Chapman-Enskog-maximum entropy method on time-dependent neutron transport equation

The time-dependent neutron transport equation in semi and infinite medium with linear anisotropic and Rayleigh scattering is proposed. The problem is solved by means of the flux-limited, Chapman-Enskog-maximum entropy for obtaining the solution of the time-dependent neutron transport. The solution gives the neutron distribution density function which is used to compute numerically the radiant energy density E(x,t), net flux F(x,t) and reflectivity R_f. The behaviour of the approximate flux-limited maximum entropy neutron density function are compared with those found by other theories. Numerical calculations for the radiant energy, net flux and reflectivity of the proposed medium are calculated at different time and space.     

Equations of the surface harmonics method for solving time-dependent neutron transport problems and their verification

Time-dependent equations of the surface harmonics method (SHM) are obtained for planar one-dimensional geometry. The equations are verified by calculations of test problems from Benchmark Problem Book ANL-7416, and the capabilities and efficiency of applying the SHM for solving the time-dependent neutron transport equation in the diffusion approximation are demonstrated. The results of the work show that the implementation of the SHG for full-scale computations will make possible substantial progress in the efficient solution of time-dependent problems of neutron transport in nuclear reactors.     

二维柱几何各向异性输运问题的数值计算方法

本文研究了求解二维输运问题的各向异性三角网间断有限元数值方法。详细讨论了求解过程,给出了解的预估公式,证明了数值解的存在唯一性和数值方法的稳定性。给出了各向异性问题的二维数值计算结果及钨——碳临界装置TCCA^[11]的二维数值计算结果。并与国内外S_N数值计算及实验结果进行比较,取得了令人满意的结果。     

The FN solution of the time-dependent neutron transport equation for a sphere with forward scattering

The one-speed time-dependent and stationary neutron transport equation in spherical geometry with forward scattering is considered. A formal equivalence between the transport equations for a critical and for a decaying system is established. By considering the pseudo-slab problem the scaled transport equation is solved using the F_N method. Numerical values of radii for a critical and time-dependent systems are tabulated as a function of the scattering parameters and the fundamental decay constant. Some of the results are discussed and compared with others obtained using various methods. The results agree for four or five significant figures with the published results. It is shown that the F_N method yields good numerical results for the problem considered. Finally, a few remarks about the effect of the forward anisotropy on the radius is also given.     

Dynamics of water in real space and time

Owing to marked advances in instrumentation in X-ray and neutron scattering the time-dependent pair correlation function, the Van Hove function, can now be determined by inelastic X-ray and neutron scattering measurements. The local dynamics of water in real space and time is visualised by this approach. We discuss how the dynamic properties, such as viscosity and diffusion, can be elucidated through the Van Hove function of water.     

裂变中子角关联分布的数值模拟

为了实现对自发裂变中子源能量、多重性和中子角关联分布的数值模拟,开发了根据裂变过程,逐步给出裂变中子多重性、能量和角分布等参数的NESF数值模拟程序,并将该程序集成到现有中子输运软件中.重点介绍我们开发的用于模拟自发裂变中子源能量、多重性和中子角关联分布的程序的背景、物理依据、程序流程,以及基于该程序开展的中子角关联分布特征与核部件特征关联的数值模拟.     

Effect of the momentum dependence of nuclear symmetry potential on the transverse and elliptic flows

In the framework of the isospin-dependent Boltzmann-Uehling-Uhlenbeck transport model, the effect of the momentum dependence of nuclear symmetry potential on nuclear transverse and elliptic flows in the neutron-rich reaction ¹³²Sn+¹²⁴Sn at a beam energy of 400MeV/nucleon is studied. We find that the momentum dependence of nuclear symmetry potential affects the rapidity distribution of the free neutron to proton ratio, the neutron and the proton transverse flows as a function of rapidity. The momentum dependence of nuclear symmetry potential affects the neutron-proton differential transverse flow more evidently than the difference of neutron and proton transverse flows as well as the difference of proton and neutron elliptic flows. It is thus better to probe the symmetry energy by using the difference of neutron and proton flows since the momentum dependence of nuclear symmetry potential is still an open question. And it is better to probe the momentum dependence of nuclear symmetry potential by using the neutron-proton differential transverse flow the rapidity distribution of the free neutron to proton ratio.     

The surface cooling effect in radiative transfer

The halfspace radiative equilibrium problem with an incident beam of energy is analyzed by both the equation of transfer and the diffusion approximation. The spatial dependence of the source function is shown to exhibit (unexpected) surface cooling for all angles of incidence. For grazing incidence, the source function additionally exhibits a maximum within the halfspace. The diffusion results agree qualitatively with these transport findings for near normal incidence, but not for grazing incidence. The relationship of this problem to one in neutron transport theory is established, graphical results are presented, and the relevance of this analysis to understanding detailed radiation-hydrodynamic computer results for a certain class of problems is discussed.     

The exact solution of the time-dependent equation of radiative transfer in the interior of a semi-infinite atmosphere

An exact solution to the time-dependent radiative transfer equation for the interior intensity in a semi-infinite atmosphere exhibiting temporal capture is obtained. The intensity is constructed from a solution found in neutron transport theory and can be expressed in terms of quadratures of elementary functions. The origin of the form of the emergent intensity found by Matsumoto is given, as well as a similarity relation and the relationship of the intensities in absorbing and nonabsorbing media.     

Neutron velocity distribution from a superthermal solid 2H2 ultracold neutron source

We have determined for the first time the velocity distribution of neutrons from a solid ²H₂ ultracold neutron (UCN) source. The spectrum rises sharply above 4.5m/s and has a maximum around 7m/s after transport in an 8m long guide. The number of neutrons in the UCN velocity range (< 7m/s) may be increased by a factor of two by placing the experiment 1m above the UCN source level.     

用二维含时Fokker-Planck方程分析Tokamak中α粒子的输运

按分布函数的定义不同,描述高能带电粒子在等离子体中输运的-Planck方程有不同的形式。从数值计算的观点出发对两种不同形式的Fokker-Planck方程作了比较和评价,并指出Fokker-Planck碰撞项可解释为速度空间的对流扩散项。在此基础上用有限差分方法求解二维(速度一维,几何一维)含时Fokker-Planck方程,编制了计算程序CAPT,并将其应用于α粒子的输运研究。最后计算了典型的Tokamak D-T聚变堆参数下α粒子的损失,并给出了堆内α粒子的分布及损失α粒子的速度分布。     

二维柱几何非定常中子输运方程基于格式的界面预估校正并行算法

针对二维柱几何非定常中子输运方程的Sn-间断有限元方法,提出基于格式的界面预估校正并行算法.数值算例表明,该并行算法在精度与并行度等诸方面均具有良好的性质,与已有的基于隐式格式的并行扫描算法相比,对于二维中子输运大规模计算问题,并行计算效率较高,并行加速比可增加-倍以上,且可保持原隐式格式的计算精度.     

Consideration of the spin-orbit interaction in the description of nucleon transfers upon heavy ionic nuclei collisions

A difference scheme is proposed for the numerical solution of a time-dependent Schr?dinger equation with spin-orbit interaction. Evolution of an external neutron wave function with the minimum full moment projection onto the internuclear axis and the probability of neutron transfer upon frontal collisions of ⁴⁰Ca and ⁹⁶Zr nuclei are calculated.     

Application of jacobi polynomial methods to the one-speed transport equation

The transport equations associated with radiation damage studies are often solved using expansions in Legendre polynomials. The radiation damage distribution functions which satisfy these equations may be sharply peaked in the forward direction, while the Legendre polynomials, as a set, are isotropic. This situation requires the use of many terms in the Legendre expansion in order to adequately represent the distribution functions. The Jacobi polynomials, on the other hand, can have strong peaking built into their associated weight function. To test the usefulness of the Jacobi polynomials we use them to solve the simple, one-speed, neutron transport equation. The results are then compared to the exact theory and to the results of applying Legendre methods to the same problem. This sample calculation demonstrates the advantage of the Jacobi polynomials in strongly non-isotropic situations.     

用多群蒙特卡罗方法计算快中子核临界keff和通量密度

 用多群蒙特卡罗方法对快中子核裂变系统进行了临界计算。有效增殖因子keff的计算值与实验结果符合。计算所得中子通量密度的空间分布在球形裂变系统中随半径增大单调下降。中子通量密度的能量分布在由高浓缩铀组成的活性区内呈单一能量极大值,其对应能量对于裸球核裂变系统和具有反射层裂变系统分别为0.35MeV和0.25MeV,而在由天然铀组成的反射层中在0.1MeV附近出现能量双峰。由通量密度所得中子能谱在无反射层球形裂变系统中随半径增加变硬,在有反射层球形裂变系统中随半径增加变软。     

以中子作外源的假想核弹头主动探测

通过对不同入射能量的中子在假想的核弹头中的输运计算,分析了弹头中的裂变材料芯部的核裂变、各层对中子的吸收和(n,xn)反应以及出壳中子随角度的变化,论证了以外中子源(不随时间变化的外源)对弹头作主动探测的可行性.通过对14 1MeV脉冲中子源和产生的缓发中子在模型中的输运计算,分析了用脉冲外中子源产生的缓发中子探测核弹头的可行性.     

Calculation of Prompt Fission Neutron Lifetimes by the Monte Carlo Method

An algorithm for calculation of prompt fission neutron lifetimes in a nuclear reactor by the Monte Carlo method is described. Evaluation of the importance function is carried out with solution of the neutron transport equation without solving the adjoint equation. The results of the prompt neutron lifetime calculations performed within some critical experiments are presented and compared with the experimental results.     

Radial Distribution Function Analysis of the Amorphous Barrier Layer in Magnetic Spin Tunnel Junctions

Spin tunnel junctions consist of two ferrromagnetic layers separated by an amorphous insulating barrier layer which is a few nanometers thick. The barrier layer is the most critical layer in terms of magnetic transport properties and yet, of all the layers, the structure of this layer has been the least investigated, mainly due to difficulties in carrying out structural investigations of nanovolumes of amorphous materials. In this paper we demonstrate how the technique of radial distribution function analysis using electrons can be used to investigate such small volumes, by applying it to the aluminium oxide amorphous layer in a junction. The analysis results in a radial distribution function which matches those obtained by neutron and X-ray diffraction from bulk material.     

Zur allgemeinen kinetischen Theorie von partiell ionisierten Plasmen in zeitabhängigen Magnetfeldern und elektromagnetischen Zusatzfeldern

A general method is given for the calculation of the electron distribution function of a weakly ionized plasma in external time-dependent magnetic fields and additional electromagnetic fields. The Boltzmann equation of kinetic theory is solved taking into account elastic collisions between electrons and neutrals. The isotropic part f⁰ of the distribution function follows from a general linear integro-differential equation and contains all known standard distributions (Druyvesteyn, Davydov, Margenau and others) as special cases. The direction-dependent part f¹ gives the transport tensors.     

Zum allgemeinen Dispersionsgesetz der linearen Boltzmanngleichung

The conditions for the existence of particular solutions are investigated for the space- and time-dependent linear Boltzmann-equation which describes the neutron field. The regular solutions correspond to a discrete spectrum of parameters. Therefore, such particular states can be isolated asymptotically in suitable experiments. The number of possible asymptotic neutron-field-experiments is determined by the number of possible combinations of discrete parameter values corresponding to regular solutions. In the course of the analysis, two possible types of new experiments were found: the instationary exponential experiment and the neutron-wave experiment with damped excitation. The formulation of the problem has been extended to include the energy dependence of neutron distribution functions.