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Journal of Electrostatics 63 (2005) 775–780

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doi:10.1016/j

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Electric fields coupled with ion space charge.Part 1: measurements

Jorg Meyera,�, Andreas Marquarda, Marc Poppnerb,Rainer Sonnenscheinc

aUniversity of Karlsruhe, D-76128 Karlsruhe, GermanybDaimlerChrysler, Research and Technology, Ulm, Germany

cDornier GmbH/DaimlerChrysler, Research and Technology, Friedrichshafen, Germany

Available online 19 March 2005

Abstract

In order to obtain a detailed understanding of the particle charging processes occurring in a

corona charging system, information on local charging conditions with respect to ion space

charge is essential, especially in arrangements with highly inhomogeneous charging conditions.

To obtain information on such local electrical data, spatially resolved measurements of space

potential, field strength and ion flux were performed in a point-plane arrangement, which

serves as a simplified model of an inhomogeneous configuration. Applicability and limitations

of an invasive current probe technique were investigated in different spatial regions of the

discharge set-up. The resulting local data can be used for comparison with numerical

simulations.

r 2005 Elsevier B.V. All rights reserved.

Keywords: Spatially resolved measurement; Electric field; Ion flux; Charging conditions; Point-plane

arrangement

1. Introduction and basics

Results obtained from experiments using corona chargers with stronglyinhomogeneous charging conditions (residence time t, ion concentration r) differ

see front matter r 2005 Elsevier B.V. All rights reserved.

.elstat.2005.03.044

nding author. Tel.: +49721 608 6567; fax: +49721 608 6563.

dress: joerg.meyer@mvm.uka.de (J. Meyer).

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J. Meyer et al. / Journal of Electrostatics 63 (2005) 775–780776

substantially from theoretical predictions for a homogeneous r � t product [1].Thus, more detailed knowledge of local electrical data in a corona charger isessential to predict charging, movement and deposition of particles which enterthe device.A point-plane corona arrangement—which serves as a simple example for more

complex charging devices—was used to produce a strongly inhomogeneous chargingregime (Figs. 1 and 2). Special attention was paid to establish stable and definedcorona conditions with respect to the corona regime (neg. glow), dischargeatmosphere (gas composition, temperature (293K) and humidity (40% rel.)) andthe boundary conditions (set-up shielded by grounded Faraday cage).An invasive technique using a spherical probe of adjustable potential allows for

measurements of the current caused by collection of ions on the surface of thesampling sphere. This technique was developed by Collins et al. [2] and is in principlelimited to homogeneous electrical fields and low ion concentrations r. Since the E-field changes very little across the length scale of the probe sphere (radiusrP ¼ 1:5mm), it is assumed that the technique can still be used here [3]. Varyingprobe potential FP around the local space potential FR in a unipolar ion atmosphereresults in probe current IP, which is given by two linear sections with a quadratictransition in between (Eq. (1)):

IP ¼

0; FR � FP43rPj~ERj; L;

�prm

j~ERjð3rPj~ERj � ðFR � FPÞÞ

2; FR � FPj jo3rPj~ERj; M;

4prPrmðFR � FPÞ; FR � FPo� 3rPj~ERj; N;

8>>><>>>:

(1)

(m: el. mobility of ions), resulting in a current–voltage characteristic as shown inFig. 3. From that, FR can be derived at the intersection of the linear section N withthe abscissa, while the slope of section N is proportional to the quotient of ion flux j~jj

collection electrode1.5 m

0.3

m

pointelectrode(-60 kV)

1.6

m

2.3 m

current probeon xy-stack

faraday cage(grounded)

HV

shieldedcurrent

measurement

2.0

m

HV

Icorona

Iprobe

probesphere

shieldedsupport

0.8 m

Fig. 1. Experimental set-up (left: top view, right: front view): point-plate corona arrangement with

measurement device for local electrical data (all housed in Faraday cage).

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collection plate

corona needle

x

y

x/y

probe

position:

0/20

0/80

150/150

210/210

0/240

270/270

90/80

30/2090/20

150/20

210/20

270/20

0/140

0/200

0/270

Fig. 2. Coordinate system and individual measuring points (coordinates in mm from plate centre).

prob

e cu

rren

t I p

probe potential ΦP

L

M

N

ΦR

0

unipolar

Fig. 3. Calculated IP–FP characteristic: spherical probe in hom. E-field and unipolar ion atmosphere.

J. Meyer et al. / Journal of Electrostatics 63 (2005) 775–780 777

and local field strength j~ERj and thus to r:

dIP

dFP¼ �4prP

j~jj

j~ERj¼ �4prPrm. (2)

The local field strength j~ERj can generally be calculated from the dimension of thequadratic section, which is difficult and susceptible to errors, if measured data scattersignificantly. Therefore, a least-squares fit was used to determine j~jj; j~ERj; and FR

from measured IP–FP characteristics.

2. Experimental results

The influence of the measurement probe on the corona discharge was examined bydetermining the corona current while varying FP around FR for different probe

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J. Meyer et al. / Journal of Electrostatics 63 (2005) 775–780778

positions. The corona current IC normalised with the corona current at FP ¼ FR vs.the deviation of the probe potential from the local space potential FP–FR is shownfor the line from point to plate (Fig. 4a), whilst Fig. 4b shows the data for a lineparallel to the plate and for the diagonal line (xEy), respectively. Only in the vicinity(x ¼ 270mm) of the corona needle is IC significantly influenced by the probepotential (over 75%).In the vicinity (x ¼ 20mm) of the collection plate, the measured probe

characteristics match the predicted shape almost perfectly, as illustrated by the

0.95

1

1.05

-2 -1 0 1 2 3

x = 20 mmx = 80 mmx = 140 mmx = 200 mmx = 240 mmx = 270 mm

y = 0 mm

Probe potential - local space potential ΦP-ΦR [kV]

rel.

coro

na c

urre

nt I C

/ I C

,ΦR [-

]

0.98

1

1.02

0.98

1

1.02

-2 -1 0 1 2 3

Probe potential - local space potential ΦP -ΦR [kV]

x = 20 mm

x ≈ y

y = 270 mmy = 150 mmy = 0 mm

x = 20 mmy = 0 mm

x = 150 mmy = 150 mm

x = 270 mmy = 270 mm

rel.

coro

na c

urre

nt I C

/ I C

,ΦR [-

]

(a) (b)

Fig. 4. Influence of probe on discharge: normalised corona current vs. FP–FR (a) y ¼ 0mm; (b) x ¼

20mm and xEy, respectively.

-40

-30

-20

-10

0

10

-6 -4 -2 0

probe potential Φp [kV]

prob

e cu

rren

t Ip

[nA

]

x = 20 mm, y = 0 mm

measured datafitted probe current

-10

-8

-6-4

-2

0

2

-6 -4 -2 0probe potential Φp [kV]

prob

e cu

rren

t Ip

[nA

]

x = 20 mm, y = 270 mm

-1000

-800

-600

-400

-200

0

200

-47 -45 -43 -41

probe potential Φp [kV]

prob

e cu

rren

t I p

[nA

]

x = 270 mm, y = 0 mm

-25

-20

-15

-10

-50

5

-21 -19 -17 -15probe potential Φp [kV]

prob

e cu

rren

t Ip

[nA

]

x = 270 mm, y = 270 mm

(a) (b)

(c) (d)

Fig. 5. Measured IP–FP characteristic and corresponding least square fit for different probe positions.

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0

50

100

150

200

250

0 100 200 300

y / mm

0

1

2

3

4

5x = 20 mm

E [

kV/m

] j

[�A

/m2 ]

j / E

[10-9

C/(

s·V

·m)]

-Φ

[kV

]

E

[kV

/m]

j / E

[10-9

C/(

s·V

·m)]

5

0

100

150

200

250

300

350

0 100 200 300

x / mm

0

1000

2000

3000

4000

5000

6000

7000y = 0 mm

j [�

A/m

2 ]

0

100

200

300

0 100 200 3000.0

0.3

0.6

0.9x ≈ y

E

[kV

/m]-

j

[�A

/m2 ]

j / E

[10-9

C/(

s·V

·m)]

x / mm

(a)

(b)

(c)

-Φ [

kV]

-Φ [

kV]

Fig. 6. Measured local electrical data FP (triangles, m), E (squares, &), j (diamonds, }) and j=E�r(bullets, �) for (a) x ¼ 20mm (parallel to collection plate), (b) y ¼ 0mm (from corona needle to plate), (c)

xEy (diagonal line towards stray field).

J. Meyer et al. / Journal of Electrostatics 63 (2005) 775–780 779

corresponding IP–FP plots for two individual measurements (Fig. 5a and b).However, near the corona needle (x ¼ 270mm; y ¼ 0mm; Fig. 5c) and at theouter regions of the stray field of the set-up towards the surrounding Faradaycage (x ¼ 270mm; y ¼ 270mm; Fig. 5d), the deviation between measured data and

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J. Meyer et al. / Journal of Electrostatics 63 (2005) 775–780780

least-squares fit increases. While the determination of FR and the slope of the linearsection N (and from that j~jj=j~ERj�r) is still possible with acceptable precision, thedimension of the quadratic section becomes harder to detect leading to an increasingerror for j~ERj and thus for j~jj:Average values for FR, j~jj; j~ERj and j~jj=j~ERj (Fig. 6) were determined from at least

four individual measurements, with error bars indicating the standard deviation sfor all measurements at one location. As expected, s is small for the area near thecollection plate (Fig. 6a), and increases both towards the corona tip (Fig. 6b) and thestray field (Fig. 6c). Also, errors for j~jj and j~ERj are generally larger than for FR andj~jj=j~ERj: The E-field is rather flat on the axis from corona needle to the collectionplane with only a slight increase near the corona tip (as can be expected qualitativelyfrom the effect of the ion space charge), while ion flux and ion concentration increasedrastically towards the needle electrode. In spite of a significant drop along thediagonal line xEy (Fig. 6c), field strength and ion concentration stay rather high inthe stray field, being only halved compared to the centre position near the collectionplate (x ¼ 20mm; y ¼ 0mm).As the gradient of the electric field is (due to the space charge effects) rather low,

even at positions near the corona needle (x ¼ 2002270mm; y ¼ 0mm), theassumption of a quasi-homogenous E-field—as a prerequisite for the applicabilityof the measurement technique—holds true. Indeed, in the vicinity of the coronaneedle, at x ¼ 240mm; y ¼ 0mm; the E-field changes only 1.2% across the probediameter, when approximating the local gradient of the electric field strengthbetween position x ¼ 200 and 270mm (at y ¼ 0mm) by a linear correlation.

3. Conclusions

The determination of local electrical data was successfully completed for thelargest region of a point-plate corona arrangement. However there are someconcerns on the accuracy of the data in the very close vicinity of the coronaelectrode. The quantitative data can now be used to validate simulations of FR and rfor the same set-up [4]. These simulations in turn can be used to calculategeometrically more complex charging devices, which are not measurable by thetechnique shown in this paper without extensive further work.

References

[1] A. Marquard, J. Meyer, A. Bredin, G. Kasper, Unipolar charging of nanoparticles at inhomogeneous

N � t-products and charge-loss-relations, J. Aerosol Sci. (Abstracts of EAC) I (2004) S429–S430.

[2] J.A. Collins, Y. Linde, S.A. Self, Spherical probes for corona discharges, J. Electrostat. 4 (1978)

377–389.

[3] M. Poppner, R. Sonnenschein, J. Meyer, Electric fields coupled with ion space charge. Part 2:

computation, J. Electrostat. 63 (2005) 781–787, these proceedings; doi:10.1016/j.elstat.2005.03.045.

[4] J. Meyer, Elektrische Koronaaufladung submikroner Partikeln und deren EinfluX auf die

Oberflachenfiltration, Shaker, Aachen, 2002.