Subcritical System Research Articles

Probability of Initiation in Coupled Multiplying Assemblies

Neutron chain survival and ultimate divergence in coupled multiplying assemblies, linked by intercepted leaking neutrons, are considered. Nonlinear equations are formulated for the dynamic probability of survival and static probability of initiation (POI) with assembly intercept fractions computed using a view factor model. Numerical solutions are obtained for up to four coupled assemblies, revealing a sensitive dependence on interassembly coupling strength. The results indicate that a chain will not diverge with certainty in a subcritical or critical system but that divergence will occur with some probability POI > 0 that increases with coupling strength. Additionally, at k eff = 1 , the stable subcritical solution branch is observed to bifurcate into two branches, one of which is shown through linear stability analysis to be unstable.

On the convergence of the fixed point method for solving neutron transport alpha eigenvalue problems

It was shown that the Fixed Point Method (also known as the Rayleigh Quotient Method) is several times faster than the Critical Search Method for solving neutron transport alpha eigenvalue problems. It was also shown that the Fixed Point Method is able to determine the alpha eigenvalues of sub-critical systems that are beyond the reach of the Critical Search Method. Despite these significant advances, the Fixed Point Method remains an unproven algorithm. This report provides a proof.

Production cross sections of 102mRh and 108mAg in proton bombed natPb target with 400 MeV energy

The accelerator-driven subcritical system (ADS) is a competitive option for next-generation nuclear energy systems. Production cross sections of long-lived residual radioactive nuclides in a proton-nuclide reaction are basic quantities for the calculation of accumulated radioactivity in the use of ADS systems. This work presents the production cross sections of 102mRh and 108mAg in a natural lead (natPb) target activated by 400 MeV protons. The natPb target was irradiated by a 400 MeV proton beam in NRC “Kurchatov Institute” and measured two decades later by a low background gamma spectrometer in China Jinping Underground Laboratory (CJPL). A spectrum analysis method based on simulated single-isotope spectrum and Bayesian peak fitting was employed to compute the activities and production cross sections of the residual nuclides. The experimentally measured cross-sections for 102mRh and 108mAg were 0.72 ± 0.05 mb and 0.76 ± 0.09 mb respectively. These values are approximately twice as high as those predicted by the QGSP_INCLXX_HP model and fall within the range predicted by the INCL4+ABLA and LAQGSM+GEM2 models for mass numbers A=102 and A=108. These findings offer new experimental insights for ADS research and provide a practical benchmark for theoretical models concerning proton-lead interactions.

Measurement of fast neutron induced (n,γ) reaction cross-section of 68Zn, 96Zr, 121Sb and 123Sb in the energy range of 1 to 2 MeV

The (n,γ) reaction cross-section for the elements 68Zn, 96Zr, 121Sb and 123Sb, present in the reactor structural/shielding materials, was measured by neutron activation technique in the neutron energy region of 1–2 MeV as very limited data is available in this energy range. Further, the neutron spectrum peaks in this energy region for the fast breeder reactors and proposed accelerator driven sub-critical systems. The natural strontium (natSr) element was used as a neutron flux monitor by considering effective combined reaction cross-section for 86Sr(n,γ)87Srm and 87Sr(n,n′)87Srm reactions. The pellets of mixture of sample and monitor were irradiated by a quasi-mono energetic fast neutron beam, generated by 7Li(p,n)7Be reaction at FOTIA, Bhabha Atomic Research Centre, Mumbai, India. The activity of activation products was measured by off-line gamma-ray spectrometry using High Purity Germanium Detector (HPGe). The present data with improved uncertainty and covariance analysis enhance the cross-section data base for better constraining the evaluated data and theoretical models. The theoretical (n,γ) reaction cross-sections were calculated using TALYS 1.96, which could reasonably explain the present data with the Fermi gas level density prescription.

Nuclear Transmutation of 99Tc Utilizing Proton Spallation and Compact Subcritical Assembly

An innovative design is introduced for neutron transmutation employing a proton accelerator in conjunction with a compact subcritical system. The transmutation converter comprises a spherical target enveloped by a subcritical assembly. The subcritical assembly consists of a moderator and low-enriched uranium in shell plates. The subcritical assembly has an inner radius of 10 cm and a thickness of 40 or 55 cm. The material used for the target is lead, and beryllium or beryllium oxide is used as a moderator. Low-enriched uranium in the subcritical assembly contains 5% 235U. The transmutation half-life is inversely proportional to the integral of epithermal 99Tc capture rates. The MCNP6 simulation demonstrates that the transmutation half-life is less than 1 year when exposed to 1-GeV protons at 5 mA. Additionally, it is notable that this half-life can be further reduced with increased proton energies and currents. Previous studies have reported that the 99Tc transmutation half-life using fast reactors and an accelerator-driven system ranges from tens to hundred years; this design concept represents a substantial advancement to previous research efforts.

Refrigerant charge estimation method based on data-physic hybrid-driven model for the fault diagnosis of transcritical CO2 heat pump system

The transcritical CO2 heat pump system is a promising and excellent heating scheme. However, the operating pressure of the transcritical CO2 heat pump system is high, and refrigerant leakage is a frequent problem. It is worth noting that the operating principle of CO2 heat pump systems is unique. Thus, conventional refrigerant charge estimation methods for subcritical systems cannot be directly applied to transcritical systems. In this study, a novel refrigerant charge estimation method for the transcritical CO2 heat pump system is proposed. Based on the heat and mass transfer characteristics of the transcritical system, the grey box model constrained by physical laws is constructed. Based on the machine learning algorithm, the correction model of the grey box model is built. The hybrid model combines the advantages of the high generalization ability of the physic-driven model and the nonlinear fitting ability of the data-driven model. The results show that the novel estimation method can accurately predict the refrigerant charge, enabling fault diagnosis of refrigerant leakage. The data-driven correction model can improve the prediction accuracy of the grey box model. The Mean Relative Error of the hybrid-driven model can be controlled within 5 %.

Control strategy for the core power in an accelerator drive sub-critical system

This paper reports the control strategy for the core power in an accelerator drive sub-critical (ADS) system. In an ADS system, the intense external neutron source provided by a proton accelerator coupled to a spallation target is used to drive a sub-critical reactor. The proposed control strategy is to control the reactor power by adjusting the proton beam power, where the beam power is adjusted by changing either the duty factor or the intensity of the proton beam. As an example, the reactor power control of the China initiative Accelerator Driven System (CiADS) facility has been studied by adjusting the beam power. Firstly, the beam power is set roughly by assigning a new duty factor, where the duty factor is set by changing the beam macro-pulse length and the pulse repetition rate of the proton beam. Both the pulse length and the repetition rate are assigned by a timing system. Secondly, the power is adjusted precisely by changing the beam intensity. To change continuously the beam intensity, an adjustable aperture is used to block the outer particles of the beam line in the accelerator. In order to evaluate the proposed control strategy, a CiADS core model is built based on the multi-node point reactor dynamics model. Three cases, the start of the facility, the decrease of core power and the increase of core power, have been simulated with the model. The simulation results indicate that the control strategy for the core power by changing either the duty factor or the intensity of the proton beam works very well during the operation of the facility.

Asymptotic behavior of $$L^2$$-subcritical relativistic Fermi systems in the nonrelativistic limit

Asymptotic behavior of $$L^2$$-subcritical relativistic Fermi systems in the nonrelativistic limit

Highly efficient selective extraction of Li from spent LiNixCoyMnzO2 assisted with activated pyrite in a subcritical water system

As the strategic importance of Li in the energy sector increases, selective Li extraction technology from spent lithium-ion batteries (LIBs) is attracting increasing attention. Current Li extraction processes typically suffer from lengthy procedures, high costs, and low efficiency. To improve the efficiency of Li extraction, a novel approach to achieve efficient Li recovery is proposed in this study, namely, reacting pyrite (FeS2) with LiNixCoyMnzO2 (NCM) powder in a subcritical water reduction (SWR) system. The reducing solvent environment created by the enhanced reaction of FeS2 with subcritical water converts the high−valent metals in NCM to a low-valent state, causing the collapse of the stable laminar structure and allowing Li+ to be released smoothly. After dual activation through mechanochemical and roasting processes, more than 99 % of Li is preferentially extracted under optimal conditions. Furthermore, Li+ in solution is converted into highly pure Li2CO3, while other metallic elements remain in the residue. Using inexpensive FeS2 for efficient Li extraction without adding additional chemical reagents is a promising approach for recovering spent LIBs.

Sensitivity and perturbation analysis of alpha-eigenvalue with time-dependent Monte Carlo perturbation techniques

Sensitivity analysis and perturbation calculation methods for prompt neutron decay constants α using the Monte Carlo method, such as iterative fission probability (IFP), differential operator sampling (DOS), and correlated sampling (CS), have been proposed thus far. However, these methods require a significant amount of memory storage. The method developed in this study applies DOS and CS techniques during a time-dependent Monte Carlo simulation for the pulsed neutron method in subcritical systems. The time variation of the neutron flux is fitted to an exponential function during the time range when the flux decays with the fundamental mode α. By applying the least squares method to the results of time-dependent DOS and CS, the sensitivity coefficients with respect to nuclear data and the change in α due to perturbation can be calculated. In contrast to the existing methods that require storing the total fission or time sources per generation over several (∼10) generations, the proposed method only needs to store the weighting coefficient of a single source particle until it dies. The additional memory storage per parameter is comparable to that of conventional time-dependent Monte Carlo simulations and much less than that of existing methods. Numerical tests for the proposed method have demonstrated the accuracy and usefulness of the time-dependent DOS and CS methods.

Development and Verification of Neutron Kinetics Parameter Calculation Program Applicable to Subcritical Systems of Long-Life Reactors

The fundamental prompt neutron delayed constant α, the effective delayed neutron fraction β eff , and the effective neutron generation time Λ eff are important for accurate measurements of keff in subcritical systems. In this paper, based on the open-source program OpenMC, a module with the function of calculating the α-eigenvalue is developed based on the k-α iterative method. Based on the nodal expansion method (NEM), an adjoint neutron flux calculation program was developed, which in turn used the idea of coupling the k-α iterative method with the NEM to obtain the neutron kinetics parameters (α, β eff , and Λ eff ) of the subcritical system and allowed for a more accurate keff under the subcritical system as compared to the traditional k-mode program. In this paper, the results of the α-eigenvalues calculated by the program are validated using the Godiva benchmark and the MUSE-4 device as computational objects. The accuracy of the results for β eff and Λ eff was verified with the KUCA (Kyoto University Critical Assembly) benchmark. The results of the keff calculations using k-mode and α-mode are compared with the ADS benchmark. The results show that the calculation program (α-mode) can obtain keff under the subcritical system more accurately, which makes up for the shortcomings of the traditional program, which cannot be calculated under the deep subcritical system. The relative error between the calculated and reference values was less than 750 pcm at deep subcriticality (keff = 0.899). The error was less than 400 pcm at the deeper subcritical system (keff = 0.952), which can satisfy the demand for neutron dynamics parameters and keff calculation in the subcritical system. The program can also continue to be upgraded in the later stage in the calculation method and other aspects.

Monte Carlo iterative k-source method for fixed-source calculations in nearly critical subcritical systems

In addition to the conventional fixed-source method, the iterative k-source (IKS) method is another Monte Carlo algorithm used for solving fixed-source problems. In contrast to the fixed-source method, the IKS method iterates the fission sources for each generation, which is similar to the k-eigenvalue calculation. The IKS method does not require following long-chain fission reactions until the end, even for a nearly critical subcritical system. The source-multiplication factor, ks, which is supposed to be less than unity, is calculated for each cycle. However, ks occasionally or frequently exceeds unity in a nearly critical system owing to statistical fluctuations, in which case the result of the IKS method is biased. To eliminate this bias, the frequency at which ks exceeds unity should be minimized by increasing the source size per cycle. As demonstrated in this study, the computational efficiency of the IKS method is three to ten times that of the conventional fixed-source method.

Recommended operating conditions and performance evaluation of commonly used hydrofluoroolefin (HFO) and hydrochlorofluoroolefin (HCFO) refrigerants in organic Rankine cycle

The application of the first three generations of organic refrigerants, namely, CFCs, HCFCs, and HFCs, in an organic Rankine cycle has been widely investigated. As environmentally friendly successors to the above three generations of refrigerants, hydrofluoroolefins (HFOs) and hydrochlorofluoroolefins (HCFOs) have also attracted increasing research interest for their application in the organic Rankine cycle (ORC). Based on molecular complexity, characteristic points on saturation liquid and vapor curve and area of characteristic regions in temperature-entropy (T-s) diagram, eight common hydrofluoroolefins (HFOs) and hydrochlorofluoroolefins (HCFOs) are classified, analyzed, and evaluated. In addition, the type of heat source and specific operating conditions in which these eight hydrofluoroolefins (HFOs) and hydrochlorofluoroolefins (HCFOs) are most effective are recommended. The results show that molecular complexity of hydrofluoroolefins (HFOs) and hydrochlorofluoroolefins (HCFOs) mainly depends on the length of the C chain, and then on the number and location of Cl and F atoms. HFO-1243zf has the best comprehensive evaluation indicator, and it is noteworthy as a recommended working fluid for subcritical ORC systems. The result obtained in this paper may provide a reference for the design and actual operation of Organic Rankine Cycle system using HFO and HCFO as working fluids.

Reactor Physics Monitoring of a Source-Driven Subcritical System in Stationary State by Deterministic and Probabilistic Deep Neural Networks

Reactivity measurement methods, like the Amplified Source Method (ASM), link observable quantities to integral physics parameters characterizing subcritical assemblies (SCAs). These methods were mostly derived from point reactor kinetics, which assumes fundamental mode distribution. However, in SCAs, external sources cannot be neglected, leading to a nonideal response, such as the detector position dependence of measured k eff . This work investigates deterministic and probabilistic deep learning (DL) in determining k eff and kinetics/subcritical parameters using core map and foil/active detector responses as inputs, which distinguishes DL from neutronics codes. Convolutional neural networks surpassed dense neural networks with higher accuracy, while assigning a strong signature to appropriate core map features. Expansion into multi-input networks, which also process reaction rates, highlighted DL’s flexibility by accurate prediction regardless of reaction type. Uncertainty quantification of DL was done using Monte Carlo (MC) Dropout and Bayesian neural network (BNN). The results favored BNN over MC Dropout, showing greater improvement with increasing data. An assessment of ASM, applicable in a SCA at source equilibrium, showed a reactivity bias of up to −3.59%Δk/k (−4.86 $). In contrast, DL had a maximum bias of only 0.38%Δk/k (0.5 $). Underestimation by ASM represents a nonconservative scenario in criticality safety, while DL proved robust against spatial effects. This demonstrates DL’s potential in ensuring reactivity margins and a safe approach to criticality in reactor operation regimes where standard techniques can fail.

Enhanced transmutation of minor actinides by incorporation of multi-beam design in Accelerator-Driven subcritical system

This study aims to identify the optimal beam design for incinerating the long-lived minor actinides in Accelerator-Driven System (ADS). All the analyses were performed using the MCNP6.1 code with cross-section library ENDF/B-VII. In this study, a depletion method for ADS was conducted and analyses were exercised to investigate the burnup performances for the various arrangements of a three-proton beam design. The influences of the various arrangements of the three-proton beam design were used as a criterion for comparison. It was found that the dual proton beam arrangement demonstrated the best depletion result for the incineration of minor actinides.

Solubilization and structural changes of lignin in naked oat stems during subcritical water autohydrolysis

In this study, the solubilization and structural changes of lignin in naked oat stems were investigated under subcritical water autohydrolysis systems (170–210 °C, 0.68–1.85 MPa). In this system, Hemicellulose was preferentially hydrolyzed in the liquid water at elevated temperatures, leading to the production of acetic acid and glucuronic acid, which acidified the reaction system. Under acidic and high-temperature conditions, lignin primarily underwent degradation and condensation reactions. At autohydrolysis temperatures below 190 °C and autohydrolysis pressures below 1.22 MPa, lignin degradation was predominant, realizing a maximum lignin removal of 47.8 % and breakage of numerous β-O-4 bonds from lignin. At autohydrolysis temperatures above 190 °C and autohydrolysis pressures above 1.22 MPa, lignin condensation dominated, with an increase in the amount of organic acids generated upon hemicellulose degradation, leading to condensation reactions with the degraded low-molecular-weight lignin. The degree of lignin condensation was positively correlated with the temperature of the reaction system. This study provides essential insights into the dynamic changes in the structure of lignin in both the hydrolysis residue and hydrolysis solution during subcritical water autohydrolysis.

Effects of Pb and Bi on mechanical properties and fracture modes of bcc iron symmetrical tilt grain boundaries

The internal structural material T91 in the accelerator driven subcritical reactor system (ADS) has encountered the challenge of liquid metal embrittlement caused by Pb and Bi. Therefore, it is of utmost importance to gain a comprehensive understanding of their embrittlement mechanism. The effects of Pb and Bi on the surface energy of surfaces and separation work and fracture toughness of grain boundaries in body center cubic (BCC) Fe are examined using first-principles calculation. Pb and Bi atoms reduce the surface energy and grain boundary cohesion strength of BCC Fe, with a more significant decrease in surface energy. Meanwhile, the segregation of Pb and Bi in the grain boundary reduces the fracture toughness of the grain boundary. By comparing different surface energy and separation work, it is found that BCC pure Fe is more prone to intergranular fracture, while the presence of Pb and Bi causes cleavage fracture. This elucidates the low-temperature fracture mode of BCC-Fe and reveals the potential mechanism of brittle cleavage fracture caused by Pb and Bi in BCC-Fe. The derived results are discussed in terms of electronic structure and show good agreement with experimental results in the literature, ultimately contributing to a thorough understanding of the intrinsic mechanism of liquid metal embrittlement of T91 steel.

Waste Heat Conversion to Power via Organic Rankine Cycle

several studies have been carried out on how to recover waste heat using Organic Rankine cycle. Each study applied different working conditions, power scale and cycle configuration, hence an assessment of working fluids is given for specific case. As a result, no single working fluid have been identified that would meet an entire heat source temperature levels. This motivated us to examine various substances for use as working fluids for subcritical ORC systems operating in the temperature range (543 - 633K). In this study, with a given finite thermal source, performance of working fluid candidates are evaluated and assessed using four criteria: thermal efficiency, exergy efficiency, total exergy destruction and net power output. Results of the study indicate that from a performance point of view, the linear alkanes such as nonane seem to be a suitable fluid in the temperature range (543-573K). Beyond aforementioned temperature range it appears that aromatic hydrocarbons such as toluene, ethylbenzene, P-xylene, O-xylene, propylbenzene preformed better. Under this condition, they represent comparably similar proposed screening criteria parameters and comparably high evaporating pressure, with only occasional slight differences between them.

Beam physics design of a superconducting linac

The China initiative Accelerator-Driven subcritical System (CiADS) project aims to design and build the world’s first accelerator-driven subcritical system demonstration facility. The facility will attain 2.5 MW thermal power in 2026 to realize accelerator-target-reactor coupling experiments. As the first approved accelerator-driven subcritical system facility, the CiADS driver linac will adopt cutting-edge accelerator technologies to achieve the challenging goals of high beam power and high reliability. The accelerator will operate in cw mode to produce a 500 MeV, 5 mA proton beam. To meet the extremely high demands on beam availability, the linac design lays strong emphasis on beam loss control and increased fault tolerance via a novel fault-compensation method. The accelerator complex consists of a room temperature front-end section, a main linac that employs superconducting accelerator technologies, and a high-energy beam transport line. The beam-loss-oriented beam dynamics design of the driver linac complex is presented in the paper. Published by the American Physical Society 2024

Steady-state analysis of the 1970 Windscale nuclear criticality incident

This paper presents several steady-state neutron transport models which are used to determine the behaviour of the nuclear criticality incident that occurred at the Windscale Works in 1970. The transfer vessel involved in this incident contained two immiscible fissile liquids (an aqueous phase and an organic phase) which had been disturbed such that an emulsion layer formed between them. Infinite domains of the aqueous, organic, and emulsion phases were modelled to enable the understanding of the effects of nuclear data library, neutron transport code and material on the calculated kinetics data, effective multiplication factor and macroscopic neutron cross sections. Six possible configurations of the 1970 Windscale criticality incident were simulated using three-dimensional models in MCNP, two-dimensional models in academic research code EVENT, and one-dimensional models in a collision probability (CP) code. Quantities of interest, such as reactivity, scalar neutron flux, neutron absorption and production rates, and kinetics data are presented. System reactivity, mean neutron generation time and neutron absorption and production rates are shown to increase with increasing emulsion thickness, whereas the total scalar neutron flux is shown to decrease. It is determined that the volume of organic phase present during the transient was likely to be around 39.0 L, as the emulsion thickness required to reach criticality (6.5 cm) was within the range cited in the literature. EVENT and the CP code showed deficiencies when calculating the scalar neutron flux through the plenum gas at the top of the transfer vessel, with the CP code overestimating the total scalar neutron flux in the system by as much as 19 %. The intrinsic neutron source, subcritical multiplication and subcritical power of the system were computed using Monte Carlo simulations. It was shown, by use of the Hansen criteria, that the subcritical system was likely to be in a strong neutron source regime (such that stochastic variations in neutron population are negligible when regarding nuclear criticality transients). In addition, it was computed that a vessel containing 39.0 L of organic solvent had a subcritical power of 10.81 ±0.03μW.