Evaluating the JEFF 3.1, ENDF/B‑VII.0, JENDL 3.3, and JENDL 4.0 nuclear data libraries for a small 100 MWe molten salt reactor with plutonium fuel

Cici Wulandari · Abdul Waris · Sidik Permana · Syeilendra Pramuditya

Abstract This study evaluated the nuclear data libraries for a small 100 Mega Watt electric (MWe) Molten Salt Reactor with plutonium fuel. The reactor has a power output of 100 MWe, which meets the demand for electricity generation in several regions or provinces outside Java Island. Several nuclear data libraries, such as JEFF 3.1, ENDF/B-VII.0, JENDL 3.3, and JENDL 4.0, were used for a more comprehensive evaluation. LiF—BeF2—ThF4—PuF4 was used as the initial fuel composition. The thorium and plutonium concentrations in the fuel salt were varied to obtain the optimum fuel composition, leading to critical conditions. The results showed some neutronic parameters, such as the conversion ratio, neutron spectra, and effective multiplication factors, from three different nuclear data libraries. By changing the plutonium concentration in the initial fuel salt composition, the minimum plutonium loaded for the reactor criticality during 2000 days of operation time was determined to be 0.995, 0.91, 0.87, and 0.90 mol% for JEFF 3.1, ENDF/B-VII.0, JENDL 3.3, and JENDL 4.0, respectively.The differences in the values of each parameter were due to several factors, such as the cross-section values and number of nuclides in the nuclear data libraries. Several safety parameters were also investigated to ensure the possibility of utilizing PuF4 in the reactor.

Keywords Neutronics · Plutonium · Small MSR · Thorium · SRAC

1 Introduction

Indonesia is an archipelago country with various islands of different sizes, but they are mostly small. The energy demand on these islands is relatively low, approximately 100 MWe, owing to their low populations. However, electricity transmission from large islands to small islands is not yet possible. Therefore, a small nuclear reactor is needed to meet the energy demand of developing areas, such as those in several regions or provinces in Indonesia outside of Java Island, of approximately 100 MWe. This would also allow the reduction in carbon emissions to help address climate change.

One of the reactor types that can generate small power outputs is the Molten Salt Reactor (MSR). The MSR is a type of Generation IV nuclear power technology that uses molten salt as fuel. Dissolved salt is mixed with fission products, and actinides circulate through the active core to the primary heat exchanger [1]. Based on graphite moderator utilization, this reactor can be operated in the thermal, epithermal, and fast neutron spectra. Moreover,this reactor was designed using advanced systems in terms of inherent safety, proliferation resistance, energy sustainability, and waste burning. These systems are potentially interesting for the development and research of MSR technology.

The Oak Ridge National Laboratory pioneered MSR concepts, such as the aircraft reactor experiment [2, 3], MSR experiment [4], and molten salt breeder reactor [5]. These projects described the basic concept of MSR technology,including a re-evaluation of reactor performance and the development of other systems, such as waste burning and fuel reprocessing [6, 7]. In addition, the concept of thorium molten salt nuclear energy synergetics (THORIMS-NES) [8,9] has recently been studied in Japan for several MSR types with different power outputs. The FUJI-U3 reactor [10, 11]is a THORIMS-NES concept with a power output of 200 MWe that uses233U/232Th as the primary fuel. Because the power output in the FUJI reactor can be adjusted, there is a high probability of it being designed for a small reactor.

The FUJI-Pu reactor [12] is one of the reactor types developed using the THORIMNES concept. Some plutonium isotopes were considered to be the starting fuel in this reactor. The goal was to replace233U as an initial fissile used in other FUJI reactor concepts, such as FUJI-12, FUJIII, and FUJI-U3. FUJI-Pu is a 1- and 2-region [13] reactor core with a high neutron flux at the center of the core. The neutron flux distribution is an important parameter because it is related to the reactor safety system and fission intensity in the reactor [14]. The design of a 3-region core was introduced to provide flattening neutron flux in the reactor core[10]. Therefore, a small MSR should adopt the design of the 3-region core concept and the utilization of plutonium as an initial fuel.

In our previous study, the neutronic performances of FUJI MSR using plutonium fuel [15] and plutonium/minor-actinide fuel [16—18] were evaluated using the standard reactor analysis code (SRAC (Ver. 2002)), which was established by the Japan Atomic Energy Research Institute using the nuclear data library JENDL 3.2 [19]. However, the nuclear data library utilized in previous studies is outdated, and newer versions, such as JENDL 3.3 [20] and JENDL 4.0[21], are currently available.

This study investigated the optimization of plutonium fuel loading on the neutronic performance of a small 100 MWe MSR. The initial fuel salt composition used was LiF—BeF2—ThF4—PuF4. Several plutonium isotopes employed in PuF4, such as238Pu,239Pu,240Pu,241Pu, and242Pu. The plutonium isotope with odd mass numbers was utilized as a fissile material. At the same time, the plutonium isotope with even mass numbers and232Th was used as a fertile material. Based on a previous study, this fuel scheme is feasible for producing233U with Th/Pu as the starting fuel[22], which leads to achieving sustainable energy from thorium utilization in the MSR [23—25].

This study aimed to obtain the minimum required PuF4fuel concentration for 2000 days of reactor operation without a refueling scheme by varying the plutonium concentration in the initial fuel salt. It was assumed that on day 2001,chemical processing of the fuel salt would be performed,which is based on the FUJI-U3 reactor study [10]. The utilization of plutonium in fuel salts aimed to burn weaponsgrade plutonium (WGPu) [26, 27] in the MSR and reduce the risk of nuclear proliferation [28]. Although this scenario is only intended for theoretical research, the utilization of WGPu as a fuel in MSR is very promising in terms of energy resources, radiation level, and heat generation.

Moreover, several nuclear data libraries, such as JEFF 3.1 [29], ENDF/B-VII.0 [30], JENDL 3.3, and JENDL 4.0,were employed to provide information on trans-plutonium sensitivity and to show the neutronic parameter dependence on nuclear data libraries. JENDL 3.3 and JENDL 4.0 were compared to obtain the neutronic parameter sensitivity in small MSR based on the evaluation of the two libraries.JENDL 3.3 is reported to have overestimated cross-section values for some nuclides compared to JENDL 4.0. To compare trans-plutonium, the JENDL, ENDF, and JEFF libraries were compared. In addition, the effect of the plutonium concentration on some neutronic parameters, such as the neutron spectra, conversion ratio (CR), and effective multiplication factor, was analyzed in this study. Moreover, a safety analysis was also considered, such as the moderator temperature coefficient (MTC), Doppler reactivity coefficient (DRC), and control rod worth (CRW), to show the possibility of plutonium utilization in the reactor.

2 Reactor specification

Table 1 lists the small 100 MWe MSR parameters adopted from the FUJI-U3 reactor [10]. However, in this study, the power output of the reactor was half that of FUJI-U3. It is considered to meet the energy demand of small islands in Indonesia (approximately 100 MWe). The geometry of the active core was a cylinder consisting of several hexagonal graphite layers and a cylindrical fuel channel. The reactor was equipped with a graphite moderator with a density of 1.8 g/cm3that can slow down neutrons to the thermal energy region. The lifespan of the graphite moderator was related to the neutron irradiation process during reactor operation [31].The fuel used was thorium-WGPu with eutectic fluoride salts of lithium and beryllium [32] as the heat transfer media from the active core to the secondary loop.

Figure 1 shows the small MSR active core design divided into three regions with different fuel volume fractions. Previous studies numerically showed that the flattening of theneutron flux distribution and graphite lifespan could be enhanced by varying the fuel volume fraction in the active core [33, 34]. Therefore, the excessive reactivity at one point in the active core can be avoided. In addition, different fuel volume fractions affect the size of the fuel channel. Figure 2 shows the layout of hexagonal graphite and cylindrical fuel channels for different core regions. In this study, the sideto-side length (p) of hexagonal graphite was 20 cm, and the diameters of the fuel channel were 12.56, 10.36, and 12.40 cm for the Core 1 (d1), Core 2 (d2), and Core 3 (d3)regions, respectively (Table 2).

Table 1 The parameters of a small 100 MWe Molten Salt Reactor

Fig. 1 (Color online) The core configuration in the radial and axial direction with one-fourth of the active core

Fig. 2 The layout of hexagonal graphite and the cylindrical fuel channel for different core regions

3 Calculation methods

In this study, variations in the fuel salt composition were employed to obtain the reactor criticality, which is provided in Tables 3, 4, 5, and 6 for JENDL 3.3, JENDL 4.0, ENDF/B-VII.0, and JEFF 3.1, respectively. The percentage concentration of both LiF and BeF2was fixed at 72 and 16 mol%,respectively, while the total percentage concentration of ThF4and PuF4was 12 mol%. The percentage PuF4concentration to the total percentage ThF4and PuF4concentration was varied to achieve reactor criticality. The WGPu isotopic compositions [26] are presented in Table 7.

The neutronic performance was evaluated using the diffusion method in the SRAC 2006 program code. The SRAC system was designed to perform neutronic aspect calculations for the various reactors. This system can also produce cross-sectional groups (macroscopic and microscopic), fuel channel calculations, core calculations, and burnup analyses. The fuel channel in this study was calculated using the PIJ module of the SRAC 2006 code, which uses a collision probability technique. In the SRAC system, the structure number of the energy group is 107, which is compressed into 30 groups (24 groups of fast neutron energies and six groups of thermal neutron energies) [10]. The geometry of the fuel channel was modeled, as shown in Fig. 2. The fuel channel calculation obtained the macroscopic cross-sectional value for every burnup step. In this study, the burnup step was set to 100 days for 2000 days of reactor operation. These results were used in the core calculations using the CITATION module. The core geometry is shown in Fig. 1 and is divided into 65 radial and 32 axial zones. The fuel and graphite moderators in the core calculation were homogenized to obtain the cross-sectional groups.

This study assumed that the reactor operated continuously for 2000 days without a refueling scheme. If the effective multiplication factor for 2000 days of operation was still below unity, the percentage of PuF4was augmented. The calculations were performed using similar parameters for different nuclear data libraries. Several nuclear data libraries were used: JEFF 3.1, ENDF/B-VII.0, JENDL 3.3, and JENDL 4.0. JEFF was created by the European Nuclear Energy Agency, JENDL was established by the Japan Atomic Energy Agency, and ENDF was developed by the US Cross-Section Evaluation Working Group. The year of release and number of nuclides in each nuclear data library are listed in Table 8.

Table 2 Radius, height, and fuel volume fractions of the core regions

Table 3 Variation of the fuel salt composition for JENDL 3.3

Table 4 Variation of the fuel salt composition for JENDL 4.0

Table 5 Variation of the fuel salt composition for ENDF/B-VII.0

Table 6 Variation of the fuel salt composition for JEFF 3.1

Table 7 Weapons-grade plutonium composition for all nuclear data libraries [20]

Table 8 Comparisons of the released year and number of nuclides of JENDL 3.3, JENDL 4.0, and JEFF 3.1

4 Results and discussion

4.1 Effect of PuF4 concentration on reactor criticality

The effective multiplication factor (keff) values as a function of operation time for 0.80% mol of the PuF4concentration in the fuel for JENDL 3.3, JENDL 4.0, ENDF/BVII.0, and JEFF 3.1 are shown in Fig. 3. The trend of thekeffvalue was similar to that of all cases wherein it decreases during the operation time. This fact is estimated by subtracting the fissile material (239Pu) to maintain fission in the active core. Moreover, thekeffvalue of the JEFF 3.1 library was the lowest, followed by ENDF/B-VII.0,JENDL 4.0, and JENDL 3.3. Thus, 0.80 mol% loaded PuF4concentration is insufficient to maintain the critical condition for 2000 days of operation time for all cases.The calculated critical operation time of the reactor with 0.80 mol% PuF4concentration in the fuel for JENDL 3.3,JENDL 4.0, ENDF/B-VII.0, and JEFF 3.1 was 1400, 1300,1200, and 600 days, respectively.

In general, the above results on the differences in the criticality conditions (keff) can be analyzed by comparing the total number of nuclides of the three libraries used, as shown in Table 8.

As shown in Table 8, the number of nuclides in each library was diverse. For instance, the JENDL 4.0 library is an updated version of JENDL 3.3, with the number of nuclides changing from 337 to 406. Based on reference, 30 fission products were added to JENDL 4.0, as were several updated cross-section values, such as a neutron capture cross section of232Th,238Pu, and241Am in the thermal energy range [21]. Therefore, the calculation with JENDL 3.3 has an underestimated criticality value compared to that with JENDL 4.0.

Fig. 3 (Color online) Comparison of keff values with 0.80 mol% PuF4 fuel for JENDL 3.3, JENDL 4.0, ENDF/B-VII.0, and JEFF 3.1

Based on thekeffvalue between ENDF/B-VII.0 and JENDL 4.0, as shown in Fig. 3, the value of ENDF/B-VII was slightly lower than that of JENDL 4.0. The number of nuclides in JENDL 4.0 is greater than that in ENDF/B-VII.0,which can lead to a difference in thekeffvalue. As shown in Fig. 3, the calculation using JEFF 3.1 had a lowerkeffvalue than that using JENDL 4.0. Even though the number of nuclides on JEFF 3.1 is lower than that on JENDL 4.0.Therefore, it can be predicted that there is an underestimated cross-section value in the JEFF 3.1 calculation compared to the JENDL 4.0 calculation. In addition, the following calculation results and discussion specifically explain the influence of these four libraries on the neutronic performance of a small MSR with plutonium fuel.

The influence of increasing the PuF4concentration on the criticality of the reactor is presented in Fig. 4. For JENDL 3.3 in Fig. 4a, PuF4concentration varied from 0.70 up to 0.87 mol%, where thekeffvalue increased as the PuF4concentration increased. For JENDL 4.0 in Fig. 4b, the PuF4concentration rose from 0.70 up to 0.90 mol%, in which thekeffvalue trend was similar to JENDL 3.3. For ENDF/B-VII.0 in Fig. 4c, the concentration of PuF4varied from 0.70 up to 0.91 mol%. Finally, for JEFF 3.1 in Fig. 4d, PuF4concentration varied from 0.70 up to 0.995 mol%, where thekefftrend was also similar to that of the other libraries.Based on the obtained results, the increasingkeffvalue was parallel to the increasing PuF4concentration. This is related to the greater fissile material loaded in the reactor, whose PuF4concentrations are presented in Tables 9, 10, 11, and 12 for JENDL 3.3, JENDL 4.0, ENDF/B-VII.0, and JEFF 3.1, respectively. Moreover, as shown in Fig. 16, the addition of PuF4increased the hardness of the neutron spectrum.Therefore, the effectiveness of the plutonium fission process was higher because239Pu is fissile superior in the fast energy region. Therefore, thekeffvalue obtained was also higher.

As mentioned above, the small MSR was operated for 2000 days without refueling. However, the minimal PuF4concentrations in loaded fuel for JENDL 3.3, JENDL 4.0,ENDF/B-VII.0, and JEFF 3.1 were 0.87, 0.90, 0.91, and 0.995 mol%, respectively.

The criticality differences may also have arisen from the different values of the radiative neutron capture cross section of some nuclides in JEFF 3.1, ENDF/B-VII.0, JENDL 3.3,and JENDL 4.0. Figure 5 depicts the radiative neutron capture cross section for important nuclides, such as233U,232Th,239Pu,241Pu, and241Am, in the fast, resonance, and thermal energy ranges from these nuclear libraries. Figure 5a shows that the capture cross sections of233U in these libraries are slightly different in the resonance and fast energy regions.The capture cross section in ENDF/B-VII.0 was the highest,followed by that in JENDL 4.0, JEFF 3.1, and JENDL 3.3.However, the values coincided in the thermal energy range for all nuclear data libraries.

In Fig. 5b, the capture cross sections of232Th for the four libraries were also different, with the lowest value being for JENDL 4.0 in the resonance and thermal energy range. This means that the probability of the neutron capture process of232Th for JENDL 4.0 was lower than that for JENDL 3.3 and JEFF 3.1. However, the capture cross section of232Th in JENDL 4.0 was slightly similar within ENDF/B-VII.0,which could lead to a slight similarity in reactor criticality. In this fuel salt,232Th was the primary fertile material.Therefore, the neutron capture cross-section differences from the nuclear data libraries can affect233U production,generating different criticality conditions.

In Fig. 5c, d, the capture cross sections of239Pu and241Pu for the four nuclear data libraries had similar conditions to the233U capture cross section, where the differences were insignificant. However, in the fast energy range, the value for JEFF 3.1 was the highest followed by JENDL 3.3, JENDL 4.0, and ENDF/B-VII.0. The capture cross section of241Am for all libraries used also had a different value, with the highest value shown in JENDL 4.0, especially in terms of thermal energy, as presented in Fig. 5e. Meanwhile, the JEFF 3.1 trend was similar to that of JENDL 3.3 and ENDF/B-VII.0 in the thermal and fast energy regions. When JENDL 3.3 and JENDL 4.0 were compared, it was found that JENDL 3.3 had an underestimated value of capture cross section,where the number of absorbed neutrons decreased, resulting in a higherkeffvalue.

Fig. 4 Comparison of the keff value with various PuF4 concentrations for a JENDL 3.3, b JENDL 4.0, c ENDF/B-VII.0, and d JEFF 3.1

Table 9 PuF4 concentration for each plutonium isotope and 241Am with JENDL 3.3

The criticality also refers to the microscopic fission cross section, which is described as the fission probability between a neutron and nuclide. Figure 6a—e shows the microscopic fission cross section of a fissile in the reactor.A comparison of the microscopic fission cross sections of233U for JENDL 3.3, JENDL 4.0, ENDF/B-VII.0, and JEFF 3.1 is shown in Fig. 6a. This shows that the values in the thermal energy region were higher than those in the fast energy region. This indicates that the fission probability of233U is higher in the thermal energy region, which is suitable for the reactor under consideration. The microscopic fission cross sections of232Th for the four nuclear data libraries are shown in Fig. 6b. Although232Th is a fertile material, it still has a fission probability, especiallyin the fast energy region. JENDL 3.3 and JENDL 4.0, produce fission cross-section values of232Th in all energy ranges, while JEFF 3.1 and ENDF/B-VII.0 only produce values in the fast energy range. Although the value is relatively low, this discrepancy can lead to differences in the obtainedkeffvalues. The fissionability of232Th in the JEFF library is only considered in the fast energy region,whereas the JENDL library is considered in all energy ranges. Therefore, the JEFF and ENDF/B-VII.0 library will have a lowerkeffvalue than the JENDL library, as shown in Fig. 3.

Table 10 PuF4 concentration for each plutonium isotope and 241Am with JENDL 4.0

Table 11 PuF4 concentration for each plutonium isotope and 241Am with ENDF/B-VII.0

Table 12 PuF4 concentration for each plutonium isotope and 241Am with JEFF 3.1

As the primary fissile material in this reactor, the microscopic fission cross section of239Pu for all libraries used is shown in Fig. 6c. The microscopic fission cross sections of239Pu for JEFF 3.1 and JENDL 3.3 are slightly different in the resonance and fast energy ranges. Similar to239Pu,the microscopic fission cross section of241Pu for different nuclear data libraries is presented in Fig. 6d, where the value difference is insignificant. The microscopic fission cross section of241Am is shown in Fig. 6e. In the thermal energy range, JENDL 4.0 is first, followed by ENDF/BVII.0, JENDL 3.3, and JEFF 3.1. Again, the values are slightly different for the four nuclear data libraries, which results in a discrepancy in the criticality conditions.

4.2 EffectofPuF4 concentration on conversion capability

Fig. 5 Radiative neutron capture cross sections of a 233U, b 232Th, c 239Pu, d 241Pu, and e 241Am

Fig. 6 (Color online) Fission cross sections of a 233U, b 232Th, c 239Pu, d 241Pu, and e 241Am

Fig. 7 (Color online) The conversion ratio of 0.80 mol% WGPu fuel with JENDL 3.3, JENDL 4.0, ENDF/B-VII.0, and JEFF 3.1

The conversion capability of the reactor is described by the CR value. It is defined as the ratio of the generated fissile to the consumed fissile in the reactor core, and it also represents the reactor performance in terms of sustainable fuel supply. When CR > 1.0, the reactor has a breeding capability.The conversion process of fertile materials can generate fissile materials through neutron capture. Figure 7 shows the conversion capability of the reactor for different nuclear data libraries. The results indicate that the CR trends of JENDL 3.3, JENDL 4.0, ENDF/B-VII.0, and JEFF 3.1 are similar in that the value increases with an increase in the reactor operation time. This shows that the amount of converted fertile material increases during the operation time, as well as fissile material production. The increasing CR is estimated from the contribution of the transmutation of2132Th and plutonium isotopes with even mass numbers, such as238Pu,240Pu, and242Pu, in the fuel salt. For instance,233U can be produced through the neutron capture process of232Th, and239Pu can be generated from a nuclear reaction similar to that of238Pu. Based on the data, the CR of 0.80 mol% PuF4for all libraries used is different, with that for JEFF 3.1 being 1.94%, 2.04%, and 3.46% higher than that for ENDF/BVII.0, JENDL 4.0, and JENDL 3.3, respectively.

The difference in the CR values in the four nuclide data libraries can be caused by differences in the number of nuclides and cross-section values in each library. For instance,232Th is the main fertile material in the reactors.The neutron capture cross section of232Th in the JEFF 3.1 library is highest compared to that in the ENDF/BVII.0 and JENDL libraries. Hence, it can cause the CR value in JEFF 3.1 to be higher than that in other libraries.Meanwhile, in both JENDL libraries, the neutron capture cross section of232Th at JENDL 3.3 is higher than that of JENDL 4.0. However, the CR value of the JENDL 3.3 library was lower than that of the JENDL 4.0, library. This could be due to the neutron capture cross-section factor of other nuclides, as shown in Fig. 5e, which shows that the neutron capture cross section of241Am of JENDL 4.0 is higher than that of JENDL 3.3.

Moreover, regarding the radiative neutron capture cross section of nuclear data libraries, some heavy nuclides should be discussed, for example233Pa, which is produced from a capture reaction between232Th and neutrons. The capture cross section of233Pa in the JENDL 4.0 library was higher than that in JEFF 3.1,ENDF/B-VII.0, and JENDL 3.3, especially in the thermal energy range. Additionally, the capture cross section of241Am in the JENDL 4.0 library was the highest, as shown in Fig. 5e.233Pa and241Am are heavy nuclides in the reactor that can absorb neutrons and reduce the neutron population. In addition, the capture cross-section difference of plutonium isotopes with even mass numbers was not significant between the three nuclear data libraries, and only240Pu had a high value in JEFF 3.1.Moreover, the differences were not substantially affected by the CR because of the low concentration of240Pu in the molten salt.

The influence of the PuF4concentration on the conversion capability is shown in Fig. 8 for (a) JENDL 3.3, (b)JENDL 4.0, (c) ENDF/B-VII.0, and (d) JEFF 3.1. These data indicate that the CR trend is almost the same for all nuclear data libraries, which decreases as the PuF4concentration increases. Increasing the PuF4concentration in the fuel salt affects the ThF4concentration, which balances the fuel salt composition. The ThF4concentration diminishes with increasing PuF4concentration (see Tables 4, 5, 6, and 7 for JENDL 3.3, JENDL 4.0, ENDF/B-VII.0, and JEFF 3.1, respectively. As the primary fertile material in fuel,thorium plays an important role in adjusting the breeding capability of the reactor. This is due to the high absorption cross section of232Th in the thermal energy range.Therefore, a higher Th concentration in the reactor core augments the CR.

Furthermore, increasing PuF4in the fuel salt also increases the concentration of some even mass number plutonium isotopes. In this case, the percentage isotopic composition of plutonium isotopes with even mass numbers was smaller than that of plutonium isotopes with odd mass numbers. Therefore, the conversion capability was not significantly affected by the conversion of plutonium isotopes,even with mass numbers. However, the conversion capability is mainly contributed to by Th conversion in the fuel salt.For instance, as shown in Fig. 9, the atomic density change of232Th with JEFF 3.1 is the highest, followed by that with JENDL 4.0, ENDF/B-VII.0, and JENDL 3.3.

Figure 10 shows the change in the238Pu atomic density for different nuclear data libraries, which increased during the operating period. The changes in the JENDL 4.0 library were more significant than those in JEFF 3.1, JENDL 3.3,and ENDF/B-VII.0. This indicates that neutron capture by238Pu at JENDL 4.0 is lower than that at JEFF 3.1, JENDL 3.3, and ENDF/B-VII.0. Therefore, the number of238Pu in JENDL 4.0 at the end of reactor operation is higher than that in the other three libraries.

Fig. 8 (Color online) The conversion ratio with various concentrations of WGPu fuel for a JENDL 3.3, b JENDL 4.0, c ENDF/B-VII.0, and d JEFF 3.1

Figure 11 shows that the atomic density of239Pu decreases during operation time for all libraries used. The difference in the atomic density of239Pu is not significantly different in all libraries used. However, the reduction in the atomic density of239Pu in JENDL 3.3 is more significant than that of ENDF/B-VII.0, JEFF 3.1, and JENDL 4.0 (Table 13). It indicates that the fission rate of239Pu is higher in JENDL 3.3 compared to in the other three libraries. It may affect the higherkeffvalue in the JENDL 3.3 library, as shown in Fig. 3.

Figure 12 shows the change in the atomic density of241Am during reactor operation for different nuclear data libraries. The change in the JEFF 3.1 library is lower than that in the ENDF/B-VII and JENDL libraries. This means that the conversion process of241Am, either through fission reactions or transmutation in JEFF 3.1, occurs more frequently than in the other three libraries. Therefore, it may cause the conversion capability in JEFF 3.1 to become higher than that of the other libraries. This difference could also be due to the different conversion rates of241Pu, which then produces241Am in the reactor.

Fig. 9 (Color online) The change of 232Th atomic density for different nuclear data libraries

Fig. 10 (Color online) The change in 238Pu atomic density for different nuclear data libraries

4.3 Effect of the nuclear data library on the neutron spectrum

The neutron spectrum, which describes the neutron flux distribution in the reactor core based on the energy range, is another significant parameter in nuclear reactor studies. In this analysis, the neutron spectrum was explained by the relative flux per unit lethargy, which is the neutron flux multiplied by the neutron energy. For example, the spectrum of 0.80 mol% of the PuF4concentration with different nuclear data libraries as a function of energy at the beginning of a cycle of the reactor is depicted in Fig. 13, which shows for each region: (a) Core 1, (b) Core 2, and (c) Core 3. The neutron spectrum from each region exhibited a similar trend for all three nuclear data libraries. However, the neutron spectra in the thermal energy range were lower than those in the fast energy range for all the core regions. In other words, the obtained neutron spectra were difficult to obtain in all regions of the reactor core. This is due to the high eta value of the loaded plutonium in the fast energy range, which is defined as the ratio of the total generated neutrons to the total absorbed neutrons in the reactor core.

Fig. 11 (Color online) The change in 239Pu atomic density for different nuclear data libraries

In the thermal energy range, the neutron spectrum for JENDL 3.3 is the highest, followed by that for ENDF/BVII.0, JEFF 3.1, and JENDL 4.0. This is because of the higher capture cross section of232Th and238Pu in JENDL 3.3 than in JENDL 4.0 [19]. For comparison, the neutron spectrum in the thermal energy range for Core 2 is shown in Fig. 14. This shows that the neutron spectra in ENDF/B-VII.0 and JEFF 3.1 are more thermalized than those in JENDL 4.0. Therefore, there is an overestimated value for ENDF/B-VII.0 and JEFF 3.1. Because239Pu is used as the main fissile in this reactor and is also a superior fissile in the fast energy range, the obtainedkeffvalues in ENDF/B-VII.0 and JEFF 3.1 are lower than those in JENDL 4.0, as shown in Fig. 3.

Moreover, the thermal peak in the Core 2 region was the highest, followed by that in the Core 1 or 3 region. For instance, Fig. 15 compares the neutron spectra of all regions for JENDL 4.0. This result is due to the large moderator fraction utilized in the Core 2 region, which impacts the moderating process of fast neutrons into thermal neutrons.Consequently, the number of moderators utilized in the active core is proportional to the peak of the neutron spectrum in the thermal energy range. Furthermore, the impact of the peaks of the radiative neutron capture cross section and fission cross section of233U,239Pu, and241Pu at 1 eV energy is predicted to induce the peak neutron spectrum in the thermal energy range.As shown in Fig. 16, increasing the PuF4concentration also affected the neutron spectrum, especially in the thermal energy range. In addition, the obtained neutron spectrum becomes harder with increasing PuF4concentration, owing to the higher total plutonium utilized in the fuel salt.

Table 13 Atomic density of 239Pu (atom/barn cm) during operation time

Fig. 12 (Color online) The change in the 241Am atomic density for different nuclear data libraries

4.4 Safety parameter analysis (MTC, DRC, and CRW)

Regarding the safety aspect, several safety parameters, such as MTC, DRC, and CRW, were analyzed to determine the minimal PuF4concentration required in the reactor. Figure 17 shows the change in reactor reactivity as a function of moderator temperature for the four different nuclear libraries. The moderator temperature was varied from 800 to 1200 K. The reactivity value decreased with increasing moderator temperature for all nuclear libraries. The MTC value was examined based on the ratio of the reactor reactivity change to the moderator temperature change. In this case, the MTC values for all nuclear libraries were negative,as shown in Table 12.

Figure 18 depicts the reactor reactivity as a function of temperature for the four nuclear libraries, in which the reactivity values decreased with increasing temperature. The temperature was varied from 800 to 1200 K. The DRC value could be evaluated based on the ratio of the reactor reactivity change to temperature change. As shown in Table 12,the DRC values of the reactors were negative for all the nuclear libraries. This shows that the reactor with the minimal PuF4concentration required had inherent safety criteria.In accordance with the present results, previous studies have demonstrated that the temperature coefficient must be negative [35, 36].

In addition, the CRW value was analyzed, which is defined as the subtraction of the reactor reactivity without a control rod and the reactivity with control rod insertion.In this study, several control rod distribution models were varied. In Model 1, the reactor was calculated without a control rod, whereas in Model 2, the reactor was equipped with control rod 1. Model 3 was designed with control rods 1 and 2, whereas Model 4 was arranged using control rods 1, 2, and 3, as shown in Fig. 19. The control rod was B4C(90% boron-enriched) [37]. In this study, the CRW value was calculated for the minimal PuF4concentration required for the JENDL 4.0 library. As presented in Table 13, the initialkeffand reactivity of Model 1 were the highest, followed by those of Model 2, 3, and 4, because of the lowest neutron absorption in Model 1. The CRW value of Model 4 was the highest, followed by that of Model 3 and 2, owing to the significant number of control rods utilized in the reactor. As a common feature, the reactivity of the reactor decreased with an increase in the control rod amount in the reactor(Tables 14 and 15).

5 Conclusion

Fig. 13 (Color online) Comparison of the neutron spectrum with WGPu fuel of 0.80%mol for all regions: a Core 1, b Core 2, and c Core 3

A study evaluating the JEFF 3.1, JENDL 3.3, ENDF/BVII.0, and JENDL 4.0 nuclear data libraries for a small 100 MWe MSR with plutonium fuel was conducted. The variation in the PuF4concentration in the reactor core affected some parameters, such as criticality, conversion capability, and neutron spectra. In the criticality analysis,thekeffvalue increased with the increase in PuF4concentration, and this value diminished with operation time.The reactor can be operated in critical conditions with the minimum concentration of PuF4fuel loaded of about 0.995 mol% for JEFF 3.1, 0.91 mol% for ENDF/B-VII.0,0.90 mol% for JENDL 4.0, and 0.87 mol% for JENDL 3.3.The diverse obtained values of the evaluated parameters show trans-plutonium’s sensitivity with different nuclear data libraries. The obtained results also show that the reactor can burn at least as much plutonium fuel as the minimum concentration of PuF4required to achieve reactor criticality. The CR decreased with increasing PuF4concentration, and this parameter increased with operating time.When comparing the neutron spectra in the Core 1, 2, and 3 areas, it is clear that the fuel volume fraction impacts the neutron distribution, which becomes more difficult as the fuel volume fraction increases. The results obtained from all nuclear data libraries have different values, and JENDL 4.0 is more representative of the neutronic calculation results of the small MSR. Based on the obtained neutron spectrum in Core 2 in the thermal energy range, for JENDL 4.0, JENDL 3.3, JEFF 3.1, and ENDF/B-VII.0, there were some overestimated cross-section values in JENDL 3.3, JEFF 3.1, and ENDF/B-VII.0. In the safety analysis, the MTC and DRC values were negative for the minimum concentration PuF4required case, which demonstrated that the reactor had an inherent safety feature. The B4C control rod insertion in the reactor had an impact on the reactor reactivity and CRW value, in which the reactivity decreased and the CRW value increased.Author contributionsAll authors contributed to the study conception and design. Data collection and analysis were performed by Cici Wulandari, Abdul Waris, Sidik Permana, and Syeilendra Pramuditya. The first draft of the manuscript was written by Cici Wulandari and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

Fig. 14 (Color online) Comparison of the neutron spectrum of the Core 2 region in the thermal energy range

Fig. 15 (Color online) Comparison of the neutron spectrum in all region cores for JENDL 4.0

Fig. 16 (Color online) Comparison of the neutron spectrum for several PuF4 concentrations in the Core 2 region with JENDL 4.0

Fig. 17 (Color online) The reactivity with different moderator temperatures for JENDL 3.3, JENDL 4.0, ENDF/B-VII.0, and JEFF 3.1

Fig. 18 (Color online) The reactivity with different temperatures for JENDL 3.3, JENDL 4.0, ENDF/B-VII.0, and JEFF 3.1

Fig. 19 (Color online) Control rod distribution in the reactor

Table 14 Moderator temperature coefficient (MTC) and Doppler reactivity coefficient (DRC) values of the reactor for different nuclear libraries

Table 15 Initial keff, reactivity, and Doppler reactivity coefficient(DRC) values for different reactor models