A solution of the neutron diffusion equation in hemispherical symmetry using the homotopy perturbation method

The homotopy perturbation method is used to formulate a new analytic solution of the neutron diffusion equation both for a sphere and a hemisphere of fissile material. Different boundary conditions are investigated; including zero flux on boundary, zero flux on extrapolated boundary, and radiation boundary condition. The interaction between two hemispheres with opposite flat faces is also presented. Numerical results are provided for one-speed fast neutrons in ²³⁵U. A comparison with Bessel function based solutions demonstrates that the homotopy perturbation method can exactly reproduce the results. The computational implementation of the analytic solutions was found to improve the numeric results when compared to finite element calculations.     

Neutronics analysis of a stacked structure for a subcritical system with LEU solution driven by a D-T neutron source for 99Mo production

The utilization of neutrons markedly affects the medical isotope yield of a subcritical system driven by an external D-T neutron source.The general methods to improve the utilization of neutrons include moderating,multiplying,and reflecting neutrons,which ignores the use of neutrons that backscatter to the source direction.In this study,a stacked structure was formed by assembling the multiplier and the low-enriched uranium solution to enable the full use of neutrons that backscatter to the source direction and further improve the utilization of neutrons.A model based on SuperMC was used to evaluate the neu-tronics and safety behavior of the subcritical system,such as the neutron effective multiplication factor,neutron energy spectrum,medical isotope yield,and heat deposi-tion.Based on the calculation results,when the intensity of the neutron source was 5×1013 n/s,the optimized design with a stacked structure could increase the yield of 99Mo to 182 Ci/day,which is approximately 16％higher than that obtained with a single-layer structure.The inlet H2O coolant velocity of 1.0 m/s and initial temperature of 20℃were also found to be sufficient to prevent boiling of the fuel solution.     

Study of the neutron multiplication effect in an active neutron method

The neutron multiplication effect appears when an item contains large amounts of nuclear material. The neutron multiplication effect in this paper means the effect of subsequent fission reactions which are caused by fission neutrons produced by interrogation neutrons from a neutron generator. The previous active neutron method could not distinguish between first-fission and subsequent-fission neutrons and might overestimate the amount of nuclear material. However, the neutron multiplication effect in the active neutron method has not been adequately investigated. We discuss the evaluation method of the multiplication effect in the fast neutron direct interrogation method, one of the active neutron methods, using simulations with the Monte Carlo code MVP and experiments involving uranium waste drums. The first-generation neutrons from an external neutron source generate fission neutrons called second-generation neutrons, the second-generation neutrons generate third-generation neutrons, and so on. This study supposes that the neutron multiplication effect is mainly caused by the third-generation neutrons under the condition that the fourth-generation neutrons are much fewer. This paper proposes a correction method for the neutron multiplication effect in the measured data.     

Gas-cooled thorium reactor at various fuel loadings and its modification by a plasma source of extra neutrons

This work presents the results of computer simulation of neutronic processes in a high-temperature gas-cooled thorium reactor for 30 different options of core loading.To guarantee stable and long-term reactor operation (7-10 years),the quantity of fuel compact dispersion phase and starting fuel composition was selected.It is demonstrated that it is possible in principle to substitute the near-axial recirculation zone of the reactor core by a long magnetic trap with a high-temperature plasma column for generating thermonuclear neutrons.The distribution of neutron yield along the length of the plasma source is also presented.Such a thorium reactor,with a near-axial source of extra neutrons,can be applied for researching thermophysical and neutronic characteristics of dispersion thorium fuel to improve its properties.The results of the work are of great interest from the perspective of future advancement of the thermonuclear power industry,by means of creation of a hybrid installation based on a thorium reactor with a long plasma column as a source of additional neutrons.     

Prediction Method in Numerical Simulation of Dynamics Based on Prompt and Delayed Neutrons in Multiplying Systems

The basic elements of a method of numerical simulation of processes based on prompt and delayed neutrons in multiplying systems are presented. The method is based on predicting the contribution of the instantaneous state of the system to its state at subsequent definite times and summing the predicted contribution as a systematic transition is made to a new moment in time. The key element of the method is determining the initiation functions – the probabilities that a neutron emitted by a source in a prescribed volume of the system initiates a prompt fission neutron in a definite volume of the system sometime after emission. A procedure is proposed for determining the initiation functions; this procedure is based on the first-collision probability method and uses the standard stationary computer codes. The material presented in this paper comprises the basic results of the first stage in the development of the numerical model for full-scale simulation of the dynamics of the subcritical blanket of an experimental accelerator-driven subcritical system under construction at the Institute of Theoretical and Experimental Physics. It is noted that the model being developed can be used to analyze many important processes in other types of multiplying systems.     

Space-energy distribution of neutrons in a homogeneous moderator

The moderation of neutrons in a homogeneous medium with an arbitrary isotope composition is investigated using the method of spherical harmonics. The dependence of the mean free path of neutrons on lethargy is taken into account approximately. At short distances from the source, the distribution function does not depend on the approximation order in using the method of spherical harmonics, while it coincides with the results of the age approximation; a more accurate estimate of the limits within which the age approximation can be applied is given. At large distances, the spatial dependence of the distribution function is completely defined by the spatiat distribution of primary neutrons, while the angular distribution and the energy spectrum of moderated neutrons do not depend on the coordinates. The results obtained by calculating the spatiat distribution of indium neutrons in water for nqonoenergetic and polyenergetic sources are given.Translated from Atomnaya Énergiya, Vol. 17, No. 1, pp. 34–44, July, 1964     

Mockup tests for developing the CARR-CNS with a two-phase thermo-siphon loop

The cold neutron source (CNS) is a facility to increase cold neutrons by scattering thermal neutrons in liquid hydrogen or deuterium around 20 K. For extracting a stable cold neutron flux from the CNS, the liquid quantity in the moderator cell should be maintained stably against disturbance of nuclear heating. The China Institute of Atomic Energy (CIAE) is now constructing the China Advanced Research Reactor (CARR: 60 MW). and designing the CARR-CNS with a two-phase thermo-siphon loop consisting of a condenser, two moderator transfer tubes and an annular cylindrical moderator cell. The mock-up tests were carried out using a full-scale loop with Freon-113,for validating the self-regulating characteristics of the loop, the void fraction less than 20% in the liquid hydrogen of the moderator cell, and the requirements for establishing the condition under which the inner shell has only vapor. The density ratio of liquid to vapor and the volumetric evaporation rate due to heat load are kept the same as those innormal operation of the CARR-CNS. The results show that the loop has the self-regulating characteristics and the inner shell contains only vapor, while the outer shell liquid. The local void fraction in the liquid increases with increasing of the loop pressure.     

Superfluid Helium in a Subcritical Core

The results of a numerical simulation of a superthermal source of ultracold neutrons on superfluid helium near a subcritical core of an electronuclear system are examined. It is shown that for a limited core power and using cold filters to produce the spectrum of neutrons entering the cryostat zone with liquid helium, the heat release in helium with adequate volume can be limited to a reasonable value 1 W. Various versions of the MCNP code are used. The heat release from rays and neutrons with different energies is estimated for two positions of the cryostat relative to the vertical center of the plane of the core. It is shown that a spatial ultracold-neutron density exceeding 10³ cm^–3 can be obtained with additional conversion of cold neutrons on a solid-deuterium layer surrounding the helium vessel.     

Radiation damage in non-fissile metallic alloys

A general survey is presented of radiation-induced displacement damage in non-fissile metallic alloys. The importance of the spatial arrangement of the vacancies and interstitials so produced is highlighted, especially as a guide to formulating an appropriate gauge for the various radiation-induced phenomena considered—i.e. hardening, embrittlement, growth, creep, swelling and fracture. The present level of theoretical understanding and the technological import of these phenomena are also assessed.     

Influences of Neutron Source Spectrum and Thermal Neutron Scattering Law Data on the MCNPX Simulation of a Cyclotron-Based Neutron Field for Boron Neutron Capture Therapy

In our previous study, the simulation of a cyclotron-based neutron field for boron neutron capture therapy (BNCT) using a (p,n) spallation source with the MCNPX code was validated through measurements of the neutron energy spectrum behind the moderator assembly and the thermal neutron distribution in an acrylic phantom using reaction rates of ¹⁹⁸Au. These validations showed that the simulation generally well reproduced the measurements. However, some discrepancies between the measurements and the calculation remained for clinical trials. In this paper, we investigated the influences of neutron source spectrum and thermal neutron scattering law data in the simulation to resolve those discrepancies. We also compared measured and calculated neutron doses behind the moderator assembly with results obtained using a tissue equivalent proportional counter. We clarified that the neutron source spectrum calculated using the LA150 data led to the overestimation of high-energy neutrons in a phantom, but this overestimation did not significantly affect the neutron dose distribution in a phantom, because a dominant part of the absorbed dose is due to neutrons of energies below 1MeV. The study of the influence of neutron scattering law data in a phantom also indicated that the use of selected S(α,β) data led to an improvement in the simulation of thermal neutron behavior.     

基于武器级铀的核弹头内部炸药探测的模拟研究

在军备控制核查技术领域,核弹头内部炸药的探测是一项重要的研究。本文利用GEANT4软件研究了基于武器级铀的核弹头(即铀弹头)内部炸药的被动探测法(利用铀弹头内部裂变中子作为中子源)的可行性,计算得到了从铀弹头中出射的γ射线能谱,能谱的形状与预期相符,但由于铀弹头内部裂变中子与炸药中~(14) N反应产生的特征γ光子的事例率太低,该方法可能不适用于铀弹头的现场测量。因此又利用GEANT4软件研究了铀弹头内部炸药的主动探测法(利用铀弹头外部的中子源对铀弹头进行辐照)的可行性。研究结果表明,主动探测法可在1h内实现对铀弹头内部炸药中~(14) N的探测和确认,进而能为判定铀弹头内部是否含有炸药提供重要依据。     

A New Static and Dynamic One-Point Equation and Analytic and Numerical Calculations for a Subcritical System

In this study we derived a new one-point equation based on the balance of fission neutrons. The equation has the same form as the conventional equation using k _eff which represents the neutron balance in the whole core. The variables of the new equation are the number of fission neutrons and delayed neutron precursors, and the coefficients are the multiplication rates of prompt fission neutrons, delayed neutrons and source neutrons. In the conventional equation, the variables are weighted by the adjoint flux; in other words, they are adjusted to the critical state. The variables in the new equation correspond to actual values even in a deep subcritical state; hence, the physical meaning of each term is clear.

The dynamic behavior of a slab core with an external source was analyzed through calculations based on the new equation. Deterministic and probabilistic calculations of the equation were performed for a typical accelerator-driven system in the static state.     

柱形金属铀次临界系统瞬发中子衰减常数测量

次临界核系统的瞬发中子衰减常数α与反应性有着重要联系。采用²⁵²Cf随机脉冲源法测量了一柱形金属次临界系统的瞬发中子衰减常数。为对源中子的影响进行分析,借助蒙特卡罗模拟方法建立模型进行了模拟,对源直穿中子和核系统瞬发中子时间分布特性进行了比较,分析了源中子对瞬发中子衰减曲线的影响。模拟结果表明,对该柱形金属铀系统,源中子注入100 ns后源直穿中子对核系统瞬发中子的影响可忽略。根据分析结果选取了合理起始道,对实验数据进行单指数最小二乘拟合,得到该次临界系统的α为15.5μs^-1。     

Analysis of Cell Configuration Effects on Nuclear Characteristics in a Lead-Bismuth Cooled Core for TRU Incineration

Sensitivity of the core characteristics to the fuel pin cell parameters change is analyzed for a lead-bismuth cooled reactor to incinerate transuranic nuclides. The pitch-to-diameter ratio is changed for a parametric study to investigate the effects of the coolant-to-fuel ratio. Not only the Zr-based fuel of TRU+Zr but also the Th-based fuel of TRU+Th+Zr is considered in order to investigate the sensitivity of nuclear characteristics of the fuel pin cell to neutron energy spectrum as well as effects of the fuel type on the core performance. For the sensitivity analyses, the neutron spectrum, the criticality performance parameters, and the non-fissile actinides destruction factor are evaluated. The obtained results clarify the unique property of nuclear characteristics of the fuel pin cell and give some useful information for design optimization of a lead-bismuth cooled reactor for TRU transmutation.     

Calculation of the pulsed Feynman- and Rossi-alpha formulae with delayed neutrons

In previous works, the authors have developed an effective solution technique for calculating the pulsed Feynman- and Rossi-alpha formulae. Through derivation of these formulae, it was shown that the technique can easily handle various pulse shapes of the pulsed neutron source. Furthermore, it was also shown that both the deterministic (i.e., synchronizing with the pulsing of neutron source) and stochastic (non-synchronizing) Feynman-alpha formulae can be obtained with this solution technique. However, for mathematical simplicity and the sake of insight, the formal derivation was performed in a model without delayed neutrons. In this paper, to demonstrate the robustness of the technique, the pulsed Feynman- and Rossi-alpha formulae were re-derived by taking one group of delayed neutrons into account. The results show that the advantages of this technique are retained even by inclusion of the delayed neutrons. Compact explicit formulae are derived for the Feynman- and Rossi-alpha methods for various pulse shapes and pulsing methods.     

Virtual sampling in variational processing of Monte Carlo simulation in a deep neutron penetration problem

In a further study of virtually processed Monte Carlo estimates in neutron transport, a shielding problem has been studied. The use of virtual sampling to estimate the importance function at a certain point in the phase space depends on the presence of neutrons from the real source at that point. But in deep penetration problems, not many neutrons will reach regions far away from the source. In order to overcome this problem, two suggestions are considered: (1) virtual sampling is used as far as the real neutrons can reach, then fictitious sampling is introduced for the remaining regions, distributed in all the regions, or (2) only one fictitious source is placed where the real neutrons almost terminate and then virtual sampling is used in the same way as for the real source. Variational processing is again found to improve the Monte Carlo estimates, being best when using one fictitious source in the far regions with virtual sampling (option 2). When fictitious sources are used to estimate the importances in regions far away from the source, some optimization has to be performed for the proportion of fictitious to real sources, weighted against accuracy and computational costs. It has been found in this study that the optimum number of cells to be treated by fictitious sampling is problem dependent, but as a rule of thumb, fictitious sampling should be employed in regions where the number of neutrons from the real source fall below a specified limit for good statistics.     

The use of monodirectional neutron sources for the investigation of shielding (B-2 apparatus in a BR-5 reactor)

The report describes the B-2 apparatus, installed in a BR-5 fast reactor, for investigating the passage of neutrons through various shielding materials. It is shown that the monodirectional neutron disc source used in this apparatus makes it possible to obtain detailed information on the spatial-energy and angular distributions of the neutrons in the shielding. The effect of the angular distribution of the radiation leaving the source on the attenuation factor of this radiation in shielding was also investigated.In conclusion I would like to express my sincere thanks to A. I. Leipunskii for valuable advice during the formulation of the scheme of investigations concerning the passage of neutrons in different media from monodirectional sources, and I. I. Bondarenko, V. V. Orlov, V. I. Kukhtevich, Yu. A. Kazanskii, B. I. Sinitsyn, E. S. Matusevich, B. P. Shemetenko, Sh. S. Nikolaishvili, V. P. Mashkovich, and A. A. Abagyan for discussing the results of this work; and, finally, D. S. Pinkhasik 'and N. N. Aristarkhov for considerable help in making the B-2 apparatus.     

用缓发中子探测核弹头的技术探索

根据缓发中子的时间特征行为分析了缓发中子的中子输运过程,讨论了缓发中子探测核弹头的技术与方法。研究表明,测量缓发中子可以有效地探测到核弹头。但在不知道核弹头的内部设计信息的情况下,需用其他方法加以配合才能甄别真假核弹头。     

可控中子源密度测井仪的密度响应特性与算法研究

在可控中子源密度测井中，脉冲中子源的中子产额存在波动，采用探测器绝对计数的密度算法受地层环境、测量条件的影响较大，因此会导致密度算法的精度较差。为提高密度测量的稳定性和精确性，本文针对可控中子源一体化测井仪的研发需要，建立了适合所研发仪器的密度算法：首先，结合蒙特卡罗数值模拟软件MCNP对新型一体化测井仪及地层进行了建模；然后，利用所建模型，模拟了在不同岩性、孔隙度条件下可控中子源发射的快中子与地层物质的相互作用过程，并通过记录γ探测器的近、远非弹性散射γ计数和俘获γ计数，中子探测器的近热中子及近超热中子计数信息，获得了一体化测井仪探测器计数与地层密度之间的响应关系，并对影响密度算法的主要因素进行了分析；最后，在密度响应特性分析的基础上，提出了使用近超热中子与近热中子计数比、近远非弹γ计数比来提高稳定性和精确性的可控中子源密度测井新算法。采用新密度算法对所建模型进行计算，结果表明，砂岩、灰岩、白云岩3种岩性下计算的密度与真密度非常接近，其相对误差小于6%。与哈里伯顿和斯伦贝谢算法的计算结果相比，本文方法显示了更好的效果：公式参数少、没有探测器的绝对计数、精确度高。