Effect of neutron spectrum on subcritical multiplication factor in accelerator-driven system

Progress in Nuclear Energy 116 (2019) 158–167

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Effect of neutron spectrum on subcritical multiplication factor in accelerator-driven system

T

Naoto Aizawaa,∗, Masao Yamanakab, Tomohiko Iwasakia, Cheol Ho Pyeonb a b

Tohoku University, Aoba 6-6-2-01, Aramaki-aza-Aoba, Aoba-ku, Sendai, 980-8579, Japan Institute for Integrated Radiation and Nuclear Science, Kyoto University, Asashiro-nishi, Kumatori-cho, Sennan-gun, Osaka, 590-0494, Japan

A R T I C LE I N FO

A B S T R A C T

Keywords: Accelerator-driven system Reaction rate Subcritical multiplication factor Neutron spectrum KUCA

A subcritical multiplication factor k s is the key parameter to determine the neutron multiplication in acceleratordriven system (ADS). The k s deduction method in experiments has been developed on the basis of the previous experimental results with soft spectrum core but the applicability of the previous deduction method to hard neutron spectrum core is not obvious. The present study performs the ADS experiments composed of uraniumlead (UePb) zoned subcritical core and the spallation neutron source at Kyoto University Critical Assembly, and the reaction rates distributions are measured in the hard neutron spectrum core. The previous k s deduction method is applied to the experimental data and the calculation results obtained by the combined use of MVP and PHITS, and the calculated k s values do not agree with the experimental data due to the hard neutron spectrum originating from the UePb zoned fuel region. By taking account of the hard spectrum effect in the UePb zone into the previous k s deduction method, the revised k s values in the experiments agree well with the calculated ones. Thus, the hard neutron spectrum is concluded to have a significant impact on the k s deduction method, and should be taken into account to deduce k s appropriately.

1. Introduction An accelerator-driven system (ADS) has been studied for effective minor actinide transmutation, and is composed of high-power particle accelerator, spallation target and subcritical core. The research activities in the field of reactor physics related to a subcritical core have proceeded in parallel to the engineering developments of experimental reactors such as MYRRHA (Van den Eynde et al., 2015) and large-scale reactors (Tsujimoto et al., 2004; Mansani et al., 2012). The fundamental characteristics of a subcritical core have been investigated through the zero-power experiments which combined the core with an accelerator neutron source. Some representative experimental programs of the ADS experiments with deuterium-tritium (DT) neutron source have been performed in MUSE (Lebrat et al., 2008), GUINEVERE (Uyttenhove et al., 2011) and YALINA-Booster (Tesinsky et al., 2011; Bécares et al., 2013), and the experiments with using both DT and spallation neutron sources have been actively carried out at the Kyoto University Critical Assembly (KUCA) (Pyeon et al., 2018a, 2015, 2012, 2008, 2007; Shahbunder et al., 2010a, 2010b, 2010c). The power of ADS (P ) is determined by the neutron intensity and the neutron multiplication in a core as follows (Seltborg et al., 2003):

P=

Ef k s Q, ν 1 − ks

(1)

where E f is a released energy per fission, ν is the average number of fission neutrons per fission and k s is the subcritical multiplication factor (Nishihara et al., 2003; Kobayashi and Nishihara, 2000). A neutron source intensity is represented by Q , and is dependent on the beam power from an accelerator. The subcritical multiplication factor k s shows the balance between the amounts of source neutrons and fission neutrons rather than the effective neutron multiplication factor k eff in a subcritical core. k s is the basic parameter that describes the neutron multiplication in a subcritical core, and the measurement and estimation of k s are essential to control the ADS operation appropriately. The k s deduction method has been developed by using the experimental results of reaction rates obtained with neutron activation analysis in a series of the experimental studies at KUCA, and applied to the ADS experiments with DT neutrons and spallation neutrons obtained by 100 MeV protons from fixed-field alternating gradient (FFAG) accelerator (Pyeon et al., 2018a, 2015; Shahbunder et al., 2010a, 2010b, 2010c). These experiments have been mainly performed in a polyethylene (PE) -moderated and –reflected core that has a relatively soft

∗

Corresponding author. E-mail addresses: [email protected] (N. Aizawa), [email protected] (M. Yamanaka), [email protected] (T. Iwasaki), [email protected] (C.H. Pyeon). https://doi.org/10.1016/j.pnucene.2019.04.006 Received 29 October 2018; Received in revised form 29 March 2019; Accepted 12 April 2019 Available online 28 April 2019 0149-1970/ © 2019 Elsevier Ltd. All rights reserved.

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neutron spectrum, and the activation materials employed for the reaction rate measurements are sensitive to thermal neutrons. However, the actual ADS has a hard neutron spectrum in the core to transmute minor actinides effectively, and the applicability of the k s deduction method to a hard spectrum core is not clear. The main objective of the present study is to examine the effect of hard neutron spectrum on the deduction of k s through the ADS experiments with uranium-lead (UePb) zoned core driven by spallation neutrons at KUCA. Section 2 reviews the methodology of the conventional k s deduction method proposed in the previous studies, and the outline of experiments and calculations is described in Section 3. In Section 4, the conventional k s deduction method is applied to the experiments with the hard spectrum core, and on the basis of the application results, the k s deduction method in the hard spectrum core is discussed in conjunction with the verification of the experimental results with numerical simulations. Conclusions are presented in Section 5 and the present study is summarized.

Fig. 1. Cross sections of

2. Methodology of the k s deduction

(2)

Cf =

L : Loss operator, P : Production operator, ϕs : Neutron flux in external neutron source system, S : Source neutron term.

F , F+S

(3)

where F shows the fission neutron production rate and S is the production rate of source neutrons by external source described in the following equations: ∞

F=

V

0

∫ ∫ s (r , E ) dEdr. V

0

In(n,n’) in JENDL-4.0.

∫0

Ethermal

ν ΣUf − 235 (E ) ϕs (E ) dE

Ethermal

ΣcIn − 115 (E ) ϕs (E ) dE

∫0

≈

ν σUf − 235 (Ethermal ) N U − 235 σ cIn − 115 (Ethermal ) N In − 115

, (8)

3.1. Experimental settings

(4)

ADS experiments with UePb zoned core were carried out with spallation neutrons generated by the reactions of 100 MeV proton beams and solid lead-bismuth (PbeBi) target in the KUCA A-core, which is basically the PE-moderated and reflected core. Fig. 2 shows the top view of the reference core configuration in the experiments. The core consisted of PE moderated normal fuel assemblies “F”, UePb zoned fuel assemblies “f” and PE moderators “p.” The fuel part of the normal fuel assembly “F” was composed of 60 unit cells of two 1/16″ highly-enriched uranium (HEU) plates and 1/8″ PE plate as shown in Fig. 3 (a), and the fuel part was sandwiched by PE blocks. In the case of the UePb zoned fuel assembly, the PE plates in the central 40 fuel cells were replaced with Pb ones from the normal fuel assembly (see Fig. 3 (b)). The PbeBi target was located at the 700 mm height from the bottom of the core. The detailed information was referred to the benchmark report (Pyeon and Yamanaka, 2018b). The experiments involving the reaction rate measurements were carried out with four different subcriticalities by changing the number of normal fuel assemblies as shown in Fig. 4 for each core configuration. The In wire was used as the activation material for the measurement of 115In(n,γ) 116mIn reaction rate distributions, and the In wire was set between (13–14) along (A-P) (black bold lines in Fig. 4) at a height of 700 mm from the core bottom. The In foil was employed as an activation foil located at (D-E, 15) adjacent to the neutron target for the measurements of source neutron production rates to utilize the characteristic of In that the threshold of 115In(n,n’) 115mIn reaction is about 0.3 MeV. The detailed

0

(5)

The activation foil and wire are set at the location of the neutron source and the core region, respectively, and ks is deduced from the experimental data of reaction rates at wire position RRwire (r ) and that at foil RR′ foil (r ) by using some conversion coefficients for Eqs. (4) and (5) (Pyeon et al., 2018a, 2015; Shahbunder et al., 2010a, 2010b, 2010c) as follows:

∫

F ≈ A⋅Cf

RRwire (r ) dr ,

fuel reg .

S ≈ Cs

115

3. Experimental setting and numerical analyses

∞

S=

In(n,γ) and

∞

∫ ∫ Pϕs (r , E ) dEdr = ∫ ∫ νΣf (r , E ) ϕs (r , E ) dEdr , V

115

where Ethermal is the arbitrary energy in thermal neutron region with the proportionality, and N X is the number density of nuclide X. The constant A is calculated with the one dimensional fission reaction rates at wire positions and the three dimensional ones in the core obtained by numerical analyses. As for the activation foil set at the target, thorium (Th), niobium (Nb) and In were selected due to their high reaction threshold energy over some hundreds keV. The coefficient Cs is derived by the relation between the reaction rate of the foil and the number of source neutrons on the basis of Eq. (7) and the numerical analysis.

On the basis of the transport equation, ks is defined in Eq. (3) (Nishihara et al., 2003; Kobayashi and Nishihara, 2000).

ks ≡

U(n,f),

cores employed in the previous experiments had soft spectra due to the use of PE moderator, and the coefficient Cf was derived from the approximation that 115In absorption cross sections are proportional to 235 U fission ones in thermal neutron energy (E < 0.1 eV ) as shown in Fig. 1. The coefficient Cf was represented as follows:

The steady-state neutron transport equation in a subcritical core with external neutron source is as follows:

Lϕs (r , E ) = Pϕs (r , E ) + s (r , E ),

235

∫ foil pos .

(6)

RR′ foil (r ) dr , (7)

Cf : The conversion coefficient of arbitrary reactions of activation wire to 235U fission neutrons, A : The constant of variable separation to convert one-dimensional reaction rates to three-dimensional ones, Cs : The conversion coefficient of arbitrary reactions of activation foil to source neutron production rate. The indium (In) wire was employed in successive KUCA experiments to obtain the reaction rate distributions in the core region. The 159

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Fig. 2. Top view of UePb zoned core in ADS experiments configured at KUCA A-core.

obtained from the eigenvalue calculation were compared with the experimental data (Pyeon and Yamanaka, 2018b) for four experiment cases to validate the single MVP calculations regarding the neutron behavior under 20 MeV. Furthermore, the fixed-source calculations of MVP, combined with source neutron database generated by PHITS calculations, were performed to evaluate the reliability of the reaction rate calculations of activation materials. Finally, the conversion coefficients defined in Eqs. (6) and (7) were calculated by the use of the fixed-source calculation results, and k s was deduced on the basis of the coefficients. The total number of history in the eigenvalue calculation was 1E+8 (1E+5 histories/cycle × 1,000 active cycle), and the 1σ statistical error was kept within 0.02% in keff. In the PHITS calculations, the proton beam was modelled by a circular Gaussian beam with the full width at half maximum of 2.0 cm, and the total number of proton histories was 1E+8 (1E+5 histories/cycle × 1,000 active cycle). The fixed-source calculations were performed with 1E+8 histories (2.5E+5 histories/cycle × 400 active cycle) by sampling the source neutron data of spatial positions, directional vectors and energy from the database generated by PHITS. The 115In(n,γ) 116mIn reaction rates of the In wire had the 1σ statistical error of less than 6% in the fixed-source calculations. The nuclear data libraries employed in this study was described in the next section, and the temperature point in each library was 297 K.

specifications of the activation wire and foil are presented in Table 1. The FFAG accelerator was operated with the frequency of 20 Hz and the repetition of 100 ns, and the beam current of about 0.05 nA. The 100 MeV proton beam was transported horizontally at 700 mm height from the core bottom with the size of 25 mm diameter. 3.2. Numerical analyses Numerical simulations were necessary to obtain the coefficients for the k s deduction and evaluate the effect of hard neutron spectrum attributable to uranium-lead (UePb) zoned core on the k s deduction. The neutronics simulations in a reactor core are generally based on nuclear data libraries, which contain neutron cross section data files under 20 MeV because the neutron reactions are dominated by the neutrons under 20 MeV. However, the transport of the high energy particles more than 20 MeV must be taken into account in the present study since the ADS experiments employed the spallation neutron source generated by 100 MeV proton. The numerical simulations were performed with the combined use of two Monte Carlo codes: PHITS (Sato et al., 2013) and MVP (Nagaya et al., 2005, 2017). PHITS was employed to calculate the spallation reactions between beam and target, and the neutron transport over 20 MeV with the use of the built-in nuclear reaction model; MVP was to calculate the neutron transport under 20 MeV with the use of the nuclear data library on the basis of spallation neutron information of spatial positions, directional vectors and energy by PHITS. In the present study, the eigenvalue calculations by MVP were performed and the subcriticalities (reactivities from critical state) 160

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Fig. 3. Configuration of fuel assemblies employed in ADS experiments.

4. Results and discussions

4.2. Reaction rates

4.1. Subcriticalities

The comparisons of reaction rates between experiments and calculations were performed to examine the reproducibility of the experiments by the numerical simulations with the combined use of PHITS and MVP including the effects of over 20 MeV neutrons. Fig. 5 shows the one example of the neutron distribution over 20 MeV in Case A simulated by PHITS. PHITS simulated the generation and transport of spallation neutrons rather than fission reactions, and the similar distributions were obtained in other three cases. The numerical calculations by MVP were performed with the fixed-source calculation mode on the basis of high-energy neutron data from PHITS with the use of ENDF/B-VII.1 for transport calculations and JENDL/D-99 library (Kobayashi et al., 2002) for reaction rate calculations. The reaction rates of the activation wire/foil were equivalent to the saturation activity D∞ [1/s], and the reaction rates in the experiments were derived on the basis of the counting rate of radiation from the activation materials. D∞ was calculated with the following equation:

The eigenvalue calculations were performed by using different three libraries: ENDF/B-VII.1 (Chadwick et al., 2011), JEFF-3.2 (OECD Nuclear Energy Agency, 2016) and JENDL-4.0 (Shibata et al., 2011) under 20 MeV neutron energy. The subcriticalities (reactivities from critical state) in the experiments were obtained from the benchmark data (Pyeon and Yamanaka, 2018b) of the extrapolated area ratio method with the use of BF3 detectors. The numerical and experimental results are listed in Table 2. The calculated subcriticalities almost agreed within the range of the standard deviation except for Case A. The reference calculation result in the benchmark was 2037 ± 4.1 pcm and also outside the standard error range in Case A. The difference in Case A was presumed to result from experimental conditions. Regarding the difference among various nuclear data libraries, the subcriticalities with JENDL-4.0 were the much larger than others. Pyeon et al. (2016) reported that the slight differences in a reactivity were seen by changing 27Al nuclear data from JENDL-4.0 to ENDF/BVII.0 and JEFF-3.1. In addition, the elastic and capture cross sections of 27 Al were reported to be sensitive to keff around 1 MeV and 0.1 eV, respectively at KUCA A-core (Pyeon et al., 2018c). As the results of the detailed comparisons among the various nuclear data libraries, about 1% differences were seen around the thermal neutron region in the capture cross sections of 27Al between JENDL-4.0 and ENDF/B-VII.1. Hence, the discrepancies in the subcriticality calculations were attributed to the variation of nuclear data libraries. From these comparisons, MVP eigenvalue calculations were able to reproduce the subcriticalities obtained in the experiments well regardless of the variation of nuclear data libraries, and MVP was applicable to the experimental analysis under 20 MeV neutron condition.

Reaction rate [1/ s] = D∞ =

λTc C , εD εE (1 − e−λTi ) e−λTw (1 − e−λTc )

(9)

λ : decay constant [1/s], C : counting rate of the emitted γ-ray [1/s], Tc : measurement counting time of the emitted γ-ray [s], Ti : irradiation time in the core [s], Tw : waiting time before starting γ-ray measurement [s], εD : γ-ray detection efficiency [%], εE : γ-ray emission rate from foil/wire [%]. The counting rate of the emitted γ-ray C was measured in the experiment, and D∞ was obtained by substituting C into Eq. (9). The measurement data in the experiments are presented in Appendix A. The standard error of each measurement data was 9–16% for In wire and 161

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Fig. 4. Enlarged view of UePb zoned core in ADS experiments. Number in parenthesis is the number of HEU fuel plate. Table 1 Specifications of the activation wire and foil. Type

reaction

Threshold

Size

Wire

115

–

1.0 mm diameter and about 680 mm long 1.0 × 1.0 × 0.1 mm

In(n,γ) In 115 In(n,n’) 115m In 116m

Foil

About 0.3 MeV

Table 2 Comparisons of subcriticality between calculations and experiments. Unit: pcm. Experimenta

Case

Case Case Case Case

about 3% for In foil at the target, by considering the error propagation of the parameters in Eq. (9). The influences of the accelerator operation condition and the handling of activation materials were not contained in the error. Fig. 6 shows the comparison results of the In wire reaction rate

a

A B C D

1769 3703 4595 5124

± ± ± ±

11 26 104 50

MVP calculation JENDL-4.0

ENDF/B-VII.1

JEFF-3.2

2487 4016 4924 5400

2202 3699 4610 5097

2159 3678 4555 5059

± ± ± ±

10 10 10 10

± ± ± ±

9.8 10 10 11

± ± ± ±

9.7 9.8 10 10

Experiment was derived from the benchmark data (Pyeon and Yamanaka, 2018b).

162

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Fig. 7. Measured reaction rate distributions at the core region. The error bars mean the 1σ error.

Fig. 5. Distribution of neutrons over 20 MeV at a height of 700 mm from the core bottom in Case A.

reaction rates with the simulations, the calculated reaction rates were approximately identical to the experimental ones within the 1σ errors as seen in Fig. 6 of the C/E (Calculation/Experiment) values. The large discordances seen around the target, especially at the negative positions from the target, in each case were considered to be caused by the low calculation accuracies in Monte Carlo calculations because the In wires at their positions were adjacent to air region. Some reaction rates in the PE and fuel regions were outside the 1σ error ranges but within the 2σ error ranges. Hence, the reaction rates were considered to be reproduced well by the simulations. Focusing on the reaction rates in the core regions in more detail, the reaction rates at the UePb zoned fuel region were relatively small compared to those at the normal fuel region as shown in Fig. 7, even

distributions at each case. The experimental and the numerical results of the reaction rates/saturation activities were compared with using the values in unit volume, and all reaction rates of the In wire in Fig. 6 were normalized by that of the In foil at PbeBi target. The distribution profiles in the calculations were consistent with those in the experiments; there are large peaks observed at around 4 cm from the target in both the calculated and experimental distributions, and Cases A and B had a small peak around 18 cm in the PE region. The peaks near 4 cm from the target are due to the moderation of source neutrons by PE, and the peaks around 18 cm are produced by the moderation of fission neutrons originating from the core region. As for the reproducibilities of

Fig. 6. Distributions of reaction rates and their calculation-to-experiment ratios. The error bars mean the 1σ error. The left vertical axis is for reaction rate, and right vertical axis is for the Calculation/Experiment (C/E) ratio. 163

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though the influence of the distance between the neutron source and each fuel region was considered. The similar distributions in the fuel region were obtained by the simulations. These trends were explained by the difference of moderation effect quantitatively; the UePb zoned fuel region was less moderated than the normal fuel region, and the difference in the neutron spectrum affected the fission distributions as well as the 115In capture reaction rates. Thus, the reaction rate calculations from combining MVP and PHITS reproduced the experimental results well, including the effect of neutron spectrum. The combined use of PHITS and MVP codes was verified to be applicable to the analysis of the ADS experiments driven by highenergy spallation neutrons over 20 MeV.

4.3. Effect of neutron spectrum on subcritical multiplication factor The comparisons of the reaction rate distributions in the previous section indicated that the UePb zoned fuel region had hard neutron spectrum relative to the normal fuel region. In this section, the effect of the neutron spectrum on the deduced k s was examined through the application of the conventional k s deduction method to the experiments with the UePb zoned core, and the k s deduction method in the hard spectrum core was discussed. The subcritical multiplication factor k s was deduced with the conventional deduction method of Eq. (3) through (7). As mentioned in Sec. 2, the coefficients Cf , A and Cs were necessary for the sake of the k s deduction. The coefficient Cf (= 0.309) was calculated from Eq. (8) with the use of the proportionality between 115In(n,γ) and 235U(n,f) cross sections in thermal neutron region as shown in Fig. 1. A and Cs were derived by the MVP calculations. The k s values were deduced with three zone patterns: all core region, UePb zoned fuel region and normal fuel region to see the effect of neutron spectrum at each zone. The reaction rate data of In wire employed for the k s deduction were ranged along (13–14, J-P) for all core region, (13–14, J-L) for UePb zoned region and (13–14, M-P) for normal fuel region, respectively (see Fig. 4 for wire positions). Table 3 presents the results of k s values with the comparison between calculations and experiments by the conventional method. The “direct calculations” were derived by using total number of fission neutrons and source neutrons on the basis of Eqs. (4) and (5) rigorously, and the other calculation and experiment values were derived with reaction rates on the basis of Eqs. (6) and (7). The k s values by the experiments almost agreed with those by the calculations within the experimental error of 1σ, but both of them were much larger than

Fig. 8. Neutron spectra at each wire position in Case A. The wire positions are shown in Fig. 4 (a).

direct calculations of more reliable values. Moreover, the deduced values in both calculations and experiments were different among three cases although the k s values were determined uniquely; the k s values derived with the reaction rates of the normal fuel region were relatively closer to the direct calculations than those of the UePb zoned fuel region. Fig. 8 shows the neutron spectra at each wire position in Case A, and these comparisons showed that the thermal neutron peaks were small especially in the UePb zoned fuel region ((A), (B) and (C)) compared to those in normal fuel region ((D), (E) and (F)). These differences of neutron spectra between fuel regions affected the 115In capture reactions as shown in Fig. 9; 115In capture reactions in the UePb zoned fuel region were dominated by the resonance cross sections around 1.5 eV. These results indicated that the Cf definition in Eq. (8), which is approximated that the cross sections of 115In(n, γ) were proportional to those of 235U(n, f) in thermal neutron energy, was not appropriate for the hard spectrum core region. The effect of hard spectrum should be taken into account to deduce appropriate k s values in a hard neutron spectrum core. The definition of Cf in the conventional deduction method had been available for less than 0.1 eV of neutron energy, and it was expanded to whole energy range by using the energy-integrated reaction rates to consider the effect of hard spectrum as follows:

Cf = Table 3 Subcritical multiplication factor k s deduced with previous Cf value (= 0.309.). Calculationa

Experiment

Case A

Direct calculation UePb zoned fuel region Normal fuel region All core region

0.6881 0.7735 0.7261 0.7403

± ± ± ±

0.0032 0.0249 0.0151 0.0127

– 0.7880 ± 0.0528 0.7488 ± 0.0436 0.7599 ± 0.0336

Case B

Direct calculation UePb zoned fuel region Normal fuel region All core region

0.5135 0.6221 0.5533 0.5739

± ± ± ±

0.0020 0.0169 0.0096 0.0082

– 0.6633 ± 0.0505 0.6005 ± 0.0369 0.6226 ± 0.0294

Case C

Direct calculation UePb zoned fuel region Normal fuel region All core region

0.4528 0.5704 0.4885 0.5138

± ± ± ±

0.0018 0.0147 0.0079 0.0069

– 0.5739 ± 0.0385 0.4898 ± 0.0281 0.5220 ± 0.0229

Case D

Direct calculation UePb zoned fuel region Normal fuel region All core region

0.4207 0.5279 0.4147 0.4418

± ± ± ±

0.0015 0.0160 0.0068 0.0063

– 0.5396 ± 0.0371 0.4396 ± 0.0248 0.4624 ± 0.0212

∞ ∫fuel reg . ∫0 ν ΣUf − 235 (r , E ) ϕs (r , E ) dEdr ∞ In − 115 Σc (r , fuel reg . 0

∫

∫

E ) ϕs (r , E ) dEdr

=

235 (r ) dr ∫fuel reg . νRRUf ,−wire − 115 (r ) dr ∫fuel reg . RR cIn, wire

. (10)

Table 4 provides the comparison results of k s deduced with revised

a The errors accompanied with the calculated values were statistical errors in MVP.

Fig. 9. 164

115

In capture reaction rate spectra at each wire position in Case A.

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Table 4 Subcritical multiplication factor k s deduced with revised Cf values. Calculationa

Experiment

Cf

Case A

UePb zoned fuel region Normal fuel region All core region

0.6881 ± 0.0213 0.6881 ± 0.0140 0.6881 ± 0.0115

0.7060 ± 0.0456 0.7128 ± 0.0409 0.7101 ± 0.0308

0.200 ± 0.004 0.257 ± 0.003 0.239 ± 0.002

Case B

UePb zoned fuel region Normal fuel region All core region

0.5135 ± 0.0188 0.5135 ± 0.0123 0.5135 ± 0.0100

0.5582 ± 0.0434 0.5616 ± 0.0354 0.5638 ± 0.0273

0.198 ± 0.005 0.264 ± 0.004 0.242 ± 0.003

Case C

UePb zoned fuel region Normal fuel region All core region

0.4528 ± 0.0157 0.4528 ± 0.0101 0.4528 ± 0.0083

0.4563 ± 0.0316 0.4540 ± 0.0268 0.4610 ± 0.0209

0.193 ± 0.004 0.268 ± 0.004 0.242 ± 0.003

Case D

UePb zoned fuel region Normal fuel region All core region

0.4207 ± 0.0173 0.4207 ± 0.0097 0.6881 ± 0.0213

0.4322 ± 0.0316 0.4457 ± 0.0262 0.7060 ± 0.0456

0.201 ± 0.005 0.317 ± 0.005 0.200 ± 0.004

a

The errors accompanied with the calculated values were statistical errors in MVP.

spectrum effect. From these results, the k s deduction method was applicable to the source-driven core with hard spectrum by revising Cf with the consideration of spectrum effect. 5. Conclusion The deduction of a subcritical multiplication factor (k s ) was conducted for a hard neutron spectrum subcritical core to examine the effect of neutron spectrum on the previous k s deduction method developed on the basis of the experiments with relatively soft neutron spectrum, through the reaction rate measurements in the UePb zoned core with spallation neutrons at KUCA. The numerical simulations with the combined use of MVP and PHITS were performed to support the k s deduction. The previous k s deduction method was applied to the experiments involving the reaction rate distributions at first, and large discrepancies were observed between the calculation value derived from the number of fission neutrons and source neutrons on the basis of the definition equation and the other results including experiments. The root cause of the discrepancy was attributed to the approximation involving in deriving the conversion coefficients Cf with thermal energy, as it was not appropriate for the hard spectrum in UePb zoned fuel region. The revised Cf value was defined to take into account of the effect of hard spectrum, and as a result, the experimental values showed good agreements with the calculations. In conclusion, the spectrum effect had a significant influence on the k s deduction, and should be considered to deduce k s appropriately for the ADS core.

Fig. 10. C/E∗ of subcritical multiplication factor with the different subcriticalities. ∗C/E: calculation/experiment.

Cf values for each fuel region. The Cf values were obtained through the results of MVP calculations. The calculated k s values agreed with the direct calculations, and the experimental values were also well-agreed with the calculations as shown in Fig. 10 of the C/E trends with the different subcriticalities. With respect to the difference of the fuel regions, the discrepancies among the fuel regions were also decreased, and Cf values became small in UePb zoned fuel region compared to the previous Cf (0.309) as presented in Table 4. The smaller Cf in the UePb zoned region was explained by the increase of the denominator of 115In capture reaction rates in Eq. (10) due to the increase of resonance capture reactions by hardened neutron spectrum. The Cf values in the normal region were also smaller than the previous Cf due to the leaked neutrons originating from the UePb zoned region. The k s deductions with different fuel regions indicated that the deduced k s values were available with the use of the appropriate coefficients by considering the

Acknowledgements This work has been carried out in part under the visiting Researcher's Program of the Institute for Integrated Radiation and Nuclear Science, Kyoto University. The authors are grateful to all the staff at KUCA and FFAG accelerator facility for their assistance during the experiment.

Appendix A. Measurement results of D∞ in the experiments The measurement data in the experiments are tabulated in Tables A.1 - A.3. The standard errors shown in the tables are calculated with considering the error propagation of the parameters in Eq. (9). Table A.1 Measured saturated activities D∞ of In wires in the experiments. Unit [Bq/s] In wire position from the target [cm]

Case A

Case B

Case C

54.25

4.45E+02 ± 4.27E+01

1.50E+02 ± 2.34E+01

2.57E+02 ± 3.35E+01

Case D 2.19E+02 ± 2.99E+01

(continued on next page) 165

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Table A.1 (continued) In wire position from the target [cm]

Case A

51.75 49.25 46.75 44.25 41.75 39.25 36.75 34.25 31.75 29.25 26.75 24.25 21.75 19.25 16.75 14.25 11.75 9.25 6.75 4.25 1.75 −0.75 −3.25 −5.75 −8.25

2.76E+02 3.77E+02 5.51E+02 5.78E+02 5.31E+02 6.45E+02 1.05E+03 9.79E+02 1.07E+03 1.32E+03 1.11E+03 1.10E+03 2.60E+03 4.37E+03 5.12E+03 4.95E+03 4.76E+03 5.37E+03 6.40E+03 7.08E+03 6.37E+03 3.12E+03 2.21E+03 1.92E+03 1.68E+03

Case B ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

2.72E+01 4.69E+01 6.41E+01 6.69E+01 6.30E+01 7.40E+01 1.13E+02 1.06E+02 1.15E+02 1.40E+02 1.19E+02 1.20E+02 2.57E+02 4.19E+02 4.88E+02 4.74E+02 4.58E+02 5.14E+02 6.09E+02 6.71E+02 6.07E+02 3.12E+02 2.29E+02 2.02E+02 1.83E+02

1.63E+02 2.07E+02 1.96E+02 1.57E+02 2.77E+02 3.28E+02 3.54E+02 4.27E+02 4.84E+02 4.49E+02 4.22E+02 5.27E+02 1.25E+03 2.11E+03 2.35E+03 2.67E+03 2.95E+03 4.30E+03 5.44E+03 6.52E+03 5.46E+03 2.59E+03 2.05E+03 1.70E+03 1.54E+03

Case C ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

2.57E+01 2.98E+01 2.94E+01 2.51E+01 3.77E+01 4.34E+01 4.58E+01 5.35E+01 5.88E+01 5.63E+01 5.39E+01 6.39E+01 1.33E+02 2.14E+02 2.33E+02 2.64E+02 2.91E+02 4.14E+02 5.18E+02 6.17E+02 5.21E+02 2.59E+02 2.12E+02 1.79E+02 1.67E+02

2.04E+02 1.89E+02 1.56E+02 2.26E+02 2.69E+02 4.01E+02 3.86E+02 4.20E+02 4.38E+02 4.68E+02 4.50E+02 6.33E+02 1.14E+03 2.03E+03 2.77E+03 3.51E+03 4.63E+03 5.63E+03 8.06E+03 8.70E+03 7.78E+03 3.88E+03 3.08E+03 2.30E+03 2.18E+03

Case D ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

2.79E+01 2.68E+01 2.37E+01 3.12E+01 3.57E+01 4.88E+01 4.71E+01 5.13E+01 5.30E+01 5.65E+01 5.43E+01 7.22E+01 1.19E+02 2.03E+02 2.68E+02 3.37E+02 4.40E+02 5.31E+02 7.53E+02 8.12E+02 7.28E+02 3.75E+02 3.02E+02 2.32E+02 2.20E+02

1.92E+02 1.98E+02 2.64E+02 1.84E+02 2.81E+02 3.19E+02 4.87E+02 4.78E+02 5.52E+02 6.34E+02 9.50E+02 1.31E+03 1.96E+03 2.43E+03 3.33E+03 3.97E+03 5.50E+03 7.27E+03 9.86E+03 1.07E+04 8.63E+03 4.22E+03 3.47E+03 2.84E+03 2.58E+03

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

2.77E+01 2.85E+01 3.49E+01 2.72E+01 3.71E+01 4.11E+01 5.78E+01 5.66E+01 6.41E+01 7.17E+01 1.02E+02 1.35E+02 1.95E+02 2.38E+02 3.21E+02 3.80E+02 5.20E+02 6.81E+02 9.18E+02 9.95E+02 8.06E+02 4.05E+02 3.38E+02 2.81E+02 2.57E+02

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

1.45E+03 1.33E+03 1.36E+03 1.65E+03 1.35E+03 1.79E+03 1.99E+03 2.74E+03 2.76E+03 3.05E+03 3.51E+03 5.05E+03 6.36E+03 9.49E+03 1.11E+04 1.53E+04 1.80E+04 2.50E+04 3.18E+04 4.42E+04 4.83E+04 3.71E+04 1.88E+04 1.59E+04 1.34E+04 1.24E+04

Table A.2 Measured reaction rates of In wires in the experiments. Unit [#/cm3/s] In wire position from the target [cm]

Case A

54.25 51.75 49.25 46.75 44.25 41.75 39.25 36.75 34.25 31.75 29.25 26.75 24.25 21.75 19.25 16.75 14.25 11.75 9.25 6.75 4.25 1.75 −0.75 −3.25 −5.75 −8.25

2.35E+04 1.39E+04 2.05E+04 3.02E+04 3.08E+04 2.65E+04 3.70E+04 5.74E+04 5.16E+04 5.74E+04 6.63E+04 5.88E+04 6.25E+04 1.34E+05 2.34E+05 2.62E+05 2.43E+05 2.56E+05 2.95E+05 3.33E+05 3.89E+05 3.20E+05 1.65E+05 1.26E+05 1.02E+05 8.72E+04

Case B ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

2.25E+03 1.37E+03 2.55E+03 3.51E+03 3.56E+03 3.14E+03 4.25E+03 6.13E+03 5.60E+03 6.16E+03 6.99E+03 6.33E+03 6.77E+03 1.32E+04 2.25E+04 2.51E+04 2.33E+04 2.46E+04 2.82E+04 3.16E+04 3.68E+04 3.05E+04 1.65E+04 1.30E+04 1.08E+04 9.49E+03

7.77E+03 8.06E+03 1.05E+04 9.74E+03 7.63E+03 1.34E+04 1.61E+04 1.69E+04 2.02E+04 2.32E+04 2.19E+04 2.00E+04 2.55E+04 5.92E+04 1.02E+05 1.13E+05 1.26E+05 1.44E+05 2.05E+05 2.60E+05 3.12E+05 2.71E+05 1.23E+05 9.83E+04 8.23E+04 7.25E+04

Case C ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

1.21E+03 1.27E+03 1.51E+03 1.46E+03 1.22E+03 1.82E+03 2.13E+03 2.18E+03 2.53E+03 2.81E+03 2.74E+03 2.55E+03 3.10E+03 6.28E+03 1.04E+04 1.12E+04 1.25E+04 1.42E+04 1.98E+04 2.48E+04 2.95E+04 2.59E+04 1.23E+04 1.01E+04 8.68E+03 7.85E+03

1.27E+04 9.92E+03 9.29E+03 7.34E+03 1.10E+04 1.30E+04 1.95E+04 1.83E+04 2.07E+04 2.10E+04 2.30E+04 2.13E+04 3.03E+04 5.52E+04 9.74E+04 1.31E+05 1.75E+05 2.21E+05 2.71E+05 3.91E+05 4.23E+05 3.74E+05 1.86E+05 1.49E+05 1.12E+05 1.05E+05

Case D ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

1.65E+03 1.36E+03 1.32E+03 1.12E+03 1.51E+03 1.71E+03 2.37E+03 2.24E+03 2.53E+03 2.55E+03 2.77E+03 2.58E+03 3.46E+03 5.80E+03 9.73E+03 1.27E+04 1.68E+04 2.10E+04 2.56E+04 3.65E+04 3.94E+04 3.50E+04 1.80E+04 1.46E+04 1.13E+04 1.06E+04

Table A.3 Measured saturated activities D∞ and reaction rates of In foils at the target in the experiments. case Case Case Case Case

Reaction rate [#/cm3/s]

D∞ [Bq/s] A B C D

1.53E+03 1.19E+03 2.00E+03 2.34E+03

± ± ± ±

3.53E+01 3.10E+01 5.87E+01 7.62E+01

166

1.70E+04 1.43E+04 2.17E+04 2.88E+04

± ± ± ±

3.92E+02 3.72E+02 6.39E+02 9.41E+02

1.06E+04 9.20E+03 9.46E+03 1.25E+04 9.11E+03 1.35E+04 1.55E+04 2.31E+04 2.33E+04 2.63E+04 3.10E+04 4.69E+04 6.17E+04 9.52E+04 1.13E+05 1.59E+05 1.89E+05 2.64E+05 3.39E+05 4.75E+05 5.21E+05 3.97E+05 1.96E+05 1.64E+05 1.35E+05 1.24E+05

Progress in Nuclear Energy 116 (2019) 158–167

N. Aizawa, et al.

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