Particle and energy dependence of the statistical fluctuations of an ionization chamber current

Nuclear Instruments and Methods in Physics Research B 95 (1995) 7-13

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Beam Interactions with Materials & Atoms

ELSEVIER

Particle and energy dependence of the statistical fluctuations of an ionization chamber current Lidia Purghel, Nicolae V~lcov

*

Institute of Atomic Physics, P.O. Box MG-6, Bucharest, Romania

Received 21 February 1994; revised form received 27 June 1994 Abstract

For the purpose of getting more detailed information concerning the processes leading to statistical fluctuations of an ionization chamber current, measurements with various radioactive sources have been done. By using the experimental arrangement described elsewhere [A. Necula et al. Nucl. Instr. and Meth. A 332 (1993) 501] the mean value and the standard deviation of the ionization current for 3H (water vapours), 6°Co (sealed source), SgKr (gas), 2°4T1 (8 mm diameter disk) and 239pu (10 mm diameter disk), beta, gamma and alpha sources have been measured. A statistical model explaining the experimental data is proposed.

1. I n t r o d u c t i o n

An experimental study of statistical fluctuations of the ionization current produced by gamma-rays in a normal pressure air-filled ionization chamber has been recently performed [1]. The main conclusions were the following: - the variance of the ionization current is proportional to the mean value of the ionization current and to the transmitted frequency bandwidth of the measuring circuit, - For the same mean value of the ionization current, the variance of the ionization current does not depend on the chamber volume, space distribution of the gamma field or the polarity of the biasing voltage, - the statistical fluctuations of the ionization current could be explained as fluctuations of the total number of interactions of gamma-rays inside and nearby the ionization chamber, leading to electrons traveling inside the chamber volume during the integration time. A detailed analysis of the complex physical process, including gamma-ray interactions, ionizations produced by secondary electrons and collection of the resulted ionelectron pairs (called "pairs" in the following) is quite difficult, due to the poor knowledge of the rate of producing gamma-ray interactions as well of the energy, lost by secondary electrons in the chamber volume. In order to learn more about the mechanism leading to the statistical fluctuations of the ionization current, the use of other radioactive sources, particularly those emitting alpha or

* Corresponding author.

beta particles seems to be more suitable. As it is wellknown, for alpha and beta radioactive sources the rate of emission of ionizing particles and the energy loss inside the chamber volume are better determined (especially for the stopped ones at rest in the chamber volume particles).

2. Experimental

arrangement

The experimental arrangement, the same as that previously used [1], is shown in Fig. 1. The current of the ionization chamber IC flowing through the load resistor R = 10 l° 1~ produces a voltage signal, measured by a Keithley 614 digital electrometer connected as a voltmeter. Thus the voltage signal with 5 digits readings provides for a 10 -15 A resolution, on the 0.2 V scale. Two types of atmospheric pressure, air-filled ionization chambers have been used: - 10 1 volume model CIS-NM-10-TC chamber, working as a tritium and high-sensitivity gamma-ray detector in the MT-1 monitor, made by Nuclear and Vacuum Factory in Bucharest, used with gaseous and water vapours sources, - 2 1 volume model CIS-NM-2000 chamber, working as a gamma detector in the MFG-83 gamma-ray nuclear power station background monitor, made by Nuclear and Vacuum Factory in Bucharest, used with solid sources. The 2°4T1 solid beta source was mounted on the bottom of the ionization chamber supposed to be oriented with the symmetry axis in a vertical position, while for the 239pu alpha source a special geometry, shown in Fig. 2, has been used. A 5 mm diameter collimator selects only the quasi-

0168-583X/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSDI 0168-583X(94)00334-3

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L. Purghel, N. Wdcov/Nucl. Instr. andMeth, in Phys. Res. B 95 (1995) 7-13

\

L

_

Fig. 1. Experimental arrangement. IC - Ionization chamber, K - Coaxial cable, SIT 3002 - High voltage supply, Keithley 614 - Digital electrometer, STR 404 - Reference voltage supply, ENDIM 621.01 - Chart recorder.

parallel to the electrodes alpha-particles entering, directly or through a stopping foil, in the electric field between the inner and the outer electrodes. Both ionization chambers are cylindrical, the outer electrode being biased at 400 V, while the inner one being connected through a load resistor to the ground. The integration time constant for all measurements was equal to about 2 s.

deviation with the radioactive sources listed in Table 1 were performed. The type (third column) and the energy of decay (sixth column) correspond to transitions, predominantly contributing to the ionization current. The obtained results are shown in Tables 2 and 3. Table 2 contains the measured mean value (second column):

i=l ,k, nk=l and the standard deviation (third column)

3. Results

~

o-=

Series of 100 measurements (15% statistical error at a 95% confidence level), for the evaluation of the standard

1

~

_~

~-1

(I,-I)k=l

Table 1 Radioactive sources used in measurements Radionuclide

Physical state

Type of decay

Activity

Energy [keV]

[kBq] 3H

water vapours

60Co

sealed source

beta gamma

SSKr

gas 8 mm O disk 10 mm Q disk

beta beta alpha

204T1 239pu

Table 2 Results for 3H and

239

239pu

3H

3.7 )<

2.3 )< 10 6 10 4

-

647 380

4.2 )<

104

-

18.6 ( 1 0 0 % ) 1173 (99.89%) 1333 (99.98%) max 687 (99.6%) max 763 (97.5%) 5156 (73%) 5143 (15.1%) 5105 (11.7%) max

• Pu radloactwe sources

Radionuclide

239pu +

[kBq/m 3]

A1 stopping foil

i [pA]

o[pA]

K

52 20 800

0.56 0.22 0.094

1 1 1.18

ff2p [keV]

Q

N [)<1041

o'/] [×10 4]

K/ff~

[pC]

4150 1600 5.7

208 80 3200

1.06 1.06 1.19 )< 10 4

108 110 1.2

97 97 1.1

[)<10-4]

L. Purghel, N. VMcov /Nucl. Instr. and Meth. in Phys. Res. B 95 (1995) 7-13

(or produced by interactions) during the effective integration time 2 r (see Appendix A) and a the number of pairs produced by one ionizing particle, equal to

120

a =Ep/e,

~16

--O

l

I I I I.____._~

(2)

where Ep is the energy, lost by the ionizing particle and e the mean energy loss for producing one pair. (2) The measured quantity is the voltage signal U across the load resistor R, but due to the parallel capacitor C the current through the load resistor I R may differ from the ionization chamber current I. Whereas for large values of the integration time constant there is a proportionality between the collected charge Q and the voltage signal U:

._

I

I I

9

O = CU,

(3)

where: O = f/+2~l dt = 2rlAv.

(4)

We have for the mean values only:

Fig. 2. Alpha source geometry of measurement. O - outer electrode, I - inner electrode, C - collimator.

of the ionization current, for the radioactive sources emitting ionizing particles stopped at rest in the chamber volume. Similar data for the radioactive sources emitting ionizing particles (or producing ionizing particles through interactions) loosing only a part of their energy in the chamber volume are presented in Table 3 (second and third columns).

iR=i.

(5)

By denoting by ~R the standard deviation of IR, the experimental coefficient of variation, we have to deal with, is: o" % o"v o"o

i

iR

-

U

-

(6)

0

(3) As a product of statistically independent variables N and o~ the collected charge coefficient of variation is given by:

4. Discussion

By assuming the total number of ionizing particles to be characterised by a Poisson statistical distribution the standard deviation is:

4.1. A proposed statistical model In order to carry out a statistical analysis of the physical process leading to the ionization current, the following assumptions were used: (1) All pairs produced in the ionization chamber sensitive volume are collected, consequently: O=eNa,

(1)

cru = X/~.

(8)

As concerns the standard deviation of the number of pairs produced by one ionizing particle the following relationship may be used: % '-- ~

(9)

where Q is the collected electric charge, e the electron charge, N the total number of ionizing particles emitted

where F represents the Fano factor [2] and for N particles producing pairs during the effective integration time 2 r the standard deviation becomes:

Table 3 Results for

60Co, 85Kr and 2°4T1 radioactive sources

~

Radionuclide

] [pa]

o[pa]

K

6°Co 85Kr 2°4T1

253 252 32

0.22 0.21 0.074

1 1 1

o-/ KV~ [ × 10- 3 pal/z ]

/~p [keV]

/V [ × 10 6]

13.8 13.2 13.1

121 106 104

1.78 2.27 0.26

(10)

~

By introducing Eqs. (8) and (10) into Eq. (7) and by observing that ~ > 100 for the radioactive sources used in the measurements, F is always less than unity and as N --- -N, we obtain: O-Q

/1

- VN +

F

1

(11)

10

L. Purghel, N. VMcov / Nucl. Instr. and Meth. in Phys. Res. B 95 (1995) 7-13

In order to take into account the energy distribution of the ionizing particles, a correction factor K (1 < K < 1.25) has been introduced (see Appendix B) and Eq. (11) must be replaced by: o*?

crQ 0

K 1/'~"

(12)

4.2. First check of the model Because the experimental coefficient of variation depends, according to Eq. (12), only on the number of ionizing particles, two radioactive sources with the same rate of emission but different mean values of the ionizing particle energy should be characterized by the same coeffi-

cient of variation. For such a check the same collimated alpha source with and without an aluminium stopping foil ( ~ 5 ~m thick) was used. The 5 mm diameter collimator selects the quasiparallel to the electrodes alpha-particles (see Fig. 2) providing that the same number of alpha-particles are before and after the stopping foil. For a given N, the mean value of the ionization current is proportional to a (or Ep), thus ffTpmay be deduced from the measured i value. The obtained results are summarized in the first two lines of Table 2. Due to the slowing-down effect of a 10 mm air layer, the energy of the alpha-particles at the output of the collimator is 4150 keV. By introducing the aluminium stopping foil, the mean energy of the alpha-particles is lowered to 1600 keV. As can be seen in Table 2, though the mean value of the ionization current (second column) and the alpha-particle energy (fifth column) were

G' ,

,

AI12

I

O,O9"t

0,08

0,07

0,06'

0,05

0,03,

0,02'

0,01'

" 0

; 10

I 20

I 30

I /*0

I SO

I 8)

I -~7O ~:F. (keV 112 )

Fig. 3. The o'/KV/i vs. E~p dependence.

11

L. Purghel, N. VMcov /NucL Instr. and Meth. in Phys. Res. B 95 (1995) 7-13

decreased by more than 2.5 times, the coefficient of variation remains the same (eighth column). 4.3. Second check of the model

By taking into account the difficulty to get radioactive sources with the same N value for a wider ionizing particle energy range, other relationships beside Eq. (12) have to be used for checking the statistical model. For this purpose, from Eqs. (1), (2), (4) and (12) we get:

5. Conclusions

O"

KV~ = const~p-p.

(13)

In this way the linearity of the experimental cr/K~f] vs. ~/Ep dependence for different radioactive sources proves the correctness of the proposed model. The dependence o-/KV/i vs. ~ - p is shown in Fig. 3. A straight line is drawn, using the data taken from Table 2 for 239pu (point 1), 239pu + stopping foil (point 2) and 3H (point 3). The agreement is good, especially if taking into account that the ratio of the highest ionizing particle energy to the lowest one is as much as 730 and that the straight line fits, actually, four points, including the origin of coordinates. 4.4. Third check of the model

Whereas Eq. (13) indicates the general trend of statistical fluctuations of the ionization current, a more quantitative check concerning the calculated absolute values would be desirable. This may be done by using again the data contained in Table 2. The mean number of ionizing particles emitted during the integration time (see Eqs. (1), (2) and (4)) is: =

tion time, may be obtained, for any radioactive source. For illustration, the results are shown in Fig. 3 and Table 3 for 6°Co, 85Kr and 2°4T1 (points 4, 5 and 6 in Fig. 3). The fact that about the same value was obtained for 6°Co, 85Kr and 2°4T1 may be explained by the constant stopping power for electrons in the 0.2-1.2 MeV energy range [3] associated with the cutoff effect on the electron energy spectrum.

2rEi eEp'

The analysis of the results leads to the following conclusions: (1) The proposed statistical model proves a good agreement with the experimental data concerning the statistical fluctuations for radioactive sources emitting, or producing by interactions, short range ionizing particles. (2) By starting from the proposed model a new method of studying some physical processes in ionization chambers has been suggested. The simplest way to get such an information is based on Eq. (12), permitting to obtain the number of ionizing particles emitted, or produced by interactions, during the integration time, from the measured coefficient of variation. Then, from Eqs. (1) and (4), by using the measured mean value of the ionization current, the ionizing particle energy may be deduced.

Acknowledgements This research was Ministry of Research is due to C. Condor, valuable collaboration

supported in part by the Romanian and Technology. Acknowledgement M. Ionita and I. Ploscaru for their concerning the measurements.

(14)

By introducing in this relationship the mean values of the ionization current (second column) and the mean ionizing particle energy (fifth column), the mean number of ionizing particles (seventh column) and the calculated coefficient of variation (ninth column) are obtained. The difference between the experimental (eight column) and the calculated (ninth column) coefficient of variation does not exceed the assumed 15% statistical uncertainty.

Appendix A For a constant current generator I (ionization chamber) working on a simple integrating circuit, shown in Fig. 4, the shot-noise (for simplicity we shall refer in the following only to the shot-noise fluctuations) variance for an I mean value of the current [4]: j

(A.1)

0.2 = 2 e ] A f = - - A w "fr

4,5. Applications of the model

The proposed statistical model may be used, to obtain valuable information concerning detection processes in ionization chambers. By using the measured mean value and variance of the ionization current, from the straight line shown in Fig. 3 the mean value of the ionizing particle energy and then from Eq. (14) the mean number of emitted (or produced by interactions) particles during the integra-

_

CR= ~o

Fig. 4. Equivalent output circuit of an ionization chamber.

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L. Purghel, N. VMcov /Nucl. Instr. and Meth. in Phys. Res. B 95 (1995) 7-13

Appendix B

corresponds to a constant spectral density: 0-2 a~o

Sl(°O

d ~r

The number of pairs produced by a single ionizing particle represents, generally, a ratio of two fluctuating quantities, e and Ep:

(A.2)

The spectral density of the voltage signal across the RC integrating circuit is [5]:

a = Ep/E.

(A.3)

S v ( tO) = ]Z(ito) 12Sl( tO),

As • and Ep may be considered statistically independent variables, we have:

where Z(i w) represents the impedance of the integrating circuit:

O'a =

R 1 + itor'

Z(iw)

(B.1)

R2 dto=

f 1+

where 0-~

d

0.)2,/- 2 'IT

'IT'/"

(B.2)

(A.4) Ep

rAoJ >> 1 we have: and Eq. (A.4) becomes: Rad

(a.5)

2r 1

~

i

V~

(B.3)

0-E__=Z~>> ~a=a,

The coefficient of variation is: o-

V~ ETv'

In order to calculate the coefficient of variation o'~//E?p, simple mathematical functions for ionizing particle energy spectra can be used. Such simplified functions are shown in Fig. 5 for Compton scattering electrons (Fig. 5a) and beta-decay electrons (Fig. 5b). The corresponding calculated mean values and standard deviations of the energy are also shown. By observing that usually:

arctg rA w = ~r/2,

o-u

~-~a

and arctg rh w.

For large integration time constants

0-2=

1 o'~'

do,)

R2d

-

,

~G ]

a

The variance of the voltage signal across the RC integrating circuit is given by:

~2 = is,:(o,)

2+

Ep

v~'

we may write:

where N represents the number of elementary charges carried on by the current i during the "effective" integration time 2r.

IfI

o-,,

~rG

1 0-~

(B.4)

2t

-~:TEM 1 , I ~';--~v-~-~EM (a)

EM

Ejp

mE M

l*m ECTE.

-

' ~E. G'4 ~ { b)

EM

E,~

Eo EM -E~I~--~-Cd Eo Eo

-E~

,~3 Eo d.DX(Eo_gl - """ E. 64 • (c}

Fig. 5. Simple/unctions describingionizing particle energyspectra: (a) Compton electronspectrum, (b) Beta spectrum,(c) cutoff Compton electron spectrum.

L. Purghel, N. Wflcov/ NucL Instr. and Meth. in Phys. Res. B 95 (1995) 7-13 By introducing Eq. (B.4) in Eq. (7) we obtain:

% 0-=

+u1

G

K

(12)

where K represents the correction factor:

(
K=

1+

.

(B.5)

Let us mention that the K-values are substantially decreased for the so-called "cutoff spectra", corresponding to the cases when the ionizing particle energies in the spectrum exceed the maximum energy of the particle to be stopped at rest in the chamber volume. By denoting by E 0 the "cutoff ionizing particle energy" the distorted energy spectrum fa(E) will be composed of the initial energy distribution:

fd(E) = f ( E )

for E <~Eo,

13

The calculated values of the correction factor K for all radioactive sources used in our measurements are shown in Tables 1 and 2 (fourth column). A test concerning the errors introduced by the simplified functions shown in Fig. 5 has been done, by comparing the K-values obtained with the experimental beta spectrum of tritium and with the simplified function (Fig. 5b) for E M = 18.6 keV and m = 0.166. The K-values were: Kexp = 1.18, Kfunct = 1.15. For a rougher estimation the following K-values could be used: K = 1,

for alpha-radioactive sources,

K = 1.13 + 0.10,

for beta-radioactive sources,

K = 1.08 + 0.08,

for gamma-radioactive sources,

by adding a 9% uncertainty in the calculations concerning the beta and gamma-radioactive sources.

and a delta-function around E0: f~(E)=Aa(E-E0)

f o r E > E o,

where A represents the fraction of the initial energy spectrum above Eo:

a = f ~ M f ( E ) dE. A distorted Compton electron spectrum is shown in Fig. 5c. A similar approach may be used for a distorted Fermi beta spectrum.

References [1] A. Necula, L. Purghel, N. V~lcov, Nucl. Instr. and Meth. A 332 (1993) 501. [2] U. Fano, Phys. Rev. 42 (1947) 26. [3] Int. Commissionon RadiationUnits and Measurements,ICRU Rep. 37, WashingtonD.C. (1984). [4] E. Kowalski, Nuclear Electronics(Springer, Berlin, 1970). [5] D.R. Cox and D.V. Hinkley, Theoretical Statistics (Chapman and Hall, London, 1974).