Raport INT 17511

THE GAS AMPLIFICATION FACTORIN Kr ISO-PENTANE FILLED

PROPORTIONAL COUNTERS

TADEUSZ Z. KOWALSKI

The gas amplification factor in Кг + iso-p«ntanefilled proportional counters

Mzaocnienie gazowe w licznikach proporcjonalnychnapełnionych mieszaniną Kr + izopentan

Газовое усиление в пропорциональных счётчикахЛ наполненных смесью Кр + изопентан

Twtau*z Z. Kmmlsttl

*

Cracew

Matryce wykonano według dostarczonych oryginałów

This report has been reproduced directly from

the best available copy

Rozprowadza - Распространяв! - Available from:OŚRODEK INFORMACJI O ENERGII JĄDROWEJ

00.901 Warszawa, PKiN, XI p. »

Wydaje:INSTYTUT fIZYKI I TECHNIKI JĄDROWEJ AGH - KRAKÓW

30-059 Kraków, «i. Mickiewicza 30

Wyłoni. 1. Nakład -455-f-23 eaz.

РоамЛЛгчк. kl. I I I, Al. 63 в

Zamówienie яг 51 83 ISSN 0302-W34Dało dostarczenia

T-ł-H»maszynopisu przez autora: styczeń

Ar*, druk. 1,0Oddano do produkcji 3 III 1*63

Druk ukończono w marcu 1963!»83

w Zoitłodzte Graficznym Akademii Górmcao-Hułnitz«i im. S. SrOiiico, Kroków, vi Man'rł*slv Lipcowego 16

»

SummaryMeasurements of gas amplification in a proportional counterwith Кг/iso-pentane mixtures were t»lc*n; at pressuresranging from 160 to 970 hPa. A new formula for gas amplifi-cation in a proportional counters was derived. Л goodagreement between the formula and experimental data wasfound over the range of variables studied. I D Z U ^ . * Ц

StreszczenieV pracy wykonano pomiary wzmocnienia gazowego w liczniKachproporcjonalnych napełnionych mieszaniną Kr/izopentandla ciśnień całkowitych mieszaniny od 1бО do 970 hPa.Na podstawie tych pomiarów wyprowadzono nową formułę nawspółczynnik wzmocnienia gazowego w licznikach proporcjonal-nych. Uzyskano zgodność wyńilfów pomiarów z przewidywaniamiteorii w całym zakresie pracy licznika, w którym wykonanopomiary.

РезюмеПредставлены результаты измерений гьзо^огс усиленияпропорционального,счётчика наполненого смесьюКр/изопентак, под давлением от 160 ао S70hfb при iC'̂ C..Используя этие результаты получено нозую формулу КОгазовое усиление. Полученные результаты хорошо опись-ваются этой формулой.

Contents

1. Introduction u 5

2. Experimental 5

3. Theory- 6

4. Conclusion ................................... 11

5. Acknowledgments • 14

References 15

1. Introduction

In recent years interest has grown it» proportional counters

which have found wide application in «any fields of ionizing

radiation detection.*

The mechanism of gas multiplication process in proportio-

nal counters was investigated theoretically by several

authors [6-ю]. Various authors making a proper assumption

have derived different expressions for gas gain in propor-

tional counters ал a function of the applied potential, geo-

metrical parameters of the detector and fill gas pressure.

There is some controversy as the applicability of the various

gas gain formulae. These expressions don't describe tfce gaś

amplification factors over the range of variables

Studied[6,11-1A].

In this laboratory Kr/isopentane filled proportional

counters have been developed for M8ssbauer effect spectro-

metry [15,16J.

The date gathered for Kr/isopentane mixtures [1] indicate

that none of the previously obtained formulae can satisfa-

ctorily describe the experimental dependence of the gas am-

plification factor over the whole range of measurements.

Taking this into consideration it seems useful tc develop

a theory of gas amplification for this type of counter.

2. Experimental •

The apparatus employed for the present experiments isidentical witc that described in the previous paper [l].

The measurements of gas amplification factor forKrypton - filled proportional counter having iso-pentanequench gas additives have been made over the wide rangecf changes of the concentration of vapour of iso-pentane.The measurements were taken for the following pressures;160, 290, 5>3O and 970 hPa at 20°C. The range of gas multipli-cation was from 1 to 6'10 j'

The results are presented, for krypton spectroscopically

—5 ~hpure, Кг + 8.66*10 iso-pentane and Kr + 4.12*10 iso-penta-ne i fig 1 and for Kr + 1.13%, 1.92*, A.1# iso-pentane infig. 2.3. Theory

The number of electrons in electron avalanche can be calcula-ted using a standard expressions for gas gain [3],

Nfrj « No exp(|o<(r]drj hi

g

or N(SJ - No exp|ra S a p j-Ą*- - Ś | J /2/

where:r. - the starting point of gas amplification,r - the distance of electron avalanche from the center

of the counter,N - the number of primary ionization electrons,N(r] - the number of electrons in electron avalanche in dis-

tance r from the anode wire,г - radius of anode wire,. .S , S, S - the value of E/p for г., г and rft, respectively,

' /E - electrical field strength, p-fill gas pressure/,Ok - the first To^nsend coefficient /as a function of г or Si.

If dr «A» N is the number of electrons in electronavalanche in distance r +Afrom the center of the counterand the formulae /1/ and /2/ could be transformed into fora

and N(S) - N o exp[ra S a -S^|^ &S), /2'/

where: ,Л - aean distance between the collision of. an' electron in the

'direction of the electric field.

~\cressure

mixtures""—^Kr spectr.pure

Kr+8.66-10"5

iso-pentane

Kr+4.12*10"*iso-pentane

970 hPa

12

11-

10

530 hPa

9

8

7

290 hPa

6•

5

160hPaV

\

3

2

i '

200 600

Fig. 1

1000 1400 1800 2200

Applied potential (volts)

Gas"amplification factor, A, for Kr spectroscopicaliy pure,

Кг + 8.66*10- iso^pentane, Кг + k.12*10 iso-pentane

f i l led proportional counters.for the pressures: ifcO, <?Э0,

530 and 970 hPa, at 20°c.

ю

2.р- 290 ЬРа5.р« 970 hPa

3. р- 290 hPa

1Kr* 1.927. iso-pentan*

200 600 Ю00 КОО «00 2200 2600Applied potential (volts)

Fig. 2Gas amplification factor, A, for Кг • 1.13%, 1.92%, 4.1%iso-pentane f i l l ed proportional counters for the pressures:160, 290, 550 and 970 hPa at 20°C.

As - the change of S corresponding toX.Assuming thatt- there ii only the ionization of sain gas In the electronavalanche,

- the space charge effects, recombination of electron-ionpairs, photoelectric effect at the cathode and electronattachement due to impurities can be neglected,

the growth of number of electrons.In an electron avalanchein the distance r one can calculate using expression '3/

M(r) -No(r*A) . И (^--.-^jJ^-- , /3/

wheret- the concentration of qvenching gas,

. - the electron cross-section for ionizing impact withatoms of main gas,

О - to ta l electron cross-section for Interaction with atomsof main gas,

6- - total electron cross-section for interaction with mole-cules of quenching gas.

Using expressions /2'/ and /3/ one can develop* the fol-lowing formula

Expanding of the expression /4/ into a series we canobtain a general equatiom tar сЦ&), '

kś* - Ъ& - г. S -^Й- AS /5/

where:1 - C ,

Taking into consideration As * -̂ '••£.. I US

JL_ J^^ j j i . _tóL_ . P Г * " ^

r k radius of cathode, U- voltage supply]

it leads to the expression /6/

A 4j - В ̂

The first Tovnsend coefficient is a square function of theelectron cross-section for ionizing impact with atoms of maingas. Putting the exact expression for electron cross-section5u as a function of electron energy one obtains a formulafor <Ąs) .

The electron cross-section 6. / for energy a. little.higher than.the i<-nization energy/ increases linearly vithincreasing the energy of electrons [2], and can be expressed:

4 )where £ - kinetic energy of electron,

£. - the ionization .energy of main gas,a - the coefficient of proportionality.

Assuming that the energy of electron can be representedby the mean electron^energy of Druyvesteyn_electron distri-bution function[£» £"• O.57«e»E«Js-» where £ - mean electronenergy of Druyvesteyn electron distribution function,e - eleeentary charge, /~- mean free path of electron, УС - ave-rage electron energy lost in elastic impacts vith molecu-les r*lj for b*. one gets

śĄ - a (lpS - £ ) where 1 - 0.57*eV£r /?''

We can substitute function /7'/ and the dependence X " -Гй6 t •* • P

4 and Л , respectively.

It

Hence

.For a proportional counter we may aasume that [6]

- -2L is a funotioD of S only,S is a characteristic constant of the given'gas,1

so 1пА/(р г S | is a function ot S only

^_ . I'M JJ . ,(S.) «,IS1

where A- N(SJ/N Q.JWe can substitute function /8/ in place of =aSi. and for

gas amplification in a proportional counter we obtain

• A iins a - A 2 S S * к /io/

Formula /10/ includes four constants A , А.., А„ and K. Theconstants A . А.,, Л-, and К are the function of microscopic

O i c.

property of filling gas and have to be deduced from measu-rements.

The experimental results for the spectroscopically purekrypton, Kr-+ 8.66*10 iso-pentane, Kr • A.12'10~ iso-pentaneara plotted according to formula /10/ in fig. 3 and forKr 4- 1.1394, 1.92*, 4.1* iso-pentan* in fig. h.

The complete agreement with a straightline law enablesus to accept equation /10/ as the proper one.

k. ConclusionThe new formula for gas* amplification factor in proportio-

nal counter was obtained and verified for Кг/iao-pentanemixtures.

On the basis of the verification it may be supposed thatequation /10/ can be usefulnes for the majority of gases used

11

с 10"'

40

3.0

£

IX)

F(Se)- A,

0ХК

• 1. Krypton spectr. pure

2. Kr + 8.66*10 isopentane3. Kr+ 4.12*10"*isopentane

Q06 006 0Л2 0.14 F(So)

Fig. 3Gas amplification factor. A, giren as 1пА//р г S ) , forКг spectr. pure, Kr * 8.66*10~' iso-pentane,JCr > 4.12*10~ iso-pentane filled proportional countersplotted against T(Sj - A 1lnS e - A o/S a - kz\.

2. Кг3. Kr

Kr • 1,13*/» isopentane«• 1,92*4 isopentane

isopentane

0,08 0,10 0,12 0,14 F(Sa)

Mg. kGas amplification factor, A, given as lxA.Ąp r& S^ forКг • 1.13%, 1.92*. 4.1Jt iso-pentane f i l l ed proportionalcounters plotted against F{sJ - *<{Ь&Л - A 2 * s

a " Ao^Sa'

13

in proportional countess.Constanta appropriate te the proposes foraula have been

determined for the analysed mixtures. The constants A , A.and A 2 «re given in table 1.

Table 1.Parameters A .

•"-̂ Parameter,*F i l l g u — . ^ ^

Kr speetrpure

Kr • 8.66*10" !

iso-pentane

'кг • 4.12'10""*iso-pentane

Kr • 1.13* •iso-pentane

Kr • 1.92*iso-pentane

Kr • 4.1*iso-pentane

A1 and A2

- 0.335

- 0.632

- 0.202

- 0.778

- 0.64

- 0.605

*, И

1.91*tO"2

2.81*10-2

1.38*10"2

3.57*10"2

3.17*10"2

3.16*10*2

A2[.*..V-2]

6.52*10-5

'3.8*10-5

1.67.10"*

-2.7*1O"5

1.23*10"6

-7.06'10"6

5. AcknowledgmentsI wish to express my sincere gratitude to Assistant

Professor Or K.V. Ostrowski and to Assistant ProfessorDr K. Jeleń for their valuable suggestions and encouragementrendered during the course of this work.

References

1. Т.Z. Kowalski, Raport INT /I Cracow 1983 /Submittedto Nuci. Instr. and Metn./

2. S.A. Korff, Electron and Nuclear Counters, New York 1946.3. M. Baabynek, Nuci. Instr. and Meth. 112/1973/103.4-. M.J. Druyvesteyn, Physica 10/1950/61, 1/1935/ЮОЗ. .5. J. Groszkowski, Technique of nigh vacuum, WNT, Warsaw

1978.6. A. Zastawny, J. Sci. Instr. 43/1966/179.7. И.Е, Rose and S.A. Korff, Phys. Rev. 59/19M/85C6. L.G. Khristov, Dokl. Bulg.Akad. NauK 10/1947/4f>3.9. S.C. Curran and J.D. Craggs, Counting tubes /Academic

Press, New York 19^9/.10. W. Diethorn, Report NYO-6628/1956/.11. G.E. Kocharov and C.A. Xorolev, Izvest. Akad. Лаик S23K,

Ser. Fiz. 27/1963/301.Kiser, Appl. Sci. Res. B8/1960/163.Hendricks, Nuci. Inrtr. and Meth. 102/1972/309.Specht and P. Armbruster, NuKieonik 7/1965/S.

B. Bednarek, if. Jagusztyn, K. Jrlerl, K;V. OstrowsKi,E. Rulikowska-Zaręoska, Z. Sanok, К. Tereszko, M. Wali-górski, Raport INT 96/1, Cracow 1976, / in polish/.E. Rulikowska, Thesis, University of Mining and Metallurgy

Cracow 197' /unpublished/.

12.13.14.

R.¥R.VH.J

15

- ZAKŁAD•• GRAFłCZNr — •

- A G H «KRAKÓW—

JSSN0M2-KB4