Neutronics analysis of a subcritical blanket system driven by a gas dynamic trap-based fusion neutron source for ⁹⁹Mo production

Neutronics analysis of a subcritical blanket system driven by a gas dynamic trap-based fusion neutron source for 99 Mo production 1 equal first-author 2 equal 2 corresp * yuncheng_han@163.com * yuncheng_han@163.com yuncheng_han@163.com https://orcid.org/0000-0003-1622-1003 2 3 4 https://orcid.org/0000-0001-7533-7546 1 1 2 School of Nuclear Technology and Chemistry & Biology and Hubei Key Laboratory of Radiation Chemistry and Functional Materials, Hubei University of Science and Technology, Xianning 437100, China School of Nuclear Technology and Chemistry & Biology and Hubei Key Laboratory of Radiation Chemistry and Functional Materials, Hubei University of Science and Technology, Xianning 437100, China Institute of Nuclear Energy Safety Technology, Hefei Institutes of Physical Science, Chinese Academy of Sciences, Hefei 230031, China Institute of Nuclear Energy Safety Technology, Hefei Institutes of Physical Science, Chinese Academy of Sciences, Hefei 230031, China Nuclear Reactors Research Centre, National Nuclear Research Institute, Ghana Atomic Energy Commission, Box LG 80, Legon-Accra, Ghana Nuclear Reactors Research Centre, National Nuclear Research Institute, Ghana Atomic Energy Commission, Box LG 80, Legon-Accra, Ghana Teaching and Research Section of Nuclear Medicine, School of Basic Medical Sciences, Hefei Institutes of Physical Science, Anhui Medical University, Hefei 230031, China Teaching and Research Section of Nuclear Medicine, School of Basic Medical Sciences, Hefei Institutes of Physical Science, Anhui Medical University, Hefei 230031, China Gamma-emitting radionuclide 99m Tc is globally used for the diagnosis of various pathological conditions owing to its ideal single-photon emission computed tomography (SPECT) characteristics. However, the short half-life of 99m Tc ( T 1/2 = 6 h) makes it difficult to store or transport. Thus, the production of 99m Tc is tied to its parent radionuclide 99 Mo ( T 1/2 = 66 h). The major production paths are based on accelerators and research reactors. The reactor process presents the potential for nuclear proliferation owing to its use of highly enriched Uranium (HEU). Accelerator-based methods tend to use deuterium-tritium (D-T) neutron sources but are hindered by the high cost of tritium and its challenging operation. In this study, a new 99 Mo production design was developed based on a deuterium-deuterium (D-D) gas dynamic trap fusion neutron source (GDT-FNS) and a subcritical blanket system (SBS) assembly with a low-enriched Uranium (LEU) solution. GDT-FNS can provide a relatively high neutron intensity, which is one of the advantages of 99 Mo production. We provide a Monte Carlo-based neutronics analysis covering the calculation of the subcritical multiplication factor ( k s ) of the SBS, optimization design for the reflector, shielding layer, and 99 Mo production capacity. Other calculations, including the neutron flux and nuclear heating distributions, are also provided for an overall evaluation of the production system. The results demonstrated that the SBS meets the nuclear critical safety design requirement ( k s < 0.97) and maintained a high 99 Mo production capacity. The proposed system can generate approximately 157 Ci 99 Mo for a stable 24 h operation with a neutron intensity of 1×10 14 n/s, which can meet 50% of China's demand in 2025. Gas dynamic trap Fusion neutron source Molybdenum-99 Low-enriched uranium Subcritical blanket system Introduction 1 According to the World Nuclear Energy Association (WNA) [ 1 1 ], over 10000 hospitals worldwide use radioisotopes for the diagnosis and treatment of diseases. It is estimated that approximately 90% of radioisotopes are used in diagnostic procedures, among which 99m Tc is the most commonly used, which benefits from its ideal characteristics of single-photon emission computed tomography (SPECT). Further analysis also demonstrates that the use of 99m Tc constitutes approximately 80% of nuclear medicine procedures, while 85% are used for diagnostic scans ( Updated April 2022) [ 1 1 ]. However, the production of 99m Tc ( T 1/2 = 6 h) is tied to its mother radionuclide 99 Mo ( T 1/2 = 66 h), which makes the study of 99 Mo production an essential research topic. The production of 99m Tc consists of two steps: 1) production of 99 Mo via mechanisms indicated in the schematic diagram of Fig. 1 Fig. 1 (neutron-fission, gamma-fission, neutron-gamma, gamma-neutron, etc.) and 2) separation of 99m Tc after it decays from 99 Mo through the emission of beta particles [ 2 2 ]. As indicated, 99 Mo and 99m Tc have short half-lives. Nonetheless, unlike the relatively short half-life of 99m Tc ( T 1/2 = 6 h), which is the main hindrance for its transport, the half-life of 99 Mo ( T 1/2 = 66 h) allows a relatively adequate time for transportation. Based on the half-life and transport time, the kinetics of producing 99m Tc depend on the production of 99 Mo; that is, under normal circumstances, the resulting product 99 Mo is transported to the target country immediately after production, and subsequently its decayed product ( 99m Tc) is quickly extracted and used in hospitals or nuclear medical centers. The global shortage of 99 Mo has recently been mainly attributed to aging nuclear reactors and their decommissioning [ 3 3 - 5 5 3-5 ]. A typical example is the event of the National Research Universal (NRU) in Canada, which produced approximately 40% of the world's 99 Mo supply but ceased production by October 31 st , 2016 [ 3 3 ]. Currently, most 99 Mo isotopes are produced by the fission process with HEU reactors. These nuclear reactors are the Belgian Reactor 2 (BR-2), High Flux Reactor (HFR) in the Netherlands, LVR-15 Reactor in the Czech Republic, Maria Research Reactor (Maria) in Poland, Open Pool Australian Light Water Reactor (OPAL), and South African Fundamental Atomic Research Installation (Safari-1) [ 6 6 ]. Additional information regarding 99 Mo production, specific reactors, and target materials are listed in Table 1 Table 1 . Most of these reactors are not only facing the problems of aging and decommissioning, but also pose great risks of nuclear proliferation. * 6-day Ci  99 Mo: a 6-day Ci is the measurement of the remaining radioactivity of 99 Mo six days after it leaves the processing facility (end of processing (EOP)) ** In March 2021 HFR started using LEU for the production of radioisotopes. 1 1 Country 1 1 Reactor 1 1 Targets 1 1 Capacity * 1 1 Start 1 1 Est. stop 1 1 Belgium 1 1 BR-2 1 1 HEU 1 1 6500 1 1 1961 1 1 2026 1 1 Netherlands 1 1 HFR 1 1 LEU ** 1 1 6200 1 1 1961 1 1 2022 1 1 Australia 1 1 OPAL 1 1 LEU 1 1 3500 1 1 2006 1 1 2030 1 1 Czech Republic 1 1 LVR-15 1 1 HEU 1 1 3000 1 1 1989 1 1 2028 1 1 South Africa 1 1 Safari-1 1 1 LEU 1 1 3000 1 1 1965 1 1 2025 1 1 Poland 1 1 Maria 1 1 LEU 1 1 2200 1 1 1974 1 1 2030 1 1 Russia 1 1 RIAR: three 1 1 HEU 1 1 890 1 1 1961-70 1 1 USA 1 1 MURR 1 1 HEU 1 1 750 1 1 1966 1 1 Argentina 1 1 RA-3 1 1 LEU 1 1 400 1 1 1967 1 1 2027 1 1 Total 1 1   1 1   1 1 26,440 1 1   1 1   To solve the problems of 99 Mo shortage and the nuclear proliferation of HEU targets, scientists have proposed a series of new methods to replace the path of HEU fission to produce 99 Mo. These methods can be divided into three categories: 1) 235 U(n, f) 99 Mo reaction in LEU reactors [ 7 7 , 8 8 ]; 2) solid target irradiation based on an accelerator, such as the neutron capture 98 Mo(n, γ) 99 Mo reaction [ 9 9 - 13 13 9-13 ], 100 Mo(n, 2n) 99 Mo reaction [ 14 14 , 15 15 ], 100 Mo(p, 2n) 99 Mo reaction [ 16 16 ], 100 Mo(γ, n) 99 Mo reaction [ 17 17 ], and photon-induced reaction of 238 U fission 238 U(γ, f) 99 Mo [ 18 18 ]; and 3) LEU solution fission of the 235 U(n, f) 99 Mo reaction in subcritical systems [ 19 19 - 23 23 19-23 ]. Among these, the last method is the most efficient and reliable means of production and has become a prime choice for 99 Mo production owing to the following advantages:1) compared to the solid target irradiation method based on an accelerator, the LEU solution can be effectively recovered and reused, thus significantly reducing the generation of radioactive waste; 2) the LEU fission method has a high production efficiency and low cost; and 3) comparing the LEU solution in subcortical systems to the HEU fission method, there is an advantage of avoiding nuclear critical safety accidents, and it also prevents nuclear proliferation. It is also relatively easy to apply for a license for construction and operation. In 2021, Han et al. [ 22 22 , 23 23 ] proposed a subcritical 99 Mo production system driven by an accelerator-based D-T neutron source, in which the accelerated deuterium ions bombard the tritium target, and the deuterium-tritium fusion reaction generates neutrons. The LEU solution target is then irradiated by neutrons for the fission of 235 U via the 235 U(n, f) 99 Mo reaction. Although this method does not require a supply of HEU, it has the disadvantage of using tritium. In addition to its high cost, it is difficult to obtain licenses for owning and operating tritium. In this study, we propose a new design for 99 Mo production based on the LEU subcritical blanket system (SBS). The system is driven by a gas dynamic trap-based fusion neutron source (GDT-FNS). However, instead of the normal deuterium-tritium fusion reaction, a deuterium- deuterium (D-D) fusion reaction neutron is used to induce fission in 235 U. In addition to the apparent advantage of avoiding the HEU system, our proposed 99 Mo production system has numerous advantages, such as a compact structure, high neutron source intensity, and lack of tritium consumption, leading to low capital costs. To ensure the design safety and process optimization for the SBS 99 Mo production path, a neutronics analysis of the production system was performed using the SuperMC code (Monte Carlo Particle Transport code). A detailed neutronics analysis is provided for an overall evaluation of the production system, including the analysis of the subcritical multiplication factor ( k s ), neutron flux, and heat deposition. A set of optimization parameters of the production system was obtained by maintaining a relatively high production rate and safety standard, including the geometric size, material components, and concentration of the LEU solution. Model and Method 1 The LEU solution SBS driven by GDT-FNS mainly includes GDT-FNS and a 99 Mo SBS, as shown in the schematic diagram in Fig. 2 Fig. 2 . The SBS is arranged in the high neutron flux region of the GDT, forming a fan-shaped blanket structure. Detailed descriptions are provided in sections 2.1 and 2.2. Gas Dynamic Trap-based Fusion Neutron Source (GDT-FNS) 2 A GDT is a type of axisymmetric magnetic mirror device [ 24 24 , 25 25 ]. Under the action of a specific magnetic field, the warm plasma constrained in the GDT vacuum chamber frequently collides and causes a fusion reaction, which can provide D-D or D-T fusion neutron sources, and the neutrons are high at both ends and low in the middle. This type of neutron source has the advantages of a high neutron flux, large testing space, compact structure, and low construction cost. The GDT-FNS not only meets the performance of fusion materials/components, but its resulting high neutron flux can be used to conduct the study of applied nuclear technology, such as medical isotope production, neutron photography, neutron irradiation (breeding), and for the low-dose neutron effect in cells. In this study, the GDT-FNS designed by the Hefei Institute of Physical Science [ 26 26 , 27 27 ] was used to analyze the neutronics of a solution-based-LEU SBS. Quasi-monoenergetic neutrons with an energy of approximately 2.5 MeV were generated by means of the D-D ( <math id="M1"><mrow><mmultiscripts><mtext>H</mtext><mprescripts/><mn>1</mn><mn>2</mn></mmultiscripts><mo>+</mo><mmultiscripts><mtext>H</mtext><mprescripts/><mn>1</mn><mn>2</mn></mmultiscripts><mo>→</mo><mmultiscripts><mtext>H</mtext><mprescripts/><mn>2</mn><mn>3</mn></mmultiscripts><mtext>e</mtext><mo>+</mo><mmultiscripts><mtext>n</mtext><mprescripts/><mn>0</mn><mn>1</mn></mmultiscripts></mrow></math> ) reaction in the central vacuum system (CVS). As indicated in Fig. 2 Fig. 2 , a GDT-FNS mainly includes a neutral beam injection system (NBI), CVS, magnetic coil (MC), and a high neutron flux region. The main parameters of the GDT-FNS with the D-D operation are listed in Table 2 Table 2 . Owing to the axisymmetric characteristics of GDT-FNS, SBSs with flexible settings can be arranged in the high neutron flux region to meet the increasing demand of 99 Mo production. * At the start of discharge when the plasma beta is near zero. 1 1 Parameters 1 1 Value 1 1 Total length of GDT-FNS (cm) 1 1 2000 1 1 Length of high neutron flux region (cm) 1 1 100 1 1 Plasma tube radius at high neutron flux region (cm) 1 1 35 1 1 Vacuum vessel radius at high neutron flux region (cm) 1 1 100 1 1 Magnetic field in center (T) 1 1 0.76 (0.94 * ) 1 1 Magnetic field in plug (T) 1 1 25.8 1 1 NBI power (MW) 1 1 50 1 1 NBI angle (°) 1 1 45 1 1 NBI energy (keV) 1 1 70 1 1 Gas feed rate (eq A) 1 1 4200 1 1 Peak fast ion density (m −3 ) 1 1 7×10 19 1 1 Bulk plasma density (m −3 ) 1 1 5×10 19 1 1 Electron temperature (eV) 1 1 1150 1 1 Bulk ion temperature (eV) 1 1 2340 1 1 Total neutron intensity of GDT-FNS (n/s) 1 1 9.04×10 15 1 1 Neutron intensity of high neutron flux region (n/s) 1 1 8.54×10 14 The plasma parameters of the GDT-FNS system were simulated using the 1-D code DOL [ 28 28 ], which is based on a nonstationary numerical model describing the confinement of two different plasma components. During the simulations, a pure deuterium beam was injected into the central vacuum chamber, and the axial distributions of the D-D neutron generation rate were obtained, as shown in Fig. 3 Fig. 3 . The results demonstrate two high neutron flux regions, which are between the −700–−600 cm and 600–700 cm axial positions of the GDT-FNS. This important finding is the main reason for arranging the SBS in the high neutron flux region. Subcritical Blanket System (SBS) 2 The SBS for the production of 99 Mo is arranged in the high neutron flux region of the GDT-FNS and forms a fan-shaped blanket structure. The main material components of the SBS include the LEU solution, solution container, reflector, and shielding layer. A schematic of the SBS 99 Mo production model is shown in Fig. 4 Fig. 4 . Based on the preliminary analysis and considering the FNS design constraints, certain geometrical and material parameters were fixed, such as the dimensions and specific material composition. The SBS was 100 cm long and less than 100 cm thick. The thickness of the LEU solution ranged between 30–50 cm, and the solid angle of the LEU solution relative to the central axis of the neutron source was between π/4-π/3. Thus, the variable parameters that need to be optimized for this study include the thicknesses of the LEU solution, reflector, and shielding, and the material types for the reflector and shielding layer. Considering the LEU solution, the UO 2 SO 4 solution was selected with varying U concentrations (60 g/L to 150 g/L), with a 235 U enrichment of 19.75%. The low margin (60 g/L) was selected to obtain a considerable output of 99 Mo, and the upper limit (150 g/L) was based on the saturated U (UO 2 SO 4 ) concentration at room temperature. Calculation Method 2 Calculation program and uncertainty 3 The neutronics parameters of the SBS were calculated using the Super Monte Carlo Simulation Program (SuperMC) version 3.2 [ 29 29 ] coupled with ENDF-VII cross-section libraries. Herein, the steady-state neutronics parameters of the SBS mainly included the k s , neutron energy spectrum, activity of the produced 99 Mo, and heat deposition. In this study, 10 million statistical particles were used for each neutronics calculation, and the corresponding statistical uncertainties were less than 1%, except for the calculations of the energy deposition, where the statistical uncertainties were less than 3%. Subcritical multiplication factor 3 The critical safety state of a subcritical system can be characterized by the k s when the fission system has an externally driven neutron source. Parameter k s is defined as the ratio of the fission neutron number to the total neutron number in the system [ 30 30 , 31 31 ], as shown in Eq. (1). <math display="block" id="M2"><mrow><msub><mi>k</mi><mtext>s</mtext></msub><mo>=</mo><mfrac><mrow><mi>W</mi><mi>v</mi></mrow><mrow><mi>W</mi><mi>v</mi><mo>+</mo><msub><mi>s</mi><mn>0</mn></msub></mrow></mfrac></mrow></math> Here, <math id="M3"><mrow><msub><mi>s</mi><mn>0</mn></msub></mrow></math> is the intensity of the externally driven neutron source [n/s], <math id="M4"><mi>W</mi></math> is the fission reaction rate [fission/s], and <math id="M5"><mi>v</mi></math> is the average number of neutrons generated by a fission reaction. The parameter k s is usually required to be less than 0.98 to ensure the operational safety of a subcritical system [ 32 32 - 36 36 32-36 ]. The calculation of k s was performed with a general source card (SDEF), where the energy spectrum was obtained from the first wall of the high neutron flux region of the GDT-FNS. The first wall neutron energy spectrum served as the external driver neutron source. Activity and specific activity of produced 99 Mo 3 To evaluate the efficiency of the 99 Mo production and usage rate of U, we defined the total activity of 99 Mo produced by the SBS in one day (24 h operation) as A [Ci/day], and the daily 99 Mo produced per unit mass of 235 U as the specific activity ( SA ) [Ci/kg/day]. The amount of produced 99 Mo is increased by 235 U fission and reduced by its own decay. Thus, the number of 99 Mo nuclides [N(t)] at time t [s] changes according to equation (2) as follows: <math display="block" id="M6"><mrow><mfrac><mrow><mtext>d</mtext><mi>N</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow><mrow><mtext>d</mtext><mi>t</mi></mrow></mfrac><mo>=</mo><mi>Y</mi><mtext>ΣΦ</mtext><mo>−</mo><mi>λ</mi><mi>N</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo></mrow></math> where <math id="M7"><mrow><mi>N</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></math> is the number of 99 Mo nuclides at time t [s], λ is the decay constant of 99 Mo, <math id="M8"><mi>Y</mi></math> is the fission yield of 99 Mo (0.061), Σ is the macroscopic fission cross-section of 235 U [barns], and Φ is the neutron flux [cm −2 ·s −1 ]. By defining <math id="M9"><mrow><mi>A</mi><mo>=</mo><mi>λ</mi><mi>N</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></math> and integrating Eq. (2), an activity Eq. (3) is obtained, which is consistent with the generalized activity equation[ 37 37 ]. <math display="block" id="M10"><mrow><mi>A</mi><mo>=</mo><mi>Y</mi><mtext>ΣΦ</mtext><mrow><mo>(</mo><mrow><mn>1</mn><mo>−</mo><msup><mi>e</mi><mrow><mo>−</mo><mi>λ</mi><mi>t</mi></mrow></msup></mrow><mo>)</mo></mrow></mrow></math> However, in an SBS, the activity equation can be modified to obtain Eq. (4) as follows: <math display="block" id="M11"><mrow><mi>A</mi><mo>=</mo><mi>Y</mi><msub><mi>N</mi><mtext>U</mtext></msub><msub><mi>σ</mi><mtext>f</mtext></msub><msub><mi>S</mi><mn>0</mn></msub><mrow><mo>(</mo><mrow><mn>1</mn><mo>−</mo><msup><mi>e</mi><mrow><mo>−</mo><mi>λ</mi><mi>t</mi></mrow></msup></mrow><mo>)</mo></mrow><mo>=</mo><mi>Y</mi><mfrac><mrow><msub><mi>N</mi><mtext>A</mtext></msub></mrow><mi>M</mi></mfrac><mi>m</mi><msub><mi>σ</mi><mtext>f</mtext></msub><msub><mi>S</mi><mn>0</mn></msub><mrow><mo>(</mo><mrow><mn>1</mn><mo>−</mo><msup><mi>e</mi><mrow><mo>−</mo><mi>λ</mi><mi>t</mi></mrow></msup></mrow><mo>)</mo></mrow></mrow></math> In this case, the neutron flux ( Φ ) is replaced with <math id="M12"><mrow><msub><mi>S</mi><mn>0</mn></msub></mrow></math> , that is, the external neutron source intensity [n/s] from the high neutron flux region of the GDT-FNS. Σ is equal to <math id="M13"><mrow><msub><mi>N</mi><mtext>U</mtext></msub><msub><mi>σ</mi><mtext>f</mtext></msub></mrow></math> , where <math id="M14"><mrow><msub><mi>σ</mi><mtext>f</mtext></msub></mrow></math> [barns] is the average micr oscopic fission cross-section of a 235 U atom. <math id="M15"><mrow><msub><mi>N</mi><mi>U</mi></msub></mrow></math> is the total number of 235 U atoms in the SBS, which is equal to <math id="M16"><mrow><msub><mi>N</mi><mtext>A</mtext></msub><mi>m</mi><mo>/</mo><mi>M</mi></mrow></math> , where <math id="M17"><mrow><msub><mi>N</mi><mtext>A</mtext></msub></mrow></math> is the Avogadro constant (6.02×10 23 ), M is the relative atomic mass of 235 U equal to 235, and m is the mass of 235 U[g] in the LEU solution. In this study, <math id="M18"><mrow><msub><mi>σ</mi><mtext>f</mtext></msub></mrow></math> was calculated by setting the tally 4 card and multiplier card FM4 in the input file. Therefore, by substituting the <math id="M19"><mrow><msub><mi>σ</mi><mtext>f</mtext></msub></mrow></math> values into Eq. (4), the daily production of 99 Mo in SBS can be evaluated. Neutron and gamma flux calculation 3 The neutron and gamma flux can be calculated with a tally 4 [ 38 38 ] card by setting the different particle types [Neutron (N) or Photon (P)] using Eq. (5): <math display="block" id="M20"><mrow><msub><mo>∅</mo><mtext>p</mtext></msub><mo>=</mo><mo>∫</mo><mtext>d</mtext><mi>E</mi><mo>∫</mo><mtext>d</mtext><mi>t</mi><mo>∫</mo><mtext>dΩ</mtext><mi>φ</mi><mrow><mo>(</mo><mrow><mover accent="true"><mi>r</mi><mo>→</mo></mover><mo>,</mo><mover accent="true"><mi>Ω</mi><mo>^</mo></mover><mo>,</mo><mi>E</mi><mo>,</mo><mi>t</mi></mrow><mo>)</mo></mrow><mo>,</mo></mrow></math> where <math id="M21"><mrow><msub><mo>∅</mo><mtext>p</mtext></msub></mrow></math> is the neutron or gamma flux of the point detector [particles/cm 2 ], ( <math id="M22"><mover accent="true"><mi>r</mi><mo>→</mo></mover></math> , <math id="M23"><mover accent="true"><mi>Ω</mi><mo>^</mo></mover></math> ,E,t) is the angular flux [particles/(cm 3 /sh/MeV/rad)], <math id="M24"><mover accent="true"><mi>r</mi><mo>→</mo></mover></math> is the position vector [cm], E is the energy of the incident particle [MeV] , <math id="M25"><mtext>Ω</mtext></math> is the direction vector, and <math id="M26"><mi>t</mi></math> is time [sh;1sh = 10 −8 s]. To evaluate the neutron flux distribution of the SBS, the heterogeneous coefficient K H is introduced. This is defined as the ratio of the maximum value of the core thermal neutron flux to the average value. K H is generally required to be less than 1.4 in a design [ 39 39 ]. Nuclear heat deposition 3 The nuclear heat deposition was calculated using a tally 6 card (T6) combined with a superimposed mesh tally card (FMESH). The calculation result for T6 is the average energy deposition on the calculated cell, as shown in Eq. (6) [ 38 38 ]. <math display="block" id="M27"><mrow><msub><mi>H</mi><mtext>t</mtext></msub><mo>=</mo><mfrac><mrow><msub><mi>ρ</mi><mi>a</mi></msub></mrow><mi>m</mi></mfrac><mo>∫</mo><mtext>d</mtext><mi>E</mi><mo>∫</mo><mtext>d</mtext><mi>t</mi><mo>∫</mo><mtext>d</mtext><mi>V</mi><mo>∫</mo><mtext>dΩ</mtext><msub><mi>σ</mi><mtext>t</mtext></msub><mrow><mo>(</mo><mi>E</mi><mo>)</mo></mrow><mi>H</mi><mrow><mo>(</mo><mi>E</mi><mo>)</mo></mrow><mtext>φ</mtext><mrow><mo>(</mo><mrow><mover accent="true"><mi>r</mi><mo>→</mo></mover><mo>,</mo><mover accent="true"><mi>Ω</mi><mo>^</mo></mover><mo>,</mo><mtext>E</mtext><mo>,</mo><mtext>t</mtext></mrow><mo>)</mo></mrow><mo>,</mo></mrow></math> where <math id="M28"><mrow><msub><mi>H</mi><mtext>t</mtext></msub></mrow></math> is the total energy deposition in the cell [MeV/g], <math id="M29"><mrow><msub><mi>ρ</mi><mtext>a</mtext></msub></mrow></math> is the atom density (10 24 atoms/cm 3 ), m is the cell mass [g], <math id="M30"><mrow><msub><mi>σ</mi><mtext>t</mtext></msub><mrow><mo>(</mo><mi>E</mi><mo>)</mo></mrow></mrow></math> is the microscopic total cross section [barns], and H ( E ) is the heating number [MeV/collision]. Results and Discussion 1 Neutron Spectrum of the High Neutron Flux Region of GDT-FNS 2 The neutron spectrum is a significant parameter of GD-FNS, which can affect the fission reaction efficiency. In this study, the neutron generation rate ( Fig. 3 Fig. 3 ) was used as the input data to calculate the neutron spectrum. The neutron spectrum of the plasma tube in the high-neutron-generation-rate region was obtained using the SuperMC program. The statistical error of the calculated neutron spectrum was ensured to be less than 1%. The spectral distributions are shown in Fig. 5 Fig. 5 . The results demonstrated that neutrons with an energy of approximately 2.5 MeV had the highest proportion, which is owing to the D-D reaction producing neutrons with an average energy of 2.5 MeV. In the subsequent neutronics design of the SBS, the calculated neutron spectrum is used as the external driver neutron source. Preliminary Design of the SBS 2 The 99 Mo production by the SBS aims to achieve 50% of China's projected 99 Mo demand by 2025. China's current 99 Mo heavily relies on imports, as demand continues to grow. China's demand for medical 99 Mo was estimated to be approximately 16000 6-day Ci in 2019 [ 40 40 ]. Considering an annual growth rate of 5% [ 5 5 ], the estimated 99 Mo demand in 2025 will be approximately 21500 6-day Ci (i.e., 59 6-day per day). Determining these estimates requires the consideration of the decay losses during the separation and purification of the generated 99 Mo. Approximately 80% of the originally produced 99 Mo is lost during the 6-day period. However, approximately 10% [ 41 41 ] of the 99 Mo cannot be extracted by chemical separation and purification processes. Therefore, the daily 99 Mo demand is estimated to be 298 Ci in 2025 and 447 Ci in 2035. When determining the preliminary design of the SBS, the following constraints were considered: 1) To ensure the nuclear critical safety of the LEU solution SBS, k s must be less than 0.98 [ 32 32 - 36 36 32-36 ]. However, considering the neutron source fluctuation and measurement uncertainty, as well as other uncertain factors, k s was limited to less than 0.97 to provide sufficient critical safety margins. 2) The U concentration was limited to range between 60–150 g/L. The upper limit, as indicated in the earlier sections, is owing to the saturation of UO 2 SO 4 at 150 g/L. 3) The SA should be as high as possible. The initial conditions for the calculation models were set as follows: the inner diameter of the plasma tube was 35 cm, the inner and outer radii of the LEU solution were between 37–74 cm, the thickness of the LEU solution container wall was 1 cm, the solid angle of the LEU solution was betweenπ/4–π/3, and the thickness of the top and bottom reflectors was 5 cm. The back reflector was composed of a Be material with a thickness of 8 cm. There was a shielding thickness of 8 cm for materials composed of W, B, and polyethylene (PE) (Mass ratio 4:3:3). Different parameters of k s , A , and SA , were calculated by changing the U concentration and solid angle. The corresponding calculation results are listed in Table 3 Table 3 . Note: A is the daily 99 Mo production of one SBS; SA is the specific activity (daily 99 Mo production of 1 kg 235 U). 1 1 Case 1 1 Solid angle (rad) 1 1 U concentration(g·L −1 ) 1 1 LEU volume (L) 1 1 235 U mass (kg) 1 1 k s 1 1 A (Ci) 1 1 SA (Ci·kg −1 ) 1 1 1 1 1 π/4 1 1 100 1 1 145.2 1 1 2.904 1 1 0.9465 1 1 92.5 1 1 31.9 1 1 2 1 1 π/4 1 1 105 1 1 145.2 1 1 3.049 1 1 0.9671 1 1 130 1 1 42.6 1 1 3 1 1 5π/18 1 1 95 1 1 161.3 1 1 3.065 1 1 0.9410 1 1 91.7 1 1 29.9 1 1 4 1 1 5π/18 1 1 100 1 1 161.3 1 1 3.226 1 1 0.9612 1 1 125 1 1 38.7 1 1 5 1 1 5π/18 1 1 105 1 1 155.5 1 1 3.266 1 1 0.9681 1 1 156 1 1 47.8 1 1 6 1 1 π/3 1 1 95 1 1 193.5 1 1 3.677 1 1 0.9576 1 1 143 1 1 38.9 As shown in Table 4 Table 4 , the k s of case 5 satisfies the critical safety condition (less than 0.97), and the A is 156 C i . This activity is close to the 50% medical 99 Mo demand for the projected Chinese market by 2025 (149 Ci). In addition, the SA of case 5 is the largest, indicating that the 235 U use is also the most efficient compared to the other cases. Based on the results in Table 4 Table 4 , case 5 was selected as the preliminary scheme for the subsequent optimization design, including optimizing the U concentration, and the material types and sizes of the reflector and shielding. 1 1 Zone 1 1 Length (cm) 1 1 Thickness (cm) 1 1 Material 1 1 Plasma at SBS 1 1 90 1 1 35 1 1 D 1 1 Plasma tube 1 1 90 1 1 1 1 1 Fe 1 1 LEU solution 1 1 90 1 1 36 1 1 UO 2 SO 4 aqueous solution, 235 U enrichment: 19.75%, U concentration 105g/L 1 1 LEU solution container 1 1 90 1 1 1 1 1 Fe 1 1 Reflector 1 1 Back reflector 1 1 90 1 1 8 1 1 Be 1 1 Top & bottom reflector 1 1 54 1 1 5 1 1 Side reflector 1 1 90 1 1 8 1 1 Shielding layer 1 1 90 1 1 15 1 1 W/B/PE 1 1 Parameters 1 1 Value 1 1 k s 1 1 0.9685 1 1 SA 1 1 48 Ci/day·kg 1 1 Yield of 99 Mo 1 1 157 Ci/day 1 1   1 1   The Impact of Uranium Concentration on the SBS 2 To study the influence of various U concentrations on the performance of the SBS 99 Mo production, the conditions of case 5 shown in Table 4 Table 4 were selected for the detailed calculations with varying U concentrations. The volume of the LEU solution was set at 155.5 L, while the 235 U enrichment was fixed at 19.75%. The distribution of the varying U concentrations, the corresponding changes in the neutron multiplication factor k s , and the daily 99 Mo production A are shown in Fig. 6 Fig. 6 . Based on the results shown in Fig. 6 Fig. 6 , there is a general increasing dependence of both k s and A on the increasing U concentration. In particular, the following can be deduced:1) As expected, the value of k s demonstrates a strong dependence on the U concentration because it sharply increases as the U concentration increases. However, note that at a U concentration of 110 g/L, the k s exceeds the design safety limit of 0.97. 2) Conversely, while the daily 99 Mo production A increases gently with an increasing U concentration, there is a sharp increase when the U concentration is above 90 g/L. 3) The most favorable condition in terms of the design nuclear critical safety is when the U concentration is just below 105 g/L, where k s is less than 0.97. Therefore, the U concentration was set to 105 g/L in the final design model. Optimal Design of Reflector 2 The reflector is arranged on the outside of the LEU solution and can reflect the neutrons back into the U solution to minimize neutron leakage and improve the use of neutrons. The selection of the reflector material and size has an important influence on the efficiency of the 99 Mo production and its associated k s . The commonly used reflectors are Be metal, BeO, graphite (GR), heavy water (D 2 H), zirconia (ZrO 2 ), among others. In this section, case 5 is adopted for the calculation, and the thickness of the back reflector is set to 8 cm, while the other parameters remain unchanged. The values of k s were calculated by changing the reflector materials, the results of which are shown in Fig. 7 Fig. 7 . The k s values obtained using different reflector materials demonstrate a maximum value for the case of Be as a reflector, which indicates that Be presents the best reflector effect for the selected conditions. Therefore, Be was selected as the reflective material for the SBS design. The subsequent optimization (calculation) process for k s and A was performed by changing the thickness of the Be reflector. The results are shown in Fig. 8 Fig. 8 . The calculation results demonstrate that the values of k s and A increase as the thickness of the Be reflector increases. This trend emphasizes the beneficial effect of neutron use in SBS, with a corresponding benefit to the 99 Mo production. In addition, the optimum thickness of the Be reflector is approximately 10 cm; beyond 10 cm, only a marginal increase in A is observed with a relatively significant increase in k s . Thus, to benefit from the capital cost of the reflector material, minimizing the geometric dimension of the entire SBS while improving the critical safety, a reflector thickness of 10 cm was plausible. Shielding Layer Optimization Design 2 A shielding layer was used to reduce the neutrons and gamma radiation in the environment. Different shielding materials have varying shielding abilities for neutrons and gamma-rays. Eight types of materials were selected for the shielding study to reasonably select the material and thickness of the shielding layer; eight types of materials were chosen for the shielding study. The eight types of materials were Fe, Pb, W, Fe/B (weight ratio 1:1), W/B (weight ratio 1:1), Fe/PE (weight ratio 1:1), W/PE (weight ratio 1:1), and W/B/PE (weight ratio 4:3:3). The shielding performances of the different materials were evaluated with a thickness of 8 cm. The corresponding k s values and average neutron fluxes outside the shielding layer were calculated. The results and their distributions are shown in Fig. 9 Fig. 9 . The results demonstrate that the different shielding materials have little influence on the k s value, that is, the difference between the maximum (0.9695) and minimum values (0.9667) is only 0.0028, as shown in Fig. 9 Fig. 9 . This indicates that W/B/PE had the best shielding effect for neutrons, which is expected because B has a very good thermal neutron absorption ability; PE is a good neutron moderator, while W, Fe, and Pb, have good gamma shielding. Overall, considering the shielding performance of the material against the neutrons and gamma rays and avoiding the toxic lead material, the composite material of W/B/PE was selected as the shielding material. The influence of the varying W/B/PE thicknesses on k s and the shielding performance were further studied. The calculation results are shown in Fig. 10 Fig. 10 , which demonstrate that k s presents no significant change as the shielding thickness increases because the shielding material contains B, which absorbs neutrons. However, the average neutron flux and gamma flux outside the shielding layer decrease with an increase in the thickness of the shielding material. According to the requirements of the shielding design, to limit the radiation impact from thermal neutron-activated products, the thermal neutron flux should be less than 1×10 5 cm −2 ·s −1 , and the gamma flux should be less than 4×10 10 cm −2 ·s −1 [ 42 42 , 43 43 ]. The results demonstrate that when the thickness of W/B/PE is 15 cm, the average neutron flux outside the shielding layer is 4.31×10 4 cm −2 ·s −1 , whereas the average gamma flux is 2.10×10 7 cm −2 ·s −1 with k s = 0.9685. These values meet the requirements of shield design and nuclear critical safety margin. Neutron Flux Distribution of SBS 2 The radial and axial neutron flux distributions of the SBS were calculated, the results of which are shown in Fig. 11 (a) and (b) Fig. 11 (a) and (b) , respectively, demonstrating that the neutron flux in the U fission zone is of the order of 10 11 n/cm 2 ·s (average of 3.73 ×10 11 n/cm 2 .s; peak value of 4.94 ×10 11 n/cm 2 ·s). In addition, the neutron flux rapidly decreases after exiting the reflector layer (i.e., in the shielding layer). This sharp decrease confirms the effectiveness of the shielding materials indicated in the previous sections. In the axial direction, the neutron flux remains constant across the U solution, whereas the neutron flux at both ends of the reflector layer sharply decreases. The average neutron flux was calculated to be 3.88×10 11 n/cm 2 ·s and the maximum neutron flux was 4.72×10 11 n/cm 2 ·s. As defined in Section 2.4.4, K H can be calculated as 4.72×10 11 /3.88×10 11 = 1.22, which meets the design requirements (K H needs to be less than 1.4). This demonstrates that the radial and axial neutron flux distributions in the SBS are relatively uniform, which is beneficial for the efficient use of 235 U and the safe operation of the system. The neutron energy spectrum characteristics of the U solution layer, outer U container, reflector layer, and shielding layer were calculated as shown in Fig. 12 Fig. 12 . The results demonstrate that there are two thermal neutron peaks in the thermal neutron region (10 −8 –10 −6 MeV) and a fast neutron peak (approximately 2.5 MeV). The two thermal neutron peaks are owed to the H 2 O in the U solution, which served as a neutron moderator. This moderation causes many neutrons to be moderated into thermal neutrons. The fast neutron peak appears because the external neutrons driving the SBS are mainly the 2.5 MeV neutrons (D-D reaction neutrons). In addition, fast neutrons were produced by the fission of 235 U. Nuclear Heat Distribution of SBS 2 To obtain the distribution of the nuclear heat in each component of the SBS, a tally card (T6) combined with FMESH was used to calculate the nuclear heat deposition. The visualization function of the SuperMC code was used to display the results, as shown in Fig. 13 (a) and (b) Fig. 13 (a) and (b) . The results demonstrate that the nuclear heat is mainly deposited in the LEU solution, with a maximum nuclear heat of 1.53×10 −1 W/cm 3 at the central position. The minimum nuclear heat was determined to be 4.57×10 −3 W/cm 3 at the edge position. The average nuclear heat was 7.01×10 −2 W/cm 3 , and the total nuclear heat was 10.9 kW. The average nuclear heat in the reflector layer was found to be 1.21×10 −4 W/cm 3 , while the average nuclear heat in the shielding layer was 5.57×10 −5 W/cm 3 . The nuclear heats of the reflector and shielding layers were approximately 2–3 orders of magnitude lower than that of the LEU solution. This is because the nuclear heat mainly arises from the fission energy generated by the fission of 235 U, and the nuclear heat of the reflector and shielding layers is mainly from neutrons and gamma radiation energy deposition, which is significantly lower than the fission energy. COMSOL [ 44 44 ] was used to simulate the cooling system; according to the simulation results, the fuel solution may boil within 2 h if a cooling system is not added. The simulation results also demonstrate that a supplied inlet H 2 O coolant temperature of 22 °C and flow velocity of 1.0 m/s will be sufficient to maintain the fuel solution temperature below 90 °C. Based on the aforementioned analysis, the optimized design results for the 99 Mo production by SBS driven by GDT-FNS are listed in Table 4 Table 4 . Conclusion 1 In this study, an LEU SBS driven by GDT-FNS for 99 Mo production was proposed. A neutronics analysis of the 99 Mo production system was conducted using the Monte Carlo method (SuperMC code). The neutronics analysis includes the calculation of the neutron spectrum in the region of the high neutron generation rate of the GDT-FNS. The analysis also covers the preliminary design and optimization assessments related to different U concentrations and their 99 Mo production activities. Other analyses include the optimization design of the reflector and shielding layer, neutron flux, and the nuclear heat distribution of the SBS. In all optimization cases, the designed system must meet the safety requirements and the amount of 99 Mo production necessary to meet 50% of China's projected 99 Mo demand in 2025. The preliminary assessment, as shown in case 5 in Table 4 Table 4 , demonstrated the most favorable conditions, where the U concentration was 105 g/L for an LEU solution of 155.5 volume/L with a mass of 3.266 kg and a subcritical multiplication factor of 0.9681. A further analysis was performed by placing the upper limit of the LEU solution volume at 155.5 and varying the mass of the LEU (19.75% enrichment) in the solution. The distribution was compared with the daily 99 Mo production and its impact on the subcritical multiplication factor. Based on this analysis, the most favorable condition in terms of the designed nuclear critical safety was a U concentration of 105 g/L for  a k s value near 0.97. Other analyses included shielding and reflector material selection and design optimization. Calculations demonstrated that Be (10 cm thick) and W/B/PE (15 cm thick) were suitable for serving as the reflector and shielding layers. The main optimized parameters are summarized as follows: 1. The optimal value for the subcritical multiplication factor (k s ) for the designed SBS was 0.9685, while the average neutron flux and gamma flux outside the shielding layer were found to be 4.31×10 4 n/cm 2 s and 2.10×10 7 n/cm 2 s, respectively. The distribution of the neutron flux and nuclear heating in the SBS were relatively uniform, as indicated by the K H -value of 1.12, which further ensures the enhanced operational safety of the system. 2. The SBS allows for a high 235 U use, that is, 48 Ci 99 Mo can be produced from 1 kg of 235 U. 3. A total of 157 Ci 99 Mo can be produced by one SBS per day. Because the GDT-FNS is an axisymmetric structure and the solid angle of the SBS is only 5π/18, multiple SBSs can be simultaneously arranged in the high neutron flux region of the GDT-FNS. According to the calculations, two and three of the SBSs designed in this study for the 99 Mo production can meet the demand of the Chinese market by 2025 and 2035, respectively. 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Tech. 2020 , 31 ( 12 ): 115 ( 2020 ). doi: 10.1007/s41365-020-00833-3 http://doi.org/10.1007/s41365-020-00833-3 Simulation of a molten salt fast reactor using the COMSOL multiphysics software The conception and design were originally proposed by Yun-Cheng Han, to which all authors contributed. The material preparation, data collection, and analysis, were performed by Hou-Hua Xiong, Qiu-Sun Zeng, and Yun-Cheng Han. The first draft of this manuscript was written by Hou-Hua Xiong. All authors have commented on all versions of the manuscript, and have read and approved the final manuscript. The authors thank Dr. Vadim Prikhodko from Budker Institute of Nuclear Physics, Russian Academy of Sciences (BINP RAS) for his suggestions on the GDT-FNS plasma parameters. 10.1007/s41365-023-01206-2 This study was supported by Anhui Provincial Key R&D Program (202104g0102007), Hefei Municipal Natural Science Foundation (2022011), Collaborative Innovation Program of Hefei Science Center, Chinese Academy of Sciences (2022HSC-CIP024) and International Partnership Program of Chinese Academy of Sciences (116134KYSB20200001). 2022-11-18 2023-02-09 2023-02-11 2023-04-17 2023-06-07 © 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. 2023 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/s41365-023-01206-2 http://dx.doi.org/10.1007/s41365-023-01206-2 . Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. 2023 38407953 The data that support the findings of this study are openly available in Science Data Bank at https://www.doi.org/10.57760/sciencedb.07299 and http://resolve.pid21.cn/31253.11.sciencedb.07299 Data Availability Statement Nuclear Science and Techniques 4 34