Study on dynamic characteristics of fission products in 2 MW molten salt reactor

Study on dynamic characteristics of fission products in 2 MW molten salt reactor 1 2 first-author https://orcid.org/0000-0002-4671-5816 1 1 https://orcid.org/0000-0002-7825-2457 1 2 https://orcid.org/0000-0003-2572-2133 1 1 https://orcid.org/0000-0001-6034-5308 Xu-Zhong Kang 1 Gui-Feng Zhu (https://orcid.org/0000-0003-4661-8159) 1 1 corresp Corresponding author, yanrui@sinap.ac.cn Corresponding author, yanrui@sinap.ac.cn yanrui@sinap.ac.cn https://orcid.org/0000-0002-5747-2194 Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201800, China. Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201800, China. University of Chinese Academy of Sciences, Beijing 100049, China. University of Chinese Academy of Sciences, Beijing 100049, China. In this study, a numerical flow model of the fission products (FPs) in the primary loop system of a molten salt reactor (MSR) was established and solved using Mathematica 7.0. The simulation results were compared with those of the ORIGEN-S program in the static burnup mode, and the deviation was found to be less than 10%, which indicates that the results are in good agreement. Furthermore, the FPs distribution in the primary loop system under normal operating conditions of the 2 MW MSR was quantitatively analyzed. In addition, the distribution phenomenon of the FPs under different flow rate conditions was studied. At the end of life, the FPs activity in the core region (including active region, and upper and lower plenum region) accounted for 77.3%, and that in the hot leg #1, main pump, hot leg #2, heat exchanger, and cold leg region accounted for 1.2%, 16.15%, 0.99%, 2.5%, and 1.9%, respectively, of the total FPs in the primary loop under normal operating conditions. The proportion of FPs in the core decreased with the increase in flow rate in the range of 2.24–22400 cm 3 s -1 . The established analytical method and conclusions of this study can provide an important basis for radiation safety design of the primary loop, radioactive source management design, thermal hydraulic safety analysis, and radiochemical analysis of FPs of 2 MW MSRs. Molten salt reactor Fission products Radioactive source term Primary loop system Flow model 1 Introduction 1 The United States demonstrated the feasibility of molten salt reactors (MSRs) with the Aircraft Reactor Experiment (1954) [ 1 1 , 2 2 ] and Molten Salt Reactor Experiment (1965–1969) [ 3 3 , 4 4 ] . Molten salt breeder reactor [ 5 5 , 6 6 ] and denatured molten salt reactor [ 7 7 ] were designed by Oak Ridge National Laboratory (ORNL) for the purpose of breeding after the successful operation of the MSRs. During 2001–2003, the concept of fluoride cooled high temperature reactor was jointly developed by ORNL, Sandia National Laboratories, and University of California, Berkeley [ 8 8 - 10 10 8-10 ] . In recent years, extensive analysis and research have been conducted on the safety characteristics and physical theory of MSRs [ 11 11 - 13 13 11-13 ] . In 2011, the thorium-based molten salt reactor nuclear energy system (TMSR) project was set up by the Chinese Academy of Sciences. An MSR (TMSR-LF1) with 2 MW thermal power has been planned to be constructed by 2020 [ 14 14 - 16 16 14-16 ] . In recent years, extensive research has been conducted on the physical characteristics and molten salt characteristics of MSRs by the TMSR team in China [ 17 17 - 22 22 17-22 ] . Numerous types of fission products (FPs) are produced during 235 U fission; moreover, the composition of FPs is extremely complex. These nuclides comprise various types, namely, stable, long life, and very short life nuclides. After the start-up of an MSR, the FPs flow out of the reactor core into the pipes and equipment of the primary loop system. It is a very complicated evolution process, in which hundreds of FPs flow and decay simultaneously in the primary loop system. In the primary loop system of MSRs, FPs act not only as a flowing heat source but also as a flowing radiation source, which is an important source in both thermal-hydraulic and radiation shielding designs. Static point-burnup code has generally been used to simulate the evolution of FPs of conventional pressurized water reactors (PWR) for more than 40 years now, since the first ORIGEN version was released in 1973 [ 23 23 ] . Typical point-burnup codes include ORIGEN, ORIGEN2, and ORIGEN-S [ 24 24 , 25 25 ] . The nuclear fuel of PWR is fixed in the assembly structure, i.e., after the fuel assembly is loaded into the core, the position of the fuel assembly remains fixed throughout the entire life of a cycle. Static point-burnup code is widely suitable for all fixed-fuel type reactors. However, MSRs have no fixed fuel assembly structure and use molten fluoride (chloride is sometimes used as a carrier salt in fast spectrum MSRs) as the nuclear fuel. Molten fuel is used both as a fuel and coolant, and the flowing effect of the fuel salt causes the FPs flowing out of the core to escape the absorption of neutrons in the core, thereby breaking the evolution equilibrium of FPs nuclides and their daughters in the primary loop system. This has an important impact on the concentration and total inventory of FPs. Therefore, the static point-burnup code is no longer suitable for FPs analysis in MSRs. Based on the above discussion, a dynamic model of FPs transport and evolution in the primary loop system of an MSR (MSRFP 1.0) was established based on Mathematica 7.0. In this work, the static simulation results were preliminarily compared and verified with the results of the reference program ORIGEN-S, and the dynamic characteristics of FPs of the MSR were analyzed as well. Computations indicate that the fuel salt flowing effect is not negligible for FPs inventory and distribution analysis in the MSR. 2 Model and Method 1 In this study, a 2 MW MSR (TMSR-LF1) designed by the TMSR team is studied. The calculation model and design parameters of the TMSR-LF1 are shown in Fig. 1 Fig. 1 and Table 1 Table 1 (scheme design stage). The core diameter and height of the MSR are 190 cm and 180 cm, respectively. ASME-N10003 nickel-based alloy material is used to make the reactor vessel and all the metal structures in the primary loop of TMSR-LF1. The fluid fuel salt enters the reactor vessel through the lower plenum and flows into the active region. After reaching the upper plenum, the fuel flows upward through an assembled lattice of vertical graphite stringers, thereby forming the core. There are six control rod channels (shutdown and power regulation), one neutron source channel, and four measurement channels in the active region. The structure and functions of the graphite assembly are shown in Fig. 2 Fig. 2 . In this work, KENO-VI [ 26 26 ] (based on 238 group cross-section library) in the SCALE6.1 package was used to calculate the neutron energy spectrum. The primary advantage of the 3-D Monte Carlo neutron transport program is that it can accurately model the geometry, and consider the axial and radial flux distribution of the core. Further, 238 groups of neutron energy spectrum in each material region were obtained through the entire core neutron transport. Finally, region-averaged and flux-weighted one group cross sections were generated using the module KMART, which was used to solve the burnup equation. 1 1 Parameters 1 1 Values 1 1 Thermal power (MW) 1 1 2 1 1 Life (a) 1 1 20 1 1 Full power operation days (d) 1 1 300 1 1 Reactor inlet, outlet temperature (℃) 1 1 600, 650 1 1 Fuel type 1 1 LiF-BeF 2 -UF 4 1 1 Uranium fuel enrichment (wt%) 1 1 19.75 1 1 Secondary coolant 1 1 FNaBe 1 1 Flow rate of primary loop (VF) (cm 3 s -1 ) 1 1 2.24×10 4 1 1 Fuel assembly material 1 1 Graphite 1 1 Main vessel and internals materials 1 1 ASME-N10003 The primary loop components were constructed using ASME-N10003, which forms the boundary of the fuel salt. The purpose of LF1 was to demonstrate the safety, reliability, and maintainability of the 2 MW MSR. Because of its small size, it was not intended to be a breeder, and no fuel (UF 4 and ThF 4 ) was added or processed during the operation. The calculated inventory, as mentioned below, represents the sum of all fission products in the fuel salt of the entire primary loop discharged after 300 effective full power days. A layout of the TMSR-LF1 core and primary loop system is shown in Fig. 3 Fig. 3 . First, the fuel salt flows out from the upper plenum to the hot leg section, to the main pump, then into the heat exchanger, and finally returns to the core through the cold leg section. The core includes the active region, and upper and lower plenum. The heat present in the primary loop is first exchanged with the secondary loop through the main salt-salt heat exchanger, and then with the air environment through the salt-air heat exchanger. In the established mathematical model, the primary loop system was divided into eight solvable regions (computational meshes): active region, upper plenum, hot leg section (#1, #2), main pump, heat exchanger, cold leg section, and lower plenum. Because the main pump is located at the middle of the hot leg section, the hot leg section is divided into two parts in the mathematical model, hot leg section #1 and #2. The fuel salt volume parameters in each region of the primary loop are listed in Table 2 Table 2 . 1 1 Different region 1 1 Fuel salt volume (cm 3 ) 1 1 Active region 1 1 5.90 × 10 5 1 1 Upper plenum 1 1 3.82 × 10 5 1 1 Hot leg #1 1 1 1.55 × 10 4 1 1 Main pump 1 1 2.50 × 10 5 1 1 Hot leg #2 1 1 1.55 × 10 4 1 1 Main heat exchanger 1 1 4.00 × 10 4 1 1 Cold leg 1 1 3.10 × 10 4 1 1 Lower plenum 1 1 6.70 × 10 5 1 1 Total 1 1 1.99 × 10 6 The following assumptions were made for the mathematical model: (1) The model is a 1-D flow problem, and the radial flow in the pipeline is not considered; (2) The volume of the molten salt fluid is incompressible and the density is constant; (3) The FPs are not deposited on the surfaces of metal and graphite components in the primary loop system; (4) Conservative assumptions: the on-line removal of FPs gases was not considered; (5) Conservative assumptions: the leakage of FPs from the primary loop system was not considered The established mathematical model is as follows: <math display="block" id="M1"><mtable columnalign="left"><mtr><mtd><mfrac><mrow><mtext>d</mtext><msub><mi>N</mi><mrow><mi>i</mi><mo>,</mo><mi>j</mi></mrow></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow><mrow><mtext>d</mtext><mi>t</mi></mrow></mfrac><mo>=</mo><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><mrow><msub><mi>γ</mi><mrow><mi>k</mi><mo>,</mo><mi>i</mi></mrow></msub></mrow></mstyle><msub><mi>σ</mi><mrow><mi>k</mi><mo>,</mo><mi>f</mi><mo>,</mo><mi>j</mi></mrow></msub><msub><mi>N</mi><mrow><mi>k</mi><mo>,</mo><mi>j</mi></mrow></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><msub><mi>Φ</mi><mi>j</mi></msub><mo>+</mo><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><mrow><msub><mi>σ</mi><mrow><mi>k</mi><mo>→</mo><mi>i</mi><mo>,</mo><mi>j</mi></mrow></msub></mrow></mstyle><msub><mi>N</mi><mrow><mi>k</mi><mo>,</mo><mi>j</mi></mrow></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><msub><mi>Φ</mi><mi>j</mi></msub><mo>+</mo><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><mrow><msub><mi>b</mi><mrow><mi>k</mi><mo>→</mo><mi>i</mi></mrow></msub></mrow></mstyle><msubsup><mi>λ</mi><mi>k</mi><mrow><mtext>dec</mtext></mrow></msubsup><msub><mi>N</mi><mrow><mi>k</mi><mo>,</mo><mi>j</mi></mrow></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mo>−</mo><msub><mi>σ</mi><mrow><mi>i</mi><mo>,</mo><mi>f</mi><mo>,</mo><mi>j</mi></mrow></msub><msub><mi>N</mi><mrow><mi>i</mi><mo>,</mo><mi>j</mi></mrow></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><msub><mi>Φ</mi><mi>j</mi></msub><mo>−</mo><mo stretchy="false">(</mo><msub><mi>σ</mi><mrow><mi>i</mi><mo>,</mo><mi>j</mi></mrow></msub><mo>−</mo><msub><mi>σ</mi><mrow><mi>i</mi><mo>,</mo><mi>f</mi><mo>,</mo><mi>j</mi></mrow></msub><mo stretchy="false">)</mo><msub><mi>N</mi><mrow><mi>i</mi><mo>,</mo><mi>j</mi></mrow></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><msub><mi>Φ</mi><mi>j</mi></msub><mo>−</mo><msubsup><mi>λ</mi><mi>i</mi><mrow><mtext>dec</mtext></mrow></msubsup><msub><mi>N</mi><mrow><mi>i</mi><mo>,</mo><mi>j</mi></mrow></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mo>+</mo><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>m</mi><mo>=</mo><mn>1</mn></mrow><mi>a</mi></munderover><mrow><msubsup><mi>λ</mi><mrow><mi>i</mi><mo>,</mo><mi>m</mi><mo>→</mo><mi>j</mi></mrow><mrow><mtext>flowin</mtext></mrow></msubsup><msub><mi>N</mi><mrow><mi>i</mi><mo>,</mo><mi>m</mi></mrow></msub></mrow></mstyle><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>−</mo><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>m</mi><mo>=</mo><mn>1</mn></mrow><mi>a</mi></munderover><mrow><msubsup><mi>λ</mi><mrow><mi>i</mi><mo>,</mo><mi>j</mi><mo>→</mo><mi>m</mi></mrow><mrow><mtext>flowout</mtext></mrow></msubsup><msub><mi>N</mi><mrow><mi>i</mi><mo>,</mo><mi>j</mi></mrow></msub></mrow></mstyle><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math> where n =1, ……, i , ……, represent the type of nuclide to be solved; a =1, ……, j , ……, represent the number of regions divided for the primary loop system; N i , j ( t ) represents the atomic density of the nuclides i in region j ; γ i , i represents the fission yields of nuclide k to nuclide i ; σ k , f , j represents the fission reaction cross section of nuclides k in region j ; σ i , j represents the microscopic cross section of nuclear reactions, excluding the fission reactions of nuclides i in region j ; Φ j represents the neutron flux density in region j ; σ k → i , j represents the microscopic cross section of nuclide i produced by the nuclear reaction of nuclide k in region j ; b k → i represents the decay branching ratio of nuclide k to nuclide i ; <math id="M2"><mrow><msubsup><mi>λ</mi><mi>i</mi><mrow><mi>d</mi><mi>e</mi><mi>c</mi></mrow></msubsup></mrow></math> represents the decay constant of nuclide i . Further, the first item on the right of Eq. (1) represents the fission production rate of nuclide i from nuclide k in region j . The specific expression is given by Eq. (2). The fission yield matrix γ k , i is an n-dimensional matrix, which is a sparse matrix with most of its elements being 0. For non-fissile nuclides, the corresponding matrix element is 0, and the FPs in this study mainly originate from 235 U. <math display="block" id="M3"><mrow><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><mrow><msub><mi>γ</mi><mrow><mi>k</mi><mo>,</mo><mi>i</mi></mrow></msub></mrow></mstyle><msub><mi>σ</mi><mrow><mi>k</mi><mo>,</mo><mi>f</mi><mo>,</mo><mi>j</mi></mrow></msub><msub><mi>N</mi><mrow><mi>k</mi><mo>,</mo><mi>j</mi></mrow></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><msub><mi>Φ</mi><mi>j</mi></msub><mtext>=</mtext><msup><mrow><mrow><mo>{</mo><mrow><mtable><mtr><mtd><mrow><msub><mi>γ</mi><mrow><mn>1</mn><mo>→</mo><mn>1</mn></mrow></msub></mrow></mtd><mtd><mrow><msub><mi>γ</mi><mrow><mn>1</mn><mo>→</mo><mn>2</mn></mrow></msub></mrow></mtd><mtd><mo>⋯</mo></mtd><mtd><mrow><msub><mi>γ</mi><mrow><mn>1</mn><mo>→</mo><mi>n</mi></mrow></msub></mrow></mtd></mtr><mtr><mtd><mrow><msub><mi>γ</mi><mrow><mn>2</mn><mo>→</mo><mn>1</mn></mrow></msub></mrow></mtd><mtd><mrow><msub><mi>γ</mi><mrow><mn>2</mn><mo>→</mo><mn>2</mn></mrow></msub></mrow></mtd><mtd><mo>⋯</mo></mtd><mtd><mrow><msub><mi>γ</mi><mrow><mn>2</mn><mo>→</mo><mi>n</mi></mrow></msub></mrow></mtd></mtr><mtr><mtd><mo>⋯</mo></mtd><mtd><mo>⋯</mo></mtd><mtd><mo>⋯</mo></mtd><mtd><mo>⋯</mo></mtd></mtr><mtr><mtd><mrow><msub><mi>γ</mi><mrow><mi>n</mi><mo>→</mo><mn>1</mn></mrow></msub></mrow></mtd><mtd><mrow><msub><mi>γ</mi><mrow><mi>n</mi><mo>→</mo><mn>2</mn></mrow></msub></mrow></mtd><mtd><mo>⋯</mo></mtd><mtd><mrow><msub><mi>γ</mi><mrow><mi>n</mi><mo>→</mo><mi>n</mi></mrow></msub></mrow></mtd></mtr></mtable></mrow><mo>}</mo></mrow></mrow><mi>Τ</mi></msup><mo>×</mo><mrow><mo>{</mo><mrow><mtable><mtr><mtd><mrow><msub><mi>σ</mi><mrow><mn>1</mn><mo>,</mo><mi>f</mi><mo>,</mo><mi>j</mi></mrow></msub></mrow></mtd><mtd><mrow/></mtd><mtd><mrow/></mtd><mtd><mrow/></mtd></mtr><mtr><mtd><mrow/></mtd><mtd><mrow><msub><mi>σ</mi><mrow><mn>2</mn><mo>,</mo><mi>f</mi><mo>,</mo><mi>j</mi></mrow></msub></mrow></mtd><mtd><mrow/></mtd><mtd><mrow/></mtd></mtr><mtr><mtd><mrow/></mtd><mtd><mrow/></mtd><mtd><mo>⋱</mo></mtd><mtd><mrow/></mtd></mtr><mtr><mtd><mrow/></mtd><mtd><mrow/></mtd><mtd><mrow/></mtd><mtd><mrow><msub><mi>σ</mi><mrow><mi>n</mi><mo>,</mo><mi>f</mi><mo>,</mo><mi>j</mi></mrow></msub></mrow></mtd></mtr></mtable></mrow><mo>}</mo></mrow><mo>×</mo><mrow><mo>{</mo><mrow><mtable><mtr><mtd><mrow><msub><mi>N</mi><mrow><mn>1</mn><mo>,</mo><mi>j</mi></mrow></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow></mtd></mtr><mtr><mtd><mrow><msub><mi>N</mi><mrow><mn>2</mn><mo>,</mo><mi>j</mi></mrow></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow></mtd></mtr><mtr><mtd><mo>⋮</mo></mtd></mtr><mtr><mtd><mrow><msub><mi>N</mi><mrow><mi>n</mi><mo>,</mo><mi>j</mi></mrow></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow></mtd></mtr></mtable></mrow><mo>}</mo></mrow><mo>×</mo><msub><mi>Φ</mi><mi>j</mi></msub></mrow></math> <math id="M4"><mrow><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><mrow><msub><mi>σ</mi><mrow><mi>k</mi><mo>→</mo><mi>i</mi><mo>,</mo><mi>j</mi></mrow></msub></mrow></mstyle><msub><mi>N</mi><mrow><mi>k</mi><mo>,</mo><mi>j</mi></mrow></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><msub><mi>Φ</mi><mi>j</mi></msub></mrow></math> represents the production rate of nuclide i , which originates from the reaction of nuclide k with the neutrons in region j , as shown in Eq. (3). <math display="block" id="M5"><mrow><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><mrow><msub><mi>σ</mi><mrow><mi>k</mi><mo>→</mo><mi>i</mi><mo>,</mo><mi>j</mi></mrow></msub></mrow></mstyle><msub><mi>N</mi><mrow><mi>k</mi><mo>,</mo><mi>j</mi></mrow></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><msub><mi>Φ</mi><mi>j</mi></msub><mtext>=</mtext><msup><mrow><mrow><mo>{</mo><mrow><mtable><mtr><mtd><mrow><msub><mi>σ</mi><mrow><mn>1</mn><mo>→</mo><mn>1</mn><mo>,</mo><mi>j</mi></mrow></msub></mrow></mtd><mtd><mrow><msub><mi>σ</mi><mrow><mn>1</mn><mo>→</mo><mn>2</mn><mo>,</mo><mi>j</mi></mrow></msub></mrow></mtd><mtd><mo>⋯</mo></mtd><mtd><mrow><msub><mi>σ</mi><mrow><mn>1</mn><mo>→</mo><mi>n</mi><mo>,</mo><mi>j</mi></mrow></msub></mrow></mtd></mtr><mtr><mtd><mrow><msub><mi>σ</mi><mrow><mn>2</mn><mo>→</mo><mn>1</mn><mo>,</mo><mi>j</mi></mrow></msub></mrow></mtd><mtd><mrow><msub><mi>σ</mi><mrow><mn>2</mn><mo>→</mo><mn>2</mn><mo>,</mo><mi>j</mi></mrow></msub></mrow></mtd><mtd><mo>⋯</mo></mtd><mtd><mrow><msub><mi>σ</mi><mrow><mn>2</mn><mo>→</mo><mi>n</mi><mo>,</mo><mi>j</mi></mrow></msub></mrow></mtd></mtr><mtr><mtd><mo>⋯</mo></mtd><mtd><mo>⋯</mo></mtd><mtd><mo>⋯</mo></mtd><mtd><mo>⋯</mo></mtd></mtr><mtr><mtd><mrow><msub><mi>σ</mi><mrow><mi>n</mi><mo>→</mo><mn>1</mn><mo>,</mo><mi>j</mi></mrow></msub></mrow></mtd><mtd><mrow><msub><mi>σ</mi><mrow><mi>n</mi><mo>→</mo><mn>2</mn><mo>,</mo><mi>j</mi></mrow></msub></mrow></mtd><mtd><mo>⋯</mo></mtd><mtd><mrow><msub><mi>σ</mi><mrow><mi>n</mi><mo>→</mo><mi>n</mi><mo>,</mo><mi>j</mi></mrow></msub></mrow></mtd></mtr></mtable></mrow><mo>}</mo></mrow></mrow><mi>Τ</mi></msup><mo>×</mo><mrow><mo>{</mo><mrow><mtable><mtr><mtd><mrow><msub><mi>N</mi><mrow><mn>1</mn><mo>,</mo><mi>j</mi></mrow></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow></mtd></mtr><mtr><mtd><mrow><msub><mi>N</mi><mrow><mn>2</mn><mo>,</mo><mi>j</mi></mrow></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow></mtd></mtr><mtr><mtd><mo>⋮</mo></mtd></mtr><mtr><mtd><mrow><msub><mi>N</mi><mrow><mi>n</mi><mo>,</mo><mi>j</mi></mrow></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow></mtd></mtr></mtable></mrow><mo>}</mo></mrow><mo>×</mo><msub><mi>Φ</mi><mi>j</mi></msub></mrow></math> <math id="M6"><mrow><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><mrow><msub><mi>b</mi><mrow><mi>k</mi><mo>→</mo><mi>i</mi></mrow></msub></mrow></mstyle><msubsup><mi>λ</mi><mi>k</mi><mrow><mtext>dec</mtext></mrow></msubsup><msub><mi>N</mi><mrow><mi>k</mi><mo>,</mo><mi>j</mi></mrow></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow></math> represents the production rate of nuclide i , which arises from the decay of nuclide k in region j , as represented by Eq. (4). In Eq. (4), <math id="M7"><mrow><msub><mi>b</mi><mrow><mi>k</mi><mo>→</mo><mi>i</mi></mrow></msub></mrow></math> represents the decay branch ratio, which is an n-dimensional sparse matrix, and <math id="M8"><mrow><msubsup><mi>λ</mi><mi>k</mi><mrow><mtext>dec</mtext></mrow></msubsup></mrow></math> represents the decay constant of nuclide k , which is an n-dimensional diagonal matrix. <math display="block" id="M9"><mrow><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><mrow><msub><mi>b</mi><mrow><mi>k</mi><mo>→</mo><mi>i</mi></mrow></msub></mrow></mstyle><msubsup><mi>λ</mi><mi>k</mi><mrow><mtext>dec</mtext></mrow></msubsup><msub><mi>N</mi><mrow><mi>k</mi><mo>,</mo><mi>j</mi></mrow></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mtext>=</mtext><msup><mrow><mrow><mo>{</mo><mrow><mtable><mtr><mtd><mrow><msub><mi>b</mi><mrow><mn>1</mn><mo>→</mo><mn>1</mn></mrow></msub></mrow></mtd><mtd><mrow><msub><mi>b</mi><mrow><mn>1</mn><mo>→</mo><mn>2</mn></mrow></msub></mrow></mtd><mtd><mo>⋯</mo></mtd><mtd><mrow><msub><mi>b</mi><mrow><mn>1</mn><mo>→</mo><mi>n</mi></mrow></msub></mrow></mtd></mtr><mtr><mtd><mrow><msub><mi>b</mi><mrow><mn>2</mn><mo>→</mo><mn>1</mn></mrow></msub></mrow></mtd><mtd><mrow><msub><mi>b</mi><mrow><mn>2</mn><mo>→</mo><mn>2</mn></mrow></msub></mrow></mtd><mtd><mo>⋯</mo></mtd><mtd><mrow><msub><mi>b</mi><mrow><mn>2</mn><mo>→</mo><mi>n</mi></mrow></msub></mrow></mtd></mtr><mtr><mtd><mo>⋯</mo></mtd><mtd><mo>⋯</mo></mtd><mtd><mo>⋯</mo></mtd><mtd><mo>⋯</mo></mtd></mtr><mtr><mtd><mrow><msub><mi>b</mi><mrow><mi>n</mi><mo>→</mo><mn>1</mn></mrow></msub></mrow></mtd><mtd><mrow><msub><mi>b</mi><mrow><mi>n</mi><mo>→</mo><mn>2</mn></mrow></msub></mrow></mtd><mtd><mo>⋯</mo></mtd><mtd><mrow><msub><mi>b</mi><mrow><mi>n</mi><mn>1</mn><mo>→</mo><mi>n</mi></mrow></msub></mrow></mtd></mtr></mtable></mrow><mo>}</mo></mrow></mrow><mi>Τ</mi></msup><mo>×</mo><mrow><mo>{</mo><mrow><mtable><mtr><mtd><mrow><msubsup><mi>λ</mi><mn>1</mn><mrow><mtext>dec</mtext></mrow></msubsup></mrow></mtd><mtd><mrow/></mtd><mtd><mrow/></mtd><mtd><mrow/></mtd></mtr><mtr><mtd><mrow/></mtd><mtd><mrow><msubsup><mi>λ</mi><mn>2</mn><mrow><mtext>dec</mtext></mrow></msubsup></mrow></mtd><mtd><mrow/></mtd><mtd><mrow/></mtd></mtr><mtr><mtd><mrow/></mtd><mtd><mrow/></mtd><mtd><mo>⋱</mo></mtd><mtd><mrow/></mtd></mtr><mtr><mtd><mrow/></mtd><mtd><mrow/></mtd><mtd><mrow/></mtd><mtd><mrow><msubsup><mi>λ</mi><mi>n</mi><mrow><mtext>dec</mtext></mrow></msubsup></mrow></mtd></mtr></mtable></mrow><mo>}</mo></mrow><mo>×</mo><mrow><mo>{</mo><mrow><mtable><mtr><mtd><mrow><msub><mi>N</mi><mrow><mn>1</mn><mo>,</mo><mi>j</mi></mrow></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow></mtd></mtr><mtr><mtd><mrow><msub><mi>N</mi><mrow><mn>2</mn><mo>,</mo><mi>j</mi></mrow></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow></mtd></mtr><mtr><mtd><mo>⋮</mo></mtd></mtr><mtr><mtd><mrow><msub><mi>N</mi><mrow><mi>n</mi><mo>,</mo><mi>j</mi></mrow></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow></mtd></mtr></mtable></mrow><mo>}</mo></mrow></mrow></math> <math id="M10"><mrow><msub><mi>σ</mi><mrow><mi>i</mi><mo>,</mo><mi>f</mi><mo>,</mo><mi>j</mi></mrow></msub><msub><mi>N</mi><mrow><mi>i</mi><mo>,</mo><mi>j</mi></mrow></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><msub><mi>Φ</mi><mi>j</mi></msub></mrow></math> represents the disappearance rate of nuclide i through fission in region j , where σ i , f , j is an n-dimensional diagonal matrix, as shown in Eq. (5). <math display="block" id="M11"><mrow><msub><mi>σ</mi><mrow><mi>i</mi><mo>,</mo><mi>f</mi><mo>,</mo><mi>j</mi></mrow></msub><msub><mi>N</mi><mrow><mi>i</mi><mo>,</mo><mi>j</mi></mrow></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><msub><mi>Φ</mi><mi>j</mi></msub><mtext>=</mtext><mrow><mo>{</mo><mrow><mtable><mtr><mtd><mrow><msub><mi>σ</mi><mrow><mn>1</mn><mo>,</mo><mi>f</mi><mo>,</mo><mi>j</mi></mrow></msub></mrow></mtd><mtd><mrow/></mtd><mtd><mrow/></mtd><mtd><mrow/></mtd></mtr><mtr><mtd><mrow/></mtd><mtd><mrow><msub><mi>σ</mi><mrow><mn>2</mn><mo>,</mo><mi>f</mi><mo>,</mo><mi>j</mi></mrow></msub></mrow></mtd><mtd><mrow/></mtd><mtd><mrow/></mtd></mtr><mtr><mtd><mrow/></mtd><mtd><mrow/></mtd><mtd><mo>⋯</mo></mtd><mtd><mrow/></mtd></mtr><mtr><mtd><mrow/></mtd><mtd><mrow/></mtd><mtd><mrow/></mtd><mtd><mrow><msub><mi>σ</mi><mrow><mi>n</mi><mo>,</mo><mi>f</mi><mo>,</mo><mi>j</mi></mrow></msub></mrow></mtd></mtr></mtable></mrow><mo>}</mo></mrow><mo>×</mo><mrow><mo>{</mo><mrow><mtable><mtr><mtd><mrow><msub><mi>N</mi><mrow><mn>1</mn><mo>,</mo><mi>j</mi></mrow></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow></mtd></mtr><mtr><mtd><mrow><msub><mi>N</mi><mrow><mn>2</mn><mo>,</mo><mi>j</mi></mrow></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow></mtd></mtr><mtr><mtd><mo>⋮</mo></mtd></mtr><mtr><mtd><mrow><msub><mi>N</mi><mrow><mi>n</mi><mo>,</mo><mi>j</mi></mrow></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow></mtd></mtr></mtable></mrow><mo>}</mo></mrow><mo>×</mo><msub><mi>Φ</mi><mi>j</mi></msub></mrow></math> <math id="M12"><mrow><mo stretchy="false">(</mo><msub><mi>σ</mi><mrow><mi>i</mi><mo>,</mo><mi>j</mi></mrow></msub><mo>−</mo><msub><mi>σ</mi><mrow><mi>i</mi><mo>,</mo><mi>f</mi><mo>,</mo><mi>j</mi></mrow></msub><mo stretchy="false">)</mo><msub><mi>N</mi><mrow><mi>i</mi><mo>,</mo><mi>j</mi></mrow></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><msub><mi>Φ</mi><mi>j</mi></msub></mrow></math> represents the disappearance rate of nuclide i in region j , which refers to other nuclear reaction pathways except fission reactions. The expression is similar to Eq. (5), and is not expanded here. <math id="M13"><mrow><msubsup><mi>λ</mi><mi>i</mi><mrow><mi mathvariant="normal">dec</mi></mrow></msubsup><msub><mi>N</mi><mrow><mi>i</mi><mo>,</mo><mi>j</mi></mrow></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow></math> represents the decay rate of nuclide i in region j . <math id="M14"><mrow><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>m</mi><mo>=</mo><mn>1</mn></mrow><mi>a</mi></munderover><mrow><msubsup><mi>λ</mi><mrow><mi>i</mi><mo>,</mo><mi>m</mi><mo>→</mo><mi>j</mi></mrow><mrow><mtext>flowin</mtext></mrow></msubsup><msub><mi>N</mi><mrow><mi>i</mi><mo>,</mo><mi>m</mi></mrow></msub></mrow></mstyle><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>=</mo><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>m</mi><mo>=</mo><mn>1</mn></mrow><mi>a</mi></munderover><mrow><mfrac><mrow><mi>V</mi><msub><mi>F</mi><mrow><mi>m</mi><mo>→</mo><mi>j</mi></mrow></msub><msub><mi>N</mi><mrow><mi>i</mi><mo>,</mo><mi>m</mi></mrow></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow><mrow><mi>V</mi><mi>o</mi><mi>l</mi><mi>u</mi><mi>m</mi><msub><mi>e</mi><mi>j</mi></msub></mrow></mfrac></mrow></mstyle></mrow></math> represents the inflow of nuclide i from region m to region j . In Eq. (6), <math id="M15"><mrow><mi>V</mi><msub><mi>F</mi><mrow><mi>m</mi><mo>→</mo><mi>j</mi></mrow></msub></mrow></math> represents the volume flow, which is a dimensional flow transfer matrix of different regions. Because the problem is a 1-D unidirectional flow problem, the matrix elements are non-zero only between the adjacent regions in the flow direction. Volume j represents the volume of fuel salt in region j . <math display="block" id="M16"><mrow><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>m</mi><mo>=</mo><mn>1</mn></mrow><mi>a</mi></munderover><mrow><mfrac><mrow><mi>V</mi><msub><mi>F</mi><mrow><mi>m</mi><mo>→</mo><mi>j</mi></mrow></msub><msub><mi>N</mi><mrow><mi>i</mi><mo>,</mo><mi>m</mi></mrow></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow><mrow><mi>V</mi><mi>o</mi><mi>l</mi><mi>u</mi><mi>m</mi><msub><mi>e</mi><mi>j</mi></msub></mrow></mfrac></mrow></mstyle><mtext>=</mtext><msup><mrow><mrow><mo>{</mo><mrow><mtable><mtr><mtd><mn>0</mn></mtd><mtd><mrow><mi>V</mi><msub><mi>F</mi><mrow><mn>1</mn><mo>→</mo><mn>2</mn></mrow></msub></mrow></mtd><mtd><mo>⋯</mo></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd><mtd><mo>⋯</mo></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mo>⋯</mo></mtd><mtd><mo>⋯</mo></mtd><mtd><mo>⋯</mo></mtd><mtd><mo>⋯</mo></mtd></mtr><mtr><mtd><mrow><mi>V</mi><msub><mi>F</mi><mrow><mi>a</mi><mo>→</mo><mn>1</mn></mrow></msub></mrow></mtd><mtd><mn>0</mn></mtd><mtd><mo>⋯</mo></mtd><mtd><mn>0</mn></mtd></mtr></mtable></mrow><mo>}</mo></mrow></mrow><mi>Τ</mi></msup><mo>×</mo><mrow><mo>{</mo><mrow><mtable><mtr><mtd><mrow><msub><mi>N</mi><mrow><mn>1</mn><mo>,</mo><mi>j</mi></mrow></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow></mtd></mtr><mtr><mtd><mrow><msub><mi>N</mi><mrow><mn>2</mn><mo>,</mo><mi>j</mi></mrow></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow></mtd></mtr><mtr><mtd><mo>⋮</mo></mtd></mtr><mtr><mtd><mrow><msub><mi>N</mi><mrow><mi>n</mi><mo>,</mo><mi>j</mi></mrow></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow></mtd></mtr></mtable></mrow><mo>}</mo></mrow><mo>×</mo><mfrac><mn>1</mn><mrow><mi>V</mi><mi>o</mi><mi>l</mi><mi>u</mi><mi>m</mi><msub><mi>e</mi><mi>j</mi></msub></mrow></mfrac></mrow></math> <math id="M17"><mrow><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>m</mi><mo>=</mo><mn>1</mn></mrow><mi>a</mi></munderover><mrow><msubsup><mi>λ</mi><mrow><mi>i</mi><mo>,</mo><mi>j</mi><mo>→</mo><mi>m</mi></mrow><mrow><mtext>flowout</mtext></mrow></msubsup><msub><mi>N</mi><mrow><mi>i</mi><mo>,</mo><mi>j</mi></mrow></msub></mrow></mstyle><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>=</mo><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>m</mi><mo>=</mo><mn>1</mn></mrow><mi>a</mi></munderover><mrow><mfrac><mrow><mi>V</mi><msub><mi>F</mi><mrow><mtext>j</mtext><mo>→</mo><mi>m</mi></mrow></msub><msub><mi>N</mi><mrow><mi>i</mi><mo>,</mo><mi>j</mi></mrow></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow><mrow><mi>V</mi><mi>o</mi><mi>l</mi><mi>u</mi><mi>m</mi><msub><mi>e</mi><mi>j</mi></msub></mrow></mfrac></mrow></mstyle></mrow></math> represents the outflow of nuclide i from region j to region m , which is similar to Eq. (6). The input parameters, such as fission yield, decay constant, cross section, volume, and flow rate are read by Mathematica 7.0, and the differential equations are solved numerically. The nuclide concentration N i , j ( t ) in each region is obtained, following which the radioactivity A i , j ( t ) in region j is obtained, as given by Eq. (7): <math display="block" id="M18"><mrow><msubsup><mi>A</mi><mrow><mtext>i,j</mtext></mrow><mrow/></msubsup><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>=</mo><msub><mi>N</mi><mrow><mtext>i,j</mtext></mrow></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><msub><mtext>λ</mtext><mtext>i</mtext></msub><mi>V</mi><mi>o</mi><mi>l</mi><mi>u</mi><mi>m</mi><msub><mi>e</mi><mi>j</mi></msub><mo>.</mo></mrow></math> At the start-up of the reactor, the initial values of all FPs are set to 0. 3 Results and Discussion 1 3.1 Numerical verification 2 The nuclear data of fission yield, half-life, and decay branch ratio used in the MSRFP 1.0 calculation are obtained from the ENDFB VII.1 database. To verify the correctness and rationality of the MSRFP 1.0 program in the mathematical model and nuclear data selection, the total inventory evolution curve and the activity of key nuclides of MSRFP 1.0 and ORIGEN-S were compared in the static burnup mode (flow rate = 0), as shown in Fig. 4 Fig. 4 and Table 3 Table 3 . It can be seen that the total inventory over one cycle and the radioactivity of 71 main FPs nuclides at the end of life (EOL) are in good agreement with a deviation of less than 1% and 10%, respectively. It was preliminarily verified that the mathematical model and the nuclear data are reasonable and correct, and the calculation results of MSRFP 1.0 are reliable. 1 2 FPs 2 1 Activity (Bq) 1 2 Relative Deviation 1 2 FPs 2 1 Activity (Bq) 1 2 Relative Deviation 1 2 FPs 2 1 Activity (Bq) 1 2 Relative Deviation 1 1 ORIGEN-S 1 1 MSRFP 1.0 1 1 ORIGEN-S 1 1 MSRFP 1.0 1 1 ORIGEN-S 1 1 MSRFP1.0 1 1 83m Kr 1 1 3.38×10 14 1 1 3.54×10 14 1 1 4.63% 1 1 90 Y 1 1 7.27×10 13 1 1 7.59×10 13 1 1 4.36% 1 1 143 Pr 1 1 3.61×10 15 1 1 3.94×10 15 1 1 9.00% 1 1 85 Kr 1 1 9.54×10 12 1 1 1.01×10 13 1 1 5.94% 1 1 91 Y 1 1 3.54×10 15 1 1 3.74×10 15 1 1 5.75% 1 1 144 Pr 1 1 1.79×10 15 1 1 1.88×10 15 1 1 5.25% 1 1 85m Kr 1 1 7.93×10 14 1 1 8.48×10 14 1 1 6.93% 1 1 137m Ba 1 1 6.93×10 13 1 1 7.17×10 13 1 1 3.37% 1 1 147 Nd 1 1 1.41×10 15 1 1 1.48×10 15 1 1 5.10% 1 1 87 Kr 1 1 1.61×10 15 1 1 1.66×10 15 1 1 3.01% 1 1 139 Ba 1 1 4.03×10 15 1 1 4.27×10 15 1 1 6.07% 1 1 147 Pm 1 1 2.61×10 14 1 1 2.73×10 14 1 1 4.82% 1 1 88 Kr 1 1 2.20×10 15 1 1 2.32×10 15 1 1 5.26% 1 1 140 Ba 1 1 3.91×10 15 1 1 4.11×10 15 1 1 5.14% 1 1 148 Pm 1 1 7.94×10 12 1 1 8.11×10 12 1 1 2.24% 1 1 131m Xe 1 1 1.97×10 13 1 1 2.07×10 13 1 1 4.93% 1 1 123 Sn 1 1 6.25×10 11 1 1 6.24×10 11 1 1 -0.09% 1 1 148m Pm 1 1 5.13×10 12 1 1 5.13×10 12 1 1 0.06% 1 1 133 Xe 1 1 4.07×10 15 1 1 4.43×10 15 1 1 8.87% 1 1 125 Sn 1 1 6.23×10 12 1 1 6.27×10 12 1 1 0.65% 1 1 151 Sm 1 1 1.54×10 12 1 1 1.57×10 12 1 1 1.69% 1 1 133m Xe 1 1 1.23×10 14 1 1 1.29×10 14 1 1 4.89% 1 1 127 Sn 1 1 6.00×10 13 1 1 6.18×10 13 1 1 2.96% 1 1 154 Eu 1 1 3.57×10 10 1 1 3.58×10 10 1 1 0.29% 1 1 135 Xe 1 1 3.72×10 15 1 1 3.76×10 15 1 1 1.24% 1 1 124 Sb 1 1 9.49×10 09 1 1 8.78×10 09 1 1 -7.46% 1 1 155 Eu 1 1 2.03×10 12 1 1 1.93×10 12 1 1 -4.76% 1 1 135m Xe 1 1 7.35×10 14 1 1 7.67×10 14 1 1 4.38% 1 1 125 Sb 1 1 4.02×10 12 1 1 4.14×10 12 1 1 2.96% 1 1 156 Eu 1 1 1.51×10 13 1 1 1.50×10 13 1 1 -1.00% 1 1 131 I 1 1 1.81×10 15 1 1 1.91×10 15 1 1 5.32% 1 1 127 Sb 1 1 1.00×10 14 1 1 1.04×10 14 1 1 3.20% 1 1 160 Tb 1 1 1.00×10 09 1 1 9.36×10 08 1 1 -6.71% 1 1 132 I 1 1 2.72×10 15 1 1 2.84×10 15 1 1 4.58% 1 1 125m Te 1 1 6.83×10 11 1 1 7.07×10 11 1 1 3.43% 1 1 95 Zr 1 1 3.96×10 15 1 1 4.15×10 15 1 1 4.77% 1 1 133 I 1 1 4.21×10 15 1 1 4.42×10 15 1 1 5.02% 1 1 127 Te 1 1 9.73×10 13 1 1 1.00×10 14 1 1 3.16% 1 1 97 Zr 1 1 3.85×10 15 1 1 3.77×10 15 1 1 -2.07% 1 1 134 I 1 1 4.92×10 15 1 1 5.15×10 15 1 1 4.76% 1 1 129 Te 1 1 3.25×10 14 1 1 3.35×10 14 1 1 3.12% 1 1 95 Nb 1 1 3.79×10 15 1 1 4.01×10 15 1 1 5.84% 1 1 135 I 1 1 3.95×10 15 1 1 4.14×10 15 1 1 4.78% 1 1 129m Te 1 1 6.21×10 13 1 1 6.43×10 13 1 1 3.49% 1 1 95m Nb 1 1 4.58×10 13 1 1 4.30×10 13 1 1 -6.15% 1 1 134 Cs 1 1 1.11×10 12 1 1 1.14×10 12 1 1 3.33% 1 1 131 Te 1 1 1.62×10 15 1 1 1.70×10 15 1 1 4.78% 1 1 99 Mo 1 1 3.85×10 15 1 1 4.03×10 15 1 1 4.76% 1 1 136 Cs 1 1 5.59×10 12 1 1 5.88×10 12 1 1 5.16% 1 1 131m Te 1 1 2.59×10 14 1 1 2.68×10 14 1 1 3.50% 1 1 99m Tc 1 1 3.39×10 15 1 1 3.55×10 15 1 1 4.79% 1 1 137 Cs 1 1 7.33×10 13 1 1 7.58×10 13 1 1 3.40% 1 1 132 Te 1 1 2.71×10 15 1 1 2.83×10 15 1 1 4.63% 1 1 103 Ru 1 1 1.92×10 15 1 1 1.99×10 15 1 1 3.80% 1 1 138 Cs 1 1 4.22×10 15 1 1 4.32×10 15 1 1 2.31% 1 1 133 Te 1 1 2.34×10 15 1 1 2.46×10 15 1 1 5.13% 1 1 106 Ru 1 1 1.14×10 14 1 1 1.13×10 14 1 1 -1.12% 1 1 88 Rb 1 1 2.22×10 15 1 1 2.33×10 15 1 1 5.25% 1 1 140 La 1 1 3.99×10 15 1 1 4.11×10 15 1 1 3.05% 1 1 103m Rh 1 1 1.92×10 15 1 1 1.98×10 15 1 1 3.38% 1 1 89 Sr 1 1 2.91×1015 1 1 2.99×10 15 1 1 2.61% 1 1 141 La 1 1 3.67×10 15 1 1 3.86×10 15 1 1 5.17% 1 1 106 Rh 1 1 1.16×10 14 1 1 1.13×10 14 1 1 -2.25% 1 1 90 Sr 1 1 7.25×10 13 1 1 7.60×10 13 1 1 4.94% 1 1 142 La 1 1 3.67×10 15 1 1 3.84×10 15 1 1 4.76% 1 1 110m Ag 1 1 2.14×10 09 1 1 2.16×10 09 1 1 0.93% 1 1 91 Sr 1 1 3.65×10 15 1 1 3.86×10 15 1 1 5.64% 1 1 141 Ce 1 1 3.66×10 15 1 1 3.85×10 15 1 1 5.33% 1 1 115m Cd 1 1 3.02×10 11 1 1 3.10×10 11 1 1 2.59% 1 1 92 Sr 1 1 3.72×10 15 1 1 3.89×10 15 1 1 4.70% 1 1 144 Ce 1 1 1.79×10 15 1 1 1.88×10 15 1 1 5.29% 1 1 Total 1 1 1.14×10 17 1 1 1.19×10 17 1 1 4.65% There are two possible reasons for the deviation between ORIGEN-S and MSRFP1.0 results: (1) Different nuclear databases: the nuclear data used in MSRFP1.0 is ENDF/B-Ⅶ.1, whereas that in ORIGEN-S is ENDF/B-Ⅶ.0. (2) Because of the real-time flow of fuel salt, compared with the static burnup mode, the solving speed of the burnup equation with the flow term is lower. To ensure the calculation time, we simplify the size of the solution matrix. Only 235 U fission was considered as the source of fission products; however, a few other actinide nuclides contribute to some fission products as well. Although the contribution of other actinides to fission products is much smaller than that of 235 U, it influences the calculation results to a certain degree. 3.2 Inventory simulation at start-up and shutdown conditions 2 The solubility characteristics of FPs in fluorine salts are related to the chemical properties of FPs and the chemical potential of fluorine salts. The FPs were categorized to six types based on their general chemical properties [ 27 27 ] : (1) Noble gas elements: Kr, Xe; (2) Noble metal elements: Nb, Mo, Tc, Ru, Te, Pd, Rh, Ag, As, Se; (3) Transition metal elements: Y, Zr, Cd, In, Sn, Sb, Ga, Zn; (4) Lanthanide metal elements: La, Ce, Pr, Pm, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er; (5) Active metal elements (including alkali and alkaline-earth metals): Cs, Rb, Ba, Sr; (6) Halides: I, Br. The relative activity evolution over time of each category of the FPs was simulated, as shown in Fig. 5 Fig. 5 . The half-life data of the main FPs are provided in Table 4 Table 4 , and the evolution curves of the major FPs were simulated for the start-up and shutdown conditions, as shown in Fig. 6 (a)–(f) Fig. 6 (a)–(f) . At the EOL, the radioactive inventory of the FPs and their corresponding proportions are: (1) Noble gas elements: 1.39 × 10 16 Bq (11.24%); (2) Noble metal elements: 2.02 × 10 16 Bq (16.29%); (3) Transition metal elements: 2.11 × 10 16 Bq (17.03%); (4) Lanthanide metal elements: 2.56 × 10 16 Bq (20.64%); (5) Active metal elements: 2.36 × 10 16 Bq (19.01%); (6) Halides: 1.95 × 10 16 Bq (15.78%). 2 1 FPs with short life 2 1 FPs with medium life 2 1 FPs with long life 1 1 FPs 1 1 Half-life 1 1 FPs 1 1 Half-life 1 1 FPs 1 1 Half-life 1 1 83m Kr 1 1 1.83 h 1 1 131m Xe 1 1 11.8 d 1 1 85 Kr 1 1 10.8 a 1 1 85m Kr 1 1 4.48 h 1 1 133 Xe/ 133m Xe 1 1 5.24 d/2.19 d 1 1 134 Cs 1 1 2.07 a 1 1 87 Kr 1 1 1.27 h 1 1 131 I 1 1 8.03 d 1 1 137 Cs 1 1 30.1 a 1 1 88 Kr 1 1 2.84 h 1 1 136 Cs 1 1 13.2 d 1 1 90 Sr 1 1 28.8 a 1 1 135 Xe 1 1 9.14 h 1 1 89 Sr 1 1 50.5 d 1 1 125 Sb 1 1 2.76 a 1 1 135m Xe 1 1 15.3 min 1 1 90 Y 1 1 2.67 d 1 1 147 Pm 1 1 2.62 a 1 1 132 I 1 1 2.30 h 1 1 91 Y 1 1 58.5 d 1 1 151 Sm 1 1 90.0 a 1 1 133 I 1 1 20.8 h 1 1 140 Ba/ 140 La 1 1 12.8 d/1.68 d 1 1 154 Eu 1 1 8.60 a 1 1 134 I 1 1 52.5 min 1 1 123 Sn 1 1 12.9 d 1 1 155 Eu 1 1 4.75 a 1 1 135 I 1 1 6.57 h 1 1 125 Sn 1 1 9.64 d 1 1 106 Ru 1 1 1.02 a 1 1 138 Cs 1 1 33.4 min 1 1 124 Sb 1 1 60.2 d 1 1   1 1   1 1 88 Rb 1 1 17.8 min 1 1 127 Sb 1 1 3.85 d 1 1   1 1   1 1 91 Sr 1 1 9.63 h 1 1 125m Te 1 1 57.4 d 1 1   1 1   1 1 92 Sr 1 1 2.71 h 1 1 129m Te 1 1 33.6 d 1 1   1 1   1 1 137m Ba 1 1 2.55 min 1 1 131m Te 1 1 1.39 d 1 1   1 1   1 1 139 Ba 1 1 1.38 h 1 1 132 Te 1 1 3.20 d 1 1   1 1   1 1 127 Sn 1 1 2.10 h 1 1 141 Ce 1 1 32.5 d 1 1   1 1   1 1 127 Te 1 1 9.35 h 1 1 144 Ce 1 1 285 d 1 1   1 1   1 1 129 Te 1 1 1.16 h 1 1 143 Pr 1 1 13.6 d 1 1   1 1   1 1 131 Te 1 1 25.0 min 1 1 147 Nd 1 1 11.0 d 1 1   1 1   1 1 141 La 1 1 3.92 h 1 1 148 Pm/ 148m Pm 1 1 5.37 d/41.3 d 1 1   1 1   1 1 142 La 1 1 1.52 h 1 1 156 Eu 1 1 15.2 d 1 1   1 1   1 1 144 Pr 1 1 17.3 min 1 1 160 Tb 1 1 72.3 d 1 1   1 1   1 1 97 Zr 1 1 16.7 h 1 1 95 Zr/ 95 Nb/ 95m Nb 1 1 64.0 d/35.0 d/3.61 d 1 1   1 1   1 1 99m Tc 1 1 6.01 h 1 1 99 Mo 1 1 2.75 d 1 1   1 1   1 1 103m Rh 1 1 56.1 min 1 1 103 Ru 1 1 39.2 d 1 1   1 1   1 1 106 Rh 1 1 30.1 s 1 1 110m Ag 1 1 250 d 1 1   1 1   1 1   1 1   1 1 115m Cd 1 1 44.6 d 1 1   1 1   Figure 5 Figure 5 shows that noble gases and halides accumulate and attain equilibrium rapidly after the reactor start-up, because of the short half-life of the main nuclide. The most important noble gas radionuclides are 85 Kr ( T 1/2 =1.7 a) and 133 Xe ( T 1/2 =5.24 d), and the activity of 133 Xe at EOL is 4.07 × 10 15 Bq, accounting for 86.4% of the total noble gas activity. The activity of 85 Kr at EOL is 1.01 × 10 13 Bq, accounting for 0.214% of the total noble gas activity. Although 85 Kr radioactivity accounts for a small ratio of the total radioactivity under normal operating conditions, 85 Kr has a long-term impact on the environment because of its long half-life, as shown in Fig. 6(a) Fig. 6(a) . It can be considered that other noble gas nuclides will decay to a negligible level after a 30-day shutdown of the reactor. The half-life of halides is usually relatively shorter; therefore, the activity of halides exhibit rapid growth and decay during reactor start-up and shutdown. The half-life of 131 I is 8.03 d, which is the longest half-life among all the evaluated halide curves. Therefore, it can be considered that the activity of halides will decay rapidly to a negligible level after approximately two months from the shutdown of the reactor. In addition to the long half-life of the fission product 85 Kr, several other FPs with long-term radioactive effects are present: 137 Cs, 134 Cs, 90 Sr/ 90 Y, 125 Sb, 147 Pm, 151 Sm, 154 Eu, 155 Eu, and 106 Ru. Although the half-life of 90 Y is only 2.67 d, it has a strong long-term radioactivity as the daughter product of 90 Sr. Table 5 Table 5 shows the types of radiation emitted during the decay of the main long-lived fission product nuclides. This table indicates that, most FPs, excluding 90 Sr and 106 Ru, with long-term radioactivity have different intensities of γ-radiation during decay. Among the several long-lived FPs, 137 Cs and 90 Sr are the two key fission product nuclides for radioactive waste treatment and disposal. Whereas 137 Cs exhibits pure beta decay, its daughter product 137m Ba exhibits strong gamma radioactivity. Further, 90 Sr exhibits pure beta decay, which mainly deposits in bone tissue, and 137 Cs is distributed uniformly throughout the body once inhaled or ingested. Both these nuclides are the main contributors to the public exposure dose [ 28 28 ] . Calculations indicate that, at 300 years after shutdown of the 2 MW experimental MSR, the radioactivity of 137 Cs and 90 Sr/ 90 Y will be 1.51 × 10 11 Bq, accounting for 49.14% of the total fission product activity. Furthermore, after 300 years of shutdown, another nuclide would be left over, i.e., 151 Sm (1.56 × 10 11 Bq), whose activity is similar to the total activity of 137 Cs and 90 Sr/ 90 Y. Although gamma rays are emitted as well by 151 Sm decay, the energy and probability are lower than those of 137 Cs and 90 Sr/ 90 Y, i.e., 21.543 keV and 0.0314%, respectively. 1 2 FPs 2 1 Decay 2 1 β particle 2 1 γ ray 1 1 Decay type 1 1 Branch ratio (%) 1 1 Energy (keV) 1 1 Intensity (%) 1 1 Energy (keV) 1 1 Intensity (%) 1 1 85 Kr 1 1 β - 1 1 100 1 1 173.4 1 1 0.434 1 1 513.99 1 1 0.434 1 1 1 1 1 1 1 1 687.4 1 1 99.563 1 1 1 1 1 1 134 Cs 1 1 β - 1 1 100 1 1 88.6 1 1 27.28 1 1 604.721 1 1 97.62 1 1 1 1 1 1 1 1 657.9 1 1 70.23 1 1 795.864 1 1 85.53 1 1 137 Cs 1 1 β - 1 1 100 1 1 513.97 1 1 94.4 1 1 616.657( 137m Ba) 1 1 84.99 1 1 1 1 1 1 1 1 1175.63 1 1 5.6 1 1 1 1 1 1 90 Sr 1 1 β - 1 1 100 1 1 546.0 1 1 100.0 1 1   1 1   1 1 90 Y 1 1 β - 1 1 100 1 1 519.4 1 1 0.0115 1 1 2186.24 1 1 0.0000014 1 1 1 1 1 1 1 1 2280.1 1 1 99.9885 1 1 1 1 1 1 125 Sb 1 1 β - 1 1 100 1 1 130.6 1 1 18.0 1 1 427.874 1 1 29.8 1 1 1 1 1 1 1 1 303.3 1 1 40.6 1 1 600.597 1 1 17.77 1 1 147 Pm 1 1 β - 1 1 100 1 1 224.6 1 1 99.994 1 1   1 1   1 1 151 Sm 1 1 β- 1 1 100 1 1 55.2 1 1 0.91 1 1 21.543 1 1 0.0314 1 1 1 1 1 1 1 1 76.7 1 1 99.09 1 1 1 1 1 1 154 Eu 1 1 β- 1 1 99.98% 1 1 249.2 1 1 28.6 1 1 123.07 1 1 40.4 1 1 1 1 ε 1 1 0.02% 1 1 571.3 1 1 36.3 1 1 723.3 1 1 20.06 1 1 1 1 1 1 1 1 841.0 1 1 16.8 1 1 996.29 1 1 10.48 1 1 1 1 1 1 1 1 1845.7 1 1 10.0 1 1 1004.76 1 1 18.01 1 1 1 1 1 1 1 1 1 1 1 1 1274.429 1 1 34.8 1 1 1 1 1 1 1 1 1 1 1 1 1596.4804 1 1 1.797 1 1 155 Eu 1 1 β- 1 1 100 1 1 146.9 1 1 47 1 1 86.545 1 1 30.7 1 1 1 1 1 1 1 1 165.7 1 1 25 1 1 105.305 1 1 21.2 1 1 1 1 1 1 1 1 252.2 1 1 17.6 1 1 1 1 1 1 106 Ru 1 1 β - 1 1 100 1 1 39.4 1 1 100 1 1   1 1   3.3 Comparison of simulations of the dynamic and static modes 2 After the FPs flow out of the core, the total amount of neutron poisons that reacts with the neutrons in the core decreases, consequently weakening the neutron poisoning effect; in addition, it has a better neutron economy because of the reduced neutron capture [ 30 30 ] . In the dynamic model, the activity of the FPs with larger absorption cross sections will be higher than the calculated results in the static mode. For example, 135 Xe is a typical neutron poison that mainly originates from the decay of its precursor 135 I and the fission of 235 U. The microscopic absorption cross section of 135 Xe is approximately 2.7 × 10 6 barn at a neutron energy of 0.025 eV. In the 2 MW MSR, the spectrum-weighted average absorption cross section of 135 Xe is 3.0 × 10 5 barn. Fig. 7 Fig. 7 shows the total activity evolution curve of 135 Xe over time for both dynamic and static modes. It can be seen that 135 Xe attains saturation equilibrium activity in approximately 40 h after the reactor start-up, after which the radioactivity does not change significantly. The equilibrium activities of the dynamic and static models are 3.89 × 10 15 Bq and 3.76 × 10 15 Bq, respectively, and the relative deviation is 3.46%. Furthermore, the FPs that are mainly produced by nuclear reactions are reduced by the outflow of the mother nucleus. A typical example is 134 Cs, which is an important fission product, mainly generated by the neutron capture reaction of 133 Cs. 134 Cs emits strong gamma rays (604.721 keV, 97.62%; 795.864 keV, 85.53%), and is frequently used as an important radioactive tracer and fuel burnup measurement nucleus [ 31 31 ] . It is one of the main sources of soil γ external radiation dose rate after nuclear accidents, and an essential item used to inspect air and food (such as water, milk, meat, and seafood). A large quantity of 134 Cs is usually present in the waste water of radioactive treatment plants. Fig. 8 Fig. 8 shows the total activity evolution curve of 134 Cs over time for the dynamic and static models. It can be seen that the absolute deviation between the two models increases with time. At EOL, the activities of the dynamic and static models were 8.43 × 10 11 Bq and 1.14 × 10 12 Bq, respectively, and the relative deviation is 26.05%. 3.4 Flowing state simulation results 2 The flow of fuel salt has a significant impact on the distribution of short-lived FPs in the primary loop. Generally, stable nuclides and long-lived FPs are relatively uniformly distributed in the primary loop [ 32 32 ,33] ; however, some short-lived nuclides exist mainly in the core. The larger the flow rate, the higher the proportion of short-lived nuclides flowing out of the core. In this work, the FPs activity in different regions of the primary loop was simulated under different flow rates, as shown in Fig. 9 (a)–(f) Fig. 9 (a)–(f) . It can be seen that, after reactor start-up, the activity of FPs in the core increases to 5.48 × 10 16 Bq in about 20 s, then increases slowly, and finally tends to attain equilibrium. In the simulated flow range (2.24–22400 cm 3 s -1 ), with the increase in flow rate, the activity of FPs in the core decreases monotonously, whereas the activity of FPs in the conduit and the equipment increases monotonously. a–Core, b–Hot leg #1, c–Main pump, d–Hot leg #2, e–Heat exchanger, f–Cold leg The distribution of FPs at EOL under different flow rates is shown in Table 6 Table 6 . It can be seen that, under normal operating conditions (flow rate = 22400 cm 3 s -1 ), the distribution of FPs in the primary loop system is as follows: core: 2.99 × 10 17 Bq (77.51%), hot leg #1: 4.63 × 10 15 Bq (1.20%), main pump: 6.23 × 10 16 Bq (16.15%), hot leg #2: 3.82 × 10 15 Bq (0.99%), heat exchanger: 99.65 × 10 15 Bq (2.50%), Cold leg: 7.37 × 10 15 Bq (1.91%). 1 2 Flow rate (cm 3 s -1 ) 6 1 Activity (Bq) 1 1 Core 1 1 Hot leg #1 1 1 Main pump 1 1 Hot leg #2 1 1 Heat exchanger 1 1 Cold leg 1 2 2.24 1 1 3.64×10 17 1 1 2.02×10 15 1 1 1.60×10 16 1 1 9.50×10 14 1 1 2.27×10 15 1 1 1.68×10 15 1 1 94.13% 1 1 0.52% 1 1 4.14% 1 1 0.25% 1 1 0.59% 1 1 0.43% 1 2 11.2 1 1 3.53×10 17 1 1 2.59×10 15 1 1 2.27×10 16 1 1 1.36×10 15 1 1 3.31×10 15 1 1 2.47×10 15 1 1 91.48% 1 1 0.67% 1 1 5.88% 1 1 0.35% 1 1 0.86% 1 1 0.64% 1 2 22.4 1 1 3.49×10 17 1 1 2.84×10 15 1 1 2.59×10 16 1 1 1.55×10 15 1 1 3.78×10 15 1 1 2.83×10 15 1 1 90.37% 1 1 0.74% 1 1 6.71% 1 1 0.40% 1 1 0.98% 1 1 0.73% 1 2 112 1 1 3.38×10 17 1 1 3.40×10 15 1 1 3.42×10 16 1 1 2.07×10 15 1 1 5.08×10 15 1 1 3.82×10 15 1 1 87.42% 1 1 0.88% 1 1 8.85% 1 1 0.54% 1 1 1.31% 1 1 0.99% 1 2 224 1 1 3.33×10 17 1 1 3.62×10 15 1 1 3.81×10 16 1 1 2.31×10 15 1 1 5.70×10 15 1 1 4.30×10 15 1 1 86.04% 1 1 0.94% 1 1 9.84% 1 1 0.60% 1 1 1.47% 1 1 1.11% 1 2 2240 1 1 3.15×10 17 1 1 4.31×10 15 1 1 5.03×10 16 1 1 3.07×10 15 1 1 7.66×10 15 1 1 5.82×10 15 1 1 81.62% 1 1 1.12% 1 1 13.03% 1 1 0.80% 1 1 1.98% 1 1 1.51% 1 2 22,400 1 1 2.99×10 17 1 1 4.63×10 15 1 1 6.23×10 16 1 1 3.82×10 15 1 1 9.65×10 15 1 1 7.37×10 15 1 1 77.51% 1 1 1.20% 1 1 16.15% 1 1 0.99% 1 1 2.50% 1 1 1.91% In the simulated flow range (2.24–22400 cm 3 s -1 ), with the increase in flow rate, the total activity of FPs in the core decreases monotonously from 3.64 × 10 17 Bq (94.13%) to 2.99 × 10 17 Bq (77.51%) because of the outflow of the short-life FPs from the core. Accordingly, the proportion of FPs in the equipment outside the core, such as loop circuit, main pumps, and heat exchangers, increases monotonously with the increase in flow rate. 4 Conclusion 1 In this work, a numerical simulation program MSRFP 1.0 was established for FPs flow and distribution characteristics of a 2 MW MSR primary loop system based on Mathematica 7.0, and the results were preliminarily verified using the reference program ORIGEN-S in the static burnup model. The deviation between the results of MSRFP 1.0 and ORIGEN-S was less than 10%, which indicates that the results are in good agreement. The FPs under normal operating conditions of the 2 MW MSR was analyzed. The results indicate that the flow of fuel salt significantly influences the distribution of FPs in the primary loop. The total activity of some FPs, such as 135 Xe and 134 Cs, were found to be affected by fuel salt flow. The analysis results and main conclusions of this study can be used as a reference for radiation shielding and thermal-hydraulic safety design of the primary loop system for 2 MW MSRs. In MSRs, tritium, a key activation product, is produced in the presence of Li and Be. In addition, heavy metals are converted into actinide nuclides such as Np, Pu, Am, and Cm. Tritium is extremely active and diffuses easily even through alloy walls at high temperatures. Tritium can easily enter the atmosphere and water, thereby posing biological radiation risks. Actinides usually have a very long life (such as 237 Np with the half-life of 2.14 × 10 6 years). Therefore, actinides become the main radioactive sources at hundreds of years after the spent fuel is discharged. Because of the availability of various fission products and the complexity of decay chain evolutions, many fission products have short half-life, and their distribution in the primary loop system of 2 MW MSRs is significantly affected by the flow. Therefore, only the fission products were especially studied in this work, and actinide nuclides and activated products were not studied. However, activated products and actinide nuclides play a very important role in influencing the environment and long-term radioactive waste storage and treatment. References E.S. Bettis , W.B. Cottrell , E.R. Mann et al ., The aircraft reactor experiment—operation . Nucl. Sci. Eng . 2 , 841 - 853 ( 1957 ) https://doi.org/10.13182/nse57-a35497 https://doi.org/10.13182/nse57-a35497 The aircraft reactor experiment—operation R. Briant . Collection of papers on the aircraft reactor experiment [J]. Nucl. Scie.Engi . 2 , 797 - 853 ( 1957 ). Collection of papers on the aircraft reactor experiment A.M. Weinberg , M.W. Rosenthal , P.N. Haubenreich et al ., Collection of papers on the molten salt reactor experiment . Nucl. Appl. Technol.   8 ( 2 ), 105 - 219 ( 1970 ) Collection of papers on the molten salt reactor experiment D. Scott , A.G. Grindell , Components and systems development for molten-salt breeder reactors . ( Oak Ridge National Laboratory , Oak Ridge, Tennessee , 1967 ), ORNL Report-TM-1855 . https://doi.org/10.2172/4367859 https://doi.org/10.2172/4367859 Components and systems development for molten-salt breeder reactors R.C. Robertson , O.L. Smith , R.B. Briggs et al ., Two-fluid molten-salt breeder reactor design study . ( Oak Ridge National Laboratory , Oak Ridge, Tennessee , 1970 ), ORNL Report-4528 . https://doi.org/10.2172/4093364 https://doi.org/10.2172/4093364 Two-fluid molten-salt breeder reactor design study J.L. Anderson , P.N. Haubenreich , R.C. Robertson et al . Conceptual design study of a single-fluid molten salt breeder reactor . ( Oak Ridge National Laboratory , Oak Ridge, Tennessee , 1971 ), ORNL Report-4541 . https://doi.org/10.2172/4030941 https://doi.org/10.2172/4030941 Conceptual design study of a single-fluid molten salt breeder reactor J. R. Engel , H. F. Bauman , J. F. Dearing , et al . Conceptual design characteristics of a denatured molten-salt reactor with once-through fueling . ( Office of Scientific and Technical Information , 1980 ). http://dx.doi.org/10.2172/5352526 http://dx.doi.org/10.2172/5352526 Conceptual design characteristics of a denatured molten-salt reactor with once-through fueling C. W. Forsberg , P. F. Peterson , P. S. Pickard . Molten-salt-cooled advanced high-temperature reactor for production of hydrogen and electricity . Nucl. Technol . 144 ( 3 ), 289 - 302 ( 2003 ). https://dx.doi.org/10.13182/nt03-1 https://dx.doi.org/10.13182/nt03-1 Molten-salt-cooled advanced high-temperature reactor for production of hydrogen and electricity R. C. William , D. B. Timothy , H. William , et al . Updated generation Ⅳ reactors integrated materials technology program plan, Revision 2 . ( Oak Ridge National Laboratory , Oak Ridge, Tennessee , 2005 ), ORNL Report-TM2005/556 . Updated generation Ⅳ reactors integrated materials technology program plan, Revision 2 S.R. Greene , J.C. Gehin , D.E. Holcomb et al ., Pre-Conceptual Design of a Fluoride-Salt-Cooled Small Modular Advanced High Temperature Reactor (Sm AHTR). Technical Report TM-2010/199 , ( Oak Ridge National Laboratory , Tennessee , 2011 ). https://doi.org/10.2172/1008830 https://doi.org/10.2172/1008830 Pre-Conceptual Design of a Fluoride-Salt-Cooled Small Modular Advanced High Temperature Reactor (Sm AHTR). Technical Report TM-2010/199 M. S. Cheng , Z. M. Dai . Preliminary safety analysis of molten salt breeder reactor . Nucl. Tech . 36 , 060601 ( 2013 ). https://doi.org/10.11889/j.0253-3219.2013.hjs.36.060601 https://doi.org/10.11889/j.0253-3219.2013.hjs.36.060601 (in Chinese) Preliminary safety analysis of molten salt breeder reactor G. C. Li , Y. Zou , C.G. Yu et al . Model optimization and analysis of Th-U breeding based on MSFR . Nucl. Tech . 40 , 020603 ( 2017 ). https://doi.org/10.11889/j.0253-3219.2017.hjs.40.020603 https://doi.org/10.11889/j.0253-3219.2017.hjs.40.020603 . (in Chinese) Model optimization and analysis of Th-U breeding based on MSFR Y. F. Liu , L.W. Mei , X.Z. Cai et al . Physics research for Molten Salt Reactor with different core boundaries . Nucl. Tech . 36 , 030601 ( 2013 ). (in Chinese) Physics research for Molten Salt Reactor with different core boundaries M.H. Jiang , H.J. Xu , Z.M. Dai , Advanced fission energy program-TMSR nuclear energy system . Bull. Chin. Acad. Sci . 27 ( 3 ), 366 - 374 ( 2012 ). https://doi.org/10.3969/j.issn.1000-3045.2012.03.016 https://doi.org/10.3969/j.issn.1000-3045.2012.03.016 . (in Chinese) Advanced fission energy program-TMSR nuclear energy system R. Yan , S.H. Yu , Y. Zou , et al .,. Study on neutronics design of ordered-pebble-bed fluoride-salt-cooled high-temperature experimental reactor . Nucl. Sci. Tech . 29 , 81 ( 2018 ). https://doi.org/10.1007/s41365-018-0414-0 https://doi.org/10.1007/s41365-018-0414-0 Study on neutronics design of ordered-pebble-bed fluoride-salt-cooled high-temperature experimental reactor G.C. Li , Y. Zou , C.G. Yu et al ., Influences of 7Li enrichment on Th-U fuel breeding for an improved molten salt fast reactor (IMSFR) . Nucl. Sci. Tech . 28 , 97 ( 2017 ). https://doi.org/10.1007/s41365-017-0250-7 https://doi.org/10.1007/s41365-017-0250-7 Influences of 7Li enrichment on Th-U fuel breeding for an improved molten salt fast reactor (IMSFR) S. H. Yu , Y. F. Liu , P. Yang et al ., Effect analysis of core structure changes on reactivity in molten salt experimental reactor , Nucl. Tech . 42 , 020603 ( 2019 ). https://doi.org/10.11889/j.0253-3219.2019.hjs.42.020603 https://doi.org/10.11889/j.0253-3219.2019.hjs.42.020603 (in Chinese) Effect analysis of core structure changes on reactivity in molten salt experimental reactor G. F. Zhu , R. Yan , S.H. Yu et al ., An application of direct statistical method for kinetics parameters in TMSR-SF1 , Nucl. Tech . 41 : 050603 ( 2018 ). https://doi.org/10.11889/j.0253-3219.2018.hjs.41.050603 https://doi.org/10.11889/j.0253-3219.2018.hjs.41.050603 (in Chinese) An application of direct statistical method for kinetics parameters in TMSR-SF1 R. M. Ji , R. Yan , X.X. Li et al . Effect of TRISO-particles distributions in pebble fuel . Nucl. Tech . 40 : 100604 ( 2017 ). https://doi.org/10.11889/j.0253-3219.2017.hjs.40.100604 https://doi.org/10.11889/j.0253-3219.2017.hjs.40.100604 (in Chinese) Effect of TRISO-particles distributions in pebble fuel B. Zhou , R. Yan , et al ., Analysis of decay heat in primary loop of molten salt reactor under normal conditions , Nucl. Tech . 41 , 040602 ( 2018 ). https://doi.org/10.11889/j.0253-3219.2018.hjs.41.040602 https://doi.org/10.11889/j.0253-3219.2018.hjs.41.040602 (In Chinese) Analysis of decay heat in primary loop of molten salt reactor under normal conditions X. B. Wang , D. W. Long , T.J. Zhu et al ., Electrochemical behaviors of Ln3+ in LnF3-LiCl-KCl molten salt , Nucl. Tech . 41 , 060301 ( 2018 ). https://doi.org/10.11889/j.0253-3219.2018.hjs.41.060301 https://doi.org/10.11889/j.0253-3219.2018.hjs.41.060301 (In Chinese) Electrochemical behaviors of Ln3+ in LnF3-LiCl-KCl molten salt T. H. Yang , Y. Luo , H.Y. Fu et al ., The influence of fluorides on the distillation behaviors of molten LiCl-KCl , Nucl. Tech . 41 , 120301 ( 2018 ). https://doi.org/10.11889/j.0253-3219.2018.hjs.41.120301 https://doi.org/10.11889/j.0253-3219.2018.hjs.41.120301 (In Chinese) The influence of fluorides on the distillation behaviors of molten LiCl-KCl A. G. A. Croff . User’s Manual for the Origen2 Computer Code . ( Oak Ridge National Laboratory , Oak Ridge, Tennessee , 1980 ), ORNL Report-7175 . https://doi.org/10.2172/5285077 https://doi.org/10.2172/5285077 User’s Manual for the Origen2 Computer Code M.A. Jessee , M.D. DeHart . TRITON, A Multipurpose Transport, Depletion, and Sensitivity and Uncertainty Analysis Module(Oak Ridge National Laboratory, Oak Ridge, Tennessee, 2011), ORNL Report-TM-2005/39,Book 3, Sect. T1 TRITON, A Multipurpose Transport, Depletion, and Sensitivity and Uncertainty Analysis Module(Oak Ridge National Laboratory, Oak Ridge, Tennessee, 2011), ORNL Report-TM-2005/39,Book 3, Sect. T1 I.C. Gauld . ORIGEN-S, Depletion Module to Calculate Neutron Activation, Actinide Transmutation, Fission Product Generation, and Radiation Source Terms (ORNL, Oak Ridge, 2011), ORNL Report-TM-2005/39,Book 1, Sect. F7 . ORIGEN-S, Depletion Module to Calculate Neutron Activation, Actinide Transmutation, Fission Product Generation, and Radiation Source Terms (ORNL, Oak Ridge, 2011), ORNL Report-TM-2005/39,Book 1, Sect. F7 D. F. Hollenbach , L. M. Petrie et al . KENO-VI: A Monte Carlo Criticality Program with generalized quadratic geometry . United States : N. p. , 1993 . Web . KENO-VI: A Monte Carlo Criticality Program with generalized quadratic geometry R. E. Thoma , Chemical aspects of MSRE operations .( Oak Ridge National Laboratory , Oak Ridge, Tennessee , 1971 ) http://dx.doi.org/10.2172/4675946 http://dx.doi.org/10.2172/4675946 Chemical aspects of MSRE operations M.A.A. Aslani , S¸. Aytas , S. Akyil et al ., Activity concentration of caesium-137 in agricultural soils . J. Environ. Radioact . 65 , 131 - 145 ( 2003 ). https://doi.org/10.1016/S0265-931X(02)00092-9 https://doi.org/10.1016/S0265-931X(02)00092-9 Activity concentration of caesium-137 in agricultural soils J. R. Guo . Fission product analysis technology . ( Atomic Energy Press , Beijing , 2008 ),p. 136 Fission product analysis technology D. LeBlanc , Molten salt reactors: a new beginning for an old idea . Nucl. Eng. Des . 240 , 1644 - 1656 ( 2010 ). https://doi.org/10.1016/j.nucengdes.2009.12.033 https://doi.org/10.1016/j.nucengdes.2009.12.033 Molten salt reactors: a new beginning for an old idea Z. Li , P. X. Li , Z.Q. Gao et al . A method for determining 137Cs in seawater by using 134Cs as tracer . Radiat. Prot . 34 ( 4 ), 250 - 254 ( 2014 ) (in Chinese) A method for determining 137Cs in seawater by using 134Cs as tracer J. H. Wu , C. Guo , X.Z. Cai et al ., Flow effect on 135I and 135Xe evolution behavior in a molten salt reactor , Nucl. Eng. Des . 314 , 318 - 325 ( 2017 ). https://doi.org/10.1016/j.nucengdes.2017.01.019 https://doi.org/10.1016/j.nucengdes.2017.01.019 . Flow effect on 135I and 135Xe evolution behavior in a molten salt reactor B. Zhou , R. Yan , et al ., Analysis of Xenon Dynamic Characteristics in Primary Loop System of MSR , Nucl. Power Eng . 39 ( 05 ), 19 - 24 ( 2018 ). (in Chinese) Analysis of Xenon Dynamic Characteristics in Primary Loop System of MSR 10.1007/s41365-020-0730-z This work was supported by the Chinese Academy of Sciences TMSR Strategic Pioneer Science and Technology Project (No.XDA02010000), and The Frontier Science Key Program of Chinese Academy of Sciences (No. QYZDY-SSW-JSC016). 2019-11-02 2019-12-27 2020-01-01 2020-01-31 2020-02-01 2021-04-10 © China Science Publishing & Media Ltd. (Science Press), Shanghai Institute of Applied Physics, the Chinese Academy of Sciences, ChineseNuclear Society and Springer Nature Singapore Pte Ltd. 2020 This is a post-peer-review, pre-copyedit version of an article published in Nuclear Science and Techniques. The final authenticated version is available online at: http://dx.doi.org/10.1007/s41365-020-0730-z http://dx.doi.org/10.1007/s41365-020-0730-z . 2020 Nuclear Science and Techniques 2 31