Building on the above background, our earlier work assessed the neutronic and thermo-hydraulic feasibility of the (²³²Th-²³³U-²³⁵U)O₂ as an advanced fuel option for water-cooled reactors (Rifai et al. 2025a, 2025b; Uzun et al. 2025). In the present study, the emphasis shifts from general assembly-level performance to the management and transmutation of TRU, motivated by their dominant contribution to the long-term radiotoxicity and heat load of spent fuel. In thermal spectra, several key TRU nuclides, particularly ²³⁷Np, ²⁴¹Am, and ²⁴³Am, exhibit large capture cross-sections, enabling conversion mechanisms toward fissile products, including plutonium and metastable americium isotopes, that can subsequently contribute to fission. As summarized in Table 1, the interaction behavior of these nuclides is represented by three-group microscopic fission and capture cross-sections weighted over an LWR neutron spectrum. All cross-sections are expressed in barns (1 b=10^-24 cm²). For the present classification, the thermal, epithermal, and fast ranges are defined as E < 0.625eV, 0.625 eV ≤ E < 100 keV, and 100 keV ≤ E ≤ 20 MeV, respectively. Capture dominates for several nuclides, especially neptunium and americium isotopes, whereas ²³⁸Np, ²⁴²Am, ^242mAm, ²⁴³Cm, and ²⁴⁵Cm exhibit comparatively stronger fission responses in one or more energy ranges. These spectrum-averaged values are intended to characterize the dominant interaction pathways; their magnitudes, particularly in the resonance region, remain dependent on the neutron spectrum and resonance self-shielding treatment. In addition, the pronounced epithermal absorption features of several TRU isotopes can strengthen negative reactivity feedback through Doppler broadening and moderator-temperature-induced spectral changes. This behavior is particularly relevant to thorium-based fuels, for which stable feedback characteristics constitute an important design requirement (OECD/NEA 2013).

From a core/assembly design standpoint, the large neutron-capture cross-sections of TRU isotopes motivate their use not only as transmutation candidates but also as burnable absorber (BA) material for reactivity management (Zou et al. 2021). In LWR practice, BAs are typically deployed either as integral fuel burnable absorbers (IFBAs) incorporated into fuel rods or as burnable absorber rods (BPRs) inserted in guide-tube locations (OECD/NEA 2013). In the context of the IFBA configuration, the absorber can either be mixed with or coated onto the fuel. The choice between homogeneous and heterogeneous recycling of TRU plays an essential role in the impact on fuel design. Homogeneous absorber addition within the fuel matrix can impose, however, well-known penalties: it couples absorber depletion with fuel swelling and fission-gas behavior, may degrade thermo-mechanical performance under irradiation, and can exacerbate local power/temperature gradients (Washington 2016). To mitigate these drawbacks, the present study employs a heterogeneous TRU implementation, where the TRU inventory is applied as a thin region rather than being uniformly mixed with the fuel. Distributing the absorber over a larger surface effectively increases the reactive interface area, reduces local flux depression and resonance self-shielding, and introduces an additional lattice-design degree of freedom to tailor the spectral hardening/softening seen by the adjacent fuel region (Bae and Hong 2015; Radi et al. 2024). Accordingly, this study adopts a heterogeneous TRU implementation (varying thickness and spatial layout) and benchmarks it against pure (²³²Th-²³³U-²³⁵U)O₂ and UO₂ configurations. The densities and initial heavy-metal compositions of the three fuel materials are provided in Table 2, while the detailed isotopic vector used to define the TRUO₂ layer is reported in Table 3.

To identify an effective strategy for TRU transmutation within PWR-compatible architectures, two baseline fuel assemblies were considered. The primary reference geometry is a typical Westinghouse 17×17 PWR fuel assembly, selected to provide a well-established benchmark for comparing fuel and geometry effects. This assembly contains 264 fuel rods and 24 guide tubes arranged in a square lattice with an assembly pitch of 21.5 cm and serves just for benchmark comparison. The assembly is fueled with UO₂ and (²³²Th-²³³U-²³⁵U)O₂. The overall layout is shown in Fig. 1, and the main geometric specifications are reported in Table 4 (Schulz 2006). In addition to the conventional solid-pin reference, a 13×13 dual-cooled annular assembly was analyzed. In this concept, each fuel rod is cooled simultaneously by external coolant flow and an internal coolant channel, thereby increasing the effective heat-transfer area and shortening the conduction distance through the fuel. To maintain adequate flow through the inner channel and to benefit from improved heat-transfer coefficients, annular designs typically employ larger rod dimensions than standard solid pins. Consequently, for the same assembly envelope, the rod population is reduced from 264 (17×17 solid) to 160 (13×13 annular), while the lattice pitch is increased from 1.26 cm to 1.65 cm to accommodate the dual-cooling paths and associated structural requirements. As discussed in prior studies, the dual-cooled annular arrangement can lower peak fuel temperatures, strengthen margins to cladding overheating and fuel melting, and improve DNB-related safety limits, enabling substantial power-density uprates relative to conventional solid-fuel lattices under comparable boundary conditions (Kazimi and Hejzlar 2006; Hejzlar and Kazimi 2007). Consistent with these design objectives, both assemblies in this work retain the same assembly pitch (21.5 cm) and active length (426.7 cm), while differing in lattice size, rod count, and coolant-flow topology (Table 4). For the neutronic evaluations, all assembly models were treated with reflective boundary conditions on the outer perimeter to represent an infinite lattice (assembly-level) environment. To isolate intrinsic fuel- and geometry-driven effects, control rods and conventional burnable absorbers were not included in the reference calculations. The coolant/moderator was modeled as light water at nominal PWR conditions, and soluble boron was neglected in the base configuration.

The neutronic characteristics of the investigated assemblies, including neutron-flux distributions, power-peaking behavior, reactivity coefficients, and isotopic evolution, were evaluated using the deterministic lattice-physics code DRAGON5, developed at Polytechnique Montréal (Marleau et al. 2021). The multigroup neutron cross-sections were generated from the ENDF/B-VIII.0 evaluated nuclear-data library in DRAGLIB format using the 361-group Santamarina-Hfaiedh energy mesh (SHEM-361)(Hébert 2008). Resonance self-shielding was treated using the generalized Stamm’ler method. Geometry definition and collision-probability tracking were performed through the GEO and EXCELT modules, whereas neutron-flux calculations and isotopic depletion were carried out using the ASM, FLU, and EVO modules under reflective boundary conditions (Rifai et al. 2025a, 2025b; Kabach et al. 2026).

Reflective boundary conditions imposed on the lateral assembly surfaces represent an infinite two-dimensional array of identical fuel assemblies. Accordingly, the eigenvalue calculated by DRAGON corresponds to the infinite multiplication factor, k_inf, and does not explicitly account for radial or axial neutron leakage from a finite reactor core. The reference temperatures were set to 900 K for the fuel and 600 K for the gap, cladding, and moderator regions. For each fuel composition and assembly configuration, DRAGON5 calculated k_inf as a function of burnup, together with the corresponding neutron-flux spectra, reaction rates, macroscopic cross-sections, and nuclide inventories.

The assembly-level DRAGON5 calculations were independently verified using the continuous-energy Monte Carlo code MCNP6. Consistent fuel-assembly geometries, material compositions, temperatures, moderator densities, reflective boundary conditions, and ENDF/B-VIII.0 nuclear data were used in the two computational models (Werner 2017). All MCNP calculations were subsequently carried out with 200 active cycles and 50,000 neutron histories per cycle (1.0×10⁷ active histories), yielding one-standard-deviation statistical uncertainties generally around 21 pcm.

Fuel-depletion calculations were performed at a constant heavy-metal-normalized specific power density, P_SPD, of 40 kW/kgHM (Laranjo de Stefani et al. 2019; Mahbuba Nabila and Hossain Sahadath 2022). The normalization was based on the initial heavy-metal inventory, thereby providing a consistent burnup rate for all investigated fuel compositions and assembly geometries. Because the solid and dual-cooled annular assemblies contain different heavy-metal inventories, the use of a common specific power density does not imply that they have identical total assembly powers. All configurations were irradiated over a common interval of 1500 EFPDs. At the imposed specific power density, this duration corresponds to an end of the irradiation cycle burnup of 60 GWd/tHM: B_max = P_SPD t_irr = (40kW/kgHM)·(1500EFPDs) = 60 GWd/tHM.

The Linear Reactivity Model (LRM) was employed to translate the assembly-level k_inf evolution into approximate fuel-cycle parameters (Driscoll et al. 1991; Burns et al. 2020). Because the reflective assembly calculations do not explicitly represent neutron leakage from a finite core, a reactivity-equivalent leakage allowance, L, was introduced. The leakage-adjusted reactivity was calculated as:

$\rho =\frac{k_{\text{inf}}-(1+L)}{k_{\text{inf}}}$ (1)

In Eq. (1), ρ is the leakage-adjusted reactivity, k_inf is the infinite multiplication factor, and L is the assumed leakage allowance. The corresponding criticality condition is k_inf = 1+L. Thus, the ideal infinite-lattice condition L=0 gives a threshold of k_inf = 1.000, whereas an allowance of L=0.03 gives a threshold of k_inf = 1.030. Leakage allowances of 0%, 1%, 2%, and 3% were investigated to quantify their influence on the estimated critical burnup and fuel-cycle parameters. The 3% allowance was retained as the principal large-PWR screening condition, consistent with previous applications of the LRM to low-leakage three-batch PWR cores (Burns et al. 2020). The lower values were included to assess the sensitivity of the conclusions to the assumed leakage penalty.

The same leakage allowances were applied to all configurations to establish a controlled comparison. They should not be interpreted as calculated physical leakage fractions for the individual assembly types. Actual finite-core leakage depends on core dimensions, reflector characteristics, fuel-loading pattern, batch arrangement, neutron spectrum, and the spatial distributions of burnup and power.

For each leakage allowance, the single-batch critical burnup, B_SB, was determined from two consecutive depletion points, B_i and B_i+1, that bracketed the corresponding threshold. Local linear interpolation was performed according to $B_{SB}=B_i+\frac{(1+L)-k_{inf}\left(E_i\right)}{k_{inf}\left(E_{i+1}\right)-k_{inf}\left(E_{i+1}\right)}(B_{i+1}-B_i)$.

The multi-batch discharge burnup was calculated from B_SB using:

${\mathrm{B}}_{\text{Discharge}}=\frac{2{\mathrm{N}}_{\mathrm{NB}}}{({\mathrm{N}}_{\mathrm{NB}}+1)}{\mathrm{B}}_{\mathrm{SB}}$ (2)

where N_NB is the number of fuel batches in the reactor core. For the three-batch refueling strategy adopted in this study, N_NB = 3, and the estimated discharge burnup becomes B_Discharge = 1.5 B_SB.

The corresponding equilibrium cycle length was obtained as:

${\mathrm{T}}_{\text{cycle}}=\frac{2}{({\mathrm{N}}_{\mathrm{NB}}+1)}\frac{{\mathrm{B}}_{\mathrm{SB}}}{{\mathrm{P}}_{\mathrm{SPD}}}$ (3)

Burnup expressed in GWd/tHM is numerically equivalent to MWd/kgHM. Therefore, when P_SPD is expressed in MW/kgHM, Eq. (3) gives T_cycle directly in EFPDs. For the adopted three-batch scheme and P_SPD==0.040 MW/kgHM.

The inherent neutronic feedback behavior of the investigated configurations was characterized through the fuel-temperature coefficient (FTC) and moderator-temperature coefficient (MTC). The FTC primarily reflects Doppler broadening of resonance absorption in fertile and transuranic nuclides, particularly ²³²Th, ²³⁸U, and the loaded plutonium and minor-actinide isotopes. The MTC represents the combined reactivity response to moderator-temperature and density variations and is influenced by the moderator-to-fuel ratio, neutron-spectrum hardness, resonance escape probability, and thermal utilization (Rifai et al. 2025a, 2025b; Uzun et al. 2025).

Both coefficients were evaluated under boron-free conditions using temperature-branch calculations. For the FTC calculation, the fuel temperature was increased by ΔT_f = 100 K while the moderator temperature and density were maintained at their reference values. The coefficient was calculated as:

$\text{FTC}=\frac{\mathrm{k}\left({\mathrm{T}}_{\mathrm{f}}\right)-{\mathrm{k}}_{\mathrm{o}}}{{\mathrm{k}}_{\mathrm{o}}\mathrm{\Delta }{\mathrm{T}}_{\mathrm{f}}}$ (4)

For the MTC calculation, the moderator temperature was increased by ΔT_m = 20 K, from 580 to 600 K, while its density was correspondingly reduced from 0.7678 to 0.7119 g/cm³. The fuel temperature remained fixed:

$\mathrm{MTC}=\frac{\mathrm{k}\left({\mathrm{T}}_{\mathrm{m},{\mathrm{p}}_{\mathrm{m}}}\right)-{\mathrm{k}}_{\mathrm{o}}}{{\mathrm{k}}_{\mathrm{o}}\mathrm{\Delta }{\mathrm{T}}_{\mathrm{m}}}$ (5)

Here, k₀ is the multiplication factor at the reference state, k(T_f) is the multiplication factor at the perturbed fuel temperature, and k(T_m,ρm) is evaluated at the perturbed moderator temperature and corresponding density. Both coefficients were converted to pcm/K by multiplying the calculated values by 10⁵.

The burnup-dependent k_inf curves presented in Fig. 3 show that introducing TRU as a heterogeneous TRUO₂ ring produces substantial BOC reactivity suppression relative to the corresponding TRU-free annular configuration. The adopted TRU vector therefore produces a net burnable-absorber-like effect at BOC, when neutron capture and local spectral effects outweigh the fission contribution from the fissile plutonium isotopes. This interpretation is consistent with the nuclear-reaction characteristics reported in Table 1, which indicate strong neutron-capture behavior for several minor actinides in a thermal LWR spectrum, particularly ²³⁷Np, ²⁴¹Am, and ²⁴³Am. As burnup increases, the initial reactivity penalty progressively decreases because of the depletion and transmutation of strongly absorbing isotopes and the contribution of fissile nuclides retained or produced through capture and decay pathways.

For the TRU-free configurations presented in Fig. 3, the k_inf of the solid UO₂ pin, Type_1, decreases from 1.3676 to 0.9013 over the investigated burnup interval, whereas the corresponding thorium-based pin decreases from 1.4121 to 0.9324. The TRU-free annular configuration, Type_2, exhibits a comparable trend, with k_inf decreasing from 1.3321 to 0.8895 for UO₂ and from 1.3868 to 0.9312 for (²³²Th-²³³U-²³⁵U)O₂. In both the solid and annular geometries, the thorium-based matrix maintains a higher k_inf at the beginning and end of the investigated burnup interval, providing additional reactivity margin for accommodating TRU loading.

As further shown in Fig. 3, introducing a 0.1 mm TRUO₂ ring markedly reduces the BOC k_inf. For the UO₂ fuel, the BOC values are 1.1354, 1.1168, and 1.1060 for Types 3, 4, and 5, respectively. The corresponding values for the thorium-based matrix are 1.2139, 1.1945, and 1.1813. The TRUO₂ ring therefore provides substantial initial reactivity suppression relative to the TRU-free configurations. At the same time, the thorium-based matrix retains a higher k_inf than UO₂ for every corresponding TRU ring position and thickness.

Nevertheless, the progressive reduction in BOC k_inf from Type_3 to Type_5 cannot be attributed exclusively to the radial position of the ring. As illustrated in Fig. 2, moving a ring of fixed thickness outward increases its TRUO₂ volume and initial TRU mass while displacing a larger volume of matrix fuel. The k_inf differences in Fig. 3 consequently represent the coupled effects of radial position, initial TRU inventory, matrix-fuel displacement, local spectral conditions, fission within the TRU vector, and spatial and energy self-shielding.

The influence of increasing the ring thickness from 0.1 to 0.3 mm is not strictly monotonic. For example, Fig. 3 shows that the BOC k_inf of the UO₂ Type_3 configuration decreases from 1.1354 at 0.1 mm to 1.1180 at 0.2 mm before increasing to 1.1296 at 0.3 mm. Similar nonlinear responses are observed for Types 4 and 5. This behavior arises from competition among the increased TRU inventory, displacement of matrix fuel, fission in ²³⁹Pu and ²⁴¹Pu, neutron capture by fertile and minor-actinide isotopes, and self-shielding within the TRU-containing region. As the TRUO₂ ring becomes thicker, the local neutron flux can become increasingly depressed within the strongly absorbing material, reducing the incremental reactivity effect of additional TRU mass (Department of Energy 1993; Zohuri 2019).

At the end of the simulated burnup interval, the Type_4 configurations with thicker TRUO₂ rings retain higher k_inf values. For the UO₂ matrix, k_inf increases from 0.9402 for the 0.1 mm ring to 0.9638 and 0.9912 for the 0.2 and 0.3 mm rings, respectively. The corresponding values for the thorium-based matrix are 0.9951, 1.0142, and 1.0377. These endpoint values correspond to the common maximum burnup considered in the calculations and do not necessarily represent the individual discharge burnup of each configuration. The improved late-burnup reactivity retention of the thicker-ring configurations is primarily associated with their larger initial and residual inventories of fissile ²³⁹Pu and ²⁴¹Pu, together with the progressive depletion of capture-dominant TRU isotopes such as ²³⁷Np and ²⁴¹Am. Consequently, the 0.3 mm ring maintains a greater fissile contribution at high burnup despite the diminishing BOC reactivity-suppression efficiency caused by self-shielding.

The FTC and MTC at BOC values calculated for the solid, TRU-free annular, and TRU-containing pin-cell configurations are summarized in Table 5. All configurations preserve negative FTC and MTC. The addition of TRU generally makes the FTC more negative than the TRU-free references, consistent with stronger resonance absorption and enhanced Doppler sensitivity (Lewis and Tsvetkov 2009). For example, the reference UO₂ solid pin (Type_1) FTC is equal to -1.93 pcm/K, whereas the TRU ring cases cluster near -3 pcm/K. At 0.1 mm, FTC is -3.33 (Type_3, UO₂), -3.40 (Type_4, UO₂), and -3.35 (Type_5, UO₂). The thorium-based fuel shows the same qualitative behavior, with FTC increasing in magnitude from -2.29 (Type_1) to values around -3.4 to -3.5 for the 0.1 mm TRU ring cases (Type_4 and Type_5 both -3.51 pcm/K). Overall, (²³²Th-²³³U-²³⁵U)O₂ tends to exhibit FTC magnitudes comparable to or slightly larger than the corresponding UO₂ cases, which is favorable for prompt Doppler stabilization.

The MTC trends provide the strongest discriminator among Types 3–5 because they reflect how TRU loading and placement shift the moderation-absorption balance. For UO₂, the reference MTC values are -46.52 pcm/K (Type_1) and -47.02 pcm/K (Type_2). Introducing a thin TRU ring at 0.1 mm strengthens the magnitude substantially: -62.61 (Type_3), -60.34 (Type_4), and -56.31 (Type_5). For the thorium-based matrix, the reference MTC values are less negative (-28.40 for Type_1 and -28.47 for Type_2), but the TRU rings again deepen the coefficient at 0.1 mm to -45.10 (Type_3), -44.55 (Type_4), and -42.70 (Type_5). The results suggest that introducing TRU systematically amplifies the negative moderation feedback in both fuel matrices, while the thorium-based composition maintains a less negative MTC than UO₂ under otherwise similar conditions.

For larger ring thicknesses, the MTC magnitude collapses in several configurations, consistent with enhanced resonance self-shielding and local spectrum hardening in the TRU-containing region, which diminishes the reactivity sensitivity to moderator density and temperature perturbations. This behavior becomes especially clear at 0.3 mm. For UO₂, MTC drops from about -60 pcm/K at 0.1 mm to -19.90 (Type_4, 0.3 mm) and -9.95 (Type_5, 0.3 mm). For the thorium-based fuel, the reduction is even more severe for Type_3 (0.3 mm), where MTC reaches -9.35 pcm/K, while Type_5 (0.3 mm) reaches -12.47 pcm/K. These less negative MTC values are less desirable from a passive-safety perspective and indicate that excessive TRU inventory can undermine moderation feedback even if FTC remains negative.

The reduction in MTC magnitude at larger ring thicknesses reflects the combined effects of increased TRU loading, matrix-fuel displacement, local spectrum modification, and stronger self-shielding within the TRU-containing region. Although the MTC remains negative for every configuration in Table 5, the comparatively small magnitudes obtained for several 0.3 mm cases indicate weaker passive reactivity feedback and are therefore less favorable from a safety perspective.

Considering the BOC suppression and late-burnup reactivity behavior presented in Fig. 3, the initial TRU inventories reported in Table 4, and the FTC and MTC results summarized in Table 5, Type_4 provides the most balanced engineering compromise among the investigated fixed-thickness designs. It combines stronger BOC suppression than Type_3 with more favorable moderator-temperature feedback than the outer Type_5 configuration in the principal screening cases. Its FTC also remains strongly negative for both matrix fuels.

Accordingly, the selection of Type_4 should be interpreted as an engineering compromise among configurations that differ in both position and TRU inventory, rather than as evidence that the intermediate position is intrinsically optimal under equal-TRU-mass conditions. The Type_4 configurations containing 0.1-, 0.2-, and 0.3 mm TRUO₂ rings were therefore propagated to the assembly-level analysis.

The BOC k_inf values calculated using DRAGON were first compared with independent continuous-energy MCNP results. As reported in Table 8, the absolute percentage differences relative to MCNP range from 0.008% for Case-5 to 0.261% for the reference assembly, with an average of approximately 0.144%. DRAGON slightly overpredicts the MCNP results for the reference assembly and Cases 1, 5, and 6, while slightly underpredicting the remaining configurations. Nevertheless, the difference remains below 0.3% for every case, with no systematic positive or negative bias. This close agreement supports the consistency of the DRAGON models used for the subsequent depletion calculations.

Fig. 5 shows that k_inf decreases continuously with burnup for all the investigated configurations. This behavior primarily reflects fissile-nuclide depletion and fission-product accumulation, partially compensated by fertile-to-fissile conversion and the irradiation-dependent evolution of the heavy-nuclide inventory. The solid UO₂ reference assembly decreases from k_inf = 1.39840 at BOC to 0.89590 at the end of the irradiation cycle. Case-1, representing the TRU-free dual-cooled UO₂ assembly, decreases from 1.35977 to 0.88895. Under the adopted lattice dimensions and moderation conditions, the dual-cooled UO₂ configuration therefore exhibits lower reactivity than the solid reference throughout most of the investigated burnup interval.

Introducing TRUO₂ rings into the dual-cooled UO₂ assembly produces substantial BOC reactivity suppression. The initial k_inf decreases to 1.30309, 1.28547, and 1.27576 for Cases 2–4 as the TRUO₂ ring thickness increases from 0.1 to 0.3 mm. Relative to the TRU-free Case-1, these changes correspond to reactivity reductions of approximately 3199, 4251, and 4843 pcm, respectively. The BOC behavior reflects the combined effects of neutron absorption by the minor-actinide component, displacement of the UO₂ matrix, and local spectral and self-shielding effects. Although the initial TRU vector contains fissile ²³⁹Pu and ²⁴¹Pu, their positive contribution is insufficient to compensate for the overall absorption penalty of the complete TRU composition at BOC. This ordering progressively reverses during burnup. At the end of the irradiation cycle, k_inf increases from 0.90583 for Case-2 to 0.91764 for Case-3 and 0.92771 for Case-4. As shown in Fig. 3, all three TRU-containing UO₂ configurations maintain higher k_inf values at the end of the simulated burnup interval than both the TRU-free Case 1 and the solid UO₂ reference. This behavior is consistent with fission in the initially loaded plutonium isotopes, net depletion of several initially loaded Pu and Am isotopes, and redistribution of neutron absorption and fission among the evolving daughter actinides. Increasing the TRUO₂ ring thickness strengthens these late-burnup contributions, although it simultaneously increases the TRU inventory and the amount of displaced UO₂ matrix fuel. The improved reactivity retention is also reflected in the reactivity swing between BOC and at the end of the irradiation cycle. The swing decreases from approximately 38,950 pcm for Case-1 to 33,655, 31,183, and 29,408 pcm for Cases 2–4, respectively. Heterogeneous TRU loading therefore flattens the burnup-dependent reactivity evolution despite imposing a substantial initial reactivity penalty. This reduction in reactivity swing could facilitate excess-reactivity management, although its practical benefit would depend on the corresponding control requirements and full-core loading strategy.

The thorium-based assemblies exhibit stronger reactivity retention than the corresponding UO₂ configurations. The solid (²³²Th-²³³U-²³⁵U)O₂ assembly, Case-5, decreases from k_inf = 1.43354 to 0.91444 at the end of the irradiation cycle. The corresponding TRU-free dual-cooled configuration, Case-6, decreases from 1.40803 to 0.91729. Although Case-6 begins below Case-5, it slightly exceeds the solid thorium-based assembly at the end of the irradiation cycle, indicating improved high-burnup reactivity retention in the dual-cooled configuration.

This behavior arises from the combined effects of the modified lattice moderation and the ²³²Th(n,γ)²³³Th→²³³Pa→²³³U conversion chain. Irradiation-induced regeneration of ²³³U partially compensates for depletion of the initially loaded fissile isotopes, while the favorable neutron economy of ²³³U supports criticality at elevated burnup (Rifai et al. 2025b; Uzun et al. 2025). The calculated improvement nevertheless represents the coupled response of the complete ²³²Th-²³³U-²³⁵U system and should not be interpreted as evidence of net fissile breeding.

Cases 7–9 combine (²³²Th-²³³U-²³⁵U)O₂ matrix with TRUO₂ loading. Their BOC k_inf values are 1.36374, 1.34932, and 1.34048, respectively. Relative to the TRU-free Case-6, these values represent reactivity reductions of approximately 2307, 3090, and 3579 pcm. These penalties are smaller than those obtained for the corresponding UO₂-TRU configurations, demonstrating that the reactivity effect of a comparable TRU ring loading depends strongly on the surrounding fuel matrix and its associated neutron spectrum.

At the end of the irradiation cycle, the k_inf values increase with TRUO₂ ring thickness to 0.93821, 0.95451, and 0.97071 for Cases 7–9, respectively. All three configurations exceed both the solid UO₂ and (²³²Th-²³³U-²³⁵U)O₂ reference values at the same burnup. Case-9 provides the highest value among all the investigated configurations, exceeding the solid UO₂ reference by 0.07481 in k_inf, or approximately 8.3%. Its reactivity swing is also reduced to approximately 28,417 pcm, compared with 37,996 pcm for the TRU-free Case-6. This improved reactivity holding results from the combined fission contributions of the initially loaded ²³³U, ²³⁹Pu, and ²⁴¹Pu; regeneration of ²³³U following neutron capture in ²³²Th; and progressive depletion of part of the capture-dominant initial TRU inventory.

Table 9 assesses the sensitivity of the calculated cycle-performance parameters to neutron-leakage allowances ranging from 0% to 3%. Despite affecting the absolute cycle-performance values, neutron leakage does not alter the principal ranking of the configurations over the investigated 0–3% range. Within the UO₂ family, Case-1 consistently provides the lowest cycle performance. Increasing the TRUO₂ ring thickness progressively improves Cases 2–4, but none surpasses the solid UO₂ reference. In contrast, the thorium-based configurations consistently provide higher discharge burnups and longer cycle durations. Cases 7–9 improve systematically with increasing TRUO₂ ring thickness, and Case-9 remains the highest-performing configuration under every leakage allowance.

Under the reference 3% leakage allowance, the solid UO₂ assembly reaches a discharge burnup of 55.11 GWd/tHM and a cycle duration of 459.26 EFPDs. Case-1 decreases these quantities to 48.98 GWd/tHM and 408.16 EFPDs. The cycle durations of Cases 2–4 progressively increase to 408.95, 415.92, and 428.44 EFPDs, with corresponding discharge burnups of approximately 49.08, 49.91, and 51.42 GWd/tHM. Thus, the 0.1 mm TRUO₂ ring in Case-2 provides only a marginal recovery relative to Case-1, whereas the thicker rings produce increasingly discernible improvements. Nevertheless, Case-4 remains approximately 6.7% below the cycle duration of the solid UO₂ reference.

The (²³²Th-²³³U-²³⁵U)O₂ configurations retain substantially greater irradiation potential under the same leakage allowance. Cases 5 and 6 reach discharge burnups of approximately 61.68 and 60.63 GWd/tHM and cycle durations of 513.96 and 505.28 EFPDs, respectively. These durations exceed that of the solid UO₂ reference by approximately 11.9% and 10.0%. Introducing TRUO₂ rings increases the discharge burnup to approximately 63.98, 67.37, and 71.36 GWd/tHM for Cases 7–9, with corresponding cycle durations of 533.15, 561.41, and 594.70 EFPDs. Relative to the solid UO₂ reference, these cycle durations represent increases of approximately 16.1%, 22.2%, and 29.5%, respectively.

The burnup-dependent number densities presented in Fig. 6, with the values at the end of the irradiation cycle summarized in Table 10, reveal two contrasting actinide-transmutation and fertile-conversion regimes. In the UO₂-based configurations, neutron capture by ²³⁸U continuously produces ²³⁹Pu through fertile conversion, whereas the thorium-based matrix redirects fertile conversion toward ²³³U production through ²³²Th and ²³³Pa. Introducing a TRUO₂ ring superimposes the transmutation of the initially loaded Np, Pu, Am, and Cm isotopes on these matrix-dependent conversion processes.

In the following discussion, Th, U, and Pu are classified as major actinides, whereas Np, Am, and Cm are classified as minor actinides. The term TRU refers collectively to the reported Np, Pu, Am, and Cm isotopes. Their burnup evolution is governed by competition among fission, radiative capture, radioactive decay, fissile-nuclide regeneration, and production of daughter actinides. The groupwise variations discussed below were determined by summing the number densities of the isotopes explicitly reported in Table 10. They therefore represent changes in aggregate atom concentration under the common normalization adopted in the depletion calculations, rather than changes in absolute isotope mass or total assembly inventory.

The ²³⁵U number density decreases monotonically in all uranium-containing configurations. In the UO₂-based cases, this depletion is partly compensated by in situ production of fissile plutonium. Neutron capture in ²³⁸U initiates the conversion sequence ${}^{238}\mathrm{U}(\mathrm{n},\gamma ){}^{239}\mathrm{U}\stackrel{{\beta }^{-}}{\to }{}^{239}\mathrm{Np}\stackrel{{\beta }^{-}}{\to }{}^{239}\mathrm{Pu}$. The relatively small fractional depletion of ²³⁸U therefore masks a continuous fertile-to-fissile conversion flow toward ²³⁹Pu. The evolution of ²³⁹Np reflects the persistence of this pathway. Because its half-life, 2.4 days, is short relative to the burnup period, its number density is controlled primarily by the balance between production and beta decay rather than by long-term accumulation.

This conversion mechanism dominates the reference assembly and Case-1, neither of which contains initially loaded TRU. Accordingly, the number densities of the reported Pu and minor-actinide isotopes are zero at the beginning of the irradiation cycle. The irradiation-generated ²³⁹Pu progressively contributes to fission and to the formation of ²⁴⁰Pu, ²⁴¹Pu, and ²⁴²Pu through successive neutron-capture and radioactive-decay reactions. In particular, fissile ²³⁹Pu and ²⁴¹Pu partially compensate for ²³⁵U depletion and provide increasing reactivity support with burnup.

Cases 2–4 retain this ²³⁸U-driven conversion mechanism while introducing a nonzero TRU concentration within the annular fuel. Between the beginning and the end of the irradiation cycle, the combined number density of the five reported Pu isotopes increases by approximately 183.3%, 108.4%, and 65.5% in Cases 2, 3, and 4, respectively. The decreasing relative increase with TRUO₂ ring thickness is partly associated with the larger initial Pu concentration used as the reference for the percentage calculation. More importantly, the results demonstrate that plutonium production in the UO₂ matrix exceeds the net removal of the initially loaded Pu over the investigated irradiation interval. The evolution of ²³⁷Np reinforces this interpretation. Its number density increases by approximately 113.1%, 53.2%, and 10.9% in Cases 2–4, respectively, indicating that increasing the TRUO₂ ring thickness progressively shifts the balance from net production toward more effective removal. Neutron capture by ²³⁷Np forms ²³⁸Np, which may undergo fission or decay to ²³⁸Pu. The simultaneous evolution of ²³⁷Np and ²³⁸Pu therefore reflects capture-driven redistribution within the TRU vector in addition to direct actinide destruction. An analogous redistribution occurs within the Pu chain, where successive neutron captures transfer part of the ²³⁹Pu and ²⁴¹Pu toward the heavier ²⁴⁰Pu and ²⁴²Pu isotopes.

Although this conversion limits net TRU reduction, it provides an important neutronic benefit. The generation of ²³⁹Pu and ²⁴¹Pu sustains the fission source after substantial ²³⁵U depletion and improves reactivity retention at the end of the irradiation cycle. At the beginning of the irradiation cycle, several capture-dominant isotopes in the loaded TRU vector impose negative reactivity worth. Their subsequent depletion by fission or conversion into daughter nuclides, together with the integrated fission contribution of ²³⁹Pu and ²⁴¹Pu, produces a burnable-absorber-like reactivity response and reduces the burnup-dependent reactivity swing. Thus, the same ²³⁸U-driven plutonium-production mechanism that limits net TRU depletion in Cases 2–4 also contributes to their reactivity retention during irradiation.

The minor-actinide evolution nevertheless exposes the principal fuel-cycle limitation of this production-dominated regime. Although the ²⁴¹Am number density decreases by approximately 47.8%, 54.8%, and 68.0% in Cases 2–4, respectively, ²⁴³Am accumulates sufficiently to produce aggregate changes of approximately +53.1%, +21.4%, and -4.8% for the two reported Am isotopes. The progressive improvement from Case-2 to Case-4 indicates that increasing the TRUO₂ ring thickness enhances the net reduction of the reported Am population. However, the pronounced depletion of ²⁴¹Am cannot be interpreted as an equivalent reduction in total americium because neutron capture transfers part of the actinide population toward ²⁴³Am and subsequently toward curium. This redistribution reflects the strong competition between fission and capture that characterizes minor-actinide irradiation in a thermal neutron spectrum.

Consistent with these neutron-capture transmutation sequences, ²⁴⁴Cm and ²⁴⁵Cm accumulate in all three UO₂-based TRU configurations. Their combined number densities increase by approximately 625.0%, 489.7%, and 493.3% in Cases 2–4, respectively. These large relative changes are amplified by the low initial Cm concentrations and do not imply that curium becomes the dominant component of the TRU vector. Nevertheless, even limited Cm buildup is important because curium contributes disproportionately to decay heat and spontaneous-neutron emission. Its formation may therefore increase the requirements for spent-fuel cooling, shielding, transport, reprocessing, and remote fuel fabrication.

When the reported Np, Pu, Am, and Cm isotope number densities are combined, their aggregate values increase by approximately 175.9%, 103.6%, and 62.1% in Cases 2–4, respectively. The decreasing net accumulation with increasing TRUO₂ ring thickness demonstrates that a larger target loading improves the competition between TRU removal and irradiation-induced actinide production. However, none of the UO₂-based TRU cases achieve net depletion of the reported TRU population because the ²³⁸U-rich matrix continuously produces Pu and subsequently feeds the formation of heavier actinides. Cases 2–4 are consequently better characterized as TRU-recycling and isotopic-redistribution configurations with appreciable late-cycle fissile support than as net configuration-level TRU burners.

Replacing UO₂ with the (²³²Th-²³³U-²³⁵U)O₂ matrix fundamentally changes this balance. The gradual depletion of ²³²Th and the buildup of ²³³Pa confirm sustained fertile conversion through ${}^{232}\mathrm{Th}(\mathrm{n},\gamma ){}^{233}\mathrm{Th}\stackrel{{\beta }^{-}}{\to }{}^{233}\mathrm{Pa}\stackrel{{\beta }^{-}}{\to }{}^{233}\mathrm{U}$. Despite this continuous production, the ²³³U number density decreases with burnup in all thorium-based cases, demonstrating that its combined consumption through fission and radiative capture exceeds its regeneration through ²³³Pa decay. These configurations therefore achieve partial ²³³U regeneration rather than net breeding. Nevertheless, the favorable thermal and epithermal neutron economy of ²³³U allows this partial regeneration to provide substantial fissile support at high burnup.

Within Cases 7–9, the end of the irradiation cycle ²³³U number density increases with TRUO₂ ring thickness. This trend reflects not only ²³³U production but also redistribution of the fission source between the thorium matrix and the TRU-containing region. A larger contribution from the initially loaded fissile Pu reduces the fraction of assembly power supplied by ²³³U and may therefore preserve more of its initial concentration. Simultaneously, neutron absorption and self-shielding within the TRUO₂ ring alter the local spectrum and the neutron flux available for capture in ²³²Th. The end of the irradiation cycle ²³³U concentration is consequently governed by the combined effects of regeneration, fission consumption, radiative capture, and fissile-load sharing.

The accumulation of ²³¹Pa and ²³²U demonstrates that irradiation also activates secondary thorium-cycle pathways. Although their concentrations remain substantially lower than that of ²³²Th, these isotopes have important fuel-cycle implications. In particular, the ²³²U decay chain contains intense high-energy gamma emitters that increase shielding and remote-handling requirements during spent-fuel storage, transport, reprocessing, and refabrication (Baldová 2014). The associated radiation field may strengthen the intrinsic proliferation resistance of irradiated thorium fuel, but it simultaneously complicates the practical implementation of a closed thorium fuel cycle.

Against this thorium-conversion background, Cases 7–9 exhibit a markedly different Pu response from Cases 2–4. Because the thorium-based matrix contains no ²³⁸U, the conventional ²³⁸U-to-²³⁹Pu production sequence is absent. The initially loaded plutonium inventory therefore receives no contribution from fertile ²³⁸U conversion during irradiation. The number densities of ²³⁹Pu, ²⁴⁰Pu, and ²⁴¹Pu decrease, whereas ²³⁸Pu and ²⁴²Pu accumulate. The reductions in ²³⁹Pu reach approximately 97.2%, 96.6%, and 97.5% in Cases 7, 8, and 9, respectively. The corresponding decreases are approximately 85.8%, 71.7%, and 73.6% for ²⁴⁰Pu and 58.4%, 47.3%, and 59.0% for ²⁴¹Pu. These changes arise from both fission and capture-driven conversion. Consequently, the disappearance of a fissile Pu isotope does not correspond exclusively to fission destruction because part of its concentration is transferred toward heavier Pu and minor-actinide isotopes.

Despite the accumulation of ²³⁸Pu and ²⁴²Pu, the combined number density of the five reported Pu isotopes decreases by approximately 67.8%, 63.6%, and 67.1% in Cases 7–9, respectively. The thorium-based matrix therefore allows Pu-removal reactions to dominate by suppressing the continuing ²³⁸U-driven Pu source present in Cases 2–4. Its principal advantage lies in redirecting fertile conversion from the ²³⁸U-Pu chain toward the ²³²Th-²³³U chain. This substitution retains a mechanism for late-cycle fissile support while enabling substantial net depletion of the reported Pu concentration.

The ²³⁷Np response provides further evidence that transmutation performance depends on more than the initial target concentration. Its number density increases by approximately 10.9% in Case-7 but decreases by approximately 13.6% and 37.8% in Cases 8 and 9, respectively. Increasing the ring thickness therefore shifts the balance from net Np production to net depletion. The accompanying increase in ²³⁸Pu is associated primarily with its formation in the surrounding fuel region through ²³⁷Np neutron capture followed by the beta decay of ²³⁸Np. It should therefore not be interpreted as ²³⁸Pu accumulation within the initially loaded TRUO₂ ring. The observed ²³⁷Np response within the TRUO₂ ring results from the combined effects of its initial concentration, the local neutron spectrum, spatial flux depression, resonance self-shielding, neutron capture, and fission.

Americium undergoes an analogous redistribution. The ²⁴¹Am number density decreases by approximately 90.0%, 86.3%, and 91.9% in Cases 7–9, whereas ²⁴³Am increases by approximately 101.2%, 80.5%, and 62.5%, respectively. Combining the two reported isotopes yields net Am reductions of approximately 21.8%, 26.8%, and 36.8%. The pronounced depletion of ²⁴¹Am therefore overstates the reduction of the reported americium population because capture and decay processes continue to feed ²⁴³Am. Nevertheless, the progressive improvement from Case-7 to Case-9 indicates that increasing the TRUO₂ ring thickness strengthens the overall Am depletion, even though the remaining isotope vector shifts toward heavier and less readily fissioned species.

The associated buildup of curium remains the principal countervailing effect. The combined ²⁴⁴Cm and ²⁴⁵Cm number densities increase by approximately 395.8%, 335.6%, and 377.1% in Cases 7–9, respectively. The production of ²⁴⁴Cm is principally associated with neutron capture by ²⁴³Am followed by the decay of ²⁴⁴Am, while further neutron capture contributes to ²⁴⁵Cm formation. The lower relative increase in Case-8 does not establish a monotonic dependence on ring thickness; instead, it illustrates the sensitivity of higher-actinide production to relatively small changes in the competition among formation, capture, and fission.

When all the reported Np, Pu, Am, and Cm isotope number densities are combined, Cases 7–9 achieve aggregate reductions of approximately 56.3%, 55.0%, and 59.7%, respectively. The thorium matrix thus changes the configuration-level endpoint balance from strong net TRU accumulation in Cases 2–4 to substantial net depletion in Cases 7–9. Case 9 provides the largest aggregate reduction in the reported TRU inventory and also maintains favorable reactivity at the end of the simulated burnup interval. However, the slightly smaller reduction obtained for Case-8 confirms that transmutation performance does not vary linearly with TRUO₂ ring thickness. Increasing the thickness raises the initial target concentration but also intensifies resonance and spatial self-shielding, depresses the local neutron flux, perturbs the spectrum, and modifies the competition between fission and capture. These opposing mechanisms produce diminishing and, for some isotopes, non-monotonic improvements as the TRU loading increases.

The isotopic changes provide a consistent physical explanation for the different criticality responses of the two fuel matrices. In Cases 2–4, continuous in situ production of ²³⁹Pu through ²³⁸U fertile conversion, followed by the formation of ²⁴¹Pu, contributes to reactivity retention but prevents net depletion of the reported TRU population. In Cases 7–9, this Pu-production sequence is absent; most of the initially loaded fissile Pu is depleted, while partial regeneration and improved preservation of ²³³U compensate for part of the associated reactivity loss. The end of the irradiation cycle k_inf of the thorium-based TRU configurations is therefore governed by the evolving fissile composition of the complete heavy-metal vector rather than by the remaining TRU concentration alone.

The fissile inventory ratio (FIR) is used to evaluate the ability of each fuel configuration to retain and regenerate its fissile potential during irradiation. For consistency with established reactor-physics studies, the term FIR is retained; however, its isotope basis is stated explicitly. The inventory considered comprises the fissile nuclides ²³³U, ²³⁵U, ²³⁹Pu, and ²⁴¹Pu, together with the fissile precursors ²³³Pa and ²³⁹Np. Although ²³³Pa and ²³⁹Np are not themselves fissile, they are credited because they decay to ²³³U and ²³⁹Pu with half-lives of approximately 27 and 2.36 days, respectively. This precursor-credit convention has also been applied in previous FIR assessments of uranium- and thorium-containing fuels by Liu and Cai 2013 and is consistent with the fuel-cycle inventory treatment reported by (IAEA 2012). Accordingly, ²³³Pa contributes only to the thorium-based cases, whereas ²³⁹Np associated with the ²³⁸U conversion chain contributes only to the UO₂-based cases.

Fig. 7 shows that FIR decreases continuously with burnup in all configurations. This behavior indicates that fission and neutron capture remove the credited nuclides faster than they are produced through fertile conversion. However, the rate of decline varies moderately during irradiation as the relative contributions of the initially loaded and newly generated fissile nuclides evolve. In the UO₂-based configurations, neutron capture by ²³⁸U followed by radioactive decay produces ²³⁹Np and subsequently ²³⁹Pu. In the thorium-based configurations, neutron capture by ²³²Th produces ²³³Pa, which subsequently decays to ²³³U. These conversion pathways partially compensate for fissile consumption but remain insufficient to prevent the overall decrease in FIR over the investigated burnup range.

Clear differences are observed among the UO₂-based configurations. The reference case exhibits the greatest FIR reduction and reaches approximately 0.333 at the end of the irradiation cycle. Case-1 retains a higher terminal FIR of approximately 0.387. Further improvements are obtained in Cases 2–4, whose end of the irradiation cycle values increase systematically to approximately 0.429, 0.447, and 0.469, respectively. In the TRU-containing cases, the initially loaded fissile Pu contributes to energy production alongside ²³⁵U, while fertile conversion of ²³⁸U continuously produces ²³⁹Pu, partially compensating for the depletion of the fissile inventory. The improvement with increasing TRUO₂ ring thickness can therefore be attributed to the combined influence of fissile-load sharing, fertile conversion, and configuration-dependent spectral, flux-depression, and self-shielding effects. A comparable improvement is observed for the thorium-based family. At the end of the irradiation cycle, FIR increases from approximately 0.420 in Case-5 to 0.449 in Case-6 and then to approximately 0.457, 0.462, and 0.469 in Cases 7, 8, and 9, respectively. In Cases 7–9, the initially loaded ²³⁹Pu and ²⁴¹Pu also share the fission burden with ²³³U and ²³⁵U. The progressive improvement in FIR with TRUO₂ ring thickness consequently reflects partial ²³³U regeneration, redistribution of the fission source between the matrix and the TRU-containing ring, and configuration-dependent preservation of the credited nuclides.

Case-9 reaches the highest terminal FIR among the thorium-based cases and attains approximately the same value as Case-4. Although both configurations retain about 46.9% of their respective initial credited inventories at the end of the irradiation cycle, the underlying mechanisms differ. Case-4 benefits from continued production along the ²³⁸U to ²³⁹Pu chain, whereas Case-9 relies principally on partial ²³³U regeneration and fissile-load sharing with the initially loaded Pu. This distinction is important because identical FIR values do not necessarily indicate identical isotopic compositions, conversion efficiencies, or reactivity characteristics.

Fig. 8 displays the evolution with burnup of the two most influential neutron-absorbing fission products in thermal systems, ¹³⁵Xe and ¹⁴⁹Sm, for all investigated fuel options. Their importance stems from their extremely large microscopic absorption cross-sections, which make their inventories strongly coupled to short-term reactivity behavior and to the overall neutron economy during burnup (Duderstadt and Hamilton 1976; Jevremovic 2009). Although both nuclides are fission products, their inventories evolve differently because their production and removal pathways operate over different time scales. Moreover, their concentrations depend on the fission yields of the contributing fissile isotopes and on the fraction of the total fission rate supplied by each isotope at a given burnup. The comparison among the investigated fuels must therefore consider the evolving contributions of ²³³U, ²³⁵U, ²³⁹Pu, ²⁴¹Pu, and any other isotope contributing appreciably to the fission rate.

The evaluated cumulative thermal-fission yields provide a quantitative basis for this interpretation. According to the ENDF/B-VIII.0 neutron-induced fission-yield sublibrary, the cumulative ¹³⁵Xe yields are approximately 6.259%, 6.539%, 7.608%, and 7.170% per fission for ²³³U, ²³⁵U, ²³⁹Pu, and ²⁴¹Pu, respectively. The corresponding cumulative ¹⁴⁹Sm yields are approximately 0.778%, 1.082%, 1.217%, and 1.474%. Thus, thermal fission of ²³⁹Pu and ²⁴¹Pu produces higher cumulative yields of both poisons than ²³³U fission, with the isotope dependence being particularly pronounced for ¹⁴⁹Sm (Brown et al. 2018).

For ¹³⁵Xe, the calculated inventories exhibit the expected rapid build-up at the very beginning of burnup, followed by a gradual decrease with burnup in all configurations. This behavior is consistent with ¹³⁵Xe being governed by the ¹³⁵I to ¹³⁵Xe decay chain and by two competing loss mechanisms: radioactive decay to ¹³⁵Cs and neutron absorption to ¹³⁶Xe. Once the early transient has passed, the ¹³⁵Xe concentration approaches a quasi-stationary regime where production from the ¹³⁵I precursor is closely balanced by these removal mechanisms; the slow decline observed at higher burnup indicates that the balance progressively shifts toward ¹³⁵Xe destruction. Two effects act in the same direction: first, the fissile composition changes with burnup (e.g., increasing contribution of bred isotopes and TRU fission components), which modifies the effective fission yields feeding the ¹³⁵I chain; second, under fixed-power conditions the neutron field adapts as the fuel depletes, so the spectrum and the relative importance of (n,γ) reactions on ¹³⁵Xe evolve, leading to a slightly more efficient ¹³⁵Xe depletion at higher burnup.

The difference between cases in Fig. 8 is also systematic and highlights the impact of TRU addition. In the UO₂-based cases, TRU-containing cases (Cases 2–4) exhibit higher ¹³⁵Xe levels than the reference and Case-1 over most of the burnup period, and the ¹³⁵Xe inventory increases with TRU content, with Case-4 remaining the highest. This trend is consistent with a larger fraction of power being carried by Pu isotopes in the TRU cases, which changes the fission-product source term feeding the iodine-xenon chain and, simultaneously, alters the neutron spectrum and capture environment. In contrast, in the thorium-based options (Cases 5–6), the ¹³⁵Xe inventories are clearly lower and decrease more steeply with burnup, reflecting a different fissile vector dominated by ²³³U production and consumption, together with a neutron-capture environment that favors ¹³⁵Xe burnup. When TRU is introduced into the thorium matrix (Cases 7–9), ¹³⁵Xe rises relative to the TRU-free thorium cases, and again increases with TRU content (Case-7 < Case-8 < Case-9), confirming that the added TRU enhances the fission-product source strength associated with Pu fissions and shifts the balance toward higher ¹³⁵Xe concentrations.

For ¹⁴⁹Sm, Fig. 8 shows a qualitatively different evolution. In all cases, ¹⁴⁹Sm increases rapidly at the beginning of burnup and then reaches a maximum at low-to-intermediate burnup, followed by a progressive decline toward the end of the irradiation cycle. This “rise peak decrease” pattern is expected because ¹⁴⁹Sm is produced both directly in fission and indirectly through decay of ¹⁴⁹Pm, while it is removed only by neutron capture (it is effectively stable on reactor time scales). During the early burnup stage, production dominates and the inventory climbs; as burnup increases, the cumulative absorption of ¹⁴⁹Sm becomes significant, and the system transitions toward a regime where capture to heavier samarium isotopes gradually overcomes net production, producing the observed downturn. The location and amplitude of the maximum, therefore, reflect the interplay between the effective ¹⁴⁹Sm production rate per unit power (controlled by the fissile vector and its fission yields) and the efficiency of neutron-capture removal (controlled by flux level, spectrum, and the competing absorption in other strong absorbers, including actinides and other fission products).

The comparative ordering of the ¹⁴⁹Sm curves mirrors, to a large extent, the xenon trends and again underscores the role of TRU. In the UO₂-based cases, adding TRU markedly increases the ¹⁴⁹Sm inventory and amplifies the peak, with Case-4 showing the highest values, followed by Cases 3 and 2, while the reference and Case-1 remain lower. This indicates that TRU loading strengthens the generation of samarium precursors through the modified fission contribution of plutonium isotopes and the associated yield structure, while also reshaping the neutron spectrum and capture competition in a way that delays complete samarium burnup. In the (²³²Th-²³³U-²³⁵U)O₂-based cases, Cases 5–6 show the lowest ¹⁴⁹Sm levels throughout burnup and a more pronounced decline at high burnup, consistent with a neutron-capture environment and fissile evolution that favor ¹⁴⁹Sm transmutation. When TRU is combined with thorium (Cases 7–9), samarium inventories increase relative to the TRU-free (²³²Th-²³³U-²³⁵U)O₂ options, and the peak height grows with TRU content, confirming that the TRU contribution reintroduces a stronger Pu-fission component and elevates the ¹⁴⁹Sm source term. The behaviors in Fig. 8 are consistent with the actinide evolution discussed previously. Configurations that sustain larger plutonium and minor-actinide inventories, and therefore a larger fraction of fissions in Pu isotopes, tend to exhibit systematically higher ¹³⁵Xe and ¹⁴⁹Sm concentrations. This coupling is not only a matter of fission yields; it also reflects the way TRU loading modifies the neutron spectrum and redistributes absorption among actinides and fission-product poisons. Consequently, the TRU-rich UO₂ cases (especially Case-4) combine strong actinide absorption with elevated poison inventories, which is consistent with their steeper reactivity penalties at the BOC and their altered depletion trajectory as burnup progresses.

Fig. 9 compares the burnup evolution of the total radioactivity associated with (a) actinide nuclides and (b) non-actinide nuclides for all investigated configurations. This metric is directly relevant to back-end considerations because actinides govern the long-term radiotoxicity and heat load of spent fuel, whereas non-actinides (dominated by fission products) largely control the short- to intermediate-term activity after discharge (Kang and von Hippel 2001). In the present results, all fuel assemblies exhibit a pronounced rise at the very beginning of burnup, followed by smoother trends as depletion production mechanisms approach quasi-steady regimes.

For the actinide inventory, the activity increases rapidly at low burnup and then continues to rise more gradually up to the end of the irradiation cycle. The initial jump is consistent with the fast establishment of short-lived actinide daughters and precursors generated by neutron captures and subsequent beta decays within the fertile fissile conversion chains, superimposed on the progressive build-up of higher actinides through successive captures. After this early transient, the curves show a sustained increase because the actinide vector becomes progressively heavier with burnup (growth of americium/curium in TRU-containing fuels and build-up of thorium-cycle intermediates in Th-based options), and many of these nuclides have high specific activities. A clear comparative feature is that, within each fuel family, increasing the TRU loading level is accompanied by lower actinide activity at medium and high burnup. This behaviour is consistent with the actinide-evolution results reported earlier: configurations with higher TRU content exhibit stronger net depletion of key fissile plutonium and americium isotopes (notably ²³⁹Pu/²⁴¹Pu and ²⁴¹Am), thereby reducing the contribution of these high-importance actinides to the total activity. At the same time, curium isotopes are produced, but their build-up does not compensate for the reduction of the dominant contributors, leading to a net decrease of the integrated actinide activity as TRU loading increases. This ranking is evident at the end of the irradiation cycle, where the actinide activity decreases from the reference and low-TRU options toward the higher-TRU configurations.

The non-actinide activity follows a different pattern: it rises steeply during the first few GWd/tHM and then tends toward a slowly varying plateau. This is the expected signature of fission-product inventories governed by near-equilibrium between production (proportional to fission rate and cumulative yields) and removal by radioactive decay and neutron capture. Once the principal short-lived and medium-lived fission products reach saturation, additional burnup primarily redistributes activity among nuclides with longer half-lives, producing only moderate changes in the integrated non-actinide activity. The differences among the configurations are partly associated with the isotope-dependent cumulative fission-product yields of the principal fissile nuclides, particularly ²³³U, ²³⁵U, ²³⁹Pu, and ²⁴¹Pu. However, fission yields alone do not determine the calculated activity. The contribution of each fission product also depends on the isotope-specific fission rate, radioactive-decay chain, neutron-capture removal rate, and irradiation history. The narrower spread among cases compared with the actinide activity indicates that variations in fuel composition and neutron spectrum have a less pronounced effect on the integrated non-actinide activity. At high burnup, the TRU-containing thorium-based configurations exhibit the lowest calculated non-actinide activity. This tendency is interpreted as the combined consequence of their evolving fissile composition, isotope-dependent fission-product yields, and subsequent decay and neutron-capture reactions.

The energy released through neutron-induced reactions in the fuel is dominated by nuclear fission, with smaller contributions from other exothermic reaction channels, particularly radiative capture (Insulander Björk et al. 2011; Alam Prianka and Haque Prodhan 2024). The heavy-metal-normalized neutron-induced power at burnup B can be expressed as:

$P_n(B)=\frac{1}{M_{HM}}\int \mathrm{\Phi }(r,B)\sum _i{N}_i(r,B)\sum _r{\sigma }_{r,j}(B)Q_{r,i}^{rec}dV$ (6)

where P_n(B) is the neutron-induced specific power in GW/tHM, M_HM is the initial heavy-metal mass, V is the fuel volume, Φ(r,B) is the neutron flux, N_i(r,B) is the atomic density of nuclide i, σ_r,i(B) is the effective cross-section for reaction r, and Q_r,i^rec is the corresponding recoverable energy release (Marleau et al. 2021).

When only fission is retained, Eq. (6) reduces to the conventional fission-power expression containing σ_f,i(B)Q_f,i^rec. Fig. 10 presents the calculated neutron-induced specific power, whereas Fig. 11 shows the radioactive-decay contribution. All configurations were depleted under a constant total specific-power normalization of 0.040 GW/tHM. At each burnup step, the neutron flux was adjusted so that the neutron-induced and radioactive-decay contributions satisfied the power balance.

$P_n(B)+P_d(B)=P_{\text{set}}=0.040\mathrm{GW}/\mathrm{tHM}$ (7)

where P_d(B) is the radioactive-decay specific power associated with the radionuclide inventory at burnup B, P_set is the prescribed total specific power, and the approximate equality accounts for numerical precision and rounding. The radioactive-decay contribution is calculated from

$P_d(B)=\frac{1}{M_{HM}}\sum _i{\lambda }_j(B)N_i(B,t_c)E_{d,j}^{rec}$ (8)

where λ_j, N_i, and E_d,j^rec are, respectively, the decay constant, total inventory, and recoverable decay energy of radionuclide j, while t_c denotes cooling time. The values plotted in Fig. 11 were evaluated directly from the inventory at each irradiation state without applying a subsequent finite cooling interval. They therefore correspond to t_c = 0 within the adopted depletion-chain representation and do not constitute post-shutdown decay-heat curves as a function of cooling time.

Fig. 10 shows that the neutron-induced power remains close to the imposed normalization throughout irradiation, with only a small progressive decrease. This near-constant behavior is expected by construction and should not be interpreted as an independent demonstration that neutron-induced power is insensitive to fuel composition. Changes in the fissile inventory, neutron spectrum, and reaction-rate distribution primarily modify the flux required to maintain the prescribed power and redistribute the energy release among the contributing nuclides and reactions. The slight decline in P_n is the complementary response to the increasing radioactive-decay contribution. Near the end of the irradiation cycle, for example, P_n is approximately 0.03972-0.03973 GW/tHM, while P_d is approximately 2.71×10^-4-–2.82×10^-4 GW/tHM. Their sum remains close to 0.040 GW. Fig. 10 therefore serves primarily as a verification of the numerical power balance rather than as an independent performance indicator for ranking the fuel configurations.

In contrast, Fig. 11 reveals a monotonic increase in radioactive-decay power with burnup for every configuration. At the first irradiated state, 0.04 GWd/tHM, the calculated decay power ranges from approximately 3.93×10^-5 to 5.75×10^-5 GW/tHM. Near the end of the irradiation cycle, it reaches approximately 2.71×10^-4-2.82×10^-4 GW/tHM. The decay contribution consequently increases from approximately 0.10–0.14% of the prescribed total power at the beginning of irradiation to about 0.68–0.71% at the highest investigated burnup. The initially rapid increase reflects the establishment of short-lived fission-product and precursor inventories, whereas the more gradual evolution at higher burnup results from the competing effects of continuous production, neutron-induced transmutation, radioactive decay, and the accumulation of longer-lived radionuclides.

Within the UO₂-based fuels, the TRU-containing Cases 2–4 generally exhibit higher decay power than the reference configuration and Case-1, with Case-4 producing the highest values over most of the irradiation range. This ordering is physically consistent with the influence of TRU loading on the burnup-dependent Pu fission fractions, isotope-specific fission-product yields, and formation of higher actinides. Nevertheless, the aggregate decay-power curves do not demonstrate that curium or any other individual actinide controls the differences among the cases. At zero cooling time, short-lived fission products and their precursors are expected to provide a substantial contribution. A nuclide-resolved decomposition would therefore be required to quantify separately the contributions from fission products, actinides, and activation products separately.

The thorium-based, TRU-free Cases 5 and 6 exhibit the lowest decay-power values over most of the investigated burnup range. Introducing TRU into the thorium matrix progressively increases the decay power from Case-7 to Case-9. This behavior is consistent with the increasing contribution of Pu isotopes to the total fission rate and the resulting changes in fission-product and actinide inventories. Nevertheless, the thorium-based TRU configurations generally remain below their UO₂-based counterparts. The relative separation among the configurations decreases as irradiation proceeds. The difference between the maximum and minimum decay-power values is approximately 46% at 0.04 GWd/tHM but decreases to about 4% near the end of the irradiation cycle. This convergence reflects the development of a broadly shared fission-product decay source under the common specific-power history. Composition-dependent fission fractions, fission yields, capture pathways, and actinide inventories nevertheless preserve a measurable separation among the cases.

The reactivity feedbacks quantified in this work are reported in Table 11; all coefficients were calculated at BOC. The FTC exhibits a consistent trend toward stronger (more negative) Doppler feedback as the fissile vector becomes richer in actinides with pronounced resonance structure. The reference case shows the least negative FTC (-1.72 pcm/K), while all modified cases display more negative values. In the UO₂-based cases, FTC shifts from -2.21 pcm/K in Case-1 to about -2.47 to -2.50 pcm/K in Cases 2–4. This strengthening is consistent with enhanced Doppler broadening of resonance absorption in fertile and transuranic isotopes as fuel temperature increases, which increases the probability of non-fission captures and reduces reactivity. In the (²³²Th-²³³U-²³⁵U)O₂-based cases, the FTC magnitude is also reinforced compared with the reference, rising from -2.01 pcm/K (Case-5) and -2.31 pcm/K (Case-6) to approximately -2.56 to -2.60 pcm/K in Cases 7–9. The progressive increase across Cases 7–9 indicates that adding TRU and increasing its contribution to the actinide inventory augments resonance absorption pathways, thereby amplifying the Doppler component of feedback.

In contrast, the MTC is the coefficient that most clearly differentiates the fuel families. The UO₂-based configurations exhibit strongly negative moderator feedback. The reference case already shows a large negative MTC (-39.58 pcm/K), and the magnitude becomes more negative when moving from Case-1 (-42.85 pcm/K) to Cases 2–4 (approximately -52 to -55 pcm/K). This behavior is consistent with a moderator temperature increase slightly hardening the spectrum and reducing the effectiveness of thermal utilization in a system largely governed by ²³⁵U and by plutonium isotopes whose fission probability decreases as neutrons shift upward within the thermal range. In addition, TRU loading increases parasitic absorption competition and tends to harden the spectrum, both of which can intensify the negative reactivity response to moderator heating, explaining why Cases 2–4 reach the most negative MTC values in Table 11.

The thorium options show a systematically weaker moderator feedback, particularly in the TRU-free cases. Cases 5 and 6 have MTC values of -20.90 and -23.28 pcm/K, roughly half the magnitude of the reference UO₂ case. This reduced sensitivity is because ²³³U can exhibit comparatively higher fission effectiveness in the upper-thermal to near-epithermal range (Kabach et al. 2024); the spectral shift associated with increased moderator temperature does not penalize reactivity as strongly as in a purely ²³⁵U-dominated situation; depending on design and spectrum, this mechanism may even drive the MTC toward small magnitudes. When TRU is introduced in the (²³²Th-²³³U-²³⁵U)O₂ matrix in Cases 7–9, the MTC becomes more negative; changing from -31.33 to -35.27 pcm/K. This trend demonstrates that increasing the TRUO₂ ring thickness strengthens the negative reactivity response to moderator-density reduction by modifying the local spectrum and the isotope-dependent balance of fission and absorption.

The authors have declared that no competing interests exist.

No ethical statement was reported.

The authors accept full responsibility for the content of the manuscript, including the disclosure of any use of AI.

No AI tools were used in the preparation of this manuscript.

No funding was reported.

All authors have contributed equally.

O. Kabach https://orcid.org/0000-0002-3978-7555

All of the data that support the findings of this study are available in the main text.