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PUBLICATIONS

NBS Technical Note 1223

Calibration of Aspirator-Type Ion

Counters and Measurement of

Unipolar Charge Densities

Misakian, McKnight, Fenimore

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No. 1223

1986

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Tm he National Bureau of Standards' was established by an act of Congress on March 3, 1901. The

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NBS Technical Note 1223

Calibration of Aspirator-Type Ion

Counters and Measurement of

Unipolar Charge Densities

Martin Misakian, Ronald McKnight, Charles Fenimore

Center for Electronics and

Electrical Engineering

National Engineering Laboratory

National Bureau of Standards

Gaithersburg, MD 20899

Issued May 1986

' ^

\

U.S. DefMirtnMnt of Commerce

Malcolm Baldrige, Secretary National Bureau of Standards

Ernest Ambler, Director
National Bureau of Standards U.S. Government Printing Office For sale by the Superintendent

Technical Note 1223 Washington: 1986 of Documents,

Natl. Bur. Stand. (U.S.), U.S. Government Printing Office,

Tech. Note 1223 Washington, DC 20402

74 pages (May 1986)

CODEN: NBTNAE

i
TABLE OF CONTENTS

Page

LIST OF FIGURES v

LIST OF TABLES viii

ABSTRACT 1

1. INTRODUCTION 1

2. THEORY OF OPERATION OF ASPIRATOR -TYPE ION COUNTERS 1

3. APPARATUS FOR GENERATING KNOWN UNIPOLAR

ION DENSITIES AND ELECTRIC FIELDS 4

3.1 Ion Density Profile In Parallel Plate Apparatus 4

3.2 Electric Field Perturbations Due To Aperture 8

3.3 Influence of Air Motion 9

4. ION TRAJECTORIES AND LOSSES 10

5. CALCULATED CHARGE DENSITY 18

6. MEASUREMENT RESULTS: PERTURBATION OF ELECTRIC FIELD 21

6.1 Space Potential Probe 21

6.2 Space Potential Measurements 23

6.3 Discussion of Results 28

7. MEASUREMENT RESULTS: COMPARISON OF CALCULATED

AND MEASURED ION DENSITIES 28

7.1 Calculated and Measured Ion Densities 28

7.2 Discussion of Results 32

8. CHARGE DENSITY MEASUREMENTS B^ \^H

MONOPOLAR HIGH VOLTAGE LINE 34

8.1 Measurements In Ground _ane 35

8.2 Measurements Above Ground Plane 38

9. SUMMARY 44

10. ACKNOWLEDGMENTS .' 45

iii
Page

11. APPENDIX A: ION LOSSES DUE TO FRINGING

ELECTRIC FIELDS FROM ION COUNTERS 46

12. APPENDIX B: FLUID FLOW THROUGH AN

APERTURE IN A PLANE 53

13. APPENDIX C: EQUATIONS OF MOTION FOR ION TRAJECTORIES 59

14. REFERENCES AND NOTES 63

iv
LIST OF FIGURES

Page

Figure 1. Schematic view of aspirator- type ion counters (a) cylindrical

geometry (b) parallel plate

geometry '

Figure 2. Schematic view of NBS parallel plate apparatus.

The arrangement shown is appropriate for

generating an electric field with positive space

charge. The top and bottom plates of the parallel

plate system are located in the planes z = d and

z = 0. The corona wires are oriented parallel

to one another and are perpendicular to the

plane of the figure (

Figure 3. Normalized charge density profiles for two current

densities, 1 x 10 A/m amd 0.1 x 10 A/m . The calculated results assume that V = 2650 V,

K = 1.3 X 10 m /Vs, and d = 0.17m5 ,

Figure 4. Schematic view showing that perturbations of electric

field due to an aperture in the ground plane and

air motion do not extend across the parallel

plate spacing

Figure 5. Ion trajectories for air speed in plane of

aperture of 1 m/s . The solid curves show

influence of 15 kV/m electric field. Dashed

curves are for no electric field. The time -of

-flight for all trajectories is 50 ms. The

volume occupied by the ions that enter the

aperture when E 5^ 0, V , exceeds volume of

air, V, which enters in the same time. Inset

shows effect of mobility value on trajectory

near aperture 13

Figure 6. Ion trajectories for air speed of 6 m/s in plane

of aperture. The solid curves show influence of

15 kV/m electric field. Dashed curves are for no electric field. The time-of -flight for all

trajectories is 50 ms. The volume occupied by

the ions that enter aperture when E 3^ 0, V , exceeds volume of air, V, which enters in same

time 15

Figure 7 . Schematic view showing influence of Coulomb

repulsion on ions below plane of aperture.

The effects of the electric field above the

aperture are ignored 17

Figure 8. Hemi -ellipse and coordinates for calculating

charge density, p 20
Page

Figure 9. Schematic view of space potential probe after

Penney and Matick [24,25] 22

Figure 10. Measurements of space potential at 9.5 cm and

8.5 cm above the bottom plate of parallel plate

system for conditions described in text. The

measured potential difference agrees well with

the calculated value of 112 V 24

Figure 11. Measurements of the current density on the

surface of the bottom plate. The measurements

are obtained with a moveable probe and normalized

with respect to the average of 17 measurements in

a circular area of 0.7 m diameter. The average

unormalized J value is near 0.25 x 10 A/m 25

Figure 12. Measurements of space potential perturbation due

to 5 cm X 5 cm aperture in ground plane as a function of height above ground plane 27

Figure 13. Top view of ion counter entrance with dashed

outline of aperture located 10 cm above

entrance. Nominal dimensions are indicated.

The spacing between the collecting and polarizing

electrodes is 2 cm 29

Figure 14. Positive charge density measurements, p , as a function of average air velocity in plane of

aperture. Calculated values of the charge density p , are shown assuming that y and z are 13.75 cm and

17 cm respectively. Typical error bars are indicated

at u = Im/s . As the air speed increases, the surface on which the electric field perturbation remains

negligible is represented approximately by a truncated hemi -ellipsoid as shown in inset 31

Figure 15. Positive charge density measurements for the same conditions as in figure 14 and with the

introduction of a 5 cm long duct below the

plane of the aperture. An estimate of ion

losses in the duct due to Coulomb repulsion

and diffusion, assuming no turbulence, is

shown with a solid curve 31

Figure 16. Schematic view of experimental arrangement.

Elevated ground plane is located on a table.

Relevant dimensions are given in text; figure

is not to scale 36

vx
Page

Figure 17. Ion density measurements (solid circles) for

different volumetric flow rates M. The ion

density values at the surface of the ground

plane determined from eq (5) are designated as

p . Estimates of duct losses due to Coulomb

repulsion are shown as solid curves 37

Figure 18. Schematic view of experimental arrangement for

above-ground measurements. The polarizing

voltage for the ion counter is produced with

a battery. Not shown are various measuring

instruments, high voltage power supply, etc 39

Figure 19. Above-ground ion density measuements at two air

flow rates and as a function of ion counter

potential. The unperturbed space potential at

the height of the aperture, which is 2.54 cm

in diameter, is indicated on the horizontal axis 40

Figure 20. Schematic view of electric field lines terminating

on and leaving ion counter near aperture when ion

counter is at space potential. The negative

charges induced by the electric field repel

some negative ions as they approach the aperture

under the combined influence of the electric

field and air motion 42

Figure 21. Ion density measurements at different flow rates

and as a function of ion counter potential when

there is inadequate shielding of the external

electric field 43

Figure Al. (a) Two dimensional geometry used in finite

element calculations. (b) Computer -generated

high level triangulation for geometry (a)

Inside the cross-hatched area the triangulation

was too dense to be displayed 47

Figure A2 . (a) Boundary conditions used in finite element

calculation. (b) Computer generated equipotential

curves, plotted in units of u = 0.1 48

Figure A3. (a) Boundary conditions and geometry used for a model calculation in which the polarizing plates

protrude in front of collector plates. (b) Computer

generated equipotential cuirves , plotted in units

of u = 0.1 49

Figure A4. Trajectories of ions entering the ion counter

at different initial locations. The geometry

is that of figure A3 51

vii
Page

Figure A5 . Ion counter output current as a function of

polarizing voltage for different plate

configurations . The displacement between the

leading edges of the collection and polarizing

plates is x. Positive values of x correspond

to a situation where the polarizing plates

protrude in front on the collector plates.

For X = 0, the leading edges were flush.

Because the ion density is independent of

polarizing voltage over the range plotted,

the ion counter current should be constant.

The spacing of the parallel plates is near 1 cm and the air speed, averaged over the area of

the ion counter aperture, is near 42 cm/s ....

Figure Bl. The boundary conditions for flow through aperture

of area Q

Figure B2 . Estimating u near fi

Figure B3 . Air speed versus height above a 5.1 cm x 5.1 cm aperture in a plane. The measured values were

obtained using three flow rates through the

opening, 0.37»x_10 m /s (D) , 0.69 x 10 m /s (o)

,

and 1.7 x 10 m /s (A). The data have been

normalized to unity at d = 0.5 cm

52

53

55

57

LIST OF TABLES

Table 1

.

Table Bl.

Space potential perturbations,

A comparison of theory to experiment for normalized

air speed into a small opening (5.1 cm x 5.1 cm),

u(0.5 cm) = 1

Page

26

56

viii
Calibration of Aspirator- type Ion Counters

and Measurement of Unipolar Charge Densities

ABSTRACT

The characterization of a parallel plate apparatus which can produce a unipolar ion density that is suitable for calibrating aspirator- type ion

counters operating in the ground plane is described. The influence of a dc

electric field, air motion, Coulomb repulsion and diffusion on the transport

of ions into the ion counter are examined to determine their effects on instrument calibration and measurements in the vicinity of high voltage dc

transmission lines. An ion density which is known with an uncertainty of less

than ±9% is used to check the performance of an ion counter with and without a duct at its entrance. The results of laboratory measurements of ion density

under a monopolar high voltage line, which complement the studies with the

parallel-plate apparatus, are also described.

Key words: Calibration; instrumentation; ion counter; ion density;

measurement; transmission line; unipolar. /

1 . INTRODUCTION

During the operation of high voltage dc (HVDC) transmission lines,

significant amounts of air ions are generated because of the normally present

corona. Speculation regarding possible environmental effects due to the ions

and associated electric field has led to increased interest in the

characterization of a number of electrical parameters in the vicinity of HVDC

transmission lines [1-81. The parameters of interest include the electric

field strength E, the ion current density J, and the unipolar ion density p. The authors have previously reported on sources of error during measurements

of E using electric field mills and vibrating-plate probes [4,8], and during

measurements of J using Wilson plates [6,8]. This study considers errors during the measurement of p using aspirator- type ion counters in the presence

of dc electric fields comparable in magnitude to those found near HVDC

transmission lines and in bioeffects exposure systems. A major problem in

determining the measurement uncertainty has been the difficulty in performing

an experimental calibration of the instrumentation. This report describes an effort to develop a known unipolar ion density in a parallel plate apparatus

which is suitable for calibrating aspirator- type ion counters operating in the

ground plane. The influence of a dc electric field, air motion, Coulomb

repulsion and diffusion on the transport of ions into the ion counter are examined to determine their effects during instrument calibration and during

ion density measurements. Laboratory measurements of ion densities beneath a monopolar high voltage line are also described.

2. THEORY OF OPERATION OF ASPIRATOR- TYPE ION COUNTERS

A brief description of an aspirator- type ion counter is presented here

with some discussion of possible mechanisms which can introduce uncertainties

during a measurement. More complete accounts of the operation of ion counters

are given by Israel [9] and Tammet [10]. An aspiration- type ion counter

consists of a capacitor through which air is drawn. Provision is made for

applying a dc voltage across the capacitor electrodes and for measuring the
ion current due to ions of one polarity reaching one of the electrodes. The

applied voltage is made sufficiently large so that at a given rate of air

flow, nearly all the ions impinge on the capacitor electrodes. Schematic

views of cylindrical and parallel plate ion-counter designs are shown in

figure 1. A cylindrical geometry was used as early as 1901 by Ebert [11];

parallel plate geometries have been used in more recent times [12]

.

Under ideal conditions, the measured charge density, p , is given by the

expression [9]

,

P^ = I/M , (1)

where I is the measured ion current and M is the laminar volumetric flow rate

of the air through the capacitor. Equation (1) is valid for ions with

mobilities equal to or greater than a "critical mobility" which is given by

[9]

k^ = M^yCV , (2)

where C is the capacitance, e is the permittivity of free space, and V is the

voltage across the capacitor. Commercial instruments are frequently

configured with selectable voltages to allow operation with different critical

mobilities. It is common practice to assume that all the ions are singly

charged and to convert the measured charge density to an equivalent number of

ions per unit volume.

Ion counter measurements can be subject to many systematic errors. For

example, the parallel-plate ion counter can show significant loss of small

ions if the electrode geometry is not properly designed. The polarizing

plates (plates with applied voltage) must be sufficiently recessed behind the

collecting plates, or fringing electric fields can precipitate ions to the

enclosure walls. Measurement results demonstrating this effect are shown in

figure A5 of Appendix A. A useful empirical guide is that the polarizing

plates be recessed two plate spacings behind the front of the collector

plates. However, the influence of fringing fields is best shown for a given

instrument by measuring the ion current as a function of polarization voltage.

A further discussion of ion losses due to fringing field effects is given in

Appendix A.

Measurement of the volumetric flow rate, M, is straightforward if a suitable flow meter is used, but this is usually not done in commercial

instruments. For these devices, the flow rate is determined by the

manufacturer and is included in a given instrument calibration. If the

counter is operated in a situation where there are external winds (not

normally a problem during laboratory studies), then the air flow through the

instrument can be affected and the stated instrument calibration may become

invalid. In parallel plate systems, an additional problem arises because of

the inactive region existing between the outside collecting plates and the ion

counter enclosure (figure 1-b) . Air flow in this region is measured as part

of the volumetric air flow but does not efficiently contribute ions to the

measured current. Correction for the ion losses due to the inactive regions

cannot be readily made.
Collecting

electrode

i^:

c

<I>

E^

1_

D

TS^

M

lo: T^

(a)

Collecting

electrode

X

:^^

4

M

(b)

Figure 1. Schematic view of aspirator-type ion counters (a) cylindrical

geometry (b) parallel plate geometry.
Vibrations of the electrodes can result in large noise signals which may

obscure the actual signal if the space charge densities are small. Parallel

plate counters are more susceptible to these microphonic problems than are cylindrical systems, but for all systems the effect depends on the individual

construction and the magnitude of the vibration.

Polarizing potentials should be applied using a stable power source, e.g.

batteries. Instabilities in the power supply will result in perturbations of

the ion density measurement, since the polarizing potential is capacitlvely

coupled to the electrometer used to measure the ion current.

In addition to the processes noted above, external dc electric fields can influence the number of ions that enter an ion counter and reach the

collecting plates. Diffusion of ions may also have an effect. For the ion

densities found in the vicinity of HVDC transmission lines, ion losses due to

Coulomb repulsion can be a factor. The effects of an external electric field,

diffusion and Coulomb repulsion on the operation of an ion counter in the

ground plane are considered in detail in Section 4.

The above listing of effects which can influence an ion density

measurement is not complete but demonstrates that the simple use of eq (1) can lead to significant errors.

3. APPARATUS FOR GENERATING KNOWN UNIPOLAR ION DENSITIES AND ELECTRIC FIELDS

As noted earlier, a factor which contributes to uncertainty in performing

ion density measurements is the difficulty in generating a known ion density

for experimentally calibrating the instrumentation. Because the measurements

of interest involve the presence of large dc electric fields external to the

ion counter, it is desirable to have an apparatus which can produce a controllable electric field as well as a known ion density. Bracken and

Furumasa have reported on the use of a coaxial cylinder apparatus for testing

the performance of an ion counter but do not consider in detail the

uncertainties associated with the operation of the apparatus [13]. A parallel

plate apparatus for producing known dc electric fields with ions has been

developed at NBS for evaluation of electric field strength meters [4] and is

used in the present study as a means for producing a known ion density. This

section considers the unperturbed ion density in the parallel plate system and

theoretical estimates of the electric field perturbation due to presence of

the ion counter aperture and air motion through the aperture. The

perturbation of the electric field due to an aperture is modelled with a circular aperture instead of a square aperture which is actually used during

the experimental study. This approximate approach permits establishing a useful analytic relationship between the electric field and space-potential

perturbations and is not expected to affect the semi -quantitative conclusions

reached later. The results of measurements which help to characterize

experimentally the extent of the field perturbations are described in

Section 6.

3.1 Ion Density Profile In Parallel Plate Apparatus

Because the NBS parallel plate apparatus has been described in detail

previously [4], it is discussed only briefly here. A schematic view of the
apparatus is shown in figure 2. Ions generated by stainless steel corona

wires are directed both upward (to the cap) and downward to the first screen. Ions not collected on the first screen continue downward to the second screen

which is the top "plate" of a parallel plate system. The ions which pass

through the top plate travel a distance d to the bottom plate and form the

current density J. Electrically isolated current sensing patches mounted on

the bottom plate are used to measure J. The side dimensions of the parallel

plates are 1.7 m x 1.7 m and the spacing is near 0.17 m for the present

studies

The solution of Poisson's equation in one dimension yields expressions

for the electric field strength, E(z) , and electric space potential, $(z)

between the parallel plates [4]

E(z) = [E^ + 2J(d-z)/K£ l-""/^ , and (3)

$(z) = V^-(K£ /3J)[(E ^ too + 2J(d-z)/K£ )^/^-E^] , (4) o o

where V is the potential of the top plate (z=d) , E is the electric field at

the top plate, and K is the average mobility.

Following procedures described in Ref . [4] , the values of K and E can be

determined experimentally, thus permitting the calculation of E from eq (3)

for a given current density. The constitutive relation for conduction current

density,

J = pKE . (5)

can then be used to determine the total charge density, p , as a function of z. It should be noted that J is approximately constant between the parallel

plates because there are no sinks or sources of ions in this region. The ion

density decreases and the electric field increases as a function of distance,

z , from the top plate

Figure 3 shows the results of model calculations of normalized positive

ion density for J = 1.0 x 10 A/m , K = 1.3 x lO' m /Vs , V^ = 2650 V, and

d = 0.17 m. A decrease of 49% in ion density occurs between the top and

bottom plates. Reducing J by a factor of ten while keeping K, V and d fixed

results in a decrease of ion density between the plates of only 6.0%. The

relatively small change in p for the second case suggests that the parallel

plate apparatus may be used for generating a "known" or calculable ion density

(i.e., in this example, known within about ±3%) for calibrating an aspiratortype ion counter operating in the ground plane. However, in order to use eqs

(3) and (5) to calculate the unperturbed charge density profile, it must be

shown that (1) the perturbation of the electric field due to the aperture of

the ion counter does not extend significantly to the upper plate of the

apparatus, and (2) the influence of the air motion due to operation of the ion

counter is likewise restricted mainly to the region near the aperture.

Figure 4 shows schematically the conditions described above.
CAP

Corona wires

• • • • • • • • • •

Electric

field probe

Ion counterx-Z = d

z=o

Isolated elements for

J measurement

Fig'ore 2. Schematic view of NBS parallel plate apparatus. The arrangement

shown Is appropriate for generating an electric field with

positive space charge. The top and bottom plates of the parallel

plate system are located in the planes z » d and z » 0. The corona wires are oriented parallel to one another and are perpendicular to the plane of the figure.
1.0

UJo

a. ^x

< o

I CI. 0.8 o CL

a

Sa'

lij >- N 1- ^ co < z 0.6

s HI cc o

O

z

0.4

T I I I r

J = 1.0x10"'^A/m

J I I L 2 4 6 8 10 12 14 16 18

DISTANCE FROM TOP PLATE (cm)

Figure 3. Normalized charge density profiles for two current densities,

1 X 10 A/m amd 0.1 x 10 /A/m . The calculated results assi

V^ - 2650 V, K - 1.3 X 10 m /Vs , and d - 0.17 m.

Vt

\tt I I I I I I I I I I I I I t t I I I I I I ! i Region of significant

/- Top I u plateiait;

I I 3 I I't 3 I I I t 3 I I t I I r I t I

Equipotentials

Figure 4. Schematic view showing that perturbations of electric field due to

an aperture in the ground plane and air motion do not extend

across the parallel plate spacing.
3.2 Electric Field Perturbations Due To Aperture

An estimate of the electric field perturbation due to an aperture in the

ground plane can be made by numerically calculating the electric field for the

geometry shown in figure 4, in the absence of space charge. Such a calculation has been performed at NBS [14], but the uncertainties in the field

values and the associated space potentials are not well characterized.

Analytic expressions for the electric field and potential for an aperture in

the ground plane of a large parallel plate system have been derived by Fry

[15]. The electric potential, $' , and field, E' , along the symmetry axis

(z-axis) are given by

$' = E [z/2 + R/tt + (z/tt) tan''''(z/R)] , (6) u

and

E' = E [(1/2) + zR/7r(R^ + 7}) + (I/tt) tan"-^(z/R)] , (7)

where E is the unperturbed uniform electric field (prior to introduction of

aperture) and R is the radius of the aperture. Expressing eqs (6) and (7) as normalized by the unperturbed potential (E z) and unperturbed uniform electric

field (E ), respectively, we have u

($'/E z) = [1/2 + R/ttz + ( I/tt) tan" -"-(z/R)] , (8) u

and

(E'/E ) = [1/2 + zR/7r(R^+z^) + (I/tt) tan" ""-(z/R) ] . (9

As z increases, the departure of $' and E' from the corresponding uniform

field values decreases and the magnitude of the electric field perturbation

approaches twice the value of the space potential perturbation [16], i.e.,

limit |(E'-E )/E I = 2 |($'-E z)/E zl . (10)

Z-KJO ' ^ u ' u' ' u ' u

'

At a height of four radii above the aperture (along z-axis), the perturbation

of $' is + 0.16% and the perturbation of E' is -0.32%. At a given height, the

perturbations decrease as a function of distance from the z-axis [15].

It is noted that the perturbation of the space -charge -free electric field

predicted by eq (9) for an aperture will be more than that actually produced

by an ion counter, which is an aperture connected to a conducting tube.

However, the perturbations predicted by eq (9) are expected to be less than

the actual values in an electric field with significant amounts of space

charge because the aperture will not only perturb the surface charge densities

on the parallel plates (space-charge free case) , but also the volume charge

density between the plates.
3.3 Influence of Air Motion

In a practical situation, the measurements could be affected by air

motion due to the ion counter and by external sources such as wind,

ventilating equipment, etc. The present experiment was designed to elucidate

the effects of air motion produced by the ion counter, so all other sources of

air motion were negligible. The perturbation of the electric field via

perturbation of ion trajectories due to air motion produced by the ion counter

cannot be readily calculated because the air velocity is a complicated

function of position. However, knowledge of the air speed as a function of

distance from the aperture does provide some insight into the problem.

Several approximate theoretical treatments of air flow through an aperture can

be found in textbooks. For example. Lamb [17] provides theoretical

descriptions for non-viscous flow through an aperture using a two-dimensional

analysis, a three-dimensional analysis in prolate spheroidal coordinates, and

a three dimensional analysis assuming sinks in the plane of the aperture which

increase in strength as the edge of the aperture is approached. A model

calculation assuming sinks of constant strength in the plane of the aperture

is developed in Appendix B and is found to be in better agreement with

measurements along the central axis of an aperture (see figure B3) than any of

-* the above models. The constant sink model predicts a velocity u given by the

expression

u(r) = (-u^/27r)^|r-r'|"\r-r')dx'dy' , (11)

-> -> where u is the air speed in the plane of the aperture, r and r' are position

vectors above and in the plane of the aperture respectively, x' ,y' are Cartesian coordinates in the plane of the aperture, and Q is the area of the

aperture. Along the central axis of a circular aperture of radius R, eq (11)

reduces to

u = u^[l - z/(R^+z^)^/^] , (12)

where the z axis is taken to be the central axis.

How well eq (11) describes the air velocity away from the z-axis is not

clear. A comparison of preliminary off -axis air velocity measurements with

calculated values using eq (11) indicates that near an aperture, the

calculated values are too high. Air velocity measurements further from the

aperture were made difficult by ambient air motion and uncertainty in the

calibration of the instrumentation used for the measurements. However, an accurate expression for air velocity, while desirable, is not critical for

determining several semi -quantitative results regarding the transport of ions

into an ion counter.

Equation 12 indicates that at a point four radii above the aperture, the

calculated air speed is 3% of u . To put this result into perspective, it

should be noted that the average air speed at the entrance of a commercial ion

counter can be as high as 1 m/s . This compares with a drift velocity of about

1.4 m/s for a positive ion in a 10 kV/m electric field. Thus, close to the
aperture, the air speed can be comparable to the ion drift velocity and

significant perturbation of the electric field (in addition to perturbation

due to the aperture) may occur. It appears that the influence of air motion

caused by the fan in the ion counter at a distance of four radii above the

aperture, ~3 cm/s in the above example and of the same order of magnitude as ambient air currents, will be small.

An approximate view of how the electric field is affected by air motion

can be obtained by solving Poisson's equation assuming a constant air flow

parallel to the unperturbed electric field direction. Then the current

density is taken to be J = p(KE+W), where W is the air velocity, and the

expressions analogous to eq (3) and (4) are found to be

E(z) = -(W/K) + [N^+2J(d-z)/K£: ] "^^^

, and (13)

$(z) = V + (W(d-z)/K) - (Ke /3J) { [N^+2J (d-z)/K£ ]^/^-N^} , (14)

where N = (W/K)+E . Comparisons of E(z) calculated with W = and W 5^ permits rough estimates of the influence of air motion. For example, for the

experimental conditions in Sections 6 and 7, the change in E(z) 11.3 cm above

the bottom plate is less than 0.04% when W is changed from zero to 3 cm/s.

The model calculation may not be unreasonable because the air velocity rapidly

decreases as a function of distance from the aperture and changes slowly at a distance of four radii above the aperture (i.e., nearly constant, see

fig. B3) . The "effective radius" of the aperture used during the measurements

in Sections 6 and 7 is 2.8 cm. Thus, for the experimental conditions of the

present study, it appears that significant perturbations of the electric field

due to air motion do not extend to the top plate of the parallel plate system

(d=0.17m).

4. ION TRAJECTORIES AND LOSSES

The transport of ions into an aspirator- type ion counter under the

influence of an electric field and air motion is examined in a semiquantitative manner in this section. The actual ion trajectories are not

calculated because perturbations of an electric field with space charge by an aperture with air flowing through it are not readily characterized. In the

model that is considered, it is assumed that the ions travel along

trajectories determined by the addition of the ion drift velocity (product of

ion mobility and electric field strength) and air velocity, and do not

contribute to the magnitude or direction of the electric field which is

essentially space -charge free. The trajectories are taken to be in the

vertical y-z plane.

The electric field is found by taking the negative gradient of the

electric potential derived by Fry for a uniform space -charge -free electric

field perturbed by a circular aperture of radius R in the ground plane [15],

E' = -V$' , (15)

10
where

*' = A{sinhA + (2/7r)[l + sinhA-tan" (sinhA) ] )sin/i , (16)

A and /i are oblate spheroidal coordinates and are related to Cartesian

coordinates by the equations

y = R coshA cos/i (17)

z = R sinhA sin/x , (18)

and A is E R/2 . A circular aperture is used to approximate the square

aperture of the ion counter that is used during the measurements described in

Sections 6 and 7, but this approximation should not significantly affect the

conclusions reached here.

The horizontal and vertical drift velocities , v and v , are given by

y z ° -^

V = KE' , and (19)

y y

V = KE' , (20)

z z

where

E' = -(AS sin/xcos/zsinhA/B) + (AT sin/iiCosy^coshA/B) ,

2 2 E' = -(AS sin /icoshA/B) - (AT cos /xsinhA/B) ,

S = [coshA + (2/7r)coshAtan' (sinhA) + (2/7r)tanhA] ,

T = [sinhA + (2/7r) + (2/7r) sinhA tan" (sinhA)] ,

and

2 2

B = R(cosh A - cos /i)

Useful expressions relating the hyperbolic and trigonometric functions to

Cartesian coordinates in the y-z plane are [15]

2R^sinh^A = y^+z^-R^+[(y^+z^-R^)^+4R^z^]-^/^ , (21)

2R^cosh^A = y^+zW+[(y^+z^-R^)^+4R^z^]-^/^ , (22)

2b^sin^/x = R^-y^-z^+[(y^+z^-R^^+4R^z^]^/^ , and (23)

2b^cos^/i = y^+zW-[(y^+z^-R^)^+4R^z^]^/^ . (24)

11
For negative values of z, the negative root must be used in eq (21) when

solving for sinhA.

Equation 11 is used to obtain the air velocity components above the

aperture. As noted earlier, the air velocity values along the z-axis are well

predicted by eq (11) but the off- axis values appear to be too high. However,

the off -axis inaccuracies should not affect the conclusions of this section.

For a square aperture of side dimension 2R, eq (11) can be integrated to

give the following expressions for the horizontal and vertical velocity

components , u and u : y z

u = -(u /27r)log[(R+F)(-R+G)/(-R+F)(R+G)] , and (25)

u^ = -(uy27r)[tan"^(R(y+R)/zG) - tan'^(R(y-R)/zF) ] , (26)

2 2 2 1/2 where F = [R +(y-R) +z ] ^ , and

G = [R^+(y+R)^+z^]"^/^ .

In the y-z plane where the ion trajectories are calculated, the edge of the

square aperture coincides with that of the circular aperture assumed for the

drift velocity equations.

The equations of motion for positive ions under the influence of the

electric field and air motion through the aperture are for z>0

dy/dt = V + u , and (27)

dz/dt = V + u , (28)

z z

where the ion drift and air velocities are given by eqs (19) -(20) and

eqs (25)-(26). Below the plane of the aperture, the air speed is approximated

by a constant velocity, u , parallel to the z-axis. The steps for obtaining

eqs (19) , (20) , (25) and (26) are outlined in Appendix C.

Equations (27) and (28) have been solved on a computer using a variable

step-variable integration method with software developed at NBS [18]

.

Examples of trajectories for E = 15 kV/m, u = 1 m/s , R = 0.025 m, and

K = 1.3 X 10' m /Vs are shown with solid lines in figure 5. The time-offlight to the plane of the aperture for each trajectory was arbitrarily taken

-3

to be 50 X 10 s. Also shown in figure 5, with dashed lines, are ion

trajectories assuming no electric field; the time-of -flight is again

.3

50 X 10 s. The surfaces that bound the trajectories with and without an electric field define volumes of charge that reach the aperture during the

asstomed time interval. Ignoring possible loss mechanisms in and below the

12
0.024 0.026 0.028

cm

Figure 5. Ion trajectories for air speed in plane of aperture of 1 m/s. The

solid curves show influence of 15 kV/m electric field. Dashed

curves are for no electric field. The time-of-f light for all

trajectories is 50 ms. The volume occupied by the ions that enter

the aperture when E * 0, V , exceeds volume of air, V, which

enters in the same time. Inset shows effect of mobility value on trajectory near aperture.

13
plane of the aperture, the significance of the different volumes can be seen

by examining the expression for measured ion density, eq (1),

P^ = I/M . (29)

Expressing I as charge per unit time, Q/t, and M as air volume per unit time,

V/t,

P^ = Q/V . (30)

The charge Q can be expressed as the product of average charge density, p , 3. and volvime, V , occupied by the charge. Then

Pma= P V'/V . (31)

When there is no electric field, the volume of charge that enters the aperture

coincides with the volume of air (V = V) and the measured charge density

equals the average charge density in space. With an electric field, V is

greater than V and the measured charge density will exceed the average value

in space and thus be in error.

As the air speed is increased, the difference between V and V decreases

and p approaches p . Figure 6 shows ion trajectories with and without an electric field for u equal to 6 m/s . While the air speed may be

unrealistically high for typical ion counter operation, the smaller difference

between V and V is apparent.

Losses in and below the plane of the aperture can occur because of ion

trajectories which terminate near the edge of the aperture. For example, the

inset in figure 5 suggests that some trajectories less than ~1 mm from the

-4 2 edge of the aperture (K = 1.3 x 10 m /Vs) will not "clear" the aperture.

This would represent approximately 8% of the ions that reach the aperture

assuming a uniform charge density across the aperture.

It should also be noted that the trajectory calculations in figure 5 (except for the inset) have been performed for a single ion mobility value,

-4 2

1.3 x 10 m /Vs. A distribution of mobilities normally exists and ions with

-4 2 mobilities greater than 1 . 3 x 10 m /Vs could also fail to clear the aperture

as shown in the inset of figure 5. Interestingly, if the product of mobility

and electric field (drift velocity) is kept constant, the trajectory remains

unchanged for a given air speed.

If a duct of the same cross section as the aperture is introduced below

the aperture, loss of ions will occur via collisions with the wall of the

duct. Assuming for simplicity that the trajectories in figure 5 remain

unaffected by the duct, calculations show that ions entering the aperture 5 mm

from the edge (y = 2 cm) will collide with the duct about 1 . 3 cm below the

plane of the aperture. This loss as well as the loss of other ions passing

through the aperture further from the z-axis would amount to about 36% of the

14
14, I T—-^

12 - ^

10 -

- V

^- Uo =6 m/s

8 "" ..^-"^ E=15kV/m

- K^LSxIO'^^m^/Vs

6

-

_ ~^H\ '' 1 /x

E 4 o ^

- /'\

' 1 J" \

1 / // \ /-Uq = 6 m/s

/ / W \/ E=°

2

' ///"V/

' /\A

1 //"-"I (l^^\^^^^\^^v^^\^^^^\^^^^^\V\^^^^\v^^^^'^^^^^^^\^^"^^^

2 4\ 4 6 8 10 cm

-2

1

1 ^Edge of aperture

1

1

-4 - -

-6

Figure 6. Ion trajectories for air speed of 6 m/s in plane of aperture. The

solid curves show influence of 15 kV/m electric field. Dashed

curves are for no electric field. The time-of-flight for all

trajectories is 50 ms. The volume occupied by the ions that enter

aperture when E .' o i V, exceeds volume of air, V, which enters in same time.

15
total number of ions reaching the aperture, again assuming that the ion

density were uniform over the area of the aperture.

The excess ions entering an ion counter due to an external electric field

which attracts ions to the ion counter and the ion losses which subsequently

occur to the walls of the ion counter was noted by Swann early in this century

[19]. He concluded that the ion current to the walls was just equal to the excess ion current due to the electric field, independent of air speed, and

that the electric field did not influence the ion density measurement [20].

However, because Swann appears to assume that all of the electric field lines

terminate on the walls of the ion counter, his conclusion that all the excess

ion current goes to the walls must be qualified. Some field lines could

terminate on the electrodes of the ion counter and contribute to a higher ion

density measurement. For example, calculations show that field lines within a radius of 5 mm of the center of the aperture will travel at least 4.5 cm below

the plane of the aperture before reaching an imaginary wall at a radius of

2.5 cm.

An ion loss mechanism which has been ignored above, because of the

simplifying assumption that the ion contribution to the electric field is

negligible, is one which considers Coulomb repulsion between the ions. In

reality charge densities in the vicinity of dc transmission lines can exceed

_ o o 1 X 10 C/m [1] and the Coulomb interactions are not insignificant. The

loss mechanism can be approximately modelled by considering a circular

cylinder of charge initially of density p(z=0) extending downward from the

aperture along the z-axis as shown schematically in figure 7. Ignoring the

electric field which penetrates the aperture from above, ions at the outer

surface of the cylinder will experience a radially outward electric field

given by, from Gauss' law,

E = p(z=0)R/2£ , (32)

and a drift velocity of

V = KE = Kp(z=0)R/2£ . (33)

Under the influence of the air velocity u along the z-axis, the ions will

travel downward a distance L after a time L/u . In the same time, the

radially outward displacement, s, will be approximately

s«v^L/u =Kp(z=0)RL/2£ u . (34) d ' o ' o o

If there is a cylindrical duct of radius R below the aperture, the radially

displaced ions will be lost to the duct. The fraction of ions lost can be

estimated by comparing ion densities in disks of thickness Az near the

aperture and at a distance L below the aperture. The ratio of the densities

is given by

/?(z=L)/p(z-0) = 7rR^AzA(R+s)^Az = R^/(R+s)^ . (35)

16
p(z-L)

S=:Kp(z = o)RL/2eoUo

Figure 7. Schematic view showing influence of Coulomb repulsion on ions

below plane of aperture. The effects of the electric field above

the aperture are ignored.

17
The results using this expression are in good agreement with more exact

treatments of the problem which are Independent of geometry. For example, it can be shown that [21]

p(z2)/p(z^) = [l+(p(z^)Kr/£^)]"^ , (36)

where t is the time -of- flight between points z^ and z..

Loss of ions to the duct by diffusion represents yet another loss

mechanism. For a cylindrical cloud of charge, the average square of the

displacement in the radial direction because of diffusion is given by [22]

2 r = 4Dt

or

where D is the diffusion coefficient. Equation (37) can be rewritten in terms

of the ion mobility using the Einstein equation [22]

K = eD/kT , (38)

where e is the ionic charge, k is the Boltzmann constant and T is the

temperature in degrees Kelvin. That is

s' = [4kTKr/e]-"-/^ = [4kTKL/u e]^^"^ . (39)

The lateral displacement of the ions due to the combined effects of Coulomb

repulsion and diffusion as a circular cylinder of charge moves below the

aperture can be estimated by adding s and s' . The relative importance of

Coulomb repulsion and diffusion is found by examining the ratio of s and s'.

That is,

s/s' = (p(z=0)R/4£ )(Kre/u kT)^'^ . (40)

For the experimental conditions in Section 7, s/s' is of the order of unity in

a 5 cm long duct.

5. CALCULATED CHARGE DENSITY

In Section 3.1 it was shown that for sufficiently small ion current

densities, the uncertainty in the value of the charge density between parallel

plates could be made relatively small, i.e., ±3% for the example considered.

Here it is shown that the charge density which the ion counter should measure

18
in the parallel plate system can be determined with an uncertainty less than

one-half the range of values given by p{z.) .

In the presence of a dc electric field, the ion current t?irough the plane

of the aperture of the ion counter is given by

I = / p(x,y,0)(u+v).dS ^41;

-+ -* where dS is an element of area in the plane of the aperture of area S, u is

-> the air velocity and v is the ion drift velocity. If all of the ion current

were to reach the collecting electrodes of the ion counter, the measured

charge density obtained using eq (1) would be

p^ = I/M = Jg p(x,y,0)u.dS/Jg u.dS + Jg p(x,y,0)v.dS/Jg u-dS . (42)

The second term in eq (42) is considered an error to the measurement [19]

because the validity of eq (1) rests on the assumption that the ions are transported into the ion counter only by the air that flows through the ion

counter [10]. As noted earlier, it is expected that the contribution of the

second term can be made negligible provided there is adequate shielding of the

electric field. Thus, the charge density which should be measured in the

absence of electric field effects (and ion losses below the plane of the

aperture) is given by the first term of eq (42) . If the first term in eq (42)

can be calculated from theory, it can serve as the known value of charge

density which is used to calibrate ion counters.

Lack of knowledge of the charge density in the plane of the aperture,

because of perturbations, prevents the evaluation of the first term in

eq (42). However, the integrals can be determined on a surface for which the

perturbations of the charge density become negligibly small. This surface

coincides with the surface on which the electric field perturbations become

negligible and is designated S .

The shape of S can be estimated at low air speeds by examining the

spatial dependence of the electric field perturbation due to an aperture in

the absence of space charge. An examination of the ratio E'/E in the y-z

plane (see eqs (19) and (20)) shows that surfaces of nearly equal perturbation

(absolute value) are, because of axial symmetry, hemi -ellipsoids . The

intersection of the surface with the y-z plane yields a hemi -ellipse with

semi -minor and semi -major axes y and z as shown in figure 8. Thus, the

calculated charge density can be expressed as

p^ = L p(z)u.dS/J_ u-dS = (J/K) L p'(z)u.dS/r u-dS (43)

O O CO

where

19
Aperture

Perturbation of E

and p 21

Figure 8. Hemi-ellipse and coordinates for calculating charge density, p

20
-^ 2222 221/2 dS = a(y,z)(27ryyz^)[z^(z^-z^) + y^z^J-'/^dz ,

a(y,z) = [(2y/y^)j + (2z/z^)k]/[ (2y/y^)^ + (2z/z^)2]^/2 ,

A A

->u = u i + u k , y-^ z

and p(z) = (J/K)p'(z) = J/K[E ^+2J(d-z)/K£ ]^^'^.

A The vector a(y,z) is a unit vector normal to the hemi-ellipse in the y-z

A A plane; j and k are unit vectors parallel to the y and z axes respectively.

The uncertainty in the value of p is dependent, in part, on how well y , z and the distribution of relative air velocities on S are known [23]. The

distribution of relative air velocities on the surface of integration is the

relevant parameter because u can be

o numerator and denominator of eq (43)

.

relevant parameter because u can be factored out of the integrals in the

o ^

6. MEASUREMENT RESULTS: PERTURBATION OF ELECTRIC FIELD

From the preceeding sections it is recalled that in order to calculate

the ion density in the parallel plate apparatus, it must be demonstrated that

the perturbation of the electric field due to the aperture of the ion counter

does not significantly extend to the top plate. A similar restriction applies

to the influence of air motion due to air being drawn through the ion counter.

The approximate theory presented earlier on electric field perturbations due

to an aperture and air flow through an aperture suggests that a parallel plate

apparatus with spacing greater than four times the radius of the ion counter

aperture may be adequate for producing a known ion density. In the following

sections, measurements of the perturbed electric space potential in the

parallel plate system as a function of distance above an aperture in the

bottom plate are described and compared with space potential values without an aperture. The measurements are performed with the presence of space charge.

An estimate of the electric field perturbation is then made using eq (10)

.

The effect of air flow through the aperture on the space potential is also

examined.

6.1 Space Potential Probe

Measurements of the electric space potential between the parallel plates,

in the presence of space charge , were made with a space potential probe very

similar in design to one reported by Penney and Matick [24] and Matick [25].

A sketch of the probe with its nominal dimensions is shown in figure 9. The

operation of the probe is described briefly here; a full account is given in

[24] and [25] . The space potential probe is supported between the parallel

plates approximately along an equipotential surface (i.e., horizontally) with

a copper- tube handle. The copper handle and frame support brass guard

cylinders which contain the 0.0066 cm diameter stainless steel wire probe.

21
Teflon

spacers

1.27 cm diameter

copper tubing

94 cm

Handle

1

High voltage 39 cm

power supply

0.0066cm

diameter

probe

wire

-^

21cm

Slanted face

-90 cm- i

Guard cylinder 1.1 cm

diameter brass tubing -

Teflon spacer

Screws

/ 86 cm

Electrostatic voltmeter

Figure 9. Schematic view of space potential probe after Penney and Matick

22
The slanted ends of the guard cylinders are oriented to face the bottom

grounded plate. By varying the voltage on the guard cylinders, V , and

measuring the potential on the wire probe, V . with an electrostatic

voltmeter, Penney and Matick report that a graph of wire potential versus

guard- cylinder potential shows a plateau in the value of V when the guard

potential is near and at the space potential. The voltage of the plateau is

the largest space potential intercepted by the wire probe plus a small

additional potential due to charging of the wire.

The NBS potential measurement data do not show the well defined plateau

reported by Penney and Matick, but do indicate relative space potentials with

sufficient sensitivity for performing perturbation measurements. For example,

figure 10 shows plots of probe -wire potential versus guard- cylinder potential

at heights of 8.5 cm and 9.5 cm above the bottom plate of the parallel plate

system. The difference in space potential for the two positions is determined

by examining the intersection of the experimental curves with the line given

by V =V . Calculation of the difference in space potential for the two

P g

heights is performed using eq (4) for the measured values of

J(1.14 X 10'^ A/m^), V^(1800 V), K(1.34 x lO'^ m^/Vs) , and d(0.15 m) , and

amounts to 112 V [4] . The (vertical) difference in the measured potentials at

the points of intersection with the line V =V is about 109 V which is in good

g P

agreement with the calculated value. The results in figure 10 show that a difference in potential of about 9% (the change from 8.5 cm to 9.5 cm) is

readily seen with this measurement technique and that potential differences of

less than 1% can also be resolved. The absence of a well defined plateau may

be due to insufficient isolation of the wire probe from ground because, at a given height, the value of the measured potential (point of intersection) is

consistently lower than the calculated space potential.

6 . 2 Space Potential Perturbation Measurements

The calculated vertical ion density profiles in figure 3 indicate that an

ion density that varies by 6% between the parallel plates can be generated

-ft 9 when V =2650 V, J=0.1 x 10 A/m , and d=0.17 m. Measurements of the current

density profile on the bottom plate of the parallel plate system using a flat

moveable probe reveal, for the above conditions, variations of the current

density as large as ±9% near the center of the plate and temporal fluctuations

-ft 9 of about ±3%. By increasing J to near 0.25 x 10 A/m (while maintaining V

and d fixed) and increasing the drift region between the first screen and top

plate from 8 cm [4] to 12 cm, the nonuniformity in J can be decreased.

Figure 11 shows measurements of the current density on the bottom plate as well as the locations of a 5 cm x 5 cm aperture for an ion counter, an electrically isolated patch for measuring current (to determine J), and an electric fieldmeter probe (field mill) . Each value of current density is the

average of 10 measurements which in turn are time average measurements lasting

1.7 seconds. The standard deviation of the 10 measurements is typically less

than 2%. Each current density value in figure 11 has been normalized by the

average of 17 measurements in a circular area of 0.7 m diameter. Ignoring the

23
1.40 -

% 1.36

Z

111 H 1.32

O

Q.

1X1 m

O

£ 1.28

I UJ

1.24

1.20

I

' 1

' r

Vg=Vp

0.8 1.0 1.2 1.4 1.6 1.8

GUARD-CYLINDER POTENTIAL (kV)

Figure 10. Measurements of space potential at 9.5 era and 8.5 cm above the

bottom plate of parallel plate system for conditions described in

text. The measured potential difference agrees well with the

calculated value of 112 V.

24
160

140

120

100

E 80

o

60

40

20

-| 1

1 1 T T

0.99 1.01 1.02 1.04 1.10 1.10

• • • • • •

1.01

0.99 0.95 1.00 1.04 1.02 1.06 0.99

1.05 1.01 0.96 1.01

• 0.99

Probe • 1.02 1.00 1.03 \ 0.97

• • • \ •

1.04 1.03 0.97

0.98 1.01 0.99

• • •

^x Current sensing element

097 1-01 1.02

Aperture

1.01 1.03 / 1.00

-••• 1.08 1.07 1.04 ^__''06___^ 102 1.04 1.07

• •••

1.03 1.01 1.04

• • • 1.00 1.02 1.05 1.04

• • • •

20 40 60 80

cm

100 120 140 160

Figure 11. Measurements of the current density on the surface of the bottom

plate. The measurements are obtained with a moveable probe and

normalized with respect to the average of 17 measurements in a circular area of 0-7 m diameter. The average unormalized J value

is near 0.25 x 10 A/m .

25
temporal fluctuations, most of the current density values in a circular area

of 1 m diameter are within 4% of the central average.

With V =2650 V, d=0 . 17 , J=0.25 x 10 " A/m , and the current density

profile shown in figure 11, measurements of the space potential were made as a function of height above the bottom plate with and without a 5 cm x 5 cm

aperture. The space potential probe was located over the aperture (see

fig. 11) and could be moved vertically with a screw-driven vertical

displacement apparatus located outside the parallel plate system. The "noaperture" condition was established by sliding a sheet of stretched aluminum

foil over the aperture. Figure 12 shows examples of graphs of probe

potential, V , versus guard potential, V , near the intersections with the

r o line V =V at various heights above the bottom plate with and without the

P g

aperture. The perturbation of the space potential due to the aperture are expressed in volts and percentages at each height. For purposes of comparison

with perturbations predicted by eq (8) , which is valid only for space-charge

free conditions, the "radius" of the square aperture is made to satisfy the

2 2 relation ttR =25 cm , i.e., R=2.82 cm. Table 1 shows the results of

perturbation measurements made over a period of several days. Uncertainties

in the perturbation measurements are shown in parentheses in Table 1 and are

due mainly to uncertainties in reading the electrostatic voltmeters used to

measure the probe potential and small drifts in the electrostatic voltmeter

reading. As expected, the measured perturbations of the space potential

exceed the values predicted by a theory that ignores space charge.

Measurements at significantly greater distances above the aperture were

prevented by possible contact between the space potential probe and a portion

of the top plate which extends downward along the perimeter (fig. 1)

Table 1 Space Potential Perturbations

%Perturbation %Perturbation

of ^' feq(8)

Measured ( o^O)

0.16 0.37, 0.31, 0.48, 0.37 (±0.10)

0.37 0.70, 0.68 (±0.15)

1.16 1.86, 1.60, 1.83, 1.80 (±0.20)

5.96 7.05, 6.28 (±0.4)

The additional perturbation due to air motion was examined by drawing air

through the aperture. The air flow was measured with a turbine- type flowmeter

and the air speed in the plane of the aperture was calculated by assuming a uniform velocity across the opening. No measureable (i.e. >0.1%) change in

space potential could be observed at a height of 11.3 cm (4R) above the

aperture for average air speeds between 1.6 m/s to 6 . 6 m/s in the plane of the

aperture

Height Above

Bottom Plate

4R

3R

2R

I.IR

26
11.3 cm 5.6 cm

1820

(4xR) /^Vp=Vg 930

(2xR) ^Vp=Vg

^ 1800

Aperture / A—No

/ 1 aperture

>

a

>

920

910

^^— Aperture

>

^ 1790 1 16.5 V( 1.8%)

1780 ^y 6.5 V(0.4%)

900

[/\\ 1

1 ^No aperture

1770 , ' 1 1 890

8(

1 1 1 16(DO 1700 1800 1900 DO 900 1000 1100

Vg(V) Vg (V)

1360 -

1320

Vp=Vg

No aperture

1200 1300 1400 1500

Vg(V)

500

9 490

Q>

480 -

470 -

460

(l.lxR)

Aperture

No aperture

J I 300 400 500 600

Vg(V)

Figure 12. Measurements of space potential perturbation due to 5 cm x 5 cm aperture in ground plane as a function of height above ground

plane.

27
6.3 Discussion of Results

The measurements of the preceeding section (for V =2650 V,

K=1.3 X 10 m /Vs, d=0.17 m, J=0.25 x 10 ' A/m ) indicate that the space

potential perturbation due to the aperture at a distance of four radii above

the aperture is about 0.4%. If the electric field perturbation at four radii

above the aperture is estimated using eq (10), a perturbation of less than -1%

is expected. The perturbation of E will be smaller yet at the top plate which

is 0.17 (6R) above the aperture. For points off the z-axis, the perturbation

decreases further.

The absence of any change in probe wire potential because of air flow

past the wire four radii above the aperture may not indicate an absence in

space potential perturbation. Hara and coworkers have shown that for a cylinder of radius 0.1 m in an electric field with conditions comparable to

those in the present measurements, the cylinder potential remains unaffected

13 by air motion if the leakage resistance to ground is less than order 10 ohms

[20]. It is recalled in this regard that the low space potential measurements

reported earlier suggested insufficient resistance between the wire probe and

ground. Therefore, one must rely in part on the theoretical arguments made

earlier that perturbations of the electric field due to air motion for air

speeds of 1 m/s in the plane of the aperture will be insignificant (i.e.

<0.1%) near the top of the parallel plate system.

7. MEASUREMENT RESULTS: COMPARISON OF CALCULATED AND MEASURED ION DENSITY

7.1 Calculated and Measured Ion Densities

Experimental and theoretical results have been presented that suggest for

the conditions V =2650 V, K=1.3xlO" m /Vs , d=0.17 m, J=0. 25x10 " A/m , and a square aperture of side dimension 0.05 m, significant perturbations of the

electric field do not extend to the top plate of the parallel plate apparatus.

With approximately the same conditions (the value of K increased slightly to

near 1.4x10 m/Vs), measurements of the ion density were made in the ground

plane and compared with calculated values of the charge density. A schematic

view of the entrance to the ion counter with some nominal dimensions is given

in figure 13. The collector plates in the ion counter are recessed about 10 cm below the plane of the 5 cm x 5 cm aperture and are 7 cm wide. The

polarizing plates are recessed behind the collecting plates 3.5 cm. The

lengths of the collector and polarizing plates are 18 cm and 14 cm respectively and the spacing is 2 cm. A three terminal measurement of the

parallel plate capacitance yielded a value of 212 pF. Polytetrafluorethylene

(PTFE) is used to fill the space between the plates and ion counter housing

and is recessed behind the collecting plates by 6 . 5 cm. The square aperture

at the entrance of the ion counter is approximately centered over the parallel

plates as shown with dotted lines in figure 13. The polarizing voltage for

all the measurements was 429 V which was adequate for capturing all the small

ions for the air flow rates used during the measurements . That is , the

-7 2 critical mobility, k , in eq (2) varied between 2.16x10 m /Vs to
13 cm

PTFE

Collecting

electrodes

Outline of aperture

(5 cm X 5 cm)

Polarizing

electrodes

(Recessed 3.5 cm)

Figure 13. Top view of ion counter entrance with dashed outline of aperture

located 10 cm above entrance. Nominal dimensions are indicated.

The spacing between the collecting and polarizing electrodes is

2 cm.

29
1.58x10 m /Vs as the flow rate was increased from 2.22x10 m /s to

-3 3 16.2x10 m /s . A pump was used to draw air through the ion counter and the

air flow was measured with a turbine -type flowmeter. The air flow through the

ion counter could be changed by varying the amount of ambient air which was leaked into the pump

.

Figure 14 shows the results of positive charge density measurements, p , as a function of average air velocity in the plane of the aperture, assuming a constant velocity across the aperture. Also shown are calculated values of

the charge density, p , which are determined using eq (43) and assuming values

for y and z of 13.75 cm and 17 cm respectively. Comparisons of measured and

calculated charge density values with the introduction of a 5 cm x 5 cm metal

duct extending 5 cm below the plane of the aperture are shown in figure 15.

The uncertainty in calculating p is estimated by considering the

uncertainties in the terms of eq (43) . The uncertainty in K is less than

±6% [4] . The uncertainty in J is less than ±6% and takes into account the

variation in J on the bottom plate, time averaging of the current

measurements, uncertainty of the area of the current sensing patch, and

calibration of the electrometer used for the current measurement. E is

o determined from the expression [4]

3JV /Ke = (E^ + 2Jd/K£ )-'-"^

- E

^

, (44)

t' o o o o

and is dependent on the uncertainties in J and K. The uncertainty in d is

less than 0.5%.

The influence of these uncertainties on the value of p is considered in

c two parts, (1) the effect on the integral in the numerator in eq (43) and (2)

the effect on the factor multiplying the integral (J/K) ; the integral in the

denominator is a constant. The uncertainties in the values of the parameters

under the integral sign, for a given y ,z pair, leads to an uncertainty in

the value of the integral of less than 0.6%.

The values of J and K are determined independently and a root-mean-square

(rms) summation could be used to find their combined uncertainty in the

quotient multiplying the integral. However, because the 0.6% uncertainty in

the integral is correlated with J and K, it is arbitrarily added to the

uncertainty in J , i.e., 6% + . 6% = 6 . 6%

.

As indicated above, the values of y and z are taken to be 13.75 cm and

^o o 17 cm respectively. The value of z is obtained by considering the decrease

in the values of measured space potential perturbations (Table 1) as extrapolated to the top plate of the parallel -plate system. At the top plate,

the space potential perturbation appears to be about 0.2% or less. The

electric field perturbation is estimated to be (Section 6.3) about 0.4% or less and considered negligible. The added perturbation due to air motion

30
^ 1-2

COE

O

O 1.1

X

>

W 1.0

LUQ

LUO

<

I

o

0.9 -

—I r p(z=0.17)

o x--

_o _o. -O

-^ O

a

p p

Top plate

Bottom plate

Uo ~ 2 m/s f

-v^S2,p(z = 0.17)

r

± ±

\

-Si,p (z)

yo

2 3 4 5

AVERAGE AIR SPEED (m/s)

Figure 14. Positive charge density measurements, p , as a function of average air

velocity in plane of aperture. Calculated values of the charge density,

p , are shovm assimiing that y and z are 13.75 cm and 17 cm

c o o respectively. Typical error bars are indicated at u = Im/s . As the air

speed increases, the surface on which the electric field perturbation

remains negligible is represented approximately by a truncated hemiellipsoid as shown in inset.

E 1.1

*^O

h-o

X 1.0

>-H

coz

LUQ 0.9

LUo

cc<

X

o 0.8

-

^

1 1 1 1 1 1

-

/With duct losses _q,.. ^o

, L J ..-'dy^y^ o^^^ ^ X ^ / ^^ / ^o

( {

.1 1 1 1 1

1

AVERAGE AIR SPEED (m/s)

Figure 15. Positive charge density measurements for the same conditions as in

figure 14 and with the introduction of a 5 cm long duct below the plane

of the aperture. An estimate of ion losses in the duct due to Coulomb

repulsion and diffusion, assuming no turbulence, is shown with a solid curve

.

31
through the ion counter for u = 1 m/s is also considered negligible.

Assuming that the spatial dependence of the electric field perturbation

(absolute value) is the same as for the space-charge free case, y is 13.75

cm.

The calculated value of charge density, p , is not highly sensitive to

the choice of y when y is so far from the aperture. Allowing an uncertainty

of ±3 cm (22%) in the value of y leads to less than ±0.9% uncertainty in the

value of p . This uncertainty in y also takes into account some uncertainty

in the distribution of relative air velocities on the surface of integration,

S . The value of p is not expected to be very dependent on the velocity

distributions because, while not isotropic, the distribution of relative air

velocities changes slowly on the surfaces that are considered. The total

estimated rms uncertainty is therefore taken to be

2 2 2 1/2 [(6.0%) + (6.6%) + (0.9%) ]/

which is less than 9%.

The uncertainty in the values of p is estimated to be less than ±6%. m

This figure includes uncertainties in the calibrations of the electrometer

used for measuring ion current and the flowmeter for measuring air flow, and

statistical fluctuations in the ion current and air flow measurements. The

scatter in the measured values of p indicates the reproducibility of the

measurements

7.2 Discussion of Results

The results in figure 14 show that while the measured ion density is less

than the calculated charge density when u is about 1 m/s, within the

uncertainties of the measurement and calculation there is agreement between

the values of p and p . The lower measured value may be due to ion losses in

m c the region between the 5 cm x 5 cm aperture and the 7.2 cm x 8.2 cm opening to

the collecting plates (fig. 13) as well as within the ion counter itself. The

region between the 5 cm x 5 cm aperture and collecting plates is difficult to

model. The airflow is better approximated as a free jet than airflow through

a duct. Turbulence at the boundary of the expanding jet occurs [26] and

causes mixing with the surrounding air at rest, leading to loss of some ions.

Rough calculations of lateral displacement of ions due to Coulomb repulsion

and lateral movement of the neutral air, i.e., superposition of displacements,

show ion losses that are greater than indicated by the data, which seems unlikely. Thus, while ion losses occur, it may be that the turbulence, in the

form of eddy currents of air at the boundary of the jet, prevent the escape of some ions. No attempt was made to theoretically correct the p values in

figure 14 for losses below the 5 cm x 5 cm aperture.

32
As the air speed through the ion counter is increased, the spatial extent

of the electric field (and charge density) perturbation will increase.

Assuming for simplicity that the air motion does not greatly change the charge

density at the top plate, /3(z=0.17 m) , an approximate expression for the

calculated charge density is given by

p^ - [Jg P(z)u-dS + /g p(z=0.17)u.dS]//g ^g u.dS

- [L p(z)u.dS + p(z=0.17)L u.dS]/r u-dS (45)

^1 ^2 ^r^2

where S- and S- are, as shown schematically in figure 14, portions of the

boundary surface where the electric field perturbation becomes negligible. As

the air speed increases, S, will increase relative to S.. . The contribution of

the second term in eq (45) to p will increase because of the large p value

ip{7.) is greatest for z=0.17) and the increasing surface area. The larger

values of p at the higher air speeds likely reflect, in part (duct losses

will also decrease), the increased value of the "calculated" charge density.

It is noted that the average air speeds in commercial ion counters are normally less than 1 m/s and the loss of ions in such devices due to Coulomb

repulsion and other loss mechanisms could be significant. This is also

suggested by the extrapolation of the measured charge density values in

figure 14 to air speeds below 1 m/s.

Introducing a square duct that extends 5 cm below the plane of the

aperture has a significant impact on the values of p as shown in figure 15.

The solid curve in figure 15 is the calculated density taking into account ion

losses due to Coulomb repulsion and diffusion [eqs (35) and (38)] in the duct

and assuming no further losses below the duct. An effective radius of

0.0282 m is assumed for the square duct (see Section 6.2 and Appendix B) . The

solid curve can only be regarded as a rough approximation because of the use

of eqs (35) and (38) in a square duct, and because the effects of turbulence,

which may be present in the duct for u > 0.6 m/s, are ignored [27]. As in

the case where there is no duct, the ion losses decrease as u is increased,

reflecting fewer losses in and below the duct, and a larger value of p .

The generally good agreement between calculated and measured values of

charge densities in figures 14 and 15 near u =1 m/s supports Swann's [19]

prediction that the extra ions which arrive at the aperture because of the

external electric field (compare V and V in figures 5 and 6) are lost before

reaching the collecting electrodes of the ion counter. The number of extra

ions that are lost is significant. The approximate results in figure 5 indicate that when u is 1 m/s and E is 15 kV/m, more than twice as many ions

could arrive at the aperture than would when there was no electric field

[i.e., (V'/V)>2]. The average electric field strength between the parallel

33
plates for the ion density measurements shown in figures 14 and 15 is near

15.6 kV/m.

It was noted in Section 4 that any electric field lines terminating on

the collecting plates of the ion counter could contribute to an excessively

high measurement of ion density. The error from this effect will increase if u is decreased or if the external electric field, E, is increased because of

o the greater discrepancy between the volumes V and V in eq (31) . Therefore it

is desirable to have some length of duct in front of the collecting electrodes

of the ion counter to provide shielding against the external field. The

appropriate length of duct can be determined experimentally by observing

whether significant ion current to the collecting electrodes can be detected

in the presence of the electric field (with ions) when there is no air flow,

i.e. M=0 . However, for the large ion densities in the vicinity of HVDC

transmission lines, the effects of Coulomb repulsion can cause significant

loss of ions to the duct. The additional loss due to diffusion may be

comparable in magnitude [eq (40)]. Correction for these losses using eq (34)

and (39) cannot be readily made, in general, because p , K and the influence

of turbulence are not known. There may be some advantage in placing an aperture at the entrance of the duct which is smaller in cross -sectional area

than the duct. The measurement results in figures 14 and 15 show that this

step can significantly reduce ion losses to the duct. Making u as large as practically possible also reduces ion losses. It is cautioned, however, that

adding a duct and aperture to a commercial ion counter could affect the

airflow, M, because of an increased load on the fan.

While the above steps can reduce the effects of an external electric

field and ion losses to a duct, it appears that an experimental calibration

will still be required in order to perform charge density measurements with a known uncertainty. The calibration can be a function of average air speed and

ion density because of the possible effects of Coulomb repulsion, turbulence

and diffusion.

In closing this section, it is interesting to note the relation between

p and the calculated value of p in the ground plane. The latter quantity has

been used as the "known" value of the charge density during experimental

checks of ion counters [13]. For the parallel plate geometry and electrical

conditions during the present study, p exceeded the charge density in the

ground plane by about 5.8%. The difference would be greater if the ion

contribution to the electric field strength were larger.

8. CHARGE DENSITY MEASUREMENTS BENEATH MONOPOLAR HIGH VOLTAGE LINE

In addition to the studies using the NBS parallel plate apparatus,

laboratory measurements of charge densities under a monopolar high voltage

line have been performed. While the unperturbed charge densities are not

characterized as well as in the parallel plate apparatus , the measurement

results support the observations made in earlier sections.

34
8 . 1 Measurements in Ground Plane

Figure 16 is a schematic view of the experimental arrangement used to

generate an electric field and current densities at the ground plane similar

to those near a HVDC transmission line. The monopolar line, which was 4 m

long and 2 m high was connected to a variable high voltage power supply. A

square table 1.2 m on a side and 0.3 m high was erected under the line and

served as a local ground plane. The table was covered with aluminum, with a line-to- table spacing of 1.7 m. As indicated, the ion counter described in

Section 7.1 was located under the table with an inlet 7.5 cm in diameter

located in the ground plane. Other instrumentation included a field mill for

measuring the electric field and surface mounted current sensors for

determining the vertical current density. These current sensors, located on either side of the ion counter inlet and along with the field mill and ion

counter inlet, were colinear with the high voltage line. The experiments were

performed in a laboratory in which there was limited temperature and humidity

control. During the experiments, the temperature varied from 21-27°C and the

relative humidity from 55-70%. It should be noted that the value of electric

field and current density could not be independently varied, but were

determined (for fixed geometry) by the line operating voltage.

The table shown in figure 16 was constructed with a movable center

section so that the field and current densities along the line could be mapped

for different operating conditions . This was done to determine the uniformity

along the line and to insure that the results were not dependent on precise

locations of sensing elements. For the line operating voltages of 28, 36, and

47 kV, the electric field and ion current densities along a 0.7 m distance

were uniform to within ±3%, for both positive and negative line voltage. For

these operating voltages, the nominal electric field had values of 14.8, 20.8,

and 29.8 kV/m respectively. The corresponding vertical current densities were

2 0.1, 0.21, and 0.43 //A/m . Slightly lower values were observed for negative

voltage. In practice, the line voltage was adjusted to give the same electric

field at the surface of thor both positive and negative voltages.

For a given line operating condition, the air flow through the ion

counter was varied and the charge density determined using eq (1) . The flow

rates were measured using a turbine flow meter. Polarizing potentials were

such that for all flow rates, there was complete collection of small ions.

During these measurements, the electric field and current to the sensing

elements on either side of the counter inlet were also recorded, and used to

calculate the charge density at the surface of the ground plane, p , using

-4 2 eq (5). A mobility of 1.4 x 10 m /Vs was assumed for positive ions and

-4 2 1.8 X 10 m /Vs for negative ions. The results of measurements of p with

positive ions for two electric field strengths as a function of air flow are shown in figure 17

Because of the complicated duct geometry, the duct losses due to Coulomb

repulsion are estimated using eq (36)

p/p = [1 + (p KL/£ u

)]'-^ (46)

o o oo

35
DC line

7

Current

probe

Ion counter

inlet

Ion counter

Field mill

Elevated

ground plane

/////////////////

Figure 16. Schematic view of experimental arrangement. Elevated ground plane

is located on a table. Relevant dimensions are given in text;

figure is not to scale.

36
1 1 1 1 1

1 1 1 1 1 I r —r- -1

10.0 PQ

9.0 - ^ E = 29.8 kV/m — • ^^^ • C 8.0 - • -

^i*^ E • ^^^

O /

eo • /

O /

^ 7.0 - • / - X /

s.^ /

>1-§ 6.0 - ' -

LUQ

HIg5.0

<

— « ~ Pq

I

^

E=14.8kV/m O • 4.0 —

. •^-'^^""^ —

3.0 -

1 1 1 1 1

, Corrected for

estimated duct loss

1 1 1 1 1 1 1 1 1 2 4 6 8 10 12 14 16 18 20 22 24 26 28

M(x10^m^/s)

Figure 17. Ion density measurements (solid circles) for different volumetric

flow rates M. The ion density values at the surface of the ground

plane determined from eq (5) are designated as p . Estimates of

duct losses due to Coulomb repulsion are shown as solid

curves.

37
where L is the length of the duct and u is the average air speed. Due to the

bend in the duct, the calculated values of p using eq (46) represent the upper

limit on the charge density which can reach the ion counter because of losses

due to Coulomb repulsion. The solid curves in figure 17 show the predicted

charge densities for two electric field strengths, taking into account duct

losses due to Coulomb repulsion using eq (46) . The good fit to the data

-3 3 points when M is near 18 x 10 m /s is fortuitous because the value of K is

assumed and p instead of p is used in the calculation. The reasonably good

fit of the curves to the remainder of the data indicates that Coulomb

repulsion can account for much of the ion losses, and that the charge density

measurements appear to be independent of the external electric field as predicted by Swann.

8 . 2 Measurements Above Ground Plane

Ion counters are often operated above the ground plane for reasons of

convenience. If the ion counter assembly is referenced to ground potential,

ions will either be attracted to or repelled from the ion counter, depending

on the polarity of the ions. As noted in Section 6, Swann predicted that the

extra ions that are attracted to ion counter because of the external electric

field will not reach the collecting electrodes. This prediction was checked

by measuring the charge density above the ground plane under a monopolar line;

the external electric field near the ion counter was varied by changing the

reference potential of the ion counter assembly.

A schematic view of the experimental arrangement is shown in figure 18

The parallel plate ion counter described earlier was raised 0.43 m above the

ground plane in a horizontal orientation with insulating supports; the

aperture at the entrance was 2.54 cm in diameter and the distance to the

collecting electrodes was increased to about 24 cm. A battery operated

electrometer, also isolated from ground, was used to measure the ion current.

Measurements of the electric field and current density were made in the ground

plane using a vibrating plate probe [4] and flat current sensor [6]. Both

quantities were uniform within ±10% along the central region of the line.

Charge density measurements were made for various line voltages, and one representative set of results is shown in figure 19. The line voltage was

-60 kV and the electric field and current density were 27.2 kV/m and

2 0.63 /iA/m respectively directly under the line. The electric field in the

vicinity of the ion counter was controlled by varying the potential of the ion

counter with a high voltage dc power supply. Approximate measurements of the

unperturbed space potential at heights corresponding to the aperture were

performed with an electrostatic voltmeter and radioactively equilibrated

antenna [28] , and are indicated on the horizontal axis with a cross-hatched

-3 3 area. Charge densities were measured at two flow rates, 4.8 x 10 m /s and

-3 3 15.4 X 10 m /s. The scatter in the data is due in part to fluctuating air

currents in the room which can affect the flow of ions from the monopolar line

to the ion counter.

The data again suggests that the measurement is independent of the

external electric field for changes in the ion counter potential of

approximately 25 kV [29] . Losses begin to occur as the ion counter potential

38
-^

Corona wire

^

2.1 m

To blower,

electrometer

Ion counter

Variable

DC supply — Insulated

supports —

7 7~1 1~/ / / / 7 //////

h

Front inlet

r

0.43 m

///////// i —7—/—T

Figure 18. Schematic view of experimental arrangement for above-ground

measurements. The polarizing voltage for the ion counter is

produced with a battery. Not shown are various measuring

instruments, high voltage power supply, etc.

39
12

^10

O

00O

>-

CO

m

o

UJO

<

I

o

8

-

fo 6

-

4

-

2 -

1 1 1 1 1 1

. , - - -,

^ \o

£^ -—A-O ^_—0_A_^0 0_

o A o o ° - -.-' °

c^ o / o

«/ o ^

o _ /

/

/<^ 9 ^ q/

/

/ A M = 4.8x10~^m^/s

9i

/ o M = 15.4x10"^m/s

o

; _ A

oi

k

• ^- Unperturbed space

o^ y^ potential at aperture

, / if 1 1 1 1 —

-20 -15 10 -5 5 10 15

ION COUNTER POTENTIAL (kV)

20 25

Figure 19. Above-ground ion density measuements at two air flow rates and as

a function of ion counter potential. The unperturbed space

potential at the height of the aperture, which is 2.54 cm in

diameter, is indicated on the horizontal axis.

40
approaches the unperturbed space potential. At space potential, the ion

losses are significant. This result is interesting because the perturbation

of the electric field by the ion counter is a minimum at this point.

A qualitative explanation for the loss in ion current is provided in

figure 20. Figure 20 shows a schematic view of the ion counter with electric

field lines terminating on and leaving the ion counter, when the ion counter

is at space potential. Some negative ions with trajectories that approach the

ion counter at and from below the height of the aperture will be repelled by

the negative induced charges on the ion counter. This repelling action of the

induced charges will begin before the ion counter reaches space potential and

will increase as the ion counter voltage is made more negative. Swann

considered a similar effect when an ion counter was oriented vertically [30].

The above results indicate that the excess ions drawn to the region of

the aperture have a small effect on the measurements when they are preferentially attracted to the case of the ion counter and thus grounded

through the biasing power supply. If the field configuration is such that the

ions are repelled from the vicinity of the aperture, these ions are not

counted and significant errors can result. Therefore, the reference potential

of the ion counter should be such that charges induced near the aperture by

the external electric field attract the ions which are measured. For example,

as seen from the results in figure 19, when the ion counter is in a horizontal

orientation, a positive reference potential is appropriate. Alternatively,

simple electrostatic considerations show that loss of ions can be avoided by

operating the ion counter in a vertical orientation and referenced to ground

potential. It is recognized, however, that this latter orientation may be more

prone to degradation due to contamination.

The effect of an external electric field which enters the opening of an ion counter and reaches the collecting electrodes is considered next.

Measurements of ion densities with the NBS ion counter configured so that

there is insufficient electrical shielding are shown in figure 21. The ion

density measurements were made at three flow rates as a function of reference

potential of the ion counter assembly. The experimental arrangement is

similar to that shown in figure 18. The small aperture and associated cover

plate is removed and allows greater exposure of the collecting electrodes to

the external electric field. In this configuration, the opening of the ion

counter is 13 cm x 10.5 cm and the collecting electrodes are recessed 10 cm from the opening (see figure 13) . No corrections of the data have been made

for duct losses, which would make the differences between the different flow

rates greater than shown in figure 21. The ion density measurement is now

very dependent on the external electric field (i.e., reference potential) and

flow rate. For a given flow rate, the measured ion density increases with

electric field strength because the volume of ions entering the ion counter

(V in figures 5 and 6) is increasing relative to the volume of air, V. For a given external electric field (fixed potential on ion counter) , the measured

ion density increases with decreasing flow rate because the decrease in the

volume of air entering the ion counter is greater than the corresponding

decrease in the volume of ions

As noted in Section 7.2, a check for electric field penetration to the

collecting electrodes can be made by observing if there is significant ion

current to the collecting electrodes when there is no air flow; the ion

41
t

M 1 Mil

+ + + + ++ +

+

Aperture ^ -

a n i\ li

Ion counter

Figure 20. Schematic view of electric field lines terminating on and leaving

ion counter near aperture when ion counter is at space potential.

The negative charges induced by the electric field repel some negative ions as they approach the aperture under the combined

influence of the electric field and air motion.

42
15.0

CO 10.0

£

o

X

CO

z

LUO

O 5.0

I I L

M = Flow (m^/sx10^)

13-11-9 -6-3 5 10 15

ION COUNTER POTENTIAL (kV)

Figure 21. Ion density messurementa at different flow rates and as a function

of ion counter potential when there is inadequate shielding of the

external electric field.

43
counter, with its large opening, did show such current. vrhen the data in

figure 21 are corrected for this "leakage current," the cur\'es develop

plateaus for ion counter potentials greater than zero volts

.

9 . SUM>LmY

A parallel plate apparatus has been described which is suitable, under

certain conditions of voltage (V^) , current densitv and geometry for

t

" ' generating a charge density of kno'^'Tn value with an uncertainty of less than

±9%. The acceptability of the apparatus for this purpose was determined

theoretically and experimentally by shoving that the perturbations of the

electric field due to the ion counter aperture in the ground plane and air

flow through the aperture did not significantly extend to the top plate of the

parallel plates. Thus it was possible to calculate the unperturbed charge

density profile between the parallel plates.

Approximate calculations of ion trajectories under the influence of a dc

electric field and air motion into the counter show that the number of ions

arriving at the aperture is more than when the electric field is absent in

agreement with the predictions of Swann. The extra ions are not expected to

contribute to the ion density measurement (resulting in a measurement error)

unless a significant number of electric field lines terminate on the

collecting electrodes of the ion counter, or, equivalently , provided that the excess ions are grounded through the counter's case.

Comparison of calculated charge density values with measured values

obtained with an ion counter fabricated at NBS show good agreement within the

uncertainties of the calculation and measurements . The use of a duct with a small aperture to minimize the influence of the external electric field as well as duct losses due to Coulomb effects was discussed.

Charge density measurements under a monopolar line provide evidence that an external electric field can significantly influence charge density

measurements. The above-ground measurem.ents under a monopolar line showed

that operating the ion counter at space potential in a horizontal orientation

resulted in ion losses caused by repulsion between the ions and the induced

charges on the ion counter. The ion losses can be avoided by biasing the ion

counter potential so that ions, of the polarity to be m.easured. are attracted

to the case.

Because there are numerous loss mechanisms for ions entering an ion

counter, an experimental calibration would be desirable for characterizing the

response of the instrumentation. Unfortunately, because of the large ion

densities that are considered for measurements and the associated losses due

to Coulomb repulsion, calibration can be a function of ion density. In

addition, the calibration is valid only for those conditions in which the only

significant air flow is that due to the fan of the ion counter. During

outdoor measurements, wind for example, may introduce additional m.easurement

uncertainty.

44
10 . ACKNOWLEDGMENTS

The authors are pleased to acknowledge the early contributions of

Ralph Kotter to the ion density measurement problem, the assistance of

Roberta Cummings during the preparation of the manuscript, and the help of

William Anderson and James Hagler during the ion trajectory calculations.

Stimulating conversations with A. V. Phelps, W. A. Hoppel, R. V. Anderson and

J. C. Willett are also acknowledged. The support of the Electric Energy

Systems Division of the Department of Energy made this study possible.

45
11. APPENDIX A: ION LOSSES DUE TO FRINGING ELECTRIC FIELDS FROM ION COUNTERS

As noted in Section 2, significant ion losses can occur due to fringing

electric fields from an aspirator- type ion counter. The losses will depend on geometry, polarizing voltage, and volumetric air flow through the system.

Results of a simplified model calculation and laboratory measurements are presented here to illustrate the possible magnitude of the problem.

A.l Ion Trajectories

An ab-initio analysis of the motion of ions near the ion counter inlet is

not possible because of the complicated geometry. However, insight into the

loss mechanisms can be gained by using a two-dimensional model and applying

numerical analysis methods. A finite element code, resident on NBS computers,

has been used to calculate the electric potential distributions and electric

field at the inlet of the ion counter. The geometry assumed for the model

calculation and the finite element triangulation resulting from the higher

level code adaptation of the problem are shown in figure Al . In figure A2

,

the equipotential values are displayed. A solution was generated for one -half

the geometry, since the reflection symmetry inherent in the problem was used

to specify the appropriate boundary condition on the midplane. This saves computer space and computation time. An additional simplifying feature

involves the assumption that the entrance to the counter is not open, but

closed and grounded. Along the boundary intersecting the ion counter

electrodes, the potential was assumed to vary linearly between the polarizing

and collecting plates.

The calculations are done for a polarizing potential of one unit and the

equipotentials are drawn in units of 0.1 of the polarizing potential. For the

calculation in figure A2 , the polarizing plates are recessed one plate spacing

and there is little field leakage. In contrast, figure A3 displays the

results of a calculation for a geometry where the polarizing plates protrude

one plate spacing in front of the collector plates. Here the extent of the

fringing fields is significant. Compare, for example, the location of the

0.1 equipotentials on figures A2 and A3.

While such plots are informative, they do not relate directly to the

problem of losses at the inlet. In order to provide quantitative results, a program has been written to calculate the trajectories of ions carried into

the ion counter by an air stream. The electric field as calculated using the

finite element program and an appropriate air flow velocity field, are stored

as arrays. In the program, an ion enters the counter at a particular point.

The velocitthat (and any other) point is determined by adding vectorially

the air velocity vector and the electrical velocity vector:

-* -y ->• -f -> v=v. +v„=v. +KE air E air

where K is the ion mobility and E is the electric field at the point. Using

this velocity, the ion is transported for a predetermined time and, at the new

location, the process is repeated. In this way a trajectory for the ion is

estimated.

46
@@^

igj^B 1^!:i ^TJ^^i 1^s^i

S^K

^vTc?,^ctrtj^

^

^^j9

fc>^1^T^^O^^fc^'^^

^ll^l i?^

V 4 igb.

HI

Figure A1 . (a) Two dimensional geometry used in finite element calculations,

(b) Computer-generated high level triangulation for geometry (a),

Inside the cross-hatched area the triangulation was too dense to

be displayed.

47
u = 0.0

u= 1.0

u =0.0

u = 1.0

u = 0.0 Z

dn

Figure A2. (a) Boundary conditions used in finite element calculation, (b)

Computer generated equi potential curves, plotted in units of

u = 0.1

.

48
u=0.0

7

u=0.0

u = 1.0

u = 0.0

u=1.0 du^ = 0.0

dn 7

Figure A3, (a) Boundary conditions and geometry used for a model calculation

in which the polarizing plates protrude in front of collector

plates, (b) Computer generated equi potential curves, plotted in

units of u = 0.1

49
Sample trajectories for the geometry of figure A3 are shown in figure A4.

2 The ion mobility was taken to be 1.4 cm /V«s, the polarizing voltage 100 V and

the air flow velocity was 42.4 cm/s into the counter.

A. 2 Measurement of Ion Losses and Comparison with Theory

Measurement results showing ion losses due to fringing electric fields

are presented in figure A5 . Here the relative positions of the collecting and

polarizing plates are varied and the positive ion current is measured as a function of polarization voltage. The flow rate and ion density are held

constant during the measurements . The air speed averaged over the area of the

ion counter entrance was near 42 cm/s . The data show that as the polarizing

plates move even with or forward of the collecting plates, there are large

losses of ions at the inlet. Losses can occur even when the polarizing plates

are recessed one plate spacing (~1 cm) behind the collector plates.

The trajectory calculations (fig. A4) suggest that less than about 25% of

the ions reach the collector plates for a polarizing voltage of 100 V whereas

the measured loss indicated in figure A5 is not as great. In addition to the

simplifying assumptions noted above, the discrepancy between experiment and

theory is due in part to assuming an air velocity that has no component

orthogonal to the axis of the ion counter. Actually, the streamlines will

converge as they approach the entrance of the ion counter (see Section 3.3).

50
10 cm INLET

(3.66. 10) (3.63. 10)v.\ (*.3. 101 ^\ \ -(4.6, 10)

V,j, = 42.4 cm/sec

u =

4.763 cm

DISTANCE FROM COUNTER WALL

Figure A4. Trajectories of ions entering the ion counter at different initial

locations. The geometry is that of figure A3.

51
10

-10

CO

LU

CC

LU

Q.

<

z

LU

DC

DCDO

CC

LUI-z

o

o

z

o

10

-11

10

-12

10 20 50

POLARIZING VOLTAGE

Figure A5. Ion counter output current as a function of polarizing voltage for

different plate configurations. The displacement between the

leading edges of the collection and polarizing plates is x. Positive values of x correspond to a situation where the

polarizing plates protrude in front on the collector plates. For

X = 0, the leading edges were flush. Because the ion density is

independent of polarizing voltage over the range plotted, the ion

counter current should be constant. The spacing of the parallel

plates is near 1 cm and the air speed, averaged over the area of

the ion counter aperture, is near 42 cm/s.

52
12. APPENDIX B: FLUID FLOW THROUGH AN APERTURE IN A PLANE

An aspirator type ion counter, operated in the ground plane, extracts air

from the high field side of the ground plane. This fluid (air) flow can perturb the ion distribution. This perturbation, while it may be less

important for measurement near dc transmission lines, may be significant in

biological exposure facilities and in laboratory calibration systems.

B.l Theory

A distribution of point sinks is used to model the three-dimensional,

steady air flow which is induced in a half- space by a known outflow across the

boundary. In a rotationally symmetric case, velocities are found

analytically. In the general case, numerical integration may be applied to

approximate the flow.

Air is drawn into an opening in a broad flat surface at a speed much

below that of sound. To determine the flow above the surface, the flow is

modeled as steady, irrotational , and incompressible in the upper half- space

consisting of points r = (x, y, z) such that z > 0. We wish to find the

velocity, u, satisfying the boundary conditions for r in the boundary (z = 0)

u„(r) u for r in

o (Bl)

u (r) = for r not in Q n

(B2)

Here, u is the component of u normal to the boundary and Q is the opening, an

open, bounded set of points in the boundary. We also require the velocity at

infinity to be zero:

lim |u(r) I =

|r|->co

(B3)

Thus, in the plane z = 0, we have the situation shown in figure Bl

Figure Bl . The boundary conditions for flow through aperture of area Q.

53
The central idea is to represent the flow field as a linear superposition

of point sinks over the region Q [17]. It emerges from our analysis that the

boundary conditions are satisfied and that for one simple, but important

region, Q, the velocity can be found analytically.

The continuity equation for incompressible flow is

V . u = . (B4)

Irrotationality is given by V x u = 0. The solution for a point sink at r' with volume flux m is [31]

u(r) = (-m/47r) |r-r' |"^(r-r') . (B5)

The superposition of point sinks of constant strength which are uniformly

distributed over the region Q, gives rise to the velocity field:

u(r) = (-uy27r)J^|r-r'r^(r-r')dx' dy' , (B6)

where m and u are related by m = 2u • area (Cl) and m is the volume flux into

o -^ o the sink Q from both the upper and lower half spaces. In the case that the

flux comes from the upper half only, one must replace the constant

(u^/47r) by (u^/27r) . (B7)

In the interior of the flow, for r in the proper half space z > 0, the

integrand in eq (B6) is absolutely integrable and one may differentiate

through the integral to establish that u satisfies the differential eq (B4)

Some care must be taken in establishing the boundary conditions,

eqs (B1)-(B3). When r lies outside Q but in the plane z = 0, the vector r-r'

which appears in the integrand, has a zero component in the normal direction.

The integral converges and so u(r) is defined and has a normal component of zero , i.e.,

u (r) = . (B8) n

For r in fi, the integrand in eq (B6) has a singularity at r' = r and is

not summable. Consider, however, the velocity at a small distance, d, above

—

—f the point r = (x, y, 0). At r = (x, y, d) , the velocity can be estimated and

lira u (r^) = u . (B9)

d-+o n d o

54
To show this, consider a disk centered at r and lying entirely in Q. Let

-> -+ the disk radius be R as shown in figure B2 and let r = |r'-r| . Integrating

separately over the disk and its complement in Q, and converting to polar

coordinates for the disk, one sees that at r , d « R, the normal component of

the velocity is well estimated by

2n R

u = (u /2n) J J

o

/ 2 j2,3/2

o (r +d )

'^ rdrd^ (BIO)

= u {!

o (rW)V2

(BID

As d->-0, we get ° u ->^u , which was to be shown. no

Figure B2 . Estimating u near Q.

Note that when Q is a disk, the velocity along the central axis, x given by eq (Bll) . Thus, for a circular hole.

= y is

u(0,0,z) = (0,0, u (l-a(l+ a^)'^/^))

o z/R (B13)

The validity of this model has been verified with measurements made along

the central axis (see below).. For a more complicated Q, the evaluation of

u(r) may require a quadrature. Geometric complexity is of no difficulty as long as Q can be decomposed into triangles and disks. In this case computer

software is available for the necessary calculations.

55
For application of this method to flows in a half space, the velocities

away from the boundary are accurately determined. Neglecting viscosity gives

good results because there are no upstream boundaries and consequently no sources of vorticity in the far field. The procedure runs into difficulty at

the edge of the region Q where the velocity given by this method is infinite.

This non-physical solution is the result of neglecting the boundary layer. In

the apparatus under consideration, the Reynolds number ranges from 5000 to

30000. For such values, a more accurate determination of flow field in the

upstream region is possible, because, for slightly viscous flow, a jet issues

on the downstream side of the hole. One must characterize the jet and use it

to determine the velocity, u , at the hole. Then eq (B13) may be used to find n

the upstream flow more accurately.

B.2 Comparison of Theory With Measurements

The central velocities given by'eq (B13) are found to agree with

experiment. Measurements of velocities are made along the central axis lying

over a 5.1 cm x 5.1 cm opening using a hot film anemometer. The data is used

to fit the model, eq (B13) , for a circular opening. Table Bl shows the

results of experiment and theory. The measurements are made at different flow

rates through the same opening and all data are normalized so u(0.5 cm) = 1.

Two techniques are used to find an effective R and the corresponding u . In case 1, two measurements (d, u(d)) yield two simultaneous equations in u and

R. These are solved iteratively to find the model parameters. In case 2, one

2 selects R so that ttR is equal to the known area of the opening and u is

chosen so that u(0.5 cm) = 1. Figure B3 displays the measurements and the

theoretical curve of case 2.

Table Bl. A comparison of theory to experiment for normalized air speed into

a small opening (5.1 cm x 5.1 cm), u(0.5 cm) = 1.

Measurement Theory

ICA) 2(o) 3(n) Case 1 Case 2 R

d

3.19 2.98 2.91 AD A

2.88 cm

0.0** Not Measured

0.5 1.0 1.0 1.0

1.5 .68 .72 .66

3.5 .29 .27 .25

5.5 .13 .14 .12

7.5 .08 .08 .10

1.18 1 .20 1 .26 1.21

1.00* 1 .00* 1 .04 1.00*

.68* .66* .68* .65

.31 .29 .29* .27

.16 .14 .15 .14

.09 .09 .09 .08

* Agreement is an artifact of data fitting

** No measurements made, theory gives u .

Uncertainties in the air speed measurements range from 5% for the highest

values, to 10% for the lowest values. The position of the probe is known to

within -1 mm. Assuming the model calculation to be correct, a linear error analysis shows that the uncertainty in u is <10%

.

56
u

0.5

Measurements — Three dimensional theory -- Two dimensional theory [17]

|u| normalized to u (0.5 cm) = 1.0

1.5 3.5 5.5 7.5

d (cm)

10

Figure B3. Air speed versus height above a 5.1 cm x 5.1 cm aperture in a plane. The measured values wer^ pbtained using thre^ l^low rates

through the_o

1 .7 X 10 m^/

d - 0.5 cm.

pening, 0.37 x 10 ^vnr/s (a), 0.69 x 10 "^m^/s (o), and

's (A). The data have been normalized to unity at

57
Equation (B6) can be integrated analytically for a square aperture [see

Appendix C, eq (C22)] and yields a more complicated expression for velocity

along the z-axis than eq (B13) . It is interesting to note that the

predictions of eq (B13) using an "effective radius" are in agreement with

results obtained using the more rigorously derived expression.

Comparison of theoretical predictions (see eqs (C18) and (C22) in

Appendix C) with preliminary measurements of air velocity off the central axis

and within a distance of about one diameter from the opening indicate that the

predicted values are too high. However, further measurements are required to

properly evaluate the theory for off -axis locations.

Attempts to fit the experimental data in figure B3 using the results of a two-dimensional model calculation, a three dimensional model calculation using

oblate spheroidal coordinates, and a three dimensional model calculation

assuming sinks in the plane of the aperture which increase in strength as the

edge of the aperture is approached [17] were less successful than the above

model. Results of the two-dimensional theory are shown in figure B3 as a dashed curve for comparison.

In summary, an analytic model of the flow induced by a draft through a hole in a flat boundary has been presented. The model is fully threedimensional and provides a closed form for the velocity in a problem of

interest; i.e., for an aspiration- type ion counter operated in the ground

plane. Some work is needed to implement this method on the computer. It is

interesting to note that in the evaluation of eq (B6) by quadrature, the

boundary condition, eq (Bl) , can be generalized to allow u (x) to vary over

the opening. The inclusion of the boundary layer in the model would extend

its usefulness to the edge of the half- space, but the influence of this

boundary layer at the ground plane is probably not important for the

description of the perturbations introduced by the ion counter.

58
13. APPENDIX C: EQUATIONS OF MOTION FOR ION TRAJECTORIES

The equations of motion for ion trajectories under the influence of an electric field perturbed by an aperture in the ground plane and air motion

through the aperture are given by eqs (27) and (28)

dy/dt = V + u , and (CI)

dz/dt = V + u , (C2)

where the terms on the right hand side are somewhat lengthy expressions given

by eqs (19) , (20) , (25) and (26) . An outline of the derivation of these terms

is presented below.

CI. Ion Drift Velocity

The electric potential between two parallel plates in one of which there

is a circular aperture has been determined by Fry and is given by the

expression [15]

$' = A[sinhA + (2A) + (2/7r) sinhA tan" (sinhA)] sin/x , (C3)

where A is E R/2 , R is the radius of the aperture, E is the unperturbed

electric field, and A and /j. are oblate spheroidal coordinates which are related to Cartesian coordinates by the equations

X = RcoshA cos/i cos^ 0<6<2n

y = RcoshA cos/j, sin9 0</i<7r/2 (C4)

z = RsinhA sin/z . -oo<A<oo

The equations for the electric field components are derived in the y-z plane

(d = 1^/2) without loss of generality because of the symmetry about the z-axis.

Then

-E = d^/dy = 0$/3A)(aA/ay) + (d^/dn) (dn/dy) , and (C5)

-E = d^/dz = (5$/3A)OA/az) + (d^/dfx)(di^/dz) , (C6)

z

where the prime's have been dropped for simplicity.

The expressions for d(f>/d\ and d^/dfi are readily found by differentiating

eq (C3) . They are

di/dX = A[coshA + (2/7r)coshAtan" (sinhA) + (2/7r) tanhA] sin/x , (C7)

and

d^/dpL = A[sinhA + (2/tt) + (2/n) sinhAtan' (sinhA) ] cos/i . (C8)

59
To find dX/dy, dn/dy, d\/dz and d/i/dz, we note from the chain rule that

d^/d\ = (d^/dy)(dy/dX) + (d^/dz) (8z/d\) , and (C9)

a$/5yu = 0$/3y)(ay/5/i) + (d^/dz) (dz/df^) . (CIO)

Writing eqs (C9) and (CIO) in matrix form

d^/dx\ /dy/dX dz/dx\ / d^/dy

I

. (Cll)

d^/d/j. I \ dy/dn dz/d/i/ \5$/5z

F

The elements of matrix F are readily found from eqs (C4) . That is

RsinhAcos/i RcoshAsin/i

F = I I

. (C12)

-RcoshAsin/i RsinhAcos/z

Writing eqs (C5) and (C6) in matrix form,

a$/ay\ /dX/dy dfi/dy\ /d^/dX

(C13)

a$/az / \dX/dz dfi/dz/ \d^/dn

and comparing with eq (Cll), it is seen that the 2x2 matrix in eq (C13) is

just F . The inverse of F is readily found from F and is given by

'RsinhAcos/i -RcoshAsin/z

F'-^ =1

I /d , (C14)

RcoshAsin/i RsinhAcos/i

2 2 2 -1

where D is equal to R (cosh A - cos /j.) . The elements of F are, from

eq (C13) , the sought after partial derivatives dX/dy, dfi/dy, dX/dz and dji/dz.

Combining eqs (C7) , (C8) and (C14) in eqs (C5) and (C6) and multiplying by the

average mobility K gives eqs (19) and (20) for the drift velocities v and v .

C.2 Air Velocity

The expression for air velocity that is used in calculating ion

trajectories is derived in Appendix B and is given by eq (11)

60
u(r) = -(u /I-k) JJ (r-r') |r-r' I""^ dx'dy' , (C15)

where r and r' are position vectors above and in the plane of the aperture

respectively, and x' and y' are Cartesian coordinates in the plane of the

aperture. For ion trajectories in the y-z plane,

A A r = yj + zk ,

and

A A r ' = x' i + y'

j

Equation (C15) can thus be written

u(r) = -(u /27r)/J(-x'i + (y-y')j + zk)(x'^ + (y-y')^ + z^)

""'"

' ^dx' dy' . (C16)

Equation (C15) can be integrated to yield expressions for the horizontal and

vertical velocity components u and u (u is equal to zero) in the y-z plane

if a square aperture is considered. To match the edge of the square aperture

in the y-z plane with that of a circular aperture, the side dimension of the

square aperture is taken to be 2R. The velocity component, u , is

R R

u = -(u /27r) J / (y-y')(x'^ + (y-y')^ + z^)

'^

" ^dx'dy' , (C17) ^ -R -R

which is readily integrated to give

u = -(u /27r)log[(R+F)(-R+G)/(-R+F)(R+G)] , (C18)

where

2 2 2 1/2

F = [R + (y-R) + z ] / , and

2 2 2 1/2

G = [R + (y+R) + z ] / .

The velocity component, u , is

R R u = -(u /27r) / J z[x'^ + (y-y')^ + z^j'-'-'^dx'dy' . (C19)

^ ° -R -R

2 2 2 Substituting w' = (y-y') and P = x' + z leads to

61
u = -(uz/2n) jr dx' / -(w'^ + P^)'^-^dw' , (C20)

-R

where P is a constant during integration over w' . Equation (C20) is readilyintegrated to yield

u = -(u z(y-R)/27r) J (x'^ + z^) ""^

[ (y-R)^ + x'^ + z^]'°"^dx'

^ ° -R

+ (u z(y+R)/27r) / (x'^ + z^) ' "^

[ (y+R) ^ + x'^ + z^]'°'^dx' . (C21)

-R

Both terms in eq (C21) can be integrated using the following expression from a table of integrals

r, 2 , ,-1, 2 j,-0.5j ,^, _, ^ sn-0.5 -1, , J , ,0.5^,, 2 ,,,-0.5,

J (ax +b) (ex +d) dx = [b(ad-bc)] tan {x(ad-bc) [b(cx +d) ] },

where a, b, c and d are constants that satisfy the inequality ad>bc , After

some algebra, u can be written

u = -(u /tt) [tan"''"(R(y+R)/zG)-tan"'''(R(y-R)/zF)] , (C22)

where G and F are defined above

.

62
14. REFERENCES AND NOTES

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

Fields and Ion Currents on the Celilo-Sylmar ±400 kV DC Intertie During

Fair Weather, IEEE Trans. Pow. App . Syst., Vol. PAS-97, pp. 370-378,

1978.

[ 2] M. Hara, N. Hayata, and M. Akazaki, Basic Studies on Ion Flow

Electrification Phenomena, J. Electrostatics, Vol. 4, pp. 349-365, 1978.

[ 3] M. Hara, H. Chishaki, and M. Akazaki, Calculation of Electrification

Current and Energy Resulting From Ion Flow Under D.C. Transmission

Lines, J. Electrostatics, Vol. 6, pp. 29-41, 1979.

[ 4] M. Misakian, Generation and measurement of dc electric fields with space

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

[5] M. Hara, N. Hayashi , K. Shiotsuki, and M. Akazaki, Influence of Wind and

Conductor Potential on Ground Distributions of Electric Field and Ion

Current Density at Ground Level in DC High Voltage Line to Plane

Geometry, IEEE Trans. Pow. App. Syst., Vol. PAS-101, pp. 803-814, 1982.

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

Current Density at Ground Level in the Vicinity of High Voltage D.C.

Transmission Lines, IEEE Trans. Pow. App. Syst., Vol. PAS-102, pp. 934-

941, 1983.

[ 7] P. S. Maruvada, R. D. Dallaire, and R. Pedneault, Development of FieldMill Instruments for Ground-Level and Above-Ground Electric Field

Measurement Under HVDC Transmission Lines, IEEE Trans. Pow. App. Syst.,

Vol. PAS-102, pp. 738-744, 1983.

[ 8] M. G. Comber, R. Kotter, and R. H. McKnight, Experimental Evaluation of

Instruments for Measuring D.C. Transmission Line Electric Fields and Ion

Current, IEEE Trans. Pow. App. Syst., Vol. PAS-102, pp. 3549-3557, 1983.

[9] H. Israel, Atmospheric Electricity. Vol. 1 . translated from second

German edition (1970) , available from National Technical Information

Service, Springfield, VA 22151.

[10] H. F. Tammet, The Aspiration Method For the Determination of

Atmospheric- Ion Spectra , translated from Russian (1970), available from

National Technical Information Service, Springfield, VA 22151.

[11] H. Ebert, Aspirations apparat zur Bestimmung des lonengehaltes der

Atmosphare, Phys. Z., Vol. 2, pp. 662-666, 1901.

[12] M. Knoll, J. Eichmeier, and R. W. Schon, Properties, Measurement, and

Bioclimatic Action of "Small" Multlmolecular Atmospheric Ions, in

Advances in Electronics and Electron Physics, Vol. 19, pp. 177-254,

1964.

[13] T. D. Bracken and B. C. Furumasu, Field and Ion Current Measurements in

Regions of High Charge Density Near Direct Current Transmission Lines,

63
Proceedings of the Conference on Cloud Physics and Atmospheric

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

[14] NBS Report NBSIR 83-2761, Development of Power System Measurements-

Quarterly Report, January 1 - March 31, 1983.

[15] T. C. Fry, Two Problems In Potential Theory, Am. Math. Monthly, Vol. 39,

pp. 199-209, 1932. The solution in this reference does not consider the

influence of a connecting tube (ion counter) shown in figure 4. The

presence of the tube can be expected to reduce the amount of field

perturbation above the aperture

[16] It is interesting to note that the perturbation along the z-axis of an initially uniform electric field by a conducting spheroidal boss on the

ground plane [see P. Moon and D. E. Spencer, Field Theory for Engineers

(D. Van Nostrand, 1961), p. 287ff] is also twice that for the electric

potential at large z. In the case of a conducting hemisphere, the

relative perturbation is exactly two for all points along the z-axls

greater than the radius

[17] H. Lamb, Hydrodynamics (Dover, New York, 1945), p. 98ff, p. 13ff.

[18] A variable step -variable integration algorithm, PLOD, developed at NBS

by D. Kahaner was used for the trajectory calculations. See also Guide

To Available Mathematics Software, Report No. PB84-171305 (1984),

available from National Technical Information Service, Springfield, VA

22151.

[19] W. F. G. Swann, On Certain Matters Relating to The Theory of

Atmospheric-Electric Measurements, Terr. Magnet. Atmos. Elect., Vol. 19,

pp. 205-218, 1914. Swann' s theory does not consider large ion densities

for which there is significant Coulomb repulsion between the ions and

thus may not be completely valid for the transmission line problem.

[20] Hara et al . have recently shown that the ion current to a cylindrical

object in a dc electric field with ions and an air stream is nearly

independent of air speed. While fewer ion trajectories terminate on the

cylinder at greater air speeds, the ion current to the cylinder remains

nearly the same because of the increased ion velocity. See M. Hara,

M. Yashima, T. Tsutsumi , and M. Akazaki, Electrification current and

voltage on a cylindrical object in the presence of an ion flow field in an air stream, lEE Proc .

, Vol. 132, Pt. A, pp. 59-66, 1985.

[21] W. T. Kaune, M. Gillis, and R. J. Weigel, Techniques for estimating

space-charge densities in systems containing air ions, J. Appl . Phys .

Vol. 54, pp. 6267-6273, 1983 and references cited therein. The near

equivalence between eqs (35) and (36) can be seen by substituting eq

(34) into eq (35)

[22] E. W. McDaniel and E. A. Mason, The Mobility and Diffusion of Ions in

Gases (John Wiley, New York 1973), p. lOff.

[23] Inherent in this model is the assumption that a negligible number of

ions fail to reach the aperture because of the zero air velocity at the

64
surface of the bottom plate. How well J, K, E and d can be determined

o also influences the amount of uncertainty in calculating the known ion

density using eq (42) or the approach described in figure 3.

[24] G. W. Penny and R. E. Matick, Potentials in DC Corona Fields, Trans.

AIEE, Comm. and Electr., Vol. 79, pp. 91-99, 1960.

[25] R. E. Matick, Potentials in DC Corona Fields, Doctoral Dissertation,

Carnegie -Mellon University, 1958.

[26] Profiles of the air velocity across the opening to the collecting plates

were obtained with a hot film anemometer. Large fluctuation of the

velocity near the boundary of the jet indicated the presence of the

turbulence

.

[27] While the Reynolds number will exceed 2000 in the duct for u > 0.6 m/s

and it is generally held that turbulence can first occur in tubes when

the Reynolds number is between 2000 and 3000, the onset of turbulence

may occur at much larger Reynolds numbers depending on conditions in the

initial pipe length as well as the approach to it [H. Schlichting,

Boundary Layer Theory . . Chpt. XVI (McGrawHill, New York, I960)]. For

example, Cobb reports that turbulence is observed to first occur in a circular tube when the Reynolds number is near 6000 [W. E. Cobb, Ion

Losses in the Gerdian Condenser Intake System, J. Appl. Meteorology,

Vol. 7, pp. 456-458, 1968]

.

[28] J. A. Chalmers, Atmospheric Electricity . 2nd ed, (Pergamon, Oxford,

1967), p. 128ff.

[29] Similar results have been observed during conductivity measurements

aboard aircraft. See J. H. Kraakevik, The Airborne Measurement of

Atmospheric Conductivity, J. Geophys . Res., Vol. 63, pp. 161-169, 1958.

[30] W. F. G. Swann, The Theory of the Action of the Earth's Potential

Gradient In Measurements With The Ebert Ion- Counter, Phys . Rev., Vol.

21, pp. 449-455, 1922.

[31] G. K. Batchelor, An Introduction To Fluid Mechanics (Cambridge

University Press, London, 1967), Chpt. II.

* U.S. Government Printing Office: 1986—491-070/40083 65
NBS-114A (REV. 2-8C) U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO.

NBS/TN- 1223

2. Parforming Organ. Report No, 3. Publication Date

-lay 1986

4. TITLE AND SUBTITLE

Calibration of Aspirator-type Ion Counters and

Measurement of Unipolar Charge Densities

5. AUTHOR(S)

M. Misakian, R. H. McKnight, C. Fenimore

6. PERFORMING ORGANIZATION (If jo/nt or other than NBS. see instructions)

National Bureau of Standards

Department of Commerce

Gaithersburg, MD 20899

7. Contract/Grant No.

8. Type of Report & Period Covered

Final

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

Same as item 6

10. SUPPLEMENTARY NOTES

[3J Document describes a computer program; SF-185, PIPS 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)

The characterization of a parallel plate apparatus which can produce a unipolar ion density that is suitable for calibrating aspirator-type ion

counters operating in the ground plane is described. The influence of a dc

electric field, air motion, Coulomb repulsion and diffusion on the transport

of ions into the ion counter are examined to determine their effects on instrument calibration and measurements in the vicinity of high voltage dc

transmission lines. An ion density which is known with an uncertainty of less

than ±9% is used to check the performance of an ion counter with and without a duct at its entrance. The results of laboratory measurements of ion density

under a monopolar high voltage line, which complement the studies with the

parallel-plate apparatus, are also described.

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

calibration; instrumentation; ion counter; ion density; measurement;

transmission line; unipolar

13. AVAILABILITY

pX] Unlimited

I I For Official Distribution. Do Not Release to NTIS

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

20402.

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

14. NO. OF

PRINTED PAGES

74

15. Price

USCOMM-DC 6043-P80


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