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Progress in Nuclear Energy, Vol. 35, No. 2, pp. 203-208, 1999 © 1999 Published by Elsevier Science Ltd

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P I h S0149-1970(99 )00013-X

Measurement of Effective Delayed Neutron Fraction 13 elf by Covariance-to-Mean Method

for Benchmark Experiments of 13elf at FCA

Takesh i S a k u r a i , H i r o s h i S o d e y a m a and Sh igeak i O k a j i m a

Japan Atomic Energy Research Institute, Department of Nuclear Energy Systems

Tokai-mura, Naka-gun, Ibaraki-ken, Japan 319-1195

A b s t r a c t - - Measurements of the effective delayed neutron fraction 13 eff were carried out at the FCA facility of the Japan Atomic Energy Research Institute to contribute to benchmark experiments of 13elf. These measurements were made in two cores: XIX-1 core fueled with 93% enriched uranium and XIX- 3 core fueled with plutonium. The experimental 13elf was determined with a covariance-to-mean ratio of counts of a pair of neutron detectors installed in the core. The values of 13eff were 724+13pcm and 252+5pcm in the cores of XIX-1 and XIX-3 respectively. © 1999 Published by Elsevier Science Ltd. All rights reserved.

I. I N T R O D U C T I O N

The effective delayed neutron fraction 13eff is an important parameter as a reactivity scale of nuclear reactor. Benchmark experiments of the 13eff were planned at the FCA facility of the Japan Atomic Energy Research Institute(JAERI) to improve prediction accuracy of the/3 eff of fast reactor. The experiments were carried out in three cores(Sakurai et al., 1999) providing systematic change in nuclide contribution to the 13elf: XIX-1 core fueled with 93% enriched ura- nium; XIX-2 core fueled with plutonium(92% fissile) and natural uranium; XIX-3 core fueled with the plutonium. Comparisons of the 13 elf's between wide variety of measurement methods were planned in these experiments to improve the reliability of measurements and to achieve the target accuracy of 3% required for the experimental 13 eff.

In the present work, covariance-to-mean-method was applied to the 13 eff measurements in two cores of XIX-1 and XIX-3 to contribute to the benchmark experiments. This method was proposed by modifying the variance-to-mean method which has been applied so far to the 13 elf measurements at several critical assemblies(McCulloch, 1958; Moberg and Kockum, 1973). Both methods are based on the time-domain analysis of pulse series from neutron detector(s) installed in the core. The original method determines the 13 eff using the variance-to-mean ratio of counts from detector, while the modified method determines the 13eff using the covariance- to-mean ratio of counts from a pair of detectors. The modified method therefore can avoid the correction on the 13elf for count loss caused by the detector dead time. For this reason, the

203

204 T. Sakurai et al.

modified method has the advantage over the original method when the detector count rate is high.

The present paper is focused on describing procedures and results of the 13 elf measurements by the covariance-to-mean method. The measurement method is shown in ChapiI. The mea- surement of the covariance-to-mean ratio is described in Chap.HI. Results of the [3eff are dis- cussed in Chap.IV.

H. MEASUREMENT METHOD

The covariance-to-mean ratio of counts of a pair of detectors(#1 and #2) Cov /Mear t is given by(Uh , 197o)

Coy _ e D D D s (1-13e'f)2 { 1 - 1 - e x p ( - ° t ' r ) } , (1)

: Gate time width to take the counts of detectors (sec) : Prompt neutron decay constant (sec -1) : Counting efficiency of detector defined as a ratio of the detector count rate : to the total fission rate integrated in the reactor

DD :Diven factor(Diven, 1956) Ds : Spatial correction factor(Iijima and Otsuka, 1965)* 9 : Reactivity(ZX k/k).

The influence of the delayed neutrons is neglected in these equations. When the reactor has a spontaneous fission neutron source, the correlations of the source neutrons also contribute to the covariance-to-mean ratio. This contribution is also neglected in this equation.

When a parameter a v is defined by

(1 - - ~eff) 2 ctp =- e D D D s ~13~--9-~, (2)

which corresponds to the amplitude of r.h.s, of Eq.(1), the 13 eff is expressed by

1 13eff = \I av ' (3)

1 -t- (1 -- 9$) c DD Ds

where the Ps is the reactivity in dollars unit. The f5 eff is determined from the parameters of 9s, %, e, DD and Ds. The amplitude % is obtained from the measurement of covariance-to-mean ratio. The reactivity Ps can be measured by several methods such as using a calibrated control rod. The other parameters are obtained as follows.

To determine the detector efficiency e, one needs the total fission rate which is obtained as a product of two parameters : fission rate per volume Fc~ter(S-lcm -3) measured at the core center and a fission integral normalized at the core center FT(cm3). The latter parameter is expressed by

*For the spatial correction factor, the 'Ds ' is used in place of the 'g' which was originally used by Iijima and Otsuka(1965). The spatial effect was not considered in the original expression by Uhrig. The Ds was used in the the r.h.s, of Eq.(1) to take account of this effect.

where * 'r ot e

Covariance-to-mean method 205

f ( f E f ~ d E ) dv Fr = ~eacto~ (4)

(f Zf ~b dE)0 '

where qb : Space- and energy-dependent neutron flux Y, : Region- and energy-dependent macroscopic fission cross section

(f XfqbdE)0 : Value of f rfqbdE at the core center.

For the parameters of Fr, DO and Ds, semi-experimental values can be evaluated by combination of the measured fission rate distributions, the measured reactivity worth distributions of 252Cf neutron source and calculated corrections(Sakurai et aL, 1999).

HI. MEASUREMENT OF PARAMETERS FOR 13 elf

Sakurai et al. (1999) has already described the Fcertter and the semi-experimental values for Fr, DD and Ds. Techniques are shown below for the measurements of a~ and 95.

1. Amplitude of Covariance-to-Mean Ratio The covariance-to-mean ratio was measured by means of a pair of BF3 detectors(#1 and #2)

which was installed at symmetrical positions in the radial blanket near the core/blanket interface. Neutron counts of the detectors #1 and #2 were accumulated in multichannel scalers(MCS's) #1 and #2 respectively. Both MCS's had 8192 data channels respectively and every channel as a fundamental gate width(q:) was fixed at 0.1 ms. The gate width was chosen in consideration of the prompt neutron life time. These MCS's were operated so that they simultaneously started to store the neutron detection data in each channel for a sweep. This store of data was repeated typically 1000 times, i.e. 1000 sweeps and the covariance-to-mean ratio was obtained from the 1000-sweep-data.

The measurement was made at a slightly subcritical state of-0.02 dollars in the XIX-1 core. A 252Cf neutron source of about lxl0S(sec -1) was placed in this core to keep a constant flux level at the subcritical state. The measurements were made at three subcritical states of-1.13, -1 and -0.7 dollars in the XIX-3 core where the constant flux level was kept by a significant amount of intrinsic neutron source(about 2xl0Z(sec -1)) due to spontaneous fission of plutonium isotopes. Several fission counters were installed in the radial blanket region to monitor these neutron flux levels as described by Sakurai et al. (1999).

Figures 1 show the covariance-to-mean ratios plotted against the gate width where the ratios at the wider gate width than the fundamental one were obtained by a bunching technique(Misawa et al., 1990). A least-squares fit was made using Eq.(1) for the covariance-to-mean ratios to obtain the amplitude av. The fit was made for the data in the gate widths of 0.1~1ms and 0. l~4ms in the XIX-1 and XIX-3 cores respectively. The influence of the delayed neutrons is neglected in these ranges. The measurement was repeated to check reproducibility of the amplitude ctp.

206

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Least squares fit.

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1 0 .4 1 0 .3

Gate time width (sec)

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o

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/ -1 do s

<~-Data used for the fit-~> i i

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Gate time width (sec)

(a) XIX-1 core. (b) XIX-3 core.

Fig. 1 Plots of covariance-to-mean ratio against gate time width.

2 . Reactivity The reactivity 95 was determined from a difference in the calibrated control rod position

between the critical state and the subcritical state where the covariance-to-mean ratio was mea- sured. The control rod calibration in dollars unit has already been described by Sakurai et

a/.(1999). To get the control rod position at the critical state on condition that the external or in- trinsic neutron source existed in the core, the control rod position was plotted against the inverse count rate of flux level monitor at several reactivity levels as shown in Fig.2. The y-intercept of the least-squares fit corresponds to the position at the critical state.

"~" 95 I r I I I E

v ¢.,.

o

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85

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Fig.2 Plot of control rod position against inverse count rate of flux level monitor. Error bars are smaller than the symbols.

Covariance-to-mean method

IV. RESULTS AND CONCLUSION

207

Table 1 summarizes the parameters to determine the ~eff; the ap 95 and the other param- eters. The X1X-3 core had a significant amount of spontaneous fission neutron source as dis- cussed in Chap.III. The covariance-to-mean measurements however were made at subcritical states of-0.66--1.26 dollars where the source neutrons had a small contribution to the total neutrons in the reactor. These subcriticalities correspond to the effective multiplication factors keff's of 0.998-0.996. The contribution of source neutrons to the av was estimated from the keff(Furuhashi and Inaba, 1966; Saito, 1970) and was found to be 0.2~0.4%. This contribution was used as a correction for the source neutrons on the %. In the XIX-1 core, this correction was negligibly small because the amount of neutron source was less than that in the XIX-3 core by a factor of more than 100 and the subcriticality was also less than that in the XIX-3 core.

The efficiency c was determined from the Fcev.te r which was measured at the flux level of much higher than that of the covariance-to-mean ratio measurements(Sakurai et al. 1999). The count rate of flux level monitor was used to relate the flux levels between two kinds of measure- ments. The values for the Do and Ds were also taken from Sakurai et al. (1999).

Table 1 ~eff values obtained by covariance-to-mean method

Core name and XIX-1 XIX-3

reactivity level -0.02 dollar -1.3 dollar -1.0 dollar -0.7 dollar

Amplitude of covariance-to 0.1253 0.1136 0.1533 0.2073 -mean ratio ap

Reactivity 95 (dollars) -0.0241 -1.259 -0.970 -0.665

Detector efficiency e 7.81x10 -6 4.04x10 -6 4.10x10 -6 3.95x10 -G

Diven factor DD 0.803 0.816 0.816 0.816

Spatial correction factor Ds 1.110 1.127 1.127 1.127

13elf (pcm) 7244-13(1.8%)* 253-t-5(2.1%) 2514-5(2.1%) 251+5(2.1%)

* Values in parentheses : relative uncertainty. Breakdown of uncertainty is shown in Table 2.

Table 2 shows principal sources of the uncertainty. The uncertainty of ap was estimated from the reproducibility of % at the same reactivity level as before. The 'Drift' component in the reactivity uncertainty was estimated from (a) small change of reactivity caused by core tempera- ture change etc. during the long period of covariance-to-mean measurement which was typically 2 h and (b) reproducibility of the control rod position. The uncertainties of the control rod cal- ibration, the Fcertter, Fr, DD and Ds were taken from Sakurai et al. (1999). The uncertainty of the [3eff was estimated by propagating the uncertainties of these parameters. It is noted that the uncertainty of 95 had a negligibly small contribution to that of ~eff in the XIX-1 core because the measurement was made at a slightly subcritical level of 0.02 dollars and the 95 appeares in the expression of 13eff(Eq.(3)) as (1 - p$).

Good agreement of the [3eff's within the uncertainty of the c b was found between different reactivity levels in the XIX-3 core. A mean value of these ~eff'S was adopted in this core.

208 T. Sakurai et al.

Finally, the values of 13 eye by the present method were 724-4-13pcm and 252+5pcm in the cores of XIX-1 and XIX-3 respectively and were obtained with uncertainty of about 2%.

Table 2 Principal sources of uncertainty in ~ elf by covariance-to-mean method at FCA cores

Source of uncertainty Uncertainty

Amplitude of covariance-to-mean ratio a v +2.5%

Reactivity 9s

Drift ±0.2%

Control rod calibration in dollars unit -t-2%

Detector efficiency e

Central fission rate Fcer~ter +0.7~1.2%

Relative fission integral F~ -4-1.0%

Diven factor Dr9 -4-2.0%

Spatial correction factor Ds -4-1.0%

Total (13 elf) + 1.8~2.1%

ACKNOWLEDGEMENT

The authors are grateful to FCA staff members for their support in the experiments.

REFERENCES

Diven, B.C., et aL (1956)Multiplicities of Fission Neutrons Phys. Rev. 101, 1012. Furuhashi, A., Inaba, G. (1966) Eine Korrektur der Formel fur die Rossi-cx Methode J. Nucl.

Sci. Technol. 3, 305. Iijima, T., Otsuka, M. (1965) Space-Dependent Formula for Rossi-~ Measurements. Nukleonik.

7, 488. Misawa, T., et al. (1990) Measurements of Prompt Neutron Decay Constant and Large Subcrit-

icality by the Feynman-o~ Method. Nucl. Sci. Eng. 104, 53. Moberg, L., Kockum, J. (1973) Measurement of the Effective Delayed-Neutron Fraction in

Three Different Cores of the Fast Assembly FRO. NucL Sci. Eng. 52, 343. Saito, K. (1970) Theory of Reactor Noise. JAERI 1187 (in Japanese). Sakurai, T., et aL (1999) Experimental Cores for Benchmark Experiments of Effective Delayed

Neutron Fraction ~eff at FCA. in this volume of Progress in Nuclear Energy. Uhrig, R.E. (1970) Random Noise Techniques in Nuclear Reactor Systems The Ronald Press

Company, New York.