electrodes, the air flow through the instrument and certain geometrical

characteristics of the instrument allow a calculation of the homopolar charge

per unit volume of the air being sampled. By measuring both positive and

negative charge densities, an estimate of the net space charge can be obtained

by subtraction. If the charge densities are comparable, this subtraction can

lead to a large uncertainty because of limited instrumental resolution. A

knowledge of the mobility spectrum is also required for complete evaluation of

ion counting instruments, since not all ions with mobilities below the critical

mobility for a given ion counter will be detected.

Measurements of net space charge have been made for many decades and

earlier efforts have been summarized in the literature [8]. Two methods which

have been used involve (a) the Faraday cage and (b) the "absolute" or high

efficiency particulate air (HEPA) filter. For this application, the Faraday

cage is an enclosure made of a metallic mesh immersed in a space containing

ions. Assuming the ion density is uniform and the cage is of simple geometry.
38

a solution of Poisson's equation for the appropriate geometry yields an

expression for the potential at any point inside the cage. Measurement of this

potential at one point leads to a value for net space charge.

The absolute filter is an aspiration device in which an air sample is

drawn through the filter, which is electrically isolated from ground. The HEPA

filter has a very high efficiency (> 99.7%) for removing particles of diameters

0.3 micrometer and larger from the air stream. If these particles carry

charge, this charge will be deposited on the filter and by measuring the

current to ground, and the air flow through the filter, the net charge per unit

volume may be calculated. At first glance, it would appear that the HEPA

filter would not be useful for small ions which have diameters substantially

less than 0.1 micrometer. However, previous investigators have shown some

evidence that a substantial fraction of small ions lose charge in passing

through the filter [9].

We have begun to examine systematically both ion counters and net space

charge measurement techniques to identify sources of error, to evaluate their

usefulness in determining the electrical environment around a dc transmission

line and to ascertain if suitable means for calibrating ion measuring

instruments can be developed.

B. Approach and Results

Bl. Ion Counters

One type of ion counter, which uses a parallel plate configuration, is

indicated schematically in Fig. 15. A series of parallel plates, alternately

connected, is placed in an enclosure. Air containing ions is drawn through the

assembly and, with one set of plates energized as shown, ions are precipitated
39

TO BLOWER AIR FLOW

i

POLARIZING POTENTIAL

(a)

&

(b)

Figure 15. (a) Schematic of a parallel plate ion counter.

(b) Trajectory of an ion with critical mobility K c

.
40

onto the collector plates under the action of the electric field. By

determining the volumetric air flow rate $ and the current to the collector

plates, I, the charge per unit volume p may be calculated as

P = I/$> . (7)

If the ions are assumed to be singly charged, then an expression for the number

density is

N = §

(8)

where e is the electron charge (1.6 x 10"19#C). Not all ions entering the

counter will be collected. Consider the trajectory indicated in

Fig. 15(b) for an ion which enters at the top of the interplaner space and

impinges on the collector plate just at the exit of the counter. For a given

geometry, polarizing potential, and volumetric air flow rate, an ion following

this trajectory will have what is called the "critical mobility" Kc

. All

ions which have mobilities greater than Kc will be collected. Some fraction

of those ions with mobility less than Kc will be collected as well, but the

concept of a critical mobility is useful to describe the mobility range of ions

collected.

In an extensive discussion of ion counter technology, Tammet [10]

summarizes early research on ion counters. It can be shown that the critical

mobility for a cyl indrical ly symmetric ion counter is given by

( 9 )
41

where $ is the volumetric air flow rate, C is the capacitance of the active

region of the ion counter and V the polarizing voltage. This expression

applies to parallel plate counters as well, since they are a limiting case of

cylindrical geometry with large radii.

If the current to the collector plates is measured as the polarizing

voltage is increased, an I-V characteristic curve of an ideal counter is

obtained as indicated in Fig. 16. Saturation of the current indicates all of

the ions entering the counter are being collected.

One serious source of error associated with ion counters is that of ion

loss in the inlet structure due to fringing electric fields. Some of the more

mobile small ions will be lost to the walls of the instrument and, if the space

charge is predominately made up of small ions, large errors can result. If

these losses are present, an I-V characteristic curve like that in Fig. 16 will

be observed.

The I-V characteristic curves for two different ion counters were

measured for different space charge conditions. These measurements were made

by connecting to the inlet of the counter a tube 2m long and 10 cm in

diameter. An alpha particle source which could be biased relative to ground to

provide only positive or only negative ions was placed at the inlet end of the

tube. For a fixed bias voltage and constant air flow across the source, a

constant average ion density was produced at the inlet of the counter.

Current-voltage characteristic curves were obtained for each of the two

counters. The results for the first counter are shown in Fig. 17. The

saturation is evident for both positive and negative ion measurements. In
ION

CURRENT

42

POLARIZING POTENTIAL

Figure 16. Current-vol tage characteristic curves for (a) an ideal ion

counter and (b) a counter with losses for a space charge

made up of small ions.
43

O

Q_

CD

£sj

DC

<

O

Q_

(SlINfl 3AllV13H)'lN3aanO NOI

Figure

17.

Characteristic

curves

for

an

ion

counter.

Normal

operating

voltages

for

different

mobility

ranges

are

indicated.

A

-

positive

ions,

-

negative

ions.
44

normal operation, fixed polarizing potentials as indicated on the figure would

be selected by the user to change the critical mobility. For this counter the

volumetric flow rate is constant.

Selection of different mobility ranges in the second counter is

accomplished by changing the polarizing potential and, for the largest ions, by

reducing the flow rate as well. The characteristic curves for both high and

low flow rates for this counter are shown in Fig. 18. There clearly are

substantial losses at the inlet associated with this counter. These losses

represent errors of 21 percent and 95 percent for positive ions for the

operating conditions for smaller critical mobilities. Data points for

polarizing voltages below those required for saturation are not shown for

clarity of presentation.

In the counter with losses, the polarizing plates protrude slightly beyond

the collector plates. It would appear that this design is responsible for the

large losses observed.

An ion counter assembly, in which the relative position of polarizing and

collector plates can be varied, has been designed and constructed for use in

studies of errors associated with ion counters. A series of measurements have

been made in which the relative position has been varied and for a constant

flow rate, the I-V characteristic curve generated. These measurements have

shown clearly the inlet losses associated with counters in which there are

fringing fields at the inlet to the counter assembly. Typical results are

shown in Fig. 19. The experimental configuration was the same as described

previously. Even where the polarizing plates are retracted one plate spacing,

there are still significant losses with higher polarizing potentials.
ION

CURRENT.

(RELATIVE

UNITS)

45

0 100 200 300

POLARIZING POTENTIAL (V)

gure 18 . Characteristic curves for an ion counter with losses. Normal operating voltages for different mobility ranges

are indicated, a - positive ions, - negative ions, 0“ positive ions and low volumetric air flow rate.
<v£

ojo

<o Or—

C CL

•r- I/) N «r-

•r- T3

L-(O 0) r— -C O I—

CL

(/) a* qj

-t-> L-

<o 0) ^ C L aj o

+J Oic u

C O QJ

•r— v— r- N +> r—

•r- IQ O

$-3 0

<0 +J r— -r- 0) O IA£

CL 4->

3 0) i— * o cn a) o </) U «£ • CL O) +)+) X 4-> C r- OJ flJ O O *4- WXri—i > O *1— 4-J CL O

QJ

$-cn

ji

POLARIZING

VOLTAGE
47

Other sources of error such as turbulence in the air stream, space charge

effects, losses in inlet ducting and instrument potential relative to space

potential have not been studied in detail.

B2. Net Space Charge Measurements

An absolute filter assembly was constructed for use in laboratory studies

and is shown in Figure 20. This assembly has been designed for maximum utility

and can be readily adapted for different inlet and outlet connections. A

linear scanning and support system has been particularly useful in evaluating

the performance of various ion sources in the development of a facility to

produce space charge. Volumetric air flow rate through the instrument filter

is measured using a calibrated turbine flow meter. The air-handling system has

been designed to allow the flow rate to be varied from 2 to 20 liters per

second.

The absolute filter has potential usefulness as a device which can be used

to calibrate ion counters. If a homopolar space charge is produced, then the

homopolar charge density and the net space charge density are equivalent. A

measure of net space charge density yields the absolute charge density, the

knowledge of which may be used in calibrating ion counters. The reason that

the two measurements are not directly comparable is the following. The ion

counter has associated with it some critical mobility and as a result, may or

may not collect all the ions in a given air sample. If the mobility spectrum

of the ions is known, then the counter can be operated in a mode which insures

collection of approximately all the ions. Assuming that this is the case, the

absolute filter may be used to calibrate ion counters if the absolute filter is

100 percent effective at removing ions from an air stream.
48 Io >>

+-> •i— toe

<u om

DO

1-03

09u

<oOl

«/)

+-> 09 D

O)to

(LI to

to

«o

i-09 +>

+-> «oE

09 jco

goo

CM

09

i-3

D)

measurements .
49

To show this, the absolute filter can be connected in series with an ion

counter or conductivity tube. Since only small (molecular) ions would be

expected to pass through the filter (based on the particulate trapping

efficiency), an ion counter would indicate the charge density in the exhaust

air from the absolute filter. By comparing the charge densities indicated by

the two instruments, a measure of the efficiency of the absolute filter in

removing ions from the air stream can be obtained.

This efficiency must be determined as a function of several variables

including flow rate, ion density and ion charge. These studies will use the

new space charge facility which is being developed.

In considering methods for obtaining an absolute measure of space charge

density, the technique of the Faraday cage cannot be neglected. A Faradcy cage

for this purpose is an enclosure constructed of open mesh conducting screen.

Traditionally, the Faraday cage has been used with a radioactive equilibrated

"antenna" to yield a measure of the potential at the geometrical center of a

cubic enclosure. In our considerations of Faraday cages, we have obtained

solutions to Poisson's equation for both rectangular boxes and right circular

cylinders. Figure 21 shows the geometry of these cages and Eqs. 10 and 11 are

the formal solutions of Poisson's equation with the assumption that the

potential of the boundary is zero.
50

X

Figure

21.

Geometries

of

Faraday

cages

assumed

in

the

solutions

of

Poisson's

equation

presented

in

the

text.
51

For the rectangular enclosure,

A _ 64p

9 o £ TT

0

Ei »k

(odd)

sinlf) slnffi) sin(Jf-)

i-O-k-U^)

2 + (^)

2 +

(^f)

2

]

(10)

The solution for a right circular cylinder is

= 1P-

£o

a

oo E w>

k

n Vkna >

(cosh (k

n L)-l) sinh (k

n z)

sinh (k

n L)

(cosh (

n

z

) -1 )j . (11

)

In each of these, P is the net space charge density. In Eq. 11, J 0 and

Jl are Bessel functions of zero and first order, respectively, and kn is

determined by the requirement that J 0

(k na) = 0.

A computer program has been written to evaluate a truncated series of the

form given in Eq. 10. Calculations were made for the potential at different

locations within the cage. During the course of these calculations, a

discrepancy was noted between our results and the widely used calculation of

Dodson [11] referred to by Vonnegut and Moore [8] and later reproduced by

Chalmers [2]. The potential at the geometrical center of a cube may be written
52

in simplified form as

V = const, p L

2 (12)

r where p(-o) is the net space charge in the box and L is the length of one side

I7W of the box. The constant may be evaluated by summing the relevant parts of

Eq. 1. Our solutions gave

const. = 6.37 x IQ9 (13)

while the work of Dodson, based on a semi -empirical calculation give a value

for the const. = 8 x 109 . It should be noted that the present results are in

agreement with the extensive calculations of Perper and Penney [12]. The

source of this discrepancy is unknown, although no estimate of errors inherent

in Dodson's calculation were given by Vonnegut and Moore.

C. Discussion and Conclusions

The use of ion counters and other space charge density measuring devices

to characterize the ion environment under a dc transmission line or in a

biological exposure system requires an analysis of errors associated with such

measurements and the development of techniques for an absolute calibration of

the instruments. The results presented here show the effect of one possible

source of error, the loss of ions at the inlet of an ion counter due to

fringing fields. These losses can be eliminated by properly designing the ion

counter.
53

An absolute filter assembly to be used in measuring net space charge has

been constructed and will be critically examined to determine the potential for

use in an absolute calibration of ion counters. There is good indication in

preliminary results that the use of the absolute filter in conjunction with the

space charge facility will afford a means of calibrating ion counter devices.

7. Discussions and Conclusions

Two facilities, which have been and will be used to evaluate various

instruments used to characterize the electrical environment around high voltage

dc transmission lines, have been developed. A parallel plate system for

producing a field accompanied by space charge in which the total field can be

calculated has been constructed and used to compare three different electric

field measuring instruments. The results of this work were reported in a

separate publication [3].

A specific source of error associated with measurements of vertical

current density using Wilson plates has been investigated using the parallel

plate system. Lack of coplanarity of the sensing element with the ground plane

results in a field enhancement at the surface of the sensor. The enhancement

factors for several Wilson plate configurations were determined using ac

techniques. Preliminary work using dc field and ions shows a correlation

between the ac and dc measurements for all plates except those without a guard

ring. These studies will be continued in the coming year.

A second development effort is aimed at producing a region containing a

space charge which is spatially uniform and temporally smooth. A low-speed,

air-flow facility has been used to investigate various ion source
54

configurations. Studies show that suitable space charge can be produced if a

uniform air stream is used to transport ions from the source of ionization to

the test region. The charge density produced depends on the air speed, corona

current and source configuration. The results of these studies were used to

design and fabricate a new system which will be evaluated in future work. This

source of space charge will be used to study ion measuring instruments.

A study of errors associated with measurement of homopolar space charge

density by ion counters which result from fringing fields at the center inlet

has been made. Although incomplete, the results of this work indicate that

properly designed instrumentation is required to avoid substantial error. Two

ion counters have been examined, one of which displayed a large error.

A filter system using a high efficiency particulate air filter was used in

measurements of space charge density produced in the low-speed air-flow

facility. This system has potential use in providing an absolute calibration

technique for ion counters and will be investigated further.

Much has been accomplished toward the objectives stated earlier in this

communication. As is frequently the case in a effort such as this, progress in

one area depends on results in another so that much of what is reported here

represents progress and not final results. The availability of the parallel

plate facility and the low-speed air-flow system for producing space charge

has provided test systems which will allow us in the future to concentrate more

on instrument evaluation and characterization.
55

8. References

1. IEEE Standard 644, "Recommended Practices for Measurement of Electric and

Magnetic Fields from AC Power Lines."

2. J. A. Chalmers, Atmospheric Electricity , 2nd ed. (Pergamon Press, Oxford,

1967) p. 185.

3. M. Misakian, "Generation and Measurement of DC Electric Fields with Space

Charge," Nat. Bur. Stand. (U.S.), NBSIR 80-2177 (1980).

4. P. Moon and D. E. Spencer, Field Theory for Engineers , (D. Van Nostrand

Co., Princeton, N.J., 1961).

5. W. P. Winn and L. G. Yerley, III, "Electric Field Growth in

Thunderclouds," Quart. J. R. Met. Soc., 101, 1975, p. 993.

6. E. Weber, Electromagnetic Fields (John Wiley & Sons, Inc., New York,

1950).

7. W. R. Smythe, Static and Dynamic Electricity , 3rd Ed. (McGraw-Hill Book

Co., New York, 1968, p. 131).

8. B. Vonnegut and C. B. Moore, "A Study of Techniques for Measuring the

Concentration of Space Charge in the Lower Atmosphere" (final report,

Contract AF 19 (604) 1920, 31 Jan 1958).

9. R. B. Bent, "The Testing of Apparatus for Ground Fair-Weather Space-Charge

Measurements," Journ. of Atm. and Terr. Physics, 26, 1964, p. 313.

!
56

10. H. F. Tammet, "The Aspiration Method for the Determination of AtmosphericIon Spectra," Scientific Notes of Tartu State University, Issue 195

(translated from Russian), 1970. Available from U.S. Department of

Commerce, Clearinghouse for Federal Scientific and Technical Information,

No. TT68-50499.

11. W. B. Dodson, "A Discussion of Methods for the Measurement of Space Charge

Density" (unpublished report for the Research Laboratory, American Air

Filter Company, Inc., Louisville, KY 1950).

12. S. Perper and G. W. Penney, "Electric Potentials and Fields in Rectangular

Rooms," ASHRAE Transactions, 76, 1970, p. 87.
57

Appendix I - Model Calculations of Perturbations to Ambient Fields

Caused by Instrument Support Structure

An exact calculation of the field distortion produced by the

introduction of a conducting cylinder of finite length into a uniform electric field is difficult. In the present context interest

is in the distortion produced at a considerable distance from it by

a long thin cylinder with its axis aligned with the field. An

analytical solution valid to a high degree of approximation is

feasible for this case if the cylinder is represented by a prolate

spheroid.

The field in the vicinity of a spheroid of high permittivity (or

conducting) material immersed in a previously uniform field, E 0> in

air is given in prolate spheroidal coordinates as:

E = (

Q

/ ( s i n

2 n + sin 2 e) 1 / 2

) {-a

n [sinh n

-

cosh n 0 Q i

1 (cosh n)/Qi(cosh no)]cos 6 + [cosh n

-

cosh n 0 Qi(cosh n)/Qi(cosh n 0 )]sin 9 > (Al)

where

•*a„

n

i s the unit vector normal to the n

= constant surfaces

s* i s the unit vector normal to the e = constant surfaces

Qi< y) i s a Legendre function of the second kind;

Q-|'(y) is the first derivative of Q -j ( y )

and no 1S the

value of n which defines the spheroid.

The prolate spheroidal coordinates are related to rectangular

coordinates by the equations (see also Fig. A 1 )

x = a sinh n si n e cos y

y

= a sinh n si n e sin v

z = a cosh n cos e • ( A2 ) Surfaces of constant n are prolate spheroids defined by the equation:
I

L

58

Figure A-l . Prolate spheroidal coordinates. The coordinate surfaces are

prolate spheroids, n = const., hyperboloids 0 = const., and

meridian planes ¥ = const.
59

x

2 /b 2 + y

2 /b 2 + z

2 /c 2 = 1 (A3)

where

b = a sinhn and

c = a cosh n

(Note that c

2 - b2 = a

2

)

With the major axis of the spheroid parallel to the unperturbed

field vector the field will be symmetric about the z axis and it is

advantageous to introduce the variable, r.

r = (x 2 + y

2 ) 1

/

2 = a sinh n sin e

Surfaces of constant n then may be written

r

2 /b 2 + z

2 /c 2 = 1

and surfaces of constant e.

( A4

-r 2 /b 2 + z

2 /c 2 = 1 ( A5

)

In the present application interest is in the field at a considerable

distance from the spheroid, where the perturbations resulting from

its presence are at most a few percent. Hence only the region

where n is large is of interest. In that region

sinh n = cosh n - e

r'/2

Now define a new variable, R, such that

R - aeV2 * a sinh n = a cosh n ( A5a

Then r and z in terms of this new variable become

r a R s i n e

z - R cos e
60

Also note that b - c = aen/2 = R

a, which is small relative to b and c, is approximately equal to

the semimajor axis of the conducting spheroid.

“> > It is necessary to express the unit vectors a

n and ag in

Eq. 1 in terms of the unit vectors of the new variables.

Note that for the n

= constant surface,

u(r,z) = r

2 /b 2 + z2 /c 2

du/dr = 2r/b 2

, du/dz = 2 z/c 2

The normal vector is

ft = (du/dr)a r + (du/dz)a z

= (2r/b 2 )a

r + (2z/c 2 )a

z

and the unit normal vector is

a

n = ( ( 2 r /b 2

) a r + ( 2z/c 2)

z

) / ( ( 2 r/b 2

) 2 + ( 2z/c 2

) 2) 1

= (r(c 2 /b 2 )a

r + za

z

) / ( ( rc

2 /b 2

) 2 + z

2

) 1 / 2

. (A6)

Tangent to the n

= constant surface

du(r,z) = o = 2rdr/b 2 + 2zdz/c 2

and dr/dz = - zb 2 /rc 2 .

Then the tangent vector is

p p

-> $ = ab^ a

r

- r c

c

a z

and the unit tangent vector is
61

a

0 = (zb 2

a r

- rc

2

a z )/( (zb 2

) 2 + (rc 2

) 2) 1 / 2

= (z a r

- (rc 2 /b 2

) a z

) / (

2 + ( rc

2 /b 2

) 2 ) ^

2

. (A7)

Since in the region of concern b « c « R equations A6 and A7 may be

wri tten

a

n = (r a

r + z a z

) / (

2 + z2

) 1 / 2

= (R sin e a r + R cos e a z )/(R 2

( sin 2

e + cos 2 e))^ 2

= sin e a r + cos 0 a z . (A8)

a

0 = (z a r

- r a

z

) / (

2 + z2

) 1 / 2

= (R cos 0 a r

- R sin 0 a

z )/(R 2 (cos 2

0 + sin 2

0 )

) ^ ^ 2

= cos 0 a r

- sin 0 a z . (A9)

Also in this region the n = constant surfaces are nearly spherical

(see Eq. A3). Use of spherical coordinates is then appropriate

(see Fig. A2 ) with the unit vectors ip and i 0 where

i R

« a

n and i 0 ^a 0

( A 1 0

Equation A1 involves Legendre functions of the second kind Q 0 ( y

(implicitly) and Q -j ( p ) and the derivative of Q -| ( p ) , Q -|

' ( p ) . The

fact that in the region of concern y is very large permits use of

approximate values of these functions.

Q 0 ( y ) = (1/2) 1 n ( ( 1 + y ) / ( 1 - y))

= (1/2) [

n ( 1 + y) - 1 n ( y -1 )]

= (1/2) [1/ii - (1/2)(1/ u )2 + (l/3)(l/p)3 + ...)

-(-(1/u) - (l/2)(l/u)2 - (l/3)(l/p)3 -
62

Figure A-2 . Representation of various unit vectors used in the development

of an expression for the electric field far from a conducting

prolate spheroid immersed in a uniform electric field.
63

(Since In (1 ± (1/p)) * ± 1/p - (l/2)(l/p) 2

± (l/3)(l/p)3 ...)

- 1/p ± (l/3)(l/p) 3 +

L i kewi se

Q 1

( y ) = y Qo ( u ) -

may be written for large values of y

Q,(p) = p(l/p + ( 1 /3 ) ( 1 /p

)

3 + ...]-l = (l/3p 2

) + ...

then

dQ-|(y)/dy = Q-j'(y) = -2/3y 3

.

Now substituting from Eqs. A5a, A10, All, A12, and A13 into

and noting that

( s i n h

2 n + s i n

2 0 ) 1 / 2

= [ ( R / a

2 + sin 2 e]l/2 ~ R/ a = R/(c 2 - b

2 )l/2 #

Hence in the far field

E i = (E 0 )/(R/a) {-i^tR/a + 2 cosh n 0

3 ( R / a ) 3

Q -j (cosh n Q )]cos e

+ i q

[ R

/

a - cosh n

0 /3(R/a) 2 Q-j (cosh n 0

) D sin 0}

* E 0

{ - i r[

1 + 2 cosh n 0 /3(R/a) 4

Q -j (cosh n

0

) D cos 0

+ i Q [ 1 -(cosh n 0 )/3(R/a) 3 Q

-j (cosh n

Q )]sin 0 } ,

(All )

( A 1 2 )

( A 1 3 )

Eq. A1
64

or

-* > since - i p cos e + i e sin e = - i 2

E] - - E 0 { 2 E o cosh n 0

/

3 ( R / a ) 4

Q =1 (cosh n 0

)} cos 9

- i 0 { E Q

cosh n 0 /3(R/a)° Q -j (cosh n 0

)} sin 9

* -E

0

i 2

- [ ( E 0 cosh n 0 )/3(R/a 0) 3

Q -j (cosh n 0

) ] C i q sin 9

+ i r

(

2 cos 9 )/( R/a)]

For a long, slender prolate spheroid b 0 /c 0 <<!

b

Q /c 0

= sinh n 0 /cosh n 0

* n 0 /H + Hq/ 2) « n 0

<<! .

(Using cosh n 0

« 1 + n^/2 ) and sinh n 0

- n 0

)

Note that a 0 , b 0 , and c 0 relate to the conducting spheroid.

The Legendre functions for small oq or u

= cosh no near 1 may be

approximated as

Q 0

(u ) 1 /2 [ 1 n ( 2 + n|/2 ) - 1 nn |/2 ) ] . 1/2 1 n ( 4/ n | ) -

1 n ( 2 /n o

Ol (u) » 1 n(2/n 0 )-l = 1 n (2 c

0 /b 0 )-l

Since y =. 1 + n

E /2

Hence for a long, slender prolate spheroid in the far field

E

1 “ - E o^z + [,c o

- b l)

3/2 /3R 3

( l n(2 c 0 /b 0 )-l)]
65

[i

R

2 cos 0(c 2 - b^) 1 / 2 /R + ie sin e ]

}

= - E 0

{

z + [Cq/ 3R 3

(1 n(2c 0 /b Q )-l )]

-» C

r

2 c 0 cos e/R) + i e sin 0 ]}

Consider the case of a field meter suspended at a height of two

meters midway between two 6-cm diameter, 3-meter high poles separated

by a distance of 12 meters. Then b 0= 0.03, c 0= 3, R = 6.3,

e = 1.25 radians, cos 0 = 0.32 and sin 0 = 0.95. Substitution of

these values in the above equation, recognizing that the horizontal

components of the field perturbation produced by the two poles

cancel while the verticle components add, gives the following result:

Ei = -

0 ( 1 + 0.008) l z .

Appendix References

A1 . P. Moon and D. E. Spencer, Field Theory for Engineers

(D. Van Nostrand Co., Princeton, NJ . , p. 252 ff .

)

(1961)
NBS-114A (REV. 2-80

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO.

NBSIR 81-2267

2. Performing Organ. Report No 3. Publication Date

February 1981

4. TITLE AND SUBTITLE

1980 Annual Report: Electric and Magnetic Field Measurements

5. AUTHOR(S)

R.H. McKnight, F.R. Kotter, M. Misakian, and P. Ortiz

6. PERFORMING ORGANIZATION (If joint or other than NBS, see instructions)

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

7. Contract/Grant No.

8. Type of Report & Period Covered

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

10. SUPPLEMENTARY NOTES

| 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 bl iography or literature survey , mention it here)

The NBS program is concerned with developing methods for evaluating and

calibrating instrumentation for use in measuring the electric field and

various ion-related electrical quantities in the vicinity of high-voltage

direct current (HVDC) transmission lines and in apparatus designed to

simulate the transmission line environment.

A parallel plate apparatus designed to produce electric fields in the

presence of space charge has been evaluated and used to determine the

response of two vibrating plate electric field meters and a field mill.

Errors associated with lack of coplanarity of Wilson plate sensors with

the ground plane have been investigated using both ac electric fields and

dc electric fields with space charge in a parallel plate apparatus.

A low-speed-air-flow facility has been constructed to produce a volume

containing space charge which can be used as a source of ions for evaluating

and comparing instruments designed to measure various ion related properties.

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

absolute filter; current density; high voltage dc transmission lines;

ion counter; space charge density; Wilson plates

13. AVAILABILITY

Unlimited

| | For Official Distribution. Do Not Release to NTIS

] Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C.

20402.

Order From National Technical Information Service (NTIS), Springfield, VA. 22161

14. NO. OF

PRINTED PAGES

65

15. Price

$ 8.00

USCOMM-DC 6043-P80

i!I\