Monte Carlo-Based Simulation of Reactivity and Transmutation in the CEFR Sodium-Cooled Fast Reactor

Abstract

As a representative Generation IV sodium-cooled fast reactor (Gen-IV SFR), neutron physics characteristics studies of the China Experimental Fast Reactor (CEFR) core are crucial for its safety case. In this study, a three-dimensional core model of the CEFR was developed using the Monte Carlo-based MCNP5 code, with its reliability validated through five neutronics benchmark experiments. Based on this model, the fundamental neutronics characteristics of minor actinide (MA) transmutation in the sodium-cooled fast reactor were investigated. The results demonstrate that as the minor actinide (MA) loading fraction in the core increases from 0% to 8%, the effective multiplication factor (K_eff) exhibits a significantly nonlinear decrease, accompanied by a corresponding reduction in neutron flux, necessitating increased fuel enrichment to maintain core criticality. Opposite impacts on reactivity are observed for different MA nuclides: ²³⁷Np, ²⁴¹Am, ²⁴³Am and mixed MA reduce K_eff, whereas ²⁴⁴Cm and particularly ²⁴⁵Cm significantly enhance K_eff. The reactivity change rate sharply decreased from −1242.5 to −312.7 pcm/wt%, clearly demonstrating saturation effects in MA neutron absorption. Crucially, reactivity remained deeply negative across all operational scenarios, with safety requirements being satisfied even at maximum MA loading levels, confirming the inherent safety of the proposed approach.

1. Introduction

To advance the energy transition, China is establishing a clean, low-carbon, secure, and efficient national energy system. Guided by a forward-looking vision for cleaner, smarter, and decarbonized energy development, the government has implemented a comprehensive suite of plans, policies, and measures. In September 2020, China formally announced its dual carbon goals: achieving peak carbon dioxide emissions by 2030 and carbon neutrality by 2060. This commitment entails reaching peak CO₂ emissions before 2030 and realizing net-zero emissions by 2060 [1]. The dual carbon goals have been integrated into China’s overarching framework for ecological civilization, positioning them to fundamentally reshape global energy supply-demand dynamics [2]. The optimization and transformation of China’s energy mix will remain a central task for its energy development over the coming four decades [3,4], serving as a defining feature of the nation’s decarbonization pathway.

As a clean and efficient energy source, nuclear power plays a pivotal role in addressing growing energy demands while enabling substantial reductions in greenhouse gas emissions, a strategic advantage recognized by the IPCC in deep decarbonization pathways. Against the backdrop of China’s dual carbon goals, nuclear power development is gaining strategic priority; however, the radioactive waste generated by existing thermal-neutron reactor systems fundamentally contradicts nuclear energy’s sustainable development pathway [5]. Compared to conventional reactors (0.5–1% uranium utilization), fast reactors achieve 60–70% resource efficiency [6], this helps fully utilize limited nuclear fuel resources and prolong the sustainability of nuclear energy development.

Recognized as a leading Gen-IV technology by the Generation IV International Forum (GIF) in 2002, sodium-cooled fast reactors (SFRs) emerged as one of the six most promising advanced nuclear systems due to their superior uranium utilization efficiency and unique capability for transmuting long-lived actinides attributes [7,8] that underpin significant commercial potential and substantial growth prospects [9].

Globally, two dominant nuclear fuel cycle strategies persist: the Once Through Cycle (OTC) and the Reprocessing Fuel Cycle (RFC) [10,11]. However, both approaches dispose of minor actinide (MA) through direct geological burial, which will cause long-term radioactive environmental contamination risks. The secure disposal of nuclear waste constitutes a paramount challenge for the sustainable development of nuclear energy, particularly concerning the management of long-lived high-level radioactive waste [12]. Analyses reveal that the long-term radiotoxicity of high-level waste is predominantly governed by its minor actinide (MA) constituents, characterized by exceedingly protracted decay periods [13,14]. The partitioning and transmutation strategy presents an efficacious technical pathway for the ultimate destruction of such waste [15,16]. To mitigate the radiological hazard of spent nuclear fuel and facilitate resource reutilization, the “Advanced Fuel Cycle” (AFC) concept [17] proposes separating the MA isotopes for subsequent transmutation in reactors, converting them into short-lived or stable nuclides. This process not only significantly curtails the hazardous lifetime of nuclear waste but also enables the utilization of the energy released during transmutation within the reactor system [18].

Facilities capable of serving as neutron sources for transmutation purposes encompass thermal reactors, fast reactors, and accelerator-driven subcritical systems (ADSs) [19]. Fast reactors operate with elevated neutron energy spectra. Although minor actinide (MA) nuclides have smaller fission cross-sections in fast reactors, the lower capture-to-fission ratio combined with higher neutron flux density makes MA nuclides more likely to undergo fission in fast reactors than in thermal reactors [20,21,22,23].

This study employs the Monte Carlo method to establish a three-dimensional core simulation model utilizing the particle transport software MCNP5. The model successfully executed five core physics experiments from the China Experimental Fast Reactor (CEFR) neutronics startup campaign, thereby validating its reliability. Subsequently, this validated model was employed to characterize the effects of adding MA nuclides on initial criticality and neutron flux density profiles in a sodium-cooled fast reactor core.

2. Core Modeling of the CEFR

2.1. Overview of the CEFR Core

The fundamental configuration of the China Experimental Fast Reactor (CEFR), depicted in Figure 1, incorporates a passive decay heat removal system alongside multiple advanced safety mechanisms addressing sodium fire prevention and sodium/water reaction mitigation [24].

This study employs MCNP for core criticality neutronics calculations, necessitating precise computational models incorporating detailed structural and material specifications.

Table 1. Core Primary Design Specifications of the CEFR.

Parametric	Parameter Value
Thermal power	65 MW
Active zone equivalent diameter/height	60 cm/45 cm
Fuel/First core fuel	(Pu, U) O2/UO2
235U enrichment	42.6 kg (19.6%)/236.7 kg (64.4%)
Maximum linear heat rate	430 W/cm
Neutron flux	3.7 × 1015 n/cm2·s(MAX)
Average neutron flux	1.76 × 1015 n/cm2·s
Target burnup	100,000 MWd/t
Core inlet sodium temperature	360 °C
Core outlet sodium temperature	530 °C
Main vessel dimensions	8.010 m

presents fundamental design parameters of the CEFR. The current core configuration comprises 79 fuel assemblies, one neutron source assembly, and eight control rod assemblies—specifically three safety rods (SA), three shim rods (SH), and two regulating rods (RE) [25]. Figure 2 illustrates the radial loading pattern of the initial core fuel assembly configuration.

2.2. MCNP Modeling

This study implements repetitive geometric structures within the Monte Carlo program input files to optimize computational efficiency, particularly given the prevalence of geometrically analogous components in nuclear fission reactor cores. Leveraging MCNP5’s universe declarations and lattice card functionalities, the methodology significantly reduces both input data requirements and computational overhead while ensuring rigorous representation of recurring core configurations.

Diverging from conventional pressurized water reactors employing rectangular fuel assemblies, the CEFR core configuration utilizes hexagonal lattice assemblies, LAT = 2. Modeling of minimum lattice units for fuel rod, control rod, type-I/II stainless steel bar, and B₄C absorber rod. Consequently, the modeling methodology commences with defining fundamental geometric cells encompassing the fuel pellet central hole, clad gaps, and associated material interfaces. The lattice structure is then replicated through the LAT card definition, with the resulting assembly constituting a universe cell. This designated universe cell is subsequently populated into the assembly outer duct cell via the FILL card assignment. Employing the LAT card’s geometric replication capabilities, assembly cell were systematically incorporated into the core lattice cell to finalize the CEFR core modeling.

Moreover, in CEFR neutronics benchmarks including neutron flux and power distribution calculations, all fuel cycles were simulated under cold core conditions (sodium-coolant average temperature: 250 °C), except for reactivity temperature coefficient analyses. However, dimensional changes in CEFR core components and corresponding material density variations due to temperature fluctuations induce a negative reactivity effect, undermining calculation reliability. Consequently, thermal expansion must be accounted for in pre-computation preparations, accounting for distinct linear expansion coefficients of various materials in axial and radial dimensions as specified in

Table 2. Coefficient of linear thermal expansion for reactor core materials.

Materials	Linear Expansion Coefficient
Fuel pellet	1.1 × 10−5/°C
Breeding blanket materials	1.0 × 10−5/°C
B4C neutron absorber	4.2 × 10−6/°C
Stainless steel materials	1.8 × 10−5/°C

. Primarily, the fuel pellet base within the fuel assembly serves as the reference plane for axial expansion. Regarding the axial expansion of sub-assemblies, such as fuel, reflectors, and shields, modeling employs extension originating from the bottom plane. Axial expansion modeling for control rod assemblies accounts for height increments commencing at the top. Furthermore, to maintain constant mass, material density variations are incorporated during dimensional expansion to compensate for volumetric changes. Figure 3 and Figure 4 depict the CEFR core assembly layout diagrams and fuel zone distributions generated by MCNP5.

3. MC Simulation and Transmutation Analysis of the CEFR

3.1. Neutronics Benchmark Simulation and Analysis for the CEFR

The neutronics benchmark experiments for the CEFR comprise six fundamental tests: criticality condition per fuel loading; control rod worth; sodium void reactivity effect; temperature reactivity coefficient; fuel assembly swap reactivity perturbation; reaction rate determination via activation foils. This study exclusively simulates and verifies the first five experiments. Conducted at CEFR’s zero power configuration, the simulations employ MCNP5 to validate essential reactor physics parameters, thereby contributing supplementary data for ensuring reactor operational safety.

When comparing experimental measurements with MCNP5 simulation results, it is essential to recognize that both contain inherent uncertainties. A meaningful comparison therefore does not seek perfect agreement between the datasets, but rather assesses whether they are consistent within their respective margins of error. The reliability of the results is determined by evaluating whether the discrepancy between experimental and simulated values falls within the established criterion of ±500 pcm.

3.1.1. Critical Experiment Analysis

The startup experiment commenced with the core loaded with 79 simulated fuel assemblies, positioned identically to operational fuel elements. As uranium bearing fuel assemblies sequentially and incrementally replaced simulated components from the core center outward, the reactor attained its first critical state. The core fuel assembly count was increased from 24 to 72 through extrapolation using the inverse count rate of the loading, a procedure commonly referred to as subcritical extrapolation. Following the loading of the 71st fuel assembly, the subsequent assembly insertion prompted the core to transition into a supercritical state, thereby concluding the subcritical extrapolation phase. The subsequent procedure, termed supercritical extrapolation, involves achieving criticality through control rod manipulation using the period method. Specifically, the 72nd simulated fuel assembly was replaced with an actual fuel assembly, resulting in the core loading configuration depicted in Figure 5. Criticality was then attained by axially adjusting the control rod assembly designated as RE in Figure 5.

MCNP5 code was employed for modeling, with measured and computational results tabulated in

Table 3. Comparison of simulated and experimental results for critical experiments.

Fuel Assembly Loading Positions	RE Rod Positions (mm)	Keff (Measured Value)	Keff (MCNP)	Error (pcm)
70	500	-	0.99300	-
71	500	-	0.99642	-
72	190	1.00040	0.99988	−52
72	170	1.00034	0.99979	−55
72	151	1.00025	0.99968	−57
72	70	1.00000	0.99936	−64

. The resultant model illustrated in Figure 6. This table juxtaposes experimental effective multiplication factor values against MCNP5 computational outputs, revealing a consistent underestimation of core criticality by approximately 55 pcm in the simulation assessment. The disparities in neutron cross-section libraries exert differential impacts on core reactivity [26], consequently, the MCNP5 calculations employing the ENDF/B-VI.8 library may account for the observed deviations from measured values. A comparative analysis was conducted utilizing the nuclear data libraries CENDL-3.2, ENDF/B-VI.8, JEFF-3.3, and JENDL-4.0u. Simulations of control rod worth, sodium void reactivity, assembly exchange reactivity, and temperature reactivity exhibit strong concordance across the four databases. Under standard operating conditions, with the exception of assembly exchange reactivity, which is systematically underestimated in all computations, the discrepancies between calculated and experimental values for the remaining parameters remain within one standard deviation of the measurement uncertainty.

As indicated in Table 3, insertion of regulating rod assemblies (RE) into the 72-fuel-assembly core induces negative reactivity. With all fuel assemblies loaded, adjusting RE positions from 190 mm to 70 mm achieved the experimentally measured critical state. The MCNP5 simulation yielded a reactivity insertion of −64 pcm, demonstrating excellent agreement with experimental data. This validates both the computational accuracy of the MCNP5 model and the geometric fidelity of the modeling approach.

3.1.2. Control Rod Worth Calculation

Control rod worth is defined as the reactivity change induced by control rod insertion. In sodium-cooled fast reactors, reactivity control is achieved by inserting control rod assemblies into the core and adjusting their positions. The reactivity worth of control rods at various insertion depths is characterized by their integral worth, which is defined as the total reactivity introduced when a control rod assembly is moved from an initial reference position to a specified height within the core. Thus, the integral worth represents the total change in reactivity resulting from the full insertion of one or more control rods from the top to the bottom of the core. To facilitate subsequent calculations of core reactivity parameters, such as the fuel temperature coefficient, sodium void reactivity, and assembly exchange reactivity, the differential worth of each control rod assembly is also provided. The general expression for the differential worth of a control rod is given by Equation (1). This equation calculates the reactivity change resulting from a unit displacement of the control rod assembly at various axial positions within the core, with values expressed in pcm/mm.

$${\alpha }_{\mathrm{c}}={\displaystyle \frac{d\rho }{dz}}\approx {\displaystyle \frac{\Delta \rho }{\Delta H}}$$

(1)

In the equation, $∆\rho$ denotes the reactivity change, while $∆H$ represents the displacement height of the control rod.

Since the MCNP software directly yields the effective multiplication factor from its critical source card, the reactivity is calculated using the below formula:

$$\Delta \rho ={\displaystyle \frac{k_{i+1}-k_i}{k_{i+1}{k}_i}}$$

(2)

Substituting Equation (2) into Equation (1) yields

$${\alpha }_{\mathrm{c}}={\displaystyle \frac{k_{i+1}-k_i}{k_{i+1}{k}_i\cdot \Delta H}},i=1\dots (N-1)$$

(3)

These rods serve not only to maintain reactor safety and stable operation but also to enable precise regulation of nuclear reactions to meet power demands while preventing potential accidents. This study employs an MCNP5 computational framework to simulate control rod worth in the CEFR. The initial core loading of the CEFR comprises eight control rod assemblies. Computational analyses are performed under cold core conditions, with a sodium temperature maintained at 250 °C. Expanding upon the initial critical core configuration described in the previous section, the core is augmented with the seven remaining fuel assembly positions, culminating in a total of seventy-nine fuel assemblies. Figure 7 depicts the layout for the CEFR’s first core loading. To counteract the excess reactivity arising from the seven additional fuel assemblies, the remaining compensation and adjustment control rod assemblies are incorporated into the core arrangement illustrated. For enhanced clarity in presenting computational outcomes, control rods are assigned numerical designations corresponding to their specific positions and functional roles.

Table 4. Positions of diverse control rod assemblies.

Control Rod and Rod Banks	Control Rod Positions/mm
	Change	RE1	RE2	SH1	SH2	SH3	SA1	SA2	SA3
RE1	B	501	106	240	240	239	498	500	500
	A	−1	106	240	240	239	498	500	500
RE2	B	106	499	240	240	239	498	500	500
	A	106	5	240	240	239	498	500	500
SH1	B	240	240	501	141	141	498	499	499
	A	240	240	4	141	141	498	499	499
SH2	B	239	240	151	498	151	498	500	500
	A	239	240	151	−1	151	498	500	500
SH3	B	240	239	148	150	498	498	500	500
	A	240	239	148	150	7	498	500	500
SA1	B	240	239	240	240	241	498	499	499
	A	240	239	240	240	241	498	499	499
SA2	B	240	240	240	240	240	498	499	499
	A	240	239	240	240	240	498	55	499
SA3	B	240	239	240	240	240	498	499	499
	A	240	239	240	240	240	498	499	40
3SH + 2RE	B	247	247	239	240	239	498	500	499
	A	0	5	1	−1	7	498	500	499
SH2 + SH3 + 2RE	B	247	248	501	141	141	498	500	499
	A	−2	2	501	−3	16	498	500	499
3SA	B	247	249	240	240	240	498	500	499
	A	247	249	240	240	240	46	56	40
SA1 + SA2	B	247	248	240	240	240	498	500	500
	A	247	248	240	240	240	45	54	500
2RE + 3SH + 3SA	B	247	248	240	240	240	499	500	500
	A	0	3	2	−2	0	45	56	40
2RE + SH2 + SH3 +3SA	B	248	248	500	141	141	498	500	499
	A	−2	2	500	−3	7	45	55	40

specifies the exact insertion positions for each control rod assembly drop test. Simulated values and their discrepancies relative to experimental measurements are documented in

Table 5. Comparison of calculated and measured control rod worth.

Control Rod and Rod Banks	Measured Value	Error	MCNP Calculated Value	Deviation from Measured Value
RE1	150	±9	142	−8
RE2	149	±9	147	−2
SH1	2019	±250	1908	−111
SH2	1839	±225	1856	17
SH3	1839	±226	1849	10
SA1	945	±100	942	−4
SA2	911	±100	926	15
SA3	946	±98	1000	54
3SH + 2RE	2877	±355	3040	163
SH2 + SH3 + 2RE	881	±76	1029	148
3SA	2981	±395	2854	−128
SA1 + SA2	1950	±226	1790	−160
2RE + 3SH + 3SA	6079	±989	6066	−13
2RE + SH2 + SH3 + 3SA	3899	±551	3940	41

. Additionally, due to certain test conditions initiating rod drops from partially inserted states, this study further analyzes the worth of individual control rod assemblies and full bank insertion scenarios, along with the integral worth when all assemblies are fully withdrawn. These results are presented in

Table 6. Calculated worth of fully inserted control rod assemblies.

Control Rod and Rod Banks	Control Rod Positions	Keff	Control Rod Value (pcm)
3SH+2RE+3SA	3SH+2RE+3SA fully withdrawn	1.02888
RE1	RE1 fully inserted	1.02737	−151
RE2	RE2 fully inserted	1.02739	−149
2RE	2RE fully inserted	1.02581	−307
SH1	SH1 fully inserted	1.01015	−1873
SH2	SH2 fully inserted	1.01056	−1832
SH3	SH2 fully inserted	1.01054	−1834
3SH3	3SH fully inserted	0.97339	−5549
SA1	SA1 fully inserted	1.01891	−997
SA2	SA2 fully inserted	1.01892	−996
SA3	SA3 fully inserted	1.01854	−1034
3SH + 2RE	3SH + 2RE fully inserted	0.97038	−5850
SH2 + SH3 + 2RE	SH2 + SH3 + 2RE fully inserted	0.98919	−3969
3SA	3SA fully inserted	0.99754	−3134
SA1 + SA2	SA1 + SA2 fully inserted	1.0086	−2028
2RE + 3SH + 3SA	2RE + 3SH + 3SA fully inserted	0.93872	−9016
2RE + SH2 + SH3 + 3SA	2RE + SH2 + SH3 + 3SA fully inserted	0.95932	−6956

. During the experimental campaign, reactivity compensation was applied using off target control rods while measuring each test rod, culminating in 14 distinct control rod worth measurements.

As summarized in Table 5 and Table 6, among the three control rod assembly types in the core, the regulating rod assemblies (RE) with natural ¹⁰B absorbers exhibit the lowest reactivity worth. These are predominantly positioned at the outermost periphery of the core fuel region. For safety rod assemblies (SA) and shim rod assemblies (SH) composed of identical materials, the former are positioned near the periphery of the core fuel region, while the latter reside closer to the core center. Consequently, to enhance accident tolerance, the safety rod assemblies deliver higher reactivity worth than shim rods despite identical dimensions and material composition. Even among identical rod types such as shim assemblies SH1-3, worth discrepancies arise from asymmetric core loading. Notably, SH2 and SH3 assemblies in symmetric core positions demonstrate comparable reactivity worth values.

3.1.3. Sodium Void Reactivity Experiment Simulation

The CEFR sodium void reactivity benchmark experiment entails replacing select core fuel assemblies with vacuum sealed counterparts, then adjusting control rod positions to achieve criticality for void reactivity measurement. As depicted in Figure 8, MCNP simulations evaluated five distinct fuel assembly locations.

Table 7. Control rod positions.

Control Rod	Positions/mm
SH1	239.3
SH2	239.2
SH3	239.8
SA1	498.3
SA2	499.8
SA3	499.1

confirms fixed axial positioning of SH and SA control rod assemblies at the core midplane, while RE assemblies were manipulated to attain criticality. Void reactivity coefficients were derived from comparative K_eff analyses between the modified core and the critical core.

Specially designed mock-up assemblies were employed to replace fuel assemblies in Zones 1–5 (Figure 8), with simulated sodium void reactivity results being presented in

Table 8. Comparison of calculated and measured sodium void reactivity.

Simulated Assembly Positions	RE1 Positions	RE2 Positions	Measured Value (pcm)	Error	Calculated Value (pcm)
1	277 mm	277 mm	−39.2	±5.8	−39.7
2	277 mm	277 mm	−43.4	±5.9	−39.9
3	277 mm	277 mm	−40.5	±5.7	−42.0
4	277 mm	277 mm	−40.1	±5.5	−44.3
5	277 mm	277 mm	−32.9	±5.5	−36.6

. Due to CEFR’s compact core geometry, all five zones exhibited negative void reactivity, ranging from −36.6 pcm to −44.3 pcm in MCNP5 simulations. This phenomenon confirms increased neutron leakage resulting from sodium void. The computational values fall entirely within experimental uncertainty bounds, validating both the model fidelity and code reliability. The MCNP5 simulation results further validate CEFR’s inherent safety performance. Consequently, rigorous investigation and management of sodium void reactivity effects are imperative for ensuring safe and stable operation of sodium-cooled fast reactors.

3.1.4. Reactivity Simulation for Assembly Substitution

This study selected eight distinct core positions for reactivity perturbation analysis. Target locations requiring modification, as specified in

Table 9. Assembly positions for swap reactivity testing.

Calculated Positions	1	2	3	4	5	6	7	8
1	SS	Fuel	Fuel	Fuel	Fuel	Fuel	SS	SS
2	Fuel	SS	Fuel	Fuel	Fuel	Fuel	SS	SS
3	Fuel	Fuel	SS	Fuel	Fuel	Fuel	SS	SS
4	Fuel	Fuel	Fuel	SS	Fuel	Fuel	SS	SS
S	Fuel	Fuel	Fuel	Fuel	SS	Fuel	SS	SS
6	Fuel	Fuel	Fuel	Fuel	Fuel	SS	SS	SS
7	Fuel	Fuel	Fuel	Fuel	SS	Fuel	Fuel	SS
8	Fuel	Fuel	Fuel	SS	Fuel	Fuel	SS	Fuel

and illustrated in Figure 9, comprise six fuel assemblies (positions 1–6) and two Type-I stainless steel assemblies (positions 7–8) for research substitution induced reactivity effects. During the simulation, fuel assemblies numbered 1 through 6 are sequentially substituted with SS-I reflector assemblies, while the SS-I assemblies at positions 7 and 8 are replaced with fuel assemblies. To maintain safety during measurements, the total number of fuel assemblies is constrained to a maximum of 79. Accordingly, when fuel is loaded into the SS assemblies at positions 7 and 8, SS assemblies must be installed at positions 4 and 5 to preserve this limit.

Table 10. Comparison of calculated and measured swap reactivity values.

Measurement Positions	Temperature (°C)	Keff (Before)	Keff (After)	Calculated Value (pcm)	Measured Value (pcm)	Error (pcm)
1	250	1.00033	0.99056	−984	−977	7
2	250	1.00033	0.99177	−875	−856	19
3	250	1.00033	0.99340	−772	−693	79
4	250	1.00033	0.99355	−639	−678	−39
5	250	1.00033	0.99660	−476	−373	103
6	250	1.00033	0.99492	−586	−541	45
7	250	0.9966	0.99954	210	294	84
8	250	0.99355	0.99992	582	637	55

compares experimental measurements with MCNP simulations, revealing an average measurement discrepancy of 44 pcm. The tabulated data demonstrate that fuel assembly substitutions consistently yield negative reactivity due to fuel depletion, whereas stainless steel component exchanges conversely exhibit positive reactivity. Furthermore, results indicate an inverse relationship between reactivity magnitude and proximity to the core center: substitution positions nearer the central axis manifest greater reactivity deficits. This phenomenon likely stems from diminished fuel inventory in central zones, necessitating greater reactivity compensation. Under the initial six scenarios cataloged, the absolute magnitude of reactivity perturbations induced by fuel assembly substitution progressively diminishes as stainless steel components are positioned further from the core periphery. This pattern demonstrates that loading fuel assemblies toward the radial exterior potentially yields reduced net reactivity insertion. Preceding analysis reveals that SS assemblies deployed nearer to the core center generate increasingly negative reactivity perturbations. Scenarios 7 and 8 exhibit positive reactivity feedback despite maintaining constant aggregate fuel assembly inventory. Here, SS assemblies at positions 4 and 5 (situated farther from the core) yields positive reactivity values. Crucially, while position 8 exhibits greater proximity to the core than position 7, its fuel loading configuration manifests higher reactivity due to this differential placement geometry.

3.1.5. Temperature Reactivity Coefficient Computation

In the CEFR temperature reactivity experiments, temperature variations induce changes in the physical state of materials, necessitating the incorporation of thermal expansion effects on material density and dimensional changes at specified temperatures, as shown in Figure 10. Consequently, within the MCNP model, the expansion characteristics of all solid materials are adjusted using the constant linear expansion coefficients discussed in Table 2. Furthermore, calculations of temperature effects must account for variations in the density of the sodium coolant within the CEFR, which result from changes in sodium temperature. Under standard atmospheric pressure, the density of liquid sodium in the temperature range from its melting point to boiling point can be calculated using Equation (1) [27].

$$\rho =950.0483-0.2298T-14.6045\times {10}^{-6}{T}^2+5.6377\times {10}^{-9}{T}^3$$

(4)

The calculations were performed for the reference core configuration containing 79 fuel assemblies. The temperature was increased from 250 °C to 302 °C at intervals of 250 °C, 274 °C, 283 °C, 293 °C, and 302 °C, and then decreased from 300 °C to 250 °C at similar intervals of 300 °C, 290 °C, 280 °C, 270 °C, and 250 °C. Using these two approaches, the reactivity change with respect to the average coolant temperature was measured at five distinct temperature levels. The temperature reactivity coefficient (α_T) is calculated from the control rod worth (ρ_CR) and the small reactivity difference in critical states during temperature changes (ρ_T), as shown in Equation (2).

$${\alpha }_T={\displaystyle \frac{\Delta {\rho }_T-\Delta {\rho }_{CR}}{\Delta T}}$$

(5)

The temperature effect measurement was conducted according to the following procedure. First, with the reactor in a shutdown state, the core coolant temperature was brought to the cold-state condition of 250 °C and maintained at this temperature for at least 30 min. Subsequently, the SA control rod assemblies were fully withdrawn from the core. The SH and RE control rod assemblies were then adjusted vertically within their guide tubes to achieve a slightly supercritical core state. The corresponding core temperature, control rod assembly positions, and reactivity were recorded at this condition. Following this, the core was returned to a shutdown state. The input file was then modified to reflect the next target temperature level, and the preceding procedure was repeated. This experimental sequence yielded a total of ten datasets. The control rod positions recorded during these ten steps are presented in

Table 11. Control rod assembly positions.

Temperature Variation	T (°C)	RE1 (mm)	RE2 (mm)	SH1 (mm)	SH2 (mm)	SH3 (mm)
Temperature increase	250	207	208	248	248	248
	274	212	213	254	253	254
	283	240	239	253	253	254
	293	283	283	253	253	254
	302	308	307	255	255	256
Temperature decrease	300	408	409	502	162	162
	290	283	284	254	254	254
	280	285	285	502	162	162
	270	232	232	502	162	162
	250	119	119	502	162	163

, with units in millimeters (mm).

Within the experimental data, two distinct average temperature coefficients were calculated based on the heating and cooling processes. In the CEFR experiments, approximately 14 thermocouples were installed above the reactor core to measure the average outlet sodium coolant temperature. This temperature served as the homogenized temperature for the entire core, enabling the measurement of temperature variations and the calculation of temperature reactivity coefficients. In the MCNP model, parameters in the input file were updated based on the RE and SH control rod assembly positions from Table 11. The effective neutron multiplication factor (K_eff) was then calculated at distinct temperature levels, enabling derivation of the temperature reactivity coefficient.

Table 12. Comparison of calculated and measured temperature reactivity coefficients.

Temperature (°C)	Measured Value (pcm/°C)	Calculated Value (pcm/°C)	Error
274	−3.78 ± 0.55	−4.23	−0.45
283	−3.52 ± 0.49	−3.78	−0.26
293	−3.54 ± 0.47	−3.98	−0.44
302	−3.88 ± 0.52	−4.30	−0.42
290	−4.46 ± 0.73	−4.28	0.18
280	−4.05 ± 0.58	−3.92	0.13
270	−4.31 ± 0.58	−3.99	0.32
250	−4.39 ± 0.58	−4.16	0.23

presents a comparison between the simulated temperature reactivity coefficients and experimental measurements. The average temperature coefficients calculated by MCNP5 show reasonable agreement with the experimental values, indicating the model’s acceptable accuracy.

Temperature reactivity decreases with rising temperature, resulting in a negative temperature coefficient. This phenomenon is primarily attributed to two mechanisms: (1) radial expansion of the fuel and cladding, which increases neutron leakage; (2) reduced sodium density at elevated temperatures, which hardens the neutron flux spectrum. Both effects contribute to the negative reactivity feedback. As temperature increases, enhanced resonance absorption due to the Doppler effect reduces the effective neutron multiplication factor (K_eff), further contributing to negative temperature feedback. The simulated temperature coefficients demonstrate close agreement with experimental measurements.

3.2. Study on Transmutation of MA in SFR

In MA transmutation studies, their loading concentration constitutes a key design parameter. Inappropriate loading not only reduces transmutation efficiency but may also compromise the core’s initial criticality and neutron flux distribution, thereby jeopardizing reactor safety. To achieve homogeneous mixing of MA within the core fuel, the isotopic composition of MA is specified [28] in

Table 13. Isotopic composition of MA.

Nuclides	237Np	241Am	243Am	244Cm	245Cm
Composition (%)	56.2	26.4	12	5.12	0.28

.

By modifying material cards in the MCNP5 input file, we added 2 wt% of ²³⁷Np, ²⁴¹Am, ²⁴³Am, ²⁴⁴Cm, ²⁴⁵Cm, and mixed MA nuclides. The effects of individual nuclides on K_eff were analyzed, with results presented in

Table 14. Impact of different nuclides on K_eff.

Nuclides	MA-Free	237Np	241Am	243Am	244Cm	245Cm	Mixed MA
Keff	1.00033	0.97454	0.97485	0.97487	1.00490	1.07034	0.97607
Δkeff	-	−0.02579	−0.02548	−0.02546	0.00457	0.07001	−0.02426

. As shown in the table, transmutation of ²³⁷Np, ²⁴¹Am, ²⁴³Am, and mixed MA in the sodium-cooled fast reactor suppresses K_eff. The magnitude of suppression follows the decreasing order: mixed MA < ²⁴³Am < ²⁴¹Am < ²³⁷Np. Conversely, transmutation of ²⁴⁴Cm and ²⁴⁵Cm enhances K_eff, with the increase caused by ²⁴⁵Cm significantly exceeding that from other nuclides.

Incorporating MA nuclides into nuclear fuel through homogeneous blending at concentrations of 2%, 5%, and 8% significantly impacts core neutronic behavior due to MA’s substantial neutron absorption cross-sections. Subsequent alterations in initial criticality characteristics necessitate computational evaluation of K_eff via MCNP5 simulations.

Table 15. Keff under varied MA isotopic compositions.

Composition (%)	0	2	5	8
Keff	1.00033	0.97607	0.95876	0.95022
Δkeff	-	−0.02426	−0.04157	−0.05011
Ρ (pcm)	33	−2452	−4301	−5239
Δρ	-	−2485	−1849	−938

quantitatively documents K_eff variations resulting from differential MA isotopic blending ratios.

Analysis of Table 15 reveals that K_eff progressively diminishes as the MA concentration increases. This trend indicates that MA incorporation intensifies neutron absorption phenomena, consequently diminishing the neutron utilization factor and reducing core reactivity to negative values. Restoring criticality would necessitate significantly augmenting fuel enrichment levels. The reactivity decrement induced by MA nuclides diminishes with increasing concentration ratios, attributable to neutron spectrum hardening and consequent thermal neutron depletion.

A fuel assembly was randomly selected with five fuel rods sampled radially from the core-center to the periphery, designated positions 1 to 5. Neutron flux density distributions for these rods with varying MA admixture proportions are documented graphically in Figure 11. Results demonstrate progressively diminished neutron flux density with increasing MA concentration.

4. Conclusions

Building upon validated neutronics benchmark simulations, this research employs a full-scale three-dimensional MCNP5 model to investigate the fundamental neutronics behavior of reactivity and minor actinide transmutation characteristics in sodium-cooled fast reactors. Key findings are as follows:

• Computational validation of the CEFR three-dimensional neutronics benchmark model confirms that its fundamental safety parameters and reactivity characteristics align with neutronics fundamentals. These findings provide substantial evidence for the reactor’s inherent safety features and demonstrate its rationally reliable design.
• The close agreement between MCNP5 computational outcomes and experimental measurements not only validates the program’s efficacy in neutronics calculations but also confirms the reliability of the developed three-dimensional neutronics model for CEFR.
• The transmutation of ²³⁷Np, ²⁴¹Am, ²⁴³Am, and mixed MA reduces core K_eff, whereas the transmutation of ²⁴⁴Cm and ²⁴⁵Cm enhances it. Notably, the reactivity increase induced by ²⁴⁵Cm far exceeds that attributable to all other nuclides.
• With the MA content increment from 0 wt% to 8 wt%, K_eff undergoes substantial nonlinear attenuation (1.00033→0.95022). The reactivity variation coefficient progressively diminishes from −1242.5 pcm/wt% to −312.7 pcm/wt%, indicating neutron absorption saturation effects within the MA isotopes. Crucially, all operational scenarios maintain profoundly negative reactivity values, with even peak MA loading sustaining compliance within safety margin limits. These computational results empirically substantiate the inherent neutronics safety characteristics of the MA loading scheme.