1 Introduction

In the prototype fast breeder reactor (PFBR), the status of the core during regular startups as well as during reactor shutdown is monitored by high-temperature fission counters (HTFCs) with a sensitivity of 0.2 cps/nv, which are located in the control plug above the core [1]. However, it is found that the inherent neutron source strength arising from spontaneous fission and (α,n) reactions with oxygen nuclei in the fuel is insufficient to provide an acceptable count rate for core monitoring. Therefore, auxiliary neutron source subassemblies (SSAs) are planned to provide a count rate of more than 3 cps, as required owing to safety and startup time considerations [1]. The SSA consists of antimony (Sb₂O₃) pin bundles placed in hexagonal beryllium blocks. Neutrons are produced by the threshold (1.67 MeV) photoneutron reactions in beryllium. An antimony–beryllium photoneutron source is selected owing to its ease of fabrication and handling before loading into the reactor and its capacity for regeneration during operation. The SSA is located at the interface of the core periphery and radial blanket.

The neutron and gamma source strengths were estimated using the two-dimensional (2D) neutron transport code DORT [2]. The correctness of the neutron source strength estimate depends on the antimony activation calculation, which in turn depends on the neutron flux and ¹²³Sb capture cross section. Hence, in addition to the estimation of the neutron source strength and detector count rates, sensitivity and partial validation studies are performed.

The results are partially validated and the sensitivity to the thermal neutron flux is determined by irradiating samples of antimony in the KAMINI [3] reactor. Samples of (i) bare antimony and gold and (ii) antimony and gold covered with cadmium to cut off the thermal flux are irradiated. From these experiments, the neutron-flux-spectrum-averaged one-group capture cross sections of the bare and cadmium-covered ¹²³Sb samples are obtained by the ratio method. The change in the one-group cross section indicates the effect of spectral modification.

The sensitivity and variability of saturated gamma activity with respect to the antimony capture cross section are studied by considering data from various evaluated nuclear data files (ENDFs). An ENDF presents the best cross sections from both experiments and theoretical predictions. However, such ENDFs, for example, ENDF/B-VII.1 [4], JENDL-4.0 [5], and ROSFOND [6], are produced by different group of evaluators. Owing to differences in the experimentally obtained and theoretically predicted data considered by the evaluators, the cross-section data can vary.

This paper is organized as follows. Section 2 describes core monitoring by means of neutron detectors in the PFBR in detail. Section 3 gives the geometrical details of the auxiliary SSA and the data required for modeling. Section 4 covers the calculation of the neutron source strength from the SSA and the count rate at the control plug detector locations. The variation in the source strength with burnup owing to antimony depletion and decay are also presented. Section 5 discusses the experimental validation of the ¹²³Sb capture rate. In section 6, the source strength variability with respect to the neutron spectrum in the antimony resonance capture region and the capture cross sections from different data libraries are presented.

2 PFBR core monitoring

The PFBR is a 500 MWe, sodium-cooled, pool-type, mixed-oxide-fueled demonstration fast breeder reactor under construction at Kalpakkam [7]. The active core consists of 181 fuel subassemblies with two fissile enrichment zones of PuO₂. The core is enveloped by a blanket, which is surrounded by neutron reflector and shield assemblies.

The initial core loading and first approach to criticality will be monitored by three HTFCs with a sensitivity of 0.1 cps/nv, which will be located in a special central subassembly called the instrumented central subassembly [1]. However, for routine startup of the reactor, the core will be monitored by HTFCs with a sensitivity of 0.2 cps/nv located in the control plug above the core. Because the inherent neutron source strength is insufficient to provide an acceptable count rate of more than 3.0 cps, antimony–beryllium-based auxiliary neutron SSAs will be used to provide enough source strength that startup operations can be performed safely.

3 SSA geometry and properties

The auxiliary SSA is located at the core–blanket interface (eighth ring), as shown in Fig. 1. Three possible locations for the SSA are indicated. The auxiliary SSA consists of an antimony pin bundles enveloped by a hexagonal beryllium block. The bundle has 61 pins of Sb₂O₃ arranged in a hexagonal array. Each pin has 10 capsules of Sb₂O₃stacked inside a stainless steel tube, as shown in Fig. 2. The length of each capsule is 4.4 cm. The theoretical density of Sb₂O₃ is 5.2 g/cc. The pellet density is 90% of the theoretical density, and the mass of antimony oxide is 1.88 kg. The length, mass, and density of the beryllium block are 57 cm, 6.0kg, and 1.66 g/cc, respectively. The dimensional details and a cross-sectional (X–Y) view of the SSA are given in Fig. 3.

Fig. 1.Full-screen View

Core configuration of PFBR (Numbers in parentheses represent total number of SAs in each region.)

Fig. 2.Full-screen View

Sb₂O₃ pin bundle

Fig. 3.Full-screen View

Cross-sectional view of PFBR auxiliary SSA

Antimony has two isotopes,¹²¹Sb and ¹²³Sb, which have isotopic abundances of 57.36% and 42.64%, respectively. Neutron interaction in ¹²³Sb results in production of ¹²⁴Sb, whichhas a half-life of 60.9 days. Beta decay of ¹²⁴Sb results in the production of ¹²⁴Te in an excited state. The decay scheme of ¹²⁴Te includes approximately 70 gamma transitions with energies between 148 and 2807keV. Emission of neutrons from beryllium requires gamma rays with energies greater than 1.67 MeV. Therefore, the 1.69 MeV (yield 49%) and 2.1 MeV (yield 5.7%) gamma rays from ¹²⁴Te contribute to the photoneutron production.

4 Source strength estimation

The following four calculation steps are used to estimate the SSA neutron source strength and detector count rate for modeling convenience:

(i) Estimation of activation of ¹²³Sb to ¹²⁴Sb by neutron flux in the SSA location

(ii) Estimation of gamma transport in beryllium and photoneutron yield

(iii) Modeling of neutron transport from SSA to control plug detector location

(iv) Shutdown count rate estimation

4.1 ¹²³Sb activation calculation

To determine the saturated gamma strength of the antimony pins, the neutron flux distribution in the antimony region in the SSA is required. The neutron distribution reaching the SSA (which is kept in the first row of the blanket) is estimated using a 2DRZ model of the PFBR core and radial blanket without the SSA, as shown in Fig.4a. To this end, a neutron flux calculation is performed using the deterministic 2D neutron and gamma transport code DORT and the IGC-S3 cross-section set. IGC-S3 is a coupled neutron–gamma cross-section set having 175 neutron and 42 gamma group structures, which was prepared from ENDF/B-VI.8 [8, 9]. The neutron flux in the outer core and blanket region is approximately 3.10×10¹⁵ n/cm²/s. Then, to obtain the average neutron flux in the antimony region, the neutron spectrum in the core blanket region obtained from this calculation is distributed in the antimony region, which is shown in the model in Fig.4b, and an additional transport calculation is performed.

Fig. 4.Full-screen View

(Color online) RZ model of PFBR (a) and SSA (b)

The number of gammas emitted from the antimony region is computed using the average neutron flux spectrum in the antimony region and the capture cross section of ¹²³Sb. At full power, the average neutron flux in the antimony region is found to be 2.66×10¹⁵ n/cm²/s. The estimated total ¹²³Sb capture reaction rate per SSA is 9.04×10¹⁵ s^-1.

4.3 Neutron transport from SSA to control plug detector location

After the neutron strength from the SSA is determined, the transport of neutrons from the SSA in the core to the control plug detector location is modeled by MCNP-4b [11]. Figure 5a shows a schematic diagram of the active core and detector location. The initial plan, considering uncertainties and operational convenience, is to have three SSAs at the core–blanket interface (see Fig. 1). These three SSAs are included in the beginning-of-life core and can be replaced in turn after the third, fourth, and fifth cycles of operation. There are three HTFCs located 14.8 cm vertically above the core SA head and 100 cm radially from the core center (Fig. 5b). The detector active height is 27 cm. The model consists of three SSAs and three detectors in the control plug location. In the calculation, it is assumed that the saturated neutron strength of 9.26×10¹¹ n/s/SA is distributed uniformly in each SSA region. Further, 10⁹ particle histories with the F4 tally were employed for the calculation.

Fig. 5Full-screen View

(a). Schematic of control plug detector location (LRP: Large Rotating Plug, SRP: Small Rotating Plug, CP: Control Plug, PCD: Pitch to Centre Distance); (b). Vertical cross-sectional view of MCNP model of PFBR core up to control plug (A horizontal cross-sectional view of the PFBR core is given in Fig. 1.)

4.4 Estimation of shutdown count rates

From the neutron flux calculated at the detector location in the previous step, the ²³⁵U thermal fission equivalent flux is calculated using the following expression:

${\varnothing }_{\text{fis}-\text{eq}}=\frac{\int \varnothing \left(E\right){\sigma }_f^{\text{u}-235}\left(E\right)\text{d}E}{{\sigma }_f^{\text{u}-235}\left(0.025 \text{eV}\right)}.$ (1)

The thermal cross section of ²³⁵U fission is 585.1 b. Hence, the total detector counts are calculated by multiplying the fission equivalent flux by the detector sensitivity. For the three SSAs inside the core, with an HTFC sensitivity of 0.2 cps/nv at the control plug location, the count rates estimated in the three detectors are 35.1, 38.4, and 38.6 cps, respectively. Further, the count rates from the three detectors with one SSA are 13.0, 13.8, and 14.0 cps, respectively. The small differences in the count rates are due to the asymmetry of the detector location (Fig. 5b).

The saturation source strength of the auxiliary SSA decreases during reactor operation owing to burnup of antimony. Figure 6 shows the activity buildup and decay of ¹²⁴Sb during each cycle of operation. It is assumed that each fuel cycle consists of six months of full-power operation followed by two months of shutdown for fuel handling. When the reactor is operating at full power, the source strength of the auxiliary SSA builds up from zero, and it increases to approximately 50% of saturation in two months. After six months of full-power operation, it reaches 88% of saturation at the end of the first cycle (EOC1). After two months of reactor shutdown, the ¹²⁴Sb activity decreases to 44% of saturation.

Fig. 6.Full-screen View

Antimony activity during each cycle of operation

Note that gammas produced by the core with energies above the threshold energy (1.69 MeV) will also result in neutron generation from the SSA. During full-power operation, the neutron source strength is approximately 5.56×10¹² n/s, which is 6 times larger than the neutron source strength from the SSA. However, after approximately two months of shutdown, the neutron source strength from the core gammas is 1.58×10¹⁰ n/s, which is 26 times smaller than that from a SSA.

Figure 7 shows the neutron strengths and count rates corresponding to saturation, EOC1, and one and two months after reactor shutdown. These count rates also include contributions from the inherent neutron source (INS). The INS contributions are estimated using the home-made code NSOURCE. The estimated count rates resulting from INSs at the end of one cycle, one month after shutdown, and two months after shutdown are 0.6, 0.54, and 0.49 cps, respectively.

Fig. 7.Full-screen View

Count rate and neutron strength that saturation, shutdown, and one and two months after reactor shutdown

5 Experimental validation of antimony activation

Experimental studies are performed by irradiating samples of antimony in the KAMINI reactor. Samples of (i) bare antimony (powder) and gold and (ii) antimony (powder) and gold covered with cadmium to filter the thermal flux are irradiated. The samples are irradiated separately for each case. Each sample is inserted adjacent to the core of KAMINI using the Pneumatic Fast Transit System (PFTS). Cadmium-covered foils are used to analyze the epithermal neutron activation, as the KAMINI spectrum is soft compared to that at the SSA location in the PFBR. Irradiation of gold foils serves as a reference for finding the activation cross section of antimony through the activity ratio method.

The reactor was operated at 10kW. The four samples, i.e., bare gold, bare antimony, cadmium-covered gold, and cadmium-covered antimony, were irradiated separately for 600 s each. The irradiated samples were measured using an HPGe detector at a reference position with a known full-energy peak detection efficiency. The detector has a 30% relative efficiency, and the resolution was 2.0 keV at the 1332 keV peak of ⁶⁰Co. The peak areas were evaluated using the peak fitting software APTECH. The details of the foils (powder) and their measured activities and reaction rates are given in Table 2. The measured reaction rate (R) is obtained as

where C_peak is the net peak area of the full-energy photopeak measured by the HPGe detector, y is thegamma intensity (gammas/decay), ε is the efficiency of the detector, T_d (s) is the time delay between the end of irradiation and the start of counting, T_c is the counting time (s), T_irr is the irradiation time, and N is the number of target atoms in the foil. The efficiency of the HPGe detector was obtained as a function of gamma ray energy using a ¹⁵²Eu standard.

The activation (average) cross section of gold is obtained as

where σ₂ and R₂ represent the KAMINI spectrum-averaged capture cross section and measured reaction rate of gold, respectively. The KAMINI PFTS neutron flux spectrum, φ, is measured using the foil activation technique and unfolded in 175 neutron groups [12] in these calculations. The unfolding method utilizes 10 activation reactions (activation foils) to cover the energy range of 1.0×10^-4 eV to 20 MeV. Although the error of the unfolded neutron flux has not been estimated, it is reported that the unfolded spectrum reproduces the measured reaction rates within a +10% error [12]. Then, using the ratio method as described below, the average one-group capture cross section of ¹²³Sb can be obtained if an accurate cross section of the reference sample (gold) is known.

where A₁ and A₂ are the activities of ¹²³Sb and ¹⁹⁷Au (Bq), and N₁ and N₂ are the number of atoms of ¹²³Sb and ¹⁹⁷Au, respectively; σ₁ represents the average capture cross section of ¹²³Sb. The cadmium-covered samples are sandwiched between cadmium foils. The presence of cadmium reduces not only the thermal component, but also the total neutron strength. The antimony is activated mainly by epithermal neutrons. The reduced neutron flux that activates the antimony or gold is approximated using the attenuation equation $\varphi =$ $\varphi ={\varphi }_o{e}^{-{\Sigma }_{t}t}$, where φ_o and φ are the incident and transmitted neutron fluxes, respectively; ∑_t is the macroscopic total cross section of cadmium, and t is the thickness of the cadmium foil. Then, following a methodology similar to that used for the bare samples, the average activation cross sections of the cadmium-covered gold and antimony samples are obtained. The measured activities and the cross sections obtained using Eq. (4) are given in Table 2. It is observed that, owing to the spectral change, the average capture cross section of ¹²³Sb decreases from 4.1 to 1.78 b. The measured and calculated reaction rates for bare ¹²³Sb are 1.24×10^-12 and 1.34×10^-12 reactions/atom/s, respectively. The difference between the measured and calculated values is approximately 8%. The experimental study helped to validate the one-group cross section of ¹²³Sb and hence the ¹²³Sb activation with the nearest available spectrum from KAMINI. Further sensitivity studies are presented in the following sections.

6 Source strength variability and sensitivity studies

Section 4 discussed the theoretical predictions of the neutron and gamma source strength. There is sufficient confidence in the estimated flux at the SSA location and the spectrum estimates from integral experiments and fast breeder test reactor design and operation experience [13]. However, the estimated ¹²³Sb capture rate requires further assessment. In this context, the variability of the estimates with respect to the capture cross sections of ¹²³Sb from different evaluated cross-section libraries is also assessed. The following subsections discuss (i) the prediction of the saturation gamma activity using ¹²³Sb capture cross sections from different ENDFs and (ii) the sensitivity to the neutron spectrum in the region surrounding the SSA.

6.2 Sensitivity to spectrum in the region surrounding the SSA

Because antimony activation is very sensitive to the spectral component of the flux below 100keV (which account for 80 to 90% of the reactions), the source strength was also estimated with the blanket SA replaced by a steel SA. In this case, the source strength increases by a factor of 3.9 (the ¹²³Sb capture reaction rate per atom for the steel-surrounded case is 2.72×10¹⁵ n/cm²/s, and that for the blanket-surrounded case is 6.90×10¹⁴ n/cm²/s).

Figure 8 shows the absolute neutron flux spectra at the SSA location for the SSA surrounded by a blanket SA and the SSA surrounded by steel SA, and the ¹²³Sb capture cross section. The spectral softening for the SSA surrounded by a steel SA is attributed to the fact that steel provides greater inelastic slowing down than the uranium oxide blanket material. The study indicates that the neutron source strength can be increased, if necessary, by the addition of a suitable steel SA surrounding the SSA, although this will reduce the breeding ratio.

Fig. 8.Full-screen View

Neutron flux spectra at SSA location for blanket and steel SAs

The following are the salient observations from the studies of the auxiliary source strength activation, variability, and sensitivity.

(i) The differences among the saturation gamma (>1.67 MeV) activities and neutron strengths predicted by ORIGEN2 using one-group cross sections from different ENDFs are within +2%. In addition, the DORT estimate is approximately 4% higher than the ORIGEN2 prediction.

(ii) The source strength increases by a factor of 3.5 when the SSA is surrounded by a steel SA instead of a blanket SA owing to spectral softening.

(iii) An experimental study shows that the estimated one-group cross sections are sensitive to the flux spectrum in the thermal region. The estimated one-group antimony activation cross section in the KAMINI spectrum is 4.1b (11% at < 30 eV), whereas for the PFBR spectrum, it is 1.0b (1% at < 30eV).

7 Conclusion

Using a combination of deterministic and Monte Carlo transport codes, the neutron source strength and control plug detector count rate from the auxiliary neutron SSA in the PFBR is estimated. The estimation is performed in four stages: (i) estimation of the ¹²³Sb activation using neutron flux in the SSA location, (ii) estimation of gamma transport in beryllium and photoneutron yield, (iii) modeling of neutron transport from SSA to control plug detector location, and (iv) estimation of shutdown count rate. The estimated (saturated) neutron source strength of the SSA is approximately 9.3×10¹¹ n/s/SA.

The accuracy of the neutron source strength estimate is sensitive to the neutron spectrum in the vicinity of the ¹²³Sb capture cross section resonance peak at 22 eV. Hence, the spectrum sensitivity is estimated by surrounding the SSA with a steel SA. The variability in the neutron source strength owing to the variation in the capture cross section is studied by considering data from different ENDFs. Experimental irradiation of antimony powder is also conducted and provides partial validation of the neutron source strength predictions in the absence of direct measurement of the PFBR spectrum.