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

Hou-Hua Xiong ·Qiu-Sun Zeng ·Yun-Cheng Han ·Lei Ren ·Isaac Kwasi Baidoo ·Ni Chen ·Zheng-Kui Zeng ·Xiao-Yu Wang,

Abstract Gamma-emitting radionuclide 99mTc 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 99mTc (T1/2 = 6 h)makes it difficult to store or transport.Thus, the production of 99mTc is tied to its parent radionuclide 99Mo (T1/2 = 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 99Mo production design was developed based on a deuterium-deuterium (D-D) gas dynamic trap fusion neutron source (GDTFNS) 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 99Mo production.We provide a Monte Carlo-based neutronics analysis covering the calculation of the subcritical multiplication factor (ks) of the SBS, optimization design for the reflector, shielding layer, and 99Mo 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 (ks ＜ 0.97) and maintained a high 99Mo production capacity.The proposed system can generate approximately 157 Ci 99Mo for a stable 24 h operation with a neutron intensity of 1 × 1014 n/s,which can meet 50% of China’s demand in 2025.

Keywords Gas dynamic trap ·Fusion neutron source ·Molybdenum-99 ·Low-enriched uranium ·Subcritical blanket system

1 Introduction

According to the World Nuclear Energy Association (WNA)[1], over 10,000 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 which99mTc 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 of99mTc constitutes approximately 80% of nuclear medicine procedures, while 85% are used for diagnostic scans (Updated April 2022) [1].However, the production of99mTc (T1/2= 6 h) is tied to its mother radionuclide99Mo (T1/2= 66 h), which makes the study of99Mo production an essential research topic.

Fig.1 Schematic diagram of the 99mTc production process

The production of99mTc consists of two steps: (1) production of99Mo via mechanisms indicated in the schematic diagram of Fig.1 (neutron-fission, gamma-fission, neutrongamma, gamma-neutron, etc.) and (2) separation of99mTc after it decays from99Mo through the emission of beta particles [2].As indicated,99Mo and99mTc have short half-lives.Nonetheless, unlike the relatively short half-life of99mTc(T1/2= 6 h), which is the main hindrance for its transport, the half-life of99Mo (T1/2= 66 h) allows a relatively adequate time for transportation.Based on the half-life and transport time, the kinetics of producing99mTc depend on the production of99Mo; that is, under normal circumstances, the resulting product99Mo is transported to the target country immediately after production, and subsequently its decayed product (99mTc) is quickly extracted and used in hospitals or nuclear medical centers.

The global shortage of99Mo has recently been mainly attributed to aging nuclear reactors and their decommissioning [3-5].A typical example is the event of the National Research Universal (NRU) in Canada, which produced approximately 40% of the world’s99Mo supply but ceased production by October 31st, 2016 [3].Currently, most99Mo 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].Additional information regarding99Mo production, specific reactors, and target materials are listed in Table 1.Most of these reactors are not only facing the problems of aging and decommissioning,but also pose great risks of nuclear proliferation.

To solve the problems of99Mo shortage and the nuclear proliferation of HEU targets, scientists have proposed a series of new methods to replace the path of HEU fission to produce99Mo.These methods can be divided into three categories: (1)235U(n, f)99Mo reaction in LEU reactors [7, 8]; (2)solid target irradiation based on an accelerator, such as the neutron capture98Mo(n, γ)99Mo reaction [9-13],100Mo(n,2n)99Mo reaction [14, 15],100Mo(p, 2n)99Mo reaction [16],100Mo(γ, n)99Mo reaction [17], and photon-induced reaction of238U fission238U(γ, f)99Mo [18]; and 3) LEU solution fission of the235U(n, f)99Mo reaction in subcritical systems[19-23].Among these, the last method is the most efficient and reliable means of production and has become a prime choice for99Mo 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.

Table 1 Main 99Mo production reactors[6]

In 2021, Han et al.[22, 23] proposed a subcritical99Mo 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 of235U via the235U(n,f)99Mo 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 for99Mo 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 in235U.In addition to the apparent advantage of avoiding the HEU system, our proposed99Mo 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 SBS99Mo 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 (ks), 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.

2 Model and method

The LEU solution SBS driven by GDT-FNS mainly includes GDT-FNS and a99Mo SBS, as shown in the schematic diagram in 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 Sects.2.1 and 2.2.

Fig.2 (Color online) Schematic diagram of the LEU solution SBS driven by GDT-FNS

2.1 Gas dynamic trap-based fusion neutron source(GDT-FNS)

A GDT is a type of axisymmetric magnetic mirror device[24, 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, 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 (12H+12H →23He+01n )reaction in the central vacuum system (CVS).As indicated in Fig.2, a GDT-FNS mainly includes a neutral beam injection system (NBI), CVS, magnetic coil (MC), and a highneutron flux region.The main parameters of the GDT-FNS with the D-D operation are listed in 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 of99Mo production.

Table 2 Main parameters of GDT-FNS with D-D operation

Fig.3 The axial distribution of the D-D neutron generation rate of GDT-FNS

The plasma parameters of the GDT-FNS system were simulated using the 1-D code DOL [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.The results demonstrate two high-neutron flux regions, which are between - 700 to - 600 cm and 600 to700 cm axial positions of the GDT-FNS.This important finding is the main reason for arranging the SBS in the high-neutron flux region.

2.2 Subcritical blanket system (SBS)

The SBS for the production of99Mo is arranged in the highneutron 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 SBS99Mo production model is shown in 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 UO2SO4solution was selected with varying U concentrations (60 to 150 g/L),with a235U enrichment of 19.75%.The low margin (60 g/L)was selected to obtain a considerable output of99Mo, and the upper limit (150 g/L) was based on the saturated U(UO2SO4) concentration at room temperature.

Fig.4 (Color online) Schematic structure diagram of SBS

2.3 Calculation method

2.3.1 Calculation program and uncertainty

The neutronics parameters of the SBS were calculated using the Super Monte Carlo Simulation Program (SuperMC) version 3.2 [29] coupled with ENDF-VII cross-sectional libraries.Herein, the steady-state neutronics parameters of the SBS mainly included theks, neutron energy spectrum, activity of the produced99Mo, 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%.

2.3.2 Subcritical multiplication factor

The critical safety state of a subcritical system can be characterized by thekswhen the fission system has an externally driven neutron source.Parameterksis defined as the ratio of the fission neutron number to the total neutron number in the system [30, 31], as shown in Eq.(1).

Here,s0is the intensity of the externally driven neutron source [n/s],Wis the fission reaction rate [fission/s], andvis the average number of neutrons generated by a fission reaction.The parameterksis usually required to be less than 0.98 to ensure the operational safety of a subcritical system[32-36].The calculation ofkswas 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.

2.3.3 Activity and specific activity of produced 99Mo

To evaluate the efficiency of the99Mo production and usage rate of U, we defined the total activity of99Mo produced by the SBS in one day (24 h operation) asA[Ci/day], and the daily99Mo produced per unit mass of235U as the specific activity (SA) [Ci/kg/day].The amount of produced99Mo is increased by235U fission and reduced by its own decay.Thus, the number of99Mo nuclides [N(t)] at timet[s] changes according to Eq.(2) as follows:

whereN(t) is the number of99Mo nuclides at timet[s], λ is the decay constant of99Mo,Yis the fission yield of99Mo(0.061), Σ is the macroscopic fission cross section of235U[barns], andΦis the neutron flux [cm-2s-1].

By definingA=λN(t) and integrating Eq.(2), an activity Eq.(3) is obtained, which is consistent with the generalized activity equation[37].

However, in an SBS, the activity equation can be modified to obtain Eq.(4) as follows:

In this case, the neutron flux (Φ) is replaced withS0, that is, the external neutron source intensity [n/s] from the highneutron flux region of the GDT-FNS.Σ is equal toNUσf,whereσf[barns] is the average microscopic fission cross section of a235U atom.NUis the total number of235U atoms in the SBS, which is equal toNAm∕M, whereNAis the Avogadro constant (6.02 × 1023),Mis the relative atomic mass of235U equal to 235, andmis the mass of235U [g] in the LEU solution.

In this study,σfwas calculated by setting the tally 4 card and multiplier card FM4 in the input file.Therefore, by substituting theσfvalues into Eq.(4), the daily production of99Mo in SBS can be evaluated.

2.3.4 Neutron and gamma flux calculation

The neutron and gamma flux can be calculated with a tally 4 [38] card by setting the different particle types [Neutron(N) or Photon (P)] using Eq.(5):

where ∅pis the neutron or gamma flux of the point detector[particles/cm2], (→r,^Ω,E,t) is the angular flux [particles/(cm3/sh/MeV/rad)],→ris the position vector [cm], E is the energy of the incident particle [MeV], Ω is the direction vector,andtis time [sh; 1sh = 10-8s].To evaluate the neutron flux distribution of the SBS, the heterogeneous coefficientKHis introduced.This is defined as the ratio of the maximum value of the core thermal neutron flux to the average value.KHis generally required to be less than 1.4 in a design [39].

2.3.5 Nuclear heat deposition

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].

whereHtis the total energy deposition in the cell [MeV/g],ρais the atom density (1024atoms/cm3),mis the cell mass[g],σt(E) is the microscopic total cross section [barns], andH(E) is the heating number [MeV/collision].

3 Results and discussion

3.1 Neutron spectrum of the high-neutron flux region of GDT-FNS

The neutron spectrum is a significant parameter of GDFNS, which can affect the fission reaction efficiency.In this study, the neutron generation rate (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.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.

3.2 Preliminary design of the SBS

Fig.5 Neutron spectrum in the high-neutron flux region

The99Mo production by the SBS aims to achieve 50% of China’s projected99Mo demand by 2025.China's current99Mo heavily relies on imports, as demand continues to grow.China’s demand for medical99Mo was estimated to be approximately 16,000 6-day Ci in 2019 [40].Considering an annual growth rate of 5% [5], the estimated99Mo demand in 2025 will be approximately 21,500 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 generated99Mo.Approximately 80% of the originally produced99Mo is lost during the 6-day period.However, approximately 10% [41] of the99Mo cannot be extracted by chemical separation and purification processes.Therefore, the daily99Mo 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,ksmust be less than 0.98 [32-36].However, considering the neutron source fluctuation and measurement uncertainty, as well as other uncertain factors,kswas 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 UO2SO4at 150 g/L.3) TheSAshould 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 between π/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 ofks,A, andSAwere calculated by changing the U concentration and solid angle.The corresponding calculation results are listed in Table 3.

As shown in Table 4, theksof case 5 satisfies the critical safety condition (less than 0.97), and theAis 156 Ci.This activity is close to the 50% medical99Mo demand for the projected Chinese market by 2025 (149 Ci).In addition, theSAof case 5 is the largest, indicating that the235U use is also the most efficient compared to the other cases.Based on the results in 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.

3.3 The Impact of Uranium Concentration on the SBS

To study the influence of various U concentrations on the performance of the SBS99Mo production, the conditions of case 5 shown in 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 the235U enrichment was fixed at 19.75%.The distribution of the varying U concentrations, the corresponding changes in the neutron multiplication factorks, and the daily99Mo productionAare shown in Fig.6.

Based on the results shown in Fig.6, there is a general increasing dependence of bothksandAon the increasingU concentration.In particular, the following can be deduced: (1) As expected, the value ofksdemonstrates 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, theksexceeds the design safety limit of 0.97.(2) Conversely,while the daily99Mo productionAincreases 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,whereksis less than 0.97.Therefore, the U concentration was set to 105 g/L in the final design model.

Table 3 Preliminary calculation results of the different SBS design parameters (cases 1-6)

Table 4 Final optimized design and parameters of 99Mo production SBS

Fig.6 The impact of varying the U concentration (enrichment of 19.75% and solution volume of 155.5 L) on the distribution of ks and A

Fig.7 Variations in ks using different reflector materials

3.4 Optimal design of reflector

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 the99Mo production and its associatedks.The commonly used reflectors are Be metal,BeO, graphite (GR), heavy water (D2H), zirconia (ZrO2),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 ofkswere calculated by changing the reflector materials, the results of which are shown in Fig.7.

Theksvalues 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 forksandAwas performed by changing the thickness of the Be reflector.The results are shown in Fig.8.

The calculation results demonstrate that the values ofksandAincrease as the thickness of the Be reflector increases.This trend emphasizes the beneficial effect of neutron use in SBS, with a corresponding benefit to the99Mo production.In addition, the optimum thickness of the Be reflector is approximately 10 cm; beyond 10 cm, only a marginal increase inAis observed with a relatively significant increase inks.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.

3.5 Shielding layer optimization design

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 correspondingksvalues and average neutron fluxes outside the shielding layer were calculated.The results and their distributions are shown in Fig.9.

Fig.8 ks and A values varying with the thickness of the Be reflector

Fig.9 Distributions of ks and the average neutron flux (outside the shielding layer) varying with different shielding materials

The results demonstrate that the different shielding materials have little influence on theksvalue, that is, the difference between the maximum (0.9695) and minimum values (0.9667) is only 0.0028, as shown in 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 onksand the shielding performance were further studied.The calculation results are shown in Fig.10, which demonstrate thatkspresents 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.

Fig.10 The neutron flux and gamma flux outside the shielding layer and ks varying with the thickness of the W/B/PE 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 × 105cm-2s-1, and the gamma flux should be less than 4 × 1010cm-2s-1[42, 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 × 104cm-2s-1,whereas the average gamma flux is 2.10 × 107cm-2s-1withks= 0.9685.These values meet the requirements of shield design and nuclear critical safety margin.

3.6 Neutron flux distribution of SBS

The radial and axial neutron flux distributions of the SBS were calculated, the results of which are shown in Fig.11a and b, respectively, demonstrating that the neutron flux in the U fission zone is of the order of 1011n/cm2·s (average of 3.73 × 1011n/cm2·s; peak value of 4.94 × 1011n/cm2·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 × 1011n/cm2·s and the maximum neutron flux was 4.72 × 1011n/cm2·s.As defined in Sect.2.4.4,KHcan be calculated as 4.72 × 1011/3.88 × 1011= 1.22, which meets the design requirements (KHneeds 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 of235U and the safe operation of the system.

Fig.11 a Radial neutron flux distribution of SBS; b axial neutron flux distribution of SBS

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.The results demonstrate that there are two thermal neutron peaks in the thermal neutron region (10-8to 10-6MeV)and a fast neutron peak (approximately 2.5 MeV).The two thermal neutron peaks are owed to the H2O 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 of235U.

Fig.12 (Color online) Neutron energy spectrum of the different components in SBS

3.7 Nuclear Heat Distribution of SBS

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.13a and b.

The results demonstrate that the nuclear heat is mainly deposited in the LEU solution, with a maximum nuclear heat of 1.53 × 10-1W/cm3at the central position.The minimum nuclear heat was determined to be 4.57 × 10-3W/cm3at the edge position.The average nuclear heat was 7.01 × 10-2W/cm3, and the total nuclear heat was 10.9 kW.The average nuclear heat in the reflector layer was found to be 1.21 × 10-4W/cm3, while the average nuclear heat in the shielding layer was 5.57 × 10-5W/cm3.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 of235U, 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] 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 H2O 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 the99Mo production by SBS driven by GDT-FNS are listed in Table 4.

4 Conclusion

In this study, an LEU SBS driven by GDT-FNS for99Mo production was proposed.A neutronics analysis of the99Mo 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 their99Mo 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 of99Mo production necessary to meet 50% of China’s projected99Mo demand in 2025.The preliminary assessment, as shown in case 5 in 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 daily99Mo 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 aksvalue 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:

Fig.13 (Color online) a Nuclear heat distribution in the central radial section of SBS; b nuclear heat distribution in the central axial section of SBS

1.The optimal value for the subcritical multiplication factor (ks) 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 × 104n/cm2s and 2.10 × 107n/cm2s, respectively.The distribution of the neutron flux and nuclear heating in the SBS were relatively uniform, as indicated by theKH-value of 1.12,which further ensures the enhanced operational safety of the system.

2.The SBS allows for a high235U use, that is, 48 Ci99Mo can be produced from 1 kg of235U.

3.A total of 157 Ci99Mo 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 the99Mo production can meet the demand of the Chinese market by 2025 and 2035, respectively.

The SBS driven by the GDT-FNS99Mo production system has the advantages of a high production efficiency, low nuclear waste, and low cost.Our study indicates that this system can be used as a potential facility for99Mo production.However, to make the system more feasible and practical, it is necessary to perform further detailed design studies, such as a U burnup analysis,99Mo separation, and purification technique verification.

AcknowledgementsThe 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.Author contributionsThe 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.

Data AvailabilityThe data that support the findings of this study are openly available in Science Data Bank at https:// www.doi.org/ 10.57760/ scien cedb.07299 and http:// resol ve.pid21.cn/ 31253.11.scien cedb.07299