Effect of Different Temperature and Nuclear Data Libraries in Criticality Calculations of 300 MWt Molten Salt Reactor

The Molten Salt Reactor (MSR) is a type of reactor in which coolant and fuel are blended with liquid salts. Liquid fuel enhances heat transfer and temperature control, establishing the MSR as one of the Generation IV reactor types. This study aims to analyze the impact of temperature variations on MSR reactor criticality and evaluate the effect of different nuclear data libraries, namely JENDL 3.2, JENDL 3.3, and JENDL 4.0, in neutron analysis. The observed temperature variations are 600 K, 700 K, 833 K, 903 K, and 1000 K. The analysis spans low to operational temperatures to comprehend reactor performance under differing thermal conditions. The study is conducted on a 300 MWTh MSR design, utilizing SRAC2006 with PIJ and CITATION modules for calculations. The results reveal the impact of temperature variations and nuclear data library disparities on reactor criticality. The outcomes demonstrate that higher temperatures correspond to lower values of the effective multiplication factor. At lower temperatures, neutrons experience greater moderation compared to higher temperatures. As a result, a higher number of thermal neutrons influences an increased probability of fission reactions within the reactor. Different nuclear data libraries also yield varied criticality values due to differing cross-sectional areas and quantities of data within each JENDL library. JENDL 4.0 generates the highest criticality value, attributed to elevated cross-sectional regions of each respective nuclear data entry and a greater quantity of nuclear data entries than JENDL 3.2 and JENDL 3.3.


Introduction
The development of nuclear technology has become increasingly crucial in response to global energy challenges and the need to reduce environmental impacts caused by conventional energy sources.With the growing global energy demand, the importance of renewable and environmentally friendly energy resources has become more pronounced [1][2][3].Nuclear technology offers the potential to provide sustainable, relatively clean, and highly efficient energy supplies, which can help reduce greenhouse gas emissions and dependence on fossil fuels [4][5][6].Molten Salt Reactor (MSR) represents one type of reactor that utilizes a mixture of liquid salts as fuel and coolant.This design allows for more efficient heat transfer and better temperature control than conventional nuclear reactors.MSR is considered one of the Generation IV reactor types designed to enhance efficiency and safety and reduce environmental impact and nuclear proliferation risk [7,8].There are five other types of Generation IV nuclear reactors,

Methodology
The FUJI 12 design is used as a reference for the MSR design in this research.The specifications of the MSR are presented in Table 1.The MSR design has a height and diameter of 5.4 meters and 5.2 meters, respectively.The thermal power output generated is 300 MWth.The composition of the fuel salt includes 0.22% 233 UF4, 12% ThF4, 16% BeF2, and 71.78% LiF.Fluoride is a stable salt compound that can eliminate the risk of radioactive material release from the reactor building, making it a part of this design.Flibe is used as the coolant, with BeF2 having a balanced melting temperature but high viscosity, so it is mixed with LiF to reduce viscosity [18,19].The core design consists of hexagonal graphite assemblies, each with flow channels for the salt fuel.The equivalent diameter of the hexagonal graphite is 0.20 meters, and it forms a hexagonal cylinder with a diameter of 10.95 cm for the salt fuel channels, as shown in Figure 1.Graphite is used as both a moderator and a reflector due to its ability to withstand very high temperatures.The graphite reflector and fuel channels have 0.2 meters and 0.4 cm widths, respectively.All these components are housed within a reactor vessel made of Hastelloy N, as illustrated in Figure 2. The volume fraction of the active reactor core fuel is 0.3, 0.02 for the reflector, and 0.9 for the fuel channels.
Figure 1 The Geometry of the fuel cell of MSR 300 MWth [21] The research is carried out by analyzing the impact of temperature variations on the reactor criticality in MSR.The temperatures used are 600K, 700K, 833K, 903K, and 1000K.The variation in temperature from the normal operational temperature provides insights into the reactor's performance under different thermal conditions.The density of the graphite moderator is 1.84 g/cm 3 , while the density of the liquid salt at different temperatures can be calculated using the following equation [20].
= 3.934 − 0.668 × 10 −3   (1) With   representing the fuel salt density and   representing the varied temperature, the research uses SRAC2006 with the PIJ and CITATION module.Based on the Collision Probability Method, the PIJ module is used for neutron transport calculations and fuel burning at the fuel cell level.PIJ conducts cell calculations and fuel burning, which are then homogenized and collapsed into 30 energy groups, consisting of 24 fast neutron energy groups and six thermal neutron energy groups.Next, the calculations are continuously performed using the CITATION module (multi-D Diffusion) for multidimensional diffusion calculations by incorporating the reactor core geometry with cell data obtained from the PIJ module.

Result and Discussions
The values of the effective multiplication factor for temperature variations in each use of the JENDL 3.2 nuclear data library are shown in Figure 3.The values of the effective multiplication factor at the beginning of life (BOL) and end of life (EOL) at a temperature of 600K are 1.0321 and 0.9757, respectively.Meanwhile, at a temperature of 1000K, the BOL and EOL values of the effective multiplication factor are 1.0221 and 0.967, respectively.The conversion ratio refers to the percentage of the amount of fissile fuel produced to the amount of fissile fuel used.From the calculations using different nuclear data libraries, it is found that the conversion ratio increases as the temperature used becomes higher.It is because of the high absorption cross-section at low temperatures, as shown in Figure 9.A lower absorption cross-section is obtained for higher temperatures in the thermal energy range.A high absorption cross-section decreases the number of neutrons available to initiate reactions, resulting in a smaller conversion ratio value.The macroscopic fission cross-section values shown in Figure 12 are consistent with the obtained values of the effective multiplication factor, where the fission cross-section for JENDL 4.0 is larger than that of JENDL 3.2 and JENDL 3.3.Additionally, JENDL 4.0 contains more comprehensive nuclear data, with 406 nuclides.Hence, the use of JENDL 4.0 indicates more stable results.Meanwhile, the JENDL 3.2 nuclear data library contains 340 nuclide data, and JENDL 3.3 contains 337 nuclide data.The conversion ratio values for different nuclear data library usage are shown in Figure 13.The JENDL 3.3 nuclear data library obtains a higher conversion ratio value than JENDL 3.2 and JENDL 4.0.The obtained conversion ratio values are inversely related to the effective multiplication factor, indicating that more fissile material is produced in JENDL 3.3 than the fissile material used in fission reactions.Consequently, the effective multiplication factor values for using JENDL 3.3 are smaller than those for JENDL 3.2 and JENDL 4.0.

Conclusions
This research demonstrates that increasing temperature in a specific design of the Molten Salt Reactor will decrease reactor criticality, making the reactor less efficient in sustaining a continuous nuclear chain reaction.Consequently, higher conversion ratio values are obtained at higher temperatures.At lower temperatures, neutrons undergo more moderation, producing more thermal neutrons and an increased probability of fission reactions.The macroscopic fission and absorption cross-sections are high at lower temperatures.The study also compares the usage of the JENDL 3.2, JENDL 3.3, and JENDL 4.0 nuclear data libraries.Using JENDL 4.0 yields better criticality compared to JENDL 3.2 and JENDL 3.3.In addition to having higher macroscopic fission cross-section values, JENDL 4.0 also contains more comprehensive nuclear data compared to JENDL 3.2 and JENDL 3.3.

Figure 9
Figure 9 Cross-Section Absorption with JENDL 4.0 The obtained conversion ratio values are inversely proportional to the criticality indicated by the effective multiplication factor, with high values obtained at low temperatures.The increase in the

Figure 10 Figure 11
Figure 10 Macroscopic Cross Section Fission with JENDL 4.0