Keywords

1 Introduction

Minor actinides (MA) in the spent fuel of the current pressurized water reactors (PWRs), namely neptunium (Np), americium (Am) and curium (Cm), are the main long-lived radioactive waste in the long term, which is one of the most severe issues associated with sustainable nuclear energy development [1,2,3,4]. Until now, transmutation is considered to be an effective way for nuclear waste management and tremendous works have been devoted to achieving a high transmutation capability of MA in different types of reactors, such as PWR, Gas-cooled Fast Reactor (GFR), Lead-cooled Fast Reactor (LFR), Sodium-cooled Fast reactor (SFR) and Accelerator Driven Sub-critical System (ADS) [5,6,7,8].

Molten salt reactor (MSR) is an old concept but has been gathered many attentions in recent years due to its special features [9, 10]. One of the most alluring advantages in MSR is that it operates with a liquid fuel, which permits an arbitrary core design and a flexible reprocessing system. Furthermore, the molten salt is capable to dissolve various fissile fuels (eg. enriched uranrium, 233U and transuranium elements (TRUs)), which is convenient to implement different types of fuel cycles in an MSR [11, 12]. A closed nuclear fuel cycle is expected to be realized and the utilization of nuclear fuel can be significantly improved due to the effective burning of minor actinides in an MSR. The MOlten Salt Actinide Recycler & Transmuter (MOSART) was first proposed by the Kurchatov Institute of Russia within the International Science and Technology Center project 1606 (ISTC#1606) with aims to effectively transmute TRUs [13]. A series of studies have been conducted to demonstrate the feasibility of MOSART for reducing TRU radiotoxicity. Afterwards, another fast spectrum MSR concept of the Molten Salt Fast Reactor (MSFR), which was proposed by the Centre National de la Recherche Scientifique (CNRS) to achieve a high thorium breeding ratio, was also applied to investigate the feasibility of TRU transmutation [14]. Recently, some thermal spectrum MSR concepts are also put forward to evaluate the possibility of TRU transmutation [15, 16].

Fig. 1.
figure 1

Geometrical description of the three MSR cores

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In an MSR, the MA transmutation capability is tightly related with the neutron spectrum and the MA loading in the core. The dominant transmutation way for MA is varied with the neutron spectrum since the fission and capture cross sections of MA have significant discrepancies with the neutron energy. In addition, different types of carrier salt compositions have various TRU solubility limits, which have a direct influence on the MA loading in MSR. In this paper, it is aimed to evaluate the transmutation behaviors of MA with different neutron spectra and various MA loadings in MSR, which can provide a reference for realizing various transmutation objects for different MA elements. Three typical MSR cores (thermal, epithermal and fast) are proposed to compare the MA transmutation capability. Meanwhile, two typical molten salt compositions (Flibe and FlinaK) which have different TRU solubility limits are selected to analyze the influence of MA loading on the transmutation capability. Furthermore, the radiotoxicity and safety parameters are also analyzed in detail.

A general description of the thermal, epithermal and fast MSRs and the calculation tools is presented in Sect. 2. In Sect. 3, the MA transmutation capabilities in the three MSR cores with two types of molten salts are first analyzed. And then the neutronic performances at different burnups in the thermal, epithermal and fast MSR cores are presented and discussed. The conclusions are given in Sect. 4.

2 General Description of the Geometry Models and Calculation Tools

2.1 Description of the Thermal, Epithermal and Fast MSRs

In the past, a series of MSR core designs ranging from the thermal to fast neutron spectrum have been conducted to achieve a high thorium breeding ratio in our research group [11, 12]. This work extends three typical reactor core configurations, corresponding to thermal, epithermal and fast spectrum cores, respectively. The geometrical descriptions for the three cores are shown in Fig. 1. In an MSR, the power density is a vital parameter to determine the main neutronic behaviors. Therefore, a constant thermal power of 2500 MWth and a constant fuel volume of about 46.2 m3 are designed for the three cores, respectively. Therein, two thirds of the total fuel volume is located in the core salt channels, the upper and lower plena, and the other one third is located in the heat exchangers, pipes and pumps.

Fig. 2.
figure 2

Neutron spectra of the three cores

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The core parameters are detailed in Table 1. For the thermal and epithermal MSR cores, the reactor core is a cylindrical geometry assembled with graphite hexagons and surround by the graphite reflectors. The radii of the fuel salt channel in each graphite hexagon are designed as 3 cm and 7.5 cm to obtain thermal and epithermal spectra, respectively. In the fast MSR, the graphite reflector is replaced by nickel-based alloy to prevent nuclear fissions from being decentralized to reactor’s borders. To maintain a constant fuel volume in the core, the dimension for the three MSRs varies from each other, which is designed by keeping the height and the diameter equivalent. The radial reflector with 0.5 m thickness and the axial reflectors with 1.3 m thickness are designed around the core for the three cores to improve the neutron economy. The neutron spectra of the three core configurations fueled with Th-232 and U-233 are shown in Fig. 2, which are shown as typical thermal, epithermal and fast neutron spectra.

Table 1. Main parameters of the three MSR cores
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2.2 Selection of Salt Compositions

The MA loading in the core is an important factor that determines the transmutation capability, which is a major restriction on achieving a high transmutation rate in solid-fueled reactors. In MSR, there is no fuel rod fabrication which extends the feasibility of MA mass loading. However, the solubility limit of TRU in the molten salt is an important restriction on the MA mass loading. Therefore, choice of the fuel salt is also one of the most important tasks for the MA transmutation since the solubility limit of TRU is tightly dependent on the molten salt compositions. In the past decades, the physico-chemical properties of various salt compositions were researched for selection of fuel and coolant compositions for MSR. Until now, there are three typical carrier salts proposed in different MSR designs, which are Flibe, Fli, and Flinak, respectively [19]. The Flibe salt with 99.995% of Li-7 enrichment has excellent neutron economy, and has been widely used in various MSRs. The PuF3 solubility limit for the fuel compositions of 77% LiF–17% BeF2–6% ThF4 is 4.0%. The Fli carrier salt removes BeF2 to accommodate a higher fraction of actinide tetrafluorides, which has been selected as the fuel compositions in the molten salt fast reactor (MSFR) (78% LiF–22% ThF4) for Th breeding and MA transmutation. The 78% LiF–22% ThF4 fuel salt has a worse neutron economy but has a higher solubility limit (5.2%) than the Flibe salt. Compared to the Flibe and Fli salts, the Flinak carrier salt has the highest solubility of actinides but the worst neutron economy due to the large absorptions of Na-23 and K-39. For the composition 46.5% LiF, 11.5% NaF and 42% KF, the solubility limits for ThF4, UF4, PuF3 and AmF3 are as high as 37.5%, 45%, 30%, and 43%, respectively. In this work, the Flibe and Flinak carrier salts are selected for comparing the MA transmutation capability with different MA loadings.

The initial MA mole fraction for the Flibe salt is loaded with its limit value of 4.0% while 10% of MA is loaded for the Flinak salt in the thermal, epithermal and fast MSR cores. Th-232 and U-233 are used as the fertile and fissile fuels in the three MSR cores due to the very low TRU production. To enhance the MA transmutation rate and to ensure the stability of fuel salt simultaneously, MA including Np, Am and Cm are fed online into the core to keep the total inventory of MA and Pu constant during the entire operation. Furthermore, Th-232 and U-233 are also fed into the fuel salt continuously to maintain the criticality of reactor and keep the total heavy metal inventory in the fuel salt constant.

The MA compositions come from the spent fuel of current light water reactors (LWRs), which are mainly composed of Np-237, Am-241, Am-243, Cm-243, Cm-244 and Cm-245 in the proportions of 56.2%, 26.4%, 12%, 0.03%, 5.11% and 0.26%, respectively [4].

2.3 Calculation Tools

The SCALE6.1 code system, which has powerful functions for criticality, depletion and shielding calculations for critical reactors, was used to establish the simulation model of the MSR core [17]. Meanwhile, the molten salt reactor reprocessing system (MSR-RS) developed by our research group was applied to simulate the characteristics of online refueling and reprocessing in MSR. In this paper, the MSR-RS sequence is also used to calculate MA transmutation in MSR [18]. MA is fed continuously to enhance the transmutation rate and the feeding MA inventory is adjusted by keeping the total TRUs inventory constant to assure the TRU fraction in the fuel salt below the solubility limit. Meanwhile, the total heavy metal mass in the core is always kept constant by feeding Th-232 and U-233 during the entire operation time. The 238-group ENDF/B-VII cross section database is selected, and 388 nuclides are tracked in trace quantities in this simulation which contains most of the nuclides in the fuel cycle chain with very deep burnup.

3 Results and Discussion

To evaluate the MA transmutation capability of the thermal, epithermal and fast MSRs, the neutron spectra and fission/capture cross sections of MA varying with different MA loadings are first analyzed. Then the transmutation capability and the radiotoxicity of TRU are evaluated in detail. Finally, the related safety parameters will be discussed.

3.1 Neutron Spectra Variation with Addition of MA into the Fuel Salt

Neutron spectrum is a key core parameter which determines the MA transmutation performances mainly through the capture and fission reactions. When MA is refueled into the fuel salt, the neutron spectra in the three MSR cores will have a different shift due to the variation of cross sections of MA in different neutron energies. In further, the neutron spectrum change will have an influence on the fission/capture cross sections of MA. The neutron spectrum variations with MA addition at the beginning of life in the three MSR cores are displayed in Fig. 3. One can be seen that the neutron spectra in the thermal, epithermal and fast MSR cores harden significantly with addition of MA into the fuel salt. Furthermore, the variation in the epithermal core is more obvious than those in the other two cores as most of MA have strong resonance absorptions. In addition, the neutron spectrum with the Flinak salt shifts to a slightly fast region due to the parasitic absorption of Na-23 and K-39.

Fig. 3.
figure 3

Neutron spectrum variations with MA loading in the three cores

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3.2 Transmutation Capability in the Three MSR Cores

To evaluate the transmutation capability of MA in an MSR, several parameters are introduced, namely the specific MA incineration consumption (SIC), the MA incineration ratio (TR) and the disappearance rate (DR) of each element in MA. The SIC is defined as

$$ {\text{SIC}} = { }\frac{{MA\left( {T = 0} \right) + MA\left( {feeding} \right) - MA\left( {residue} \right) - HN\left( {residue} \right)}}{P \times T} $$

where \(MA\left( {T = 0} \right)\), \(MA\left( {feeding} \right)\), \(MA\left( {residue} \right)\) and \({\text{P}}u\left( {residue} \right)\) denote the initial MA loading, the online MA feeding and the MA residue, respectively. The HN residue in the fuel salt is the total TRU inventory except MA. P is the thermal power of MSR, while T is the entire operation time.

The TR is another important parameter for evaluating the MA incineration efficiency, which is defined as the ratio of the incinerated MA mass to the total loaded MA mass and calculated by

$$ {\text{TR}} = { }\frac{{MA\left( {T = 0} \right) + MA\left( {feeding} \right) - MA\left( {residue} \right) - HN\left( {residue} \right)}}{{MA\left( {T = 0} \right) + MA\left( {feeding} \right)}} $$

In addition, the disappearance rate (DR) of each element in MA is also applied to evaluate the transmutation capability of Np, Am and Cm in the thermal, epithermal and fast MSR cores, which is defined as

$$ {\text{DR}}\left( {\text{i}} \right) = { }\frac{{M\left( i \right)\left( {T = 0} \right) + M\left( i \right)\left( {feeding} \right) - M\left( i \right)\left( {residue} \right)}}{{\left( {M\left( i \right)\left( {T = 0} \right) + M\left( i \right)\left( {feeding} \right)} \right) \times P \times T}} $$

where \(M\left( i \right)\left( {T = 0} \right)\), \(M\left( i \right)\left( {feeding} \right)\) and \(M\left( i \right)\left( {residue} \right)\) represent initial loading, the online feeding and the residue inventory of element \(i\), respectively.

Table 2. SIC and TR for two salts in the three MSR cores
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With 4% of MA in the Flibe salt and 10% of MA in the Flinak salt, the initial MA inventories are loaded as about 22 tons and 28.9 tons for the Flibe and Flinak salts, respectively. During the whole operation, the total TRU inventory is always kept constant to maintain the TRU fraction below the solubility limit. Therefore, the incinerated MA inventory is dependent on the feeding amount of MA. During the 100-year operation, the total MA feeding inventory with the Flibe salt ranges from 41.3 to 50.4 tons in the thermal, epithermal and fast MSR cores while it varies from 41.5 to 60 tons with the Flinak salt for the three cores. The STC and TR with Flibe and Flinak salts in the thermal, epithermal and fast MSR cores during 100-year operation are presented in Table 2. As most TRU nuclides have preferred fission ability in the fast neutron spectrum, which is an efficient way for MA incineration, a preferred MA transmutation capability is achieved in the fast MSR core for both of the two salts. One can be seen that the SICs with the Flibe salt for the three MSR cores at the end life of 100-year operation are 167, 185 and 206 kg/GWth.y, respectively. Due to the higher loading of MA for the Flinak salt, higher SICs are achieved correspondingly in the thermal, epithermal and fast MSR cores, which are 170, 206 and 247 kg/GWth.y, respectively. The discrepancy of SIC for the two salt compositions is more obvious in the fast spectrum due to the fact that the core with the Flinak salt hardens the spectrum more efficiently than that with the Flibe salt, which benefits the fission ability of most TRU nuclides and facilitates the MA incineration rate. The IR is an important parameter that evaluates the transmutation efficiency of MA. The IR variances of the SIC among the three MSR cores are similar for both of the two salts. However, the IR with the Flinak salt is lower than that with the Flibe salt, especially in the thermal MSR core. This is because that there is an inferior neutron economy in the Flinak salt with significant capture cross sections of Na-23 and K-39, especially in the thermal energy region. With the high MA loading and the feasibility of online refueling, MSR can attain an alluring transmutation efficiency of MA with the TR over 0.75, which means that more than 75% of MA loaded in the core is incinerated. The DR is an important indicator to evaluate the transmutation capability of a single element, which is displayed in Fig. 4. It can be seen that Np has a higher DR than the other two MA of Am and Cm as Np has a higher fraction in MA and a larger absorption cross section than those of Am and Cm, which ranges from 120.7 to 141.9 kg/GWh.y with the Flibe salt and from 122.1 to 163.3 kg/GWh.y with the Flinak salt in the above three cores. The DR of Am is inferior to that of Np due to a lower mass loading, a smaller absorption cross section and a significant production from Pu. In the transmutation chains, a significant amount of Cm will be accumulated by successive neutron captures and β decays from Np, Pu and Am, which impedes the DR of Cm significantly except its own low mass loading.

Fig. 4.
figure 4

DRs of Np, Am and Cm with Flibe and Flinak salts in the three MSR cores

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3.3 TRU Evolution and Radiotoxicity

In the transmutation chains of MAs, the disappearance ways differ significantly in different neutron energies. Some MAs such as Np-237, Am-241 and Am-243 with larger capture cross sections than their fission ones in the thermal region are transmuted by capturing neutrons consecutively to form Pu-239, Am-242, Am-242m, and Cm-245 with very large fission cross sections. In the fast neutron spectrum, most MA can be transmuted by fissions with higher fission cross sections than the capture ones. Therefore, the TRU evolution varies significantly with the neutron spectrum, which imposes a variation on the radiotoxicity.

Fig. 5.
figure 5

Evolutions of the Pu isotopes with Flibe salt for the three cores during 100-year operation

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Fig. 6.
figure 6

Evolutions of the MA isotopes with Flibe salt for the three cores during 100-year operation

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Figure 5 and Fig. 6 display the evolutions of the Pu isotopes and new created MA for the Flibe salt in the three MSR cores, respectively. One can find that the produced Pu isotopes are the majority of the new created nuclides, whose production rates are as high as about 116, 130 and 129 kg/y for the thermal, epithermal and fast cores, respectively. For the Pu isotopes, there are two main reaction chains to produce Pu-238 from Np-237 and Am-241 by successive (n, γ) and β/α decay reactions. In further, Pu-239 produced from the Pu-238 capture has a large fission cross section, which is the major disappearance way for Pu-239. Hence, the inventories of the higher Pu isotopes which are mainly produced by Pu-239 capture are much less than Pu-238. It can be seen in Fig. 5 that Pu-238 accounts for the majority of the transmuted products as the source nuclides of Np-237 and Am-241 are the main isotopes of the initial MA with the fraction of as high as about 86.2%. On the other hand, the accumulated inventory of Pu-238 in the epithermal core is higher than the other two cores due to the fact that most TRU have significant capture resonances in the epithermal region than in the fast region and the total loading of MA in the epithermal core is higher than that in the thermal core. The evolutions of the other Pu isotopes also reveal significant variations because of the different reaction cross sections and MA loadings. At the end of 100-year operation, the mass fraction of Pu-238 in the Pu isotopes is 44.4%, 57.6% and 44.9% in the thermal, epithermal and fast MSR cores, respectively, which is advantageous from the view point of non-proliferation. Similarly, the evolutions of new created MAs in the three cores reveal a significant variation which is tightly related with the MA loadings and the neutron spectrum. The production rate of the new created MA is 3.5, 4.7 and 5.5 kg/y for the thermal, epithermal and fast MSR cores, respectively, which is much lower than that of the Pu isotopes.

Fig. 7.
figure 7

Evolutions of the total radiotoxicity with Flibe and Flinak salts in the three MSR cores

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The radiotoxicity is an important parameter to evaluate the effect of radionuclides to human health by ingestion or digestion, which is defined as:

$$ R(t) = \sum\limits_{i} {R_{i} (t)} = \sum\limits_{i} {r_{i} \lambda_{i} N_{i} (t)} $$

where \(R_{i} (t)\) represents the radiotoxicity of nuclide i at time t in unit of Sv; \(r_{i}\) refers to the effective dose coefficient in Sv/Bq by ingestion for the public [20], which depends on the decay mode and the emitted energy of particles; \(\lambda_{i}\) and \(N_{i} (t)\) represent the decay constant and atoms of nuclide i, respectively. In the SCALE6.1 software system, the ORIGEN-S module is feasible to calculate the radioactivity of each nuclide and the radiotoxicity is calculated with multiplying the effective dose coefficient by the radioactivity of each nuclide.

To evaluate the radiotoxicity of MA with different MA loadings in the thermal, epithermal and fast MSR cores, the total radiotoxicities of MA and the radiotoxicities of Np, Am and Cm at the beginning and end of lifetime are chosen for discussion. One can see from Fig. 7 that the total radiotoxicitiy of MA for the Flibe salt in the three different MSR cores after 100-year operation is reduced significantly, about 45% lower than that at the beginning of lifetime. For the total radiotoxicity of MA, the highest contribution is from Cm because of the high dose coefficients of most Cm isotopes and their daughter products even though the total Cm inventory is extremely small (as shown in Fig. 8). For this reason, the total radiotoxicity of MA for the three different cores are very similar since the difference of the MA inventory can be negligible. Due to a significant accumulation of Np-238 with a very short half-life, the radiotoxicity of Np at the end of lifetime is increased slightly in the first 100 years, which is decreased rapidly in the following decay time and is about 80% lower than that at the beginning of lifetime. Am has a significant reduction on radiotoxicity, with more than an order of magnitude lower than that at the beginning of lifetime, which is the major factor to decrease the total radiotoxicity of MA.

Fig. 8.
figure 8

Evolutions of the MA radiotoxicity with Flibe salt in the thermal MSR core

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3.4 Evaluation on Safety Parameters

To evaluate the influence of MA loading on the reactor safety of the thermal, epithermal and fast MSR cores, two important parameters of the temperature feedback coefficient (TFC) and the effective delayed neutron fraction (\(\beta_{eff}\)) are analyzed in this work.

The TFC is an essential indicator for the inherent safety issues, which is required to be negative during the whole lifetime of the reactor. The total TFC in a reactor is calculated as the sum of the fuel TFC and the moderator TFC. In further, the fuel TFC can be broken down into the Doppler effect and the fuel salt expansion.

Fig. 9.
figure 9

Evolutions of the TFC with Flibe and Flinak salts in the three MSR cores

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Fig. 10.
figure 10

Evolutions of the TFC with Flibe salt in the thermal MSR core

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The evolutions of the TFC for different MA loadings in the three MSR cores are displayed in Fig. 9. One can be seen that the total TFC is significantly related with the neutron spectrum and slightly varied with the evolutions of the fuel compositions. To evaluate the contribution of TFC from fuel density, fuel Doppler and graphite, the three items of TFC for the Flibe salt in the thermal core are exampled for discussion, as shown in Fig. 10. For the MA from the spent fuel of PWR, the MA nuclides except Cm-245 (with the mole fraction in MA of 0.26%) are poisonous to reactivity, especially in a thermal region. Furthermore, Np-237 at 0.5 eV and Am-241 at 0.3 eV, 0.6 eV and 1.1 eV reveal significant capture resonance cross sections (>1000 barns), respectively, which is benefit for decreasing the TFC as the MA captures with a Doppler broadening can counteract the increased fissions of fissile nuclides with the fuel temperature increasing. In addition, when the graphite temperature is increased, the Maxwellian spectrum shifts to a higher energy region, where it is closer to the strong capture resonance cross-sections of MA. Hence, a negative graphite TFC with the value as low as about −26.6 pcm/K is obtained at the beginning of lifetime. During operation, the thermal neutron spectrum hardens gradually as the continuous feeding of MA, which is gradually away from the capture resonances of MA and increases the graphite TFC. The total TFC for the Flibe salt in the thermal MSR core which is mainly influenced by the graphite effect varies from −26.6 pcm/K to be an equilibrium value of about −8 pcm/K. As there is a minor variation on the neutron spectrum with the Flibe salt and Flinak salt, little differences on the total TFC are caused with the two different salt compositions in the same MSR core. For the epithermal MSR core, the negative effect of the graphite TFC tends to be weakened as the neutron spectrum is far away from the capture resonances of MA. The total TFC is around −5 pcm/K during the entire operation time. As there is no moderator in the fast MSR core, the total TFC is just the sum of the fuel doppler and the fuel density effects. Therefore, the total TFC is higher than the other two cores but always keeps negative with the value of about −2.5 pcm/K.

\(\beta_{eff}\) is another important parameter for both kinetics reactivity controlling safety and static reactor physics experiments. It can be defined as the ratio of the average delayed neutron number and the total average fission neutron number:

$$ \beta_{eff} = \frac{{\mathop \sum \nolimits_{i} \overline{{\nu_{D} }} \left( i \right)R_{f} \left( i \right)}}{{\mathop \sum \nolimits_{i} (\overline{{\nu_{D} }} \left( i \right) + \overline{{\nu_{P} }} \left( i \right))R_{f} \left( i \right)}} $$

where \(\overline{{\nu_{D} }} \left( i \right)\) and \(\overline{{\nu_{P} }} \left( i \right)\) denote the average delayed neutron number and the average prompt neutron number per fission for actinide i, respectively. When regarding a reactor involved with various heavy nuclides, the contribution of actinide i to the total \(\beta_{eff}\) can be separated as:

$$ \beta_{eff} \left( i \right) = \frac{{\overline{{\nu_{D} }} \left( i \right)R_{f} \left( i \right)}}{{\mathop \sum \nolimits_{i} (\overline{{\nu_{D} }} \left( i \right) + \overline{{\nu_{P} }} \left( i \right))R_{f} \left( i \right)}} $$
Fig. 11.
figure 11

Evolutions of the total \(\beta_{eff}\) with Flibe and Flinak salts in the three MSR cores

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Fig. 12.
figure 12

Evolutions of the \(\beta_{eff}\) contribution of main nuclides with Flibe salt in the thermal MSR core

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Figure 11 presents the total \(\beta_{eff}\) evolutions for different MA loadings in the thermal, epithermal and fast MSR cores. For all the cases, the total \(\beta_{eff}\) is quickly decreased in the first 20-year operation and then increased gradually during the remaining 80 years. To explore the source of the variation of \(\beta_{eff}\), the separate contributions of the main actinides in the case of 4% MA in the Flibe salt for the thermal MSR are evaluated, which is listed in Fig. 12. One can see that the \(\beta_{eff}\) of U-233 at the beginning of the lifetime is as high as 274 pcm, which accounts for the vast majority of the total \(\beta_{eff}\) (287 pcm). This is because that U-233 contributes the majority of fissions in the thermal core. When the neutron spectrum hardens, more U-233 is required which increases the total \(\beta_{eff}\) correspondingly. Furthermore, an inferior neutron economy for the Flinak salt also requires more fissile fuels for criticality. Therefore, when the neutron spectrum ranges from thermal to fast, the initial total \(\beta_{eff}\) rises from 287 pcm to 298 pcm for the Flibe salt while it increases from 289 pcm to 315 pcm for the Flinak salt. During the first 20-year operation, several fissile isotopes (Pu-239, Pu-241, Cm-245) transmuted from MA are quickly accumulated which weakens the requirement of U-233 significantly. As the single \(\beta_{eff}\) of Pu-239, Pu-241 and Cm-245 are much smaller than that of U-233, the total \(\beta_{eff}\) decreases correspondingly during the first decades of operation. Since most of the TRU nuclides have a higher ratio of fission to capture in a fast neutron spectrum, the requirement of U-233 is reduced in further. Hence, the total \(\beta_{eff}\) decreases more rapidly when the neutron spectrum hardens. The total \(\beta_{eff}\) increases gradually to be an equilibrium state in the remaining 80-year operation due to the accumulated fissile isotopes except U-233.

4 Conclusions

In this paper, the MA transmutation capabilities with different MA loadings for thermal, epithermal and fast MSRs are evaluated. The MA transmutation characteristics with two types of carrier salts and three neutron spectra are compared and discussed. The effects on neutron spectrum, SIC, TR, DR, radiotoxicity and safety parameters are analyzed.

With a significant amount of MA loading into the fuel salt, the thermal, epithermal and fast neutron spectra are all moved to a faster region due to the large captures of most MA. Benefiting the online refueling, MSR can attain a high MA transmutation capability. One can be concluded that the SICs with the Flibe salt (4% MA in the fuel salt) for the three MSR cores at the end life of 100-year operation are 167, 185 and 206 kg/GWth.y, respectively. With a higher loading of MA for the Flinak salt (10% MA in the fuel salt), higher SICs are achieved in the thermal, epithermal and fast MSR cores, which are 170, 206 and 247 kg/GWth.y, respectively. MSR can attain an alluring transmutation efficiency of MA with the TR over 0.75. In addition, the IR with the Flinak salt is lower than that with the Flibe salt, especially in the thermal MSR core, because that there is an inferior neutron economy in the Flinak salt with significant capture cross sections of Na-23 and K-39, especially in thermal energy region. With little production source, high mole faction and large captures, Np has the highest DR in three MA elements, which ranges from 120.7 to 141.9 kg/GWh.y with the Flibe salt and from 122.1 to 163.3 kg/GWh.y with the Flinak salt in the three different MSR cores. With an effective transmutation capability, the total radiotoxicitiy of MA after 100-year operation is reduced significantly, about 45% lower than that at the beginning of lifetime.

Two safety parameters of TFC and \(\beta_{eff}\) are also evaluated. The total TFC is significantly varied with different neutron spectra and MA loadings but all are located in a negative region. The total TFC in the thermal MSR is varied obviously from below −20 pcm/K to about −7.5 pcm/K during 100-year operation because the thermal neutron spectrum is tended to be a faster region with the online refueling of MA which weakens the effects of MA capture resonances. The total TFC for the epithermal MSR is kept around −5 pcm/K during the entire operation time while it is about −2.5 pcm/K for the fast MSR. The total \(\beta_{eff}\) is decreased firstly in the initial 20-year operation and then increased gradually to be an equilibrium state in the remaining 80-year operation. The total \(\beta_{eff}\) at the equilibrium state varies from about 298 pcm to 329 pcm for all cases.

In conclusion, it is feasible to transmute MA in an MSR and achieve the goals of reduction of MA long-term radioactive hazards. A higher SIC is obtained with a higher MA loading for the Flinak salt while a higher TR is achieved with a better neutron economy for the Flibe salt.