Comparative study on the reduction of tritium breeding ratio caused by inventory changes of a solid-state tritium breeding blanket in a fusion demonstration reactor using MCNP and FISPACT-II

Comparative study on the reduction of tritium breeding ratio caused by inventory changes of a solid-state tritium breeding blanket in a fusion demonstration reactor using MCNP and FISPACT-II | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Comparative study on the reduction of tritium breeding ratio caused by inventory changes of a solid-state tritium breeding blanket in a fusion demonstration reactor using MCNP and FISPACT-II Byung Chul Kim This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4632828/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 08 Aug, 2024 Read the published version in Journal of Fusion Energy → Version 1 posted 9 You are reading this latest preprint version Abstract The self-sufficient supply of tritium in the deuterium-tritium nuclear fusion demonstration reactor (DEMO) is a fundamental design requirement. But, it is hindered by depletion of tritium breeding materials resulting in reduction of tritium breeding ratio (TBR) less than the initial design value especially in the solid-state tritium breeding blanket (TBB) of the DEMO. Unlike the liquid tritium breeding blanket of DEMO, compensation measures of the depleted breeding material in the solid-state TBB will be its substitution depending on the reduction rate of TBR. To estimate the replacement period of the solid-state TBB, it is required to estimate the reduction rate of TBR according to the operation conditions of the DEMO and the physical configuration of a solid-state TBB. In this study, the representative simulation codes, MCNP and FISPACT-II, are used for assessment of the reduction rate of TBR with the benchmarking model which is modified from the one poloidal segment of the TBB in the Korean-DEMO. After 3 full power-year operations with the neutron irradiation on the benchmarking model, the TBR simulated by MCNP is reduced to 96.84% of the initially calculated TBR, but the TBR calculated by FISPACT-II is reduced to 90.57% from the initially calculated TBR. Tritium Breeding Ratio TBR Depletion of 6Li MCNP FISPACT-II K-DEMO Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 1. Introduction Because of the nuclear damage of constituent components, the replacement of a solid-state tritium breeding blanket (TBB) of the deuterium-tritium nuclear fusion demonstration reactor (DEMO) within a certain appropriate period depending on its consisting material and operation condition is inevitable as discussed in [ 1 ]. In addition, the reduction of the tritium breeding ratio (TBR) comes from the depletion of tritium breeding material ( 6 Li) by neutron irradiation ( 6 Li(n, α) 3 H reaction) is one of the limiting factors that impact the replacement period of a solid-state TBB. The operation of a DEMO is limited by self-sufficiency of tritium. Therefore it is crucial to maintain a required TBR throughout the operation of a DEMO This consideration is also adopted in the conceptual design of the Korean-DEMO [ 2 ] that will use the solid-state TBB with the water-cooled pebble beds (Li 4 SiO 4 with Be 12 Ti). The physical configuration of the TBB can be found in Fig. 1 which depicts the neutronic analysis model of the K-DEMO. The K-DEMO with deuterium and tritium fusion reaction at 2.2 GW fusion power will consume tritium at a rate of 123.2 kg per full power year (FPY). The traditional methodology for the calculation of TBR is to use a neutron transport calculation toolkit like the Monte Carlo N-Particle radiation-transport (MCNP) code [ 3 ]. However, MCNP does not consider the time-dependent changes of constituting materials that come from nuclear reactions by neutron irradiation as described in [ 4 ]. As such, the neutron spectra and other calculated reaction results like TBR by MCNP are in the condition of frozen material compositions. It means that the calculated TBR by MCNP is the case of initial material compositions of a solid-state TBB which does not account for the burn-up of 6 Li nuclide that is consumed during the tritium breeding reactions. To supplement this limitation, the widely used inventory calculation code, FISPACT-II [ 5 ], which provides the time evolution of inventory by neutron irradiation could be used. The depleted 6 Li atomic concentration and generated 3 H atomic concentration can be calculated after the specified irradiation time intervals to induce the TBR during the irradiation time interval with the fixed neutron spectra. From these results with the generated neutron during the irradiation time, the TBR and evolution of TBR can be calculated at frequent time intervals. Compared to the simulated TBR by MCNP (just one TBR with the initial material compositions and self-calculated continuous neutron spectra and nuclear reaction cross-section), FISPACT-II can calculate the change history of TBR with the fixed grouped neutron spectra but varying material compositions [ 6 ]. Contrary to MCNP, FISPACT-II does not calculate the neutron spectra. Instead, it requires the neutron spectra as the mandatory input from the results of other simulation codes like MCNP. As anticipated, FISPACT-II cannot consider the changes in neutron spectra that come from the changes in material compositions during simulation. To overcome limitations in the simulation of in-situ TBR which requires the simultaneous calculation of the evolution of neutron spectra and material composition in the solid-state TBB, the coupling of MCNP and FISPACT-II codes is attempted in this study as discussed in [ 4 , 6 ]. Compared to the once-through coupling of MCNP and FISPACT-II as in [ 6 ], the evolved material compositions of a solid-state TBB calculated by FISPACT-II are incorporated into the MCNP input model at suitable required time intervals for the calculation of the new TBR by MCNP iteratively in this study. The new TBRs with new material compositions are compared to the previously calculated TBRs with old material compositions at suitable required neutron irradiation time steps. 2. The methods for calculation The poloidal segment number (PSN) 16 of the TBB which is positioned just below the equatorial line of the K-DEMO outboard region shown in Fig. 1 . This PSN 16 is simplified as the benchmarking simulation model as shown in Fig. 2 . This model is used for benchmarking the feasibility of the coupled MCNP and FISPACT-II codes methodology. Detailed physical specifications can be found in Table 1 . The neutron source intensity for the benchmarking simulation is chosen to have the same total neutron flux in tungsten (W) as that of a W layer of PSN 16 in the K-DEMO. The parallel surfaces to the direction of neutron momentum that is perpendicular to the surface of the W plate are assigned as the reflective surfaces for MCNP simulation. It makes the benchmarking model like a semi-infinite configuration, so the TBR calculated from the benchmarking model is overestimated compared to the TBR calculated from the K-DEMO model shown in Fig. 1 . Using the SuperMC code [ 7 ], the geometrical information of the benchmarking model is converted into MCNP input format. The pure material compositions are used as material information for MCNP inputs. For instance, the reduced activation ferritic/martensitic (RAFM) steel consists of pure Fe, V, Cr, Mn, and W, respectively. For the inventory calculation to track the changes in material compositions, FISPACT-II is utilized with the TENDL2017 nuclear data library [ 8 ], except for the 22 following nuclides, taken from ENDF/BVIII: 1 H, 2 H, 3 H, 3 He, 4 He, 6 Li, 7 Li, 10 B, 11 B, 9 Be, 12 C, 13 C, 14 N, 15 N, 16 O, 17 O, 19 F, 232 Th, 233 U, 235 U, 238 U and 239 Pu. The TBR and pre-required neutron flux spectra were simulated by using MCNP with the FENDL 3.0 nuclear library [ 8 ], implying that the same cross-section data have been considered for the most important tritium producing reactions. The changed material compositions according to the neutron irradiation time step are used as the new material compositions in the next MCNP simulation if required iteratively as depicted in Fig. 3 .The results from each step are discussed in section 3 . Table 1 The detailed specifications of the neutronic analysis model for benchmarking simulation. Cell No. Material Thickness (cm) Distance from Source (cm) Mass (kg) 1 Tungsten(W) 0.5 0.5 96.2500 2 Vanadium(V) 0.1 0.6 3 RAFM + H 2 O 1.5 2.1 74.8300 4 Li 4 SiO 4 + Be 12 Ti 2.3 4.4 31.8757 5 RAFM + H 2 O 1.5 5.9 6 Li 4 SiO 4 + Be 12 Ti 2.3 8.2 31.8757 7 RAFM + H 2 O 1.5 9.7 8 Li 4 SiO 4 + Be 12 Ti 2.5 12.2 34.6475 9 RAFM + H 2 O 1.5 13.7 10 Li 4 SiO 4 + Be 12 Ti 2.9 16.6 40.1911 11 RAFM + H 2 O 1.5 18.1 12 Li 4 SiO 4 + Be 12 Ti 3.6 21.7 49.8924 13 RAFM + H 2 O 1.5 23.2 14 Li 4 SiO 4 + Be 12 Ti 3.8 27.0 52.6642 15 RAFM + H 2 O 1.5 28.5 16 Li 4 SiO 4 + Be 12 Ti 5.2 33.7 72.0668 17 RAFM + H 2 O 1.5 35.2 18 Li 4 SiO 4 + Be 12 Ti 6.6 41.8 91.4694 19 RAFM + H 2 O 1.5 43.3 20 Li 4 SiO 4 + Be 12 Ti 8.0 51.3 110.872 21 RAFM + H 2 O 1.5 52.8 22 Li 4 SiO 4 + Be 12 Ti 10.0 62.8 138.590 23 RAFM + H 2 O 1.5 64.3 3. Results 3.1 The TBR by the 1st MCNP simulation with the 1st material compositions The MCNP outputs the neutron flux spectra and TBRs in the concerned tritium breeding cells. The neutron spectra shown in Fig. 4 are simulation results with the benchmarking model. The spectra of tritium breeding cells show low neutron energy fraction below thermal neutron energy region decrease because of the absorption by tritium breeding reaction compared to the spectra of other structural component cells. The spectra of tritium breeding cells are used as the inputs for inventory calculation by FISPACT-II. The TBR calculated by the 1st MCNP with the 1st material compositions in the benchmarking model is 1.225. This 1st TBR is treated as the representative TBR of the benchmarking model. If this TBR is preserved even though there are changes in material compositions by neutron irradiation during facility operation, the replacement of the TBB for reservation of the TBR has no meaning. 3.2 The 1st inventory calculation with the 1st material compositions and the spectra from 1st MCNP simulation With the neutron spectra of the 1st MCNP simulation for each tritium breeding cell, the inventory changes of the corresponding cells are calculated by the 1st FISPACT-II calculation. From the results of inventory calculation, the depletion of 6 Li and 9 Be (neutron multiplier) nuclides and accumulation of 3 H nuclides are calculated, respectively. The atomic concentrations in atomic part per million (appm) for 6 Li, 9 Be, and 3 H nuclides are shown in Fig. 5 . The 7 Li also have contributions to the TBR as presented in [ 6 ]. So the changes in its depletion rates are also traced. It can be found that the depletion rate of 9 Be is about 2% in cell 4 after 10 FPY operations. The depletion rate of 7 Li concentration is less than that of 9 Be. So the reduced contribution to the total TBR from the depletion of 7 Li and 9 Be is negligible. It can be found that the concentration of 3 H in cell 4 which is in the nearest position from the neutron source is higher than the concentration of 6 Li in cell 4 after 7 FPY operations with the neutron irradiation in Fig. 5 . From these inventory variations with the 1st neutron spectra and total fluxes, the TBR variations according to the neutron irradiation time intervals are also calculated. The evolution of TBR during 10 FPY operations is enumerated in Table 2. If it is assumed that the availability factor of a nuclear fusion facility is 30%, 10 FPY means that the full lifetime is around 30 years even if it is not still guaranteed. During the 1 FPY to 3 FPY operations, the TBR reduction ratio of 94.89% fraction is calculated by FISPACT-II. The recommended TBR in the full K-DEMO model of Fig. 1 is 1.05 [ 1 ] for the self-sufficient tritium supply. If we use the above reduction ratio for the full K-DEMO model, the reduced TBR after 3 FPY operations causes a lack of self-sufficiency of the tritium supply. However, the TBR calculated in this section is in the condition of the frozen neutron spectra that are calculated by the 1st MCNP simulation with the 1st material compositions. So, the evolved material composition by the neutron irradiation during operation and consequent changes in neutron spectra are not considered for the calculation of the TBR. It means that there will be certain differences between the TBR by the 1st FISPACT-II calculation and the TBR by the MCNP simulation without considering the changed compositions of materials during operation. In addition, the TBR calculated by MCNP uses the local neutron energy and pointwise continuous reaction cross-section. But FISPACT-II uses the grouped neutron energy and cross section as explained in [ 5 ]. As such, the direct comparison between TBR calculated by FISPACT-II and TBR simulated by MCNP in section 3.1 is not suitable in this calculation stage. However, the tendency of the reduction of the TBR can be confirmed in 1st FISPACT-II calculation of the TBR. With the evolution of total TBR, the evolution of the TBR in each tritium breeding cell in the benchmarking model is also traced according to the full power operation time. The TBR in each tritium breeding cell is depicted in Fig. 6 . After 10 FPY operations, the differences in TBR between 5 front breeding cells are less than 10% fraction. But it does not take into account the changes of material compositions and corresponding flux changes during 10 FPY operation. So the real changes may be differ from the results of Fig. 6 . But this result may show the general trend of TBR variation in each breeding cells. The evolution of the reduction ratio of TBR, in each breeding cell, is also compared to the TBRs of each cell calculated by the 1st MCNP simulation. The reduction ratio of the TBRs from the TBRs of each cell calculated by the 1st MCNP simulation is presented in Fig. 7 . It again shows that TBRs are decreasing accordingly with operation time. Table 2. The evolution of total TBR [Steps 1 and 2]. Italic values are calculated by MCNP and other values are calculated from the inventory of the FISPACT-II simulation. The 1st material compositions (MCP) are given by the initial design condition of the K-DEMO. The average statistical error of the TBR calculated by MCNP is less than 0.01%. Note The TBR marked with * is calculated after 0.01 years irradiation. FPY TBR by 1st MCNP ,1st MCP TBR by 1st FISPACT-II, 2nd MCP Simulation TBR by 2nd MCNP , 2nd MCP TBR by 2nd FISPACT-II , 3rd MCP Simulation 0 1.225 1.174* - - 1 - 1.135 1.209 - 2 - 1.106 - 1.105 3 - 1.077 - 1.077 4 - 1.048 - 1.049 5 - 1.021 - 1.020 6 - 0.995 - 0.993 7 - 0.970 - 0.967 8 - 0.946 - 0.943 9 - 0.923 - 0.919 10 - 0.901 - 0.896 It reveals that tritium self-sufficiency is a challenging requirement in the design of the solid-state TBB of the K-DEMO. As mentioned before, the evolution of TBR induced from the inventory calculation result of FISPACT-II assumes that the neutron spectra are frozen during all irradiation intervals. But neutron irradiation makes changes in the irradiated material compositions and consequential changes in the neutron spectra as well. The real-time calculation of these variations is not possible within reasonable consumption of resources. So, the step-by-step calculation of the changes in neutron spectra with the changes in the material compositions is tried as the procedures described in the next sections. Table 3 The 2nd compositions of materials that are used for 2nd MCNP simulation for each tritium breeding cell after 1 full power year neutron irradiation. Atomic number fraction in %. The above 10 appm nuclides are enumerated. Cell # Nuclide 4 6 8 10 12 14 16 18 20 22 1st material composition for all breeding cells 9 Be 80.826 80.904 81.002 81.110 81.214 81.294 81.373 81.434 81.480 81.514 81.547 16 O 5.142 5.146 5.152 5.158 5.163 5.167 5.172 5.175 5.177 5.179 5.179 48 Ti 4.976 4.980 4.986 4.992 4.998 5.003 5.007 5.011 5.013 5.015 5.015 6 Li 4.220 4.255 4.311 4.382 4.452 4.500 4.554 4.595 4.624 4.648 4.663 28 Si 1.186 1.187 1.188 1.190 1.191 1.192 1.193 1.194 1.194 1.195 1.195 4 He 0.806 0.720 0.611 0.489 0.371 0.281 0.192 0.122 0.070 0.031 - 46 Ti 0.540 0.541 0.541 0.542 0.542 0.543 0.543 0.543 0.543 0.544 0.544 7 Li 0.520 0.519 0.518 0.518 0.518 0.518 0.518 0.518 0.518 0.518 0.518 47 Ti 0.497 0.496 0.496 0.496 0.496 0.496 0.496 0.496 0.496 0.496 0.496 3 H 0.422 0.389 0.336 0.268 0.201 0.156 0.105 0.066 0.038 0.015 - 49 Ti 0.375 0.375 0.375 0.375 0.375 0.374 0.374 0.374 0.374 0.374 0.374 50 Ti 0.364 0.364 0.365 0.365 0.366 0.366 0.366 0.367 0.367 0.367 0.367 29 Si 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 30 Si 0.040 0.040 0.040 0.040 0.040 0.040 0.040 0.040 0.040 0.040 0.040 3 He 0.010 0.010 0.008 0.007 0.005 0.004 0.003 0.002 0.001 - - 1 H 0.008 0.006 0.005 0.004 0.003 0.002 0.001 0.001 - - - 13 C 0.003 0.003 0.002 0.002 0.001 0.001 0.001 - - - - 17 O 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 12 C 0.002 0.001 0.001 0.001 0.001 - - - - - - 25 Mg 0.001 0.001 0.001 0.001 - - - - - - - 6 Li/ ( 6 Li+ 9 Be) 4.9622 4.9964 5.0530 5.1253 5.1973 5.2454 5.3003 5.3407 5.3701 5.3946 5.4089 3.3 The TBR by 2nd MCNP simulation with the 2nd material compositions from 1st inventory calculation by FISPACT-II After 1 FPY operation with the neutron irradiation, the changes in material compositions are used as material information input to the 2nd MCNP simulation to compare the TBR between the results of the 1st FIPACT-II and 2nd MCNP simulations. The detailed atomic fractions of the compositions of materials in each tritium breeding cell are enumerated in Table 3 with the 1st material compositions. The relative atomic fractions of 6 Li in the 6 Li and 9 Be bed mixtures in each breeding cell are also tabulated. As discussed in [ 9 ], the variation of the mixing ratio between the 6 Li and 9 Be nuclides can change the total TBR. These mixing ratios will change step by step in the next simulations and consequently may have an impact on the calculated TBR. However, the analysis that comes from these variations of the mixing ratios is out of the scope of this study. Table 4 The calculated TBR by the 2nd MCNP simulation with the 2nd compositions of materials by the 1st FISPACT-II simulation after 1 year neutron irradiation time interval. Cell No. TBR by 2nd MCNP after 1 year irradiation TBR by 1st MCNP 4 0.187 0.194 6 0.175 0.178 8 0.164 0.166 10 0.152 0.153 12 0.141 0.141 14 0.115 0.115 16 0.105 0.105 18 0.084 0.084 20 0.059 0.059 22 0.029 0.029 Total 1.209 1.225 The calculation results of the TBR for each breeding cell by the 2nd MCNP simulation are tabulated in Table 4 . The fraction of the TBR (1.209) by the 2nd MCNP simulation with modified material compositions is 98.69% fraction of the TBR (1.225) calculated by the 1st MCNP simulation. To see the effect of neutron spectra changes compared to the 1st MCNP simulation with the 1st material compositions, the differences in the spectra are depicted in Fig. 8 . The total flux of cell 4 at 0 year (1st MCNP simulation result) is 4.77210E-4 cm − 2 s − 1 . After the 1 year irradiation, the 1st modified material compositions are used for the 2nd MCNP simulation, the flux in the cell 4 is changed to 4.77933E-4 cm − 2 s − 1 . The spectra in cell 4 after 1-year irradiation show 0.15% increase of flux. The low neutron energy (< 100 keV) fraction of total spectra changed from 1.77734E-4 cm − 2 s − 1 to 1.79077E-4 cm − 2 s − 1 in Fig. 8 . Even though there are so little bit changes in spectra (~ 0.76%), it has an impact on the TBR. It can be clearly recognized from the cross-section of 6 Li(n, α) T reaction as shown in Fig. 9 . The flux increase comes from the decrease of neutron absorptions by the 6 Li nuclide which suffers the decrease of the atomic numbers during operation. It will lead to an increase in the TBR. But the TBR is decreased from the initial value as shown in Table 4 . Even though there is some positive impact for the tritium breeding by the increase in neutron spectra, the depletion of 6 Li overwhelms this positive impact. In the case of cell 22, the differences in the material composition are minor compared to the initial one, it is consequent that neutron spectra nearly have similar patterns. 3.4 The 2nd inventory calculation with the 2nd material compositions and the spectra from the 2nd MCNP simulation With the neutron spectra by the 2nd MCNP simulation for each breeding cell, the inventory of the corresponding cells is calculated by the 2nd FISPACT-II simulation again. The procedures done in section 3.2 are repeated. The evolution of the TBR after 2 FPY operations is calculated from the inventory of the 2nd FISPACT-II simulation. The result is also enumerated in Table 2. Because the depletion of 6 Li nuclide is continuously in progress, the TBR calculated from the inventory of the 2nd FISPACT-II simulation is slightly lower than the TBR calculated from the inventory of the 1st FISPACT-II simulation of section 3.2. The relative differences between the TBRs by the 1st and 2nd FISPACT-II simulations are also tabulated in Table 2. As time goes on, the differences increase except for 3 and 4 FPY operations 3.5 The TBR by N th MCNP simulation with N th material compositions from the (N-1) th inventory calculation by FISPACT-II The N th material compositions after (N-1) cumulative years of full power operation, can be used as material information input to the N th MCNP simulation to compare the TBR between the results of the (N-1) th FISPACT-II and N th MCNP simulations. In this step, procedures of section 3.3 are repeated and N is from 3 to the required repetition steps. In this study, only 4 steps are calculated because the anticipated replacement period of a solid-state TBB in K-DEMO is around 4 FPYs [ 1 ]. The evolution of total TBR according to the full power operation is presented for 3 and 4 iterative simulation cases in Table 5 . Even though there are anomalies in the relative difference in 9 FPY, they are results that are inferred from FISPACT-II outputs. These anomalies may come from the variation in atomic ratio of 6Li/(6Li + 9Be). The total TBR calculated using the 1st compositions of materials is decreasing step by step according to the changes in materials compositions that come from the depletion of 6 Li nuclide resulting in the breeding of tritium. Table 5 The evolution of total TBR [Steps 3 and 4]. Italic values are calculated by MCNP and other values are calculated from the inventory of the FISPACT-II simulation. The 1st material compositions (MCP) are given by the initial design condition of the K-DEMO. The % values of the 6th column are the relative differences between the 5th and 3rd column TBRs. FPY TBR by 3rd MCNP ,3rd MCP TBR by 3rd FISPACT-II ,4th MCP Simulation TBR by 4th MCNP , 4th MCP TBR by 4th FISPACT-II , 5th MCP Simulation - - - - - 1 - - - - 2 1.196 - - - 3 - 1.070 1.187 - 4 - 1.043 - 1.028 5 - 1.015 - 1.003 6 - 0.987 - 0.976 7 - 0.960 - 0.950 8 - 0.934 - 0.925 9 - 0.910 - 0.901 10 - 0.886 - 0.878 4. Discussion The summarized result for the 4 iterative simulations is depicted in Fig. 10 . From the simulation result by MCNP, the reduction ratio of the TBR from operation start to 3 FPY operation is 96.84% fraction. In the case of the TBR calculated by FISPACT-II, the reduction of the TBR from 1 FPY to 4 FPY is a 90.57% fraction. The reduction ratio from the initial TBR by the MCNP simulation is strongly dependent on the physical configurations and arrangements of the tritium breeding zones in the DEMO. So, the direct adaptation of the TBR reduction ratio of the benchmarking model into the full K-DEMO model is not suitable for the exact induction of the reduction of the TBR of the K-DEMO. Nevertheless, general characteristics of the reduction of the TBR which is found in the calculation results of the benchmarking model will be shown in the coupled MCNP-FISPACT-II simulation of the K-DEMO. In the K-DEMO, even a 1% fractional reduction of the TBR can influence the tritium supply and facility operation cost. If this reduction rate also occurred in the K-DEMO, it would be an uneasy situation for the K-DEMO operation. Whatever, the reduction of the TBR will be severe if there are no measures for compensation of the depletion 6 Li nuclide in the high neutron irradiated region of the solid-state TBB of the K-DEMO that utilize the solid-state TBB. The self-sufficient tritium supply is a demanding but challenging task in the conceptual design of the K-DEMO. The current concept of the TBB of the K-DEMO is a solid-state TBB using Li 4 SiO 4 ceramic pebble beds which will be used as the tritium breeding medium. But, as found in this study, the depletion of 6 Li nuclide used for tritium breeding is a critical concern that reduces the TBR during operation. To preserve the TBR within the design limit, it is required to estimate the reduction rate of the TBR according to the operation time. In this study, the coupled MCNP and FISPACT-II simulations are adopted as the benchmarking tools for this reduction assessment of the TBR. To see the feasibility of this methodology, the simplified benchmarking model is used for the calculation of the TBR according to operation time. The composition of materials used in the benchmarking model is as those of the K-DEMO model for the MCNP simulation [ 1 ]. Even though MCNP and FISPACT-II have their distinguishing advantages for the calculation of the TBR, there are some limitations in the real-time calculation of the TBR. To overcome these limitations, the process visualized in Fig. 3 is used. Using the proposed procedures, the step-by-step calculation of the evolution of the TBR in the benchmarking model is tried according to the operation time. The calculated TBR by FISPACT-II calculation shows a relatively less 90.14% fraction than that by the MCNP simulation after 3 FPY operations in the benchmarking model. For the conservative assessment of the reduction of the TBR, the TBR calculated by the FISPACT-II may be used, but it is strictly conservative because of the difference in the calculation methods between FISPACT-II and MCNP codes. The relative difference of TBRs (1.225 and 1.174) between the codes is about 4.2% even in an around 0 FPY operation. Therefore, an ensuring kind of experimental evidence would be necessary for the practical application of this methodology before the real fabrication stage of the K-DEMO. Different simulation codes show the reduction of TBR during the operation of the tritium breeding solid-state blanket as depicted in Fig. 10 . So, the recommended TBR 1.05 of K-DEMO will be reconsidered regarding the result of this study. Declarations Author Contribution Single author (Byung Chul Kim) responsible for whole content of the manuscript. Acknowledgments The author would like to thank the Chinese FDS Team, Hefei, China, for providing the Activation and Shutdown Dose Rate Analysis code for the neutronic analysis of this study. The National R&D Program through the National Research Foundation of Korea (NRF) supported this work funded by the Ministry of Science & ICT(EN2402, CN2401). References Byung Chul Kim 2023 Nucl ear Fusion 63 086003 K. Kim et a l 2015 Nuclear Fusion 55 053027 Werner C.J. (ed) 2017 MCNP6 User Manual, Version 2.0 LA-UR-17-29981, http://mcnp.lanl.gov/ Gilbert M.R et a l 2012 Nuclear Fusion 52 083019 FISPACT-II Website, https://fispact.ukaea.uk Packer L.W et a l 2011 J. Nucl. Mater. 417 718-22 Y. Wu 2018 Fusion Science and Technology 74 321-329 IAEA Nuclear Data Service Website, https://www-nds.iaea.org J. Park et al 2015 Fusion Eng. Des. 100 159-165 Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 08 Aug, 2024 Read the published version in Journal of Fusion Energy → Version 1 posted Editorial decision: Revision requested 28 Jul, 2024 Reviews received at journal 25 Jul, 2024 Reviews received at journal 19 Jul, 2024 Reviewers agreed at journal 08 Jul, 2024 Reviewers agreed at journal 03 Jul, 2024 Reviewers invited by journal 27 Jun, 2024 Editor assigned by journal 25 Jun, 2024 Submission checks completed at journal 25 Jun, 2024 First submitted to journal 24 Jun, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4632828","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":323947972,"identity":"5ec2ce0f-a0dd-4e27-a469-ef8b28b90b97","order_by":0,"name":"Byung Chul Kim","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAsUlEQVRIiWNgGAWjYBACAwY2hgMMFQn8EO4BorWcSZBsIEkLA2MbKVrM2Y8lHro5L02Cn4H34QOGM/cIa7HsSTtwOHdbjoRkA7uxAcONYiIcdoO9Aailos7gABubBMOHBGK1zKmQsD/Axv6DSC1sQIc15EgAwwEYEDeI0AL0S8LhnGNpEhKH2ZglEs4QoQUYYsafc2qSJfjb2xg/fDhGhBYEYAZikjSMglEwCkbBKMANABl1OPJdwJaLAAAAAElFTkSuQmCC","orcid":"","institution":"Korea Institute of Fusion Energy","correspondingAuthor":true,"prefix":"","firstName":"Byung","middleName":"Chul","lastName":"Kim","suffix":""}],"badges":[],"createdAt":"2024-06-25 01:53:36","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4632828/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4632828/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s10894-024-00455-2","type":"published","date":"2024-08-08T15:58:09+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":60480721,"identity":"1846084f-9167-4ea8-8eae-7220032ff8a8","added_by":"auto","created_at":"2024-07-17 08:40:37","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":724112,"visible":true,"origin":"","legend":"\u003cp\u003eThe neutronic analysis model of the K-DEMO (lower part of the 11.25-degree 3-D model generated by SuperMC).\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-4632828/v1/eb264b414e9b6e06f66d82ad.png"},{"id":60480720,"identity":"408c7705-a29d-4375-9648-ba870a41dd1f","added_by":"auto","created_at":"2024-07-17 08:40:37","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":280022,"visible":true,"origin":"","legend":"\u003cp\u003eThe 3-D configuration of neutronic analysis model for benchmarking simulation. Source intensity is 1.1792768E+18 n/sec with the energy of 14.1 MeV and one direction momentum.\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-4632828/v1/23b5dc907c92301b24aaa02a.png"},{"id":60480723,"identity":"17fdfaa4-dd58-4971-bf0e-9402f5ddc0fc","added_by":"auto","created_at":"2024-07-17 08:40:37","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":70612,"visible":true,"origin":"","legend":"\u003cp\u003eThe flow chart for the calculation of the evolution of the TBR with coupled MCNP and FISPACT-II codes.\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-4632828/v1/669ecb47a97b1f880994a5e6.png"},{"id":60483215,"identity":"4c450ec9-8f0d-4b70-9edc-c701340ec891","added_by":"auto","created_at":"2024-07-17 09:04:37","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":224012,"visible":true,"origin":"","legend":"\u003cp\u003eThe representative normalized neutron flux spectra in the neutronic analysis model for benchmarking simulation were obtained from MCNP simulation.\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-4632828/v1/e27247bf0f69d3802cc86672.png"},{"id":60483216,"identity":"0ee1ef7d-1bda-48c9-9d7d-f099f473555b","added_by":"auto","created_at":"2024-07-17 09:04:37","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":149143,"visible":true,"origin":"","legend":"\u003cp\u003eThe transmutation of \u003csup\u003e9\u003c/sup\u003eBe and \u003csup\u003e6\u003c/sup\u003eLi atoms during 20 FPYs irradiation in tritium breeding cells. The growth-up concentration of \u003csup\u003e3\u003c/sup\u003eH is also depicted. Atoms in the legend in decreasing order of concentration in the first irradiation time step. To see the extreme case the FPY operation is extended up to 20 FPYs.\u0026nbsp;\u003c/p\u003e","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-4632828/v1/0744cdff55a6c70c2bb69d18.png"},{"id":60481457,"identity":"16d21978-98b5-4d8a-97bd-dec646120828","added_by":"auto","created_at":"2024-07-17 08:48:37","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":143470,"visible":true,"origin":"","legend":"\u003cp\u003eThe evolution of the tritium breeding ratio is calculated from the depletion of the \u003csup\u003e6\u003c/sup\u003eLi atomic number in each tritium breeding cell. The inventory of the\u003csup\u003e 6\u003c/sup\u003eLi atomic number is simulated by FISPACT-II with the corresponding spectrum in Figure 4. To see the extreme case the FPY operation is extended up to 20 FPY.\u003c/p\u003e","description":"","filename":"floatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-4632828/v1/387659a653af3c909106c677.png"},{"id":60480727,"identity":"70e0d2e0-502f-4ca3-b9ea-7c0803c87b77","added_by":"auto","created_at":"2024-07-17 08:40:37","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":161459,"visible":true,"origin":"","legend":"\u003cp\u003eThe reduction ratios of the TBRs in each breeding cell from the initial TBRs by the 1\u003csup\u003est\u003c/sup\u003e MCNP simulation. To see the extreme case the FPY operation is extended up to 20 FPY.\u003c/p\u003e","description":"","filename":"floatimage7.png","url":"https://assets-eu.researchsquare.com/files/rs-4632828/v1/51a9535750e662adcea74507.png"},{"id":60482479,"identity":"58fe49b6-aa7e-4dbc-99d7-d62eafbe0263","added_by":"auto","created_at":"2024-07-17 08:56:37","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":153093,"visible":true,"origin":"","legend":"\u003cp\u003eThe variation of neutron fluxes simulated by the 1\u003csup\u003est\u003c/sup\u003e and 2\u003csup\u003end\u003c/sup\u003e MCNP simulations. The 2\u003csup\u003end\u003c/sup\u003e MCNP simulation uses the 2\u003csup\u003end\u003c/sup\u003e compositions of materials after 1 year of neutron irradiation. The spectra for each cell after 1 year are used as flux input for the next step of inventory calculation by FISPACT-II simulation.\u003c/p\u003e","description":"","filename":"floatimage8.png","url":"https://assets-eu.researchsquare.com/files/rs-4632828/v1/c6df957ff9a340970b804dcc.png"},{"id":60480729,"identity":"1b24b396-b3f7-40e7-859b-9bc0200e17cd","added_by":"auto","created_at":"2024-07-17 08:40:37","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":76565,"visible":true,"origin":"","legend":"\u003cp\u003eThe nuclear reaction cross–section of \u003csup\u003e6\u003c/sup\u003eLi (n, α) T from ENDF/B-VIII libraries in https://oecd-nea.org.\u003c/p\u003e","description":"","filename":"floatimage9.png","url":"https://assets-eu.researchsquare.com/files/rs-4632828/v1/8d9dce82263da25f94f779d6.png"},{"id":60481460,"identity":"c84ec176-4663-4978-9905-c1cdde41e7e5","added_by":"auto","created_at":"2024-07-17 08:48:37","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":160403,"visible":true,"origin":"","legend":"\u003cp\u003eThe evolution of total TBRs for 4 iterative simulations. To see the extreme case the FPY operation is extended up to 20 FPY.\u003c/p\u003e","description":"","filename":"floatimage10.png","url":"https://assets-eu.researchsquare.com/files/rs-4632828/v1/25803b821e50cc2eed903e97.png"},{"id":62298570,"identity":"e1a945b3-2ffa-4d2d-b18d-bfe0320a365b","added_by":"auto","created_at":"2024-08-12 16:14:45","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3458767,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4632828/v1/55e127a7-f578-4c1a-abee-57a3dc9efe76.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Comparative study on the reduction of tritium breeding ratio caused by inventory changes of a solid-state tritium breeding blanket in a fusion demonstration reactor using MCNP and FISPACT-II","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eBecause of the nuclear damage of constituent components, the replacement of a solid-state tritium breeding blanket (TBB) of the deuterium-tritium nuclear fusion demonstration reactor (DEMO) within a certain appropriate period depending on its consisting material and operation condition is inevitable as discussed in [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eIn addition, the reduction of the tritium breeding ratio (TBR) comes from the depletion of tritium breeding material (\u003csup\u003e6\u003c/sup\u003eLi) by neutron irradiation (\u003csup\u003e6\u003c/sup\u003eLi(n, α)\u003csup\u003e3\u003c/sup\u003eH reaction) is one of the limiting factors that impact the replacement period of a solid-state TBB. The operation of a DEMO is limited by self-sufficiency of tritium. Therefore it is crucial to maintain a required TBR throughout the operation of a DEMO\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThis consideration is also adopted in the conceptual design of the Korean-DEMO [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e] that will use the solid-state TBB with the water-cooled pebble beds (Li\u003csub\u003e4\u003c/sub\u003eSiO\u003csub\u003e4\u003c/sub\u003e with Be\u003csub\u003e12\u003c/sub\u003eTi). The physical configuration of the TBB can be found in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e which depicts the neutronic analysis model of the K-DEMO. The K-DEMO with deuterium and tritium fusion reaction at 2.2 GW fusion power will consume tritium at a rate of 123.2 kg per full power year (FPY).\u003c/p\u003e \u003cp\u003eThe traditional methodology for the calculation of TBR is to use a neutron transport calculation toolkit like the Monte Carlo N-Particle radiation-transport (MCNP) code [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. However, MCNP does not consider the time-dependent changes of constituting materials that come from nuclear reactions by neutron irradiation as described in [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. As such, the neutron spectra and other calculated reaction results like TBR by MCNP are in the condition of frozen material compositions. It means that the calculated TBR by MCNP is the case of initial material compositions of a solid-state TBB which does not account for the burn-up of \u003csup\u003e6\u003c/sup\u003eLi nuclide that is consumed during the tritium breeding reactions.\u003c/p\u003e \u003cp\u003eTo supplement this limitation, the widely used inventory calculation code, FISPACT-II [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e], which provides the time evolution of inventory by neutron irradiation could be used. The depleted \u003csup\u003e6\u003c/sup\u003eLi atomic concentration and generated \u003csup\u003e3\u003c/sup\u003eH atomic concentration can be calculated after the specified irradiation time intervals to induce the TBR during the irradiation time interval with the fixed neutron spectra. From these results with the generated neutron during the irradiation time, the TBR and evolution of TBR can be calculated at frequent time intervals. Compared to the simulated TBR by MCNP (just one TBR with the initial material compositions and self-calculated continuous neutron spectra and nuclear reaction cross-section), FISPACT-II can calculate the change history of TBR with the fixed grouped neutron spectra but varying material compositions [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eContrary to MCNP, FISPACT-II does not calculate the neutron spectra. Instead, it requires the neutron spectra as the mandatory input from the results of other simulation codes like MCNP. As anticipated, FISPACT-II cannot consider the changes in neutron spectra that come from the changes in material compositions during simulation.\u003c/p\u003e \u003cp\u003eTo overcome limitations in the simulation of in-situ TBR which requires the simultaneous calculation of the evolution of neutron spectra and material composition in the solid-state TBB, the coupling of MCNP and FISPACT-II codes is attempted in this study as discussed in [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. Compared to the once-through coupling of MCNP and FISPACT-II as in [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e], the evolved material compositions of a solid-state TBB calculated by FISPACT-II are incorporated into the MCNP input model at suitable required time intervals for the calculation of the new TBR by MCNP iteratively in this study.\u003c/p\u003e \u003cp\u003eThe new TBRs with new material compositions are compared to the previously calculated TBRs with old material compositions at suitable required neutron irradiation time steps.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"2. The methods for calculation","content":"\u003cp\u003eThe poloidal segment number (PSN) 16 of the TBB which is positioned just below the equatorial line of the K-DEMO outboard region shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. This PSN 16 is simplified as the benchmarking simulation model as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eThis model is used for benchmarking the feasibility of the coupled MCNP and FISPACT-II codes methodology. Detailed physical specifications can be found in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eThe neutron source intensity for the benchmarking simulation is chosen to have the same total neutron flux in tungsten (W) as that of a W layer of PSN 16 in the K-DEMO. The parallel surfaces to the direction of neutron momentum that is perpendicular to the surface of the W plate are assigned as the reflective surfaces for MCNP simulation.\u003c/p\u003e \u003cp\u003eIt makes the benchmarking model like a semi-infinite configuration, so the TBR calculated from the benchmarking model is overestimated compared to the TBR calculated from the K-DEMO model shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. Using the SuperMC code [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e], the geometrical information of the benchmarking model is converted into MCNP input format. The pure material compositions are used as material information for MCNP inputs. For instance, the reduced activation ferritic/martensitic (RAFM) steel consists of pure Fe, V, Cr, Mn, and W, respectively.\u003c/p\u003e \u003cp\u003eFor the inventory calculation to track the changes in material compositions, FISPACT-II is utilized with the TENDL2017 nuclear data library [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e], except for the 22 following nuclides, taken from ENDF/BVIII: \u003csup\u003e1\u003c/sup\u003eH, \u003csup\u003e2\u003c/sup\u003eH, \u003csup\u003e3\u003c/sup\u003eH, \u003csup\u003e3\u003c/sup\u003eHe, \u003csup\u003e4\u003c/sup\u003eHe, \u003csup\u003e6\u003c/sup\u003eLi, \u003csup\u003e7\u003c/sup\u003eLi, \u003csup\u003e10\u003c/sup\u003eB, \u003csup\u003e11\u003c/sup\u003eB, \u003csup\u003e9\u003c/sup\u003eBe, \u003csup\u003e12\u003c/sup\u003eC, \u003csup\u003e13\u003c/sup\u003eC, \u003csup\u003e14\u003c/sup\u003eN, \u003csup\u003e15\u003c/sup\u003eN,\u003csup\u003e16\u003c/sup\u003eO, \u003csup\u003e17\u003c/sup\u003eO, \u003csup\u003e19\u003c/sup\u003eF, \u003csup\u003e232\u003c/sup\u003eTh, \u003csup\u003e233\u003c/sup\u003eU, \u003csup\u003e235\u003c/sup\u003eU, \u003csup\u003e238\u003c/sup\u003eU and \u003csup\u003e239\u003c/sup\u003ePu. The TBR and pre-required neutron flux spectra were simulated by using MCNP with the FENDL 3.0 nuclear library [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e], implying that the same cross-section data have been considered for the most important tritium producing reactions.\u003c/p\u003e \u003cp\u003eThe changed material compositions according to the neutron irradiation time step are used as the new material compositions in the next MCNP simulation if required iteratively as depicted in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e.The results from each step are discussed in section \u003cspan refid=\"Sec3\" class=\"InternalRef\"\u003e3\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e 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\u003cp\u003eThickness\u003c/p\u003e \u003cp\u003e(cm)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eDistance from Source\u003c/p\u003e \u003cp\u003e(cm)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eMass\u003c/p\u003e \u003cp\u003e(kg)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTungsten(W)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e96.2500\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eVanadium(V)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eRAFM\u0026thinsp;+\u0026thinsp;H\u003csub\u003e2\u003c/sub\u003eO\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e2.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e74.8300\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLi\u003csub\u003e4\u003c/sub\u003eSiO\u003csub\u003e4\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;Be\u003csub\u003e12\u003c/sub\u003eTi\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e4.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e31.8757\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eRAFM\u0026thinsp;+\u0026thinsp;H\u003csub\u003e2\u003c/sub\u003eO\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e5.9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLi\u003csub\u003e4\u003c/sub\u003eSiO\u003csub\u003e4\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;Be\u003csub\u003e12\u003c/sub\u003eTi\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e8.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e31.8757\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eRAFM\u0026thinsp;+\u0026thinsp;H\u003csub\u003e2\u003c/sub\u003eO\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e9.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLi\u003csub\u003e4\u003c/sub\u003eSiO\u003csub\u003e4\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;Be\u003csub\u003e12\u003c/sub\u003eTi\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e12.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e34.6475\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eRAFM\u0026thinsp;+\u0026thinsp;H\u003csub\u003e2\u003c/sub\u003eO\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e13.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLi\u003csub\u003e4\u003c/sub\u003eSiO\u003csub\u003e4\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;Be\u003csub\u003e12\u003c/sub\u003eTi\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2.9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e16.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e40.1911\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eRAFM\u0026thinsp;+\u0026thinsp;H\u003csub\u003e2\u003c/sub\u003eO\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e18.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLi\u003csub\u003e4\u003c/sub\u003eSiO\u003csub\u003e4\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;Be\u003csub\u003e12\u003c/sub\u003eTi\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e3.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e21.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e49.8924\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eRAFM\u0026thinsp;+\u0026thinsp;H\u003csub\u003e2\u003c/sub\u003eO\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e23.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLi\u003csub\u003e4\u003c/sub\u003eSiO\u003csub\u003e4\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;Be\u003csub\u003e12\u003c/sub\u003eTi\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e3.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e27.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e52.6642\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eRAFM\u0026thinsp;+\u0026thinsp;H\u003csub\u003e2\u003c/sub\u003eO\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e28.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLi\u003csub\u003e4\u003c/sub\u003eSiO\u003csub\u003e4\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;Be\u003csub\u003e12\u003c/sub\u003eTi\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e5.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e33.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e72.0668\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eRAFM\u0026thinsp;+\u0026thinsp;H\u003csub\u003e2\u003c/sub\u003eO\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e35.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLi\u003csub\u003e4\u003c/sub\u003eSiO\u003csub\u003e4\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;Be\u003csub\u003e12\u003c/sub\u003eTi\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e6.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e41.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e91.4694\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e19\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eRAFM\u0026thinsp;+\u0026thinsp;H\u003csub\u003e2\u003c/sub\u003eO\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e43.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLi\u003csub\u003e4\u003c/sub\u003eSiO\u003csub\u003e4\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;Be\u003csub\u003e12\u003c/sub\u003eTi\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e8.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e51.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e110.872\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e21\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eRAFM\u0026thinsp;+\u0026thinsp;H\u003csub\u003e2\u003c/sub\u003eO\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e52.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e22\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLi\u003csub\u003e4\u003c/sub\u003eSiO\u003csub\u003e4\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;Be\u003csub\u003e12\u003c/sub\u003eTi\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e10.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e62.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e138.590\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e23\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eRAFM\u0026thinsp;+\u0026thinsp;H\u003csub\u003e2\u003c/sub\u003eO\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e64.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"3. Results","content":"\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e3.1 The TBR by the 1st MCNP simulation with the 1st material compositions\u003c/h2\u003e \u003cp\u003eThe MCNP outputs the neutron flux spectra and TBRs in the concerned tritium breeding cells. The neutron spectra shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e are simulation results with the benchmarking model. The spectra of tritium breeding cells show low neutron energy fraction below thermal neutron energy region decrease because of the absorption by tritium breeding reaction compared to the spectra of other structural component cells. The spectra of tritium breeding cells are used as the inputs for inventory calculation by FISPACT-II. The TBR calculated by the 1st MCNP with the 1st material compositions in the benchmarking model is 1.225. This 1st TBR is treated as the representative TBR of the benchmarking model. If this TBR is preserved even though there are changes in material compositions by neutron irradiation during facility operation, the replacement of the TBB for reservation of the TBR has no meaning.\u003c/p\u003e \u003cp\u003e \u003cem\u003e3.2 The 1st inventory calculation with the 1st material compositions and the spectra from 1st MCNP simulation\u003c/em\u003e \u003c/p\u003e \u003cp\u003eWith the neutron spectra of the 1st MCNP simulation for each tritium breeding cell, the inventory changes of the corresponding cells are calculated by the 1st FISPACT-II calculation. From the results of inventory calculation, the depletion of \u003csup\u003e6\u003c/sup\u003eLi and \u003csup\u003e9\u003c/sup\u003eBe (neutron multiplier) nuclides and accumulation of \u003csup\u003e3\u003c/sup\u003eH nuclides are calculated, respectively.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe atomic concentrations in atomic part per million (appm) for \u003csup\u003e6\u003c/sup\u003eLi, \u003csup\u003e9\u003c/sup\u003eBe, and \u003csup\u003e3\u003c/sup\u003eH nuclides are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eThe \u003csup\u003e7\u003c/sup\u003eLi also have contributions to the TBR as presented in [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. So the changes in its depletion rates are also traced. It can be found that the depletion rate of \u003csup\u003e9\u003c/sup\u003eBe is about 2% in cell 4 after 10 FPY operations. The depletion rate of \u003csup\u003e7\u003c/sup\u003eLi concentration is less than that of \u003csup\u003e9\u003c/sup\u003eBe. So the reduced contribution to the total TBR from the depletion of \u003csup\u003e7\u003c/sup\u003eLi and \u003csup\u003e9\u003c/sup\u003eBe is negligible.\u003c/p\u003e \u003cp\u003eIt can be found that the concentration of \u003csup\u003e3\u003c/sup\u003eH in cell 4 which is in the nearest position from the neutron source is higher than the concentration of \u003csup\u003e6\u003c/sup\u003eLi in cell 4 after 7 FPY operations with the neutron irradiation in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eFrom these inventory variations with the 1st neutron spectra and total fluxes, the TBR variations according to the neutron irradiation time intervals are also calculated. The evolution of TBR during 10 FPY operations is enumerated in Table\u0026nbsp;2.\u003c/p\u003e \u003cp\u003eIf it is assumed that the availability factor of a nuclear fusion facility is 30%, 10 FPY means that the full lifetime is around 30 years even if it is not still guaranteed. During the 1 FPY to 3 FPY operations, the TBR reduction ratio of 94.89% fraction is calculated by FISPACT-II. The recommended TBR in the full K-DEMO model of Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e is 1.05 [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e] for the self-sufficient tritium supply. If we use the above reduction ratio for the full K-DEMO model, the reduced TBR after 3 FPY operations causes a lack of self-sufficiency of the tritium supply.\u003c/p\u003e \u003cp\u003eHowever, the TBR calculated in this section is in the condition of the frozen neutron spectra that are calculated by the 1st MCNP simulation with the 1st material compositions. So, the evolved material composition by the neutron irradiation during operation and consequent changes in neutron spectra are not considered for the calculation of the TBR. It means that there will be certain differences between the TBR by the 1st FISPACT-II calculation and the TBR by the MCNP simulation without considering the changed compositions of materials during operation. In addition, the TBR calculated by MCNP uses the local neutron energy and pointwise continuous reaction cross-section. But FISPACT-II uses the grouped neutron energy and cross section as explained in [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. As such, the direct comparison between TBR calculated by FISPACT-II and TBR simulated by MCNP in section \u003cspan refid=\"Sec4\" class=\"InternalRef\"\u003e3.1\u003c/span\u003e is not suitable in this calculation stage. However, the tendency of the reduction of the TBR can be confirmed in 1st FISPACT-II calculation of the TBR.\u003c/p\u003e \u003cp\u003eWith the evolution of total TBR, the evolution of the TBR in each tritium breeding cell in the benchmarking model is also traced according to the full power operation time.\u003c/p\u003e \u003cp\u003eThe TBR in each tritium breeding cell is depicted in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e. After 10 FPY operations, the differences in TBR between 5 front breeding cells are less than 10% fraction. But it does not take into account the changes of material compositions and corresponding flux changes during 10 FPY operation. So the real changes may be differ from the results of Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e. But this result may show the general trend of TBR variation in each breeding cells.\u003c/p\u003e \u003cp\u003eThe evolution of the reduction ratio of TBR, in each breeding cell, is also compared to the TBRs of each cell calculated by the 1st MCNP simulation. The reduction ratio of the TBRs from the TBRs of each cell calculated by the 1st MCNP simulation is presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e. It again shows that TBRs are decreasing accordingly with operation time.\u003c/p\u003e \u003cp\u003e \u003cb\u003eTable\u0026nbsp;2.\u003c/b\u003e The evolution of total TBR [Steps 1 and 2].\u003c/p\u003e \u003cp\u003e \u003cb\u003eItalic\u003c/b\u003e values are calculated by MCNP and other values are calculated from the inventory of the FISPACT-II simulation.\u003c/p\u003e \u003cp\u003eThe 1st material compositions (MCP) are given by the initial design condition of the K-DEMO. The average statistical error of the TBR calculated by MCNP is less than 0.01%.\u003c/p\u003e \u003cp\u003e \u003cstrong\u003eNote\u003c/strong\u003e \u003cp\u003eThe TBR marked with * is calculated after 0.01 years irradiation.\u003c/p\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Taba\" border=\"1\"\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFPY\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTBR by\u003c/p\u003e \u003cp\u003e1st MCNP\u003c/p\u003e \u003cp\u003e,1st MCP\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eTBR by\u003c/p\u003e \u003cp\u003e1st FISPACT-II,\u003c/p\u003e \u003cp\u003e2nd MCP Simulation\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eTBR by\u003c/p\u003e \u003cp\u003e2nd MCNP\u003c/p\u003e \u003cp\u003e, 2nd MCP\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eTBR by\u003c/p\u003e \u003cp\u003e2nd FISPACT-II\u003c/p\u003e \u003cp\u003e, 3rd MCP Simulation\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e1.225\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.174*\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.135\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e1.209\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.106\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.105\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.077\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.077\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.048\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.049\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.021\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.020\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.995\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.993\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.970\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.967\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.946\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.943\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.923\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.919\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.901\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.896\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIt reveals that tritium self-sufficiency is a challenging requirement in the design of the solid-state TBB of the K-DEMO. As mentioned before, the evolution of TBR induced from the inventory calculation result of FISPACT-II assumes that the neutron spectra are frozen during all irradiation intervals. But neutron irradiation makes changes in the irradiated material compositions and consequential changes in the neutron spectra as well. The real-time calculation of these variations is not possible within reasonable consumption of resources.\u003c/p\u003e \u003cp\u003eSo, the step-by-step calculation of the changes in neutron spectra with the changes in the material compositions is tried as the procedures described in the next sections.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eThe 2nd compositions of materials that are used for 2nd MCNP simulation for each tritium breeding cell after 1 full power year neutron irradiation. Atomic number fraction in %. The above 10 appm nuclides are enumerated.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"12\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c11\" colnum=\"11\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c12\" colnum=\"12\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCell #\u003c/p\u003e \u003cp\u003eNuclide\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003e14\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003e16\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003e18\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c10\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c11\"\u003e \u003cp\u003e22\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c12\"\u003e \u003cp\u003e1st material composition for all breeding cells\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003csup\u003e9\u003c/sup\u003eBe\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e80.826\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e80.904\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e81.002\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e81.110\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e81.214\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e81.294\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e81.373\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e81.434\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e81.480\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e81.514\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cb\u003e81.547\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003csup\u003e16\u003c/sup\u003eO\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e5.142\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e5.146\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e5.152\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e5.158\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e5.163\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e5.167\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e5.172\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e5.175\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e5.177\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e5.179\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cb\u003e5.179\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003csup\u003e48\u003c/sup\u003eTi\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e4.976\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e4.980\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e4.986\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e4.992\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e4.998\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e5.003\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e5.007\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e5.011\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e5.013\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e5.015\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cb\u003e5.015\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003csup\u003e6\u003c/sup\u003eLi\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e4.220\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e4.255\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e4.311\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e4.382\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e4.452\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e4.500\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e4.554\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e4.595\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e4.624\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e4.648\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cb\u003e4.663\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003csup\u003e28\u003c/sup\u003eSi\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1.186\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.187\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.188\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1.190\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.191\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1.192\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e1.193\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e1.194\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e1.194\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e1.195\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cb\u003e1.195\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003csup\u003e4\u003c/sup\u003eHe\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.806\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.720\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.611\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.489\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.371\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.281\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.192\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.122\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.070\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e0.031\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cb\u003e-\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003csup\u003e46\u003c/sup\u003eTi\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.540\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.541\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.541\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.542\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.542\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.543\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.543\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.543\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.543\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e0.544\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cb\u003e0.544\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003csup\u003e7\u003c/sup\u003eLi\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.520\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.519\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.518\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.518\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.518\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.518\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.518\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.518\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.518\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e0.518\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cb\u003e0.518\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003csup\u003e47\u003c/sup\u003eTi\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.497\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.496\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.496\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.496\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.496\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.496\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.496\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.496\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.496\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e0.496\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cb\u003e0.496\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003csup\u003e3\u003c/sup\u003eH\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.422\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.389\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.336\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.268\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.201\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.156\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.105\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.066\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.038\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e0.015\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cb\u003e-\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003csup\u003e49\u003c/sup\u003eTi\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.375\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.375\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.375\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.375\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e 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\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.365\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.365\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.366\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.366\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.366\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.367\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.367\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e0.367\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cb\u003e0.367\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003csup\u003e29\u003c/sup\u003eSi\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.060\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.060\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.060\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.060\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.060\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.060\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.060\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.060\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.060\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e0.060\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cb\u003e0.060\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003csup\u003e30\u003c/sup\u003eSi\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.040\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.040\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.040\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.040\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.040\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.040\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.040\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.040\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.040\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e0.040\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cb\u003e0.040\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003csup\u003e3\u003c/sup\u003eHe\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.010\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.010\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.008\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.007\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.005\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.004\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.003\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.002\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cb\u003e-\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003csup\u003e1\u003c/sup\u003eH\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.008\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.006\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.005\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.004\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.003\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.002\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cb\u003e-\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003csup\u003e13\u003c/sup\u003eC\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.003\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.003\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.002\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.002\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cb\u003e-\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003csup\u003e17\u003c/sup\u003eO\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.002\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.002\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.002\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.002\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.002\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.002\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.002\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.002\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.002\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e0.002\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cb\u003e0.002\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003csup\u003e12\u003c/sup\u003eC\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.002\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003csup\u003e25\u003c/sup\u003eMg\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003csup\u003e\u003cem\u003e6\u003c/em\u003e\u003c/sup\u003e\u003cem\u003eLi/\u003c/em\u003e\u003c/p\u003e \u003cp\u003e\u003cem\u003e(\u003c/em\u003e\u003csup\u003e\u003cem\u003e6\u003c/em\u003e\u003c/sup\u003e\u003cem\u003eLi+\u003c/em\u003e\u003csup\u003e\u003cem\u003e9\u003c/em\u003e\u003c/sup\u003e\u003cem\u003eBe)\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003e4.9622\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003e4.9964\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003e5.0530\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003e5.1253\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cem\u003e5.1973\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cem\u003e5.2454\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cem\u003e5.3003\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cem\u003e5.3407\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e\u003cem\u003e5.3701\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e\u003cem\u003e5.3946\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cem\u003e5.4089\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cem\u003e3.3 The TBR by 2nd MCNP simulation with the 2nd material compositions from 1st inventory calculation by FISPACT-II\u003c/em\u003e \u003c/p\u003e \u003cp\u003eAfter 1 FPY operation with the neutron irradiation, the changes in material compositions are used as material information input to the 2nd MCNP simulation to compare the TBR between the results of the 1st FIPACT-II and 2nd MCNP simulations. The detailed atomic fractions of the compositions of materials in each tritium breeding cell are enumerated in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e3\u003c/span\u003e with the 1st material compositions. The relative atomic fractions of \u003csup\u003e6\u003c/sup\u003eLi in the \u003csup\u003e6\u003c/sup\u003eLi and \u003csup\u003e9\u003c/sup\u003eBe bed mixtures in each breeding cell are also tabulated. As discussed in [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e], the variation of the mixing ratio between the \u003csup\u003e6\u003c/sup\u003eLi and \u003csup\u003e9\u003c/sup\u003eBe nuclides can change the total TBR. These mixing ratios will change step by step in the next simulations and consequently may have an impact on the calculated TBR. However, the analysis that comes from these variations of the mixing ratios is out of the scope of this study.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eThe calculated TBR by the 2nd MCNP simulation with the 2nd compositions of materials by the 1st FISPACT-II simulation after 1 year neutron irradiation time interval.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCell\u003c/p\u003e \u003cp\u003eNo.\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTBR by 2nd MCNP\u003c/p\u003e \u003cp\u003eafter 1 year irradiation\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eTBR\u003c/p\u003e \u003cp\u003eby 1st MCNP\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.187\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.194\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.175\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.178\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.164\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.166\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.152\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.153\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.141\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.141\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.115\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.115\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.105\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.105\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.084\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.084\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.059\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.059\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e22\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.029\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.029\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTotal\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003e1.209\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003e1.225\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe calculation results of the TBR for each breeding cell by the 2nd MCNP simulation are tabulated in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e4\u003c/span\u003e. The fraction of the TBR (1.209) by the 2nd MCNP simulation with modified material compositions is 98.69% fraction of the TBR (1.225) calculated by the 1st MCNP simulation.\u003c/p\u003e \u003cp\u003eTo see the effect of neutron spectra changes compared to the 1st MCNP simulation with the 1st material compositions, the differences in the spectra are depicted in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eThe total flux of cell 4 at 0 year (1st MCNP simulation result) is 4.77210E-4 cm\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003es\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e. After the 1 year irradiation, the 1st modified material compositions are used for the 2nd MCNP simulation, the flux in the cell 4 is changed to 4.77933E-4 cm\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003es\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eThe spectra in cell 4 after 1-year irradiation show 0.15% increase of flux. The low neutron energy (\u0026lt;\u0026thinsp;100 keV) fraction of total spectra changed from 1.77734E-4 cm\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003es\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e to 1.79077E-4 cm\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003es\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003ein Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e. Even though there are so little bit changes in spectra (~\u0026thinsp;0.76%), it has an impact on the TBR.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIt can be clearly recognized from the cross-section of \u003csup\u003e6\u003c/sup\u003eLi(n, α) T reaction as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe flux increase comes from the decrease of neutron absorptions by the \u003csup\u003e6\u003c/sup\u003eLi nuclide which suffers the decrease of the atomic numbers during operation. It will lead to an increase in the TBR. But the TBR is decreased from the initial value as shown in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e4\u003c/span\u003e. Even though there is some positive impact for the tritium breeding by the increase in neutron spectra, the depletion of \u003csup\u003e6\u003c/sup\u003eLi overwhelms this positive impact. In the case of cell 22, the differences in the material composition are minor compared to the initial one, it is consequent that neutron spectra nearly have similar patterns.\u003c/p\u003e \u003cp\u003e \u003cem\u003e3.4 The 2nd inventory calculation with the 2nd material compositions and the spectra from the 2nd MCNP simulation\u003c/em\u003e \u003c/p\u003e \u003cp\u003eWith the neutron spectra by the 2nd MCNP simulation for each breeding cell, the inventory of the corresponding cells is calculated by the 2nd FISPACT-II simulation again. The procedures done in section 3.2 are repeated. The evolution of the TBR after 2 FPY operations is calculated from the inventory of the 2nd FISPACT-II simulation. The result is also enumerated in Table\u0026nbsp;2.\u003c/p\u003e \u003cp\u003eBecause the depletion of \u003csup\u003e6\u003c/sup\u003eLi nuclide is continuously in progress, the TBR calculated from the inventory of the 2nd FISPACT-II simulation is slightly lower than the TBR calculated from the inventory of the 1st FISPACT-II simulation of section 3.2.\u003c/p\u003e \u003cp\u003eThe relative differences between the TBRs by the 1st and 2nd FISPACT-II simulations are also tabulated in Table\u0026nbsp;2. As time goes on, the differences increase except for 3 and 4 FPY operations\u003c/p\u003e \u003cp\u003e \u003cem\u003e3.5 The TBR by N\u003c/em\u003e \u003csup\u003e \u003cem\u003eth\u003c/em\u003e \u003c/sup\u003e \u003cem\u003eMCNP simulation with N\u003c/em\u003e\u003csup\u003e\u003cem\u003eth\u003c/em\u003e\u003c/sup\u003e \u003cem\u003ematerial compositions from the (N-1)\u003c/em\u003e\u003csup\u003e\u003cem\u003eth\u003c/em\u003e\u003c/sup\u003e \u003cem\u003einventory calculation by FISPACT-II\u003c/em\u003e\u003c/p\u003e \u003cp\u003eThe N\u003csup\u003eth\u003c/sup\u003e material compositions after (N-1) cumulative years of full power operation, can be used as material information input to the N\u003csup\u003eth\u003c/sup\u003e MCNP simulation to compare the TBR between the results of the (N-1)\u003csup\u003eth\u003c/sup\u003e FISPACT-II and N\u003csup\u003eth\u003c/sup\u003e MCNP simulations.\u003c/p\u003e \u003cp\u003eIn this step, procedures of section 3.3 are repeated and N is from 3 to the required repetition steps. In this study, only 4 steps are calculated because the anticipated replacement period of a solid-state TBB in K-DEMO is around 4 FPYs [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThe evolution of total TBR according to the full power operation is presented for 3 and 4 iterative simulation cases in Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e5\u003c/span\u003e. Even though there are anomalies in the relative difference in 9 FPY, they are results that are inferred from FISPACT-II outputs. These anomalies may come from the variation in atomic ratio of 6Li/(6Li\u0026thinsp;+\u0026thinsp;9Be).\u003c/p\u003e \u003cp\u003eThe total TBR calculated using the 1st compositions of materials is decreasing step by step according to the changes in materials compositions that come from the depletion of \u003csup\u003e6\u003c/sup\u003eLi nuclide resulting in the breeding of tritium.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eThe evolution of total TBR [Steps 3 and 4]. \u003cb\u003eItalic\u003c/b\u003e values are calculated by MCNP and other values are calculated from the inventory of the FISPACT-II simulation. The 1st material compositions (MCP) are given by the initial design condition of the K-DEMO. The % values of the 6th column are the relative differences between the 5th and 3rd column TBRs.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFPY\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTBR by\u003c/p\u003e \u003cp\u003e3rd MCNP\u003c/p\u003e \u003cp\u003e,3rd MCP\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eTBR by\u003c/p\u003e \u003cp\u003e3rd FISPACT-II\u003c/p\u003e \u003cp\u003e,4th MCP Simulation\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eTBR by\u003c/p\u003e \u003cp\u003e4th MCNP\u003c/p\u003e \u003cp\u003e, 4th MCP\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eTBR by\u003c/p\u003e \u003cp\u003e4th FISPACT-II\u003c/p\u003e \u003cp\u003e, 5th MCP Simulation\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003e-\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003e-\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003e-\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd 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\u003cp\u003e0.934\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.925\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.910\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.901\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.886\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.878\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"4. Discussion","content":"\u003cp\u003eThe summarized result for the 4 iterative simulations is depicted in Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e. From the simulation result by MCNP, the reduction ratio of the TBR from operation start to 3 FPY operation is 96.84% fraction. In the case of the TBR calculated by FISPACT-II, the reduction of the TBR from 1 FPY to 4 FPY is a 90.57% fraction. The reduction ratio from the initial TBR by the MCNP simulation is strongly dependent on the physical configurations and arrangements of the tritium breeding zones in the DEMO. So, the direct adaptation of the TBR reduction ratio of the benchmarking model into the full K-DEMO model is not suitable for the exact induction of the reduction of the TBR of the K-DEMO.\u003c/p\u003e \u003cp\u003eNevertheless, general characteristics of the reduction of the TBR which is found in the calculation results of the benchmarking model will be shown in the coupled MCNP-FISPACT-II simulation of the K-DEMO. In the K-DEMO, even a 1% fractional reduction of the TBR can influence the tritium supply and facility operation cost. If this reduction rate also occurred in the K-DEMO, it would be an uneasy situation for the K-DEMO operation. Whatever, the reduction of the TBR will be severe if there are no measures for compensation of the depletion \u003csup\u003e6\u003c/sup\u003eLi nuclide in the high neutron irradiated region of the solid-state TBB of the K-DEMO that utilize the solid-state TBB.\u003c/p\u003e \u003cp\u003eThe self-sufficient tritium supply is a demanding but challenging task in the conceptual design of the K-DEMO. The current concept of the TBB of the K-DEMO is a solid-state TBB using Li\u003csub\u003e4\u003c/sub\u003eSiO\u003csub\u003e4\u003c/sub\u003e ceramic pebble beds which will be used as the tritium breeding medium. But, as found in this study, the depletion of \u003csup\u003e6\u003c/sup\u003eLi nuclide used for tritium breeding is a critical concern that reduces the TBR during operation. To preserve the TBR within the design limit, it is required to estimate the reduction rate of the TBR according to the operation time.\u003c/p\u003e \u003cp\u003eIn this study, the coupled MCNP and FISPACT-II simulations are adopted as the benchmarking tools for this reduction assessment of the TBR. To see the feasibility of this methodology, the simplified benchmarking model is used for the calculation of the TBR according to operation time. The composition of materials used in the benchmarking model is as those of the K-DEMO model for the MCNP simulation [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. Even though MCNP and FISPACT-II have their distinguishing advantages for the calculation of the TBR, there are some limitations in the real-time calculation of the TBR. To overcome these limitations, the process visualized in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e is used.\u003c/p\u003e \u003cp\u003eUsing the proposed procedures, the step-by-step calculation of the evolution of the TBR in the benchmarking model is tried according to the operation time. The calculated TBR by FISPACT-II calculation shows a relatively less 90.14% fraction than that by the MCNP simulation after 3 FPY operations in the benchmarking model.\u003c/p\u003e \u003cp\u003eFor the conservative assessment of the reduction of the TBR, the TBR calculated by the FISPACT-II may be used, but it is strictly conservative because of the difference in the calculation methods between FISPACT-II and MCNP codes. The relative difference of TBRs (1.225 and 1.174) between the codes is about 4.2% even in an around 0 FPY operation.\u003c/p\u003e \u003cp\u003eTherefore, an ensuring kind of experimental evidence would be necessary for the practical application of this methodology before the real fabrication stage of the K-DEMO. Different simulation codes show the reduction of TBR during the operation of the tritium breeding solid-state blanket as depicted in Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e. So, the recommended TBR 1.05 of K-DEMO will be reconsidered regarding the result of this study.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eSingle author (Byung Chul Kim) responsible for whole content of the manuscript.\u003c/p\u003e\u003cp\u003e\u003cstrong\u003eAcknowledgments\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe author would like to thank the Chinese FDS Team, Hefei, China, for providing the Activation and Shutdown Dose Rate Analysis code for the neutronic analysis of this study. The National R\u0026amp;D Program through the National Research Foundation of Korea (NRF) supported this work funded by the Ministry of Science \u0026amp; ICT(EN2402, CN2401).\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eByung Chul Kim 2023 \u003cem\u003eNucl\u003c/em\u003e\u003cem\u003eear \u003c/em\u003e\u003cem\u003eFusion\u003c/em\u003e \u003cstrong\u003e63\u003c/strong\u003e 086003\u003c/li\u003e\n\u003cli\u003eK. Kim \u003cem\u003eet a\u003c/em\u003el 2015 \u003cem\u003eNuclear Fusion\u003c/em\u003e \u003cstrong\u003e55\u003c/strong\u003e 053027\u003c/li\u003e\n\u003cli\u003eWerner C.J. (ed) 2017 MCNP6 User Manual, Version 2.0 LA-UR-17-29981, http://mcnp.lanl.gov/\u003c/li\u003e\n\u003cli\u003eGilbert M.R\u003cem\u003e et a\u003c/em\u003el 2012 \u003cem\u003eNuclear Fusion\u003c/em\u003e \u003cstrong\u003e52\u003c/strong\u003e 083019\u003c/li\u003e\n\u003cli\u003eFISPACT-II Website, https://fispact.ukaea.uk \u003c/li\u003e\n\u003cli\u003ePacker L.W \u003cem\u003eet a\u003c/em\u003el 2011 \u003cem\u003eJ. Nucl. Mater.\u003c/em\u003e \u003cstrong\u003e417\u003c/strong\u003e 718-22\u003c/li\u003e\n\u003cli\u003eY. Wu 2018 \u003cem\u003eFusion Science and Technology\u003c/em\u003e \u003cstrong\u003e74\u003c/strong\u003e 321-329\u003c/li\u003e\n\u003cli\u003eIAEA Nuclear Data Service Website, https://www-nds.iaea.org\u003c/li\u003e\n\u003cli\u003eJ. Park \u003cem\u003eet al\u003c/em\u003e 2015 \u003cem\u003eFusion Eng. Des.\u003c/em\u003e \u003cstrong\u003e100\u003c/strong\u003e 159-165 \u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"journal-of-fusion-energy","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jofe","sideBox":"Learn more about [Journal of Fusion Energy](http://link.springer.com/journal/10894)","snPcode":"10894","submissionUrl":"https://submission.nature.com/new-submission/10894/3","title":"Journal of Fusion Energy","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Tritium Breeding Ratio, TBR, Depletion of 6Li, MCNP, FISPACT-II, K-DEMO","lastPublishedDoi":"10.21203/rs.3.rs-4632828/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4632828/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe self-sufficient supply of tritium in the deuterium-tritium nuclear fusion demonstration reactor (DEMO) is a fundamental design requirement. But, it is hindered by depletion of tritium breeding materials resulting in reduction of tritium breeding ratio (TBR) less than the initial design value especially in the solid-state tritium breeding blanket (TBB) of the DEMO. Unlike the liquid tritium breeding blanket of DEMO, compensation measures of the depleted breeding material in the solid-state TBB will be its substitution depending on the reduction rate of TBR.\u003c/p\u003e \u003cp\u003eTo estimate the replacement period of the solid-state TBB, it is required to estimate the reduction rate of TBR according to the operation conditions of the DEMO and the physical configuration of a solid-state TBB. In this study, the representative simulation codes, MCNP and FISPACT-II, are used for assessment of the reduction rate of TBR with the benchmarking model which is modified from the one poloidal segment of the TBB in the Korean-DEMO. After 3 full power-year operations with the neutron irradiation on the benchmarking model, the TBR simulated by MCNP is reduced to 96.84% of the initially calculated TBR, but the TBR calculated by FISPACT-II is reduced to 90.57% from the initially calculated TBR.\u003c/p\u003e","manuscriptTitle":"Comparative study on the reduction of tritium breeding ratio caused by inventory changes of a solid-state tritium breeding blanket in a fusion demonstration reactor using MCNP and FISPACT-II","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-07-17 08:40:32","doi":"10.21203/rs.3.rs-4632828/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2024-07-28T06:24:43+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-07-25T13:57:09+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-07-19T15:53:04+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"332847793145088636270908630835905938496","date":"2024-07-08T06:27:47+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"45535258549540565965857166423951347941","date":"2024-07-03T09:07:09+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2024-06-27T06:47:18+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-06-25T16:39:23+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-06-25T14:07:31+00:00","index":"","fulltext":""},{"type":"submitted","content":"Journal of Fusion Energy","date":"2024-06-25T01:52:21+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"journal-of-fusion-energy","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jofe","sideBox":"Learn more about [Journal of Fusion Energy](http://link.springer.com/journal/10894)","snPcode":"10894","submissionUrl":"https://submission.nature.com/new-submission/10894/3","title":"Journal of Fusion Energy","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"80b160cd-60d0-42fd-86c6-4d444afa1ab5","owner":[],"postedDate":"July 17th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2024-08-12T16:06:05+00:00","versionOfRecord":{"articleIdentity":"rs-4632828","link":"https://doi.org/10.1007/s10894-024-00455-2","journal":{"identity":"journal-of-fusion-energy","isVorOnly":false,"title":"Journal of Fusion Energy"},"publishedOn":"2024-08-08 15:58:09","publishedOnDateReadable":"August 8th, 2024"},"versionCreatedAt":"2024-07-17 08:40:32","video":"","vorDoi":"10.1007/s10894-024-00455-2","vorDoiUrl":"https://doi.org/10.1007/s10894-024-00455-2","workflowStages":[]},"version":"v1","identity":"rs-4632828","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4632828","identity":"rs-4632828","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}