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PUBLICATIONS

NBSIR 82-2517

A Facility to Produce Uniform

Space Charge for Evaluating Ion

Measuring Instruments

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Electronics and Electrical Engineering

Electrosystems Division

Washington, DC 20234

June 1 982

Final Report

Prepared for r^^nartment of Energy

•GC *' "Lion of Electric Energy Systems

2Q(J hington, DC 20585

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NBSIR 82-2517

A FACILITY TO PRODUCE UNIFORM

SPACE CHARGE FOR EVALUATING ION

MEASURING INSTRUMENTS

R. H. McKnight and F. R. Kotter

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Electronics and Electrical Engineering

Electrosystems Division

Washington, DC 20234

June 1 982

Final Report

Prepared for Department of Energy

Division of Electric Energy Systems

Washington, DC 20585

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

NATIONAL BUREAU OF STANDARDS. Ernest Ambler. Director
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TABLE OF CONTENTS

Page

LIST OF FIGURES iv

Abstract . . 1

1. INTRODUCTION 2

2. EXPERIMENTAL APPROACH 3

2.1 Ionization Sources 3

2.2 Dispersal of Ions 4

2.3 Instrumentation 6

2.4 Evaluation of Ion Source Configurations ............ 7

3. DESIGN, CONSTRUCTION, AND TESTING OF A PERMANENT AIR FLOW FACILITY . 12

4. RESULTS 15

5. DISCUSSION 19

5.1 Source Calculations 19

5.2 Ion Loss to Walls 25

6. CONCLUSIONS 29

7. REFERENCES 30

i i i
LIST OF FIGURES

Page

Figure 1. Schematic (top view) of the prototype standard space charge

source 5

Figure 2. Corona ion source configurations, drawn to scale 8

Figure 3. Space charge density produced by one wire (source (b), fig. 2)

and three wire (source (d), fig. 2) source configurations .... 9

Figure 4. Comparison of ion densities produced by two different corona sources with three and seven wires, respectively 10

Figure 5. Isometric presentation of measurements of the ion density in the

test volume determined by using an absolute filter 11

Figure 6. Attenuation of space charge density by an electrical filter ... 13

Figure 7. Top view of permanent low-speed air flow facility to produce

space charge 14

Figure 8. Net space charge measurements made at midplane at locations II,

III, and IV (fig. 7) 16

Figure 9. Net space charge measurements made at midplane at locations II,

III, and IV (fig. 7)

’ 17

Figure 10. Net space charge measurements made at midplane at locations II,

III, and IV (fig. 7) 18

Figure 11. Geometry used in calculations of electrostatic potentials in

wire-duct geometry. Two-dimensional modeling is assumed .... 20

Figure 12. Equi potenti al plots for a single wire in a duct 22

Figure 13. Equi potential plots for the full two-dimensional wire-duct

problem 23

Figure 14. Equi potenti al plots for wire-duct geometry 24

Figure 15. Observed decrease in space charge density downstream from ion

source (see fig. 1) 27

Figure 16. Geometry used in theoretical development to explain ion loss in

fl ow facil i ty 28
A FACILITY TO PRODUCE UNIFORM SPACE CHARGE FOR

EVALUATING ION MEASURING INSTRUMENTS

R. H. McKnight and F. R. Kotter

Abstract

A low-speed wind tunnel containing space charge has been

constructed and evaluated. The facility is used for testing

the performance of ion counters and net space charge measuring

devices. Depending on location within the system, space charge

densities range from 2 -7 x 10-8 c/m3. The space charge density

is spatially uniform within ±5% over more than 90% of the cross

sectional area of the test volume, but decreases by approximately

20% between two positions separated by 1 m. Ion densities achieved

in this system are comparable to those found near high voltage dc

transmission lines but are free from the accompanying large electric

fiel ds.

Key words: electrostatic potential; high efficiency air particulate

(HEPA) filters; ion counters; ion density; measurement; net space

charge.

1
1. INTRODUCTION

Concern about environmental effects in the vicinity of high voltage

direct current (HVDC) transmission lines has led to interest in determining

the electrical environment near such lines. Because the parameters of

interest are generally the same as those considered by the atmospheric

scientist, it is natural to investigate the use of the previously developed

instruments in the transmission line context. The development and use of

instruments designed to determine electrical parameters associated with

atmospheric electricity phenomena has concerned atmospheric scientists for

many decades. A variety of devices have been invented to measure quantities

such as electric fields, vertical current density at ground level, space

charge densities, conductivity and ion mobilities. Using these instruments

to make measurements near a HVDC transmission line is not a routine extension

of their intended use, since both the electric field intensity and space

charge densities are significantly higher than those encountered in fair

weather atmospheric measurements. Because of this, it is necessary to evaluate

the performance of the various instruments at levels like those encountered

near the HVDC transmission line. In previously reported work, consideration

has been given to the operation of devices used to measure electric fields

[1]1 and to sensors for determining vertical current density [2]. A parallel

plate facility [1] was developed specifically for that work.

The elementary operation of devices designed to measure ion related

quantities such as space charge density (p) and air conductivity (X) can

be analyzed theoretically [3], but experimental verification of predicted

performance for these instruments has proven elusive due to the lack

of a "standard" ion source. The conditions existing near the surface of the

earth provide a source of space charge which can be used to compare instruments,

but these conditions are not at the control of the investigator and are often

highly variable. Radioactive sources have been used to provide ions

in various studies but have several drawbacks including radiation safety and

lack of control over ion production. The purpose of the effort described here

was to develop a source of space charge and a means for distributing this

space charge uniformly through a volume which would serve as a "test volume"

from which air samples containing ions could be drawn by various measuring

instruments. For maximum usefulness and versatility, the space charge in

the test volume should be uniformly distributed, temporally smooth, have

long-term stability (over a few hours), be controllable, and be unperturbed

by the measuring instrument. Various studies, such as losses in ducts, flow

rate dependence, etc., can be made without knowing the magnitude of the

space charge density. However, if instruments are to be calibrated, the

space charge density must be known. This requires a measurement of p with estimates of uncertainty. Where the ions making up p are predominately

of one sign, filtration methods can be used to determine p [4]. Ideally,

the mobility spectrum of the ions should also be known, but measurement of

this spectrum is difficult.

iNumbers in brackets refer to the literature references listed at the end

of this report.

2
The space charge density produced in the test volume should be

comparable to or greater than that found under HVDC lines. Measurements by

Bracken, et al . [5] show charge densities as large as 1.3 x 10-8 C/m3,

which corresponds to a singly charged ion density of 8 x lO'^ ions/cm3. Seme

biological experiments require even higher ion densities [6]. A space charge

density of 1.6 x 10-7 C/m3 (106 ions/cm3), therefore appears to presently

represent a practical upper limit of interest.

A number of methods for meeting the criteria discussed above can be

considered. A simple monopolar line located above a ground plane and operated

above corona threshold will approximate the transmission line environment

outside one pole. The parallel plate system mentioned earlier produces a volume containing both space charge and electric fields. While either system

might prove useful for a specific investigation, it is important to have a source of space charge in which there are no externally applied electric

fields. Only when such a source is available can studies be made without

concern for the effects of external fields on instrument operation. While

it is true that the transmission line environment has both electric fields

and ions, it is desirable to first determine how instruments respond to

different levels of space charge density and then extend these results to

the combined ion and electric field environment.

This report describes a facility developed to meet the requirements

described above. The approach is deliberately tutorial, since many problems

were encountered and solved. Much of the initial effort was exploratory and

used a developmental system which could be readily modified. The final

system described later in the report evolved from these initial experiments.

2. EXPERIMENTAL APPROACH

In the development of a test volume containing space charge, several

different technical areas were encountered. These were (1) the source of

ionization, (2) the means of dispersing the ions, and (3) instrumentation

to characterize the facility. The following discussion is assembled according

to these broad subject areas. A general discussion of design philosophy will

be presented first, with specific measurements described later in the report.

2.1 Ionization Sources

Ionization may be produced in several ways, but for practical reasons

only corona discharges and radioactive sources were considered. Radioactive

sources which emit alpha or beta particles ionize air in the immediate vicinity

of the source while photon emitters (gamma or hard x-ray) produce a more

extended region of ionization. Because there are no electric fields near the

sources (unless externally applied), there is no automatic means for transporting

charge away from the source. By contrast, high electric fields are required

to initiate and sustain corona discharge. If the applied potential is a dc

voltage, then charge of one polarity will be transported along field lines

3
away from the source of the corona, which may be a fine wire or a pointed

conductor. If a radioactive source is electrically biased, then charge of one polarity will also be transported from the region of ionization. In either case a space charge of predominantly one polarity will be present

some distance from the source. The ions produced by the sources described

above will generally be molecular sized and will have mobilities attributed

to "small" or "fast" ions. However, particulates in the vicinity of the source may also become charged. Since the space charge of interest for the

present work should be composed almost entirely of small ions, such charged

particulates present a complicating factor to be avoided if possible.

An interesting and novel approach to generating space charge was considered and rejected because of the requirement that the space charge be

made up of small ions. This approach has been used in a study of charge

buildup in large oil tankers during washing and consisted of electrifying a spray of water vapor [7]. This technique produces high space charge densities,

but not small ions.

For reasons elaborated below, the bulk of the effort reported here used

corona sources. Radioactive sources have been used and are being considered

for further use in biological studies of the effects of air ions [8]. In biological experiments such sources offer the advantage of not producing ozone

and of being audibly quiet. In his definitive work on ion counters, Tammett

[9] used radioactive sources to evaluate various features of counter performance.

2.2 Dispersal of Ions

Because of the desire to avoid having applied electric fields in the

test volume, air flow was chosen to carry the ions from the source of ionization

and disperse these ions throughout the test volume. In the initial stages of

the project, ions were produced by alpha particle sources. Small fans were

used to provide an air stream which transported the ions into closed boxes

1-3 m3 in volume. Additional fans were used to mix the air in the boxes.

Air samples containing ions were drawn by aspirating devices from the side of

the box and the exhaust air from the devices returned to the box. While

sizable ion densities were achieved in this way ( 104-105 ions/cm3), the

spatial distribution was uneven and the observed air conductivity was temporally erratic.

A series of measurements indicated that the lack of a smooth air flow across

the source of ionization might be responsible for this unsteady behavior, and

so a developmental system based on wind tunnel techniques was constructed.

This system, which provided much of the design information for the facility

described later, was constructed of heavy duty cardboard and is illustrated

schematically in figure 1. An air stream entering the low speed air flow

facility passes through a series of screens designed to reduce turbulence

and then enters a region of ionization. The air stream carries ions downstream

to the test volume from which an air sample can be extracted or into which a measuring instrument may be placed.

4
Figure 1

2.5m 0.6m 1.9m

Inlet Flow Straightener

Air Flow

Schematic (top view) of the prototype standard space charge source

5
The purpose of this design was (1) to produce a low turbulence air stream

at the source, (2) to carry the ions away from the source region in order to

avoid stray electric fields, and (3) to provide a sufficiently high volumetric

air flow through the facility so that the small volume drawn out by an aspiration

device would not significantly perturb the existing space charge density.

The admittedly crude mode of construction proved particularly useful, since

it was easy to make modifications to the system. Many different source

configurations were tried. The cardboard proved sufficiently conductive so that no effects due to surface charging were observed.

2.3 Instrumentation

Air speeds and turbulence in the flow facility were observed using a hot film anemometer. No detailed analysis of the turbulence components was attempted since the space charge density was of primary concern. The hot

film anemometer was used near the lower end of the allowable range resulting

in estimated errors of as large as ±25% for the air speed measurements.

This large uncertainty does not affect the results presented here and would

be reduced substantially with improved calibration of the anemometer.

A filtration method employing a high efficiency particulate air (HEPA)

or "absolute" filter was chosen to determine the space charge density in the

flow system. This technique, which is described in detail elsewhere [4],

actually results in a measure of net space charge but for the case of a corona

ionization source the space charge is composed almost exclusively of ions of one sign so that the polar space charge and net space charge are nearly equal . In this method, air containing ions is drawn through a HEPA filter which is

insulated from ground. Less than 0.1% of the ions pass through the

filter [4]. The net space charge density p (C/m3) is given by p

= I/(j),

where 1(a) is the current due to the ions collected by the filter and

cj) (m3/s) is the volumetric flow rate through the filter.

The filter assembly was configured so that air containing ions was drawn

into a sampling tube which extended into the test volume. This entire assembly

was moved by means of a leadscrew so that the space charge density was determined

at a given point along a horizontal traversal of the test volume. The height

of the assembly above the floor of the flow facility could be adjusted as well. In this way, a measure of the spatial distribution of the space charge

density in the test volume was determined.

The net space charge density is determined in terms of measured volumetric

air flow and ion current. Estimated uncertainty in the current measurement

is ±3%, while the volumetric air flow uncertainty varies, but may be as large as ±5%. An additional source of error involves losses in the sampling

tube attached to the filter assembly. All the data presented here were

taken at the same flow rate with the same sample tube, so that the relative

values are known to ±8%. A limited number of measurements were made using

different inlet configurations for the sampling tube (elbow, side opening,

end opening). There was less than 5% variation in these measurements. In investigating the various inlet configurations, different length sampling

tubes were used. Any losses in the tubes themselves were within the uncertainty

6
of the measurement (±5%), These experiments on sampling losses were not

extensive and were made only as part of an assessment of sources of error. More detailed investigations could be made and losses determined for various

sampling tube configurations. On the basis of this work, it is conservatively

estimated that the space charge densities presented in this report are accurate

to ±15%. This uncertainty could be reduced substantially by improving

volumetric air flow and ion current measurements and making corrections for

sampl i ng tube 1 osses,

2.4 Evaluation of Ion Source Configurations

The flow facility illustrated in figure 1 was used to investigate a variety of ionization source configurations, shown in figure 2, all using corona discharges. Since the quantity of interest was the magnitude and

spatial variation of the space charge density in the test volume, investigations

were made to determine how this quantity depended on source configuration,

corona current and air speed at the source. The fan provided three air

speeds at the source, 0.56, 0.91 and 1.12 m/s. These air speeds correspond

to volumetric flow rates through the facility of approximately 33, 54 and

66 m3/s, respectively. Measurements made near the source using the hot film

anemometer indicated the flow to be fairly uniform except near the walls.

This was to be expected since the support frames for the turbulence screens protruded into the air stream. The flow straightener shown in the figure

was removed early in the work and replaced with a bank of household furnace

filters intended to remove large particulates from the air stream.

The source configurations studied are shown in top view in figure 2, where

all the corona wires are oriented vertically and are placed between ground

"planes" of different geometries. Not shown is a source which consisted of one grounded wire on either side of a corona wire. This source, which was designed to allow the spread of space charge generated in a narrow volume,

was abandoned when it was found that corona discharge was initiated on the

ground wire at operating voltages of interest. In all sources, the corona

wire was 62 ym stainless steel and the discrete wires forming the ground

plane were 400 ym bare copper. In source "a" in figure 2, the ground

plane was ordinary aluminum window screen. The space between wire and

ground plane varied from 0.05 to 0.10 m, with 0.1 m used for most measurements.

Space charge densities were determined at different regions in the

test volume by scanning with the absolute filter assembly. Large amounts of

data were generated, and only representati ve results are presented here

(figs. 3-5). In general, it was found that the more open sources (b-e) in

figure 2 produced greater space charge density, but that the spatial distribution

was less uniform and the temporal character! sties less smooth than for the

planar source (a). In all cases, the space charge density depended most

strongly on the air speed at the source. The yield from the open sources

increased somewhat with voltage, but for source (a) the space charge density

increased by less than 10% for a change in corona voltage from 6 to 20 kV.

The total corona current in this case increased by a factor of more than 10.

7
Figure 2.

K X X X X X X

|a|

X

|b|

I ^ ’•

Ic)

Air flow ^ XXX

• ••• • ••••• *«*«•

Id!

: X I X ; X

lei

1 m

|Top view)

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 ym in diameter.

8
Figure 3

CORONA WIRE VOLTAGE (KV)

Space charge density produced by one vn re (source (b), fig. 2) and

three wire (source (d) , fig. 2) source configurations. Air

speeds shown are at the source. Errors associated with space

charge measurements are estimated to be ±15%.

9
Figure 4. Comparison of ion densities produced by two different corona sources with three and seven 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.

10
Ion

Density

(Rel.

Units)

Figure 5. 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

11
In figure 3, results obtained for sources (b) and (c) in figure 2 are

shown. The space charge density displayed is the average measured at midplane

in the test volume approximately 2 meters from the source. The planar source

(a) in figure 2 produced the most spatially uniform and temporally smooth

space charge density, although at a slightly lower level, and so this source

configuration was chosen for use in the permanent facility described later.

Figure 4 shows a comparison of ion densities produced by three and seven wire planar sources while figure 5 presents in an isometric plot scans made across

the test volume at different distances above the floor. Except for the region near the walls, the uniformity is excellent. The error bars in figures 4 and 5 represent ±5% variation. The fall off on the right hand side is a sampling

artifact due to flow perturbation as the sampling tube inlet nears the wall.

Measurements were made at different distances downstream from the source,

and the space charge density was found to diminish substantially as the distance

from the source increased. This point is discussed in further detail later

in section 5.2.

In order to evaluate the performance of an ion measuring instrument (for

example, an ion counter) over a wide range of space charge densities, it is

necessary that this quantity be variable. As is seen in figure 3, a large

variation cannot be obtained by varying corona voltage. If the air flow is to

remain constant, some other means of changing p must be devised. A simple

el ectrostatic retarding assembly (actually a repelling grid) and the response

of p in the test volume to changes in the grid voltage are indicated in figure 6.

The substantial charge density transmitted for retarding voltages above 300 V indicates a charge component with low mobility-. The use of a retarding

assembly like this is probably not advisable, since it modifies the mobility

spectrum of the ions. This will then influence the response of a measuring

instrument that has a mobility dependent response. Control of the ion density

remains a problem to be considered in future work.

3. DESIGN, CONSTRUCTION, AND TESTING OF A PERMANENT AIR FLOW FACILITY

Based on the work described above, a permanent air flow system was designed

and constructed. The system is shown in figure 7. Air flow characteristics

were improved over those for the system illustrated in figure 1 by using a

1 arger area convergence ratio (4:1), eliminating support structures which protrude

into the air stream and using a smooth transition section to maintain minimum

turbulence of the air stream in the test section. Although not utilized in

the work reported here, provision has been made to install a continuously

variable speed fan for future work.

The system is also constructed so that HEPA filters can be installed at

the inlet to ensure air entering the source region is free of particulates.

Except for the transition section, which is lined with 1/8 inch hardboard,

the system was constructed using plywood. To investigate possible charging

of the walls, measurements were made before and after covering the interior

surfaces of the transition section with grounded aluminum foil. No differences

were observed and there was no indication of charging of the walls of the system

during system evaluation.

1 2
Figure 6. Attenuation of space charge density by an electrical filter. Screen

spacing is 0.025 m. The f i Iter-to-source spacing was approximately 0.15 m.

13
—2.44 m

Test Section

-1.22 m—

Transition

1.22 m

Inlet

Figure 7. Top view of permanent low-speed air flow facility to produce space charge.

14
A hot film anemometer was used to characterize the system air flow.

Although not ideal, the flow was found to be substantially improved over the

earlier system, as was expected. Turbulence levels were significantly lower,

and the flow speed was uniform over a larger fraction of the cross section.

No attempts were made to improve the flow characteristics, since the space

charge produced in the system using an optimized ion source was very uniform.

Based on the earlier effort a planar configuration similar to (a) in figure 2 was chosen for the ion source.

4. RESULTS

A series of measurements were made in which different source parameters

were varied including:

(a) Number of corona wires (1, 3, and 9)

(b) Screen mesh size (5 cm x 5 cm and window screen)

(c) Corona voltage (7, 10, 15, and 20 kV)

(d) Air speed at the source (0.5, 0.7, and 0.95 m/s).

For all measurements the screen to corona wire spacing was 10 cm. Not all

permutations were examined, although for each source configuration all three

air speeds were used. For each source, the absolute filter system was used

in a scanning mode to determine the net space charge density at locations II,

III, and IV (fig. 7) for five different positions above the floor of the flow

system. Representative results of these measurements are displayed on figures

8, 9, and 10. What is shown on these figures is the net space charge density

measured at midplane at the three locations of interest. Indicated on the

drawings are the relative positions of the inlet and test section walls as

well as the locations of the corona wires. All results shown were for a corona voltage +10 kV, air speed at the source of 0.5 m/s and no inlet filters.

In figures 8 and 9, the ground plane was the coarse 5 cm x 5 cm structure

and there were one and three corona wires, respectively. The source in figure 10

used nine corona wires and window screen ground planes. This particular

configuration was determined earlier to be optimum in terms of the uniformity

of space charge density produced in the test section.

There is a substantial decrease in maximum ion density measured near the source (position IV in fig. 7) as the number of corona wires is increased.

This result was due to the influence of neighboring corona wires and will be

discussed later. The best uniformity was obtained for the nine wire source, a result which is in agreement with the earlier work. The higher ion densities

near the walls at position IV are probably due to the influence of the ground

support structures on the outer corona wires. A substantial decrease in ion

density was noted in going from position IV to position II (fig. 7) as is seen in figures 8-10. Important features of the measurements taken with the

new facility are summarized as follows:

15
Figure 8.

DISTANCE FROM WALL (m)

Net space charge measurements made at midplane at locations II, III, and

IV (fig. 7). Relative positions of test section inlet walls are shown.

Source configuration was one corona wire (position indicated) and coarse ground planes (see text).

16
Figure 9.

DISTANCE FROM INLET WALL (m)

Net space charge measurements made at midplane at locations II, III, and

IV (fig. 7). Source configuration was three corona wires (positions

indicated) and coarse ground planes (see text).

17
CORONA WIRES

UJZ

INLET WALLS

II I i I 0 0.30 0.6 1 0.90 1.22 DISTANCE FROM INLET WALL (m)

Figure 10. Net space charge measurements made at midplane at locations II, III, and

IV (fig. 7). Source configuration was nine corona wires (as

indicated) and window screen ground planes.

18
(a) The net positive space charge measured in the system ranged

from a maximum of 2.5 x 10-8 c/m3 to 2.2 x 10-7 c/m3.

Assuming singly charged ions, this is a range of ion

densities from 1.6 x 105/cm3 to 2.4 x 106/cm3. Negative ion

densities were approximately 30% lower. In the test volume

itself, the range of space charge density was from

2.5 X 10-8 c/m3 to 5.7 x 10-8 C/m3.

(b) Changes in corona current as large as a factor of 10 result

in only a 20% change in measured net space charge.

(c) The net space charge density decreases by a factor of 2-3 in

going from location IV to location II (fig. 7).

(d) The optimum source configuration for producing a spatially

uniform space charge is a multi -wire source with window screen ground pi anes.

The ion densities actually observed in the test section of the new facility are lower than those measured previously in the developmental system.

There are two reasons for this. The distance from source to test section is

greater and air speeds at the source are lower in the new system. A system

modification to produce substantially higher densities would involve placing an ion source between the test section and the transition. A source in this

position could produce as much as a factor of eight greater ion density in the

test section. This estimate is based on the effects of higher air speed

through the source, which results in a higher ion density (see fig. 3) and a decreased ion loss due to the source being closer to the test volume.

It is clear from the information in figures 8-10 that the space ‘charge

density becomes spatially more uniform and also decreases substantially

downstream from the ion source. Also, these figures show that, near the

source, a single wire produces a greater maximum space charge density than

do sources with three and nine wires. These observations will be discussed

in greater detail in this section.

The difference in space charge densities produced by different source

configurations can be addressed qualitatively by considering the electrical

character! sties of the ion source. This region can be modeled using a two-dimensional wire-duct geometry which has been the subject of previous

investigations with regard to electrostatic precipitator operation [10,11].

The geometry used is shown in figure 11. A solution of Laplace's equation

for the case of one wire in a duct with grounded walls is given below [12].

5. DISCUSSION

5.1 Source Calculations

CO ^ (x,y) = C Z 1 ( 1

) n = l nir

19
Wire • Duct Geometry

Figure 11

y

o <

1

5

H Sx

•y

0 X

Wire Potential = Vo

Wire Radius =R

Geomet ry

geomet ry

used in calculat

Two-di mensi ona ions of electrostatic potent

1 modeling is assumed.

iai s in wire-duct

20
C = E 1 p - n=l niT n odd

00

(j> is the electric potential, Sy is the wire to plate spacing, R, the wire

radius, and Vg, the wire potential. This solution is applicable for wires

located midway between the planes (see fig. 11). The normal ization given by

eq (2) is obtained by assuming a wire of small dimensions which is not near

the wal 1 s.

An approximate solution for the situation with an infinite array of

wires may be obtained by using the principle of superposition. The general

solution is indicated below.

Here the symbols have the same meaning as above and $x is the wire-to-wire

spacing. In practice, the series rapidly converges and for the sources

studied here, the contribution from neighboring wires falls off quickly. The

formulas here apply only for the case of no space charge. The actual solutions

with the wires in corona would involve solving Poisson's equation. This has

been done in an approximate way by a number of investigators [1A,15], It was not felt that this complication would substantially improve the understanding

of our observations and so only the Laplacian solutions are presented here.

In general, as has been shown by MacDonald [14], the presence of space charge

distorts the Lapacian solution so the equi potenti al s shown below would be

different for the Poisson's solution. Wind effects have also been neglected.

Calculations were made for the geometries of figures 8-10, where the

grounded screens of the source are assumed to be conducting, grounded planes.

Plots of the equi potenti al s are shown in figures 12-14 for the one wire, three

wire, and nine wire sources, respectively. Only a limited spatial region is

shown. The decrease in fields near a given source wire as additional wires

come nearer is evident. This would be expected to affect the current

distribution between the ground planes. Such an effect has been reported

by Oglesby and Nichols [11]. They show results which indicate that the

average current density impinging on the ground plane depends strongly on the wire-to-wire spacing and decreases sharply as the wire-to-wire spacing

becomes smaller than below the wi re-to-ground plane spacing (fig. 11).

The improved spatial uniformity downstream from the source appears to be

due to the effects of the self field of the space charge. Using the maximum

space charge measured at location IV (fig. 7) for the one wire source (fig. 8),

the field at the surface of an infinitely long cylinder of charge 0.75 m in

21
Figure 12. Equipotential plots for a single wire in a duct. Wire-duct spacing

was 0.102 m, wire radius 32 ym and wire voltage 10 kV.

22
Figure 13. Equi potent ial plots for the full two-dimensional wire-duct problem.

Wire-duct spacing was 0.102 m, wire-wire spacing 0.25 m, wire

radius 32 um and wire voltage 10 kV. This corresponds to the

three-wire source.

23
Figure 14. Equipotential plots for wi re-duct geometry. Wire-duct spacing

was 0.102 m, wire-wire spacing 0.125 m, wire radius 32 ym, and

wire voltage 10 kV . This corresponds to the nine-wire source.

24
diameter is calculated as 3.6 kV/m. The actual fields will differ from this

value and will not be uniform, but are substantial enough to cause significant

ion motion due to electrical forces for small ions with mobilities of the

order of 1 x 10-4 m2/Vs. This motion will tend to smooth out a nonuniform

distribution.

5.2 Ion Loss to Wal 1

The decrease in the ion density with increasing distance from the source

indicated in figures 8-10 was also observed in the developmental facility.

A simple theoretical argument has been developed to provide a qualitative

explanation of the observations. Because the theory assumes a constant

cross section in the flow facility and the developmental facility more nearly

satisfies this criteria, the following discussion is based on results obtained

with that system. In figure 15 the ion density as a function of the distance

downstream from the ion source (see fig. 1) is indicated. The loss in ion

density is due to a number of factors including diffusion, turbulent transport

to the walls, and the self field of the space charge itself. Recombination

is not a problem, since the space charge is unipolar. Using a simplified

diffusion calculation [16], it can be shown that for the transport times

through the system involved in the present measurements, an ion would move

by diffusion less than 1 cm from its original position (viewed in the rest

frame of the ion). Turbulent transport is certainly involved in loss of

ions near the walls. The dominant mechanism, however, appears to be that due

to the interaction between the ions themselves. A simple model has been

developed to consider this problem.

Ions in the system move as a result of wind forces and coulomb interactions

between the ions. The electrostatic forces result in an outward drift of the

ions with a resultant loss of ions to the wall and a decrease in space charge

density downstream from the source as shown in figure 15.

A simple model has been developed in an attempt to verify this explanation

for the observed decrease in space charge density. The geometry used in the

calculation below is indicated in figure 16. Assume a uniform space charge

density pq enters a cylindrical duct. The air speed in the duct is V^.

At a distance L from the inlet, all of the ions entering the duct outside of

a critical radius rg will be lost to the wall. The outward motion is caused

by the electric field due to the charge entering inside rQ. In reality,

there is a continuous expansion of the ions and a nonuniform space charge

density along the axis of the cylinder. The actual ion flow problem is very

complicated and not amenable to simple analysis. In the approach taken here,

the cylinder of charge inside rg is assumed to be long and fixed, so that an expression for the electric field can be derived using Gauss' law. This

electric field is given by

E(r) = (pQrQ2/2sQ)(l/r) r^^r^R (4)

The equation of motion for the radial movement of an ion can be written as

25
( 5 ) Vp = dr/dt = KE(r) = (KpQro2/2eo) (1/r)

where K is the mobility of the ion.

Separating variables and integrating

(r2.p^ 2)/2 = (Kpro2/2eg) T .

( 6 )

(7)

Here T is the transit time for the ions from the entrance to Z = L, which is

equal to L/V^.

As indicated in figure 15, the laboratory measurements provide a measure

of the space charge density downstream from the source. The region near the source is inaccessible. In order to relate the calculation above to the

experimental results, it is necessary to derive an expression for the fractional

loss in ion density downstream from the source.

It is clear from figure 16 that the ions lost to the wall will enter the

duct outside Cq, while the space charge observed at L will be made up of

these ions entering at radii less than rQ.

Consider the motion of a volume element Av = ttR2az through the

duct. At z = 0, the charge in the element is pqAv while at z = L only

the charge initially inside rQ remains, namely, pQTrrQ2Az. If we assume that this charge has expanded to fill Av at z = L, then the charge

density measured at z = L is given by

( 8 )

Solving eq (7) for rQ2 and substituting in eq (8),

5p = (Pq-Pl)/Pq = (R2-r^2)/R2 = KpqL/(£qV^+KpqL) . (9)

In the development above, it was assumed that all ions had the same mobility. In practice, there is a distribution of ions with different

mobilities and so K in eq (9) must be replaced with an average weighted mobility

K, which is unknown. The remaining calculation involve^ relating eq (9) to

the experimental data which requires knowledge of both K and pg. These were determined by first considering the decrease in p between z = 15 cm and

z = 68 cm. By using the space charge density measured at the _former location

as a starting point, a value of 0.88cm2/Vs was determined for K. In this

calculation, an air speed of 0.5m/^ was taken as the average through the

tunnel. Then using this value of K, pg at z = 0 was determined by using

eq (9) and the data point at z = 15 cm. This value of pg was

26
24 T

Distance from Source (m)

Figure 15. Observed decrease in space charge density downstream from ion source

(see fig. 1). Data points - i. The solid line was calculated

using the theory discussed in the text.

27
2R <=1 P

Figure 16. Geometry used in theoretical development to explain ion loss in

flow facility. Model is assumed to have cylindrical symmetry.

28
2.55 X 10 -7c/m3. This normalization could also have been obtained by

using different data points and solving two equations for the two unknowns

(pQ and K). Because the air flow in the facility was not constant,

there is some uncertainty introduced by using an average speed.

The results of the calculation are shown on figure 15. The excellent

agreement between theory and experiment is probably fortuitous, considering

the simple theory used. However, these results give considerable support to

the proposal that coulomb forces between ions are responsible for the ion

losses observed in the low speed air flow facility.

This theoretical prediction agrees remarkably well with the experiment

considering the simplicity of the model and the use of an experimental

geometry which is square rather than round. It does seem reasonable to

conclude that the ion-ion interaction in the space charge itself is the

dominant loss mechanism. A similar analysis has not been made for comparable

data negative ions. However, the decrease in charge density for negative

ions was comparable to that observed for positive ions.

6. CONCLUSIONS

The use of a low-speed air flow facility and a planar corona source has

been shown to produce a test volume in which the ion density is uniform to a few percent over the cross sectional area of the test volume. Because of ion

losses to the walls, there is a continual decrease in ion density downstream

from the source. This decrease is approximately 20% over aim length of the

test volume. Near the source space charge densities as high as 2.2 x 10-7C/m3

were measured. In the test volume itself, the maximum p obtained was

5.7 X 10-3c/m3. These values were determined using a filtration method with

an estimated uncertainty of ±15%.

The performance of the various ion source configurations studied is

qualitatively understood on the basis of electrostatic calculations. Future

improvements which would enhance the usefulness of the system include a continuously variable speed fan and a means of controlling the space charge

density. It is also desirable that a method be developed to determine the

mobility spectrum of the ions present in the system.

The space charge densities measured in the system are significantly

larger than those observed under operating HVDC transmission lines. This

facility should therefore be useful in evaluating various instruments which

measure electrical parameters, which depend on ion density. It has already

been used in studying the use of filtration methods for measuring net space

charge [4].

The calibration of ion counters or other devices used to determine space

charge densities is of importance because of concern about characterizing

the electrical environment around high voltage dc transmission lines and in

biological exposure systems. One means of doing this is to use a filtration

method to determine the space charge density in the air flow facility and

compare this density value to that measured by an ion counter. If the ion

counter is to be calibrated to within a known degree of uncertainty, then errors in measurement of flow rate, inlet losses, losses in tubes and

orientation effects will have to be investigated. The system described in

this report is ideally suited for these investigations.

29
7. REFERENCES

[1] M. Misakian, Generation and Measurement of DC Electric Fields With Space

Charge, J. Appl . Phys., Vol . 52, pp. 3135-3144, 1981.

[2] R. H. McKnight, F. R. Kotter, and M. Misakian, Measurement of Ion Current

Density at Ground Level in the Vicinity of High Voltage DC Transmission Lines,

Nat. Bur. Stand. (U.S.), NBSIR-81-2410, 27 pages, 1981.

[3] J. A. Chalmers, Atmospheric Electricity, Pergamon Press, Oxford, England

(2nd Ed., 1967).

[4] R. H. McKnight, The Measurement of Net Space Charge Density Using Air

Filtration Methods, Nat. Bur. Stand. (U.S.), NBSIR-82-2486, 28 pages,

April 1 982.

[5] T. D. Bracken, A. S. Capon and D. V. Montgomery, Ground Level Electric

Fields and Ion Currents on the Cel il o-Syl mar ± 400 KV DC Intertie During

Fair Weather, IEEE Trans. Power Appar. Syst. PAS 97 , p. 370, 1978.

[6] J. Charry, Rockefeller University (private communication).

[7] T. E. Owen and R. J. Spiegel, Bulk Carrier Operations Safety Enhancement

Project-Phase II, Volume II--Shiptank Electrostatic Model Studies, Final

Report for Contract S-38044, U.S. Dept, of Commerce, 1978.

[8] A. P. Krueger and E. J. Reed, Biological Impact of Small Air Ions, Science,

Vol . 193, pp. 1209-1213, 1976.

[9] 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 the U.S. Dept, of Commerce, Clearinghouse

for Federal Scientific and Technical Information, No. TT68-50499.

[10] H. J. White, Industrial Electrostatic Precipitation, Addison-Wesl ey

Reading, Mass., pp. 95-115, 1963.

[11] S. Oglesby, Jr. and G. B. Nichols, Electrostatic Precipitation, Vol. 8 of

Pollution Engineering and Technolojgy, Marcel Dekker, pp. 31-55, 1978.

[12] W.K.H. Panofsky and M. Phillips, Classical Electricity and Magnetism,

Addison-Wesl ey, pp. 45-51, 1955.

[13] P. Cooperman, Trans. Amer. Inst. Elec. Eng., Part 1, pp. 47-50, 1960.

[14] J. R. McDonald, W. B. Smith, and H. W. Spencer III, A Mathematical Model

for Calculating Electrical Conditions in Wire-Duct Electrostatic Precipitation

Devices, Jour. Appl . Phys. 48, pp. 2231-2243, 1977.

30
[15] G. Leutert and B. Btihlen, The Spatial Trend of Electric Field Strength and

Space Charge Density in PI ate-Type Electrostatic Precipitators, Staub, 32,

pp. 27-33, 1972.

[16] E. W. McDaniel, Collision Phenomena in Ionized Gases, John Wiley & Sons,

pp. 488-521, 1964.

31
NBS-114A (REV, 2-80

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO.

NBSIR 82-2517

2. Performing Organ. Report No. 3. Publication Date June 1982

4. TITLE AND SUBTITLE

A FACILITY TO PRODUCE UNIFORM SPACE CHARGE FOR

EVALUATING ION MEASURING INSTRUMENTS

5. AUTHOR(S)

R. H. McKmght and F. R. Kotter

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

DEPARTMENT OF COMMERCE 8. Type of Report & Period Covere WASHINGTON, D.C. 20234

Final

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

! Department of Energy

Division of Electric Energy Systems

Washington, D. C. 20585

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

bibliography or literature survey, mention it here).

A low-speed wind tunnel containing space charge has been

constructed and evaluated. The facility is used for testing

the performance of ion counters and net space charge measuring

devices. Depending on location within the system, space charge

densities range from 2 -7 x 10"^ C/m^.

spatially uniform within ±5% over more

area of the test volume, but decreases

positions separated by 1 m. Ion densities achieved in this system

are comparable to those found near high voltage dc transmission lines

but are free from the accompanying large electric fields.

The space charge density is

than 90% of the cross sectional

by approximately 20% between two

12.

KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolon s) electrostatic potential; high efficiency air particulate (HEPA) filters;

ion counters; ion density; measurement; net space charge.

13.

AVAILABILITY

I X| Uni i mi ted

I

I For Official Distribution. Do Not Release to NTIS rn 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 page:

15. Price

USCOMM-DC 8043-PI

4