Effect of reprocessing on neutrons of a molten chloride salt fast reactor

Due to their unique features, such as the inherent safety, simplified fuel cycle, and continuous on-line reprocessing, molten salt reactors (MSRs) are regarded as one of the six reference reactors in the Generation IV International Forum (GEN-IV). Molten chloride salt fast reactors (MCFRs) are a type of MSR. Compared to molten fluoride salt reactors (MFSRs), MCFRs have a higher solubility of heavy metal atoms, a harder neutron spectrum, lower accumulation of fission products (FPs), and better breeding and transmutation performance. Thus, MCFRs have been recognized as a type of MSR with great prospects for future development. However, as the most important feature for MSRs, the effect of different reprocessing modes on MCFRs must be researched in depth. As such, this study investigated the effect of different isotopes, especially FPs, on the neutronic performance of an MCFR, such as its breeding performance. Furthermore, the characteristics of the different reprocessing modes and MCFR rates were analyzed in terms of safety, radioactivity level, neutron economy, and breeding capacity. In the end, a reprocessing method suitable for MCFRs was determined through calculation and analysis, which provides a reference for the further research of MCFRs.


Introduction
As the only liquid fuel reactor retained by the GEN-IV, the MSR employs molten salt as both coolant and fuel [1,2]. It is characterized by its inherent safety, simple structure, no need to fabricate fuel assemblies, and low residual reactivity. The flow of liquid fuel allows the FPs and fissile fuel breeding in an MSR to be extracted on-line without requiring a shutdown. This enables the MSR to operate with less residual reactivity and greatly improves its breeding performance and neutron economy.
In general, fluoride salt is used as the fuel carrier salt in MSRs. The corresponding reactor is the molten fluoride salt reactor (MFSR). Research on MFSRs originates in the 1960s, during which the Oak Ridge National Laboratory (ORNL) first proposed the molten salt reactor experiment (MSRE) [3]. However, even if this concept looked promising, the MSRE was only operated for 4 years before being shut down [3]. Based on the accumulated MSRE technology and operation experiences, other MFSRs, such as the denatured molten salt reactor (DMSR) [4], molten salt breeder reactor (MSBR), and the FUJI-MSR, were proposed in succession [5,6]. More technical issues related to MSRs, such as fuel reprocessing, nuclear proliferation concerns, and the transmutation performance, have been researched, presenting many useful conclusions [4][5][6]. Since the 1990s, the National Center for Scientific Research (CNRS) has been performing research on MSRs and reassessing MSBRs [7]. It was proven that the total temperature coefficient of an MSBR is slightly positive and the lifespan of the graphite moderator in its core is rather short. Therefore, after investigating various core arrangements and their fuel reprocessing performance, a novel concept, namely the molten salt fast reactor (MSFR), was proposed [7,8]. Afterwards, Russia designed the molten salt actinide recycler and transmuter (MOSART) [9], intended for solving the problem of spent fuel reprocessing in the pressurized water reactor (PWR). Due to their simple structure, good breeding and transmutation performance as well as their inherent safety and security, MSFRs and MOSART were selected for further research [10].
Unlike fluoride salt, chloride salt can also be used as carrier salt. Different from the MFSR, the MCFR can only be designed as a MSFR due to the large neutron absorption cross section of Cl in the thermal spectrum. Compared with an MFSR, the MCFR has a harder neutron spectrum, higher solubility of heavy metal atoms, and better breeding performance [11]. The concept of MCFRs was proposed in 1950s by the ORNL. NaCl + MgCl 2 was used as carrier fuel salt, and the breeding ratio (BR) reached 1.09 [12], which provided first proof for the suitability of chlorine salt for fuel breeding. Then, more research on MCFRs was carried out in the 1960s and a new MCFR design was proposed by the United Kingdom Atomic Energy Authority (UKAEA), in which NaCl + 238 UCl 3 + PuCl 3 was used as the carrier fuel salt in the pre-concept design [13]. It achieved a very high BR, which further proved the excellent breeding performance of MCFRs. In the 1970s, the Swiss Federal Reactor Institute proposed a transmutation plan for MCFRs, the neutronics performance of MCFRs with different structures was investigated, and some research on the corrosion problem of chloride salt was carried out [14]. Furthermore, molybdenum was recommended as the main alloy material [14]. With the development of fast reactors, MCFRs are receiving more and more attention around the world. In France, a novel MCFR concept named REBUS-3700 was proposed [15], which operates at the nominal power of 3700 MWth in a closed U-Pu cycle and shows a rare combination of a good breeding capacity and a sufficiently negative temperature coefficient of reactivity (TCR). In addition, Moltex Energy in the UK has developed a stable salt fast reactor in which the chloride fuel is loaded into fuel tubes, which ensures far superior intrinsic safety and, thus, results in a great merit over other designs regarding economics [16]. Additionally, in Germany a dual fluid reactor (DFR), which combines many merits of existing reactors, was designed and researched [17]; the special design of the DFR allows for higher power density and a better fuel breeding performance.
It is well known that the most important feature of an MSR compared to solid-fuel reactors is that it can be reprocessed on-line continuously without shutting down. In general, for the different types of MSRs, the reprocessing method differs. For MSBRs and MSREs, two separate reprocessing systems were designed in multiple studies. The on-line bubbling system mainly removes gaseous and insoluble FPs such as Kr and Xe (Table 2) [3,5], while the on-line chemical reprocessing system is used for recycling heavy nuclides and removing soluble FPs to improve the breeding performance. In particular, the soluble FPs in chemical reprocessing systems are divided into three main categories: rare earth nuclides, semi-noble metals, and alkali metals. Details are provided in Table 2. Their corresponding reprocessing efficiencies are 20, 5, and 1%, respectively [18]. However, in DMSRs [4], it could achieve critical performance, with 20.0 wt% 235 U/U, and could be operated for 30 years with routine additions of denatured 235 U while no chemical processing is needed and only gaseous fission products are removed. For DFRs [17,19], a once-through cycle and a dry high temperature method are suitable due to their small core and flexible designs. Similarly, there are two reprocessing systems for MSFRs [20,21]. The online bubbling system is almost identical to the one used for MSBRs, and in the on-line chemical reprocessing system of MSFRs only 30 types of FPs need to be reprocessed, while its efficiency is 100% (Table 2). Nevertheless, there have been almost no investigations on the reprocessing of MCFRs [22,23], despite some of them being consistent with the reprocessing methods of MSFRs [24]. However, the carrier salt and neutron spectrum of MCFRs are very different from those of MSFRs [25], hence the corresponding reprocessing methods may differ. Thus, it is necessary to systematically analyze the reprocessing of MCFRs to determine an appropriate reprocessing method. Since the main purpose of MCFRs is to breed 233 U, this study mainly focused on the Th-U cycle, which has been proven to have a good breeding capacity and application prospect in both thermal and fast breeder systems [24][25][26].
The paper is organized as follows: the description of an optimized MCFR and reprocessing are introduced in Sect. 2; the calculation tools are shown in detail in Sect. 3; the impact of reprocessing on the neutronics performance of the MCFR is analyzed in Sect. 4; and the conclusions are given in Sect. 5.

General description of the MCFR
The section schematic core of the optimized MCFR is shown in Fig. 1 [27], which was designed and tailored towards breeding 233 U in a closed Th-U cycle [27]. The optimized MCFR was a 2500 MWth reactor with an active core of 25 m 3. Its other parameters are presented in detail in Table 1. The active core consisted of a compact cylinder (height/diameter ratio = 1) where the liquid chloride fuel salt flowed from the bottom to the top without a moderator. The composition of the fuel salt in this MCFR was 55 NaCl-45 (UCl 3 + ThCl 4 ) mol%, with a 37 Cl enrichment of 97% [25]. A blanket filled with a fertile salt surrounding the core was used to improve the system's breeding performance (the blue area in Fig. 1). The blanket consisted of NaCl-ThCl 4 mol% with the same density and 37 Cl enrichment as the fuel salt. Next to the blanket was a reflector (the yellow area in Fig. 1) used for neutron reflection. Surrounding the graphite reflector was a 35 cm thick B 4 C block (the green area in Fig. 1) applied to absorb escaping neutrons [27]. A Ti-based alloy acted as the structural material, surrounding the whole core.

MSR fuel reprocessing schemes
The MSR reprocessing system is shown in Fig. 2 [28,29]. It can be seen that there were two key on-line reprocessing systems. A helium bubbling system was used for removing insoluble gases and noble metallic FPs while continuously on-line. In previous studies of MSRs, almost all bubbling rates were set to 30 s [29]. The second key reprocessing system was the on-line chemical reprocessing system which removed soluble FPs. First, nuclides like U and Np were removed in gaseous forms by fluorination. Then, reductive extraction technology was applied for separating most of the actinides from fuel salt and storing them to let 233 Pa decay into 233 U. In the end, the salt in the core and blanket was recovered with a distillation handle for further utilization, leaving the remaining FPs to be removed. The reprocessing method used in a previous MFSR are listed in Table 2. It can be seen that the soluble FPs that need to be removed differ between the MSBR and MSFR [5,7]. Besides, due to the lower yield and smaller absorption cross section of the FPs in fast reactors, the reprocessing rate of an MSFR is much lower than that of an MSBR [7].

Calculation tools
Unlike traditional solid-fuel reactors, MSRs require continuous on-line refueling and removal of FPs. Thus, the depletion equation is non-homogeneous and can be defined as follows: where N i (t) and N j (t) indicate the atom numbers of nuclide i and j, respectively; λ i and λ j represent the decay constants of elements i and j; γ j→i stands for the branching ratio of the decay from element j into i; c i denotes the fictive decay  constant of nuclide i caused from on-line chemical reprocessing; f j→i represents the probability of a neutron absorption reaction from nuclide j to i; C i refers to the feed rate of nuclide i; σ i and σ j denote the absorption cross sections of nuclide i and j, respectively; and decay i is the decay constant of nuclide i.
For the burn-up calculation of the MSR, a self-developed program, TMCBurnup, which couples the TRITON module with an in-house depletion code (MODEC) was developed [30][31][32]. The plot in Fig. 3 shows a simplified flowchart of the TMCBurnup [33]. First, the parameters were initialized. Then, neutron transportation and depletion were carried out by the TRITON module [32] and MODEC [30], respectively, where Pa was extracted and FPs were removed from the active zone and blanket. Next, part of 233 U and 232 Th nuclides needed to be refueled to the core, and the total mass and ratio of reinjected 232 Th and 233 U were determined by two restrictive conditions, namely by keeping the total heavy metal inventory constant for stability and by maintaining the reactor in a critical state, respectively. The cycle calculation was performed iteratively until the preset burn-up life was reached. The burn-up of the MSR was very deep, indicating that traditional depletion codes such as ORIGEN-S [34] may    [30,33]. Thus, MODEC, a novel MSR-specific depletion code, was applied for solving this depletion equation [30]. In the MODEC program, a high-precision depletion solver was embedded to ensure accurate tracking of the evolution of nuclides. Two selectable methods, specifically an augmented matrix and fictive-nuclear method, were applied for dealing with the non-homogeneous term caused by continuous on-line feeding and reprocessing. The results of different burn-up calculation cases showed that MODEC was suitable for the depletion calculation of both fast and thermal MSRs under different reprocessing modes [33,35].
To prove the applicability of TMCBurnup, the evolution of heavy nuclides in the MSFR was calculated with different start-up fuels and compared with the reference [7], which is shown in Fig. 4a and b. The evolution of the heavy nuclides calculated by TMCBurnup was almost identical to the reference results, which confirmed the accuracy of TMCBurnup in the depletion calculation of the MSFR. Thus, it could be used for the burn-up calculation of MCFRs.
Due to the deep depletion of an MSR, it takes a long time to transition to the equilibrium state (EQL). Therefore, simulating the whole operation can be time-consuming. Sometimes, only the performance in the EQL is of interest.
In the EQL, the nuclide concentration in the reactor remains unchanged and the depletion equation can be described as follows: In order to ensure a sufficient nuclide concentration and feed rate of fuel in the EQL, more constraints are needed. During the whole operation, the number of heavy metal atoms (HM) are kept constant to ensure the stability of the physical and chemical properties of the reactor. This means that the mass of HM at the equilibrium state is kept constant, and the equation can be expressed as: where HN 0 represents the initial concentration of heavy nuclides. In addition, under the condition that the total mass of HM is constant, and the feeding rate of fuel in the EQL determines the value of k eff , which can be described as: where v j represents the neutron yield per fission of nuclide i; R f j and R a j refer to the fission reaction and absorption reaction rates of nuclide j, respectively; and R l stands for the neutron leakage rate of the whole reactor system. When using the merged single group depletion cross section to calculate the reaction rate, Eq. (5) can be written as: where stru stands for the structural material of the reactor; f j and a j represent the fission and absorption cross sections of nuclide j, respectively; and the other parameters have the same meaning as in Eqs. (1) and (4).
Based on the above rules, the molten salt reactor equilibrium-state analysis code (MESA) [33] was developed to enable a fast search for the EQL of an MSR. Its flowchart is shown in Fig. 5. MESA included three iterative processes that contained an inside, middle, and outside loop. Among them, the inner loop was used to determine the total feed rate, solving Eqs. (2) and (3). Based on the results calculated by the inner loop, the intermediate loop could then solve Eq. (5) by adjusting the ratio of fissile to fertile nuclides to keep a constant reaction rate. Finally, the outermost loop, which was coupled to a Monte Carlo transport calculation module, was implemented. Here, when k eff converged and the deviation from the preset value k 0 was less than the defined deviation, the search for the EQL was completed.
The convergence and accuracy of MESA was tested, and the results are shown in Figs. 6 and 7 and Table 3 [35], where the 'Generations' in the horizontal ordinate represent the cycle numbers of the search. It was found that the convergence of k eff and the required concentration of nuclides could be achieved within 10 steps with different start-up fissile materials, as seen in the charts. The content of heavy metals calculated by MESA was nearly identical to those calculated by TMCBurnup. Thus, the subsequent calculations of the neutronics parameters in the EQL were carried out using MESA.

Impact of reprocessing on the neutronics performance of the MCFR
In this section, the effect of reprocessing on the neutronics performance of the MCFR is explored within three steps. First, the absorption reaction rate of various FPs and their effect on the breeding ratio were studied to identify the nuclides that have a significant impact on the neutronics of the MCFR. Then, the effect of bubbling and chemical reprocessing on the neutronics of the MCFR were researched to determine the effect of the reprocessing rate on the core and blanket. Finally, the evolution of the neutronics parameters of the MCFR under different reprocessing methods was investigated to select a suitable reprocessing method for MCFRs. For this calculation, the ENDF-B/VII.0 crosssection library was applied [36]. The number of neutrons per k eff cycle was set to 10,000 and the k eff value was maintained between 1.000 and 1.005 at each step throughout the whole operation.

Effect of soluble FPs on neutronics
As evident from Sect. 2.2, chemical reprocessing is a complex process with high requirements for reprocessing technology. Therefore, this subsection mainly investigates the effects of various soluble FPs on the breeding capability of the MCFR core to determine an appropriate chemical reprocessing method for MCFRs. First, the neutronics parameters in the EQL were calculated using MESA. The content and its corresponding relative absorption ratio (RAR, the ratio of single nuclide absorption to total fission product absorption  where R c and R a stand for the neutron capture and absorption rates, respectively. This definition takes into account the amounts of the isotopes rather than their fissile nature, while the (n, 2n) reactions that lead to fissile isotope production were ignored. The results calculated by MESA showed that if the major FPs were all removed on-line at a rate of 40 L/ day, the BR was 1.246 in the EQL. In addition, the BR in the EQL without reprocessing for a single nuclide and the corresponding relative difference (Δ) with reprocessing for all soluble FPs are listed in Table 5. Since a true equilibrium state is hard to achieve, the results presented in Table 5 are purely hypothetical. It can be seen that the nuclides Sm, Nd, Pr, Ce, and Zr had a great influence on the breeding capacity.  In particular, if Zr was not removed during the operation, the BR reduced by 56.49% in the EQL and 233 U breeding could not occur. Therefore, in chemical reprocessing the removal efficiency and rate of the above FPs must be sufficiently high. However, nuclides I, Er, and Yb had a negligible effect on the BR, with the corresponding relative differences all lower than 0.01. Thus, the reprocessing requirement for these FPs can be reduced to lower the difficulty of chemical reprocessing.

Effect of He bubbling and chemical reprocessing on the breeding capacity
In this subsection, the effect of bubbling and chemical reprocessing on the BR of the optimized MCFR in an EQL was investigated using MESA. The BR of the MCFR under different He bubbling rates is shown in Fig. 8. The notation 'only core' refers to changes to the bubbling rate of the core while the He bubbling rate of the blanket was kept constant, which is the opposite of 'only blanket'. The symbol 'total' stands for the He bubbling rate resulting from simultaneous changes to the core and blanket. In this calculation, the constant He bubbling rate was set to 30 s. The results showed that the He bubbling rate had less effect on the breeding performance of the MCFR than on the thermal MSR (when  the He bubbling period was increased from 10 to 1000 s, the breeding ratio only decreased by about 1.5%) in the EQL, especially on the blanket. This is because the neutron spectra of the MCFR are much harder than those of thermal reactors, hence the absorption cross-section and yield of non-dissolved FPs generated during operation are much smaller and their impact on the neutron economy and breeding capacity are weaker. Therefore, in the subsequent experiment the He bubbling rate was set to 30 s, similar to that of the MSFR. As mentioned in Sect. 2.2, the chemical reprocessing system mainly includes two procedures, soluble FPs removal and 233 Pa extraction. In this subsection, the impact of FPs removal and 233 Pa extraction on the BR of the MCFR in an EQL were investigated separately. The constant extraction rate was set to 40 L/day, and the simulation results are shown in Fig. 9. It was found that the 233 Pa extraction rate had an evident influence on the breeding capability of the MCFR, although this effect was much smaller than that on thermal reactors such as the MSBR [5]. This resulted from 233 Pa having a long half-life of 27 days, indicating that it would absorb neutrons and decay to 234 U if not extracted in time, which would deteriorate the breeding performance of the MCFR [37]. However, because the absorption cross section of 233 Pa was smaller in the fast spectrum, the 233 Pa extraction rate had a much smaller impact on the breeding capability than in a thermal reactor [37]. Owing to the harder neutron spectra of the core, the BR reached equilibrium earlier than the blanket with increasing removal rate, and the minimum rates of 233 Pa extraction corresponding to the maximum BR of the core and blanket were 160 L/day and 280 L/day, respectively.
The impact of the soluble FPs removal rate on the breeding performance of the MCFR was also investigated, and the results are shown in Fig. 10. It can be seen that the effect of soluble FPs on the MCFR was less significant than that on the MSBR due to its significantly harder neutron spectra [5]. However, fission almost occurred in the core, resulting in significantly fewer FPs in the blanket. Therefore, the reprocessing rate required to maximize the BR in a blanket was significantly smaller than core, even if its neutron spectra were much softer than those of the core. When the removal rate of FPs in the blanket was increased to 20 L/day, the BR of the blanket was nearly at its maximum. When the BR in the core reaches this maximum, the removal rate of FPs would increase to 100 L/day.

Neutronics performance of the MCFR under different reprocessing methods
The reprocessing of MSRs reduces the neutron absorption rate of FPs and the consumption of 233 Pa and improves its breeding performance. In general, there are two main reprocessing methods in MSRs, namely continuous on-line reprocessing and batch-reprocessing. Continuous on-line reprocessing requires the extraction of fuel salt out of the reactor at a certain rate without shutting it down, while batch-reprocessing is more similar to a pressurized water reactor refueling mode. During a fixed period, all fuel is extracted for FPs removal and 233 Pa recovery. Generally, batch-reprocessing is less technically challenging than continuous on-line reprocessing. In particular, as outlined in Sect. 4.2, FPs removal is the last step of chemical reprocessing. In order to improve the separation efficiency and reduce the loss of other nuclides, a series of complex processes are needed prior to the removal of soluble FPs. In addition, the results presented in Sect. 2.2 showed that FPs removal had a relatively lower impact on the breeding performance of the MCFR than 233 Pa extraction did. Thus, it seems possible to adopt batch-and continuous on-line reprocessing for FPs removal and 233 Pa extraction, respectively. To compare the neutronics performance of the MCFR under different reprocessing modes, the evolution of the neutronics parameters under the four different reprocessing methods was investigated. The details about these reprocessing methods are presented in Table 6. In the calculation, the He bubbling period and chemical reprocessing rate were set to 30 s and 40 L/day, respectively, for both the core and the blanket (the corresponding period for batch-reprocessing was 625 days), which was consistent with the MSFR reprocessing rate [7,8].

Neutron spectra under different reprocessing modes
Neutron spectra are the internal cause of many neutronics properties, and can also inform the subsequent interpretation of simulation results, such as the actinide build-up and the evolution of the TCR. The neutron spectra in the EQL under different reprocessing modes are shown in Fig. 11a. It can be seen that the neutron spectra of mode 2 and mode 3 in the EQL were almost identical, and that the neutron spectra were hardest in mode 4.
In addition, the energy of the average lethargy-causing fission (EALF) was defined to give a quantitative description for the neutron spectra [32], which can be written as: The evolution of EALF under the four different reprocessing modes is shown in Fig. 11b. The EALF of all reprocessing modes dropped rapidly in the early stages of the operation caused by the build-up of FPs, which resulted in the moderation of neutrons in fast reactors. Then, the EALF values corresponding to modes 1-3 gradually increased, owing to a decrease in 232 Th and an increase in transuranic elements such as Pu and Np (Fig. 13 and Table 7). The EALF of mode 4 fluctuated more evidently, which may have mainly been due to removal of the FPs of the core through batchreprocessing; when FPs were removed, EALF increased significantly.

Mass evolution under different reprocessing modes
During the whole operation of the MCFR, the heavy metal atoms in the reactor core were maintained constant through on-line reprocessing and feeding to ensure stable chemical properties of the core. The plot in Fig. 12a and b shows the evolution of actinides, which took longer to reach the EQL in the MCFR than that in the MSFR due to its lower specific power [29]. The nuclides of Th, Np, and Pa reached the EQL earlier than the other actinides did. It was also found that the mass evolutions of modes 2 and 3 were almost identical, and that U and Pa reached an EQL after about 50 years under modes 2 and 3, while Pu, Cm, and Am accumulated during irradiation due to radiative capture and could not reach equilibrium during the whole operation. In general, the total mass of transuranic elements such as Pu, Np, Am, and Cm was always higher under modes 1 and 4. In particular, the mass of Np in mode 1 was 1.5 times higher than that in mode 3, which resulted in a harder neutron spectrum.
The mass of heavy nuclides and long-lived fission products (LLFPs) in the beginning of burn-up (BOB) and EQL are listed in Table 7. It was found that the mass of LLFPs under mode 1 was much higher than that of the others owing to the lack of reprocessing of soluble FPs, while the mass of LLFPs in mode 3 was the smallest. Additionally, the accumulation of FPs during the operation led to a deterioration of the neutron economy in the MCFR, which resulted in a

Radiotoxicity and decay heat under different reprocessing modes
Radiotoxicity and decay heat, which can be calculated using Eqs. (8)- (9), have a direct impact on the difficulty of reprocessing and shielding design during the operation:  where N(t) represents the number of nuclei at time t; λ i refers to the decay constant of nuclide i; E β and E γ are the radiation energy of beta and gamma decay, respectively; and r i indicates the conversion factor of radioactivity to radiotoxicity. The evolution of radiotoxicity and the decay heat during the whole operation are presented in Fig. 13. It can be seen that the radiotoxicity and decay heat of mode 4 remained the highest during the whole operation due to its having the highest contents of 233 Pa and 233 Th, both of which have the most significant impact on decay heat. The high 233 Pa content in mode 4 directly resulted in high radiotoxicity levels. In addition, due to the absence of on-line reprocessing of soluble FPs in mode 1, their content during the operation was the highest, which led to a relatively higher level of radiotoxicity and decay heat.

Breeding capacity under different reprocessing modes
Since this optimized MCFR is mainly used for breeding 233 U in the closed Th-U cycle, the breeding performance is of highest importance among the neutronics performances. Usually, the breeding performance is evaluated using three parameters, namely the BR, doubling time (DT), and the net yield of 233 U [11,38]. BR, defined in Eq. (6), determines the ratio of the rate of production and consumption of fissile nuclides. Due to the on-line reprocessing, 233 Pa needs to be removed from the core and blanket to decay into 233 U, the 233 U decayed from 233 Pa in the blanket also needs to be extracted. In addition, to ensure criticality, some of the extracted 233 U needs to be refueled into the active core. Thus, the net production of 233 U can be expressed as: where the subscript ex and re refer to extracting and refueling, respectively. Then, the net 233 U production is divided by the initial inventory of 233 U (M 0 ); when it equals 1.0, the net production of 233 U is equal to M 0 , which means that 233 U has doubled and is sufficient to start another MCFR. The time this requires is called DT. In the MCFR in this study, the value of M 0 was 5.43 t ( Table 7).
The evolution of BR and the corresponding k eff of the four different reprocessing modes are shown in Fig. 14. It was found that, due to the accumulation of FPs, the BR of mode 1 declined almost linearly with time, reducing to less than 1.00 in about 100 years. In addition, since FPs and 233 Pa were extracted by batch-reprocessing in mode 4, the corresponding BR had a saw-tooth-like shape and reached its maximum after each batch-reprocessing. In general, the BR of mode 3 was significantly larger than that of the other modes throughout the whole operation, and the average BR of mode 2 was about 0.03 smaller than that of mode 3.
In order to explore the evolution mechanism of BR under different reprocessing modes, the fission fraction of fissile nuclides was calculated. The evolution of the fission ratio of main fissile isotopes is presented in Fig. 15a, where 233 U is represented by dashed lines and 235 U by solid lines. It can be seen that 233 U played a dominant role during the whole operation, and that its minimum fission share reached more than 95% while the remaining part was almost entirely from 235 U. Therefore, the fission reaction rate of 233 U represented the disappearance rate of fissile nuclides.
The reaction rates of 232 Th and 233 U are shown in Fig. 15b. It can be seen that, in mode 3, the capture reaction rate of 232 Th was higher and the fission reaction rate of 233 U lower than that of the other modes owing to its excellent neutron economy, which indicated that 233 U had the fastest production and slowest consumption rate; thus, the BR corresponding to mode 3 was the highest. However, the capture reaction rate of 232 Th corresponding to mode 1 gradually deteriorated due to the lack of removal of soluble FPs during the whole operation. Thus, the BR of mode 1 decreased gradually to below 1.00 in about the first 100 years, which means that 233 U breeding cannot be achieved in a 100-year operation.
The plot in Fig. 16 shows the evolution of the net accumulation of 233 U during the operation, where the dotted purple line represents the initial loading of 233 U, namely M 0. The horizontal coordinate corresponding to its intersection with the net production of 233 U is the DT. The annual production of 233 U corresponding to mode 3 was significantly larger than in other modes due to the simultaneous and continuous on-line reprocessing of both 233 Pa and soluble FPs. While the annual production of 233 U in mode 1 was larger than that of mode 4 during the first 20 years (in the beginning, the slope of mode 1 was greater than that of mode 4), the net production of 233 U became negative in about 100 years due to the gradual build-up of FPs. During the whole operation, the average annual production of 233 U under the four modes was 9, 256, 237, and 142 kg and the corresponding DT was 16.2, 16.1, 15.3, and 24.9 years, respectively.

TCR under different reprocessing modes
In this subsection, the evolution of the total TCR of the four reprocessing modes was investigated. In general, there is no moderator in an MCFR and the expansion rate of structural materials can be ignored. Thus, the TCR of an MCFR is mainly determined by the fuel doppler and density coefficients, and can thus be expressed as: The evolution of the TCR is presented in Fig. 17. Due to the accumulation of FPs, the absolute value of the TCR corresponding to mode 1 decreased by about − 2.5 pcm/K compared with the initial critical value, and the TCR of the other reprocessing modes decreased by 1.3-2 pcm/K. In general, the four different reprocessing modes maintained a sufficiently negative TCR during the 200-year operation, ensuring the inherent safety of the MCFR.

Conclusion
In this paper, the effects of reprocessing on neutronics performance were investigated and analyzed based on an optimized MCFR. This study mainly including the influence of the reprocessing rate, different categories of FPs, and different reprocessing modes for an MCFR. It not only highlighted an appropriate reprocessing mode for an optimized MCFR, but also provided a reference for all types of MCFRs. The results can be summarized as follows: 1. The effect of reprocessing, especially that of the helium bubbling system, on the neutronics in the MCFR was significantly lower than that in other thermal MSRs. In addition, in the MCFR, the impact of reprocessing on the breeding performance of the blanket was significantly weaker than that of the core. The impact of 233 Pa extraction was more obvious than that of FPs removal. 2. The nuclides Sm, Nd, Pr, Ce, and Zr had a great influence on the core breeding capacity of the MCFR. In particular, if Zr was not removed during the operation, the BR was reduced by 56.49% at the equilibrium state; thus, it should be removed at a high rate and efficiency to improve the breeding performance. In addition, the nuclides I, Er, and Yb had a negligible effect on the BR at an equilibrium state, indicating that their reprocessing can be lowered to reduce the difficulty of chemical reprocessing. 3. If the FPs of the MCFR were not removed during the entire operation, the 233 U breeding could not be achieved. The batch-reprocessing for FPs faced high radiotoxicity and decay heat, which increased the shielding requirements and operating difficulties. On-line reprocessing improved the neutron economy and significantly reduced radiotoxicity in the MCFR. In addition, the net production of 233 U and the corresponding doubling time under on-line reprocessing were superior to other modes. Regarding immature chemical reprocessing technology, using batch-reprocessing for FPs and continuous on-line reprocessing for 233 Pa had a considerable effect on the breeding performance, indicating that they can be used to reduce the difficulty of chemical reprocessing. 4. In the optimized MCFR, the recommended extraction rates of 233 Pa in the blanket and core were 280 L/day and 160 L/day, respectively, and the corresponding removal rates of soluble FPs were 20 L/day and 100 L/day, which suggests that there is no need to repeatedly remove the FPs of the molten salt obtained from the reactor after 233 Pa is extracted.
Author contributions All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by Liao-Yuan He, Shao-Peng Xia, Liang Chen, Lin-Yu Hu, Rui Yan and Yang Zou. The first draft of the manuscript was written by Liao-Yuan He and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.
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