An integral equation arising in neutron transport theory

A classic problem in nuclear reactor physics is the calculation of the spatial distribution of fissile material to make the associated neutron flux distribution spatially constant. We examine a special case of that problem for an infinite slab of fissile material which is infinitely reflected on both sides by a non-multiplying material. The conditions for a constant flux are derived and lead to a singular integral equation. This equation is reduced analytically to a non-singular integral equation and the solution thereby obtained is compared with that from a direct numerical method. Some of the physical implications are examined. We also note that, contrary to a theorem for multi-group diffusion theory, the resulting total fissile loading of the system is not a minimum but rather a maximum. An important aspect of the present work is that transport theory is used and not diffusion theory. Indeed, we note that no solution exists for the corresponding diffusion theory model unless it is specially modified by the addition of generalised functions, and hence we note that the problem is intrinsically governed by transport effects.     

Sub-cell balanced nodal expansion methods using S4 eigenfunctions for multi-group SN transport problems in slab geometry

A highly accurate S₄ eigenfunction-based nodal method has been developed to solve multi-group discrete ordinate neutral particle transport problems with a linearly anisotropic scattering in slab geometry. The new method solves the even-parity form of discrete ordinates transport equation with an arbitrary S_N order angular quadrature using two sub-cell balance equations and the S₄ eigenfunctions of within-group transport equation. The four eigenfunctions from S₄ approximation have been chosen as basis functions for the spatial expansion of the angular flux in each mesh. The constant and cubic polynomial approximations are adopted for the scattering source terms from other energy groups and fission source. A nodal method using the conventional polynomial expansion and the sub-cell balances was also developed to be used for demonstrating the high accuracy of the new methods. Using the new methods, a multi-group eigenvalue problem has been solved as well as fixed source problems. The numerical test results of one-group problem show that the new method has third-order accuracy as mesh size is finely refined and it has much higher accuracies for large meshes than the diamond differencing method and the nodal method using sub-cell balances and polynomial expansion of angular flux. For multi-group problems including eigenvalue problem, it was demonstrated that the new method using the cubic polynomial approximation of the sources could produce very accurate solutions even with large mesh sizes.     

小波尺度函数展开在连续能量中子输运方程计算中的应用

小波展开能够很好地拟合剧烈变化的函数,近年来已被应用于模拟中子角注量率随角度剧烈变化的问题,并取得了令人满意的结果.中子能谱在共振区具有剧烈震荡的特性,本文介绍了利用能群与小波尺度函数展开相耦合来离散连续能量中子输运方程中能量自变量的方法.对中子注量率在共振区关于能量用小波尺度函数进行拟合,而在快中子区和热中子区利用分群计算的方法.初步的数值结果表明,该方法使有效增殖系数计算精确,并能够得到中子注量率在共振区随能量的精细分布,对共振自屏蔽的精确计算具有重要意义.     

A critique of inverse solutions to slab geometry transport problems

An inverse transport problem requires determination of the angular scattering and absorption coefficients of the medium using measurements of the intensity. Methods for solving such a problem for monoenergetic transport in a thick homogeneous (i.e. multiple-scattering) slab medium are critiqued. The methods include those that require local measurement of the intensity inside the slab plus remote measurement of the angular distributions entering and leaving (the local-&-remote methods) and those (remote methods) that require only the surface angular distributions. The possible use of these methods to determine the properties of a multi-layer slab medium is also examined.     

MCTGP：一个新的多能蒙特卡罗热谱程序

ＭＣＴＧＰ是多能蒙特卡罗热谱程序ＸＩＭＴＣ的新版本，用ＦＯＲＴＲＡＮ语言编制，可以在ＣＹＢＥＲ－１７０／８２５和ＰＣ３８６／４８６上运行。除了保留ＸＩＭＴＣ程序的全部功能外，它可以计算平板几何栅元，实现了微机上栅元的几何图形显示，增加输出＾１Ｈ、＾２Ｄ、＾１６Ｏ等主要散射核的平均散射余弦，核素数据由原来的２０种增加到３２种。对两个样本的主主案的计算结果表明，程序可靠。     

The infinite medium Green's function method for multigroup discrete ordinates transport problems in multi-layered slab geometry

Analytic solutions of the multigroup discrete ordinates transport equation with linearly anisotropic scattering and arbitrarily distributed source for multi-layered slab problems are obtained by using the infinite medium Green's function (IMGF) and Placzek's lemma. In this approach, the infinite medium Green's function is derived analytically by using the spectral analysis for the multigroup discrete ordinates transport equation and its transposed equation, and this infinite medium solution is related to the finite medium solution by Placzek's lemma. The resulting equation leads to an exact relation that represents the outgoing angular fluxes in terms of the incoming angular fluxes and the interior inhomogeneous source for each slab. For heterogeneous problems having multi-layered slabs, the slabs are coupled through the interface angular fluxes. Since all derivations are performed analytically, the method gives exact solution with no truncation error. After the interface angular fluxes are calculated by using an iterative method, the continuous spatial distribution of the angular flux (i.e. analytic solution) in each slab is given straightforwardly in terms of the IMGF and the boundary angular fluxes.     

Sources: A code for calculating (alpha,n), spontaneous fission,and delayed neutron sources and spectra

SOURCES is a computer code that determines neutron production rates and spectra from (alpha, n) reactions, spontaneous fission, and delayed neutron emission due to the decay of radionuclides in homogeneous media, interface problems, and three-region interface problems. The code is also capable of calculating the neutron production rates due to (alpha, n) reactions induced by a monoenergetic beam of alpha particles incident on a slab of target material. The (alpha, n) spectra are calculated using an assumed isotropic angular distribution in the center-of-mass system with a library of 107 nuclide decay alpha-particle spectra, 24 sets of measured and/or evaluated (alpha, n) cross sections and product nuclide level branching fractions, and functional alpha particle stopping cross sections for Z < 106. Spontaneous fission sources and spectra are calculated with evaluated half-life, spontaneous fission branching, and Watt spectrum parameters for 44 actinides. The delayed neutron spectra are taken from an evaluated library of 105 precursors. The code outputs the magnitude and spectra of the resultant neutron sources. It also provides an analysis of the contributions to that source by each nuclide in the problem.     

Study of spatial resolution of the associated alpha particle imaging–time-of-flight method

Associated alpha particle imaging based on the time-of-flight(API-TOF) technique is an advanced neutron analysis method, which is capable of discriminating material nuclides and three-dimensional imaging of the spatial distribution of material nuclei. In this paper, the spatial resolution of API-TOF and its effects are studied using mathematical analysis and Monte Carlo numerical simulation. The results can provide guidance and assist in designing of API-TOF detection devices. First, a mathematical analysis of the imaging principles of the API-TOF was carried out, and the calculation formulas of the spatial resolution of API-TOF were deduced. Next, the relationship between the device layout and the spatial resolution of the API-TOF detection device was studied. The concept of a typical API-TOF detection device with an optimized structure was proposed. Then, the spatial distribution of the spatial resolution of the typical API-TOF detection device was analyzed, and the effects of the time resolution and the neutron emission angle resolution on the spatial resolution were studied. The results show that spatial resolutions better than 1 cm can be achieved by improving the time resolution and the neutron emission angle resolution to appropriate levels. Finally, a Monte Carlo numerical simulation program was developed for the study of the APITOF and was used to calculate the spatial resolutions of the API-TOF. The comparison of the results shows that thespatial resolutions calculated based on the Monte Carlo numerical simulation are in good agreement with those calculated based on the mathematical analysis. This verifies the mathematical analysis and the evaluation of the effects of the spatial resolution of the API-TOF in this study.     

一阶中子输运方程的离散纵标有限元方法研究

利用离散纵标(SN)方法离散SN一阶多群中子输运方程,建立了基于剖分单元的有限元离散与非结构网格扫描方法相结合的求解模型。针对给定的三角形单元应用Galerkin变分,获得线性方程组,通过引入定解条件,求解线性代数方程组,获得该三角形单元所有节点上的角通量,然后对其他三角形单元进行扫描,从而解出所有节点处中子通量密度。根据上述理论模型,编制了相应的计算程序FEGT,对一系列例题进行校验的数值结果表明,该程序的计算精度满足要求。     

基于伴随粒子的快中子成像系统角分辨研究

不同于传统的快中子成像系统,采用伴随粒子成像技术无需机械准直即可消除大部分γ射线和散射中子的干扰,实现对厚重物体的高对比度成像。角分辨是影响系统成像质量的一项重要参数。通过理论分析,研究了入射离子的初始动量、靶点尺寸和探测器空间分辨等多个因素对系统角分辨的影响。利用基于GEANT4的模拟程序,计算了不同参数下被标记中子出射角分布的二维图像。分析及模拟结果表明,靶点直径和α探测器空间分辨率是影响角分辨的重要因素。为满足系统角分辨小于1°的设计目标,入射离子的初始动量变化范围应较小,靶点直径应小于1 mm,同时α探测器的空间分辨率应小于0.5 mm。     

Investigations of space-dependent safety-related parameters of a PBMR-like HTR in transient operating conditions applying a multi-group diffusion code

So far, the two-dimensional reactor dynamics code TINTE (time-dependent nucleonics and temperatures) was applied for simulations of high-temperature gas cooled reactors. One limitation of TINTE is that the neutron energy spectrum is modeled by only two energy groups, namely a thermal and a fast group. Present demands for increased numerical accuracy leads to the question of how precise the two-group approximation is compared to a multi-group approach. The recently developed multi-group derivative of TINTE called MGT (multi-group TINTE) is able to handle up to 43 neutron energy groups. In this study, different scenarios (normal operation and design-basis accidents) have been simulated for a PBMR-like HTR reactor design with MGT. The effect of an increasing number of energy groups on time- and space-dependent safety-related parameters like the fuel and coolant temperature, the nuclear heat source or the xenon concentration is studied. Different ways of calculating the material cross-sections are compared as well.     

A close-form solution to predict the total melting time of an ablating slab in contact with a plasma

An exact melt-through time is derived for a one-dimensional heated slab in contact with a plasma when the melted material is immediately removed. The plasma is composed of a collisionless presheath and sheath on a slab, which partially reflects and secondarily emits ions and electrons. The energy transport from plasma to the surface accounting for the presheath and sheath is determined from the kinetic analysis. This work proposes a semi-analytical model to calculate the total melting time of a slab based on a direct integration of the unsteady heat conduction equation, and provides quantitative results applicable to control the total melting time of the slab. The total melting time as a function of plasma parameters and thermophysical properties of the slab are obtained. The predicted energy transmission factor as a function of dimensionless wall potential agrees well with the experimental data. The effects of reflectivities of the ions and electrons on the wall, electron-to-ion source temperature ratio at the presheath edge, charge number, ion-to-electron mass ratio, ionization energy, plasma flow work-to-heat conduction ratios, Stefan number, melting temperature, Biot number and bias voltage on the total melting time of the slab are quantitatively provided in this work.     

基于LaBr3(Ce)晶体耦合SiPM阵列的可变角分辨率伽玛相机的设计与研制

编码孔径成像技术由于探测效率高、信噪比高、角分辨率好、成像质量稳定可靠等优点而广泛应用于核安全、核设施的去污及退役的测量、核医学等领域。建立通过改变编码准直器和探测器之间距离进而实现可变角分辨的伽玛成像系统。整个成像系统主要由编码准直器、位置灵敏探测(position sensitive detector, PSD)、数据采集卡以及图像重建系统组成。该成像系统的编码准直器采用修正均匀冗余阵列(modified uniformly redundant array, MURA)编码方式,为了保障对较高能量射线的探测能力,编码准直器的材料采用含钨量90%的钨铜合金,PSD通过LaBr₃(Ce)晶体耦合SiPM阵列组成,重建算法采用的是直接互卷积算法,快速高效。测试结果显示,整个位置灵敏探测器的平均能量分辨率为4.96%(662 keV);该辐射成像系统可以准确地对Am-241、Cs-137、Co-60进行清晰成像,并通过改变编码准直器和探测器之间的距离成功分辨出两个Cs-137点源的位置。     

Investigation of OPET Performance Using GATE, a Geant4-Based Simulation Software

A combined optical positron emission tomography (OPET) system is capable of both optical and PET imaging in the same setting, and it can provide information/interpretation not possible in single-mode imaging. The scintillator array here serves the dual function of coupling the optical signal from bioluminescence/fluorescence to the photodetector and also of channeling optical scintillations from the gamma rays. We report simulation results of the PET part of OPET using GATE, a Geant4 simulation package. The purpose of this investigation is the definition of the geometric parameters of the OPET tomograph. OPET is composed of six detector blocks arranged in a hexagonal ring-shaped pattern with an inner radius of 15.6 mm. Each detector consists of a two-dimensional array of 8 × 8 scintillator crystals each measuring 2 × 2 × 10 mm(3). Monte Carlo simulations were performed using the GATE software to measure absolute sensitivity, depth of interaction, and spatial resolution for two ring configurations, with and without gantry rotations, two crystal materials, and several crystal lengths. Images were reconstructed with filtered backprojection after angular interleaving and transverse one-dimensional interpolation of the sinogram. We report absolute sensitivities nearly seven times that of the prototype microPET at the center of field of view and 2.0 mm tangential and 2.3 mm radial resolutions with gantry rotations up to an 8.0 mm radial offset. These performance parameters indicate that the imaging spatial resolution and sensitivity of the OPET system will be suitable for high-resolution and high-sensitivity small-animal PET imaging.     

Stochastic transition matrix approach to stochastic transport and its implementation in two-stream transport

The “stochastic transition matrix approach” to stochastic transport is described, and its implementation is demonstrated adopting the two-stream stochastic transport model and applying it to a purely scattering, and a purely absorbing slab. The conditional averages of the angular flux are obtained analytically in these applications, and shown that they are everywhere positive in the slab within their range of validity. The correct interpretation and use of the MLP equations are emphasized.     

适用于ADS组件计算的HELIOS程序多群数据库制作研究

针对HELIOS程序用于加速器驱动次临界系统（ADS）组件计算时,程序自带多群数据库核素不全的问题,研究制作了一套适用于ADS组件计算的HELIOS程序多群数据库。基于ENDF/B VII.0,按照HELIOS程序多群数据库制作流程,针对程序自带数据库已有核素16O,重新制作45群数据库并进行微观、宏观检验,结果初步验证了多群数据库制作方法的正确性。针对自带数据库没有的核素,扩充了HELIOS程序自带112群数据库核素,并用栅元规模进行了验证,结果进一步表明多群数据库制作方法正确。针对HELIOS计算结果与MCNP基准值相对偏差较大的问题,提出了基于小背景截面的多群数据库修正方法,并对该方法进行了数值验证,结果表明该方法对计算结果有明显改进。      

Advantage of fan beam collimators for contrast recovery ofhyperfixation in clinical SPECT

The influence of the collimator on the contrast recovery of hyperfixation was studied using a dual-headed single photon emission computed tomography (SPECT) system with standard clinical acquisition parameters. Three parallel collimator sets and two fan beam collimator sets were tested with a Jaszczak phantom. The six spheres of the phantom were filled with ^99mTc, and four background levels were progressively obtained by adding radioactivity to the cylinder of the phantom, providing four hyperfixation levels. The effects of angular sampling and reconstruction filters have been tested. The statistical analysis was performed with analysis of variance (ANOVA). This study demonstrates the advantage of ultra-high resolution fan beam collimators for contrast recovery of hyperfixation with SPECT when using 64 projections over 360°, in particular when the contrast is low. The authors also demonstrate that fan beam collimators permit smaller size hyperfixation detection     

Modeling and simulation of uniformity effects in Cd/sub 1-x/Zn/sub x/Te gamma-ray spectrometers

Monte Carlo simulations of pulse height spectra for Cd/sub 1-x/Zn/sub x/Te detectors are used to investigate the effect of variations in alloy composition and carrier drift lengths on energy resolution. The results, which are based on a simple phenomenological model, show that these nonuniformities can have significant detrimental effects on spectrometer performance. For the case of Bridgman-grown material, the orientation of the growth axis relative to the detector axis is shown to be an important consideration, especially for crystals which come from the heel end of a boule, where the composition gradient due to zinc segregation is large. Other effects which we have simulated include growth striations, zinc segregation at grain boundaries, and trapping by inclusions and grain boundaries; each of these effects is detrimental to energy resolution. We conclude that material nonuniformity is a major obstacle to achieving statistically limited energy resolution in cadmium zinc telluride detectors.     

核级石墨氧化腐蚀模型研究

高温气冷堆内应用到大量核级石墨材料,对其长期氧化腐蚀行为进行研究至关重要。文章建立了综合考虑石墨内部孔隙率变化及失重率影响的石墨氧化模型,对气体在石墨内部的瞬时氧化腐蚀情况进行了模拟计算。提出氧化深度的概念,研究发现反应温度越高,反应气体在石墨内部的氧化深度越小;并与实验结果及其他模型的计算结果进行了对比,验证了模型的有效性。     

全陶瓷微密封燃料有效多群截面计算方法研究

全陶瓷微密封（FCM）燃料是一种弥散颗粒燃料。由于弥散颗粒燃料存在双重非均匀性,传统的确定论方法及蒙特卡罗方法皆难以处理这种双重非均匀效应以获得有效多群截面。本文基于超细群方法建立FCM燃料的有效多群截面计算方法。为描述燃料棒内TRISO颗粒的非均匀性,在共振能量段,通过采用超细群方法求解包含TRISO颗粒的一维球模型得到超细群缺陷因子,通过超细群缺陷因子修正所有核素的超细群截面即可将颗粒和基质均匀化。由于TRISO颗粒在热能区也存在较强的自屏效应,在热能区,利用穿透概率及碰撞概率等价得到多群缺陷因子,通过多群缺陷因子修正所有核素的多群截面将燃料和基质均匀化。均匀化后的FCM燃料组件即可视为普通压水堆燃料组件进行共振计算。利用丹可夫修正因子等价得到FCM燃料组件各燃料棒的等效一维棒模型,对一维棒模型求解超细群慢化方程从而得到共振能量段的有效自屏截面。数值结果表明,该方法能有效处理FCM燃料的双重非均匀性,得到精确的有效自屏截面。