Transmutation of long-lived fission products in an advanced nuclear energy system

Disposal of long-lived fission products (LLFPs) produced in reactors has been paid a lot attention for sustainable and clean nuclear energy. Although a few transmutation means have been proposed to address this issue, there are still scientific and/or engineering challenges to achieve efficient transmutation of LLFPs. In this study, we propose a novel concept of advanced nuclear energy system (ANES) for transmuting LLFPs efficiently without isotopic separation. The ANES comprises intense photoneutron source (PNS) and subcritical reactor, which consist of lead–bismuth (Pb-Bi) layer, beryllium (Be) layer, and fuel, LLFPs and shield assemblies. The PNS is produced by bombarding radioactive cesium and iodine target with a laser-Compton scattering (LCS) γ-ray beam. We investigate the effect of the ANES system layout on transmutation efficiency by Monte Carlo simulations. It is found that a proper combination of the Pb-Bi layer and the Be layer can increase the utilization efficiency of the PNS by a factor of ~ 10, which helps to decrease by almost the same factor the LCS γ-beam intensity required for driving the ANES. Supposing that the ANES operates over 20 years at a normal thermal power of 500 MWt, five LLFPs including 99Tc, 129I, 107Pd, 137Cs and 79Se could be transmuted by more than 30%. Their effective half-lives thus decrease drastically from ~ 106 to less than 102 years. It is suggested that this successful implementation of the ANES paves the avenue towards practical transmutation of LLFPs without isotopic separation.

With the inspiration of ADS implementation, we introduce a novel concept on advanced nuclear energy system (ANES) that is driven by a photoneutron source (PNS) (see Fig. 1). The PNS is produced by bombarding a radioactive cesium and iodine (CsI) target with a laser-Compton scattering (LCS) γ-ray beam. As the LCS γ-ray beam has sufficient high intensity, such bombardment produces an intense PNS and meanwhile realizes phototransmutation on radioactive cesium and iodine. The ANES is composed of the PNS and the reactor core which consists of lead-bismuth (Pb-Bi) layer, beryllium (Be) layer, and fuel, LLFPs and shield assemblies. In the ANES, both the transmutation and the energy production are accomplished. The fission energy production in the reactor core can be used to balance the energy consumption of PNS during transmutation, which means that the nuclear transmutation can be achieved without the need of external power supply. Moreover, one can expect to balance the initial cost for installing and operating the system, since this system could produce electricity and meanwhile lead to a large amount of heat generation during bombardment, making hydrogen fabrication possible 14 .
In this study, we present the conceptual design of the ANES for LLFPs transmutation without the requirement to isotopic separation. In our design, seven LLFPs are loaded in the reactor core for neutron transmutation and radioactive CsI target are handled with photo-transmutation while generating PNS. The implementation of the ANES is first introduced. Then the LCS energy spectrum and the ANES layout are optimized for improving the transmutation capability. In addition, the LCS beam intensity required for drive the ANES is evaluated. The results show that the proposed ANES concept may be a solution for transmuting LLFPs, albeit the existing LCS beam intensity is still a few orders of magnitudes lower than the requirement to drive the ANES at thermal power of 100 s MWt.

Results and discussions
ANES layout. The layout of the ANES is shown in Fig. 1. As an LCS γ-ray beam of high intensity irradiating the transmutation target (e.g., CsI target), a substantial population of neutrons are produced through photoneutron reactions, generating an intense PNS. Such PNS drives the ANES core, which is a subcritical one maintaining its intrinsic safety. The CsI target locates in the center of the ANES core. Considering a long-time irradiation, the cooling of the CsI target is achieved by circulation of liquid Pb-Bi alloy, which can endure higher energy density and longer operation cycle. A Be layer surrounding the Pb-Bi layer is adopted as neutron moderator. The combination of a 3 cm Pb-Bi layer and a 21 cm Be layer enhances the external neutron worth through neutron multiplication and moderation, as discussed later. The LLFPs without isotopic separation are loaded and transmuted with the excess neutrons leaked from the fuel assemblies. The k eff , is designed to be ~ 0.98. The isotopic compositions of the LLFPs depend on the type of fuel, the neutron spectrum, and the irradiation history. The LLFPs used in this study are obtained from the burnup simulation of uranium dioxide fuel (see Methods).
The thermal power of ANES is designed to be 500 MWt. The ANES core, with a height of 110 cm and a diameter of 105 cm, contains 162 fuel assemblies, 78 LLFPs assemblies, and 60 shield assemblies. Each fuel assembly consists of 61 pins composed of uranium dioxide pellets covered by stainless steel cladding. Due to the intrinsic  www.nature.com/scientificreports/ safety of the subcritical core, the ANES does not need control rods that are mandatorily used in a typical critical reactor. The LLFPs assemblies are arranged with two rows in the core, and the number of assemblies in inner and outer rows is 36 and 42, respectively. Like the fuel assembly, each LLFPs assembly incorporates 61 pins (43 LLFPs pins and 18 YD 2 pins). The CsI target has a height of 25 cm and a radius of 3 cm. The shield assembly is made of stainless steel containing 6.48% natural B 4 C. In the burnup simulation of the ANES core, we use the dynamic refueling to keep a constant neutron flux over 20 years of operation. The detailed design parameters for the ANES are shown in Table 1.

Production of PNS.
For the PNS produced by an LCS γ-ray beam, the production rate P n is highly dependent on the γ-ray spectral distribution and the GDR cross section. When neglecting the nonlinear Compton scattering effect, the cut-off energy of the LCS γ-ray beam can be obtained with E max γ = 4E L γ 2 / 1 + 4E L γ /m 0 c 2 , where E L is the photon energy of the incident laser, γ is the Lorentz factor of the electron beam from an advanced accelerator, and m 0 c 2 presents the electron energy at rest. To maximize P n , one can optimize E max γ by varying the Lorentz factor for a fixed E L . Figure 2 shows the dependence of P n on E max γ for varying CsI target thicknesses, T CsI . The P n increases first and then decrease with E max γ . Due to the convolution between the LCS γ-ray spectrum and the GDR cross section, the value of P n is peaked at E max γ ~ 20 MeV. When T CsI is larger than 25 cm, the P n gets a saturation of 0.01, which is determined by the penetration depth of the LCS γ-ray beam. It is expected to produce γ-ray beam at an extremely high intensity of 10 17 photon/s with the state-of-art of LCS facilities along with the advanced designs or concepts 27 . Consequently, the produced PNS could reach an intensity of 10 15 photon/s. Figure 3 shows the neutron spectrum and power density distributions in different assembly regions of the ANES core. In the region of LLFPs, the neutron spectrum is very similar to those in the region of fuel assemblies. The neutron flux decreases along the radial direction. In the shield region, the www.nature.com/scientificreports/ neutron flux is three orders of magnitudes lower than that in the inner fuel assemblies, indicating a good shielding for neutron radiation from the core. The power density varies mainly along with the neutron flux, as shown in Fig. 3b. The power density in the inner assemblies is obviously higher than that in the outer assemblies, which is in good agreement with the trend shown in Fig. 3a. A dip occurs in the region of LLFPs assemblies due to the absence of the fission process. The performance of the ANES can be evaluated by a few key quantities including k eff , k s , neutron generation time (Ʌ) and effectively delayed neutron fraction ( β eff ) 28,29 . The results for these quantities are displayed in Table 2. The initial value for k eff is 0.979. During two years of burnup, the k eff decreases slightly to 0.954. Accordingly, the sign of the system reactivity, ρ , is minus. According to Eq. (2), the ϕ value is obtained to be 1.3, which is visibly higher than that given by the spallation neutron source 30 .

Performance of the ANES.
According to Eq. (4), the required I γ is dependent on both the P t and the k eff . A contour plot for such dependence is shown in Fig. 4. It indicates that a higher P t requires a larger I γ , which decreases with the increasing k eff . To transmute the LLFPs efficiently, a thermal power of the order of 100 MWt is needed. Consequently, the I γ used to drive the ANES would exceed 10 19 photons/s, which is almost two orders of magnitudes higher than that of existing LCS designs 12,27 . Recently, current and future LCS facilities used to generate MeV photon beams is reviewed and next generation photon sources based on advanced accelerator is outlooked 31 , which demonstrate a vivid future for developments of LCS facilities with ultra-high intensity. Here we continue to summarize a few novel concepts to enhance the I γ , such as photon storage cavity 14,32 . This cavity aims to realize a high enhancement factor by increasing the stored laser power and reducing the laser size at focal point. It is expected that the cavity can achieve a 100 times improvement in γ-beam intensity. In addition, a conceptional design for a superconducting multi-turn energy-recovery linac (ERL) has been published, recently, by the international ERL community 33 . Such an ERL would produce a continuous-wave electron beam with extremely low emittance and very high current being capable of generating LCS photon beams with higher intensity.
In addition, the rather small cross section for LCS process (less than 665 mbarn) defines a physical restriction for the maximum photon flux which can be obtained from LCS facilities. A principle which overcomes this limitation has been discussed 31 . It uses a partially stripped ultra-relativistic ion beam, from which a resonant absorption of laser photons (which is in the Gbarn range) is followed by an atomic transition. Compared to the classical LCS process, unprecedented γ-beam intensity of the order of 10 17 photons/s could be reached due to the massively larger cross section for the laser photon absorption. Combing these various concepts together, it would be possible to reach more than 10 19 photons/s in the future.  Table 2. Key parameters of the ANES in the initial moment.

Physical quantity Value
Effective multiplication factor ( k eff ) 0.979 Cs. Similar results have been obtained in the fast neutron transmutation design 34 , although the transmutation of 137 Cs is not considered therein. The low transmutation efficiency for 93 Zr and 135 Cs is mainly due to their relatively small capture cross sections.
The linear increase of transmuted LLFPs is further used to evaluate the effective half-lives T eff , the TR and SR values for these LLFPs. The results are shown in Table 3, where the TR averaged over the irradiation time is considered. The T eff of the LLFPs decrease dramatically to the order of 10 years, while the radioactivity of LLFPs   In the region of CsI target, hybrid transmutation (i.e., photo-transmutation and neutron transmutation) should be considered due to the mixed field of photons and neutrons. With the thermal power of 500 MWt, the transmutation capability for CsI target is shown in Table 4. The T eff for 129 I, 135 Cs and 137 Cs decrease to less than 0.5 years according to Eq. (5), which includes the contribution of the photon and neutron transmutation. Compared with the only neutron transmutation on the LLFPs assemblies (see Table 3), the hybrid transmutation on CsI target can obtain two orders of magnitudes higher TR. In the photon field, the mass of transmuted 129 I is a few times larger than those of transmuted 135 Cs and 137 Cs, which is mainly caused by the difference in isotope composition. In the neutron field, the transmuted 129 I has a mass of 1.24 × 10 3 g/year, which is comparable to that transmuted in the photon field (1.88 × 10 3 g/year). However, in the 135 Cs and 137 Cs cases, the transmuted masses (induced mainly by neutron capture reactions on themselves) are less than the produced ones (induced mainly by their isotopes with mass number smaller than themselves). Since the cross section of 134 Cs(n, γ) reaction is significantly higher than that of 135 Cs(n, γ) reaction, and the isotope composition of 134 Cs is increased with the irradiation time, the production of 135 Cs can be larger than its consumption. The hybrid transmutation for 129 I reaches 3.12 × 10 3 g/year, which is almost one order of magnitude higher than those for 135 Cs and 137 Cs. This is mainly due to a high neutron capture cross section and a large isotope composition (see Table 5).
It should be noted that the TR (averaged over the seven LLFPs) can reach 1.94% per year for the ANES (see Table 3). This is slightly higher than that (1.51% per year) in a fast reactor system 34 . Meanwhile, the ANES has additional advantage to transmute radioiodine and radiocesium by the hybrid transmutation.
Optimal of the ANES layout. The neutron multiplier and moderator can be optimized in terms of absorption and moderation to ensure that the produced thermal neutrons can be effectively absorbed by the fuel assemblies in the core, which can thus enhance the neutron worth of PNS, ϕ . A Pb-Bi layer and a Be layer are used for neutron multiplication and moderation, respectively (see Fig. 1). The former also plays a key role in cooling the CsI target. The coolant and moderator dimensions are optimized to obtain a higher k s . Figure 6a presents the dependence of k s on the thickness of either coolant or moderator, T Be or PbBi in units of cm. The fitting results are exponentially correlated functions and can be uniformly expressed as where a 1 , b 1 and c 1 are fitting parameters. In the absence of the coolant, k s is merely dependent on T Be with a 1 = − 0.986, b 1 = − 0.112 and c 1 = − 0.150. As the coolant thickness is fixed to 3 cm, the value of a 1 remains unchanged, whereas b 1 increases slightly to − 0.101 and c 1 decreases to − 0.162. It is shown a sub-linear trend because the stopping power of neutrons in the moderator increases with the thickness. When the moderator thickness is higher than 15 cm, the value of k s can approach 1.0.
In the absence of the moderator, k s is only dependent on T PbBi and we have a 1 = 1.076, b 1 = − 0.200, and c 1 = − 0.015. When considering a 3-cm-thick moderator, the value of c 1 is kept unchanged, whereas a 1 increases slightly to 1.101 and b 1 increases to − 0.188. In this case, since the product of c 1 and T PbBi is much smaller than unity, Eq. (1) can be approximated as k s = a 2 + b 2 · T PbBi with a 2 and b 2 being the functions of a 1 , b 1 and c 1 . A quasi-linear trend is seen for the dependence of k s on T PbBi , as shown in Fig. 6a. This trend is caused by the fact that the coolant can also result in (n, xn) reaction, which increases the neutron flux. As a result, the neutron multiplication does not attenuate with the coolant thickness.
According to Eq. (4), one can further obtain the correlation between I γ and T Be or PbBi , as shown in Fig. 6b. Compared to the Pb-Bi layer, the Be layer has a more significant effect on both k s and I γ . The I γ decreases rapidly with T Be and then gets saturated, whereas the k s has an opposite variation trend. When T Be is larger than 21 cm, the required I γ approaches 10 17 , which is approximately one order of magnitude lower than that before optimization (for example, in the absence of both Pb-Bi layer and Be layer).
The effects of beryllium thickness on neutron multiplication and on softening of neutron spectrum are obtained and shown in Fig. 7. When T Be increases, the number of fast neutrons declines and that of thermal neutrons rises. The P n reaches a maximum value for T Be = 13 cm and then decreases slightly due to the significant absorption of the neutrons produced therein. For T Be = 13 cm and T PbBi = 3 cm, the neutron multiplication is (1) k s = a 1 + b 1 · exp(c 1 T Be or PbBi ), Table 4. Evaluated parameters obtained for transmutation of CsI target at 500 MWt. The tabulated data in photon field is obtained from Geant4 simulations, while the data in neutron field is obtained from SCALE simulations. The minus sign in neutron field on 135 Cs ( 137 Cs) suggests that the consumption of 135 Cs ( 137 Cs) is slower than its production.    Fig. 7b. The spectrum of photoneutrons has two peaks at around 1.0 MeV, which is probably induced by the neutrons from photonuclear (γ, n) and (γ, 2n) reactions at different energy regions. The neutron spectrum softens significantly in the moderator. As shown in Fig. 7b, these softened neutrons can enhance the fission cross sections of 235 U by more than two orders of magnitudes, leading to a greater neutron worth ϕ for the PNS. Note that the LLFPs are neutron poisons in any transmutation system. For different arrangements of fuel and LLFPs assemblies, the resulting neutron spectra and fluxes could also vary, thus affecting the transmutation efficiency. To elucidate such effect, we consider three scenarios for arranging fuel and LLFPs assemblies. Scenario A, B and C show that the LLFPs assembly locates at the outermost, the middle and the innermost position of the ANES core, respectively. The detailed arrangements are shown in Figs. 8a-c. Note that scenario B corresponds to the layout shown in Fig. 1. In these scenarios, the neutron flux possesses different spatial patterns, as shown in Figs. 8d,e. Among these scenarios, scenario B shows the highest neutron flux in the region of LLFPs assembly.  www.nature.com/scientificreports/ This is mainly caused by the convective effect of neutrons from the inner and outer fuel assemblies. In the scenario C, the LLFPs in the innermost position absorb many neutrons from the outer fuel assembly. As a result, the neutron flux shows a valley in the central zone, as shown in Fig. 8c.

LLFPs T eff (year) TR (%/year)
For the three scenarios shown in Fig. 8, the TR and SR values are further calculated. Figure 9 shows that scenario B results in the highest TR and SR for all LLFPs except for 137 Cs. The transmutation on 137 Cs is not sensitive to the scenarios due to its short half-life ( T 1/2 ). The transmutation capability in scenario B is almost two times higher than in scenario A. As a result, we consider that scenario B would be the priority for LLFPs transmutation.

Conclusion
We have presented a conceptual design of a ANES for efficient transmutation of LLFPs without isotopic separation. The ANES is driven by an intense PNS, which is produced by the energetic LCS γ-ray beam. The dimension of moderator and coolant is optimized, which enhances the k s and then decreases the required I γ by one order of magnitude. The performance of ANES and the transmutation capability are further analyzed. Especially, the T eff , TR and SR values are predicted for LLFPs. Supposing the thermal power is 500 MWt and the irradiation time is 20 years, transmutation percentages are higher than 35% and the SRs are larger than 1.0 for 79 Se, 99 Tc, 107 Pd, 129 I and 137 Cs. The T eff can thus be reduced from almost 10 6 years to the level of 100 years, which dramatically decreases the cooling time of these LLFPs. Transmutation efficiency is also sensitive to the position of the LLFPs assembly. A proper arrangement for both the LLFPs assembly and the fuel assembly is found to realize an efficient transmutation. We conclude that the ANES driven by an intense PNS could be a good candidate for efficient transmutation on LLFPs without the need of isotopic separation.

Methods
Computational model and method. The production of LCS γ-ray beam and the following irradiation, which induces CsI transmutation and generates the PNS, were simulated with Geant4-MCLCSS and Geant4-GENBOD 35,36 . The transmutation cross sections required for simulation were taken from the ENDF-VII library 37 . The implementation of the ANES and its performance evaluation were performed with SCALE 6.1 38,39 . In the SCALE simulations, we taken the LCS spectral distribution as input and considered physical processes, including neutron-capture and photonuclear reactions. Furthermore, all burnup calculations were performed using either the TRITON t-depl or the STARBUCS sequence 39 , the k eff has a statistical error lower than 0.1%, and the reaction rate for evaluating the transmutation efficiency is within 0.5%.

Selection of LLFPs.
In general, the major LLFPs that need to be transmuted are 79 Se, 93 Zr, 99 Tc, 107 Pd, 129 I, 135 Cs and 137 Cs. These nuclides can cause long-term radioactivity during the geological disposal of SNF. We should note that the half-life of 137 Cs is 30 years, which is much shorter than the other six fission products. www.nature.com/scientificreports/ Nevertheless, 137 Cs is included in the transmutation inventory as an isotopic companion of 135 Cs. This is because the latter can be transmuted effectively in the ANES without separation of isotopes. Namely, the transmutation of 137 Cs can be regarded as a subsidiary of 135 Cs. In addition, the CsI target used for the PNS plays an important role in the ANES system. The compositions of LLFPs were obtained from the burnup simulation of uranium dioxide pellets by fast breeder reactor core at 50 GWd/t for two years. The details of these compositions are presented in Table 5. Without isotopic separation, such compositions were used as the initial compositions of the LLFPs in the pins. All LLFPs were considered in metallic forms because their melting points are generally high, and the space volume for loading can be minimized 40 43 . These LLFPs are supposed to be dispersed homogeneously in the pins, which helps to transmute the LLFPs 44 .
Selection of CsI target. The CsI target was selected for photo-transmutation due to the following considerations: 129 I and 135 Cs are problematic radionuclides since they have high radiotoxicity and long half-lives. The 135 Cs strongly need isotopic separation for neutron-induced transmutation and the 137 Cs is practically nontransmutable in any neutron field as aforementioned. Meanwhile, both the iodine and cesium elements have GDR cross sections as high as 300 mbarn, which is visibly higher than other elements (see Table 5) and may result in a significant transmutation. From the point of view of target fabrication, the two elements have the most stable chemical form in which three problematic radionuclides can be combined. The coolant temperature of the lead-based fast reactor ranges from 400 to 600 ℃, which is lower than the melting point of the CsI target (~ 620 ℃). In the simulations, the isotopic compositions for CsI target were employed according to SNF of a typical light water reactor 12,17 . These compositions are 127 I (11.49%), 129 I (38.51%), 133 Cs (25.28%), 134 Cs (0.01%), 135 Cs (7.92%) and 137 Cs (16.80%).

Parameters of ANES.
The neutron worth ϕ represents the contribution of photoneutrons to the ANES core relative to fission neutrons 47 . As discussed above, ϕ is an essential parameter for the system design and can be defined as where k eff is the effective multiplication factor without considering the PNS, and k s is the multiplication factor considering PNS 48 . In our case, k s indicates the utilization efficiency of the ANES to the PNS. It is expressed by where F is the creation operator, S 0 is the number of photoneutrons, N is the total number of neutrons from nuclear fission and photonuclear process in the ANES, and s is the total neutron flux in the core. The thermal power of the ANES, P t , is dependent on the averaged fission energy E f , the LCS beam intensity I γ , the production rate of photoneutrons P n , and the average number of fission neutrons ν . In our study, it can be given by: It suggests that the I γ required for driving the ANES is inversely proportional to the ϕ when keeping P t constant.
The T eff is defined as the effective half-life of radionuclides considering both transmutation process and natural decay in the core, which is crucial for evaluating the transmutation capability. Here T eff is expressed as where and σ are thenatural decay constant and the effective neutron capture cross section for transmuted radionuclides, respectively. Equation (5) can be approximated as T eff ≈ ln2 σ � s as the are extremely smaller than the product of σ and s , indicating that an efficient transmutation can reduce significantly the T eff . For a transmutation system, transmutation rate ( TR ) and support ratio ( SR ) are also two important parameters 34 . Here, TR is the ratio of the amount of transmuted LLFPs to those initially loaded in a transmutation system, and SR is the ratio of the amount of transmuted LLFPs to that of produced ones. The expressions of TR and SR are www.nature.com/scientificreports/ Here N(0) and t are the total initial atomic number of LLFPs and irradiation time, respectively; Y and M are the LLFPs yield per fission of fuel materials and the total fission rate in the ANES core. When the value of σ � s t is small enough, the TR and SR can be simplified as σ � s and N(0)σ � s /YM , respectively. If SR > 1.0, those selfproduced LLFPs could be transmuted during the operation of the ANES. In our study, a direct approach to enhancing SR is to increase the number of initially loaded LLFPs. However, the TR will be decreased due to the neutron self-shielding effect in the loaded zone. As a result, it is imperative to balance the TR and SR for LLFPs of great interest.