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The behaviour of an argon discharge, long positivecolumn at medium pressure levels†EMIL I. TOADER aa Universitatea Bucureşti, Facultatea de Fizic[acaron] Str , Acadeimiei Nr. 14, Bucharest,RoumaniaPublished online: 25 Apr 2007.

To cite this article: EMIL I. TOADER (1969) The behaviour of an argon discharge, long positive column at medium pressurelevels†, International Journal of Electronics, 26:6, 553-560, DOI: 10.1080/00207216908938185

To link to this article: http://dx.doi.org/10.1080/00207216908938185

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INT. J. ELECTRONICS, 1969, VOL. 26, No.6, 553-560

The behaviour of an argon discharge, long positivecolumn at medium pressure levels'[

EMIL 1. TOADERUniversitatea Bucuresti, Faeultatea de Fiziea Str. Aeadeimiei Nr. 14,Bucharest, Roumania

[Received 3 June 1969J

In this work the contraction of the long, d.c. argon discharge positive column atmedium pressures has been studied. For our experimental conditions (\ goodagreement between the experiments and the theoretical model at medium pressuresproposed by Kagan and Ljagushchenko (1964) is obtained. At higher pressures theexperimental results present a greater contraction than anticipated by theory.

1. Introduction

The contraction phenomenon of the quasi-neutral, steady-state homo­geneous positive column in inert gas discharges at medium pressures is charac­terized primarily by a deviation of the radial distribution of the charge carrierconcentration from the standard Schottky distribution. In addition, thecouplings of the particles which make up the plasma are not subjected to theinterdependence relations of the Schottky theory.

As demonstrated previously (Toader 1966), small deviations from theapplicability requirements of the elementary diffusion theory result in thedevelopment of phenomena which cannot be overlooked. In accordance withthe experimental and theoretical results (Kagan and Ljagushchenko 1964), thecontraction phenomenon is a consequence of the new stepped excitation andionization processes and of the deviations of the electrons from the Maxwellian­type energy distribution.

The main scope of this work has been to study the behaviour of the long d.c,argon discharge positive column within the pressure range of 2 mmHg to:32 mmf-lg, and for discharge current levels from 60 mA to 300 mx.

2. Experimental conditions

The experimental device used was similar to the one described in a previouspaper (Toader 1967). A positive column was obtained over a length of DO emand in a 150 em long, 2·2 ern inside diameter discharge tube. This arrange­ment ensured good homogeneity along the plasma column, and satisfactorydischarge stability, while the positive column properties were independent ofthe length. In addition, the small end disturbances were eliminated. Theexperimental diagnosis method selected was the single and double probetechnique, with a minimum of disturbance to the plasma column cylindricalsymmetry.

t Communicated by the Author.

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554 E. I. Torula

3, Experimental results. Comparison with theory

The longitudinal electric field was obtained by the compensation method,by means of a double probe, between two points situated on the axis ofsymmetry of thc tube at a distance of 9·8 cm. Figure 1 shows the variation ofthe reduced electric field EIP as a function of the discharge current intensity forseveral pressure values, For lower discharge current levels, the reducedclcctric field EIP is practically indepcndcnt of the current intensity. Themaximum slope of the curves which show the relationship betwecn the reducedelectric field EIP and the discharge current intensity is obtained for the valuesof i bctwccn .10 ma and 100 m». On either side of this current range thecontruction decreases gradually, particularly toward the low current values.We may assume thc contraction phenomenon to disappear at values belowLm»: However, we regret that our experimental conditions have not allowedus to confirm this assumption.

Fig. 1

£ ( vOlt> )p em. m.mHq1,0 ,

DO

0.8

0.7

DB

0.5

0.4

0.3

0.2

.-5mmUgo-8mm I/g+-15mm/{gD-3?mm/{g

A closer analysis of the curves in fig. 1 shows that the ratio tl(EIP)/tliis greater at highcr pressure levels, due to the sharper decrease of the reducedelectric field with the increase of the discharge current. This may be explainedby admitting that the collision of the electrons against the excited atomsplays an important part in the ionization and excitation processes. Even if theooncontration of the excited atoms represents only a small fraction of theconccntration of thc normal state atoms, as a result of the high number ofelectrons with an energy higher than Vi- Vex the effective stepped ionizationcross-sectional area may be from one to two orders of magnitude higher thanthc effective direct ionization cross-sectional area. The contribution of the'direct and stepped ionizations has to be considered with extreme caution.

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Behaviour of an argon discharge column at medium pressures 555

The electron temperature was determined by means of the double probe.The values obtained at various pressure levels and their variation with the dis­charge current intensity are summarized in table 1. The data in the lastcolumn of this table are in agreement with the values obtained within the frame­work of the Schottky theory. The discrepancy between the experimental andtheoretical data is quite obvious. The explanation is similar to the one givenfor the longitudinal electric field. In fact, the variations of the longitudinalelectric field and electron temperature are closely related to the energy balance

Table 1

pi:60m~ {,=IOom,.. • '2QQm~ "jDQm~ T,t(17'IrnHg)

2 2.2 2Q /.7 14 145

5 2.1 1.8 1.5 1.3 1.25

10 16 14 [2 I.f 1.15

16 1.4 /3 /.1 1.0 /.10

22 - 1.2 1.0 0.95 1.0

52 - - 09 0.85 Ul

of the positive column. In the medium pressure range the electron tempera­ture seems to be dependent on the radial variable. \Ve have observed a dropin the electron temperature as the probes approached the tube wall. Thisone-way variation of the electron temperature cannot be attributed to anyexperimental error. We consider that as the method of determining theelectron temperature is improved further, it will become possible to obtainadditional information confirming or refuting this observation. At present theelectron temperature determination error is known to be relatively high(approximately 15%), and closely related to the determination precision ofotherphysical variables.

The charge carrier concentration requires additional precautions as, atmedium pressures, the mean free path of the charged particles is much shorterthan the cylindrical probe radius. Since the usual probe technique is notapplicable in this case, we used the method proposed by Zaharova et al. (1960),using the ionic current !tt the probe. The results obtained on the axis ofsymmetry of the tube are shown in table 2. A comparison of these results

Table 2p

j,$bom4 t.lillOm~ "200m~ ~·30omJt(mIl'lH9)

2 OS! II l6 1•.8

5 f.8 H 9.1 25.9

10 +.3 9.0 fB 2a3

16 76 129 196 2~8

22 - as 26.2 59.7

32 - - 29.0 46.3

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S5H E. I. To(cder

(2)

with the values obtained in the elementary diffusion theory has revealed that,within the limits of the experimental and theoretical error, a satisfactoryagreement with the theoretical results is limited to the 2 mmHg pressure levels.At higher pressures the theoretical values are lower than the experimental ones.This means that at pressures above 2 mmHg the mean ionization rate beginsto be proportional to the square of the electron concentration, and thus theprobuhility of new charged particles being nucleated along the discharge tubecentre-line is considerably higher.

The positive column contraction phenomenon at medium pressures has avery strong effect ou the intensity of the ionic current at the tube wall. In theSchottky theory the ionic current density is given by the expression:

7·8'3J p = 271';ll-'-pnok'l'.. (1)

Kngml and Ljagushchenko derived 'L new expression:

J eCD"fto 2 (1)• p = -.- y exp - - t dt,RoY

which takes into consideration all the new phenomena involved in the con­traction of the positive column.

A comparison of the experimental results obtained for the wall ionic currentdensity and the theoretical results obtained with the relations (J) and (2) isgiven in table a. While the agreement between the experimental results andthe theoreticn.l model proposed by Kagan and Ljagushchenko is satisfactory,the differences being within the experimental error range, the situation is quitedifferent when comparing the experimental results with the Schotty theory.

Tablc :{

i (mA)Pressure(mmHg)

2 ~ /0 16 22 32

roo"'"'0·21 0./0 0.07 0.05 0.04 0.025

~.60 EXPRESSION-Z- 0.1& 0." 0.0" 0.01 0.01 0.008

EXPRESSION-I- 0." O./T I.' ~. - -

1""'"'"'0.'. 0·/4 D." 006 0.05 0.82

~,fOO EKPRElSIOIV-Z- D." 0./2 0.15 MI 0.06 0.0'

EXPRESSION-I- f.OE 2.1 2.1 18 5.S -

r'"'"'O.SE 0.26 ,.., af2 0.07 004

~,200 EXPRESSION-2- 0.42 0.20 .0093 0.D7 0.06 U5

EJl.PRESSION-{- {.4 3.3 1.9 4·7 6.0 U

r""'"'~0.52 0.11 0.014 0.05 0.01 OIS

~'300 EXPRESSION-2- 0.61 0.32 0.\1 007 '.06 . 0.02

EXPRESSION_I_ 4.1 7.T 7.~ S.I 6J 1.6

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Behaviour of an argon discharge column at medium pressures 557

The discrepancy between the experimental and theoretical values increaseswith the pressure. At a pressure of 32 mmHg the calculated values arc byapproximatcly two orders of magnitude higher than the experimental results.The experiments have confirmed the reduction of the wall ionic current atmedium pressure levels with the increase of the pressure anticipated by thetheoretical model. However, if we consider the results obtained according tothe elementary diffusion theory, it is obvious that the wall ionic current densityincreases with the pressure. This increase is due to the high electron concen­tration values, which are involved directly in relation (1) and diminish the effectof the other variables,

Assuming both the electron and ion temperatures over the cross scetionof the tube to be constant, and thereby also the am bipolar diffusion coefficientindependent of r, we obtain a differential equation of thc form (Kagan andLjagushchenko 1964):

d2y 1dy " (1)

dt 2 +tdt +y-exp -y =0.

The solution of eqn. (3) satisfies the new limit conditions:

(3)

no dyy- - y' - =0 for t = 0,- G = 0' dt

y=O for t= J(~:) R

The latter condition is satisfied only whenI (4)

(5)to(no)=J(Z(;~G) R.Condition (5) enables an experimental control of the theoretical model applic­ability limits at medium pressure levels. We have checked this condition alsousing experimental data for the electron concentration, electron temperatureand longitudinal electric field. The other values were taken from the literature(Brown 19(9), assuming the EIP dependence to be satisfied. The resultsgivcn in table 4 show a satisfactory agreement between the theory and experi­ments for the investigated pressure range. The values of parameter G/no vary,the concentration increasing at higher pressure levels.

With regard to the influence of the electron temperature radial variationand of the gas temperature on the radial distribution of the charge earrier con­centration, we consider of particular interest thc conclusions reached in thework of Popescu and Popescu (19(Hi), where the electron concentration radialdistribution is given by the relation:

[ (r)J,volkTcO

n(r)=n; J o 2.405 R (6)

which generalizes the solution obtained in the Schottky theory. Relation (6)shows that the presence of temperature gradients affects the contractionphenomenon, in qualitative agreement with our experimental results.

The electron conccntration radial distribution obtained with the modelproposed by Kagan and Ljagushehenko varies only slightly with the experi­mental conditions. The high variation of the other physical values, such as

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558 E. I. Toader

wall ionic current density, electron concentration, electron temperature andlongitudinal elcctric field, is not reflected so markedly in the radial distributiontheoretical curve. To illustrate this, figs 2, 3 and 4 show the results obtained atthrec prcssurc levels, i.e. 2 mmHg, 10 mmHg and 16 mmHg. 'I'he experi­mental results were obtained using the ionic current at the moving cylindricalprobe, {I,t various distances from the centre-line. The electron concentration

Table 4

'(mAyPressure (mmH9')

2 5 JO '6 22 l2

t,(n.) 3.6 4.5 - - - -'·100 Zln.JR't. l8 4.9 8.5 173 25.7 329-----n;;:--

"In. 0.55 0.89 1.33 2.68 4.17 6.8

/;"(n.) 2,3 2.9 32 43 - -'.200 II Zln.JR';c 2.9 3.1 5.7 4.5 5.8 6.3

~.

.c/n. 0.36 042 0.53 0.88 0.95 1.02

{ t. (n.)1.6 1.8 2,4 32 42 -

(.300 IZ(n~R'" 1.72 2.1 2.6 4.3 6.7 I3

"In. 02 028 M 0.55 062 0.91

Fig. 2

nIi;

to

"46

04 ARGIN

42

00.2 44- a6

determination precision is satisfactory only up to a distance of 3 mrn from thetube WItH. The distortion of the results in the proximity of the tube wall wasprobably due to the disturbances caused by the spatial charge layer adjacentto the wall. Howcver, the actual cause of thcse disturbances is not sufficientlyclear to the author, as, according to the classical development of the theoryof the positive column phenomena, the mechanism of spatial charge layerformation should result in a reduction of the layer thickness due to the pressureincrease.

A very good agreement between the experiments and the theoretical modelat medium pressures is obtained for the 10 mmHg pressure level. The current

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Behaviour of an argon discharge column at medium pressures 559

Fig. 3

nIi;

(0

0.8

0.6

0.2

p.ro mmUg

{- IOOml

Fig. 4

nn;

p·r6mmHg{-roo mA

p'lOmmHgi·300mA

0.4 0.6

p'/6mmHg1'300mA

dependence is quite insignificant. At 16 mmHg the experimental resultspresent a greater contradiction than anticipated by the theory (see fig. 4).It is quite obvious that as the pressure increases, the discrepancy between theexperimental work and the theoretical model increases steadily.

The presence of undesired impurities had a disturbing effect throughoutthe experiments carried out to investigate the phenomenon of long positivecolumn contraction at medium pressures. When the cathode was attachedto the tube by means of a ground joint, and no special precautions were takenfor cooling the cathode part of the discharge tube, the Apiezon grease dried offand the plasma column began to spin immcdiately like a propeller at a ratewhich increased steadily with the impurities. Therefore, we abandoned thejoint-type tube design. These disturbances clearly indicate the need, in thecase of a long positive column, of removing all the contamination sources whichdistort the normal phenomena under study.

ACKNOWLEDGllIENTS

The present work has been carried out in the Gas Electronics Laboratoryof the Physics Faculty of the University of Bucharest. The author wouldlike to express his gratitude to Professor G. G. Bratescu for many fruitfuldiscussions and constructive suggestions.

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560 Behaviour of an arqon. discharge column at. medium pressures

R~;FERENCES

131\oWN, S. C., 1959, Basic Data of Plasma Plujsic« (New York: John Wiley & Sons,Inc.).

KAGAN, J. M., and LJAGUSHCHENKO, R. J., 1964, Zh. Tech. ri«, 34, 1873.POI'.I~SCU, I., and POPESCU, D., 1066, Rev. Roum, Phys., 11, 725.TOAUEI{, K I., 1966, An. Univ. Buck.-St. Nat., 16, 67; 19(;7, Int. J. Electron.,

23,417.ZAHAHOVA, V. M., KAGAN, J.l\L, MUSTAF.lN, K. S., and PERELI, V. 1.,1960, Zh. 'Peck.

r«, 30, 772.

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