Measuring the Photoneutrons Originating from D(γ, n)h Reaction after the Shutdown of an

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1 Journal of Nuclear Science and Technology ISSN: (Print) (Online) Journal homepage: Measuring the Photoneutrons Originating from D(γ, n)h Reaction after the Shutdown of an Operational BWR Masato WATANABE, Akio YAMAMOTO & Yoshihiro YAMANE To cite this article: Masato WATANABE, Akio YAMAMOTO & Yoshihiro YAMANE (2009) Measuring the Photoneutrons Originating from D(γ, n)h Reaction after the Shutdown of an Operational BWR, Journal of Nuclear Science and Technology, 46:12, To link to this article: Published online: 05 Jan Submit your article to this journal Article views: 394 Citing articles: 3 View citing articles Full Terms & Conditions of access and use can be found at

2 Journal of NUCLEAR SCIENCE and TECHNOLOGY, Vol. 46, No. 12, p (2009) ARTICLE Measuring the Photoneutrons Originating from D(, n)h Reaction after the Shutdown of an Operational BWR Masato WATANABE 1;, Akio YAMAMOTO 2 and Yoshihiro YAMANE 2 1 Electric Power Research & Development Center, Chubu Electric Power Co., Inc., 20-1 Kitasekiyama, Ohdaka-cho, Midori-ku, Nagoya , Japan 2 Nagoya University, Furo-cho, Chikusa-ku, Nagoya , Japan (Received May 20, 2008 and accepted in revised form April 14, 2009) The purpose of this study is to measure the photoneutron emission rate after the shutdown of an operational BWR. The photoneutrons originate from the D(, n)h reaction in the moderator region, while the high-energy gamma rays are generated from 140 Ba- 140 La transient equilibrium of fission products in irradiated fuel. The photoneutron emission rate is measured by means of the photoneutron signal ratio of the Start-up Range Neutron Monitor (SRNM). The ratio is defined as a ratio of the photoneutrons to neutrons originating from spontaneous fission and the oxygen (, n) reaction of actinides ( 242 Cm, 244 Cm, etc.) in irradiated fuel. The principle of the measurement of the photoneutron signal ratio is the large difference between the decay constants of the 140 Ba- 140 La transient equilibrium and those of the actinides. The measurement of the SRNM signal was continuously carried out over several months, and the photoneutron signal ratio was evaluated by using the least-squares method to fit a theoretical model to SRNM signal data. The measurements were performed in the middle of the cycle at three BWR cores. Comparisons of the measured photoneutron signal ratio and the calculated one showed reasonable agreement. This demonstrates the validity and usefulness of the measurement. The absolute value of photoneutrons in the SRNM signal ranged from approximately 1 to 35 counts per second during a five-day cooling period after shutdown. Converting the absolute value to the relative fraction of photoneutrons in the SRNM signal results in a range from approximately 2 to 50%. KEYWORDS: photoneutron, deuterium in light water, 140 La, neutron source, 242 Cm, 244 Cm, SRNM, BWR I. Introduction The surveillance of unexpected criticality events during the refueling outage of a commercial BWR is an important safety issue. Some criticality events due to the unexpected withdrawal of control rods have happened during refueling outages. For this reason, the surveillance needs highly reliable neutron monitors, and the monitors must have a function of inherent fault detection. The neutron monitor used for surveillance in BWRs corresponds to the Start-up Range Neutron Monitor (SRNM), which is a 235 U fission chamber. However, there is no neutron monitor that has a perfect inherent fault detection system. Therefore, a plant s technical specification requires a 3 cps criterion, meaning that the count rate of 3 cps or more should be maintained whenever fuel is in the core. The reason for the requirement is to ensure that the SRNM is functioning properly and that it certainly detects not noise but neutrons under the condition of a low count rate. Corresponding author, Watanabe.Masato@chuden.co.jp ÓAtomic Energy Society of Japan When the count rate of the SRNM falls below 3 cps during refueling or startup, these operations should be aborted under certain conditions. If the 3 cps criterion is not satisfied during the refueling process, the following countermeasures should be taken. One countermeasure is to use spent fuel as a strong neutron source during refueling. Spent fuel assemblies should be located adjacent to SRNMs in order to guarantee 3 cps prior to beginning the refueling process, and they may be shuffled or replaced during refueling to achieve the final core configuration for the next operating cycle. Another countermeasure for guaranteeing 3 cps is to install expensive 252 Cf startup neutron sources, which are normally only used for an initial core in which there is no inherent neutron source. The 252 Cf startup neutron sources may also be introduced when the spent fuels cannot be used, for example, when a plant restarts after a long-term outage, because such a longterm outage causes the significant decay of intrinsic neutron sources (mainly 242 Cm and 244 Cm) in the irradiated fuel and the count rate of the SRNM signal may decrease to less than 3 cps. In the actual refueling process, if we do not have confidence in the indication of the SRNM signal when the count 1099

3 1100 M. WATANABE et al. rate is as low as 3 cps, we must also take the above countermeasures to adhere to the 3 cps criterion, even though these countermeasures may not be necessary. Therefore, if we can develop an accurate prediction method of the SRNM signal, we can make a rational decision about implementing those countermeasures. To develop an accurate prediction method of the SRNM signal, we must inevitably know the neutron source intensity in the BWR core. In our previous study regarding the evaluation of neutron source intensity of a commercial BWR, 1) we measured the decrease in the rate of SRNM signals due to the decays of 242 Cm and 244 Cm in actual BWRs during a long-term outage. During the period immediately after reactor shutdown, the decrease in the rate of SRNM signals was faster than the half-life of 242 Cm (163 d), which should consist of the major part of intrinsic neutron sources in a BWR core. In the previous study, we presumed that the cause of the rapid decrease was a decrease in the amount of photoneutrons originating from the D(, n)h reaction. Here, high-energy -ray originates from the 140 Ba- 140 La transient equilibrium of fission products. The half-life of the parent 140 Ba is about 12.8 d. Consideration of these photoneutrons would contribute to the accurate prediction of the SRNM signal. The evaluation outline of SRNM signals is shown in Fig. 1. The accurate prediction requires appropriate detector efficiency as a matter of course. Here, the detector efficiency is defined as the ratio of the actual count rate (cps unit) of SRNM signal to the calculated SRNM signal that is the 235 U reaction rate at the SRNM position. However, it is impossible to accurately predict the detector efficiency " EOC for fuel unloading from the evaluation of the former cycle, because the detector efficiency of the SRNM changes due to the depletion of fissionable material ( 235 U) in the SRNM during the former cycle. However, we can estimate the detector efficiency " EOC by comparing between the measured SRNM signal I EOC and calculated SRNM signal R EOC at fuel unloading. Moreover, the detector efficiency " BOC for fuel loading is equal to " EOC at fuel unloading because SRNMs are not calibrated until the end of the fuel loading process. Therefore, we can obtain the appropriate detector efficiency " BOC for fuel loading. Note that the measured SRNM signal I EOC at fuel unloading contains photoneutrons, while the SRNM signal I BOC at fuel loading, which is carried out two or three months after shutdown, does not. Fuel unloading typically starts three days after shutdown, and the unloading is completed within one week. Neglecting photoneutrons in the calculation of SRNM signals R EOC for fuel unloading leads to a large SRNM detector efficiency " EOC, and the predicted SRNM signal I BOC is overestimated. No photoneutron measurement has been carried out in LWRs. However, there is an example of a calculation for a one-pin-cell system for PWR fuel. 2,3) These papers described that the intensity of photoneutrons was larger than that of neutrons from actinides until approximately eight hours after shutdown. With regard to BWRs, there are no calculation examples or measurements available, and there is only a comment explaining that photoneutrons were a cause of error in measurements occurring a few days after shutdown 1. Measure SRNM signal (I EOC ) at fuel unloading Note that there are many photoneutrons in I EOC. All fuels are removed from the core for the periodic inspection, then the SRNM signal is lost. 2. Calculate SRNM signal (R EOC ) at fuel unloading 3. Estimate SRNM detector efficiency ε EOC εeoc is defined as I ε = EOC EOC R EOC: End of Cycle R EOC is 235 U reaction rate at SRNM position, which is calculated by fixed-source calculation etc. The photoneutrons should be considered in R EOC. EOC If R EOC does not contain the photoneutrons, ε will be overestimated. 4. Calculate SRNM signal (R BOC ) at fuel loading BOC: Beginning of Cycle Periodic inspection term is normally 2 3 months, rarely 10 years. Note that there are no photoneutrons at this time. 5. Predict SRNM signal (I BOC ) at fuel loading I BOC = ε BOC R BOC ε BOC is equal to ε EOC because SRNMs are not calibrated in this period. SRNMs are calibrated after fuel loading. A power operation changes εboc, then εboc of a former cycle is not used for the prediction of both R BOC and R EOC. Fig. 1 Outline of procedure for evaluation of SRNM signals for fuel loading during on-site measurement of the neutron emission rate originating from actinides of irradiated fuel. 4) On the other hand, photoneutrons in a heavy-water reactor (HWR) form a main startup neutron source; many HWR measurements have been carried out. 5 8) Furthermore, at high-energy X-ray facilities, photoneutrons are also significant neutron sources for radiation exposure. 9) Therefore, the purpose of this study is to measure the photoneutron emission rate after the shutdown of an operational BWR. The photoneutron emission rate is measured by means of the photoneutron signal ratio of the SRNM. The ratio is defined as a ratio of the photoneutrons to neutrons originating from spontaneous fission and oxygen (, n) reaction of actinides ( 242 Cm, 244 Cm etc.) in irradiated fuel at zero cooling time after shutdown. We measured the photoneutron signal ratio after the shutdown of an operating commercial BWR with continuous SRNM measurements over a period of several months. In order to verify the measurement of the photoneutron signal ratio, we must estimate the photoneutron emission rate accurately using an appropriate calculation code. Con- JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY

4 Measuring the Photoneutrons Originating from D(, n)h Reaction after the Shutdown of an Operational BWR 1101 cerning the calculation of the photoneutron emission rate, the function of calculating the photonuclear reaction was recently developed in continuous-energy Monte Carlo codes (MVP 10) and MCNP 11) ). 12,13) We selected the MVP code for the calculation of the photoneutron emission rate. In this paper, we will first explain a theoretical fitting model for measuring the photoneutron signal ratio. In Sec. II, we will then describe the result of actual measurements for the photoneutron signal ratio in commercial BWR cores. Then, in Sec. III, we will describe the calculation procedure for the photoneutron signal ratio at each SRNM position to confirm of the accuracy of our measurements. The results of the comparison between the calculated and measured photoneutron signal ratio will be discussed in Sec. IV. Finally, our conclusions are given in Sec. V. II. Measurement Procedure of Photoneutron 1. Mechanism of Photoneutron Production The major reaction that produces photoneutrons five days after shutdown in a BWR is D(, n)h photonuclear reactions in light water. The target nuclide of photonuclear reactions is deuterium (D) in the light water. The high-energy gamma ray emitter is 140 La, which is produced by the 140 Ba- 140 La transient equilibrium of fission products in the fuel. In spite of a dilute concentration of deuterium in light water and a low cross-section of deuterium (, n) reactions, the abundance of gamma rays from 140 Ba- 140 La transient equilibrium in the irradiated fuels generates a significant amount of photoneutrons that are equal to the amount of neutrons from actinides in irradiated fuel. A discussion on the target nuclide of the photonuclear reaction and the high-energy gamma ray source is presented as follows. (1) Target Nuclides of Photonuclear Reactions The photoneutron production cross sections of major nuclides in the JENDL Photonuclear DATA File 2004 based on JENDL3.3 14,15) are shown in Fig. 2. According to the calculation using ORIGEN2.2 16) as described in the next section, there are few gamma ray emitters over 6 MeV five days after shutdown. Except for the deuterium, the threshold energy of the photonuclear reaction of other nuclides is noticeably greater than 6 MeV. The threshold energy of the deuterium (, n) reaction is MeV and its cross section is about 10 3 barn. In this study, we have assumed that the concentration of deuterium in light water is approximately 0.015%. The increase in deuterium concentration due to the neutron capture of hydrogen during operation is about 10 6 %, and its effect is totally negligible. (2) High-energy Gamma Ray Emitters As to the over MeV high-energy gamma ray emitters five days after the shutdown, 140 La, 132 I, 106 Rh, and 156 Eu are potential candidates based on an ORIGEN2.2 calculation. The gamma energy spectra from these nuclides, which were calculated using the SPEC5 code 15) without bremsstrahlung, are shown in Fig. 3. The SPEC5 code can be used to calculate gamma spectra with a 0.05 MeV energy mesh from the JENDL FP Decay Data File ) Table 1 Cross Section [b] Emission Rate [/decay] Fig. 3 1.E+00 1.E-01 1.E-02 1.E-03 1.E-04 H2 U238 U235 N14 Gd154 Gd157 Mn55 1.E Photon Energy [MeV] Fig. 2 1.E+00 1.E-01 1.E-02 1.E-03 1.E-04 1.E-05 1.E-06 Photoneutron production cross section E Photon Energy [MeV] La 140 Rh 106 I 132 Eu 156 Photon emission rate per decay in 0.05 MeV energy mesh Table 1 High-energy gamma ray emitted by long-life fission products Nuclide Half-life 16) Q >2:25 [a] [MeV/Bq] Radioactivity [b] [Bq/cm 3 ] [c] 140 Ba- 140 La 12.8 d, 1.68 d 1: : Te- 132 I 3.20 d, d 6: : Ru- 106 Rh 374 d, 29.8 s 1: : Eu 15.2 d 2: : [a] Q >2:25 : Summation for the multiplication of gamma rays greater than 2.25 MeV and emission rate per one decay [b] Radioactivity of daughter five days after shutdown, which was calculated using ORIGEN2.2 for 3.6 wt% enrichment 8 8 fuel bundle of 25 GWd/t and 40% VH [c] Average value of fuel bundle VOL. 46, NO. 12, DECEMBER 2009

5 1102 M. WATANABE et al. Table 2 Major neutron emitters in irradiated fuel Nuclide Half-life 16) [neutron/s/atom] [a] Radioactivity [b] [neutron/s/cm 3 ] 242 Cm 163 d 1: : Cm 18.1 y 4: : Pu 6540 y 4: : [a] Sum of spontaneous fission and oxygen (, n) reaction in ORIGEN2.2 [b] Calculation conditions are the same as those for Table 1 shows that the transient equilibrium 140 Ba- 140 La is the strongest gamma ray emitter in terms of energy photon per unit decay that is over 2.25 MeV. Table 2 shows that the neutrons from actinide are mainly due to 242 Cm and 244 Cm. These neutrons originate from spontaneous fission and oxygen (, n) reaction in the oxide fuel. 2. Theoretical Fitting Model for SRNM Signals (1) Four Major Components of SRNM Signals In order to extract the photoneutron component from an SRNM signal by the least-squares method, it is assumed that the SRNM signal five days after shutdown consists of only four components: 242 Cm, 244 Cm, photoneutrons originating from D(, n)h reaction of 140 Ba- 140 La transient equilibrium, and the constant component from actinides other than 242 Cm and 244 Cm. The SRNM signal I SRNM ðtþ five days after shutdown is assumed to consist of the following 1) components: I SRNM ðtþ ¼I Cm242 ðtþþi Cm244 ðtþþi Photo ðtþþi Const. ; ð1þ t: time from the shutdown, namely, the cooling time, I Cm242 ðtþ: SRNM signal originating from 242 Cm, T 1=2 ¼ 163 d, I Cm244 ðtþ: SRNM signal originating from 244 Cm, T 1=2 ¼ 18:1 y, I Photo ðtþ: SRNM signal originating from photoneutrons due to the D(, n)h reaction whose -ray is generated by 140 La; its half-life is the same as that of the parent 140 Ba of 12.8 d, and I Const. : SRNM signal originating from actinides other than 242 Cm and 244 Cm, which are assumed to be constant because their main component is 240 Pu with a half-life of approximately 6,540 y. The half-lives of these four components in Eq. (1) are different from each other. Therefore, fitting Eq. (1) to the SRNM signal will identify these four components. However, some problems exist in the actual fitting process as described in the next section. (2) Problems in the Measurement The first problem is that the half-lives of photoneutron I Photo ðtþ [T 1=2 of 140 Ba = 12.8 d] and 242 Cm I Cm242 ðtþ [T 1=2 ¼ 163 d] are relatively close. It is somewhat difficult to separate the photoneutron and neutron from 242 Cm under the large decline of the SRNM signal due to the decay of 242 Cm and the inherent fluctuation of SRNM signals. Therefore, for the accurate measurement of photoneutrons, we introduced a two-step measurement process shown in Sec. II-2(4). The second problem is the difference in SRNM ( 235 U fission chamber) detector efficiency for the photoneutron and neutron from actinides. The neutron energy of the photoneutrons from D(, n)h is one decade smaller than that of the actinides. In our present study, we determined that the difference in the SRNM detector efficiencies is about 5%; however, from a practical standpoint, we regarded the difference as negligible. A detailed explanation is given in Sec. II-2(5). The third problem is that the component of I Const. is too small, approximately within 1 2 cps, to be separated from the actual SRNM signal. The main component of I Const. is 240 Pu with a half-life of approximately 6,540 y. Therefore, the component of I Const. are calculated by whole-core fixedsource calculation in which the intensities of neutron sources are given based on the process computer 1) before the measurement, as described in Sec. III-4(3). (3) Arrangement of Eq. (1) for Actual Fitting For the actual fitting, we use the following detailed expressions for each term of Eq. (1), I Cm242 ðtþ ¼" SRNM Cm242 N Cm242 e Cm242 t ; I Cm244 ðtþ ¼" SRNM Cm244 N Cm244 e Cm244 t ; I Photo ðtþ ¼" SRNM La140 N Ba140 e Ba140 t ; " SRNM : SRNM detection efficiency, which is assumed to be the same for neutrons from all reactions; the validity of this assumption is described in Sec. II-2(5), Cm242 ; Cm244 : neutron emission rates per unit number density of 242 Cm and 244 Cm, respectively, La140 : photoneutron emission rate of 140 Ba- 140 La transient equilibrium, N Cm242 ; N Cm244 ; N Ba140 : atomic number densities of 242 Cm, 244 Cm, and 140 Ba, respectively, and Cm242 ; Cm244 ; Ba140 : decay constants of 242 Cm, 244 Cm, and 140 Ba, respectively. Furthermore, we define Photo/TRU, TRU/Cm, and R 244 as I Photo ð0þ Photo/TRU ¼ ; ð5þ I Cm242 ð0þþi Cm244 ð0þþi Const. I Const. TRU/Cm ¼ I Cm242 ð0þþi Cm244 ð0þ ; ð6þ R 244 ¼ N Cm244 =ðn Cm242 þ N Cm244 Þ; ð7þ Photo/TRU : ratio of photoneutrons to neutrons due to spontaneous fission and oxygen (, n) reactions of 242 Cm, 244 Cm, and other actinides at cooling time t ¼ 0, TRU/Cm : ratio of the neutrons for other actinides ( 240 Pu, 242 Pu, etc.) except for 242 Cm and 244 Cm to the sum of 242 Cm and 244 Cm at cooling time t ¼ 0, which is calculated by a whole-core fixed-source calculation before the measurement as described in Sec. III-4(3) and, R 244 : ratio of the number density for 244 Cm to the sum of 242 Cm and 244 Cm. ð2þ ð3þ ð4þ JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY

6 Measuring the Photoneutrons Originating from D(, n)h Reaction after the Shutdown of an Operational BWR 1103 Table 3 Parameters in the theoretical model 4.0 Parameter Value I SRNM Measured SRNM signal [cps] Ba140 6: [1/s] 16) Cm242 4: [1/s] 18) Cm244 1: [1/s] 18) Cm242 [a] 1: [n/s/atom] Cm244 [a] 4: [n/s/atom] Photo/TRU Fitting parameter ( ) TRU/Cm Calculated in advance ( ) R 244 Fitting parameter ( ) C SRNM Fitting parameter (0 300) Relative SRNM count rate [-] <Second Step> Measuring the ratio of the photoneutron to the the whole 242 Cm Photoneutron <First Step> Measuring the ratio of the 242 Cm to the whole [a] These values are calculated using SOURCE-4A code Finally, Eq. (1) becomes I SRNM ðtþ ¼ C SRNM Cm242 ð1 R 244 Þ e Cm242 t þ Cm244 R 244 e Cm244 t Cm242 ð1 R 244 Þþ Cm244 R 244 þ Photo/TRU ð1 þ TRU/Cm Þe Ba140 t þ TRU/Cm ; ð8þ C SRNM : constant defined as C SRNM ¼ I Cm242 ð0þþi Cm244 ð0þ: The values and ranges of all the parameters are summarized in Table 3. (4) Two-Step Fitting for Accurate Measurement of Photoneutrons It is difficult to obtain three parameters ( Photo/TRU, R 244, and C SRNM ) in Eq. (8) simultaneously by applying the leastsquares method to the actual SRNM signal because the halflives of photoneutron (T 1=2 of 140 Ba = 12.8 d) and 242 Cm (T 1=2 ¼ 163 d) are relatively close. Therefore, we proposed the two-step fitting process as shown in Fig. 4. (a) First step Two or three months after shutdown, the second terms of Eq. (8) are negligibly small, so we assumed Photo/TRU to be a proper value. Then, we evaluated the quantities of R 244 and C SRNM by fitting Eq. (8) to the actual SRNM signal. (b) Second step After obtaining R 244, we evaluated the quantities of Photo/TRU from the SRNM signal between one and two months after shutdown. (5) Difference in SRNM Detector Efficiency between Photoneutrons and Spontaneous-Fission Neutrons from Actinides In this study, we have assumed that the SRNM detector efficiencies " SRNM from Eqs. (2) through (4) are the same. Thus, in this section, we show that the difference in the SRNM detector efficiency for the photoneutron and neutron from actinides is small. The validity of this assumption is evaluated by a Monte Carlo calculation as follows. (a) Photoneutron energy spectra and generation region Neutron energy spectra originating from the spontaneous fission of 242 Cm, 244 Cm, and other actinides are almost the ð9þ 0.0 Fig Cooling Time [day] same. 1) The dominant energy range of these spontaneous fission neutrons is between 1 and 3 MeV. On the other hand, photoneutron energy spectra originating from D(, n)h reaction depend on gamma energy spectra. The energy spectra of photoneutrons due to major MeV gamma rays of 140 La in Fig. 3 range from 0:146 0:022 MeV according to the following equation, 12) E pn A 1! E 2 E Q A 2m n c 2 ða 1Þ þ E A 244 Cm sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2ðA 1ÞðE QÞ cos ; m n c 2 A Others Two-step fitting for measuring photoneutrons ð10þ A: mass of target nucleus, E : energy of photon, Q: threshold energy, m n : neutron mass, c: velocity of light, and : angle between photon and neutron flight direction. The energy of photoneutrons is lower than that of the spontaneous-fission neutrons by one decade, as shown in Fig. 5. Their intensities are normalized to a comparative level. This figure shows the neutron spectra due to major MeV gamma rays of 140 La and 244 Cm fission, which are used as neutron source energy spectra of the following bundle calculation. Their spectra are quite different from each other. The regions of neutron generation are also quite different from each other. The photoneutrons are generated in the moderator region because the deuterium exists mainly in this region, while the spontaneous-fission neutrons are generated within the fuel pin region. (b) Detector efficiency for photoneutron and actinide s spontaneous fission neutron We will then evaluate the 235 U reaction rate at the SRNM position for these neutrons under identical neutron intensity. Figure 6 shows the BWR fuel bundle system with inserted VOL. 46, NO. 12, DECEMBER 2009

7 1104 M. WATANABE et al. Photoneutron Spectra [arb. unit] Photoneutron Cm244 fission Cm Fission Spectra [arb. unit] Table 4 Differences in SRNM count rate between low-energy neutrons of photoneutrons and high-energy neutrons of spontaneous fission in a single BWR bundle Neutron source Relative 235 U reaction rate at SRNM [s 1 ] (Relative statistical error) (1) Photoneutron 53.5 (0.8%) (2) Spontaneous fission 55.8 (1.0%) (1)/(2) 0.96 Table 5 Condition of three measured BWR cores Neutron Energy [MeV] Fig. 5 Neutron energy spectra of photoneutrons and spontaneous fission for fixed source calculation CASE 1 CASE 2 CASE 3 Electric power [MWe] Number of fuel bundles Name of lattice type 19) D S N Pitch of each bundle 157 mm 152 mm 155 mm (X and Y directions) 148 mm 152 mm 155 mm Control rod pitch 305 mm 305 mm 310 mm Number of SRNM Fuel type (General Electric equivalent) (GE9) (GE9) (GE13) Core average exposure [GWd/t] Cycle length [GWd/t] Cycle condition MOC MOC MOC Measurement period [d] Cooling time [d] Process computer model COS3D COS3D LOGOS For the measurement of photoneutron, not for 242 Cm Fig control rods. The 235 U reaction rate at the SRNM position is calculated by the fixed-source calculation with MVP. One calculation is for the photoneutrons, the other is for spontaneous fission. The result of the 235 U reaction rate is shown in Table 4. The reaction rate of low-energy photoneutrons from the moderator region is approximately 4% less than that of high-energy spontaneous fission from fuel pins. The difference is neglected in the following measurement. 3. Result of Measurement for Photoneutron (1) Actual SRNM Signal Data In this study, the photoneutron signal ratio Photo/TRU was measured from the SRNM signal data of a commercial BWR. The evaluation requires more than three months of continuous SRNM signal data. Generally, it is impossible to acquire such data because the fuel assemblies are immediately reloaded following periodic inspection. 235 Example of BWR bundle cross section The condition of the three measured BWR cores is shown in Table 5. All the cases were related to unplanned outage. Therefore, our data accumulation over three months was valuable for our purpose. The three measured BWR cores in this study have different fuel lattice types, which have different fuel bundle pitches and control rod pitches. CASE 1, CASE 2, and CASE 3 were all middle of cycle (MOC) cases with cycle lengths of 2.5, 6.2, and 2.3 GWd/t, respectively. (2) Result of the Measurement The Photo/TRU measured in this study is shown in Table 6 with both R 244 measured and TRU/Cm calculated in the previous study. 1) The Photo/TRU ranges from 0.02 to This means that the relative fraction of photoneutrons in an SRNM signal ranges from approximately 2 to 50%. The result of fitting the theoretical model of Eq. (8) to the SRNM signal is shown in Fig. 7. A BWR core has between 6 to 10 SRNMs, depending on the size of the core. In this figure, the difference between solid and dashed lines is used only to make them distinct from each other, and case names indicate the core average exposure, cycle status, and number of cycles following the initial core. For example, 18G-MOC-C19 indicates that the core average exposure was 18 GWd/t in MOC, which was the nineteenth cycle following the initial core. JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY

8 Measuring the Photoneutrons Originating from D(, n)h Reaction after the Shutdown of an Operational BWR 1105 Table 6 Results of measurements of Photo/TRU CASE 1 CASE 2 CASE 3 SRNM Photo/TRU R 244 TRU/Cm Photo/TRU R 244 TRU/Cm Photo/TRU R 244 TRU/Cm A B C D E F G H J L Large fluctuation of SRNM signal caused measurement failure. SRNM count rate [cps] CASE 1: 18G-MOC-C19 A B D E G H SRNM count rate [cps] CASE 2: 24G-MOC-C12 A B C D E F G H Cooling Time [day] Cooling Time [day] SRNM count rate [cps] CASE 3: 16G-MOC-C2 A B C D E F G H J L Cooling Time [day] Fig. 7 All SRNM signals and fitting curves for evaluating the photoneutron signal ratio Photo/TRU in BWR cores (3) Absolute Value of Photoneutrons in SRNM Signal The measured absolute value I Photo after a five-day cooling period following shutdown was calculated using the following equation. I Photo ðtþ ¼C SRNM Photo/TRU ð1 þ TRU/Cm Þe Ba140 t ð11þ The result is shown in Fig. 8. These count rates range from 1 to 35 cps. The reasons for such a wide distribution of the absolute photoneutron are as follows. One is the difference in power history around each SRNM; the photoneutron emission rate is strongly affected by the power history around the SRNM because of the short half-life of 140 Ba. The other is the difference in absolute SRNM detector efficiency because the efficiencies are not calibrated at that time. (4) Notes on the Fitting Process Until five days after shutdown, a positive reactivity due to the xenon transient increases the SRNM signals; therefore, we rejected these SRNM signals. Moreover, the SRNM signals between 33 and 38 days in CASE 1 were also re- VOL. 46, NO. 12, DECEMBER 2009

9 1106 M. WATANABE et al. Measured Photoneutron Signal [cps] CASE1 18G-MOC-C19 CASE2 24G-MOC-C12 CASE3 16G-MOC-C2 A B C D E F G H J L Name of SRNM Fig. 8 Measured photoneutron signal (absolute value) in SRNM at five-day cooling after shutdown jected, because these signals fluctuated due to the activation of the primary loop recirculation pump during measurement. The measurement period of one month in CASE 2 is relatively short because a level transition of SRNM signals occurred. Fortunately, CASE 3 had no such signal fluctuation. To estimate the 95% confidence interval of the Photo/TRU as a fitting error, we assumed the upper and lower range of Photo/TRU to be about three times those of the least-squares error, based on an F-distribution as shown in Fig. 15. III. Calculation Procedure of Photoneutron 1. General Outline The outline of calculating the SRNM signal, namely, the 235 U reaction rate at an SRNM position, in this study is shown in Fig. 9. The computational codes used and the general condition of the core calculation are shown in Table 7. The procedure is based on the standard core management system for commercial BWRs. The core calculation with a fixed source is based on a few-energy group neutron diffusion theory. The neutron flux of a core with a fixed source of photoneutron or actinide is obtained by solving A ¼ M þ S f ; ð12þ M, A: generation and absorption operator of neutron diffusion equation, respectively, and S f : fixed neutron source, f ¼ PN for photoneutrons and f ¼ TRU for neutron from actinides consisting of 242 Cm, 244 Cm, and other actinides. The nuclear constants for M and A are obtained from the plant process computer based on a macroscopic depletion calculation model, 20,21) while the neutron generation rates of S PN and S TRU are described in detail in the next section. The following modeling and simplification are used in the present calculation. (a) Simple modeling of photoneutron source In order to accurately evaluate the photoneutron emission rate at each calculation node, a whole-core gamma ray transport calculation should be performed. However, we assume that the photoneutron emission rate is proportional only to the specific power (average power history) of the present Process computer (LOGOS or FNR) Fuel data (fuel type, exposure, void history, average power history) Photoneutron emission rate (MVP) F1(average power history, time) Neutron emission rate (SOURCES-4A) F2 (type, exposure, void history, time) Bundle calculation code (TGBLA) <Parameters for each node> Source of photoneutron Source of neutron from actinides Nuclear constant F3 (type, exposure, void history) F1, F2, and F3 are tabulated functions. The interpolation (parameters) is applied. time: time from the shutdown Fixed source calculation of whole BWR core by MOSRA-Light Neutron flux SRNM ( 235 U) reaction rate Fig. 9 Outline of procedure for calculating the SRNM signal JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY

10 Measuring the Photoneutrons Originating from D(, n)h Reaction after the Shutdown of an Operational BWR 1107 Table 7 Conditions for core calculations Specification Content Name of process computer TGBLA 20) /LOGOS, 21) NUPHYS 22) /FNR 23) Photoneutron emission rate MVP 10) Neutron generation rate from actinide SOURCES-4A 18) Fixed source calculation for whole core MOSRA-Light 24) Bundle calculation TGBLA 20) Number of energy groups Three (Fast, Epi-thermal, Thermal) 10 MeV, 5.53 kev, ev, 10 5 ev Calc. mesh One bundle, one mesh Approx [cm 3 ] cubic Core condition All Rod In (ARI) at 20 C Xenon-free condition cycle for simplicity. However, the neutron source from actinides is easily evaluated from the number density of the bundle calculation. (b) Using same nuclear constants for photoneutron and neutron from actinides Concerning the few group nuclear constants used in the core calculation, they may be affected by the difference in neutron energy spectra between the photoneutrons and actinides. Our sensitivity study clarifies that the difference in neutron spectrum has a small impact on the calculation result. (c) Simple SRNM reaction model A simple SRNM reaction model is used, i.e., we assume that the count rate of the SRNM is proportional to the 235 U reaction rate that is also proportional to the average neutron flux around the SRNM. 2. Fixed Neutron Source of Photoneutrons (1) Ideal Procedure for Calculating the Photoneutron Source The ideal procedure for calculating the photoneutron source S PN is as follows. First, the concentrations of 140 La at each calculational node are calculated using a whole-core microscopic depletion calculation model. Next, the wholecore gamma ray transport calculation is performed with the gamma source distribution of 140 La. Subsequently, the reaction rates of the gamma ray and deuterium are calculated by the multiplication of the gamma flux and the cross section of photoneutron production. However, these processes are not feasible because of the limited capabilities of existing process computers and high computer costs. Consequently, for the substitution of the whole-core gamma ray transport calculations, the following simplification is introduced in this study. (2) Simple Calculation of the Photoneutron Source The photoneutron emission rate at each node is assumed to be proportional only to the specific power of the present cycle at each node, considering all 24 axial nodes in the core, and the photoneutron emission rate does not depend on the fuel type, burnup, and void history. The photoneutron emission rate of i-th node SPN i is calculated as S i PN ðtþ ¼ S PN Ei MOC Ei BOC e E Ba140 t ; ð13þ core S PN : photoneutron emission rate at rated specific power (see Table 8), EMOC i, Ei BOC : i-th node exposure at MOC and BOC, respectively, E core : core average exposure, and t: the time from the shutdown of BWR operation. The detailed calculation process for the photoneutron emission rate SPN i is as follows. (a) Calculate the concentration distribution of 140 Ba as gamma source in the fuel assembly under the condition of core average power of approximately 40 W/cm 3 by TGBLA. (b) Use MVP to calculate the reaction rate of photoneutron production with reflective boundary condition, namely, in monobundle system, with the above-mentioned gamma source distribution. (c) Calculate the SPN i by multiplying the average specific power (relative value) of the present cycle and the above reaction rate of photoneutron production. (d) Calculate the radioactive decay of 140 Ba with the cooling time. (3) Discussion for Calculating the Photoneutron Source The accuracy of the above-mentioned simple calculation of the photoneutron source cannot be directly examined in this study because we do not have the microscopic depletion model and the whole-core gamma ray transport calculation model. As for not using the microscopic depletion model, the dependence on burnup and void history exhibited by the concentration of 140 Ba is small, as shown in Fig. 10. The dependence on fuel type will also be small assuming that the fuel types in the core are similar in uranium enrichment. Meanwhile, because of the short half-life of 140 Ba and modest power distribution change during normal operating cycle, the concentration of 140 Ba soon reaches the equilibrium value at nodal specific thermal power. Therefore, we can assume that the equilibrium concentration of 140 Ba is proportional to the specific power of the present cycle. As for the gamma ray transport calculation, we assume that the calculated gamma flux with reflective boundary condition, namely, a monobundle system, is the same as that of an actual finite whole core system. Neglecting the leakage of gamma rays at the periphery, top, and bottom of the core might lead to overestimation of the photoneutron production VOL. 46, NO. 12, DECEMBER 2009

11 1108 M. WATANABE et al. 2.0E-07 10, Ba Number density [10 24 /cm 3 ] 1.5E E E-08 VH=0% VH=40% VH=70% 0.0E Exposure [MWd/t] Neutron generation rate [n/sec/cm 3 ] 1, Total (Cm+Other) Cm242 Cm244 Other Photoneutron Exposure [GWd/t] Fig. 10 Calculated 140 Ba number density of various exposures and void histories (VHs) Fig. 11 Calculated neutron generation rate from actinides and photoneutrons for a representative BWR fuel at zero cooling time rate. However, the SRNMs are located at the midpoint in the axial direction, and most SRNMs are not in contact with the core periphery, so the leakage of gamma rays at SRNM nodes might be small Photo/Eig Cm/Eig 3. Fixed Neutron Source of Actinides (1) Procedure for Calculating Actinide s Neutron Source The neutrons originating from actinides S TRU are calculated by the multiplication of the atomic number density from the process computer 20 23) and neutron emission rate per nuclide, which is calculated using SOURCES-4A. In this study, the neutron generation rate originating from actinide of i-th node STRU i is calculated as Relative value [-] S i TRU ðtþ ¼X f j N j ðemoc i ; VHi MOC Þe j t g; ð14þ j j : neutron generation rate for j-th nuclide of the unit atomic number of i-th node, N j (E, VH): atomic number density of j-th nuclide, which is tabulated using exposure (E) and void history (VH) from the bundle calculation, VH i MOC : void history of i-th node at MOC, and j : decay constant of j-th nuclide. The neutron generation rate of a representative BWR fuel segment (8 8 fuel bundle, 40% void history, and 3.6 wt% 235 U enrichment) is shown in Fig. 11. The amount of neutrons from 242 Cm and 244 Cm increases exponentially with exposure while that of photoneutrons is almost constant. The neutron generation rate due to total actinides catches up with the rate due to photoneutrons at about 15 GWd/t. 4. Nuclear Constant for Core Calculation The nuclear constants for the core calculation are made by interpolation using the tabulated nuclear constants that are precalculated by the bundle calculation with fuel data (fuel type, exposure, and void history). The bundle calculation to 0.85 Σa1 vσf1 Σsl1->2 Σa2 vσf2 Name of Cross section Fig. 12 Difference between three energy group nuclear constants reduced by the spectra of fission or photoneutrons generate nuclear constants for the core calculation is normally performed as an eigenvalue problem. In this study, we used nuclear constants based on an eigenvalue problem for the fixed-source core calculation. The validity of this substitution is shown below. (1) Nuclear Constant for Photoneutron Source Relative three-energy group nuclear constants reduced with photoneutrons and 244 Cm fission spectra based on a fixed-source core calculation compared with one based on an eigenvalue calculation are shown in Fig. 12. In this figure, Photo refers to nuclear constants that are calculated as a fixed-source problem with the neutron source being photoneutrons of D(, n)h reaction, which is the same condition Σsl2->3 Σa3 vσf3 φ1/φ3 φ2/φ3 k JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY

12 Measuring the Photoneutrons Originating from D(, n)h Reaction after the Shutdown of an Operational BWR 1109 described in Sec. II-2(5). Cm refers to nuclear constants that are calculated as a fixed-source problem with the neutron source being 244 Cm s spontaneous fission. Eig refers to nuclear constants that are calculated using an eigenvalue problem. They are calculated using MVP. 25) The slowing-down cross section from fast energy to resonance energy ( sl1!2 ) of photoneutrons is approximately 6% greater than that with 244 Cm fission spectra, while the fission cross section ( f1 ) with photoneutron spectra is approximately 3% smaller than that of 244 Cm fission. However, the relative difference of k-infinity is less than 0.05%. The difference hardly affects the neutron flux distribution in the shutdown of a BWR core (subcritical system). (2) SRNM Detector Reaction Model The count rate of SRNM, I SRNM, is assumed to be proportional to the average nodal flux around the SRNM. It is calculated using the following equation. I SRNM ¼ " 4 Bundles around XSRNM i¼1 Z i ðeþ d ðeþde 4; ð15þ ": detector efficiency of the SRNM, i : average neutron flux over the i-th node around the SRNM, and d : macroscopic detector cross section of the SRNM, namely, infinite-dilution cross section of 235 U. Under this assumption, calculating the absolute value of I SRNM causes a large error due to the neglect of the gradient of thermal neutron flux at the corner. However, the Photo/TRU is a ratio between the I SRNM of S PN and I SRNM of S TRU. Thus, the above assumption does not cause a large prediction error in Photo/TRU at each SRNM position. (3) Calculations of TRU/Cm and Photo/TRU The ratio of the neutrons from other actinides ( 240 Pu, 242 Pu, etc.), excluding 242 Cm and 244 Cm, to the sum of neutrons from 242 Cm and 244 Cm at cooling time t ¼ 0 ( TRU/Cm ) is calculated by a whole-core fixed-source calculation. The procedure is as follows. Firstly, neutron sources originating from actinides, except for 242 Cm and 244 Cm, are calculated by using Eq. (14) and then the corresponding count rate of SRNM I SRNM TRU is evaluated by using Eqs. (12) and (15). Secondly, neutron sources originating from 242 Cm and 244 Cm are calculated by using Eq. (14) and then the corresponding count rate of SRNM I SRNM Cm due to the curium is evaluated by using Eqs. (12) and (15). Finally, TRU/Cm is obtained from the ratio of I SRNM Cm to I SRNM TRU, as shown in Eq. (6). Furthermore, Photo/TRU is also obtained by the same procedure of TRU/Cm. Firstly, the count rate of SRNM I SRNM Photon due to the photoneutrons is calculated by using Eqs. (12) and (15) with photoneutron source S PN of Eq. (13) and Table 8. Secondly, the count rate of SRNM I SRNM ALL TRUs due to the neutrons from all the actinides is calculated by the summation of the above-mentioned I SRNM TRU and I SRNM Cm. Finally, the Photo/TRU is obtained from the ratio of I SRNM Photon to I SRNM ALL TRUs, as shown in Eq. (5). 5. Result of Neutron Source Calculation (1) Photoneutron Distribution within a BWR Bundle A typical example of the gamma ray emission rate distribution of 140 La in a BWR fuel bundle is shown in Fig. 13(a). This figure represents the cell average distribution. Its exposure is 15 GWd/st and its void history is 40%. The result of the photoneutron emission rate [D(, n)h reaction] distribution is shown in Fig. 13(b). This figure appears to be smoother than the gamma ray emission rate distribution of 140 La (Fig. 13(a)). In addition, this figure shows that some photoneutrons are generated inside water rods and water gaps in spite of the absence of gamma ray emission of 140 La. Purely for reference, the distribution of neutron generation rate from actinides is shown in Fig. 13(c). This figure shows that the neutron generation rates of the corner fuel pins near the control rod side are strong because of soft neutron spectra, high thermal neutron flux due to the water gap, and low enrichment of the fuel pins. (2) Photoneutron Emission Rate The photoneutron emission rate at each calculational node calculated using MVP is shown in Table 8. These differences are relatively small and the total 140 La radioactive concentration almost dominates the photoneutron emission rate independent of lattice type. These rates presented in the table are average values of the photoneutron emission ratio at 15 and 30 GWd/st. The photoneutron emission rates in CASE 1, CASE 2, and CASE 3 per unit 140 La radioactivity are almost the same. (3) Core Average Neutron Source from Photoneutrons and Actinides The core average neutron source from photoneutron and actinides at zero cooling time for each case is shown in Fig. 14. This core average neutron source is corrected to adjust the calculated SRNM signal to the observed SRNM signal, which is depicted in Fig. 7. The absolute values of photoneutrons for all cases are almost the same because the average core powers of all the cases are almost the same; therefore, the photoneutron emission rates based on Eq. (13) and Table 8 are the same. Meanwhile, the neutrons originating from actinides based on Eq. (14) for each case depend on the composition of fuel burnup in the core. In Fig. 14, the SRNM count rate in CASE 1 is larger than that of CASE 3 in spite of the core average burnup of CASE 1 being almost the same as that of CASE 3. The reason is as follows. The neuron generation rate from actinides according to fuel burnup is exponentially growing as the fuel burnup increases, as shown in Fig. 9. The distribution of each bundle average burnup in CASE 3 is quite narrow, from 8.5 to 18 GWd/t, which is equal to the core average value of 15.5 GWd/t, because the cycle of CASE 3 is the second cycle with no refueling from the initial core. On the other hand, the distribution of each bundle average burnup in CASE 1 is larger, from 2.5 to 36 GWd/t, which is equal to the core average value of 18.1 GWd/t. The highburnup fuels in CASE 1 strongly emit neutrons. Therefore, the count rate of the SRNM in CASE 1 is larger than that of CASE 3. VOL. 46, NO. 12, DECEMBER 2009

13 1110 M. WATANABE et al. Control Rod Control Rod (a) SRNM Control Rod (b) SRNM (a) 140 La gamma ray emission rate (b) Photoneutron emission rate (c) Neutron generation rate from actinides (c) SRNM Fig. 13 Calculated source distribution of 140 La gamma ray, photoneutrons, and neutron from actinides for 8 8 fuel bundle of 15 GWd/st Table 8 Bundle-averaged photoneutron emission rate just after shutdown of rated power operation CASE 1 CASE 2 CASE 3 (A) Photoneutron emission rate [n/s/cm 3 ] (B) Radioactivity of 140 La [Bq/cm 3 ] 8: : : (A)/(B) 1: : : Name of lattice type D S N Fuel type Considering the photoneutron originating from only 140 La IV. Discussion 1. Comparison between Measured and Calculated Photoneutrons In order to confirm the validity of the measurement, the comparison between the measured Photo/TRU (M) and calculated Photo/TRU (C) is shown in Fig. 15. The error bars of the measurement are only the fitting error for the least-squares method. The following observations can be made from this figure. The reasonable agreement between the measured and calculated Photo/TRU shows the validity of the measurement. Although the relative fitting error of the Photo/TRU in CASE 3 is greater than the error in other cases, CASE 3 in particular had good agreement. However, some calculated Photo/TRU seems to be overestimated in CASE 1 and CASE 2. The probable causes of the overestimation of the calculated Photo/TRU are (a) overestimation of photoneutrons, and/or (b) underestimation of neutrons originating from actinides. The overestimation of photoneutrons might be due to the assumption of no gamma ray leakage from nodes mentioned in Sec. III-2(3). Alternatively, bundle-specific power near SRNMs may change much due to the control rod operation for reactivity compensation just before shutdown at MOC. JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY

14 Measuring the Photoneutrons Originating from D(, n)h Reaction after the Shutdown of an Operational BWR 1111 Calculated relative SRNM count rate at t =0 [cps] β Photo / TRU (Calculation) β Photo/TRU =0.31 CASE1 18G-MOC-C19 16G-MOC-C2 (CASE3) 18G-MOC-C19 (CASE1) β Photo/TRU =0.15 CASE2 24G-MOC-C G-MOC-C12 (CASE2) β Photo / TRU (Measurement) Cm242 Cm244 OTHER Photoneutron β Photo/TRU =0.98 CASE3 16G-MOC-C2 Fig. 14 Calculated SRNM count rate averaged over whole core at zero cooling time Fig. 15 Comparison between measured and calculated photoneutron signal ratios Photo/TRU As for neutrons from actinides, the macroscopic depletion calculation using process computer underestimates the number density of curium in fuel assemblies surrounding the inserted control rod. 1) This is because the macroscopic depletion model cannot accurately consider the change in neutron spectra due to control rod insertion. At any rate, root cause analysis requires an accurate depletion calculation 26) for curium and barium isotopes based on a microscopic depletion model considering power history, including the energy spectra change during operation. In addition, the calculation also needs an up-to-date nuclear data library to improve the burnup calculation for higher actinides. Furthermore, a whole-core gamma ray transport calculation is also required to improve the overestimation of the photoneutron emission rate. 2. Existence of Photoneutrons in SRNM Signal The result of the measurement provides us the following knowledge. During the first and second cycles, in which the fuel average burnup falls within a narrow range, the contribution of photoneutrons in SRNM signals is relatively large and it will reach approximately 50%. Then, approximately half of the SRNM signal at this time decays rapidly, and they almost disappear at the end of periodic inspections, which usually continue from two to three months. Hence, it is necessary to carefully decide whether we can remove the 252 Cf startup neutron sources from the core at the beginning of the second cycle. On the other hand, at the end of an equilibrium cycle, the contribution of the photoneutrons in SRNM signals may be smaller than in the case of CASE 1 and CASE 2 because large amounts of neutrons from actinides are generated by the EOC. However, the existence of photoneutrons in SRNM signals is still significant in order to evaluate the SRNM detector efficiency during the fuel unloading process. The efficiency evaluated will be used for the prediction of SRNM signals during the next fuel loading process in order to confirm that the SRNM signal is greater than 3 cps. V. Conclusions We measured the photoneutron emission rate of an operational BWR after shutdown using start-up range neutron monitors (SRNMs). With regard to measurement and calculation, it is assumed that SRNM signals consist of only four components: neutrons from both 242 Cm and 244 Cm, photoneutrons originating from D(, n)h reaction of 140 Ba- 140 La transient equilibrium, and the other constant components from actinides. For the accurate measurement of photoneutrons, we proposed a two-step measurement process: the first step is to measure the ratio of 242 Cm to 244 Cm, and the second step is to measure the ratio of photoneutrons originating from D(, n)h reaction due to 140 La s -ray to neutrons from actinides. This two-step measurement can effectively extract the photoneutrons in three different BWR cores. The measurement showed that the absolute values of photoneutrons in SRNM signals were between approximately 1 and 35 cps during a five-day cooling period after shutdown. By converting these absolute values to the relative fraction of photoneutrons in SRNM signals, these values ranged from approximately 2 to 50%. On the other hand, concerning the calculation of photoneutrons, we calculated the ratio of photoneutrons to neutrons from actinides in the SRNM signal, namely, photoneutron signal ratio, by a whole-core fixed-source calculation using the nodal expansion method. The photoneutron emission rate for each node was calculated using the Monte Carlo code, and the absolute value of the photoneutron emission rate was assumed to be proportional to the specific nodal power. Neutrons originating from actinides were calculated with atomic number densities based on the plant process computer. A comparison of the measured and calculated photoneutron signal ratios VOL. 46, NO. 12, DECEMBER 2009