MCNP Calculations Research Articles

Representative neutronic characteristics calculations for the VVER-1000 reactors using SRAC and MCNP5

This paper presents the results of neutronic calculations using the deterministic and Monte-Carlo methods (the SRAC and MCNP5codes) for the VVER MOX Core Computational Benchmark Specification and the VVER-1000/V392 reactor core. The power distribution and keff value have been calculated for a benchmark problem of VVER core. The results show a good agreement between the SRAC and MCNP5 calculations. Then, neutronic characteristics of VVER-1000/V392 such as power distribution, infinite multiplication factor (k-inf) of the fuel assemblies, effective multiplication factor keff, peaking factor and Doppler coefficient were calculated using the two codes.

Coulped neutronics/thermal-hydraulics calculation of VVER-1000 fuel assembly

This paper presents a computational scheme using MCNP5 and COBRA-EN for coupling neutronics/thermal hydraulics calculation of a VVER-1000 fuel assembly. A master program was written using the PERL script language to build the corresponding inputs for the MCNP5 and COBRA-EN calculations and to manage the coupling scheme. The hexagonal coolant channels have been used in the thermal hydraulics model using CORBRA-EN to simplify the coupling scheme. The results of two successive iterations were compared with an assigned convergence criterion and the loop calculation can be broken when the convergence criterion is satisfied. Numerical calculation has been performed based on a UO2fuel assembly of the VVER-1000 reactor.

Modelling of the spatial distribution of the induced activities in the RBMK-1500 reactor graphite blocks and rings/sleeves

There is one nuclear power plant (NPP) in Lithuania – the Ignalina NPP – which is under decommissioning now. The Ignalina NPP has two units with RBMK-1500 reactors, which are the most powerful and the most advanced versions of RBMK-type reactor design. Unit 1 of the Ignalina NPP was shut down at the end of 2004 and Unit 2 was shut down at the end of 2009. RBMK is a water-cooled graphite-moderated channel-type power reactor and the decommissioning of these reactors faces specific challenges for proper characterisation and disposal of irradiated reactor graphite.Apart from radiological inventory, the spatial distribution of radionuclides in the reactor graphite is also very important because it could indicate the possibilities for decontamination/treatment of the irradiated graphite. This is important for consideration of the near surface disposal option for irradiated graphite, as without treatment it usually does not meet the waste acceptance criteria.Based on that, the work presented in this paper is focused on the modelling of the induced activity spatial distribution in the Ignalina NPP RBMK-1500 reactor graphite components: blocks and rings/sleeves. The modelling was performed with MCNP and SCALE computer codes and consisted of two mains stages: modelling of the neutron flux in the reactor graphite components, and then modelling of the neutron activation in them using the already modelled neutron flux. In such a way, the spatial induced activity distribution in the analysed reactor components was obtained. Modelling results show that the thermal neutron flux is more intensive in the outer radial regions of the graphite components and this, in general, results in higher induced activities there.

Reliability of Monte Carlo simulations in modeling neutron yields from a shielded fission source

Using the combination of a neutron-sensitive 6Li glass scintillator detector with a neutron-insensitive 7Li glass scintillator detector, we are able to make an accurate measurement of the capture rate of fission neutrons on 6Li. We used this detector with a 252Cf neutron source to measure the effects of both non-borated polyethylene and 5% borated polyethylene shielding on detection rates over a range of shielding thicknesses. Both of these measurements were compared with MCNP calculations to determine how well the calculations reproduced the measurements. When the source is highly shielded, the number of interactions experienced by each neutron prior to arriving at the detector is large, so it is important to compare Monte Carlo modeling with actual experimental measurements. MCNP reproduces the data fairly well, but it does generally underestimate detector efficiency both with and without polyethylene shielding. For non-borated polyethylene it underestimates the measured value by an average of 8%. This increases to an average of 11% for borated polyethylene.

HPGe-detector shielding optimization with MCNP for the MEDINA neutron activation cell

A gamma and neutron shielding for the HPGe-detector of the MEDINA facility is designed by means of MCNP5 simulations. The performance of the shielding is validated comparing MCNP5 calculations and experimental background reduction factors for easy-to-implement shielding configurations. A good correspondence between simulations and experiment is observed, which comfort the expected background reduction factors of about 4 to 5 predicted by simulation for the neutron and photon currents entering in the detector, respectively, in the case of a complete implementation of the neutron and gamma shielding in MEDINA.

Acceleration of calculation of nuclear heating distributions in ITER toroidal field coils using hybrid Monte Carlo/deterministic techniques

Because the superconductivity of the ITER toroidal field coils (TFC) must be protected against local overheating, detailed spatial distribution of the TFC nuclear heating is needed to assess the acceptability of the designs of the blanket, vacuum vessel (VV), and VV thermal shield. Accurate Monte Carlo calculations of the distributions of the TFC nuclear heating are challenged by the small volumes of the tally segmentations and by the thick layers of shielding provided by the blanket and VV. To speed up the MCNP calculation of the nuclear heating distribution in different segments of the coil casing, ground insulation, and winding packs of the ITER TFC, the ITER Organization (IO) used the MCNP weight window generator (WWG). The maximum relative uncertainty of the tallies in this calculation was 82.7%. In this work, this MCNP calculation was repeated using variance reduction parameters generated by the Oak Ridge National Laboratory AutomateD VAriaNce reducTion Generator (ADVANTG) code and both MCNP calculations were compared in terms of computational efficiency and reliability. Even though the ADVANTG MCNP calculation used less than one-sixth of the computational resources of the IO calculation, the relative uncertainties of all the tallies in the ADVANTG MCNP calculation were less than 6.1%. The nuclear heating results of the two calculations were significantly different by factors between 1.5 and 2.3 in some of the segments of the furthest winding pack turn from the plasma neutron source. Even though the nuclear heating in this turn may not affect the ITER design because it is much smaller than the nuclear heating in the turns that are closer to the plasma source, it is our recommendation to adopt the utilization of ADVANTG in similar calculations to increase the reliability of MCNP calculations of detailed distributions of nuclear responses.

Monte Carlo simulation of prompt γ-ray spectra from depleted uranium under D-T neutron irradiation and electron recoil spectra in a liquid scintillator detector

To overcome the problem of inefficient computing time and unreliable results in MCNP5 calculation, a two-step method is adopted to calculate the energy deposition of prompt γ-rays in detectors for depleted uranium spherical shells under D-T neutron irradiation. In the first step, the γ-ray spectrum for energy below 7 MeV is calculated by MCNP5 code; secondly, the electron recoil spectrum in a BC501A liquid scintillator detector is simulated based on EGSnrc Monte Carlo Code with the γ-ray spectrum from the first step as input. The comparison of calculated results with experimental ones shows that the simulations agree well with experiment in the energy region 0.4–3 MeV for the prompt γ-ray spectrum and below 4 MeVee for the electron recoil spectrum. The reliability of the two-step method in this work is validated.

A Design of Boron Neutron Capture Therapy for Cancer Treatment in Indonesia

Boron Neutron Capture Therapy (BNCT) is an advanced form of radiotherapy technique that is potentially superior to all conventional techniques for cancer treatment, as it is targeted at killing individual cancerous cells with minimal damage to surrounding healthy cells. After decades of development, BNCT has reached clinical-trial stages in several countries, mainly for treating challenging cancers such as malignant brain tumors. The Indonesian consortium of BNCT already developed of the design BNCT for many cases of type cancers using many neutron sources. The main objective of the Indonesian consortium BNCT are the development of BNCT technology package which consists of a non nuclear reactor neutron source based on cyclotron and compact neutron generator technique, advanced boron-carrying pharmaceutical, and user-friendly treatment platform with automatic operation and feedback system as well as commercialization of the BNCT though franchised network of BNCT clinics worldwide. The Indonesian consortium BNCT will offering to participate in Boron carrier pharmaceuticals development and testing, development of cyclotron and compact neutron generators and provision of neutrons from the 100 kW Kartini Research Reactor to guide and to validate compact neutron generator development. Studies were carried out to design a collimator which results in epithermal neutron beam for Boron Neutron Capture Therapy (BNCT) at the Kartini Research Reactor by means of Monte Carlo N-Particle 5 (MCNP5) codes. Reactor within 100 kW of output thermal power was used as the neutron source. The design criteria were based on the IAEA’s recommendation. All materials used were varied in size, according to the value of mean free path for each. Monte Carlo simulations indicated that by using 5 cm thick of Ni as collimator wall, 60 cm thick of Al as moderator, 15 cm thick of 60Ni as filter, 1,5 cm thick of Bi as "-ray shielding, 3 cm thick of 6Li2CO3-polyethylene as beam delimiter, with 3-5 cm varied aperture size, epithermal neutron beam with minimum flux of 7,8 x 108 n.cm-2.s-1, maximum fast neutron and "-ray components of, respectively, 1,9 x 10-13 Gy.cm2.n-1 and 1,8 x 10-13 Gy.cm2.n-1, maximum thermal neutron per epithermal neutron ratio of 0,009, and beam minimum directionality of 0,72, could be produced. The beam did not fully pass the IAEA’s criteria, since the epithermal neutron flux was still below the recommended value, 1,0 x 109 n.cm-2.s-1. Nonetheless, it was still usable with epithermal neutron flux exceeded 5 x 108 n.cm-2.s-1. When this collimator was surrounded by 8 cm thick of graphite, the characteristics of the beam became better that it passed all IAEA’s criteria with epithermal neutron flux up to 1,7 x 109 n.cm-2.s-1. it is still feasible for BNCT in vivo experiment and study of many cases cancer type i.e.; liver and lung curcinoma. In this case, thermal neutron produced by model of Collimated Thermal Column Kartini Research Nuclear Reactor, Yogyakarta. Sodium boroncaptate (BSH) was used as in this research. BSH had effected in liver for radiation quality factor as 0.8 in health tissue and 2.5 in cancer tissue. Modelling organ and source used liver organ who contain of cancer tissue and research reactor. Variation of boron concentration was 20, 25, 30, 35, 40, 45, and 47 $g/g cancer. Output of MCNP calculation were neutron scattering dose, gamma ray dose and neutron flux from reactor. Given the advantages of low density owned by lungs, hence BNCT is a solid option that can be utilized to eradicate the cell cancer in lungs. Modelling organ and neutron source for lung carcinoma was used Compact Neutron Generator (CNG) by deuterium-tritium which was used is boronophenylalanine (BPA). The concentration of boron-10 compound was varied in the study; i.e. the variations were 20; 25; 30; 35; 40 and 45 μg.g-1 cancer tissues. Ideally, the primary dose which is solemnly expected to contribute in the therapy is alpha dose, but the secondary dose; i.e. neutron scattering dose, proton dose and gamma dose that are caused due to the interaction of thermal neutron with the spectra of tissue can not be simply omitted. Thus, the desired output of MCNPX; i.e. tally, were thermal and epithermal neutron flux, neutron and photon dose. The liver study variation of boron concentration result dose rate to every variation were0,042; 0,050; 0,058; 0,067; 0,074; 0,082; 0,085 Gy/sec. Irradiation time who need to every concentration were 1194,687 sec (19 min 54 sec);999,645 sec (16 min 39 sec); 858,746 sec (14 min 19 sec); 743,810 sec (12 min 24 sec); 675,156 sec (11 min 15 sec); 608,480 sec (10 min 8 sec); 585,807sec (9 min 45 sec). The lung carcinoma study variations of boron-10 concentration in tissue resulted in the dose rate of each variables respectively were 0.003145, 0.003657, 0.00359, 0.00385, 0.00438 and 0.00476 Gy.sec-1 . The irradiated time needed for therapy for each variables respectively were 375.34, 357.55, 287.58, 284.95, 237.84 and 219.84 minutes.

USE OF A SIMPLE THERMALISED NEUTRON FIELD FOR QUALITY ACCEPTANCE OF WHOLE BODY TLDS.

The individual monitoring service of Public Health England (PHE) uses Harshaw™ whole-body and extremity thermoluminescent dosemeters (TLDs) with high-sensitivity lithium fluoride LiF:Mg,Cu,P, together with Harshaw 8800™ automated readers. The neutron-insensitive, (6)Li-depleted variety of TLD material is used by PHE because the service provides separate neutron and photon dosemeters. The neutron dosemeters are not sensitive to photons and vice versa Since insensitivity to neutrons is a supply requirement for TLDs, there is a need to test every new (annual) consignment for this. Because it is thermal neutrons that produce a response in (6)Li TLDs, a thermal field is needed. To this end, PHE has adopted the simple approach of sandwiching the TLDs between two ISO water-filled slab phantoms. In this arrangement, the fast neutrons from an Am-Be source are effectively thermalised. Details of the method are given, together with the results of supporting MCNP calculations and some typical results.

The235U Prompt Fission Neutron Spectrum in the BR1 Reactor at SCK•CEN

The BR1 research reactor at SCK•CEN has a spherical cavity in the graphite above the reactor core. In this cavity an accurately characterised Maxwellian thermal neutron field is present. Different converters can be loaded in the cavity in order to obtain other types of neutron (and gamma) irradiation fields. Inside the so-called MARK III converter a fast 235 U(n,f) prompt fission neutron field can be obtained. With the support of MCNP calculations, irradiations in MARK III can be directly related to the pure 235 U(n,f) prompt fission neutron spectrum. For this purpose MARK III spectrum averaged cross sections for the most relevant fluence dosimetry reactions have been determined. A calibration factor for absolute measurements has been determined applying activation dosimetry following ISO/IEC 17025 standards.

Analysis Loading Height of HTR (High Temperature Reactor) Core to Obtain Criticlity of Reactor

High temperatur reactor (HTR) attract to be studied due to it has inherent safety characteristics and capabilities to produce energy economically. Design of reactor core in this study is a blend HTR 10 in China with HTR pebble-bed. The reactor has thermal power of 10 MW with inlet and outlet helium temperatures of 250 o C and 700 o C. HTR design is a cylindrical with helium gas as a coolant and graphite as a moderator. The HTR uses pebble-bed fuel composed a large amount of particles of TRISO in graphite metrics. Kernel radius used to analyse reactor core height in this research is 225 µm with enrichment of 16% in order to achieve critical condition. Reactor criticality is also influenced by the height of active reactor core where pebble-bed fuel is distributed. Calculation of the reactor criticality at any height variations active core is done with MCNP5 modelling techniques. The modelling is done by making the geometry of reactor and pebble-bed which is distributed by using body-centred cubic lattice in the reactor core. From the MCNP5 calculation, the first criticality of HTR can be achieved on the active core height of 150.9012 cm calculated from the bottom active core with criticality value of 1.00312±0.00090. The higher active reactor core is, the more increasing the reactor criticality is. This is occured due to there are many fuel balls of pebble-bed used, so that activity of fission in reactor increases. However, reactor criticality is still in stable condition in each the rise of active core height from critical core height even though reactor reactivity increases 0.01 Δk/k. The minimum of fuel needed to achieve initial criticality (critical core height) is 11,805 pebbles and 8,906 moderators.

Analysis of Doppler coefficients for typical PWR UO2 and MTR U3Si2-Al fuels using ENDF/B-VI and VII

This study was performed to evaluate the Doppler coefficients for two types of uranium fuels and to investigate the effect of the neutron cross-section on these evaluations. A series of calculations was performed using MCNP6.1 and KENO6 codes which are three-dimensional neutron transport codes based on Monte Carlo method. The typical PWR UO2 lattice and the Material Testing Reactor (MTR) U3Si2-Al lattice were considered as fuel models of this study. The latest cross-sections (ENDF/B-VI and VII) at the desired temperatures were also generated from the makxsf code, and applied to the MCNP calculations. As a result, there were some differences (about 300–400pcm) among the neutron multiplication factors (keff) at each enrichment because of the codes and nuclear data used in these evaluations. Although the Doppler coefficient was changed to be less negative with increasing uranium enrichment regardless of types of nuclear fuel, their behaviors were significantly different between those. The Doppler coefficient for UO2 fuel followed an asymptotic curve, while the coefficient for the other followed an exponential curve which more significantly became less negative with increasing uranium enrichment. Also, the Doppler coefficient for UO2 fuel was about 2 times more negative than those for U3Si2-Al fuel. It was estimated that additional study was required for investigating the cause of occurrence because there was a difference more than two standard deviation (2σ) between the Doppler coefficients derived from different cross-sections at some enrichments.

A neutron pinhole camera for PF-24 source: Conceptual design and optimization

A fast-neutron pinhole camera based on small-area (5mm × 5 mm) BCF-12 scintillation detectors with nanosecond time resolution has been designed. The pinhole camera is dedicated to the investigation of the spatial and temporal distributions of DD neutrons from the Plasma Focus (PF-24) source. The geometrical parameters of the camera have been optimized in terms of maximum neutron flux at the imaging plane by means of MCNP calculations. The detection system consists of four closely packed scintillation detectors coupled via long optical fibres to Hamamatsu H3164-10 photomultiplier tubes. The pinhole consists of specially designed 420 mm long copper collimator with an effective aperture of 1.7 mm mounted inside a cylindrical polyethylene tube. The performance of the presented detection system in the mixed (hard X-ray and neutron) radiation field of the PF-24 plasma focus device has been tested. The results of the tests showed that the small-area BCF-12 scintillation detectors can be successfully applied as the detection system of the neutron pinhole camera for the PF-24 device.

Analysis of safety parameters for the MINERVE reactor

Abstract The present study aims to show the effect of different cross section libraries on MINERVE reactor safety parameters. The MCNP5 calculation model of the MINERVE reactor facility is used to determine core and safety parameters such as axial and radial fission rate distributions, control rod worth and spectral indices. Different neutron spectra were achieved by changing the experimental lattice within the MINERVE reactor. MINERVE provides a large experimental basis for the improvement of the cross section databases. The current study calculates these parameters by MCNP5 code using three different cross section libraries (the continuous energy cross sections of the ENDFB-VI, T16-2003, and ENDF/B-VII.1 libraries). Neutronic calculations were performed for R1UO2, R1MOX, R2UO2, and R2MOX core configurations, representative of a LWR loaded with UO2, mixed oxide matrix, over moderated UO2 and over moderated MOX, respectively. The study aims to determine the most suitable cross section library to be used with MCNP5 reactor calculation code for light water reactor fuel lattice. The MCNP5 results were compared with the experimental results.

Comparative assessment of different approaches for the use of CAD geometry in Monte Carlo transport calculations

Computer aided design (CAD) is an important industrial way to produce high quality designs. Therefore, CAD geometries are in general used for engineering and the design of complex facilities like the ITER tokamak. Although Monte Carlo codes like MCNP are well suited to handle the complex 3D geometry of ITER for transport calculations, they rely on their own geometry description and are in general not able to directly use the CAD geometry. In this paper, three different approaches for the use of CAD geometries with MCNP calculations are investigated and assessed with regard to calculation performance and user-friendliness. The first method is the conversion of the CAD geometry into MCNP geometry employing the conversion software McCad developed by KIT. The second approach utilizes the MCNP6 mesh geometry feature for the particle tracking and relies on the conversion of the CAD geometry into a mesh model. The third method employs DAGMC, developed by the University of Wisconsin-Madison, for the direct particle tracking on the CAD geometry using a patched version of MCNP. The obtained results show that each method has its advantages depending on the complexity and size of the model, the calculation problem considered, and the expertise of the user.

Validation of neutron flux redistribution factors in JSI TRIGA reactor due to control rod movements

For efficient utilization of research reactors, such as TRIGA Mark II reactor in Ljubljana, it is important to know neutron flux distribution in the reactor as accurately as possible. The focus of this study is on the neutron flux redistributions due to control rod movements. For analyzing neutron flux redistributions, Monte Carlo calculations of fission rate distributions with the JSI TRIGA reactor model at different control rod configurations have been performed. Sensitivity of the detector response due to control rod movement have been studied. Optimal radial and axial positions of the detector have been determined. Measurements of the axial neutron flux distribution using the CEA manufactured fission chambers have been performed. The experiments at different control rod positions were conducted and compared with the MCNP calculations for a fixed detector axial position. In the future, simultaneous on-line measurements with multiple fission chambers will be performed inside the reactor core for a more accurate on-line power monitoring system.

TH‐AB‐BRA‐02: Generation of 3D Dosimetric Reference Datasets for Commissioning and Validation of 192Ir Brachytherapy Model‐Based Dose Calculation Software

Purpose:Previously, generic HDR 192Ir source and shielded applicator were designed by WG‐ MBDCA, the AAPM‐ESTRO‐ABG Working Group on model‐based dose calculation algorithms. TPS vendors have incorporated both into their TPS. A charge of WG‐MBDCA is to develop a limited number of well‐defined test cases and perform MBDCA dose calculations and comparisons. Here, we describe the test cases proposed, the 3D dosimetric data generation process and the 3D gamma analysis performed.Methods:A voxelized phantom of 512×512×512 voxels (HU=‐1024,Air), with each voxel being 1×1×1 mm3, containing a concentric cubic contour structure (HU=0,Water) of dimension 201×201×201 voxels, was created in the DICOM‐ RT format. Three configurations were tested: i) source located at the center with surrounding structure assigned to water to mimic TG‐43 conditions, ii) source displaced +7 cm along the × axis, iii) source located at the center with the shielded applicator in place. Advanced Collapsed‐cone Engine (ACE, Elekta) and AcurosBV (Varian) were benchmarked. Reference datasets were independently produced by different groups using BrachyDose (1010 photons), GEANT4(4×1010), Penelope (2×1010), MCNP5(2 x1010), MCNP6(1011), and ALGEBRA(4×1010) Monte Carlo (MC) dose calculation platforms.Results:For the three configurations, MC agreed within 1% for the volume bounded by the 1% isodose surface; MCNP6 data sets were designated as reference (statistical error < 0.2% across the phantom). A 2%/1mm 3D γ‐ index criteria was used, within the volume bounded by 5% isodose surface, to account for both dose difference and source placement errors in TPS. Voxel pass rates were 95.2%, 99.5% and 90% for ACE and 98%, 98.4% and 95.9% for AcurosBV, respectively.Conclusion:The evaluated test cases are suitable for MBDCA QA. DICOM‐RT files are being integrated into the joint AAPM/IROC Houston registry to support end‐user TPS software commissioning.

MCNP calculations of neutron emission anisotropy caused by the GIT-12 hardware

Abstract The MCNP6 and MCNPX calculations for the GIT-12 device in Tomsk were performed to determine the influence of the gas-puff hardware on the neutron emission anisotropy and the neutron scattering rate. A monoenergetic 2.45 MeV neutron source and F1 and F6 tallies were declared in the simulation input. A comparison between MCNP results and the measured data was made. Differences between MCNPX and MCNP6 output data were investigated. In the experiment, two nTOF scintillation detectors with the Bicron BC-408 scintillator were used to measure the neutron waveform. Four bubble BD-PND detectors were used to estimate the amount of neutrons in different places around the neutron source.

VVER-1000 cross-section library generation for ORIGEN-II based on MCNP calculations

Most nuclear burnup, depletion and radioactive decay computational codes, such as ORIGEN-II, are geometry independent and so called point codes. Consequently, the effect of reactor geometry and other reactor conditions are compiled in their own cross-section library. For several types of reactor such as PWR or BWR, the cross-section libraries are provided for ORIGEN-II code, but for Bushehr nuclear reactor which is a VVER-1000 type reactor, such cross-section library does not exist in the code. In this study, attempts have been made to generate a cross-section library for VVER-1000 type reactor. In this study, attempts have been made to generate a cross-section library for VVER-1000 type reactor. In order to model the Bushehr Nuclear reactor (BNPP) core and generate a cross-section library suitable for ORIGEN-II calculations, MCNP Monte-Carlo code was used. The validation tests were carried out by comparing the burnup results of the new library with the burnup results obtained from MCNP calculations and burnup, depletion and radioactive decay reported in BNPP reference data.

Validation of the MCNP computational model for neutron flux distribution with the neutron activation analysis measurement

The objective of this work is to demonstrate the method for validating the predication of the calculation methods for neutron flux distribution in the irradiation tubes of TRIGA research reactor (TRR-1/M1) using the MCNP computer code model. The reaction rate using in the experiment includes 27Al(n, α)24Na and 197Au(n, γ)198Au reactions. Aluminium (99.9 wt%) and gold (0.1 wt%) foils and the gold foils covered with cadmium were irradiated in 9 locations in the core referred to as CT, C8, C12, F3, F12, F22, F29, G5, and G33. The experimental results were compared to the calculations performed using MCNP which consisted of the detailed geometrical model of the reactor core. The results from the experimental and calculated normalized reaction rates in the reactor core are in good agreement for both reactions showing that the material and geometrical properties of the reactor core are modelled very well. The results indicated that the difference between the experimental measurements and the calculation of the reactor core using the MCNP geometrical model was below 10%. In conclusion the MCNP computational model which was used to calculate the neutron flux and reaction rate distribution in the reactor core can be used for others reactor core parameters including neutron spectra calculation, dose rate calculation, power peaking factors calculation and optimization of research reactor utilization in the future with the confidence in the accuracy and reliability of the calculation.