New Efficient Albedo Monte Carlo Method for Neutron Streaming Analyses

An efficient albedo Monte Carlo method newly developed has been studied by analyzing two types of experiments on neutron streaming. The method is characterized by employing the energy-angle dependent doubly differential albedos for slab, which can be calculated in a short computer time with a one-dimensional transport theory, such as the Sn method and more efficient invariant imbedding method. This paper describes the features of the present albedo Monte Carlo method, including fundamental formulas. In the analyses of the neutron streaming experiments, the calculated results agreed with the measured data within a factor of 2 for a benchmark experiment at the YAYOI reactor and within a factor of 3 for an SNR sodium duct mock-up experiment.

It is concluded that the present albedo Monte Carlo method is practical and applicable to the reactor shielding analysis concerning radiation streaming.     

Mechanical System Surveillance Test Interval Optimization

Abstract

In general, functional tests are required periodically to detect failures in standby equipment as a means of assuring their availability on demand. However, these functional tests may have an adverse impact on the system availability, because of their potential negative effects such as unavailability at the period of testing, increase of failure rate resulting from excessive wear due to testing. Therefore, in principle, there is an optimal test interval for each standby system. As it normally is difficult to determine analytically the optimal test interval for the real systems in the industry, we therefore introduce the Monte Carlo simulation method for this purpose. In this paper, a one-component system was chosen firstly to introduce the concept of test interval optimization as well as the feasibility of using Monte Carlo simulation. Secondly, a real system in the nuclear power plant. Standby-liquid-control system, was studied using Monte Carlo simulation technique. The promising results obtained confirm the concept and methodology used.     

Development of an effective dose calculation method for the downstairs room of a linac facility

ABSTRACT

An effective dose calculation method is important in the design of efficient shields in radiation facilities. Some analytical methods have been shown to provide a simple and quick design analysis; however, no suitable method exists that can be applied to a room located directly under an X-ray irradiation room. We propose a new analytical method that uses the multiple reflection ratio predetermined by a Monte Carlo simulation and the differential dose albedo given by the Chilton–Huddleston semi-empirical equation. Our method is verified by comparison with the Monte Carlo simulation, performed for the case of an electron linac facility with an accelerated energy of 10 MeV, where the shielding floor has a thickness of 1.6–2.0 m and the downstairs room has a height of 0.5–1.5 m. The difference between the effective X-ray doses in the downstairs room calculated via the proposed analytical method and the Monte Carlo simulation is less than 25% when the horizontal distance from the X-ray beam to the evaluation point exceeds 3 m and the evaluation point is set at half of the height of the room. The new analytical method can be efficiently and accurately applied to the calculation of the effective dose.     

Monte Carlo uncertainty quantification of the effective delayed neutron fraction

The applicability of Monte Carlo techniques, namely the Monte Carlo sensitivity method and the random-sampling method, for uncertainty quantification of the effective delayed neutron fraction β_eff is investigated using the continuous-energy Monte Carlo transport code, MCNP, from the perspective of statistical convergence issues. This study focuses on the nuclear data as one of the major sources of β_eff uncertainty. For validation of the calculated β_eff, a critical configuration of the VENUS-F zero-power reactor was used. It is demonstrated that Chiba's modified k-ratio method is superior to Bretscher's prompt k-ratio method in terms of reducing the statistical uncertainty in calculating not only β_eff but also its sensitivities and the uncertainty due to nuclear data. From this result and a comparison of uncertainties obtained by the Monte Carlo sensitivity method and the random-sampling method, it is shown that the Monte Carlo sensitivity method using Chiba's modified k-ratio method is the most practical for uncertainty quantification of β_eff. Finally, total β_eff uncertainty due to nuclear data for the VENUS-F critical configuration is determined to be approximately 2.7% with JENDL-4.0u, which is dominated by the delayed neutron yield of ²³⁵U.     

Applicability of non-analog Monte Carlo technique to reactor noise simulation

Reactor noise simulations have been performed with the analog Monte Carlo technique in the past. The applicability of the non-analog Monte Carlo technique, which uses “weighing” for the purpose of variance reduction, to reactor noise simulations has been discussed. The joint probability of a pair of counts and Feynman variance-to-mean ratio in the non-analog Monte Carlo technique are formulated for one-speed neutron random walk in an infinite homogeneous medium. Unlike the analog Monte Carlo technique, the fission-related correlation exists even for the number of fission neutrons ν = 1 because the neutron causing a fission survives and will contribute to subsequent detections. As a results, the joint probability and the variance-to-mean ratio has the same function of time as the analog Monte Carlo technique. The probability of an uncorrelated pair of counts for a coincidence detection within one detector is different from the analog Monte Carlo technique, which introduces an extra unknown parameter in Feynman-α method. In the two-detector system, the extra parameter does not arise and the conventional Feynman-α formula can be applied to non-analog Monte Carlo simulations. The formulations derived in this work are verified by the fact that the theoretical values agree well with the numerical results.     

Neutron Self-Shielding Factor of Scattering-Predominant Resonance Foils

The neutron self-shielding factor of ⁵⁹Co resonance foil as an example of foils whose scattering cross section predominate over their absorption cross sections was obtained by both Monte Carlo method (analog) and the collision probability method for various thicknesses of the foil. Also, the transmission and reflection probabilities of neutrons which have various energies near the resonance energy were obtained, and the effects of multiple scattering of neutrons on the neutron self-shielding factor are discussed.

The neutron self-shielding factors obtained by the Monte Carlo method and by the collision probability method agreed well with each other in the cases Σ t ～ 4.0, in which the Monte Carlo method requires considerably longer machine time. Although for the cases of large Σ t (～4.0) the agreement is not always good because of the flat flux approximation in the collision probability method, the calculation time by Monte Carlo is conveniently short. A combination of both methods is useful in obtaining the neutron self-shielding factor of resonance foils.     

Monte Carlo calculation of the effective neutron generation time

The Monte Carlo calculation of the effective (i.e. adjoint weighted) neutron generation time Λ_eff, especially for continuous energy simulations, is not straightforward nor standard in Monte Carlo codes. The use of the non-adjoint weighted neutron generation time Λ (standard in most Monte Carlo codes) as an approximation of the effective one can lead to a serious bias. We show here that the difference between Λ_eff and Λ can be more than 200% for a thermal fission system (VENUS reactor, SCK·CEN, Belgium) and more than 600% for a fast fission system (MASURCA reactor, Cadarache, France). For this, we have implemented, for the first time, in the Monte Carlo code MCNP(X), an asymptotically exact method for the calculation of Λ_eff. Our method was benchmarked against measurements in MASURCA: the difference between calculated and experimental values is less than 10%.     

Acceleration of source convergence in Monte Carlo k-eigenvalue problems via anchoring with a p-CMFD deterministic method

The Monte Carlo method is widely used in neutron transport calculations, especially in complex geometry and continuous-energy problems. However, an extended application of the Monte Carlo method to large realistic eigenvalue problems remains a challenge due to its slow convergence and large fluctuations in the fission source distribution. In this paper, a deterministic partial current-based Coarse-Mesh Finite Difference (p-CMFD) method is proposed that achieves fast convergence in fission source distribution in Monte Carlo k-eigenvalue problems. In this method, the high-order Monte Carlo method provides homogenized and condensed cross section parameters while the low-order deterministic p-CMFD method provides anchoring of the fission source distribution. The proposed method is implemented in the MCNP5 code (version 1.30) and tested on realistic one- and two-dimensional heterogeneous continuous-energy large core problems, with encouraging results.     

Study of equivalent efficiency calibration method for radioactive gas source measured on HPGe detectors

ABSTRACT

In view of the complexity of current detection efficiency calibration of radioactive gas sources, a method using solid planar sources to be equivalent to gas sources was studied. For the 50 mL gas source box, an optimal equivalent scheme was selected by Monte Carlo Simulations. Then, the full-energy-peak efficiency curve of gas sources at the measurement position of 25 cm, with source-to-detector distance of 25 cm, was fitted by measuring solid planar sources with known activity. To verify the accuracy of the efficiency curve, ⁴¹Ar, ¹³³Xe and ⁸⁷Kr gases were produced and determined by length-compensated method. Then, their full-energy-peak efficiencies at 25 cm position away from the detector were directly calibrated. The percentage efficiency deviations between interpolation from the efficiency curve and direct calibration are all less than 2.5%, which proves the accuracy of the equivalent method. This calibration method is a general one and can be also used for some other radioactive sample measurements, such as non-destructive analysis of gaseous fission product samples with a suitable source-to-detector distance.     

New Sampling Method in Continuous Energy Monte Carlo Calculation for Pebble Bed Reactors

A pebble bed reactor generally has double heterogeneity consisting of two kinds of spherical fuel element. In the core, there exist many fuel balls piled up randomly in a high packing fraction. And each fuel ball contains a lot of small fuel particles which are also distributed randomly. In this study, to realize precise neutron transport calculation of such reactors with the continuous energy Monte Carlo method, a new sampling method has been developed. The new method has been implemented in the general purpose Monte Carlo code MCNP to develop a modified version MCNP-BALL. This method was validated by calculating inventory of spherical fuel elements arranged successively by sampling during transport calculation and also by performing criticality calculations in ordered packing models. From the results, it was confirmed that the inventory of spherical fuel elements could be reproduced using MCNP-BALL within a sufficient accuracy of 0.2%. And the comparison of criticality calculations in ordered packing models between MCNP-BALL and the reference method shows excellent agreement in neutron spectrum as well as multiplication factor.

MCNP-BALL enables us to analyze pebble bed type cores such as PROTEUS precisely with the continuous energy Monte Carlo method.     

Moment-based probability tables for angular anisotropic scattering

This paper presents a strategy for taking into account anisotropy scattering into a Monte Carlo algorithm relying on the subgroup method and developed in the DRAGON lattice code. For the sake of consistency, we limited our Monte Carlo code to the same cross-section libraries available for deterministic methods. However Legendre moments for the transfer cross-sections cannot be directly used during the Monte Carlo random walk, due to the presence of non-positive parts into the distributions. The discrete angle method is proposed to deal with this limitation, following an approach initially introduced in the MORET multigroup Monte Carlo code. We selected a moment approach, originally employed to compute probability tables for resonant cross-sections, to derive consistent sums of Dirac distributions conserving Legendre moments of the angular distributions. A detailed analysis of the applicability of the moment approach is here mandatory. When the moment technique fails due to incoherent Legendre moments, the discrete angle technique is substituted by legacy semi-analytical methods. We illustrate the proposed method using critical benchmarks coming from the ICSBEP handbook by comparison toward S_N and other Monte Carlo results. The impact of the anisotropy scattering is also discussed on a PWR MOX assembly case.     

On Effective Delayed Neutron Fraction Calculations with Iterated Fission Probability

The iterated fission probability (IFP) is a quantity proportional to the asymptotic power level originated by a neutron introduced to a reactor. The effective delayed neutron fraction β_eff can be accurately calculated by the continuous-energy Monte Carlo method using IFP if a sufficiently large number of generations is considered to obtain the asymptotic state. In order to deterministically quantify the required number of generations in the IFP-based β_eff calculations, the concept of the generation-dependent importance functions is introduced to β_eff calculations. Furthermore, the most appropriate reactor property used in the IFP calculations, which reduces the required number of generations, is theoretically derived. Through numerical calculations, it is shown that several generations are required in the IFP-based β_eff calculations and that the use of the appropriate reactor property can reduce the required number of generations. An efficient procedure for the IFP-based β_eff calculations by the Monte Carlo method is also proposed.     

Calculation of Azimuthally Dependent Thermal-Neutron Albedos for Slab by Method of Invariant Embedding

The method of invariant embedding has been applied to the calculation of differential thermal-neutron albedos for a semi-infinite ordinary concrete slab. The calculations have been performed in both cases of isotropic and anisotropic scattering in the laboratory system.

The calculated albedo data are compared with those obtained by the experiments and the semi-empirical formula fitted the detailed data obtained by Monte Carlo method. The calculated results assuming isotropic scattering are in good overall agreement with the values obtained by Monte Carlo and S_N methods, but there are some errors for azimuthally anisotropic scattering when azimuthal angle becomes large.

In this method, much less computing times within given accuracy are required for azimuthally isotropic scattering, but it is pronounced that the necessary computing times are heavily dependent on N in DP _(N/2)-1 (ξ)T_N(μ) quadrature sets when the azimuthally anisotropic scattering is considered.

It is found that, except for large N for the case of azimuthally anisotropic scattering, the calculation of differential albedo data by using invariant embedding method is much faster than those by using the Monte Carlo and the discrete ordinates methods.     

Importance Determination Method for Geometry Splitting with Russian Roulette in Monte Carlo Calculations of Thick and Complicated Core Shielding Structure

In case of a shielding analysis of the geometry having thick and complicated structures with a Monte Carlo code, it is a serious problem that it takes too much computer time to obtain results with good statistics. Therefore, it is very important to reduce variances in the calculation. In this study, a method to determine the importance function in 3-dimensional Monte Carlo calculation with geometry splitting with Russian roulette was developed for the shielding analysis of thick and complicated core shielding structures. Only two essential importance ratio curves for one material enable us to determine the importance function easily in the shielding calculation.

The validity of this method was confirmed through a simple benchmark calculation. From the comparison with the result obtained by using weight window (W-W), it was shown that the present method can give an accurate result on the same level with W-W method with less trial and errors. And this method was applied to an actual reactor core shielding analysis to confirm its applicability to a 3-dimensional thick and complicated structure.

Using this method, the variance reduced calculation can be easily realized with the developed importance determination procedure, especially in case that parameter survey calculations are required in order to determine the shield thickness in a design work of a thick and complicated structure. Accordingly, it became easier to use Monte Carlo method as a powerful tool for a reactor core shielding design.     

Crystalline Phase in Surface Layers of Glass Waste Form

An integral test of γ-ray production data of iron in the latest version of Japanese Evaluated Nuclear Data Library (JENDL-3.2) has been performed by means of a shielding benchmark analysis of KfK leakage neutron and γ-ray spectrum measurements from iron spheres with a ²⁵²Cf source in the center. Two comprehensive systems which consist of a continuous-energy Monte Carlo method and a multi-group Sn transport method have been adopted in this benchmark analysis. For comparison, analyses with JENDL-3.1, FENDL-1 and ENDF/B-IV have been also carried out. The calculation using JENDL-3.2 showed a good agreement with the experiment. It has been concluded that the γ-ray production data of iron in JENDL-3.2 were applicable for use of shielding designs and analyses of the fission neutron source problem.     

Effect of Lithium on Pressure of Hydrogen in Liquid Sodium

Abstract

Neutron spectra in a cylindrical straight duct and in bent ducts with angles of 30°, 60° and 90° have been measured by the multiple foil activation and thermoluminescence dosimetry methods. Two-dimensional discrete ordinates and three-dimensional Monte Carlo calculations are executed, and the results are compared with the measurements. The flow rate at the duct entrance calculated by the DOT3.5 code is underestimated by approximately 30%, due to a conversion of the core and reflector geometry from XY to RZ geometry. The fast neutron flux in the ducts is underestimated by 20% by the MORSE-SGC/S code due to a too coarse angular mesh of the source, which does not properly represent the actual angular distribution of the fast flux, which is highly peaked forwardly into the ducts. The thermal neutron flux was overestimated by the Monte Carlo calculation. A method is proposed to calculate the angular distribution of the flow rate at the duct entrance and to calculate the source strength and the angular distribution of the flow rate at the entrance of the second leg of the duct. The results are compared with those of the transport calculations. Generally, the agreement is quite satisfactory.     

Calculation of Neutron Albedos for Slab with Invariant Imbedding Method

The albedo data are important for use in solving the radiation streaming problem with albedo techniques, such as albedo Monte Carlo and albedo-Sn methods. This paper describes a method for calculating the energy-angle dependent doubly differential albedos for slab geomery with one-dimensional transport theory, based on the invariant imbedding method as well as the Sn method. Neutron albedo data calculated by the invariant imbedding method, are compared with those calculated by the Sn method and with the experimental data. It is found that the invariant imbedding method can be used to calculate the albedo data for a semi-infinitely thick slab several dozens of times faster than when using the Sn method. The calculated results have excellent agreement with the measured values.     

Simulation Experiment about the Effects of Core Heterogeneity on the Transient Pressure Behavior in the High-Energy Excursion of Fast Reactor

Gamma-ray dose distribution was measured in an actual ship to study applicability of point kernel method popularly applied to the calculation of γ-ray dose distribution in ships which have usually compartmentalized structures. Measured distribution was used to verify applicability of Monte Carlo method to the analysis of γ-ray dose distribution in the ship. Monte Carlo method was proved to be effective for analysis of r-ray dose distribution in the ship.

Monte Carlo analysis revealed that γ-rays scattered back from steel plates constructing ship hull increase their contribution to measured dose value as the distance between the dose measuring point and γ-rays sources increases. This contribution has not been taken into account in dose distribution calculations for ships by the point kernel method with the usual buildup factor.

Present study also disclosed that feasibility of applying Monte Carlo method to the analysis of γ-rays dose distribution in ships will be enhanced remarkably by utilizing the function adopted in the subroutine RELCOL in the Monte Carlo code MORSE-CG and by applying the source direction biasing technique to save machine time and to improve statistics of the calculated results.     

Evaluation of Response of Whole-body Counter using the EGS4 Code

Responses of a whole-body counter to distribution of ingested ¹³⁷Cs within the body were evaluated using Monte Carlo simulation. The uncertainties in evaluation of ¹³⁷Cs body burdens due to counting efficiencies of the whole-body counter were estimated. It was found from calculation that counting efficiencies of the whole-body counter are largely dependent on the ¹³⁷Cs distribution within the body, and ¹³⁷Cs body burdens would be underestimated by a factor of 3 in the worst case.

To testify a calibration method for the whole-body counter using Monte Carlo simulation, counting efficiencies for simple-geometric-form models and phantoms were obtained by simulation and actual measurements. The calculations by Monte Carlo simulation are in good agreement with the measurements.     

Analysis of Transmitted Gamma-Rays by Multiple Scattering Method, (I)

Dose buildup factors and number spectra of γ-rays transmitted through a homogeneous finite slab have been estimated by the multiple scattering method, taking into account scattering — including back scattering — up to the fourth order.

The calculations were performed for 1.0, 3.0, 6.0, 8.0 and 10.0 MeV γ-rays normally incident on lead, iron and water slabs of thicknesses from 1 to 15 mfp.

The results of the above calculations are in good agreement with those from other calculations, such as by Monte Carlo and response matrix methods, especially for heavy shielding materials of practical importance and γ-rays of high incident energy.

Further, a method is proposed with which the contribution to the total dose buildup factor by the γ-rays of the fifth and higher orders of scattering can be estimated approximately. With this method, good agreement was obtained with the dose buildup factor calculated by the Monte Carlo method, even for light shielding materials and γ-rays of low incident energy.