Neutron Flux Calculations Research Articles

The Effect of Adding Minor Actinide Fuel Rods on GFR Reactor in Radiopharmaceutical Waste Production Using OpenMC Program

GFR is a generation IV reactor based on helium gas refrigeration capable of working at very high temperatures. The fast spectrum in this reactor makes it possible to use nitride-based fuel, namely Uranium Plutonium Nitride (UN-PuN). Adding minor actinide (MA) material to the primary fuel, UN-PuN can maximize reactor performance to near critical from the beginning to the end of burn-up. This study aims to analyze the effect of adding MA fuel rods to the heterogeneous core of 5 fuel variations (F1, F2, F3, F4, F5) on the probability of radiopharmaceutical waste production. The method in this research is to place MA fuel rods in this study using four designs based on the highest neutron flux value in one fuel assembly. The results of the neutron flux calculation show that the reactor’s active core’s central region (F1, F2, F3) needs to be added to MA fuel rods so that the resulting flux is more evenly distributed. The calculation of reactor criticality shows that Np fuel rod design 4 and Am fuel rod design 1 have the best keff value (keff ≈ 1) among other designs. The burn-up of MA fuel rods produces a minimal probability of producing Tc99m, Sr89, Y90, Rh105, Ag111, I231, and Sm15 radiopharmaceutical waste, even less than 1 kg.

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.

A Novel Adjoint-Based Reduced-Order Model for Depletion Calculations in Nuclear Reactor Physics

The licensing of new reactors implies the use of verified and validated neutronic codes. Numerical validation can rely on sensitivity and uncertainty studies, but they require repeated execution of time-consuming neutron flux and depletion calculations. The computational costs can be reduced by using perturbation theories. However, the uncoupled Depletion Perturbation Theory is restricted to single integral values such as nuclide density. Relying on reduced-basis approaches, which reconstruct all nuclide densities at once, is one way to get around this restriction. Furthermore, the adjoint-based reduced-order model uses the direct and adjoint equations for projection. For diffusion or transport calculations, the Exact-to-Precision Generalized Perturbation Theory was developed. Still, no models for depletion calculations are readily available. Therefore, this paper describes a novel adjoint-based reduced-order model for the Bateman Equation. It uses a range-finding algorithm to create the basis and the uncoupled Depletion Perturbation Theory for the reconstruction of the first order replaced by with a first order formulation. Our paper shows that for several perturbed cases, the depletion reduced-order model successfully reconstructs the nuclide densities. As a result, this serves as a proof of concept for our adjoint-based reduced-order model, which can perform sensitivity and uncertainty burn-up analysis in a shorter time.

Verification of shielding calculation capability of cosRMC with SINBAD fusion benchmarks

In the design of fusion reactors, extensive shielding calculations are necessary to verify the feasibility and safety of the design. The issue of deep penetration is a common and significant problem in fusion reactor shielding calculations. When the thickness of the shielding layer exceeds a certain value, the statistical error in Monte Carlo method calculations significantly increases. Therefore, it is imperative to adopt variance reduction techniques to enhance the computational accuracy for deep penetration problems. cosRMC is a reactor Monte Carlo code, and its accuracy in calculating neutron-deep-penetration shielding problems should be verified. For this purpose, three deep penetration benchmarks from Shielding Integral Benchmark Archive Database (SINBAD) were simulated by cosRMC and neutron cross section data library ENDF/B-VII.0. These benchmarks describe the penetration behaviors of neutrons in models with different geometric shapes and materials. This paper shows detailed cosRMC models based on benchmark experimental models, used to calculate neutron flux spectra at different penetration depths, which are recorded by detectors in the related benchmark experiments. In this way, a direct comparison between cosRMC results and experimental measurements is provided. In order to improve the accuracy of cosRMC in calculating deep penetration problems, the variance reduction technique of cell importance was used. The neutron flux spectrum calculated by cosRMC was compared with the neutron flux spectrum results calculated by MCNP5 and the experimental values of the benchmarks. The comparison results show that the calculations of cosRMC are in compliance with the MCNP5 reference values and experimental values, and the relative deviations between calculations of cosRMC and MCNP5 is within three time of standard errors. Therefore, this paper has verified that cosRMC can applies to neutron deep penetration problems of fusion reactors.

Development of a Neutron Imaging Facility at the Very Low Power Reactor VR-1

The paper describes the design and construction of a new neutron imaging facility at the very low-power research reactor VR-1. Neutron imaging has been under development at the VR-1 reactor as a new possible field of utilisation since 2020. The paper describes the main parts of the NIFFLER – “Neutron Imaging Facility for Learning and Research”. The detector system was designed in collaboration with the Technical University of Munich. The radial beam line modifications include different collimation ratios L/D, additional moderator configurations and the basic concept and design of the instrumentation. The paper also includes calculations of thermal neutron flux at the detector position for different radial beamline configurations. The results achieved at the training reactor VR-1 showed the potential of using neutron imaging at other low and very-low-power research reactors worldwide.

γ-photons and high-energy electrons produced by neutron irradiation in nuclear materials

Neutrons interacting with atomic nuclei in most of the materials included in the current fusion reactor designs—notably tungsten, ferritic and stainless steels, copper alloys—generate a γ-photon flux that is comparable in magnitude and energy with that of the neutrons, and which in turn generates an intense flux of high-energy electrons in the materials themselves. The occurrence of these γ- and electron fluxes has implications, among others, for the mobility of crystal defects in the materials, for the stability of the plasma, and for the internal heating of reactor components. While a highly spatially resolved numerical calculation of neutron, photon, and electron fluxes on the reactor scale is computationally unfeasible, it is possible to provide estimates based on solutions of Boltzmann's transport equation in a stationary and homogeneous material. Within their limits of validity, these estimates are robust and straightforward and they enable studying photon and electron generation in various materials, under different fission and fusion irradiation conditions and at various locations inside a reactor. We show that the irradiation environment provided by the IFMIF irradiation facility is similar to the expected fusion power plant conditions both in terms of the energy and intensity of photons and electrons generated by the neutrons in tungsten and steels.

A structural model of the long-term degradation of the concrete biological shield

The concrete biological shield (CBS) of light water reactors is exposed to high neutron radiation dose in the long term, which may lead to the degradation of the concrete’s mechanical properties. Given the important shielding role of the CBS, it is necessary to investigate the irradiation effects at the structural scale and provide estimates of the damage extent from the wall’s inner surface to study potential license renewals. For this purpose, we developed a mechanical model accounting for radiation-induced expansion, creep, and damage in concrete using the Grizzly finite element code, informed by ex-core neutron flux calculations using the VERA tool. The model was applied to a 3D CBS structure represented by the CBS wall, a steel liner, reinforcement bars, and a concrete base mat and evaluated damage at 40, 60, and 80 years of operation. The VERA model predicted a maximum fluence of approximately 2×1019 n cm−2 at 80 years of operation. The results showed that damage is highest at the inner surface of the CBS wall and gradually decreases with depth. It extends beyond the rebar after 60 years and reaches a depth of approximately 12 cm at 80 years.

Calculation of the high-energy neutron flux for anticipating errors and recovery techniques in exascale supercomputer centres

The age of exascale computing has arrived and the risks associated with neutron and other atmospheric radiation are becoming more critical as the computing power increases, hence, the expected Mean Time Between Failures will be reduced because of this radiation. In this work, a new and detailed calculation of the neutron flux for energies above 50 MeV is presented. This has been done by using state-of-the-art Monte Carlo astroparticle techniques and including real atmospheric profiles at each one of the next 23 exascale supercomputing facilities. Atmospheric impact in the flux and seasonal variations were observed and characterised, and the barometric coefficient for high-energy neutrons at each site was obtained. With these coefficients, potential risks of errors associated with the increase in the flux of energetic neutrons, such as the occurrence of single event upsets or transients, and the corresponding failure-in-time rates, can be anticipated just by using the atmospheric pressure before the assignation of resources to critical tasks at each exascale facility. For more clarity, examples about how the rate of failures is affected by the cosmic rays are included, so administrators will better anticipate which more or less restrictive actions could take for overcoming errors.

Simulating self-powered neutron detector responses to infer burnup-induced power distribution perturbations in next-generation light water reactors

Understanding how 3D power distribution will be monitored throughout reactor core volumetric space in next-generation nuclear power reactors is crucial to the design, deployment, and licensing of these reactors. Although numerous techniques exist for 3D power distribution monitoring based on the response of both in situ and ex situ sensors currently implemented or proposed for use in the US reactor fleet, crucial details about these techniques are often unclear. The publicly available documentation does not include information such as how well these techniques are characterized and optimized in their implementations and the levels of uncertainty in the inferred 3D power distribution. The work described herein investigated a recently developed 3D power distribution inferencing method as applied to two next-generation reactor simulations: (1) the NuScale small modular reactor design and (2) the Westinghouse AP1000 design, both of which contain in-core strings of vanadium self-powered neutron detectors (SPNDs). This investigation considered a range of SPND string sensor densities, as well as a range of 3D power distribution axial segment sizes. SPND response simulation is informed by neutron flux calculations in representative homogenized cores. For the different sensor densities and power distribution axial segment sizes in these simulations, the average solution error, solver iterations, and run time were tracked to parameterize the sensor-core configuration.

Comprehensive stainless steel neutron transport libraries validation

Stainless steel is an important material that is relied upon to perform consistently over time in the nuclear industry. The paper focuses on the validation of different stainless steel neutron transport libraries. The validation was performed by means of samples activation in different positions and also the measurement of the fast neutron spectrum in the energy range of 1–12 MeV using a scintillation stilbene detector. Stainless steel was used in the form of a block with a hole for the neutron source. The dosimetric reactions used for validations were 58Ni(n,p)58Co, 93Nb(n,2n)92mNb, 197Au(n,2n)196Au, 63Cu(n,g)64Cu, 197Au(n,g)198Au, 115In(n,ń)115m1In, 115In(n,g)116m1In, 55Mn(n,g)56Mn, and 181Ta(n,g)182Ta. The experimental data were compared with MCNP6.2 calculations employing ENDF/B-VIII.0, ENDF/B-VII.1, JEFF-3.3, JEFF-3.2, CENDL-3.1, JENDL-5 and INDEN transport libraries. These libraries were used for the simulation of the stainless steel block. The activation foils cross sections were taken from the IRDFF-II library. An intense standard neutron 252Cf(sf) source was placed in the centre of the stainless steel block. INDEN library is the best for the calculation of neutron flux in the range of 1–12 MeV. For the activation detectors placed at the various distances inside the block, the best library depends on the reaction studied.

MCNP6 calculation of neutron flux map in the httr during normal operation

Detailed neutron flux distribution is important to understand the neutronic behavior during operation as well as to precise the core optimization and safety analysis of a reactor. In the literature, no calculations have been performed to show the detailed neutron flux map for the high temperature engineering test reactor (HTTR) because of the limitation of the old neutronic codes and the low performance of the computing system. HTTR is a prismatic type reactor, helium gas-cooled, and graphite-moderated, providing 30 MWth power and up to 950 oC outlet temperature. The present work deals with MCNP6 Monte-Carlo calculation to determine the detailed neutron flux map in the HTTR during normal operation. At first, the calculation of neutron flux at several positions in the reactor was validated by comparing the corresponding reaction rate between the calculation and measurement. After that detailed neutron flux with the small cells of 1cm×1cm×10cm was obtained for the entire reactor core using the fmesh tally of MCNP6 code.

Influence of uranium dioxide and reflector surface on neutron yields of the nuclear hybrid fusion-fission reaction using MCUNED code

The goal of the present work is to demonstrate the effects of adding uranium dioxide (UO2) to deuterium fuel in the fusion-fission hybrid reactions. The effectiveness of applying a reflector surface on the neutron yield in D-D and D-UO2 reactions has been investigated. The neutrons yielded from the fusion reactions were considered as a neutron source for fission reactions. For this purpose, MCNPX and its extension, the MCUNED code, for D-D fusion processes and UO2 fission reactions were used to calculate the neutron yield and the generated power. Using externally evaluated nuclear data libraries, MCUNED is capable of light ion transport. The D (d), (n) 3He reaction with 0.25 gm of deuterium and the fission reactions with 0.25 and 1.0 gm of UO2 were utilized. The results showed that the calculated neutron flux from the D-D fusion reaction increased by a considerable amount when applying the reflector surface. Adding 1.0 gm of UO2 to deuterium fuel enhanced neutron flux by 4.95 times on average, outside the source with the reflector surface. The calculated power increased by about 3-folds when 1.0 gm of UO2 was added. Despite the narrow cross section of the D-D reactions used in this study, it was found that utilizing the reflector surface and UO2 or depleted uranium with restrictive high masses may be able to multiply the generated neutrons and the resulting power.

Activation analysis and evaluation of the radionuclide inventories, decay heat for European DEMO divertor components

This work presents neutron flux calculation results and specific decay heat and activity for the European DEMO reactor divertor structure. Two DEMO 2017 models were used in calculations; one with a homogenised WCLL breeder blanket and the other with a homogenised HCPB breeder blanket. The neutron flux calculations were performed using MCNP6 code with JEFF 3.2 nuclear data. Activation and decay heat calculations were performed using the FISPACT-II code with TENDL – 2017 nuclear data library.

Two different methodologies for neutron flux calculation for the isotopic depletion problem in subcritical systems driven by an external neutron source in a coarse-mesh framework

The isotopic depletion calculation is typically solved by using the quasi-static approximation. In this approximation, the neutron flux is assumed as constant along the time steps in which the burn-up cycle is divided. This work proposes two different calculation methodologies to obtain the neutron flux, used in the isotopic depletion calculation in subcritical systems driven by an external neutron source, in a coarse mesh framework. The so-called depletion calculation methodology with Coarse Mesh Finite Difference (CMFD), and depletion calculation methodology with Pseudo-Harmonic Expansion (PHE). In these methodologies, the neutron flux at the beginning of each burn-up step is calculated with CMFD and the PHE methods, respectively. In order to verify the applicability of both methodologies to an ADS-type reactor, it is simulated a 45 MW small-reactor with burn-up cycle of 90 days, and an 800 MW large-reactor with burn-up cycle of 600 days. The subcriticality adjustment mechanism is based on the effective multiplication factor, solving the neutron diffusion equation with the Nodal Expansion Method (NEM). In addition, the averaged power density and the intensity of the neutron source are evaluated throughout the burn-up cycle. The results obtained by both methodologies are in good agreement with each other.

Validation of fast neutron reactors fertile blanket depletion calculations through the analysis of the DOUBLON experiment in Phenix with TRIPOLI-4® and DARWIN3-SFR

A reliable assessment of the final inventory in the fertile blanket of a Fast Neutron Reactor is an important issue for fuel cycle physics, as it impacts safety, reprocessing and design studies. The performances of fertile blankets neutronics calculations is a long standing issue, as there as specificities in these regions that are quite challenging, especially for depletion codes.The new CEA fuel depletion calculation package is DARWIN3-SFR, which incorporates the deterministic neutronics code APOLLO3® and the depletion module MENDEL. This paper details the validation of DARWIN3-SFR for fertile blanket calculations through the re-interpretation of the DOUBLON pin-irradiation in the Phenix reactor.During this irradiation, nine pins are studied through isotopic ratios, which give us information about the depletion and, indirectly, the neutron flux calculations inside the blanket. This environment is especially challenging for neutronics codes, since there is a strong variation of the neutron energy and population over a short distance. Our recent analysis of TRAPU - which is a similar experiment, but in the core center - has proven DARWIN3-SFR to be reliable for the fuel depletion calculations of fissile subassemblies; nevertheless, its performances in the fertile blankets still require validation.We observe that, once the calculated neutron flux level has been adjusted to the experiment through the 148Nd/238U ratio, DARWIN3-SFR provides results similar to the reference stochastic code TRIPOLI-4®. However, both codes have difficulties to reproduce some of the measured isotopic ratios inside the fertile blanket. Whilst DARWIN3-SFR produces identical results for most of the isotopes analysed (234U, 235U, 236U, 238Pu, 239Pu, 240Pu), variations of the neutron spectrum lead to some disparities for the production of 241Pu and 242Pu. Indeed, the low-energy flux estimation is higher with TRIPOLI-4® than with DARWIN3-SFR in the energy range where the 240Pu has a high capture cross section, which increases the calculated production of 241Pu and 242Pu.DARWIN3-SFR and its predecessor DARWIN-2 are efficient at calculating the average neutron flux level over the entire fertile blanket. However, the results of the two codes show a strong pin-to-pin dispersion, resulting in a different shape of the neutron flux inside the blanket. With DARWIN3-SFR, the estimated neutron spectrum is softer than in DARWIN-2, which impacts the 238U capture and fission reaction rates and hence the production of plutonium.

Calculations of neutron fluxes and isotope conversion rates in a thorium-fuelled MYRRHA reactor, using GEANT4 and MCNPX

Neutronics calculations have been performed of the MYRRHA ADS Reactor with a thorium-based fuel mixture, using the simulation programs MCNPX (Waters, 2002) and Geant4 (Agostinelli, 2003). Thorium is often considered for ADS systems, and this is the first evaluation of the possibilities for thorium based fuels using a reactor design which has been developed in detail. It also extends the application of the widely-used Geant4 program to the geometry of MYRRHA and to thorium. An asymptotic 232Th/233Umixture is considered, together with the standard MOX fuel and a possible 232Th/MOX starter. Neutron fluxes and spectra are calculated at several regions in the core: fuel cells, IPS cells and the two (Mo and Ac) isotope production cells. These are then used for simple calculations of the fuel evolution and of the potential for the incineration of minor actinide waste. Results from the two programs agree and support each other and show that the thorium fuel is viable, and has good evolution/breeding properties, and that minor actinide incineration, though it will not take place on a significant scale, will be demonstrable.

Development of a dose estimation code for BNCT with GPU accelerated Monte Carlo and collapsed cone Convolution method

A new method of dose calculation algorithm, called GPU-accelerated Monte Carlo and collapsed cone Convolution (GMCC) was developed to improve the calculation speed of BNCT treatment planning system. The GPU-accelerated Monte Carlo routine in GMCC is used to simulate the neutron transport over whole energy range and the Collapsed Cone Convolution method is to calculate the gamma dose. Other dose components due to alpha particles and protons, are calculated using the calculated neutron flux and reaction data. The mathematical principle and the algorithm architecture are introduced. The accuracy and performance of the GMCC were verified by comparing with the FLUKA results. A water phantom and a head CT voxel model were simulated. The neutron flux and the absorbed dose obtained by the GMCC were consistent well with the FLUKA results. In the case of head CT voxel model, the mean absolute percentage error for the neutron flux and the absorbed dose were 3.98% and 3.91%, respectively. The calculation speed of the absorbed dose by the GMCC was 56 times faster than the FLUKA code. It was verified that the GMCC could be a good candidate tool instead of the Monte Carlo method in the BNCT dose calculations.

The evaluation of TRACE/PARCS model for BWR-4 nuclear power plant by startup test transient analyses

Abstract Generally, the thermal hydraulic (TH) codes need the results of Neutron Kinetics (NK) codes providing the reactivity properties to calculate neutron flux. Then the TH codes perform the safety analyses obtaining the responses of pressure, temperature, or water level. Two kinds of different codes calculate different physical behaviors sequentially and separately. Simultaneously computing thermal hydraulic and neutron kinetics behaviors can enhance the accuracy of the analysis. Hence, it is crucial to develop the TH-NK coupled model. This study presents the capability of the TH-NK coupled model, developed by TRACE (TRAC/RELAP Advanced Computational Engine) and PARCS (Purdue Advanced Reactor Core Simulator), for the BWR-4 nuclear power plant. The establishment of the TRACE/PARCS model presented the nodal and component modeling methodologies. This model was used to simulate two startup tests of high power level system transients. Principal system responses, calculated by the TRACE/PARCS model, were compared with the measured data in startup tests and the results of the point kinetic calculation of the TRACE (TRACE/PK) to evaluate the model. The evaluation shows that the TRACE/PARCS model can simulate the interaction between thermal hydraulic and neutron kinetics phenomena and predict the transients suitably. Through the comparison, the TRACE/PARCS model can be confident doing the analyses of normal and abnormal operational transients to predict the transient responses.

Investigating the neutronic, thermal-hydraulic, and solid mechanics analysis for AP-1000 nuclear reactor

ABSTRACT This study investigates the neutronic, thermal-hydraulic, and solid mechanics analyses for one of the central fuel assemblies with 2.35% U235 enrichment in the AP-1000 Reactor. MCNPX 2.7 computer code, which depends on a Monte Carlo algorithm, was applied to perform the neutronic calculations. Both COMSOL-Multiphysics, based on the numerical solution for the centered rod sub-channel model, and MATLAB, based on the analytical solution for the same model, were applied to perform the thermal-hydraulic analysis. COMSOL-Multiphysics was used to perform the solid mechanics analysis. The neutronic, thermal hydraulics, and solid mechanics analyses play an essential role in the control, design, and safety of nuclear reactors. The calculations of criticality, reactivity, fuel burn-up, neutron flux, and power mapping were performed.‎ From the power mapping, the hot channel was determined and its maximum PPF. Upon getting the maximum PPF, which occurred in channel number 30 and equals 1.357, the thermal-hydraulic calculations using both COMSOL-Multiphysics and MATLAB were applied to determine the temperature distribution of the fuel, clad, and coolant. The departure from nucleate boiling ratio (DNBR) distribution was calculated to determine the minimum departure from ‎nucleate boiling ratio (MDNBR). The MDNBR results were 2.154 based on the analytical approach and 2.20 based on ‎the numerical approach. These values are higher than the limiting value of 1.75, which assure that no nucleate boiling ‎problems will occur. The solid mechanics calculations were investigated by coupling three kinds of physics using COMSOL-Multiphysics (the heat transfer in solid physics to perform the thermal load, turbulence flow RANS K-OMEGA to perform the pressure load, and solid mechanics physics). This coupling was used to determine the von-Mises stress, volumetric strain, and the total displacement for both the fuel and the clad material. The total fuel outer surface displacement was calculated to assure that no surface contact would happen between the ‎fuel and clad material to avoid chemical interactions between them. The displacement was calculated to be 0.007 mm, which is less than the He-gap ‎thickness, 0.008 mm. The coupling between different physics is one of the most well-developed techniques used for simulating the exact situation inside nuclear reactors. This coupling was done using the computational fluid dynamics (CFD) approach. All the calculations for the benchmark problem (a single fuel Assembly (G-9), near Beginning of Life, hot Full Power, equilibrium Xenon, and unrodded Core) were conducted. The obtained results were within the safety limits outlined in the design control document (DCD). Eventually, the results were in line with earlier efforts that utilized different codes for simulating neutronic analysis.

Neutron flux evaluation model provided in the accelerator-based boron neutron capture therapy system employing a solid-state lithium target

An accelerator-based boron neutron capture therapy (BNCT) system employing a solid-state Li target can achieve sufficient neutron flux for treatment although the neutron flux is reduced over the lifetime of its target. In this study, the reduction was examined in the five targets, and a model was then established to represent the neutron flux. In each target, a reduction in neutron flux was observed based on the integrated proton charge on the target, and its reduction reached 28% after the integrated proton charge of 2.52 × 106 mC was delivered to the target in the system. The calculated neutron flux acquired by the model was compared to the measured neutron flux based on an integrated proton charge, and the mean discrepancies were less than 0.1% in all the targets investigated. These discrepancies were comparable among the five targets examined. Thus, the reduction of the neutron flux can be represented by the model. Additionally, by adequately revising the model, it may be applicable to other BNCT systems employing a Li target, thus furthering research in this direction. Therefore, the established model will play an important role in the accelerator-based BNCT system with a solid-state Li target in controlling neutron delivery and understanding the neutron output characteristics.