The Multigroup Neutron Diffusion Equations/1 Space Dimension
Energy Technology Data Exchange (ETDEWEB)
Linde, Sven
1960-06-15
A description is given of a program for the Ferranti Mercury computer which solves the one-dimensional multigroup diffusion equations in plane, cylindrical or spherical geometry, and also approximates automatically a two-dimensional solution by separating the space variables. In section A the method of calculation is outlined and the preparation of data for two group problems is described. The spatial separation of two-dimensional equations is considered in section B. Section C covers the multigroup equations. These parts are self contained and include all information required for the use of the program. Details of the numerical methods are given in section D. Three sample problems are solved in section E. Punching and operating instructions are given in an appendix.
The Multigroup Neutron Diffusion Equations/1 Space Dimension
International Nuclear Information System (INIS)
Linde, Sven
1960-06-01
A description is given of a program for the Ferranti Mercury computer which solves the one-dimensional multigroup diffusion equations in plane, cylindrical or spherical geometry, and also approximates automatically a two-dimensional solution by separating the space variables. In section A the method of calculation is outlined and the preparation of data for two group problems is described. The spatial separation of two-dimensional equations is considered in section B. Section C covers the multigroup equations. These parts are self contained and include all information required for the use of the program. Details of the numerical methods are given in section D. Three sample problems are solved in section E. Punching and operating instructions are given in an appendix
Multigroup neutron transport equation in the diffusion and P{sub 1} approximation
Energy Technology Data Exchange (ETDEWEB)
Obradovic, D [Boris Kidric Institute of nuclear sciences Vinca, Belgrade (Yugoslavia)
1970-07-01
Investigations of the properties of the multigroup transport operator, width and without delayed neutrons in the diffusion and P{sub 1} approximation, is performed using Keldis's theory of operator families as well as a technique . recently used for investigations into the properties of the general linearized Boltzmann operator. It is shown that in the case without delayed neutrons, multigroup transport operator in the diffusion and P{sub 1} approximation possesses a complete set of generalized eigenvectors. A formal solution to the initial value problem is also given. (author)
Discrete formulation for two-dimensional multigroup neutron diffusion equations
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Vosoughi, Naser E-mail: vosoughi@mehr.sharif.edu; Salehi, Ali A.; Shahriari, Majid
2003-02-01
The objective of this paper is to introduce a new numerical method for neutronic calculation in a reactor core. This method can produce the final finite form of the neutron diffusion equation by classifying the neutronic variables and using two kinds of cell complexes without starting from the conventional differential form of the neutron diffusion equation. The method with linear interpolation produces the same convergence as the linear continuous finite element method. The quadratic interpolation is proven; the convergence order depends on the shape of the dual cell. The maximum convergence order is achieved by choosing the dual cell based on two Gauss' points. The accuracy of the method was examined with a well-known IAEA two-dimensional benchmark problem. The numerical results demonstrate the effectiveness of the new method.
Discrete formulation for two-dimensional multigroup neutron diffusion equations
International Nuclear Information System (INIS)
Vosoughi, Naser; Salehi, Ali A.; Shahriari, Majid
2003-01-01
The objective of this paper is to introduce a new numerical method for neutronic calculation in a reactor core. This method can produce the final finite form of the neutron diffusion equation by classifying the neutronic variables and using two kinds of cell complexes without starting from the conventional differential form of the neutron diffusion equation. The method with linear interpolation produces the same convergence as the linear continuous finite element method. The quadratic interpolation is proven; the convergence order depends on the shape of the dual cell. The maximum convergence order is achieved by choosing the dual cell based on two Gauss' points. The accuracy of the method was examined with a well-known IAEA two-dimensional benchmark problem. The numerical results demonstrate the effectiveness of the new method
International Nuclear Information System (INIS)
Ozgener, B.
1998-01-01
A boundary integral equation (BIE) is developed for the application of the boundary element method to the multigroup neutron diffusion equations. The developed BIE contains no explicit scattering term; the scattering effects are taken into account by redefining the unknowns. Boundary elements of the linear and constant variety are utilised for validation of the developed boundary integral formulation
International Nuclear Information System (INIS)
Kim, Kyung-O; Jeong, Hae Sun; Jo, Daeseong
2017-01-01
Highlights: • Employing the Radial Point Interpolation Method (RPIM) in numerical analysis of multi-group neutron-diffusion equation. • Establishing mathematical formation of modified multi-group neutron-diffusion equation by RPIM. • Performing the numerical analysis for 2D critical problem. - Abstract: A mesh-free method is introduced to overcome the drawbacks (e.g., mesh generation and connectivity definition between the meshes) of mesh-based (nodal) methods such as the finite-element method and finite-difference method. In particular, the Point Interpolation Method (PIM) using a radial basis function is employed in the numerical analysis for the multi-group neutron-diffusion equation. The benchmark calculations are performed for the 2D homogeneous and heterogeneous problems, and the Multiquadrics (MQ) and Gaussian (EXP) functions are employed to analyze the effect of the radial basis function on the numerical solution. Additionally, the effect of the dimensionless shape parameter in those functions on the calculation accuracy is evaluated. According to the results, the radial PIM (RPIM) can provide a highly accurate solution for the multiplication eigenvalue and the neutron flux distribution, and the numerical solution with the MQ radial basis function exhibits the stable accuracy with respect to the reference solutions compared with the other solution. The dimensionless shape parameter directly affects the calculation accuracy and computing time. Values between 1.87 and 3.0 for the benchmark problems considered in this study lead to the most accurate solution. The difference between the analytical and numerical results for the neutron flux is significantly increased in the edge of the problem geometry, even though the maximum difference is lower than 4%. This phenomenon seems to arise from the derivative boundary condition at (x,0) and (0,y) positions, and it may be necessary to introduce additional strategy (e.g., the method using fictitious points and
Energy Technology Data Exchange (ETDEWEB)
Zanette, Rodrigo; Petersen, Caudio Zen [Univ. Federal de Pelotas, Capao do Leao (Brazil). Programa de Pos Graduacao em Modelagem Matematica; Schramm, Marcello [Univ. Federal de Pelotas (Brazil). Centro de Engenharias; Zabadal, Jorge Rodolfo [Univ. Federal do Rio Grande do Sul, Tramandai (Brazil)
2017-05-15
In this paper a solution for the one-dimensional steady state Multilayer Multigroup Neutron Diffusion Equation in cartesian geometry by Fictitious Borders Power Method and a perturbative analysis of this solution is presented. For each new iteration of the power method, the neutron flux is reconstructed by polynomial interpolation, so that it always remains in a standard form. However when the domain is long, an almost singular matrix arises in the interpolation process. To eliminate this singularity the domain segmented in R regions, called fictitious regions. The last step is to solve the neutron diffusion equation for each fictitious region in analytical form locally. The results are compared with results present in the literature. In order to analyze the sensitivity of the solution, a perturbation in the nuclear parameters is inserted to determine how a perturbation interferes in numerical results of the solution.
International Nuclear Information System (INIS)
Honeck, H.C.
1984-01-01
1 - Description of problem or function: HAMMER performs infinite lattice, one-dimensional cell multigroup calculations, followed (optionally) by one-dimensional, few-group, multi-region reactor calculations with neutron balance edits. 2 - Method of solution: Infinite lattice parameters are calculated by means of multigroup transport theory, composite reactor parameters by few-group diffusion theory. 3 - Restrictions on the complexity of the problem: - Cell calculations - maxima of: 30 thermal groups; 54 epithermal groups; 20 space points; 20 regions; 18 isotopes; 10 mixtures; 3 thermal up-scattering mixtures; 200 resonances per group; no overlap or interference; single level only. - Reactor calculations - maxima of : 40 regions; 40 mixtures; 250 space points; 4 groups
International Nuclear Information System (INIS)
Moraes, Pedro Gabriel B.; Leite, Michel C.A.; Barros, Ricardo C.
2013-01-01
In this work we developed a software to model and generate results in tables and graphs of one-dimensional neutron transport problems in multi-group formulation of energy. The numerical method we use to solve the problem of neutron diffusion is analytic, thus eliminating the truncation errors that appear in classical numerical methods, e.g., the method of finite differences. This numerical analytical method increases the computational efficiency, since they are not refined spatial discretization necessary because for any spatial discretization grids used, the numerical result generated for the same point of the domain remains unchanged unless the rounding errors of computational finite arithmetic. We chose to develop a computational application in MatLab platform for numerical computation and program interface is simple and easy with knobs. We consider important to model this neutron transport problem with a fixed source in the context of shielding calculations of radiation that protects the biosphere, and could be sensitive to ionizing radiation
International Nuclear Information System (INIS)
Modak, R.S.; Sahni, D.C.
1996-01-01
Some simple reciprocity-like relations that exist in multi-group neutron diffusion and transport theory over bare homogeneous regions are presented. These relations do not involve the adjoint solutions and are directly related to numerical schemes based on an explicit evaluation of the fission matrix. (author)
Energy Technology Data Exchange (ETDEWEB)
Zanette, Rodrigo [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Programa de Pós-Graduação em Matemática Aplicada; Petersen, Claudio Z.; Tavares, Matheus G., E-mail: rodrigozanette@hotmail.com, E-mail: claudiopetersen@yahoo.com.br, E-mail: matheus.gulartetavares@gmail.com [Universidade Federal de Pelotas (UFPEL), RS (Brazil). Programa de Pós-Graduação em Modelagem Matemática
2017-07-01
We describe in this work the application of the modified power method for solve the multigroup neutron diffusion eigenvalue problem in slab geometry considering two-dimensions for nuclear reactor global calculations. It is well known that criticality calculations can often be best approached by solving eigenvalue problems. The criticality in nuclear reactors physics plays a relevant role since establishes the ratio between the numbers of neutrons generated in successive fission reactions. In order to solve the eigenvalue problem, a modified power method is used to obtain the dominant eigenvalue (effective multiplication factor (K{sub eff})) and its corresponding eigenfunction (scalar neutron flux), which is non-negative in every domain, that is, physically relevant. The innovation of this work is solving the neutron diffusion equation in analytical form for each new iteration of the power method. For solve this problem we propose to apply the Finite Fourier Sine Transform on one of the spatial variables obtaining a transformed problem which is resolved by well-established methods for ordinary differential equations. The inverse Fourier transform is used to reconstruct the solution for the original problem. It is known that the power method is an iterative source method in which is updated by the neutron flux expression of previous iteration. Thus, for each new iteration, the neutron flux expression becomes larger and more complex due to analytical solution what makes propose that it be reconstructed through an polynomial interpolation. The methodology is implemented to solve a homogeneous problem and the results are compared with works presents in the literature. (author)
International Nuclear Information System (INIS)
Petersen, Claudio Zen; Vilhena, Marco T.; Barros, Ricardo C.
2009-01-01
In this paper the application of the Laplace transform method is described in order to determine the energy-dependent albedo matrix that is used in the boundary conditions multigroup neutron diffusion eigenvalue problems in slab geometry for nuclear reactor global calculations. In slab geometry, the diffusion albedo substitutes without approximation the baffle-reflector system around the active domain. Numerical results to typical test problems are shown to illustrate the accuracy and the efficiency of the Chebysheff acceleration scheme. (orig.)
Three-dimensional h-adaptivity for the multigroup neutron diffusion equations
Wang, Yaqi
2009-04-01
Adaptive mesh refinement (AMR) has been shown to allow solving partial differential equations to significantly higher accuracy at reduced numerical cost. This paper presents a state-of-the-art AMR algorithm applied to the multigroup neutron diffusion equation for reactor applications. In order to follow the physics closely, energy group-dependent meshes are employed. We present a novel algorithm for assembling the terms coupling shape functions from different meshes and show how it can be made efficient by deriving all meshes from a common coarse mesh by hierarchic refinement. Our methods are formulated using conforming finite elements of any order, for any number of energy groups. The spatial error distribution is assessed with a generalization of an error estimator originally derived for the Poisson equation. Our implementation of this algorithm is based on the widely used Open Source adaptive finite element library deal.II and is made available as part of this library\\'s extensively documented tutorial. We illustrate our methods with results for 2-D and 3-D reactor simulations using 2 and 7 energy groups, and using conforming finite elements of polynomial degree up to 6. © 2008 Elsevier Ltd. All rights reserved.
TASK, 1-D Multigroup Diffusion or Transport Theory Reactor Kinetics with Delayed Neutron
International Nuclear Information System (INIS)
Buhl, A.R.; Hermann, O.W.; Hinton, R.J.; Dodds, H.L. Jr.; Robinson, J.C.; Lillie, R.A.
1975-01-01
1 - Description of problem or function: TASK solves the one-dimensional multigroup form of the reactor kinetics equations, using either transport or diffusion theory and allowing an arbitrary number of delayed neutron groups. The program can also be used to solve standard static problems efficiently such as eigenvalue problems, distributed source problems, and boundary source problems. Convergence problems associated with sources in highly multiplicative media are circumvented, and such problems are readily calculable. 2 - Method of solution: TASK employs a combination scattering and transfer matrix method to eliminate certain difficulties that arise in classical finite difference approximations. As such, within-group (inner) iterations are eliminated and solution convergence is independent of spatial mesh size. The time variable is removed by Laplace transformation. (A later version will permit direct time solutions.) The code can be run either in an outer iteration mode or in closed (non-iterative) form. The running mode is dictated by the number of groups times the number of angles, consistent with available storage. 3 - Restrictions on the complexity of the problem: The principal restrictions are available storage and computation time. Since the code is flexibly-dimensioned and has an outer iteration option there are no internal restrictions on group structure, quadrature, and number of ordinates. The flexible-dimensioning scheme allows optional use of core storage. The generalized cylindrical geometry option is not complete in Version I of the code. The feedback options and omega-mode search options are not included in Version I
International Nuclear Information System (INIS)
Vondy, D.R.; Fowler, T.B.; Cunningham, G.W.
1977-11-01
The report documents the computer code block VENTURE designed to solve multigroup neutronics problems with application of the finite-difference diffusion-theory approximation to neutron transport (or alternatively simple P 1 ) in up to three-dimensional geometry. It uses and generates interface data files adopted in the cooperative effort sponsored by the Reactor Physics Branch of the Division of Reactor Research and Development of the Energy Research and Development Administration. Several different data handling procedures have been incorporated to provide considerable flexibility; it is possible to solve a wide variety of problems on a variety of computer configurations relatively efficiently
Energy Technology Data Exchange (ETDEWEB)
Vondy, D.R.; Fowler, T.B.; Cunningham, G.W.
1977-11-01
The report documents the computer code block VENTURE designed to solve multigroup neutronics problems with application of the finite-difference diffusion-theory approximation to neutron transport (or alternatively simple P/sub 1/) in up to three-dimensional geometry. It uses and generates interface data files adopted in the cooperative effort sponsored by the Reactor Physics Branch of the Division of Reactor Research and Development of the Energy Research and Development Administration. Several different data handling procedures have been incorporated to provide considerable flexibility; it is possible to solve a wide variety of problems on a variety of computer configurations relatively efficiently.
International Nuclear Information System (INIS)
Vondy, D.R.; Fowler, T.B.; Cunningham, G.W.
1975-10-01
The computer code block VENTURE, designed to solve multigroup neutronics problems with application of the finite-difference diffusion-theory approximation to neutron transport (or alternatively simple P 1 ) in up to three-dimensional geometry is described. A variety of types of problems may be solved: the usual eigenvalue problem, a direct criticality search on the buckling, on a reciprocal velocity absorber (prompt mode), or on nuclide concentrations, or an indirect criticality search on nuclide concentrations, or on dimensions. First-order perturbation analysis capability is available at the macroscopic cross section level
VARI-QUIR-3, 2-D Multigroup Steady-State Neutron Diffusion in X-Y R-Z or R-Theta Geometry
International Nuclear Information System (INIS)
Collier, George
1984-01-01
1 - Nature of physical problem solved: The steady-state, multigroup, two-dimensional neutron diffusion equations are solved in x-y, r-z, and r-theta geometry. 2 - Method of solution: A Gauss-Seidel type of solution with inner and outer iterations is used. The source is held constant during the inner iterations
On the exact solution for the multi-group kinetic neutron diffusion equation in a rectangle
International Nuclear Information System (INIS)
Petersen, C.Z.; Vilhena, M.T.M.B. de; Bodmann, B.E.J.
2011-01-01
In this work we consider the two-group bi-dimensional kinetic neutron diffusion equation. The solution procedure formalism is general with respect to the number of energy groups, neutron precursor families and regions with different chemical compositions. The fast and thermal flux and the delayed neutron precursor yields are expanded in a truncated double series in terms of eigenfunctions that, upon insertion into the kinetic equation and upon taking moments, results in a first order linear differential matrix equation with source terms. We split the matrix appearing in the transformed problem into a sum of a diagonal matrix plus the matrix containing the remaining terms and recast the transformed problem into a form that can be solved in the spirit of Adomian's recursive decomposition formalism. Convergence of the solution is guaranteed by the Cardinal Interpolation Theorem. We give numerical simulations and comparisons with available results in the literature. (author)
Final report [on solving the multigroup diffusion equations
International Nuclear Information System (INIS)
Birkhoff, G.
1975-01-01
Progress achieved in the development of variational methods for solving the multigroup neutron diffusion equations is described. An appraisal is made of the extent to which improved variational methods could advantageously replace difference methods currently used
Development of 3D multi-group neutron diffusion code for hexagonal geometry
International Nuclear Information System (INIS)
Sun Wei; Wang Kan; Ni Dongyang; Li Qing
2013-01-01
Based on the theory of new flux expansion nodal method to solve the neutron diffusion equations, the intra-nodal fluence rate distribution was expanded in a series of analytic basic functions for each group. In order to improve the accuracy of calculation result, continuities of neutron fluence rate and current were utilized across the nodal surfaces. According to the boundary conditions, the iteration method was adopted to solve the diffusion equation, where inner iteration speedup method is Gauss-Seidel method and outer is Lyusternik-Wagner. A new speedup method (one-outer-iteration and multi-inner-iteration method) was proposed according to the characteristic that the convergence speed of multiplication factor is faster than that of neutron fluence rate and the update of inner iteration matrix is slow. Based on the proposed model, the code HANDF-D was developed and tested by 3D two-group vver440 benchmark, experiment 2 of HFETR, 3D four-group thermal reactor benchmark, and 3D seven-group fast reactor benchmark. The numerical results show that HANDF-D can predict accurately the multiplication factor and nodal powers. (authors)
International Nuclear Information System (INIS)
Ritchie, A.I.M.; Wilson, D.J.
1984-12-01
A multigroup diffusion code has been used to predict the count rate from a neutron moisture meter for a range of values of soil water content ω, thermal neutron absorption cross section Ssub(a) (defined as Σsub(a)/rho) of the soil matrix and soil matrix density rho. Two dimensions adequately approximated the geometry of the source, detector and soil surrounding the detector. Seven energy groups, the data for which were condensed from 128 group data set over the neutron energy spectrum appropriate to the soil-water mixture under study, proved adequate to describe neutron slowing-down and diffusion. The soil-water mixture was an SiO 2 →water mixture, with the absorption cross section of SiO 2 increased to cover the range of Σsub(a) required. The response to changes in matrix density is, in general, linear but the response to changes in water content is not linear over the range of parameter values investigated. Tabular results are presented which allow interpolation of the response for a particular ω, Ssub(a) and rho. It is shown that R(ω, Ssub(a), rho) rho M(Ssub(a)) + C(ω) is a crude representation of the response over a very limited range of variation of ω, and Ssub(a). As the response is a slowly varying function of rho, Ssub(a) and ω, a polynomial fit will provide a better estimate of the response for values of rho, Ssub(a) and ω not tabulated
The numerical analysis of eigenvalue problem solutions in the multigroup neutron diffusion theory
International Nuclear Information System (INIS)
Woznicki, Z.I.
1994-01-01
The main goal of this paper is to present a general iteration strategy for solving the discrete form of multidimensional neutron diffusion equations equivalent mathematically to an eigenvalue problem. Usually a solution method is based on different levels of iterations. The presented matrix formalism allows us to visualize explicitly how the used matrix splitting influences the matrix structure in an eigenvalue problem to be solved as well as the interdependence between inner and outer iteration within global iterations. Particular interactive strategies are illustrated by numerical results obtained for several reactor problems. (author). 21 refs, 32 figs, 15 tabs
The numerical analysis of eigenvalue problem solutions in the multigroup neutron diffusion theory
Energy Technology Data Exchange (ETDEWEB)
Woznicki, Z I [Institute of Atomic Energy, Otwock-Swierk (Poland)
1994-12-31
The main goal of this paper is to present a general iteration strategy for solving the discrete form of multidimensional neutron diffusion equations equivalent mathematically to an eigenvalue problem. Usually a solution method is based on different levels of iterations. The presented matrix formalism allows us to visualize explicitly how the used matrix splitting influences the matrix structure in an eigenvalue problem to be solved as well as the interdependence between inner and outer iteration within global iterations. Particular interactive strategies are illustrated by numerical results obtained for several reactor problems. (author). 21 refs, 32 figs, 15 tabs.
The numerical analysis of eigenvalue problem solutions in multigroup neutron diffusion theory
International Nuclear Information System (INIS)
Woznicki, Z.I.
1995-01-01
The main goal of this paper is to present a general iteration strategy for solving the discrete form of multidimensional neutron diffusion equations equivalent mathematically to an eigenvalue problem. Usually a solution method is based on different levels of iterations. The presented matrix formalism allows us to visualize explicitly how the used matrix splitting influences the matrix structure in an eigenvalue problem to be solved as well as the interdependence between inner and outer iterations within global iterations. Particular iterative strategies are illustrated by numerical results obtained for several reactor problems. (author). 21 refs, 35 figs, 16 tabs
International Nuclear Information System (INIS)
Ceolin, Celina
2010-01-01
The objective of this work is to obtain an analytical solution of the neutron diffusion kinetic equation in one-dimensional cartesian geometry, to monoenergetic and multigroup problems. These equations are of the type stiff, due to large differences in the orders of magnitude of the time scales of the physical phenomena involved, which make them difficult to solve. The basic idea of the proposed method is applying the spectral expansion in the scalar flux and in the precursor concentration, taking moments and solving the resulting matrix problem by the Laplace transform technique. Bearing in mind that the equation for the precursor concentration is a first order linear differential equation in the time variable, to enable the application of the spectral method we introduce a fictitious diffusion term multiplied by a positive value which tends to zero. This procedure opened the possibility to find an analytical solution to the problem studied. We report numerical simulations and analysis of the results obtained with the precision controlled by the truncation order of the series. (author)
A multi-region boundary element method for multigroup neutron diffusion calculations
International Nuclear Information System (INIS)
Ozgener, H.A.; Ozgener, B.
2001-01-01
For the analysis of a two-dimensional nuclear system consisting of a number of homogeneous regions (termed cells), first the cell matrices which depend solely on the material composition and geometrical dimension of the cell (hence on the cell type) are constructed using a boundary element formulation based on the multigroup boundary integral equation. For a particular nuclear system, the cell matrices are utilized in the assembly of the global system matrix in block-banded form using the newly introduced concept of virtual side. For criticality calculations, the classical fission source iteration is employed and linear system solutions are by the block Gaussian-elimination algorithm. The numerical applications show the validity of the proposed formulation both through comparison with analytical solutions and assessment of benchmark problem results against alternative methods
International Nuclear Information System (INIS)
Woznicki, Z.I.
1983-07-01
This report presents the HEXAGA-III-programme solving multi-group time-independent real and/or adjoint neutron diffusion equations for three-dimensional-triangular-z-geometry. The method of solution is based on the AGA two-sweep iterative method belonging to the family of factorization techniques. An arbitrary neutron scattering model is permitted. The report written for users provides the description of the programme input and output and the use of HEXAGA-III is illustrated by a sample reactor problem. (orig.) [de
Energy Technology Data Exchange (ETDEWEB)
Nguyen-Ngoc, H [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires
1969-07-01
In order to reduce computing time, two and three-dimensional multigroup neutron diffusion equations in cylindrical, rectangular (X, Y), (X, Y, Z) and hexagonal geometries are solved by the method of synthesis using an appropriate variational principle (stationary principle). The basic idea is to reduce the number of independent variables by constructing two or three-dimensional solutions from solutions of fewer variables, hence the name 'synthesis method'. Whatever the geometry, we are led to solve a system of ordinary differential equations with matrix coefficients to which one can apply well-known numerical methods: CHEBYSHEV's polynomial method, Gaussian elimination. Numerical results furnished by synthesis programs written for the IBM 7094, the IBM 360-75 and the CDC 6600 computers, are confronted with those which are given by programs employing the classical finite difference method. [French] En vue de reduire le-temps de calcul, les equations de diffusion neutronique, multigroupe, a deux et trois dimensions d'espace dans les geometries cylindrique, rectangulaire (X, Y), (X, Y, Z) et hexagonale sont resolues par la methode de synthese utilisant un principe variationnel approprie (principe stationnaire). L'idee consiste a reduire le nombre de variables independantes par construction d'une solution bi ou tridimensionnelle au moyen de solutions dependant d'un nombre inferieur de variables, d'ou le nom de la methode. Dans tous les cas de geometrie, nous sommes conduits a resoudre un systeme d'equations differentielles a coefficients matriciels auquel peuvent s'appliquer les methodes numeriques courantes; methode polynomiale de TCHEBYCHEFF et methode d'elimination de GAUSS. Les resultats numeriques obtenus par nos codes de synthese programmes sur IBM 7094, IBM 360-75 et CDC 6600, sont confrontes avec ceux que fournissent les programmes adoptant la methode classique des differences finies. (auteur)
Three-dimensional h-adaptivity for the multigroup neutron diffusion equations
Wang, Yaqi; Bangerth, Wolfgang; Ragusa, Jean
2009-01-01
diffusion equation for reactor applications. In order to follow the physics closely, energy group-dependent meshes are employed. We present a novel algorithm for assembling the terms coupling shape functions from different meshes and show how it can be made
International Nuclear Information System (INIS)
Chang, Jonghwa
2014-01-01
Today, we can use a computer cluster consist of a few hundreds CPUs with reasonable budget. Such computer system enables us to do detailed modeling of reactor core. The detailed modeling will improve the safety and the economics of a nuclear reactor by eliminating un-necessary conservatism or missing consideration. To take advantage of such a cluster computer, efficient parallel algorithms must be developed. Mechanical structure analysis community has studied the domain decomposition method to solve the stress-strain equation using the finite element methods. One of the most successful domain decomposition method in terms of robustness is FETI-DP. We have modified the original FETI-DP to solve the eigenvalue problem for the multi-group diffusion problem in previous study. In this study, we report the result of recent modification to handle the three-dimensional subdomain partitioning, and the sub-domain multi-group problem. Modified FETI-DP algorithm has been successfully applied for the eigenvalue problem of multi-group neutron diffusion equation. The overall CPU time is decreasing as number of sub-domains (partitions) is increasing. However, there may be a limit in decrement due to increment of the number of primal points will increase the CPU time spent by the solution of the global equation. Even distribution of computational load (criterion a) is important to achieve fast computation. The subdomain partition can be effectively performed using suitable graph theory partition package such as MeTIS
Energy Technology Data Exchange (ETDEWEB)
Chang, Jonghwa [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)
2014-10-15
Today, we can use a computer cluster consist of a few hundreds CPUs with reasonable budget. Such computer system enables us to do detailed modeling of reactor core. The detailed modeling will improve the safety and the economics of a nuclear reactor by eliminating un-necessary conservatism or missing consideration. To take advantage of such a cluster computer, efficient parallel algorithms must be developed. Mechanical structure analysis community has studied the domain decomposition method to solve the stress-strain equation using the finite element methods. One of the most successful domain decomposition method in terms of robustness is FETI-DP. We have modified the original FETI-DP to solve the eigenvalue problem for the multi-group diffusion problem in previous study. In this study, we report the result of recent modification to handle the three-dimensional subdomain partitioning, and the sub-domain multi-group problem. Modified FETI-DP algorithm has been successfully applied for the eigenvalue problem of multi-group neutron diffusion equation. The overall CPU time is decreasing as number of sub-domains (partitions) is increasing. However, there may be a limit in decrement due to increment of the number of primal points will increase the CPU time spent by the solution of the global equation. Even distribution of computational load (criterion a) is important to achieve fast computation. The subdomain partition can be effectively performed using suitable graph theory partition package such as MeTIS.
International Nuclear Information System (INIS)
Woznicki, Z.
1979-06-01
This report presents the AGA two-sweep iterative methods belonging to the family of factorization techniques in their practical application in the HEXAGA-II two-dimensional programme to obtain the numerical solution to the multi-group, time-independent, (real and/or adjoint) neutron diffusion equations for a fine uniform triangular mesh. An arbitrary group scattering model is permitted. The report written for the users provides the description of input and output. The use of HEXAGA-II is illustrated by two sample reactor problems. (orig.) [de
Multi-group diffusion perturbation calculation code. PERKY (2002)
Energy Technology Data Exchange (ETDEWEB)
Iijima, Susumu; Okajima, Shigeaki [Japan Atomic Energy Research Inst., Tokai, Ibaraki (Japan). Tokai Research Establishment
2002-12-01
Perturbation calculation code based on the diffusion theory ''PERKY'' is designed for nuclear characteristic analyses of fast reactor. The code calculates reactivity worth on the multi-group diffusion perturbation theory in two or three dimensional core model and kinetics parameters such as effective delayed neutron fraction, prompt neutron lifetime and absolute reactivity scale factor ({rho}{sub 0} {delta}k/k) for FCA experiments. (author)
Energy Technology Data Exchange (ETDEWEB)
Ceolin, Celina; Schramm, Marcelo; Bodmann, Bardo Ernst Josef; Vilhena, Marco Tullio Mena Barreto de [Universidade Federal do Rio Grande do Sul, Porto Alegre (Brazil). Programa de Pos-Graduacao em Engenharia Mecanica; Bogado Leite, Sergio de Queiroz [Comissao Nacional de Energia Nuclear, Rio de Janeiro (Brazil)
2014-11-15
In this work the authors solved the steady state neutron diffusion equation for a multi-layer slab assuming the multi-group energy model. The method to solve the equation system is based on an expansion in Taylor Series resulting in an analytical expression. The results obtained can be used as initial condition for neutron space kinetics problems. The neutron scalar flux was expanded in a power series, and the coefficients were found by using the ordinary differential equation and the boundary and interface conditions. The effective multiplication factor k was evaluated using the power method. We divided the domain into several slabs to guarantee the convergence with a low truncation order. We present the formalism together with some numerical simulations.
FINELM: a multigroup finite element diffusion code. Part II
International Nuclear Information System (INIS)
Davierwalla, D.M.
1981-05-01
The author presents the axisymmetric case in cylindrical coordinates for the finite element multigroup neutron diffusion code, FINELM. The numerical acceleration schemes incorporated viz. the Lebedev extrapolations and the coarse mesh rebalancing, space collapsing, are discussed. A few benchmark computations are presented as validation of the code. (Auth.)
International Nuclear Information System (INIS)
van der Hagen, T.H.J.J.; Hoogenboom, J.E.; van Dam, H.
1992-01-01
This paper reports on the sensitivity of a neutron detector to parametric fluctuations in the core of a reactor which depends on the position and the frequency of the perturbation. The basic neutron diffusion model for the calculation of this so-called field of view (FOV) of the detector is extended with respect to the dimensionality of the problem and the number of energy groups involved. The physical meaning of the FOV concept is illustrated by means of some simple examples, which can be handled analytically. The possibility of calculating the FOV by a conventional neutron diffusion code is demonstrated. In that case, the calculation in n neutron energy groups leads to 2n modified neutron diffusion equations
Complex of two-dimensional multigroup programs for neutron-physical computations of nuclear reactor
International Nuclear Information System (INIS)
Karpov, V.A.; Protsenko, A.N.
1975-01-01
Briefly stated mathematical aspects of the two-dimensional multigroup method of neutron-physical computation of nuclear reactor. Problems of algorithmization and BESM-6 computer realisation of multigroup diffuse approximations in hexagonal and rectangular calculated lattices are analysed. The results of computation of fast critical assembly having complicated composition of the core are given. The estimation of computation accuracy of criticality, neutron fields distribution and efficiency of absorbing rods by means of computer programs developed is done. (author)
Multi-group neutron transport theory
International Nuclear Information System (INIS)
Zelazny, R.; Kuszell, A.
1962-01-01
Multi-group neutron transport theory. In the paper the general theory of the application of the K. M. Case method to N-group neutron transport theory in plane geometry is given. The eigenfunctions (distributions) for the system of Boltzmann equations have been derived and the completeness theorem has been proved. By means of general solution two examples important for reactor and shielding calculations are given: the solution of a critical and albedo problem for a slab. In both cases the system of singular integral equations for expansion coefficients into a full set of eigenfunction distributions has been reduced to the system of Fredholm-type integral equations. Some results can be applied also to some spherical problems. (author) [fr
International Nuclear Information System (INIS)
Ganapol, B.D.
2011-01-01
Highlights: → Coupled neutron and gamma transport is considered in the multigroup diffusion approximation. → The model accommodates fission, up- and down-scattering and common neutron-gamma interactions. → The exact solution to the diffusion equation in a heterogeneous media of any number of regions is found. → The solution is shown to parallel the one-group case in a homogeneous medium. → The discussion concludes with a heterogeneous, 2 fuel-plate 93.2% enriched reactor fuel benchmark demonstration. - Abstract: The angular flux for the 'rod model' describing coupled neutron/gamma (n, γ) diffusion has a particularly straightforward analytical representation when viewed from the perspective of a one-group homogeneous medium. Cast in the form of matrix functions of a diagonalizable matrix, the solution to the multigroup equations in heterogeneous media is greatly simplified. We shall show exactly how the one-group homogeneous medium solution leads to the multigroup solution.
International Nuclear Information System (INIS)
Halilou, A.; Lounici, A.
1981-01-01
The subject is divided in two parts: In the first part a nodal method has been worked out to solve the steady state multigroup diffusion equation. This method belongs to the same set of nodal methods currently used to calculate the exact fission powers and neutron fluxes in a very short computing time. It has been tested on a two dimensional idealized reactors. The effective multiplication factor and the fission powers for each fuel element have been calculated. The second part consists in studying and mastering the multigroup diffusion code DAHRA - a reduced version of DIANE - a two dimensional code using finite difference method
International Nuclear Information System (INIS)
Woznicki, Z.
1976-05-01
This report presents the AGA two-sweep iterative methods belonging to the family of factorization techniques in their practical application in the HEXAGA-II two-dimensional programme to obtain the numerical solution to the multi-group, time-independent, (real and/or adjoint) neutron diffusion equations for a fine uniform triangular mesh. An arbitrary group scattering model is permitted. The report written for the users provides the description of input and output. The use of HEXAGA-II is illustrated by two sample reactor problems. (orig.) [de
Energy Technology Data Exchange (ETDEWEB)
Chang, Jonghwa [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)
2014-05-15
Parallelization of Monte Carlo simulation is widely adpoted. There are also several parallel algorithms developed for the SN transport theory using the parallel wave sweeping algorithm and for the CPM using parallel ray tracing. For practical purpose of reactor physics application, the thermal feedback and burnup effects on the multigroup cross section should be considered. In this respect, the domain decomposition method(DDM) is suitable for distributing the expensive cross section calculation work. Parallel transport code and diffusion code based on the Raviart-Thomas mixed finite element method was developed. However most of the developed methods rely on the heuristic convergence of flux and current at the domain interfaces. Convergence was not attained in some cases. Mechanical stress computation community has also work on the DDM to solve the stress-strain equation using the finite element methods. The most successful domain decomposition method in terms of robustness is FETI-DP. We have modified the original FETI-DP to solve the eigenvalue problem for the multigroup diffusion problem in this study.
AMPX: a modular code system for generating coupled multigroup neutron-gamma libraries from ENDF/B
Energy Technology Data Exchange (ETDEWEB)
Greene, N.M.; Lucius, J.L.; Petrie, L.M.; Ford, W.E. III; White, J.E.; Wright, R.Q.
1976-03-01
AMPX is a modular system for producing coupled multigroup neutron-gamma cross section sets. Basic neutron and gamma cross-section data for AMPX are obtained from ENDF/B libraries. Most commonly used operations required to generate and collapse multigroup cross-section sets are provided in the system. AMPX is flexibly dimensioned; neutron group structures, and gamma group structures, and expansion orders to represent anisotropic processes are all arbitrary and limited only by available computer core and budget. The basic processes provided will (1) generate multigroup neutron cross sections; (2) generate multigroup gamma cross sections; (3) generate gamma yields for gamma-producing neutron interactions; (4) combine neutron cross sections, gamma cross sections, and gamma yields into final ''coupled sets''; (5) perform one-dimensional discrete ordinates transport or diffusion theory calculations for neutrons and gammas and, on option, collapse the cross sections to a broad-group structure, using the one-dimensional results as weighting functions; (6) plot cross sections, on option, to facilitate the ''evaluation'' of a particular multigroup set of data; (7) update and maintain multigroup cross section libraries in such a manner as to make it not only easy to combine new data with previously processed data but also to do it in a single pass on the computer; and (8) output multigroup cross sections in convenient formats for other codes. (auth)
FINELM: a multigroup finite element diffusion code
International Nuclear Information System (INIS)
Higgs, C.E.; Davierwalla, D.M.
1981-06-01
FINELM is a FORTRAN IV program to solve the Neutron Diffusion Equation in X-Y, R-Z, R-theta, X-Y-Z and R-theta-Z geometries using the method of Finite Elements. Lagrangian elements of linear or higher degree to approximate the spacial flux distribution have been provided. The method of dissections, coarse mesh rebalancing and Chebyshev acceleration techniques are available. Simple user defined input is achieved through extensive input subroutines. The input preparation is described followed by a program structure description. Sample test cases are provided. (Auth.)
Multi-level nonlinear diffusion acceleration method for multigroup transport k-Eigenvalue problems
International Nuclear Information System (INIS)
Anistratov, Dmitriy Y.
2011-01-01
The nonlinear diffusion acceleration (NDA) method is an efficient and flexible transport iterative scheme for solving reactor-physics problems. This paper presents a fast iterative algorithm for solving multigroup neutron transport eigenvalue problems in 1D slab geometry. The proposed method is defined by a multi-level system of equations that includes multigroup and effective one-group low-order NDA equations. The Eigenvalue is evaluated in the exact projected solution space of smallest dimensionality, namely, by solving the effective one- group eigenvalue transport problem. Numerical results that illustrate performance of the new algorithm are demonstrated. (author)
MCFT: a program for calculating fast and thermal neutron multigroup constants
International Nuclear Information System (INIS)
Yang Shunhai; Sang Xinzeng
1993-01-01
MCFT is a program for calculating the fast and thermal neutron multigroup constants, which is redesigned from some codes for generation of thermal neutron multigroup constants and for fast neutron multigroup constants adapted on CYBER 825 computer. It uses indifferently as basic input with the evaluated nuclear data contained in the ENDF/B (US), KEDAK (Germany) and UK (United Kingdom) libraries. The code includes a section devoted to the generation of resonant Doppler broadened cross section in the framework of single-or multi-level Breit-Wigner formalism. The program can compute the thermal neutron scattering law S (α, β, T) as the input data in tabular, free gas or diffusion motion form. It can treat up to 200 energy groups and Legendre moments up to P 5 . The output consists of various reaction multigroup constants in all neutron energy range desired in the nuclear reactor design and calculation. Three options in input file can be used by the user. The output format is arbitrary and defined by user with a minimum of program modification. The program includes about 15,000 cards and 184 subroutines. FORTRAN 5 computer language is used. The operation system is under NOS 2 on computer CYBER 825
International Nuclear Information System (INIS)
Si, S.
2012-01-01
The Universal Algorithm of Stiffness Confinement Method (UASCM) for neutron kinetics model of multi-dimensional and multi-group transport equations or diffusion equations has been developed. The numerical experiments based on transport theory code MGSNM and diffusion theory code MGNEM have demonstrated that the algorithm has sufficient accuracy and stability. (authors)
International Nuclear Information System (INIS)
Takeshi, Y.; Keisuke, K.
1983-01-01
The multigroup neutron diffusion equation for two-dimensional triangular geometry is solved by the finite Fourier transformation method. Using the zero-th-order equation of the integral equation derived by this method, simple algebraic expressions for the flux are derived and solved by the alternating direction implicit method. In sample calculations for a benchmark problem of a fast breeder reactor, it is shown that the present method gives good results with fewer mesh points than the usual finite difference method
Multigroup or multipoint thermal neutron data preparation. Programme SIGMA
International Nuclear Information System (INIS)
Matausek, M.V.; Kunc, M.
1974-01-01
When calculating the space energy distribution of thermal neutrons in reactor lattices, in either the multigroup or the multipoint approximation, it is convenient to divide the problem into two independent parts. Firstly, for all material regions of the given reactor lattice cell, the group or the point values of cross sections, scattering kernel and the outer source of thermal neutrons are calculated by a data preparation programme. These quantities are then used as input, by the programme which solves multigroup or multipoint transport equations, to generate the space energy neutron spectra in the cell considered and to determine the related integral quantities, namely the different reaction rates. The present report deals with the first part of the problem. An algorithm for constructing a set of thermal neutron input data, to be used with the multigroup or multipoint version of the code MULTI /1,2,3/, is presented and the new version of the programme SIGMA /4/, written in FORTRAN IV for the CDC-3600 computer, is described. For a given reactor cell material, composed of a number of different isotopes, this programme calculates the group or the point values of the scattering macroscopic absorption cross section, macroscopic scattering cross section, kernel and the outer source of thermal neutrons. Numerous options are foreseen in the programme, concerning the energy variation of cross sections and a scattering kernel, concerning the weighting spectrum in multigroup scheme or the procedure for constructing the scattering matrix in the multipoint scheme and, finally, concerning the organization of output. The details of the calculational algorithm are presented in Section 2 of the paper. Section 3 contains the description of the programme and the instructions for its use (author)
Energy Technology Data Exchange (ETDEWEB)
Petersen, Claudio Z. [Universidade Federal de Pelotas, Capao do Leao (Brazil). Programa de Pos Graduacao em Modelagem Matematica; Bodmann, Bardo E.J.; Vilhena, Marco T. [Universidade Federal do Rio Grande do Sul, Porto Alegre, RS (Brazil). Programa de Pos-graduacao em Engenharia Mecanica; Barros, Ricardo C. [Universidade do Estado do Rio de Janeiro, Nova Friburgo, RJ (Brazil). Inst. Politecnico
2014-12-15
In the present work we solve in analytical representation the three dimensional neutron kinetic diffusion problem in rectangular Cartesian geometry for homogeneous and bounded domains for any number of energy groups and precursor concentrations. The solution in analytical representation is constructed using a hierarchical procedure, i.e. the original problem is reduced to a problem previously solved by the authors making use of a combination of the spectral method and a recursive decomposition approach. Time dependent absorption cross sections of the thermal energy group are considered with step, ramp and Chebyshev polynomial variations. For these three cases, we present numerical results and discuss convergence properties and compare our results to those available in the literature.
Cassandre : a two-dimensional multigroup diffusion code for reactor transient analysis
International Nuclear Information System (INIS)
Arien, B.; Daniels, J.
1986-12-01
CASSANDRE is a two-dimensional (x-y or r-z) finite element neutronics code with thermohydraulics feedback for reactor dynamics prior to the disassembly phase. It uses the multigroup neutron diffusion theory. Its main characteristics are the use of a generalized quasistatic model, the use of a flexible multigroup point-kinetics algorithm allowing for spectral matching and the use of a finite element description. The code was conceived in order to be coupled with any thermohydraulics module, although thermohydraulics feedback is only considered in r-z geometry. In steady state criticality search is possible either by control rod insertion or by homogeneous poisoning of the coolant. This report describes the main characterstics of the code structure and provides all the information needed to use the code. (Author)
The isotope density inverse problem in multigroup neutron transport
International Nuclear Information System (INIS)
Zazula, J.M.
1981-01-01
The inverse problem for stationary multigroup anisotropic neutron transport is discussed in order to search for isotope densities in multielement medium. The spatial- and angular-integrated form of neutron transport equation, in terms of the flux in a group - density of an element spatial correlation, leads to a set of integral functionals for the densities weighted by the group fluxes. Some methods of approximation to make the problem uniquently solvable are proposed. Particularly P 0 angular flux information and the spherically-symetrical geometry of an infinite medium are considered. The numerical calculation using this method related to sooner evaluated direct problem data gives promising agreement with primary densities. This approach would be the basis for further application in an elemental analysis of a medium, using an isotopic neutron source and a moving, energy-dependent neutron detector. (author)
SNAP - a three dimensional neutron diffusion code
International Nuclear Information System (INIS)
McCallien, C.W.J.
1993-02-01
This report describes a one- two- three-dimensional multi-group diffusion code, SNAP, which is primarily intended for neutron diffusion calculations but can also carry out gamma calculations if the diffusion approximation is accurate enough. It is suitable for fast and thermal reactor core calculations and for shield calculations. SNAP can solve the multi-group neutron diffusion equations using finite difference methods. The one-dimensional slab, cylindrical and spherical geometries and the two-dimensional case are all treated as simple special cases of three-dimensional geometries. Numerous reflective and periodic symmetry options are available and may be used to reduce the number of mesh points necessary to represent the system. Extrapolation lengths can be specified at internal and external boundaries. (Author)
International Nuclear Information System (INIS)
Maleki Moghaddam, Nader; Afarideh, Hossein; Espinosa-Paredes, Gilberto
2015-01-01
Highlights: • The new version of neutron diffusion equation for simulating anomalous diffusion is presented. • Application of fractional calculus in the nuclear reactor is revealed. • A 3D-Multigroup program is developed based on the fractional operators. • The super-diffusion and sub-diffusion phenomena are modeled in the nuclear reactors core. - Abstract: The diffusion process is categorized in three parts, normal diffusion, super-diffusion and sub-diffusion. The classical neutron diffusion equation is used to model normal diffusion. A new scheme of derivatives is required to model anomalous diffusion phenomena. The fractional space derivatives are employed to model anomalous diffusion processes where a plume of particles spreads at an inconsistent rate with the classical Brownian motion model. In the fractional diffusion equation, the fractional Laplacians are used; therefore the statistical jump length of neutrons is unrestricted. It is clear that the fractional Laplacians are capable to model the anomalous phenomena in nuclear reactors. We have developed a NFDE-3D (neutron fractional diffusion equation) as a core calculation code to model normal and anomalous diffusion phenomena. The NFDE-3D is validated against the LMW-LWR reactor. The results demonstrate that reactors exhibit complex behavior versus order of the fractional derivatives which depends on the competition between neutron absorption and super-diffusion phenomenon
International Nuclear Information System (INIS)
Smith, L.A.; Gallmeier, F.X.; Gehin, J.C.
1995-05-01
The FOEHN critical experiment was analyzed to validate the use of multigroup cross sections and Oak Ridge National Laboratory neutronics computer codes in the design of the Advanced Neutron Source. The ANSL-V 99-group master cross section library was used for all the calculations. Three different critical configurations were evaluated using the multigroup KENO Monte Carlo transport code, the multigroup DORT discrete ordinates transport code, and the multigroup diffusion theory code VENTURE. The simple configuration consists of only the fuel and control elements with the heavy water reflector. The intermediate configuration includes boron endplates at the upper and lower edges of the fuel element. The complex configuration includes both the boron endplates and components in the reflector. Cross sections were processed using modules from the AMPX system. Both 99-group and 20-group cross sections were created and used in two-dimensional models of the FOEHN experiment. KENO calculations were performed using both 99-group and 20-group cross sections. The DORT and VENTURE calculations were performed using 20-group cross sections. Because the simple and intermediate configurations are azimuthally symmetric, these configurations can be explicitly modeled in R-Z geometry. Since the reflector components cannot be modeled explicitly using the current versions of these codes, three reflector component homogenization schemes were developed and evaluated for the complex configuration. Power density distributions were calculated with KENO using 99-group cross sections and with DORT and VENTURE using 20-group cross sections. The average differences between the measured values and the values calculated with the different computer codes range from 2.45 to 5.74%. The maximum differences between the measured and calculated thermal flux values for the simple and intermediate configurations are ∼ 13%, while the average differences are < 8%
International Nuclear Information System (INIS)
Santos, R.S. dos
1993-01-01
This paper presents a computational program to solve numerically the reactor kinetics equations in the multigroup diffusion theory. One or two-dimensional problems in cylindrical or Cartesian geometries, with any number of energy and delayed-neutron precursors groups are dealt with. The main input and output of the program are briefly discussed. Various results demonstrate the accuracy and versatility of the program, when compared with other kinetics programs. (author)
PHISICS multi-group transport neutronic capabilities for RELAP5
Energy Technology Data Exchange (ETDEWEB)
Epiney, A.; Rabiti, C.; Alfonsi, A.; Wang, Y.; Cogliati, J.; Strydom, G. [Idaho National Laboratory (INL), 2525 N. Fremont Ave., Idaho Falls, ID 83402 (United States)
2012-07-01
PHISICS is a neutronic code system currently under development at INL. Its goal is to provide state of the art simulation capability to reactor designers. This paper reports on the effort of coupling this package to the thermal hydraulic system code RELAP5. This will enable full prismatic core and system modeling and the possibility to model coupled (thermal-hydraulics and neutronics) problems with more options for 3D neutron kinetics, compared to the existing diffusion theory neutron kinetics module in RELAP5 (NESTLE). The paper describes the capabilities of the coupling and illustrates them with a set of sample problems. (authors)
Application of direct discrete method (DDM) to multigroup neutron transport problems
International Nuclear Information System (INIS)
Vosoughi, Naser; Salehi, Ali Akbar; Shahriari, Majid
2003-01-01
The Direct Discrete Method (DDM), which produced excellent results for one-group neutron transport problems, has been developed for multigroup energy. A multigroup neutron transport discrete equation has been produced for a cylindrical shape fuel element with and without associated coolant regions with two boundary conditions. The calculations are illustrated for two-group energy by graphs showing the fast and thermal fluxes. The validity of the results are tested against the results obtained by the ANISN code. (author)
FINELM: a multigroup finite element diffusion code. Part I
International Nuclear Information System (INIS)
Davierwalla, D.M.
1980-12-01
The author presents a two dimensional code for multigroup diffusion using the finite element method. It was realized that the extensive connectivity which contributes significantly to the accuracy, results in a matrix which, although symmetric and positive definite, is wide band and possesses an irregular profile. Hence, it was decided to introduce sparsity techniques into the code. The introduction of the R-Z geometry lead to a great deal of changes in the code since the rotational invariance of the removal matrices in X-Y geometry did not carry over in R-Z geometry. Rectangular elements were introduced to remedy the inability of the triangles to model essentially one dimensional problems such as slab geometry. The matter is discussed briefly in the text in the section on benchmark problems. This report is restricted to the general theory of the triangular elements and to the sparsity techniques viz. incomplete disections. The latter makes the size of the problem that can be handled independent of core memory and dependent only on disc storage capacity which is virtually unlimited. (Auth.)
Energy Technology Data Exchange (ETDEWEB)
Fletcher, J K
1973-05-01
CTD is a computer program written in Fortran 4 to solve the multi-group diffusion theory equations in X, Y, Z and triangular Z geometries. A power print- out neutron balance and breeding gain are also produced. 4 references. (auth)
LABAN-PEL: a two-dimensional, multigroup diffusion, high-order response matrix code
International Nuclear Information System (INIS)
Mueller, E.Z.
1991-06-01
The capabilities of LABAN-PEL is described. LABAN-PEL is a modified version of the two-dimensional, high-order response matrix code, LABAN, written by Lindahl. The new version extends the capabilities of the original code with regard to the treatment of neutron migration by including an option to utilize full group-to-group diffusion coefficient matrices. In addition, the code has been converted from single to double precision and the necessary routines added to activate its multigroup capability. The coding has also been converted to standard FORTRAN-77 to enhance the portability of the code. Details regarding the input data requirements and calculational options of LABAN-PEL are provided. 13 refs
The problem of resonance self-shielding effect in neutron multigroup calculations
International Nuclear Information System (INIS)
Wang Qingming; Huang Jinghua
1991-01-01
It is not allowed to neglect the resonance self-shielding effect in hybrid blanket and fast reactor neutron designs. The authors discussed the importance as well as the method of considering the resonance self-shielding effect in hybrid blanket and fast reactor neutron multigroup calculations
A multi-group neutron noise simulator for fast reactors
International Nuclear Information System (INIS)
Tran, Hoai Nam; Zylbersztejn, Florian; Demazière, Christophe; Jammes, Christian; Filliatre, Philippe
2013-01-01
Highlights: • The development of a neutron noise simulator for fast reactors. • The noise equation is solved fully in a frequency-domain. • A good agreement with ERANOS on the static calculations. • Noise calculations induced by a localized perturbation of absorption cross section. - Abstract: A neutron noise simulator has been developed for fast reactors based on diffusion theory with multi-energy groups and several groups of delayed neutron precursors. The tool is expected to be applicable for core monitoring of fast reactors and also for other reactor types with hexagonal fuel assemblies. The noise sources are modeled through small stationary fluctuations of macroscopic cross sections, and the induced first order noise is solved fully in the frequency domain. Numerical algorithms are implemented for solving both the static and noise equations using finite differences for spatial discretization, where a hexagonal assembly is radially divided into finer triangular meshes. A coarse mesh finite difference (CMFD) acceleration has been used for accelerating the convergence of both the static and noise calculations. Numerical calculations have been performed for the ESFR core with 33 energy groups and 8 groups of delayed neutron precursors using the cross section data generated by the ERANOS code. The results of the static state have been compared with those obtained using ERANOS. The results show an adequate agreement between the two calculations. Noise calculations for the ESFR core have also been performed and demonstrated with an assumption of the perturbation of the absorption cross section located at the central fuel ring
Proposal to extend CSEWG neutron and photon multigroup structures for wider applications
International Nuclear Information System (INIS)
LaBauve, R.J.; Wilson, W.B.
1976-02-01
The 239-group neutron multigroup structure recommended by the Codes and Formats Subcommittee of the cross section evaluation working group (CSEWG) for use in LMFBR design is not well suited for application in certain other areas, particularly thermal reactor design. This report describes a proposal for a neutron group structure consisting of 347 groups, which is an extension of the CSEWG group structure into the thermal range, and also includes more detail in other energy ranges important in LWR, HTGR, GCFR, and CTR design. Similarly, a proposed extension of the CSEWG 94-group photon multigroup structure to 103 groups is described. A subset of the neutron multigroup structure, consisting of 154 groups and for use in power reactor studies, is also presented
Proposal to extend CSEWG neutron and photon multigroup structures for wider applications. [Tables
Energy Technology Data Exchange (ETDEWEB)
LaBauve, R.J.; Wilson, W.B.
1976-02-01
The 239-group neutron multigroup structure recommended by the Codes and Formats Subcommittee of the cross section evaluation working group (CSEWG) for use in LMFBR design is not well suited for application in certain other areas, particularly thermal reactor design. This report describes a proposal for a neutron group structure consisting of 347 groups, which is an extension of the CSEWG group structure into the thermal range, and also includes more detail in other energy ranges important in LWR, HTGR, GCFR, and CTR design. Similarly, a proposed extension of the CSEWG 94-group photon multigroup structure to 103 groups is described. A subset of the neutron multigroup structure, consisting of 154 groups and for use in power reactor studies, is also presented.
Energy Technology Data Exchange (ETDEWEB)
Bayard, J P; Guillou, A; Lago, B; Bureau du Colombier, M J; Guillou, G; Vasseur, Ch [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires
1965-02-01
This report describes the specifications of the ALCI programme. This programme resolves the system of difference equations similar to the homogeneous problem of multigroup neutron scattering, with two dimensions in space, in the three geometries XY, RZ, R{theta}. It is possible with this method to calculate geometric and composition criticalities and also to calculate the accessory problem on demand. The maximum number of points dealt with is 6000. The maximum permissible number of groups is 12. The internal iterations are treated by the method of alternating directions. The external iterations are accelerated using the extrapolation method due to Tchebychev. (authors) [French] Ce rapport decrit les specifications du programme ALCI. Ce programme resout le systeme d'equations aux differences approchant le probleme homogene de la diffusion neutronique multigroupe, a deux dimensions d'espace, dans les trois geometries XY, RZ, R{theta}. Il permet des calculs de criticalite geometrique et de composition et calcule sur demande le probleme adjoint. Le nombre maximum de points traites est de 6000. Le nombre maximum de groupes permis est de 12. Les iterations interieure sont traitees par la methode des directions alternees. Les iterations exterieures sont accelerees par la methode d'extrapolation de Tchebychev. (auteurs)
An accurate solution of point reactor neutron kinetics equations of multi-group of delayed neutrons
International Nuclear Information System (INIS)
Yamoah, S.; Akaho, E.H.K.; Nyarko, B.J.B.
2013-01-01
Highlights: ► Analytical solution is proposed to solve the point reactor kinetics equations (PRKE). ► The method is based on formulating a coefficient matrix of the PRKE. ► The method was applied to solve the PRKE for six groups of delayed neutrons. ► Results shows good agreement with other traditional methods in literature. ► The method is accurate and efficient for solving the point reactor kinetics equations. - Abstract: The understanding of the time-dependent behaviour of the neutron population in a nuclear reactor in response to either a planned or unplanned change in the reactor conditions is of great importance to the safe and reliable operation of the reactor. In this study, an accurate analytical solution of point reactor kinetics equations with multi-group of delayed neutrons for specified reactivity changes is proposed to calculate the change in neutron density. The method is based on formulating a coefficient matrix of the homogenous differential equations of the point reactor kinetics equations and calculating the eigenvalues and the corresponding eigenvectors of the coefficient matrix. A small time interval is chosen within which reactivity relatively stays constant. The analytical method was applied to solve the point reactor kinetics equations with six-groups delayed neutrons for a representative thermal reactor. The problems of step, ramp and temperature feedback reactivities are computed and the results compared with other traditional methods. The comparison shows that the method presented in this study is accurate and efficient for solving the point reactor kinetics equations of multi-group of delayed neutrons
International Nuclear Information System (INIS)
Smith, L.A.; Gehin, J.C.; Worley, B.A.; Renier, J.P.
1994-01-01
The FOEHN critical experiments were analyzed to validate the use of multigroup cross sections in the design of the Advanced Neutron Source. Eleven critical configurations were evaluated using the KENO, DORT, and VENTURE neutronics codes. Eigenvalue and power density profiles were computed and show very good agreement with measured values
International Nuclear Information System (INIS)
Jones, D.B.
1986-01-01
EPRI-LATTICE is a multigroup neutron transport computer code for the analysis of light water reactor fuel assemblies. It can solve the two-dimensional neutron transport problem by two distinct methods: (a) the method of collision probabilities and (b) the method of discrete ordinates. The code was developed by S. Levy Inc. as an account of work sponsored by the Electric Power Research Institute (EPRI). The collision probabilities calculation in EPRI-LATTICE (L-CP) is based on the same methodology that exists in the lattice codes CPM-2 and EPRI-CPM. Certain extensions have been made to the data representations of the CPM programs to improve the overall accuracy of the calculation. The important extensions include unique representations of scattering matrices and fission fractions (chi) for each composition in the problem. A new capability specifically developed for the EPRI-LATTICE code is a discrete ordinates methodology. The discrete ordinates calculation in EPRI-LATTICE (L-SN) is based on the discrete S/sub n/ methodology that exists in the TWODANT program. In contrast to TWODANT, which utilizes synthetic diffusion acceleration and supports multiple geometries, only the transport equations are solved by L-SN and only the data representations for the two-dimensional geometry are treated
MC2-2: a code to calculate fast neutron spectra and multigroup cross sections
International Nuclear Information System (INIS)
Henryson, H. II; Toppel, B.J.; Stenberg, C.G.
1976-06-01
MC 2 -2 is a program to solve the neutron slowing down problem using basic neutron data derived from the ENDF/B data files. The spectrum calculated by MC 2 -2 is used to collapse the basic data to multigroup cross sections for use in standard reactor neutronics codes. Four different slowing down formulations are used by MC 2 -2: multigroup, continuous slowing down using the Goertzel-Greuling or Improved Goertzel-Greuling moderating parameters, and a hyper-fine-group integral transport calculation. Resolved and unresolved resonance cross sections are calculated accounting for self-shielding, broadening and overlap effects. This document provides a description of the MC 2 -2 program. The physics and mathematics of the neutron slowing down problem are derived and detailed information is provided to aid the MC 2 -2 user in preparing input for the program and implementation of the program on IBM 370 or CDC 7600 computers
On efficiently computing multigroup multi-layer neutron reflection and transmission conditions
International Nuclear Information System (INIS)
Abreu, Marcos P. de
2007-01-01
In this article, we present an algorithm for efficient computation of multigroup discrete ordinates neutron reflection and transmission conditions, which replace a multi-layered boundary region in neutron multiplication eigenvalue computations with no spatial truncation error. In contrast to the independent layer-by-layer algorithm considered thus far in our computations, the algorithm here is based on an inductive approach developed by the present author for deriving neutron reflection and transmission conditions for a nonactive boundary region with an arbitrary number of arbitrarily thick layers. With this new algorithm, we were able to increase significantly the computational efficiency of our spectral diamond-spectral Green's function method for solving multigroup neutron multiplication eigenvalue problems with multi-layered boundary regions. We provide comparative results for a two-group reactor core model to illustrate the increased efficiency of our spectral method, and we conclude this article with a number of general remarks. (author)
Diffuse scattering of neutrons
International Nuclear Information System (INIS)
Novion, C.H. de.
1981-02-01
The use of neutron scattering to study atomic disorder in metals and alloys is described. The diffuse elastic scattering of neutrons by a perfect crystal lattice leads to a diffraction spectrum with only Bragg spreads. the existence of disorder in the crystal results in intensity and position modifications to these spreads, and above all, to the appearance of a low intensity scatter between Bragg peaks. The elastic scattering of neutrons is treated in this text, i.e. by measuring the number of scattered neutrons having the same energy as the incident neutrons. Such measurements yield information on the static disorder in the crystal and time average fluctuations in composition and atomic displacements [fr
A multilevel in space and energy solver for multigroup diffusion eigenvalue problems
Directory of Open Access Journals (Sweden)
Ben C. Yee
2017-09-01
Full Text Available In this paper, we present a new multilevel in space and energy diffusion (MSED method for solving multigroup diffusion eigenvalue problems. The MSED method can be described as a PI scheme with three additional features: (1 a grey (one-group diffusion equation used to efficiently converge the fission source and eigenvalue, (2 a space-dependent Wielandt shift technique used to reduce the number of PIs required, and (3 a multigrid-in-space linear solver for the linear solves required by each PI step. In MSED, the convergence of the solution of the multigroup diffusion eigenvalue problem is accelerated by performing work on lower-order equations with only one group and/or coarser spatial grids. Results from several Fourier analyses and a one-dimensional test code are provided to verify the efficiency of the MSED method and to justify the incorporation of the grey diffusion equation and the multigrid linear solver. These results highlight the potential efficiency of the MSED method as a solver for multidimensional multigroup diffusion eigenvalue problems, and they serve as a proof of principle for future work. Our ultimate goal is to implement the MSED method as an efficient solver for the two-dimensional/three-dimensional coarse mesh finite difference diffusion system in the Michigan parallel characteristics transport code. The work in this paper represents a necessary step towards that goal.
Research on GPU-accelerated algorithm in 3D finite difference neutron diffusion calculation method
International Nuclear Information System (INIS)
Xu Qi; Yu Ganglin; Wang Kan; Sun Jialong
2014-01-01
In this paper, the adaptability of the neutron diffusion numerical algorithm on GPUs was studied, and a GPU-accelerated multi-group 3D neutron diffusion code based on finite difference method was developed. The IAEA 3D PWR benchmark problem was calculated in the numerical test. The results demonstrate both high efficiency and adequate accuracy of the GPU implementation for neutron diffusion equation. (authors)
International Nuclear Information System (INIS)
Alsmiller, R.G. Jr.; Barnes, J.M.; Drischler, J.D.
1986-01-01
For a variety of applications, e.g., accelerator shielding design, neutrons in radiotherapy, radiation damage studies, etc., it is necessary to carry out transport calculations involving medium-energy (greater than or equal to20 MeV) neutrons. A previous paper described neutron-photon multigroup cross sections in the ANISN format for neutrons from thermal to 400 MeV. In the present paper the cross-section data presented previously have been revised to make them agree with available experimental data. 7 refs., 1 fig
Second order time evolution of the multigroup diffusion and P1 equations for radiation transport
International Nuclear Information System (INIS)
Olson, Gordon L.
2011-01-01
Highlights: → An existing multigroup transport algorithm is extended to be second-order in time. → A new algorithm is presented that does not require a grey acceleration solution. → The two algorithms are tested with 2D, multi-material problems. → The two algorithms have comparable computational requirements. - Abstract: An existing solution method for solving the multigroup radiation equations, linear multifrequency-grey acceleration, is here extended to be second order in time. This method works for simple diffusion and for flux-limited diffusion, with or without material conduction. A new method is developed that does not require the solution of an averaged grey transport equation. It is effective solving both the diffusion and P 1 forms of the transport equation. Two dimensional, multi-material test problems are used to compare the solution methods.
Multi-group transport methods for high-resolution neutron activation analysis
International Nuclear Information System (INIS)
Burns, K. A.; Smith, L. E.; Gesh, C. J.; Shaver, M. W.
2009-01-01
The accurate and efficient simulation of coupled neutron-photon problems is necessary for several important radiation detection applications. Examples include the detection of nuclear threats concealed in cargo containers and prompt gamma neutron activation analysis for nondestructive determination of elemental composition of unknown samples. In these applications, high-resolution gamma-ray spectrometers are used to preserve as much information as possible about the emitted photon flux, which consists of both continuum and characteristic gamma rays with discrete energies. Monte Carlo transport is the most commonly used modeling tool for this type of problem, but computational times for many problems can be prohibitive. This work explores the use of multi-group deterministic methods for the simulation of neutron activation problems. Central to this work is the development of a method for generating multi-group neutron-photon cross-sections in a way that separates the discrete and continuum photon emissions so that the key signatures in neutron activation analysis (i.e., the characteristic line energies) are preserved. The mechanics of the cross-section preparation method are described and contrasted with standard neutron-gamma cross-section sets. These custom cross-sections are then applied to several benchmark problems. Multi-group results for neutron and photon flux are compared to MCNP results. Finally, calculated responses of high-resolution spectrometers are compared. Preliminary findings show promising results when compared to MCNP. A detailed discussion of the potential benefits and shortcomings of the multi-group-based approach, in terms of accuracy, and computational efficiency, is provided. (authors)
International Nuclear Information System (INIS)
Kelsey IV, Charles T.; Prinja, Anil K.
2011-01-01
We evaluate the Monte Carlo calculation efficiency for multigroup transport relative to continuous energy transport using the MCNPX code system to evaluate secondary neutron doses from a proton beam. We consider both fully forward simulation and application of a midway forward adjoint coupling method to the problem. Previously we developed tools for building coupled multigroup proton/neutron cross section libraries and showed consistent results for continuous energy and multigroup proton/neutron transport calculations. We observed that forward multigroup transport could be more efficient than continuous energy. Here we quantify solution efficiency differences for a secondary radiation dose problem characteristic of proton beam therapy problems. We begin by comparing figures of merit for forward multigroup and continuous energy MCNPX transport and find that multigroup is 30 times more efficient. Next we evaluate efficiency gains for coupling out-of-beam adjoint solutions with forward in-beam solutions. We use a variation of a midway forward-adjoint coupling method developed by others for neutral particle transport. Our implementation makes use of the surface source feature in MCNPX and we use spherical harmonic expansions for coupling in angle rather than solid angle binning. The adjoint out-of-beam transport for organs of concern in a phantom or patient can be coupled with numerous forward, continuous energy or multigroup, in-beam perturbations of a therapy beam line configuration. Out-of-beam dose solutions are provided without repeating out-of-beam transport. (author)
Solution for the multigroup neutron space kinetics equations by the modified Picard algorithm
Energy Technology Data Exchange (ETDEWEB)
Tavares, Matheus G.; Petersen, Claudio Z., E-mail: matheus.gulartetavares@gmail.com [Universidade Federal de Pelotas (UFPEL), Capao do Leao, RS (Brazil). Departamento de Matematica e Estatistica; Schramm, Marcelo, E-mail: schrammmarcelo@gmail.com [Universidade Federal de Pelotas (UFPEL), RS (Brazil). Centro de Engenharias; Zanette, Rodrigo, E-mail: rodrigozanette@hotmail.com [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Instituto de Matematica e Estatistica
2017-07-01
In this work, we used a modified Picards method to solve the Multigroup Neutron Space Kinetics Equations (MNSKE) in Cartesian geometry. The method consists in assuming an initial guess for the neutron flux and using it to calculate a fictitious source term in the MNSKE. A new source term is calculated applying its solution, and so on, iteratively, until a stop criterion is satisfied. For the solution of the fast and thermal neutron fluxes equations, the Laplace Transform technique is used in time variable resulting in a rst order linear differential matrix equation, which are solved by classical methods in the literature. After each iteration, the scalar neutron flux and the delayed neutron precursors are reconstructed by polynomial interpolation. We obtain the fluxes and precursors through Numerical Inverse Laplace Transform using the Stehfest method. We present numerical simulations and comparisons with available results in literature. (author)
Solution for the multigroup neutron space kinetics equations by the modified Picard algorithm
International Nuclear Information System (INIS)
Tavares, Matheus G.; Petersen, Claudio Z.; Schramm, Marcelo; Zanette, Rodrigo
2017-01-01
In this work, we used a modified Picards method to solve the Multigroup Neutron Space Kinetics Equations (MNSKE) in Cartesian geometry. The method consists in assuming an initial guess for the neutron flux and using it to calculate a fictitious source term in the MNSKE. A new source term is calculated applying its solution, and so on, iteratively, until a stop criterion is satisfied. For the solution of the fast and thermal neutron fluxes equations, the Laplace Transform technique is used in time variable resulting in a rst order linear differential matrix equation, which are solved by classical methods in the literature. After each iteration, the scalar neutron flux and the delayed neutron precursors are reconstructed by polynomial interpolation. We obtain the fluxes and precursors through Numerical Inverse Laplace Transform using the Stehfest method. We present numerical simulations and comparisons with available results in literature. (author)
International Nuclear Information System (INIS)
Erradi, L.; Karouani, K.
1994-01-01
Many multigroup neutron cross section libraries have been processed from basic evaluated nuclear data for use in neutron dosimetry, reactor shielding calculation and in the development of fusion reactors. Most of these libraries have been tested only for fission spectra and were not validated for fusion spectra. Fifteen of these libraries such as DOSCROS84, IRDF85 and ENDFB5 have been used along with the neutron spectra unfolding code SAND II to evaluate about fifteen threshold detector saturated activities. The comparison between these computed activities and the measured ones of a set of foils placed in different places along the axis of a paraffin cylinder and irradiated by 14 MeV neutrons generated by a D-T source, hence giving rise to complex spectra, leads to different types of discrepancies. The analysis of these discrepancies allows to select from these libraries the ones that can be recommended. 1 fig., 4 refs. (author)
Depletion Calculations for MTR Core Using MCNPX and Multi-Group Nodal Diffusion Methods
International Nuclear Information System (INIS)
Jaradata, Mustafa K.; Park, Chang Je; Lee, Byungchul
2013-01-01
In order to maintain a self-sustaining steady-state chain reaction, more fuel than is necessary in order to maintain a steady state chain reaction must be loaded. The introduction of this excess fuel increases the net multiplication capability of the system. In this paper MCNPX and multi-group nodal diffusion theory will be used for depletion calculations for MTR core. The eigenvalue and power distribution in the core will be compared for different burnup. Multi-group nodal diffusion theory with combination of NEWT-TRITON system was used to perform depletion calculations for 3Χ3 MTR core. 2G and 6G approximations were used and compared with MCNPX results for 2G approximation the maximum difference from MCNPX was 40 mk and for 6G approximation was 6 mk which is comparable to the MCNPX results. The calculated power using nodal code was almost the same MCNPX results. Finally the results of the multi-group nodal theory were acceptable and comparable to the calculated using MCNPX
The magnetic diffusion of neutrons; La diffusion magnetique des neutrons
Energy Technology Data Exchange (ETDEWEB)
Koehler, W C [Commissariat a l' Energie Atomique, Saclay (France).Centre d' Etudes Nucleaires
1959-07-01
The purpose of this report is to examine briefly the diffusion of neutrons by substances, particularly by crystals containing permanent atomic or ionic magnetic moments. In other words we shall deal with ferromagnetic, antiferromagnetic, ferrimagnetic or paramagnetic crystals, but first it is necessary to touch on nuclear diffusion of neutrons. We shall start with the interaction of the neutron with a single diffusion centre; the results will then be applied to the magnetic interactions of the neutron with the satellite electrons of the atom; finally we shall discuss the diffusion of neutrons by crystals. (author) [French] Le but de ce rapport est d'examiner, brievement, la diffusion des neutrons par les substances, et surtout, par des cristaux qui contiennent des moments magnetiques atomiques ou ioniques permanents. C'est-a-dire que nous nous interesserons aux cristaux ferromagnetiques, antiferromagnetiques, ferrimagnetiques ou paramagnetiques; il nous faut cependant rappeler d'abord la diffusion nucleaire des neutrons. Nous commencerons par l'interaction du neutron avec un seul centre diffuseur; puis les resultats seront appliques aux interactions magnetiques du neutron avec les electrons satellites de l'atome; enfin nous discuterons la diffusion des neutrons par les cristaux. (auteur)
International Nuclear Information System (INIS)
Alsmiller, R.G. Jr.; Barnes, J.M.; Drischler, J.D.
1986-02-01
Multigroup cross sections (66 neutron groups and 22 photon groups) are described for neutron energies from thermal to 400 MeV. The elements considered are hydrogen, 10 B, 11 B, carbon, nitrogen, oxygen, sodium, magnesium, aluminum, silicon, sulfur, potassium, calcium, chromium, iron, nickel, tungsten, and lead. The cross section data presented are a revision of similar data presented previously. In the case of iron, transport calculations using the earlier and the revised cross sections are presented and compared, and significant differences are found. The revised cross sections are available from the Radiation Shielding information Center of the Oak Ridge National Laboratory. 32 refs., 5 figs., 3 tabs
Interface discontinuity factors in the modal Eigenspace of the multigroup diffusion matrix
International Nuclear Information System (INIS)
Garcia-Herranz, N.; Herrero, J.J.; Cuervo, D.; Ahnert, C.
2011-01-01
Interface discontinuity factors based on the Generalized Equivalence Theory are commonly used in nodal homogenized diffusion calculations so that diffusion average values approximate heterogeneous higher order solutions. In this paper, an additional form of interface correction factors is presented in the frame of the Analytic Coarse Mesh Finite Difference Method (ACMFD), based on a correction of the modal fluxes instead of the physical fluxes. In the ACMFD formulation, implemented in COBAYA3 code, the coupled multigroup diffusion equations inside a homogenized region are reduced to a set of uncoupled modal equations through diagonalization of the multigroup diffusion matrix. Then, physical fluxes are transformed into modal fluxes in the Eigenspace of the diffusion matrix. It is possible to introduce interface flux discontinuity jumps as the difference of heterogeneous and homogeneous modal fluxes instead of introducing interface discontinuity factors as the ratio of heterogeneous and homogeneous physical fluxes. The formulation in the modal space has been implemented in COBAYA3 code and assessed by comparison with solutions using classical interface discontinuity factors in the physical space. (author)
Analysis of coupled neutron-gamma radiations, applied to shieldings in multigroup albedo method
International Nuclear Information System (INIS)
Dunley, Leonardo Souza
2002-01-01
The principal mathematical tools frequently available for calculations in Nuclear Engineering, including coupled neutron-gamma radiations shielding problems, involve the full Transport Theory or the Monte Carlo techniques. The Multigroup Albedo Method applied to shieldings is characterized by following the radiations through distinct layers of materials, allowing the determination of the neutron and gamma fractions reflected from, transmitted through and absorbed in the irradiated media when a neutronic stream hits the first layer of material, independently of flux calculations. Then, the method is a complementary tool of great didactic value due to its clarity and simplicity in solving neutron and/or gamma shielding problems. The outstanding results achieved in previous works motivated the elaboration and the development of this study that is presented in this dissertation. The radiation balance resulting from the incidence of a neutronic stream into a shielding composed by 'm' non-multiplying slab layers for neutrons was determined by the Albedo method, considering 'n' energy groups for neutrons and 'g' energy groups for gammas. It was taken into account there is no upscattering of neutrons and gammas. However, it was considered that neutrons from any energy groups are able to produce gammas of all energy groups. The ANISN code, for an angular quadrature order S 2 , was used as a standard for comparison of the results obtained by the Albedo method. So, it was necessary to choose an identical system configuration, both for ANISN and Albedo methods. This configuration was six neutron energy groups and eight gamma energy groups, using three slab layers (iron aluminum - manganese). The excellent results expressed in comparative tables show great agreement between the values determined by the deterministic code adopted as standard and, the values determined by the computational program created using the Albedo method and the algorithm developed for coupled neutron
Simulate-HEX - The multi-group diffusion equation in hexagonal-z geometry
International Nuclear Information System (INIS)
Lindahl, S. O.
2013-01-01
The multigroup diffusion equation is solved for the hexagonal-z geometry by dividing each hexagon into 6 triangles. In each triangle, the Fourier solution of the wave equation is approximated by 8 plane waves to describe the intra-nodal flux accurately. In the end an efficient Finite Difference like equation is obtained. The coefficients of this equation depend on the flux solution itself and they are updated once per power/void iteration. A numerical example demonstrates the high accuracy of the method. (authors)
A self-consistent nodal method in response matrix formalism for the multigroup diffusion equations
International Nuclear Information System (INIS)
Malambu, E.M.; Mund, E.H.
1996-01-01
We develop a nodal method for the multigroup diffusion equations, based on the transverse integration procedure (TIP). The efficiency of the method rests upon the convergence properties of a high-order multidimensional nodal expansion and upon numerical implementation aspects. The discrete 1D equations are cast in response matrix formalism. The derivation of the transverse leakage moments is self-consistent i.e. does not require additional assumptions. An outstanding feature of the method lies in the linear spatial shape of the local transverse leakage for the first-order scheme. The method is described in the two-dimensional case. The method is validated on some classical benchmark problems. (author)
International Nuclear Information System (INIS)
Schriewer, J.; Hehn, G.; Mattes, M.; Pfister, G.; Keinert, J.
1978-01-01
Calculations were made for different benchmark experiments in order to test the coupled multigroup neutron and gamma library EURLIB-3 with 100 neutron groups and 20 gamma groups. In cooperation with EURATOM, Ispra, we produced this shielding library recently from ENDF/B-IV data for application in fission and fusion technology. Integral checks were performed for natural lithium, carbon, oxygen, and iron. Since iron is the most important structural material in nuclear technology, we started with calculations of iron benchmark experiments. Most of them are integral experiments of INR, Karlsruhe, but comparisons were also done with benchmark experiments from USA and Japan. For the experiments with fission sources we got satisfying results. All details of the resonances cannot be checked with flux measurements and multigroup cross sections used. But some averaged resonance behaviour of the measured and calculated fluxes can be compared and checked within the error limits given. We get greater differences in the calculations of benchmark experiments with 14 MeV neutron sources. For iron the group cross sections of EURLIB-3 produce an underestimation of the neutron flux in a broad energy region below the source energy. The conclusion is that the energy degradation by inelastic scattering is too strong. For fusion application the anisotropy of the inelastic scatter process must be taken into account, which isn't done by the processing codes at present. If this effect isn't enough, additional corrections have to be applied to the inelastic cross sections of iron in ENDF/B-IV. (author)
Huang diffuse scattering of neutrons
International Nuclear Information System (INIS)
Burkel, E.; Guerard, B. v.; Metzger, H.; Peisl, J.
1979-01-01
Huang diffuse neutron scattering was measured for the first time on niobium with interstitially dissolved deuterium as well as on MgO after neutron irradiation and Li 7 F after γ-irradiation. With Huang diffuse scattering the strength and symmetry of the distortion field around lattice defects can be determined. Our results clearly demonstrate that this method is feasible with neutrons. The present results are compared with X-ray experiments and the advantages of using neutrons is discussed in some detail. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Matausek, M V [Boris Kidric Institute of Nuclear Sciences Vinca, Beograd (Yugoslavia)
1968-06-15
Programme MULTI calculates the space energy distribution of thermal neutrons in a multizone, cylindrical, infinitely long reactor lattice by using the multigroup or multipoint P{sub 3} approximation. This report presents a short description of the algorithm and the programme and gives the instructions for its exploitation. (author)
Single Crystal Diffuse Neutron Scattering
Directory of Open Access Journals (Sweden)
Richard Welberry
2018-01-01
Full Text Available Diffuse neutron scattering has become a valuable tool for investigating local structure in materials ranging from organic molecular crystals containing only light atoms to piezo-ceramics that frequently contain heavy elements. Although neutron sources will never be able to compete with X-rays in terms of the available flux the special properties of neutrons, viz. the ability to explore inelastic scattering events, the fact that scattering lengths do not vary systematically with atomic number and their ability to scatter from magnetic moments, provides strong motivation for developing neutron diffuse scattering methods. In this paper, we compare three different instruments that have been used by us to collect neutron diffuse scattering data. Two of these are on a spallation source and one on a reactor source.
Energy Technology Data Exchange (ETDEWEB)
Lillie, R.A.; Robinson, J.C.
1976-05-01
The discrete ordinates method is the most powerful and generally used deterministic method to obtain approximate solutions of the Boltzmann transport equation. A finite element formulation, utilizing a canonical form of the transport equation, is here developed to obtain both integral and pointwise solutions to neutron transport problems. The formulation is based on the use of linear triangles. A general treatment of anisotropic scattering is included by employing discrete ordinates-like approximations. In addition, multigroup source outer iteration techniques are employed to perform group-dependent calculations. The ability of the formulation to reduce substantially ray effects and its ability to perform streaming calculations are demonstrated by analyzing a series of test problems. The anisotropic scattering and multigroup treatments used in the development of the formulation are verified by a number of one-dimensional comparisons. These comparisons also demonstrate the relative accuracy of the formulation in predicting integral parameters. The applicability of the formulation to nonorthogonal planar geometries is demonstrated by analyzing a hexagonal-type lattice. A small, high-leakage reactor model is analyzed to investigate the effects of varying both the spatial mesh and order of angular quadrature. This analysis reveals that these effects are more pronounced in the present formulation than in other conventional formulations. However, the insignificance of these effects is demonstrated by analyzing a realistic reactor configuration. In addition, this final analysis illustrates the importance of incorporating anisotropic scattering into the finite element formulation. 8 tables, 29 figures.
International Nuclear Information System (INIS)
Lillie, R.A.; Robinson, J.C.
1976-05-01
The discrete ordinates method is the most powerful and generally used deterministic method to obtain approximate solutions of the Boltzmann transport equation. A finite element formulation, utilizing a canonical form of the transport equation, is here developed to obtain both integral and pointwise solutions to neutron transport problems. The formulation is based on the use of linear triangles. A general treatment of anisotropic scattering is included by employing discrete ordinates-like approximations. In addition, multigroup source outer iteration techniques are employed to perform group-dependent calculations. The ability of the formulation to reduce substantially ray effects and its ability to perform streaming calculations are demonstrated by analyzing a series of test problems. The anisotropic scattering and multigroup treatments used in the development of the formulation are verified by a number of one-dimensional comparisons. These comparisons also demonstrate the relative accuracy of the formulation in predicting integral parameters. The applicability of the formulation to nonorthogonal planar geometries is demonstrated by analyzing a hexagonal-type lattice. A small, high-leakage reactor model is analyzed to investigate the effects of varying both the spatial mesh and order of angular quadrature. This analysis reveals that these effects are more pronounced in the present formulation than in other conventional formulations. However, the insignificance of these effects is demonstrated by analyzing a realistic reactor configuration. In addition, this final analysis illustrates the importance of incorporating anisotropic scattering into the finite element formulation. 8 tables, 29 figures
Energy Technology Data Exchange (ETDEWEB)
Bore, C; Dandeu, Y; Saint-Amand, Ch [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires
1965-07-01
MUDE is a nuclear code written in FORTRAN II for IBM 7090-7094. It resolves a system of difference equations approximating to the one-dimensional multigroup neutron scattering problem. More precisely, this code makes it possible to: 1. Calculate the critical condition of a reactor (k{sub eff}, critical radius, critical composition) and the corresponding fluxes; 2. Calculate the associated fluxes and various subsidiary results; 3. Carry out perturbation calculations; 4. Study the propagation of fluxes at a distance; 5. Estimate the relative contributions of the cross sections (macroscopic or microscopic); 6. Study the changes with time of the composition of the reactor. (authors) [French] MUDE est un code nucleaire ecrit en FORTRAN II pour IBM 7090-7094. Il resout un systeme d'equations aux differences approchant le probleme de diffusion neutronique multigroupe a une dimension. Plus precisement ce code permet de: 1. Calculer la condition critique d'un reacteur (k{sub eff}, rayon critique, composition critique) et les flux correspondants; 2. Calculer les flux adjoints et divers resultats connexes; 3. Effectuer des calculs de perturbation; 4. Etudier la propagation des flux a longue distance; 5. Ponderer des sections efficaces (macroscopiques ou microscopiques); 6. Etudier l'evolution de la composition du reacteur au cours du temps. (auteurs)
Spectrum of the multigroup neutron transport operator for bounded spatial domains
International Nuclear Information System (INIS)
Larsen, E.W.
1979-01-01
The spectrum of the multigroup neutron transport operator A is studied for bounded spatial regions D which consist of a finite number of material subregions. Our main results provide simple conditions on the material cross sections which guarantee that (1) A possesses eigenvalues in the finite plane; (2) A possesses a ''leading'' eigenvalue lambda 0 which is real, not less than the real part of any other eigenvalue, and to which there corresponds at least one nonnegative eigenfunction psi/sub lambda/0; and (3) A possesses a ''dominant'' eigenvalue lambda 0 which is real, simple, greater than the real part of any other eigenvalue, and whose eigenfunction psi/sub lambda/0 satisfies psi/sub lambda/0> or =0 and ∫psi/sub lambda/0d 2 Ω>0. We give examples to illustrate the results and to show that a leading eigenvalue need not be simple, nor its eigenfunction(s) positive
The solution of the multigroup neutron transport equation using spherical harmonics
International Nuclear Information System (INIS)
Fletcher, K.
1981-01-01
A solution of the multi-group neutron transport equation in up to three space dimensions is presented. The flux is expanded in a series of unnormalised spherical harmonics. Using the various recurrence formulae a linked set of first order differential equations is obtained for the moments psisup(g)sub(lm)(r), γsup(g)sub(lm)(r). Terms with odd l are eliminated resulting in a second order system which is solved by two methods. The first is a finite difference formulation using an iterative procedure, secondly, in XYZ and XY geometry a finite element solution is given. Results for a test problem using both methods are exhibited and compared. (orig./RW) [de
Neutron-photon multigroup cross sections for neutron energies up to 400 MeV: HILO86R
International Nuclear Information System (INIS)
Kotegawa, Hiroshi; Nakane, Yoshihiro; Hasegawa, Akira; Tanaka, Shun-ichi
1993-02-01
A macroscopic multigroup cross section library of 66 neutron and 22 photon groups for neutron energies up to 400 MeV: HILO86R is prepared for 10 typical shielding materials; water, concrete, iron, air, graphite, polyethylene, heavy concrete, lead, aluminum and soil. The library is a revision of the DLC-119/HILO86, in which only the cross sections below 19.6 MeV have been exchanged with a group cross section processed from the JENDL-3 microscopic cross section library. In the HILO86R library, self shielding factors are used to produce effective cross sections for neutrons less than 19.6 MeV considering rather coarse energy meshes. Energy spectra and dose attenuation in water, concrete and iron have been compared among the HILO, HILO86 and HILO86R libraries for different energy neutron sources. Significant discrepancy has been observed in the energy spectra less than a couple of MeV energy in iron among the libraries, resulting large difference in the dose attenuation. The difference was attributed to the effect of self-shielding factor, namely to the difference between infinite dilution and effective cross sections. Even for 400 MeV neutron source the influence of the self-shielding factor is significant, nevertheless only the cross sections below 19.6 MeV are exchanged. (author)
Solution of the Multigroup-Diffusion equation by the response matrix method
International Nuclear Information System (INIS)
Oliveira, C.R.E.
1980-10-01
A preliminary analysis of the response matrix method is made, considering its application to the solution of the multigroup diffusion equations. The one-dimensional formulation is presented and used to test some flux expansions, seeking the application of the method to the two-dimensional problem. This formulation also solves the equations that arise from the integro-differential synthesis algorithm. The slow convergence of the power method, used to solve the eigenvalue problem, and its acceleration by means of the Chebyshev polynomial method, are also studied. An algorithm for the estimation of the dominance ratio is presented, based on the residues of two successive iteration vectors. This ratio, which is not known a priori, is fundamental for the efficiency of the method. Some numerical problems are solved, testing the 1D formulation of the response matrix method, its application to the synthesis algorithm and also, at the same time, the algorithm to accelerate the source problem. (Author) [pt
The Nodal Polynomial Expansion method to solve the multigroup diffusion equations
International Nuclear Information System (INIS)
Ribeiro, R.D.M.
1983-03-01
The methodology of the solutions of the multigroup diffusion equations and uses the Nodal Polynomial Expansion Method is covered. The EPON code was developed based upon the above mentioned method for stationary state, rectangular geometry, one-dimensional or two-dimensional and for one or two energy groups. Then, one can study some effects such as the influence of the baffle on the thermal flux by calculating the flux and power distribution in nuclear reactors. Furthermore, a comparative study with other programs which use Finite Difference (CITATION and PDQ5) and Finite Element (CHD and FEMB) Methods was undertaken. As a result, the coherence, feasibility, speed and accuracy of the methodology used were demonstrated. (Author) [pt
SIRIUS - A one-dimensional multigroup analytic nodal diffusion theory code
Energy Technology Data Exchange (ETDEWEB)
Forslund, P. [Westinghouse Atom AB, Vaesteraas (Sweden)
2000-09-01
In order to evaluate relative merits of some proposed intranodal cross sections models, a computer code called Sirius has been developed. Sirius is a one-dimensional, multigroup analytic nodal diffusion theory code with microscopic depletion capability. Sirius provides the possibility of performing a spatial homogenization and energy collapsing of cross sections. In addition a so called pin power reconstruction method is available for the purpose of reconstructing 'heterogeneous' pin qualities. consequently, Sirius has the capability of performing all the calculations (incl. depletion calculations) which are an integral part of the nodal calculation procedure. In this way, an unambiguous numerical analysis of intranodal cross section models is made possible. In this report, the theory of the nodal models implemented in sirius as well as the verification of the most important features of these models are addressed.
MC2-2, Calculation of Fast Neutron Spectra and Multigroup Cross-Sections from ENDF/B Data
International Nuclear Information System (INIS)
2001-01-01
1 - Description of program or function: MC 2 -2 solves the neutron slowing-down equations using basic neutron data derived from ENDF/B data files to determine fundamental mode spectra for use in generating multigroup neutron cross sections. The current edition includes the ability to treat all ENDF/B-V and -VI data representations. It accommodates high-order P scattering representations and provides numerous capabilities such as isotope mixing, delayed neutron processing, free-format input, and flexibility in output data selection. This edition supersedes previous releases of the MC22 program and the earlier MC2 program. Improved physics algorithms and increased computational efficiency are incorporated. Input data files required by MC2-2 may be generated from ENDF/B data by the code ETOE-2. The hyper-fine-group integral transport theory module of MC2-2, RABANL, is an improved version of the RABBLE/RABID codes. Many of the MC2-2 modules are used in the SDX code. 2 - Methods: The extended transport P1, B1, consistent P1, and consistent B1 fundamental mode ultra-fine-group equations are solved using continuous slowing-down theory and multigroup methods. Fast and accurate resonance integral methods are used in the narrow resonance resolved and unresolved resonance treatments. A fundamental mode homogeneous unit cell calculation is performed using either a multigroup or a continuous slowing-down treatment. Multigroup neutron homogeneous cross sections are generated in an ISOTXS format for an arbitrary group structure. A hyper-fine-group integral transport slowing down calculation (RABANL) is available as an option. RABANL performs a homogeneous or heterogeneous (pin or slab) unit cell calculation over the resonance region (resolved and unresolved) and generates multigroup neutron cross sections in an ISOTXS format. Neutron cross sections are generated by RABANL for the homogeneous unit cell and for each heterogeneous region in the pin or slab unit cell calculation
International Nuclear Information System (INIS)
Cacuci, D.G.; Univ. of Karlsruhe; Kiefhaber, E.; Stehle, B.
1998-01-01
The explicit solution developed by Cacuci for the multigroup neutron diffusion equation at interior corners in two-dimensional two-region domains has been applied to the SNR-300 fast reactor prototype design to obtain the exact behavior of the multigroup fluxes at and around typical corners arising between absorber/fuel and follower/fuel assemblies. The calculations have been performed in hexagonal geometry using four energy groups, and the results clearly show that the multigroup fluxes are finite but not analytical at interior corners. In particular, already the first-order spatial derivatives of the multigroup fluxes become unbounded at the corners between follower and fuel assemblies. These results highlight the need to treat properly the influence of corners, both for the direct calculation and for the reconstruction of pointwise neutron flux and power distributions in heterogeneous reactor cores
International Nuclear Information System (INIS)
Ford, W.E. III; Arwood, J.W.; Greene, N.M.; Petrie, L.M.; Primm, R.T. III; Waddell, M.W.; Webster, C.C.; Westfall, R.M.; Wright, R.Q.
1987-01-01
Multigroup P3 neutron, P0-P3 secondary gamma ray production (SGRP), and P6 gamma ray interaction (GRI) cross section libraries have been generated to support design work on the Advanced Neutron Source (ANS) reactor. The libraries, designated ANSL-V (Advanced Neutron Source Cross-Section Libraries), are data bases in a format suitable for subsequent generation of problem dependent cross sections. The ANSL-V libraries are available on magnetic tape from the Radiation Shielding Information Center at Oak Ridge National Laboratory
International Nuclear Information System (INIS)
Lozano, Juan-Andres; Garcia-Herranz, Nuria; Ahnert, Carol; Aragones, Jose-Maria
2008-01-01
In this work we address the development and implementation of the analytic coarse-mesh finite-difference (ACMFD) method in a nodal neutron diffusion solver called ANDES. The first version of the solver is implemented in any number of neutron energy groups, and in 3D Cartesian geometries; thus it mainly addresses PWR and BWR core simulations. The details about the generalization to multigroups and 3D, as well as the implementation of the method are given. The transverse integration procedure is the scheme chosen to extend the ACMFD formulation to multidimensional problems. The role of the transverse leakage treatment in the accuracy of the nodal solutions is analyzed in detail: the involved assumptions, the limitations of the method in terms of nodal width, the alternative approaches to implement the transverse leakage terms in nodal methods - implicit or explicit -, and the error assessment due to transverse integration. A new approach for solving the control rod 'cusping' problem, based on the direct application of the ACMFD method, is also developed and implemented in ANDES. The solver architecture turns ANDES into an user-friendly, modular and easily linkable tool, as required to be integrated into common software platforms for multi-scale and multi-physics simulations. ANDES can be used either as a stand-alone nodal code or as a solver to accelerate the convergence of whole core pin-by-pin code systems. The verification and performance of the solver are demonstrated using both proof-of-principle test cases and well-referenced international benchmarks
International Nuclear Information System (INIS)
Grimstone, M.J.
1978-06-01
The WRS Modular Programming System has been developed as a means by which programmes may be more efficiently constructed, maintained and modified. In this system a module is a self-contained unit typically composed of one or more Fortran routines, and a programme is constructed from a number of such modules. This report describes one WRS module, the function of which is to solve a set of multigroup diffusion equations for a system represented in one-dimensional plane, cylindrical or spherical geometry. The information given in this manual is of use both to the programmer wishing to incorporate the module in a programme, and to the user of such a programme. (author)
SNAP-3D: a three-dimensional neutron diffusion code
International Nuclear Information System (INIS)
McCallien, C.W.J.
1975-10-01
A preliminary report is presented describing the data requirements of a one- two- or three-dimensional multi-group diffusion code, SNAP-3D. This code is primarily intended for neutron diffusion calculations but it can also carry out gamma calculations if the diffuse approximation is accurate enough. It is suitable for fast and thermal reactor core calculations and for shield calculations. It is assumed the reader is familiar with the older, two-dimensional code SNAP and can refer to the report [TRG-Report-1990], describing it. The present report concentrates on the enhancements to SNAP that have been made to produce the three-dimensional version, SNAP-3D, and is intended to act a a guide on data preparation until a single, comprehensive report can be published. (author)
International Nuclear Information System (INIS)
Jakab, J.
1979-05-01
Local approximations of neutron flux density by 2nd degree polynomials are used in calculating light water reactors. The calculations include spatial kinetics tasks for the models of two- and three-dimensional reactors in the Cartesian geometry. The resulting linear algebraic equations are considered to be formally identical to the results of the differential method of diffusion equation solution. (H.S.)
International Nuclear Information System (INIS)
Ilieva, K.; Belousov, S.; Apostolov, T.
1998-01-01
The verification of calculated neutron fluence onto the WWER-440/230 pressure vessel is very topical task in particular referring that some of this type of reactors have been operated the major part of its design lifetime. Since the induced activity from the neutron irradiation onto the elements is a simple response of neutron flux the neutron fluence verification usually is done using the measured activity of radionuclides produced during reactor operation. Calculational and experimental results of 54 Mn induced activity of scraps from inner wall of Unit 1 reactor pressure vessel after 18th cycle and detectors irradiated behind the vessel during the 18th cycle of Unit 1 at Kozloduy NPP as well as neutron flux attenuation through the WWER-440/230 pressure vessel are presented. Neutron cross sections libraries generated on the base of ENDF/B-IV and ENDF/B-VI have been used in the calculations. The comparative analysis of evaluated activities and attenuation coefficient demonstrates the better reliability of the neutron fluence calculations by the libraries based on ENDF/B-VI than by ones on ENDF/B-IV. The extreme rarity of data for the activity of scraps from the WWER-440 reactor vessel and its combination with the data for the detectors irradiated behind the vessel makes them especially attractive for verification of calculational methods of neutron fluence onto the WWER-440 vessel with dummy cassettes loading. (author)
APPLE, Plot of 1-D Multigroup Neutron Flux and Gamma Flux and Reaction Rates from ANISN
International Nuclear Information System (INIS)
Kawasaki, Hiromitsu; Seki, Yasushi
1983-01-01
A - Description of problem or function: The APPLE-2 code has the following functions: (1) It plots multi-group energy spectra of neutron and/or gamma ray fluxes calculated by ANISN, DOT-3.5, and MORSE. (2) It gives an overview plot of multi-group neutron fluxes calculated by ANISN and DOT-3.5. The scalar neutron flux phi(r,E) is plotted with the spatial parameter r linear along the Y-axis, logE along the X-axis and log phi(r,E) in the Z direction. (3) It calculates the spatial distribution and region volume integrated values of reaction rates using the scalar flux calculated with ANISN and DOT-3.5. (4) Reaction rate distribution along the R or Z direction may be plotted. (5) An overview plot of reaction rates or scalar fluxes summed over specified groups may be plotted. R(ri,zi) or phi(ri,zi) is plotted with spatial parameters r and z along the X- and Y-axes in an orthogonal coordinate system. (6) Angular flux calculated by ANISN is rearranged and a shell source at any specified spatial mesh point may be punched out in FIDO format. The shell source obtained may be employed in solving deep penetration problems with ANISN, when the entire reactor system is divided into two or more parts and the neutron fluxes in two adjoining parts are connected by using the shell source. B - Method of solution: (a) The input data specification is made as simple as possible by making use of the input data required in the radiation transport code. For example, geometry related data in ANISN and DOT are transmitted to APPLE-2 along with scalar flux data so as to reduce duplicity and errors in reproducing these data. (b) Most the input data follow the free form FIDO format developed at Oak Ridge National Laboratory and used in the ANISN code. Furthermore, the mixture specifying method used in ANISN is also employed by APPLE-2. (c) Libraries for some standard response functions required in fusion reactor design have been prepared and are made available to users of the 42-group neutron
MENDF71x. Multigroup Neutron Cross Section Data Tables Based upon ENDF/B-VII.1
International Nuclear Information System (INIS)
Conlin, Jeremy Lloyd; Parsons, Donald Kent; Gardiner, Steven J.; Gray, Mark Girard; Lee, Mary Beth; White, Morgan Curtis
2015-01-01
A new multi-group neutron cross section library has been released along with the release of NDI version 2.0.20. The library is named MENDF71x and is based upon the evaluations released in ENDF/B-VII.1 which was made publicly available in December 2011. ENDF/B-VII.1 consists of 423 evaluations of which ten are excited states evaluations and 413 are ground state evaluations. MENDF71x was created by processing the 423 evaluations into 618-group, downscatter only NDI data tables. The ENDF/B evaluation files were processed using NJOY version 99.393 with the exception of 35 Cl and 233 U. Those two isotopes had unique properties that required that we process the evaluation using NJOY version 2012. The MENDF71x library was only processed to room temperature, i.e., 293.6 K. In the future, we plan on producing a multi-temperature library based on ENDF/B-VII.1 and compatible with MENDF71x.
International Nuclear Information System (INIS)
Seed, T.J.; Miller, W.F. Jr.; Brinkley, F.W. Jr.
1977-03-01
TRIDENT solves the two-dimensional-multigroup-transport equations in rectangular (x-y) and cylindrical (r-z) geometries using a regular triangular mesh. Regular and adjoint, inhomogeneous and homogeneous (k/sub eff/ and eigenvalue searches) problems subject to vacuum, reflective, white, or source boundary conditions are solved. General anisotropic scattering is allowed and anisotropic-distributed sources are permitted. The discrete-ordinates approximation is used for the neutron directional variables. An option is included to append a fictitious source to the discrete-ordinates equations that is defined such that spherical-harmonics solutions (in x-y geometry) or spherical-harmonics-like solutions (in r-z geometry) are obtained. A spatial-finite-element method is used in which the angular flux is expressed as a linear polynomial in each triangle that is discontinous at triangle boundaries. Unusual Features of the program: Provision is made for creation of standard interface output files for S/sub N/ constants, angle-integrated (scalar) fluxes, and angular fluxes. Standard interface input files for S/sub N/ constants, inhomogeneous sources, cross sections, and the scalar flux may be read. Flexible edit options as well as a dump and restart capability are provided
International Nuclear Information System (INIS)
Kulakovskij, M.Ya.; Savitskij, V.I.
1981-01-01
The errors of multigroup calculating the neutron flux spatial and energy distribution in the fast reactor shield caused by using group and age approximations are considered. It is shown that at small distances from a source the age theory rather well describes the distribution of the slowing-down density. With the distance increase the age approximation leads to underestimating the neutron fluxes, and the error quickly increases at that. At small distances from the source (up to 15 lengths of free path in graphite) the multigroup diffusion approximation describes the distribution of slowing down density quite satisfactorily and at that the results almost do not depend on the number of groups. With the distance increase the multigroup diffusion calculations lead to considerable overestimating of the slowing-down density. The conclusion is drawn that the group approximation proper errors are opposite in sign to the error introduced by the age approximation and to some extent compensate each other
International Nuclear Information System (INIS)
Calloo, A.A.
2012-01-01
In reactor physics, calculation schemes with deterministic codes are validated with respect to a reference Monte Carlo code. The remaining biases are attributed to the approximations and models induced by the multigroup theory (self-shielding models and expansion of the scattering law using Legendre polynomials) to represent physical phenomena (resonant absorption and scattering anisotropy respectively). This work focuses on the relevance of a polynomial expansion to model the scattering law. Since the outset of reactor physics, the latter has been expanded on a truncated Legendre polynomial basis. However, the transfer cross sections are highly anisotropic, with non-zero values for a very small range of the cosine of the scattering angle. Besides, the finer the energy mesh and the lighter the scattering nucleus, the more exacerbated is the peaked shape of this cross section. As such, the Legendre expansion is less suited to represent the scattering law. Furthermore, this model induces negative values which are non-physical. In this work, various scattering laws are briefly described and the limitations of the existing model are pointed out. Hence, piecewise-constant functions have been used to represent the multigroup scattering cross section. This representation requires a different model for the diffusion source. The discrete ordinates method which is widely employed to solve the transport equation has been adapted. Thus, the finite volume method for angular discretization has been developed and implemented in Paris environment which hosts the S n solver, Snatch. The angular finite volume method has been compared to the collocation method with Legendre moments to ensure its proper performance. Moreover, unlike the latter, this method is adapted for both the Legendre moments and the piecewise-constant functions representations of the scattering cross section. This hybrid-source method has been validated for different cases: fuel cell in infinite lattice
International Nuclear Information System (INIS)
Nakagawa, Masayuki; Katsuragi, Satoru; Narita, Hideo.
1976-07-01
The multi-group treatment has been used in the design study of fast reactors and analysis of experiments at fast critical assemblies. The accuracy of the multi-group cross sections therefore affects strongly the results of these analyses. The ESELEM 4 code has been developed to produce multi-group cross sections with an advanced method from the nuclear data libraries used in the JAERI Fast set. ESELEM 4 solves integral transport equation by the collision probability method in plate lattice geometry to obtain the fine neutron spectrum. A typical fine group mesh width is 0.008 in lethargy unit. The multi-group cross sections are calculated by weighting the point data with the fine structure neutron flux. Some devices are applied to reduce computation time and computer core storage required for the calculation. The slowing down sources are calculated with the use of a recurrence formula derived for elastic and inelastic scattering. The broad group treatment is adopted above 2 MeV for dealing with both light any heavy elements. Also the resonance cross sections of heavy elements are represented in a broad group structure, for which we use the values of the JAERI Fast set. The library data are prepared by the PRESM code from ENDF/A type nuclear data files. The cross section data can be compactly stored in the fast computer core memory for saving the core storage and data processing time. The programme uses the variable dimensions to increase its flexibility. The users' guide for ESELEM 4 and PRESM is also presented in this report. (auth.)
International Nuclear Information System (INIS)
Ragusa, J. C.
2004-01-01
In this paper, a method for performing spatially adaptive computations in the framework of multigroup diffusion on 2-D and 3-D Cartesian grids is investigated. The numerical error, intrinsic to any computer simulation of physical phenomena, is monitored through an a posteriori error estimator. In a posteriori analysis, the computed solution itself is used to assess the accuracy. By efficiently estimating the spatial error, the entire computational process is controlled through successively adapted grids. Our analysis is based on a finite element solution of the diffusion equation. Bilinear test functions are used. The derived a posteriori error estimator is therefore based on the Hessian of the numerical solution. (authors)
International Nuclear Information System (INIS)
Ford, W.E. III; Arwood, J.W.; Greene, N.M.; Moses, D.L.; Petrie, L.M.; Primm, R.T. III; Slater, C.O.; Westfall, R.M.; Wright, R.Q.
1990-09-01
Pseudo-problem-independent, multigroup cross-section libraries were generated to support Advanced Neutron Source (ANS) Reactor design studies. The ANS is a proposed reactor which would be fueled with highly enriched uranium and cooled with heavy water. The libraries, designated ANSL-V (Advanced Neutron Source Cross Section Libraries based on ENDF/B-V), are data bases in AMPX master format for subsequent generation of problem-dependent cross-sections for use with codes such as KENO, ANISN, XSDRNPM, VENTURE, DOT, DORT, TORT, and MORSE. Included in ANSL-V are 99-group and 39-group neutron, 39-neutron-group 44-gamma-ray-group secondary gamma-ray production (SGRP), 44-group gamma-ray interaction (GRI), and coupled, 39-neutron group 44-gamma-ray group (CNG) cross-section libraries. The neutron and SGRP libraries were generated primarily from ENDF/B-V data; the GRI library was generated from DLC-99/HUGO data, which is recognized as the ENDF/B-V photon interaction data. Modules from the AMPX and NJOY systems were used to process the multigroup data. Validity of selected data from the fine- and broad-group neutron libraries was satisfactorily tested in performance parameter calculations
The numerical analysis of eigenvalue problem solutions in the multigroup diffusion theory
International Nuclear Information System (INIS)
Woznick, Z.I.
1994-01-01
In this paper a general iteration strategy for solving the discrete form of multidimensional neutron diffusion equations is described. Usually the solution method is based on the system of inner and outer iterations. The presented matrix formalism allows us to visualize clearly, how the used matrix splitting influences the structure of the matrix in an eigenvalue problem to be solved as well as the independence between inner and outer iterations within global iterations. To keep the page limit, the present version of the paper consists only with first three of five sections given in the original paper under the same title (which will be published soon). (author). 13 refs
CHARTB multigroup transport package
International Nuclear Information System (INIS)
Baker, L.
1979-03-01
The physics and numerical implementation of the radiation transport routine used in the CHARTB MHD code are discussed. It is a one-dimensional (Cartesian, cylindrical, and spherical symmetry), multigroup,, diffusion approximation. Tests and applications will be discussed as well
International Nuclear Information System (INIS)
Prati, A.; Anaf, J.
1988-09-01
The IBM version of the multigroup diffusion code 2DB was implemented in the IEAv CDC CYBER 170/750 system. It was optimized relative to the use of the central memory, limited to 132 K-words, through the memory manager CMM and its partition into three source codes: rectangular and cylindrical geometries, triangular geometry and hexagonal geometry. The reactangular, triangular and hexagonal geometry nodal options were revised and optimized. A fast reactor and a PWR type thermal reactor sample cases were studied. The results are presented and analized. An updated 2DB code user's manual was written in Portugueses and published separately. (author) [pt
International Nuclear Information System (INIS)
Ganesan, S.; Muir, D.W.
1992-01-01
Selected neutron reaction nuclear data libraries and photon-atomic interaction cross section libraries for elements of interest to the IAEA's program on Fusion Evaluated Nuclear Data Library (FENDL) have been processed into MATXSR format using the NJOY system on the VAX4000 computer of the IAEA. This document lists the resulting multigroup data libraries. All the multigroup data generated are available cost-free upon request from the IAEA Nuclear Data Section. (author). 9 refs
Numerical method for solving the three-dimensional time-dependent neutron diffusion equation
International Nuclear Information System (INIS)
Khaled, S.M.; Szatmary, Z.
2005-01-01
A numerical time-implicit method has been developed for solving the coupled three-dimensional time-dependent multi-group neutron diffusion and delayed neutron precursor equations. The numerical stability of the implicit computation scheme and the convergence of the iterative associated processes have been evaluated. The computational scheme requires the solution of large linear systems at each time step. For this purpose, the point over-relaxation Gauss-Seidel method was chosen. A new scheme was introduced instead of the usual source iteration scheme. (author)
Solution of multi-group diffusion equation in x-y-z geometry by finite Fourier transformation
International Nuclear Information System (INIS)
Kobayashi, Keisuke
1975-01-01
The multi-group diffusion equation in three-dimensional x-y-z geometry is solved by finite Fourier transformation. Applying the Fourier transformation to a finite region with constant nuclear cross sections, the fluxes and currents at the material boundaries are obtained in terms of the Fourier series. Truncating the series after the first term, and assuming that the source term is piecewise linear within each mesh box, a set of coupled equations is obtained in the form of three-point equations for each coordinate. These equations can be easily solved by the alternative direction implicit method. Thus a practical procedure is established that could be applied to replace the currently used difference equation. This equation is used to solve the multi-group diffusion equation by means of the source iteration method; and sample calculations for thermal and fast reactors show that the present method yields accurate results with a smaller number of mesh points than the usual finite difference equations. (auth.)
CITATION, 3-D Multigroup Diffusion with 1. Order Perturbation and Criticality Search
International Nuclear Information System (INIS)
Fowler, T.B.; Vondy, D.R.; Cunningham, G.W.
1995-01-01
1 - Description of problem or function: CITATION is designed to solve problems using the finite-difference representation of neutron diffusion theory, treating up to three space dimensions with arbitrary group-to-group scattering. X-y-z, theta-r-z, hexagonal-z, and trigonal-z geometries may be treated. Depletion problems may be solved and fuel managed for multi-cycle analysis. Extensive first-order perturbation results may be obtained given microscopic data and nuclide concentrations. Statics problems may be solved and perturbation results obtained with microscopic data. CITATION-2-3-VP2 is a vectorized version for FACOM VP-100 and VP-200 vector computers. 2 - Method of solution: Explicit, finite-difference approximations in space and time have been implemented. The neutron-flux-eigenvalue problems are solved by direct iteration to determine the multiplication factor or the nuclide densities required for a critical system. CITATION-2-3-VP2: Algorithms for the inner-outer iterative calculations are adapted to vector computers. The SLOR method, which is used in the original CITATION code, and the SOR method, which is adopted in the revised code, are vectorized by odd-even mesh ordering. 3 - Restrictions on the complexity of the problem: CITATION has been designed to attack problems which can be run in a reasonable amount of time. Storage of data is allocated dynamically to give the user flexibility in dimensioning. Typically, a finite-difference diffusion problem could have 200 depleting zones, 10,000 nuclide densities, and 30,000 space-energy point flux values
CITATION-LDI2, 2-D Multigroup Diffusion, Perturbation, Criticality Search, for PC
International Nuclear Information System (INIS)
2001-01-01
1 - Description of program or function: CITATION is designed to solve problems using the finite difference representation of neutron diffusion theory, treating up to three space dimensions with arbitrary group to group scattering. X-y-z, theta-r-z, hexagonal z, and trigonal z geometries may be treated. Depletion problems may be solved and fuel managed for multi-cycle analysis. Extensive first order perturbation results may be obtained given microscopic data and nuclide concentrations. Statics problems may be solved and perturbation results obtained with microscopic data. This version of CITATION was released by ORNL as CITATION - Rev. 2, Supplement 3 in July 1972 and ran on mainframes. It was first ported to PC by AECL in October 1988. CITATION-PC included in the March 1996 package involved minor changes including the removal of overlay statements introduced in 1988. CITALDI-PC is a new modified version with list-directed input. The codes in this package accept cross sections in CITATION format. Macroscopic data may be entered according to format specifications in Section 008 of the published report. Microscopic data format is specified in Section 105. There are no codes in RSIC's code collection to generate data in CITATION format. 2 - Method of solution: Explicit, finite difference approximations in space and time have been implemented. The neutron-flux-eigenvalue problems are solved by direct iteration to determine the multiplication factor or the nuclide densities required for a critical system
International Nuclear Information System (INIS)
Tittle, C.W.
1992-01-01
Diffusion theory has been successfully used to model the effect of fluid invasion into the formation for neutron porosity logs and for the gamma-gamma density log. The purpose of this paper is to present results of computations using a five-group time-dependent diffusion code on invasion effects for the pulsed neutron thermal decay time log. Previous invasion studies by the author involved the use of a three-dimensional three-group steady-state diffusion theory to model the dual-detector thermal neutron porosity log and the gamma-gamma density log. The five-group time-dependent code MGNDE (Multi-Group Neutron Diffusion Equation) used in this work was written by Ferguson. It has been successfully used to compute the intrinsic formation life-time correction for pulsed neutron thermal decay time logs. This application involves the effect of fluid invasion into the formation
Homogenization of neutronic diffusion models
International Nuclear Information System (INIS)
Capdebosq, Y.
1999-09-01
In order to study and simulate nuclear reactor cores, one needs to access the neutron distribution in the core. In practice, the description of this density of neutrons is given by a system of diffusion equations, coupled by non differential exchange terms. The strong heterogeneity of the medium constitutes a major obstacle to the numerical computation of this models at reasonable cost. Homogenization appears as compulsory. Heuristic methods have been developed since the origin by nuclear physicists, under a periodicity assumption on the coefficients. They consist in doing a fine computation one a single periodicity cell, to solve the system on the whole domain with homogeneous coefficients, and to reconstruct the neutron density by multiplying the solutions of the two computations. The objectives of this work are to provide mathematically rigorous basis to this factorization method, to obtain the exact formulas of the homogenized coefficients, and to start on geometries where two periodical medium are placed side by side. The first result of this thesis concerns eigenvalue problem models which are used to characterize the state of criticality of the reactor, under a symmetry assumption on the coefficients. The convergence of the homogenization process is proved, and formulas of the homogenized coefficients are given. We then show that without symmetry assumptions, a drift phenomenon appears. It is characterized by the mean of a real Bloch wave method, which gives the homogenized limit in the general case. These results for the critical problem are then adapted to the evolution model. Finally, the homogenization of the critical problem in the case of two side by side periodic medium is studied on a one dimensional on equation model. (authors)
International Nuclear Information System (INIS)
Kasselmann, S.; Druska, C.; Lauer, A.
2010-01-01
The energy spectra of fast and thermal neutrons from fission reactions in the FZJ code TINTE are modelled by two broad energy groups. Present demands for increased numerical accuracy led to the question of how precise the 2-group approximation is compared to a multi-group model. Therefore a new simulation program called MGT (Multi Group TINTE) has recently been developed which is able to handle up to 43 energy groups. Furthermore, an internal spectrum calculation for the determination of cross-sections can be performed for each time step and location within the reactor. In this study the multi-group energy models are compared to former calculations with only two energy groups. Different scenarios (normal operation and design-basis accidents) have been defined for a high temperature pebble bed reactor design with annular core. The effect of an increasing number of energy groups on safety-related parameters like the fuel and coolant temperature, the nuclear heat source or the xenon concentration is studied. It has been found that for the studied scenarios the use of up to 8 energy groups is a good trade-off between precision and a tolerable amount of computing time. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Lozano, Juan Andres; Aragones, Jose Maria; Garcia-Herranz, Nuria [Universidad Politecnica de Madrid, 28006 Jose Gutierrez Abascal 2, Madrid (Spain)
2008-07-01
More accurate modelling of physical phenomena involved in present and future nuclear reactors requires a multi-scale and multi-physics approach. This challenge can be accomplished by the coupling of best-estimate core-physics, thermal-hydraulics and multi-physics solvers. In order to make viable that coupling, the current trends in reactor simulations are along the development of a new generation of tools based on user-friendly, modular, easily linkable, faster and more accurate codes to be integrated in common platforms. These premises are in the origin of the NURESIM Integrated Project within the 6. European Framework Program, which is envisaged to provide the initial step towards a Common European Standard Software Platform for nuclear reactors simulations. In the frame of this project and to reach the above-mentioned goals, a 3-D multigroup nodal solver for neutron diffusion calculations called ANDES (Analytic Nodal Diffusion Equation Solver) has been developed and tested in-depth in this Thesis. ANDES solves the steady-state and time-dependent neutron diffusion equation in three-dimensions and any number of energy groups, utilizing the Analytic Coarse-Mesh Finite-Difference (ACMFD) scheme to yield the nodal coupling equations. It can be applied to both Cartesian and triangular-Z geometries, so that simulations of LWR as well as VVER, HTR and fast reactors can be performed. The solver has been implemented in a fully encapsulated way, enabling it as a module to be readily integrated in other codes and platforms. In fact, it can be used either as a stand-alone nodal code or as a solver to accelerate the convergence of whole core pin-by-pin code systems. Verification of performance has shown that ANDES is a code with high order definition for whole core realistic nodal simulations. In this paper, the methodology developed and involved in ANDES is presented. (authors)
Energy Technology Data Exchange (ETDEWEB)
Shestakov, A I; Offner, S R
2006-09-21
We present a scheme to solve the nonlinear multigroup radiation diffusion (MGD) equations. The method is incorporated into a massively parallel, multidimensional, Eulerian radiation-hydrodynamic code with adaptive mesh refinement (AMR). The patch-based AMR algorithm refines in both space and time creating a hierarchy of levels, coarsest to finest. The physics modules are time-advanced using operator splitting. On each level, separate 'level-solve' packages advance the modules. Our multigroup level-solve adapts an implicit procedure which leads to a two-step iterative scheme that alternates between elliptic solves for each group with intra-cell group coupling. For robustness, we introduce pseudo transient continuation ({Psi}tc). We analyze the magnitude of the {Psi}tc parameter to ensure positivity of the resulting linear system, diagonal dominance and convergence of the two-step scheme. For AMR, a level defines a subdomain for refinement. For diffusive processes such as MGD, the refined level uses Dirichet boundary data at the coarse-fine interface and the data is derived from the coarse level solution. After advancing on the fine level, an additional procedure, the sync-solve (SS), is required in order to enforce conservation. The MGD SS reduces to an elliptic solve on a combined grid for a system of G equations, where G is the number of groups. We adapt the 'partial temperature' scheme for the SS; hence, we reuse the infrastructure developed for scalar equations. Results are presented. We consider a multigroup test problem with a known analytic solution. We demonstrate utility of {Psi}tc by running with increasingly larger timesteps. Lastly, we simulate the sudden release of energy Y inside an Al sphere (r = 15 cm) suspended in air at STP. For Y = 11 kT, we find that gray radiation diffusion and MGD produce similar results. However, if Y = 1 MT, the two packages yield different results. Our large Y simulation contradicts a long-standing theory
Energy Technology Data Exchange (ETDEWEB)
Shestakov, A I; Offner, S R
2007-03-02
We present a scheme to solve the nonlinear multigroup radiation diffusion (MGD) equations. The method is incorporated into a massively parallel, multidimensional, Eulerian radiation-hydrodynamic code with adaptive mesh refinement (AMR). The patch-based AMR algorithm refines in both space and time creating a hierarchy of levels, coarsest to finest. The physics modules are time-advanced using operator splitting. On each level, separate 'level-solve' packages advance the modules. Our multigroup level-solve adapts an implicit procedure which leads to a two-step iterative scheme that alternates between elliptic solves for each group with intra-cell group coupling. For robustness, we introduce pseudo transient continuation ({Psi}tc). We analyze the magnitude of the {Psi}tc parameter to ensure positivity of the resulting linear system, diagonal dominance and convergence of the two-step scheme. For AMR, a level defines a subdomain for refinement. For diffusive processes such as MGD, the refined level uses Dirichet boundary data at the coarse-fine interface and the data is derived from the coarse level solution. After advancing on the fine level, an additional procedure, the sync-solve (SS), is required in order to enforce conservation. The MGD SS reduces to an elliptic solve on a combined grid for a system of G equations, where G is the number of groups. We adapt the 'partial temperature' scheme for the SS; hence, we reuse the infrastructure developed for scalar equations. Results are presented. We consider a multigroup test problem with a known analytic solution. We demonstrate utility of {Psi}tc by running with increasingly larger timesteps. Lastly, we simulate the sudden release of energy Y inside an Al sphere (r = 15 cm) suspended in air at STP. For Y = 11 kT, we find that gray radiation diffusion and MGD produce similar results. However, if Y = 1 MT, the two packages yield different results. Our large Y simulation contradicts a long-standing theory
International Nuclear Information System (INIS)
2005-01-01
A - Description of program or function: (1) Problems to be solved: MVP/GMVP can solve eigenvalue and fixed-source problems. The multigroup code GMVP can solve forward and adjoint problems for neutron, photon and neutron-photon coupled transport. The continuous-energy code MVP can solve only the forward problems. Both codes can also perform time-dependent calculations. (2) Geometry description: MVP/GMVP employs combinatorial geometry to describe the calculation geometry. It describes spatial regions by the combination of the 3-dimensional objects (BODIes). Currently, the following objects (BODIes) can be used. - BODIes with linear surfaces: half space, parallelepiped, right parallelepiped, wedge, right hexagonal prism; - BODIes with quadratic surface and linear surfaces: cylinder, sphere, truncated right cone, truncated elliptic cone, ellipsoid by rotation, general ellipsoid; - Arbitrary quadratic surface and torus. The rectangular and hexagonal lattice geometry can be used to describe the repeated geometry. Furthermore, the statistical geometry model is available to treat coated fuel particles or pebbles for high temperature reactors. (3) Particle sources: The various forms of energy-, angle-, space- and time-dependent distribution functions can be specified. (4) Cross sections: The ANISN-type PL cross sections or the double-differential cross sections can be used in the multigroup code GMVP. On the other hand, the specific cross section libraries are used in the continuous-energy code MVP. The libraries are generated from the evaluated nuclear data (JENDL-3.3, ENDF/B-VI, JEF-3.0 etc.) by using the LICEM code. The neutron cross sections in the unresolved resonance region are described by the probability table method. The neutron cross sections at arbitrary temperatures are available for MVP by just specifying the temperatures in the input data. (5) Boundary conditions: Vacuum, perfect reflective, isotropic reflective (white), periodic boundary conditions can be
REX1-87, Multigroup Neutron Cross-Sections from ENDF/B
International Nuclear Information System (INIS)
Gopalakrishnan, V.; Ganesan, S.
1988-01-01
1 - Description of program or function: The program calculates self- shielding factors for reactor applications from a pre-processed (linearized) evaluated nuclear data file in the ENDF/B format. 2 - Method of solution: Bondarenko definition of multigroup self- shielding factors invoking narrow resonance treatment is used. 3 - Restrictions on the complexity of the problem: a) Maximum no. of energy group is 620. b) Only the built-in forms of the weighting functions can be chosen. c) The program is strictly limited to resolved resonance region from physical considerations
Neutron transport equation - indications on homogenization and neutron diffusion
International Nuclear Information System (INIS)
Argaud, J.P.
1992-06-01
In PWR nuclear reactor, the practical study of the neutrons in the core uses diffusion equation to describe the problem. On the other hand, the most correct method to describe these neutrons is to use the Boltzmann equation, or neutron transport equation. In this paper, we give some theoretical indications to obtain a diffusion equation from the general transport equation, with some simplifying hypothesis. The work is organised as follows: (a) the most general formulations of the transport equation are presented: integro-differential equation and integral equation; (b) the theoretical approximation of this Boltzmann equation by a diffusion equation is introduced, by the way of asymptotic developments; (c) practical homogenization methods of transport equation is then presented. In particular, the relationships with some general and useful methods in neutronic are shown, and some homogenization methods in energy and space are indicated. A lot of other points of view or complements are detailed in the text or the remarks
Diffuse neutron scattering signatures of rough films
International Nuclear Information System (INIS)
Pynn, R.; Lujan, M. Jr.
1992-01-01
Patterns of diffuse neutron scattering from thin films are calculated from a perturbation expansion based on the distorted-wave Born approximation. Diffuse fringes can be categorised into three types: those that occur at constant values of the incident or scattered neutron wavevectors, and those for which the neutron wavevector transfer perpendicular to the film is constant. The variation of intensity along these fringes can be used to deduce the spectrum of surface roughness for the film and the degree of correlation between the film's rough surfaces
Derivation of the neutron diffusion equation
International Nuclear Information System (INIS)
Mika, J.R.; Banasiak, J.
1994-01-01
We discuss the diffusion equation as an asymptotic limit of the neutron transport equation for large scattering cross sections. We show that the classical asymptotic expansion procedure does not lead to the diffusion equation and present two modified approaches to overcome this difficulty. The effect of the initial layer is also discussed. (authors). 9 refs
A multigroup flux-limited asymptotic diffusion Fokker-Planck equation
International Nuclear Information System (INIS)
Liu Chengan
1987-01-01
A more perfrect flux-limited method is applied to combine with asymptotic diffusion theory of the radiation transpore, and the high peaked component in the scattering angle is treated with Fokker-Planck methods, thus the flux-limited asymptotic diffusion Fokker-Planck equation has been founded. Since the equation is of diffusion form, it retains the simplity and the convenience of the classical diffusion theory, and improves precision in describing radiation transport problems
The Suppression of Energy Discretization Errors in Multigroup Transport Calculations
International Nuclear Information System (INIS)
Larsen, Edward
2013-01-01
The Objective of this project is to develop, implement, and test new deterministric methods to solve, as efficiently as possible, multigroup neutron transport problems having an extremely large number of groups. Our approach was to (i) use the standard CMFD method to 'coarsen' the space-angle grid, yielding a multigroup diffusion equation, and (ii) use a new multigrid-in-space-and-energy technique to efficiently solve the multigroup diffusion problem. The overall strategy of (i) how to coarsen the spatial an energy grids, and (ii) how to navigate through the various grids, has the goal of minimizing the overall computational effort. This approach yields not only the fine-grid solution, but also coarse-group flux-weighted cross sections that can be used for other related problems.
Numerical solution of multigroup diffuse equations of one-dimensional geometry
International Nuclear Information System (INIS)
Pavelesku, M.; Adam, S.
1975-01-01
The one-dimensional diffuse theory is used for reactor physics calculations of fast reactors. Computer program based on the one-dimensional diffuse theory is speedy and not memory consuming. The algorithm is described for the three-zone fast reactor criticality computation in one-dimensional diffusion approximation. This algorithm is realised on IBM 370/135 computer. (I.T.)
Thermal neutron diffusion parameters in homogeneous mixtures
Energy Technology Data Exchange (ETDEWEB)
Drozdowicz, K.; Krynicka, E. [Institute of Nuclear Physics, Cracow (Poland)
1995-12-31
A physical background is presented for a computer program which calculates the thermal neutron diffusion parameters for homogeneous mixtures of any compounds. The macroscopic absorption, scattering and transport cross section of the mixture are defined which are generally function of the incident neutron energy. The energy-averaged neutron parameters are available when these energy dependences and the thermal neutron energy distribution are assumed. Then the averaged diffusion coefficient and the pulsed thermal neutron parameters (the absorption rare and the diffusion constant) are also defined. The absorption cross section is described by the 1/v law and deviations from this behaviour are considered. The scattering cross section can be assumed as being almost constant in the thermal neutron region (which results from the free gas model). Serious deviations are observed for hydrogen atoms bound in molecules and a special study in the paper is devoted to this problem. A certain effective scattering cross section is found in this case on a base of individual exact data for a few hydrogenous media. Approximations assumed for the average cosine of the scattering angle are also discussed. The macroscopic parameters calculated are averaged over the Maxwellian energy distribution for the thermal neutron flux. An information on the input data for the computer program is included. (author). 10 refs, 4 figs, 5 tabs.
Thermal neutron diffusion parameters in homogeneous mixtures
International Nuclear Information System (INIS)
Drozdowicz, K.; Krynicka, E.
1995-01-01
A physical background is presented for a computer program which calculates the thermal neutron diffusion parameters for homogeneous mixtures of any compounds. The macroscopic absorption, scattering and transport cross section of the mixture are defined which are generally function of the incident neutron energy. The energy-averaged neutron parameters are available when these energy dependences and the thermal neutron energy distribution are assumed. Then the averaged diffusion coefficient and the pulsed thermal neutron parameters (the absorption rare and the diffusion constant) are also defined. The absorption cross section is described by the 1/v law and deviations from this behaviour are considered. The scattering cross section can be assumed as being almost constant in the thermal neutron region (which results from the free gas model). Serious deviations are observed for hydrogen atoms bound in molecules and a special study in the paper is devoted to this problem. A certain effective scattering cross section is found in this case on a base of individual exact data for a few hydrogenous media. Approximations assumed for the average cosine of the scattering angle are also discussed. The macroscopic parameters calculated are averaged over the Maxwellian energy distribution for the thermal neutron flux. An information on the input data for the computer program is included. (author). 10 refs, 4 figs, 5 tabs
TEMPEST-2, Thermalization Program for Neutron Spectra and Multigroup Cross-Sections
International Nuclear Information System (INIS)
Gowins, G.
1984-01-01
Description of problem or function: TEMPEST2 is a neutron thermalization program based upon the Wigner-Wilkins approximation for light moderators and the Wilkins approximation for heavy moderators. A Maxwellian distribution may also be used. The model used may be selected as a function of energy. The second-order differential equations are integrated directly rather than transformed to the Riccati equation. The program provides microscopic and macroscopic cross-section averages over the thermal neutron spectrum
Creation and validation of a neutron-gamma coupled multigroup cross section library
International Nuclear Information System (INIS)
Devan, K.; Gopalakrishnan, V.; Lee, S.M.
1995-01-01
The task of creating our own neutron-gamma coupled library was taken up. By using 1985 version of NJOY code system, a coupled set called IGC-DE4-S1 in ANISN format for 25 nuclides has been arrived at based on ENDF/B-IV neutron library and DLC-99 gamma library, with Legendre order of up to 5. The flow chart for the creation of coupled set is given. 5 refs, 1 fig., 3 tabs
International Nuclear Information System (INIS)
Yang, W.S.; Lee, C.H.
2008-01-01
Under the fast reactor simulation program launched in April 2007, development of an advanced multigroup cross section generation code was initiated in July 2007, in conjunction with the development of the high-fidelity deterministic neutron transport code UNIC. The general objectives are to simplify the existing multi-step schemes and to improve the resolved and unresolved resonance treatments. Based on the review results of current methods and the fact that they have been applied successfully to fast critical experiment analyses and fast reactor designs for last three decades, the methodologies of the ETOE-2/MC 2 -2/SDX code system were selected as the starting set of methodologies for multigroup cross section generation for fast reactor analysis. As the first step for coupling with the UNIC code and use in a parallel computing environment, the MC 2 -2 code was updated by modernizing the memory structure and replacing old data management package subroutines and functions with FORTRAN 90 based routines. Various modifications were also made in the ETOE-2 and MC 2 -2 codes to process the ENDF/B-VII.0 data properly. Using the updated ETOE-2/MC 2 -2 code system, the ENDF/B-VII.0 data was successfully processed for major heavy and intermediate nuclides employed in sodium-cooled fast reactors. Initial verification tests of the MC 2 -2 libraries generated from ENDF/B-VII.0 data were performed by inter-comparison of twenty-one group infinite dilute total cross sections obtained from MC 2 -2, VIM, and NJOY. For almost all nuclides considered, MC 2 -2 cross sections agreed very well with those from VIM and NJOY. Preliminary validation tests of the ENDF/B-VII.0 libraries of MC 2 -2 were also performed using a set of sixteen fast critical benchmark problems. The deterministic results based on MC 2 -2/TWODANT calculations were in good agreement with MCNP solutions within ∼0.25% Δρ, except a few small LANL fast assemblies. Relative to the MCNP solution, the MC 2 -2/TWODANT
Energy Technology Data Exchange (ETDEWEB)
Yang, W. S.; Lee, C. H. (Nuclear Engineering Division)
2008-05-16
Under the fast reactor simulation program launched in April 2007, development of an advanced multigroup cross section generation code was initiated in July 2007, in conjunction with the development of the high-fidelity deterministic neutron transport code UNIC. The general objectives are to simplify the existing multi-step schemes and to improve the resolved and unresolved resonance treatments. Based on the review results of current methods and the fact that they have been applied successfully to fast critical experiment analyses and fast reactor designs for last three decades, the methodologies of the ETOE-2/MC{sup 2}-2/SDX code system were selected as the starting set of methodologies for multigroup cross section generation for fast reactor analysis. As the first step for coupling with the UNIC code and use in a parallel computing environment, the MC{sup 2}-2 code was updated by modernizing the memory structure and replacing old data management package subroutines and functions with FORTRAN 90 based routines. Various modifications were also made in the ETOE-2 and MC{sup 2}-2 codes to process the ENDF/B-VII.0 data properly. Using the updated ETOE-2/MC{sup 2}-2 code system, the ENDF/B-VII.0 data was successfully processed for major heavy and intermediate nuclides employed in sodium-cooled fast reactors. Initial verification tests of the MC{sup 2}-2 libraries generated from ENDF/B-VII.0 data were performed by inter-comparison of twenty-one group infinite dilute total cross sections obtained from MC{sup 2}-2, VIM, and NJOY. For almost all nuclides considered, MC{sup 2}-2 cross sections agreed very well with those from VIM and NJOY. Preliminary validation tests of the ENDF/B-VII.0 libraries of MC{sup 2}-2 were also performed using a set of sixteen fast critical benchmark problems. The deterministic results based on MC{sup 2}-2/TWODANT calculations were in good agreement with MCNP solutions within {approx}0.25% {Delta}{rho}, except a few small LANL fast assemblies
Energy Technology Data Exchange (ETDEWEB)
Oliva, Amaury M.; Filho, Hermes A.; Silva, Davi M.; Garcia, Carlos R., E-mail: aoliva@iprj.uerj.br, E-mail: halves@iprj.uerj.br, E-mail: davijmsilva@yahoo.com.br, E-mail: cgh@instec.cu [Universidade do Estado do Rio de Janeiro (UERJ), Nova Friburgo, RJ (Brazil). Instituto Politecnico. Departamento de Modelagem Computacional; Instituto Superior de Tecnologias y Ciencias Aplicadas (InSTEC), La Habana (Cuba)
2017-07-01
In this paper, we propose a numerical methodology for the development of a method of the spectral nodal class that will generate numerical solutions free from spatial truncation errors. This method, denominated Spectral Deterministic Method (SDM), is tested as an initial study of the solutions (spectral analysis) of neutron transport equations in the discrete ordinates (S{sub N}) formulation, in one-dimensional slab geometry, multigroup approximation, with linearly anisotropic scattering, considering homogeneous and heterogeneous domains with fixed source. The unknowns in the methodology are the cell-edge, and cell average angular fluxes, the numerical values calculated for these quantities coincide with the analytic solution of the equations. These numerical results are shown and compared with the traditional ne- mesh method Diamond Difference (DD) and the coarse-mesh method spectral Green's function (SGF) to illustrate the method's accuracy and stability. The solution algorithms problems are implemented in a computer simulator made in C++ language, the same that was used to generate the results of the reference work. (author)
International Nuclear Information System (INIS)
Hill, T. R.; Reed, W. H.
1980-01-01
1 - Description of problem or function: TIMEX solves the time- dependent, one-dimensional multigroup transport equation with delayed neutrons in plane, cylindrical, spherical, and two-angle plane geometries. Both regular and adjoint, inhomogeneous and homogeneous problems subject to vacuum, reflective, periodic, white, albedo or inhomogeneous boundary flux conditions are solved. General anisotropic scattering is allowed and anisotropic inhomogeneous sources are permitted. 2 - Method of solution: The discrete ordinates approximation for the angular variable is used with the diamond (central) difference approximation for the angular extrapolation in curved geometries. A linear discontinuous finite element representation for the angular flux in each spatial mesh cell is used. Negative fluxes are eliminated by a local set-to-zero and correct algorithm. The time variable is differenced by an explicit technique that is unconditionally stable so that arbitrarily large time-steps can be taken. Two acceleration methods, exponential extrapolation and re-balance, are utilized to improve the accuracy of the time differencing scheme. 3 - Restrictions on the complexity of the problem: Variable dimensioning is used so that any combination of problem parameters leading to a container array less than MAXCOR can be accommodated. In addition, the CDC version permits the use of extended core storage less than MAXECS
International Nuclear Information System (INIS)
Kodeli, I.; Aldama, D. L.; De Leege, P. F. A.; Legrady, D.; Hoogenboom, J. E.; Cowan, P.
2004-01-01
As part of the IRTMBA (Improved Radiation Transport Modelling for Borehole Applications) project of the EU community's 5. framework program a special purpose multigroup cross-section library was prepared for use in deterministic and Monte Carlo oil well logging particle transport calculations. This library is expected to improve the prediction of the neutron and gamma spectra at the detector positions of the logging tool, and their use for the interpretation of the neutron logging measurements was studied. Preparation and testing of this library is described. (authors)
Procedure to Generate the MPACT Multigroup Library
Energy Technology Data Exchange (ETDEWEB)
Kim, Kang Seog [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
2015-12-17
The CASL neutronics simulator MPACT is under development for the neutronics and T-H coupled simulation for the light water reactor. The objective of this document is focused on reviewing the current procedure to generate the MPACT multigroup library. Detailed methodologies and procedures are included in this document for further discussion to improve the MPACT multigroup library.
Vectorization of three-dimensional neutron diffusion code CITATION
International Nuclear Information System (INIS)
Harada, Hiroo; Ishiguro, Misako
1985-01-01
Three-dimensional multi-group neutron diffusion code CITATION has been widely used for reactor criticality calculations. The code is expected to be run at a high speed by using recent vector supercomputers, when it is appropriately vectorized. In this paper, vectorization methods and their effects are described for the CITATION code. Especially, calculation algorithms suited for vectorization of the inner-outer iterative calculations which spend most of the computing time are discussed. The SLOR method, which is used in the original CITATION code, and the SOR method, which is adopted in the revised code, are vectorized by odd-even mesh ordering. The vectorized CITATION code is executed on the FACOM VP-100 and VP-200 computers, and is found to run over six times faster than the original code for a practical-scale problem. The initial value of the relaxation factor and the number of inner-iterations given as input data are also investigated since the computing time depends on these values. (author)
Two-dimensional multigroup finite element calculation of fast reactor in diffusion approximation
International Nuclear Information System (INIS)
Schmid, J.
1986-06-01
When a linear element of triangular shape is used the actual finite element calculation is relatively simple. Extensive programs for mesh generation were written for easy inputting the configuration of reactors. A number of other programs were written for plotting neutron flux fields in individual groups, the power distribution, spatial plotting of fields, etc. The operation of selected programs, data preparation and operating instructions are described and examples given of data and results. All programs are written in GIER ALGOL. The used method and the developed programs have demonstrated that they are a useful instrument for the calculation of criticality and the distribution of neutron flux and power of both fast and thermal reactors. (J.B.)
Energy Technology Data Exchange (ETDEWEB)
Greene, N.M.; Ford, W.E. III; Petrie, L.M.; Arwood, J.W.
1992-10-01
AMPX-77 is a modular system of computer programs that pertain to nuclear analyses, with a primary emphasis on tasks associated with the production and use of multigroup cross sections. AH basic cross-section data are to be input in the formats used by the Evaluated Nuclear Data Files (ENDF/B), and output can be obtained in a variety of formats, including its own internal and very general formats, along with a variety of other useful formats used by major transport, diffusion theory, and Monte Carlo codes. Processing is provided for both neutron and gamma-my data. The present release contains codes all written in the FORTRAN-77 dialect of FORTRAN and wig process ENDF/B-V and earlier evaluations, though major modules are being upgraded in order to process ENDF/B-VI and will be released when a complete collection of usable routines is available.
International Nuclear Information System (INIS)
Greene, N.M.; Ford, W.E. III; Petrie, L.M.; Arwood, J.W.
1992-10-01
AMPX-77 is a modular system of computer programs that pertain to nuclear analyses, with a primary emphasis on tasks associated with the production and use of multigroup cross sections. AH basic cross-section data are to be input in the formats used by the Evaluated Nuclear Data Files (ENDF/B), and output can be obtained in a variety of formats, including its own internal and very general formats, along with a variety of other useful formats used by major transport, diffusion theory, and Monte Carlo codes. Processing is provided for both neutron and gamma-my data. The present release contains codes all written in the FORTRAN-77 dialect of FORTRAN and wig process ENDF/B-V and earlier evaluations, though major modules are being upgraded in order to process ENDF/B-VI and will be released when a complete collection of usable routines is available
Nodal deterministic simulation for problems of neutron shielding in multigroup formulation
International Nuclear Information System (INIS)
Baptista, Josue Costa; Heringer, Juan Diego dos Santos; Santos, Luiz Fernando Trindade; Alves Filho, Hermes
2013-01-01
In this paper, we propose the use of some computational tools, with the implementation of numerical methods SGF (Spectral Green's Function), making use of a deterministic model of transport of neutral particles in the study and analysis of a known and simplified problem of nuclear engineering, known in the literature as a problem of neutron shielding, considering the model with two energy groups. These simulations are performed in MatLab platform, version 7.0, and are presented and developed with the help of a Computer Simulator providing a friendly computer application for their utilities
An extension of implicit Monte Carlo diffusion: Multigroup and the difference formulation
International Nuclear Information System (INIS)
Cleveland, Mathew A.; Gentile, Nick A.; Palmer, Todd S.
2010-01-01
Implicit Monte Carlo (IMC) and Implicit Monte Carlo Diffusion (IMD) are approaches to the numerical solution of the equations of radiative transfer. IMD was previously derived and numerically tested on grey, or frequency-integrated problems . In this research, we extend Implicit Monte Carlo Diffusion (IMD) to account for frequency dependence, and we implement the difference formulation as a source manipulation variance reduction technique. We derive the relevant probability distributions and present the frequency dependent IMD algorithm, with and without the difference formulation. The IMD code with and without the difference formulation was tested using both grey and frequency dependent benchmark problems. The Su and Olson semi-analytic Marshak wave benchmark was used to demonstrate the validity of the code for grey problems . The Su and Olson semi-analytic picket fence benchmark was used for the frequency dependent problems . The frequency dependent IMD algorithm reproduces the results of both Su and Olson benchmark problems. Frequency group refinement studies indicate that the computational cost of refining the group structure is likely less than that of group refinement in deterministic solutions of the radiation diffusion methods. Our results show that applying the difference formulation to the IMD algorithm can result in an overall increase in the figure of merit for frequency dependent problems. However, the creation of negatively weighted particles from the difference formulation can cause significant numerical instabilities in regions of the problem with sharp spatial gradients in the solution. An adaptive implementation of the difference formulation may be necessary to focus its use in regions that are at or near thermal equilibrium.
Two-Dimensional Space-Time Dependent Multi-group Diffusion Equation with SLOR Method
International Nuclear Information System (INIS)
Yulianti, Y.; Su'ud, Z.; Waris, A.; Khotimah, S. N.
2010-01-01
The research of two-dimensional space-time diffusion equations with SLOR (Successive-Line Over Relaxation) has been done. SLOR method is chosen because this method is one of iterative methods that does not required to defined whole element matrix. The research is divided in two cases, homogeneous case and heterogeneous case. Homogeneous case has been inserted by step reactivity. Heterogeneous case has been inserted by step reactivity and ramp reactivity. In general, the results of simulations are agreement, even in some points there are differences.
International Nuclear Information System (INIS)
Obradovic, D.
1970-04-01
In the study of the nuclear reactors space-time behaviour the modal analysis is very often used though some basic mathematical problems connected with application of this methods are still unsolved. In this paper the modal analysis is identified as a set of the methods in the mathematical literature known as the Galerkin methods (or projection methods, or sometimes direct methods). Using the results of the mathematical investigations of these methods the applicability of the Galerkin type methods to the calculations of the eigenvalue and eigenvectors of the stationary and non-stationary diffusion operator, as well as for the solutions of the corresponding functional equations, is established (author)
International Nuclear Information System (INIS)
Hill, T.R.; Reed, W.H.
1976-01-01
TIMEX solves the time-dependent, one-dimensional multigroup transport equation with delayed neutrons in plane, cylindrical, spherical, and two-angle plane geometries. Both regular and adjoint, inhomogeneous and homogeneous problems subject to vacuum, reflective, periodic, white, albedo or inhomogeneous boundary flux conditions are solved. General anisotropic scattering is allowed and anisotropic inhomogeneous sources are permitted. The discrete ordinates approximation for the angular variable is used with the diamond (central) difference approximation for the angular extrapolation in curved geometries. A linear discontinuous finite element representation for the angular flux in each spatial mesh cell is used. The time variable is differenced by an explicit technique that is unconditionally stable so that arbitrarily large time steps can be taken. Because no iteration is performed the method is exceptionally fast in terms of computing time per time step. Two acceleration methods, exponential extrapolation and rebalance, are utilized to improve the accuracy of the time differencing scheme. Variable dimensioning is used so that any combination of problem parameters leading to a container array less than MAXCOR can be accommodated. The running time for TIMEX is highly problem-dependent, but varies almost linearly with the total number of unknowns and time steps. Provision is made for creation of standard interface output files for angular fluxes and angle-integrated fluxes. Five interface units (use of interface units is optional), five output units, and two system input/output units are required. A large bulk memory is desirable, but may be replaced by disk, drum, or tape storage. 13 tables, 9 figures
International Nuclear Information System (INIS)
Ferri, A.A.
1986-01-01
Nodal methods applied in order to calculate the power distribution in a nuclear reactor core are presented. These methods have received special attention, because they yield accurate results in short computing times. Present nodal schemes contain several unknowns per node and per group. In the methods presented here, non linear feedback of the coupling coefficients has been applied to reduce this number to only one unknown per node and per group. The resulting algorithm is a 7- points formula, and the iterative process has proved stable in the response matrix scheme. The intranodal flux shape is determined by partial integration of the diffusion equations over two of the coordinates, leading to a set of three coupled one-dimensional equations. These can be solved by using a polynomial approximation or by integration (analytic solution). The tranverse net leakage is responsible for the coupling between the spatial directions, and two alternative methods are presented to evaluate its shape: direct parabolic approximation and local model expansion. Numerical results, which include the IAEA two-dimensional benchmark problem illustrate the efficiency of the developed methods. (M.E.L.) [es
International Nuclear Information System (INIS)
Pashchenko, A.B.; Wienke, H.; Ganesan, S.
1996-01-01
Selected neutron reaction nuclear data evaluations and photon-atomic interaction cross section libraries for elements of interest to the IAEA's program on Fusion Evaluated Nuclear Data Library (FENDL) have been processed into GENDF and MATXS format using the NJOY system by R.E. MacFarlane, in VITAMIN-J group structure with VITAMIN-E weighting spectrum. This document summarizes the resulting multigroup data library FENDL/MG version 1.1. The data are available costfree, upon request from the IAEA Nuclear Data Section, online or on magnetic tape. (author). 7 refs, 1 tab
International Nuclear Information System (INIS)
Kim, Jung-Do; Lee, Jong Tai
1986-01-01
Description of problem or function: Format: TEMPEST and MUFT; Number of groups: 246 thermal groups in TEMPEST Format and 54 fast groups in MUFT Format. From this library, the program SPOTS4 generates a 172-54 group library as input to the code LEOPARD. Nuclides: H, O, Zr, C, Fe, Ni, Al, Cr, Mn, U, Pu, Th, Pa, Xe, Sm, B and D. Origin: ENDF/B-4; Weighting spectrum: 1/E + U 235 fission spectrum. Data library of thermal and fast neutron group Cross sections to generate input to the program LEOPARD. The data is based on ENDF/B-4 and consists of two parts: (1) 246 thermal groups in TEMPEST Format. (2) 54 fast groups in MUFT Format. From this library, the program SPOTS4 generates a 172-54 group library as input to the code LEOPARD (NESC0279)
Neutron diffusion: connection with the theory of browniam motion
International Nuclear Information System (INIS)
Dellagi, Mohamed
1977-01-01
The displacement of the neutron projection on an axis Ox and its density of probability are introduced instead of describing the diffusion theory with neutron density, as is usual. If the point source O is isotropic and neutron monoenergetic, the brownian particle described by Langevin's equation and neutron have the same time correlation of velocity [fr
International Nuclear Information System (INIS)
Geemert, René van
2014-01-01
Highlights: • New type of multi-level rebalancing approach for nodal transport. • Generally improved and more mesh-independent convergence behavior. • Importance for intended regime of 3D pin-by-pin core computations. - Abstract: A new multi-level surface rebalancing (MLSR) approach has been developed, aimed at enabling an improved non-linear acceleration of nodal flux iteration convergence in 3D steady-state and transient reactor simulation. This development is meant specifically for anticipating computational needs for solving envisaged multi-group diffusion-like SP N calculations with enhanced mesh resolution (i.e. 3D multi-box up to 3D pin-by-pin grid). For the latter grid refinement regime, the previously available multi-level coarse mesh rebalancing (MLCMR) strategy has been observed to become increasingly inefficient with increasing 3D mesh resolution. Furthermore, for very fine 3D grids that feature a very fine axial mesh as well, non-convergence phenomena have been observed to emerge. In the verifications pursued up to now, these problems have been resolved by the new approach. The novelty arises from taking the interface current balance equations defined over all Cartesian box edges, instead of the nodal volume-integrated process-rate balance equation, as an appropriate restriction basis for setting up multi-level acceleration of fine grid interface current iterations. The new restriction strategy calls for the use of a newly derived set of adjoint spectral equations that are needed for computing a limited set of spectral response vectors per node. This enables a straightforward determination of group-condensed interface current spectral coupling operators that are of crucial relevance in the new rebalancing setup. Another novelty in the approach is a new variational method for computing the neutronic eigenvalue. Within this context, the latter is treated as a control parameter for driving another, newly defined and numerically more fundamental
GPU-accelerated 3D neutron diffusion code based on finite difference method
Energy Technology Data Exchange (ETDEWEB)
Xu, Q.; Yu, G.; Wang, K. [Dept. of Engineering Physics, Tsinghua Univ. (China)
2012-07-01
Finite difference method, as a traditional numerical solution to neutron diffusion equation, although considered simpler and more precise than the coarse mesh nodal methods, has a bottle neck to be widely applied caused by the huge memory and unendurable computation time it requires. In recent years, the concept of General-Purpose computation on GPUs has provided us with a powerful computational engine for scientific research. In this study, a GPU-Accelerated multi-group 3D neutron diffusion code based on finite difference method was developed. First, a clean-sheet neutron diffusion code (3DFD-CPU) was written in C++ on the CPU architecture, and later ported to GPUs under NVIDIA's CUDA platform (3DFD-GPU). The IAEA 3D PWR benchmark problem was calculated in the numerical test, where three different codes, including the original CPU-based sequential code, the HYPRE (High Performance Pre-conditioners)-based diffusion code and CITATION, were used as counterpoints to test the efficiency and accuracy of the GPU-based program. The results demonstrate both high efficiency and adequate accuracy of the GPU implementation for neutron diffusion equation. A speedup factor of about 46 times was obtained, using NVIDIA's Geforce GTX470 GPU card against a 2.50 GHz Intel Quad Q9300 CPU processor. Compared with the HYPRE-based code performing in parallel on an 8-core tower server, the speedup of about 2 still could be observed. More encouragingly, without any mathematical acceleration technology, the GPU implementation ran about 5 times faster than CITATION which was speeded up by using the SOR method and Chebyshev extrapolation technique. (authors)
GPU-accelerated 3D neutron diffusion code based on finite difference method
International Nuclear Information System (INIS)
Xu, Q.; Yu, G.; Wang, K.
2012-01-01
Finite difference method, as a traditional numerical solution to neutron diffusion equation, although considered simpler and more precise than the coarse mesh nodal methods, has a bottle neck to be widely applied caused by the huge memory and unendurable computation time it requires. In recent years, the concept of General-Purpose computation on GPUs has provided us with a powerful computational engine for scientific research. In this study, a GPU-Accelerated multi-group 3D neutron diffusion code based on finite difference method was developed. First, a clean-sheet neutron diffusion code (3DFD-CPU) was written in C++ on the CPU architecture, and later ported to GPUs under NVIDIA's CUDA platform (3DFD-GPU). The IAEA 3D PWR benchmark problem was calculated in the numerical test, where three different codes, including the original CPU-based sequential code, the HYPRE (High Performance Pre-conditioners)-based diffusion code and CITATION, were used as counterpoints to test the efficiency and accuracy of the GPU-based program. The results demonstrate both high efficiency and adequate accuracy of the GPU implementation for neutron diffusion equation. A speedup factor of about 46 times was obtained, using NVIDIA's Geforce GTX470 GPU card against a 2.50 GHz Intel Quad Q9300 CPU processor. Compared with the HYPRE-based code performing in parallel on an 8-core tower server, the speedup of about 2 still could be observed. More encouragingly, without any mathematical acceleration technology, the GPU implementation ran about 5 times faster than CITATION which was speeded up by using the SOR method and Chebyshev extrapolation technique. (authors)
Homotopy analysis method for neutron diffusion calculations
International Nuclear Information System (INIS)
Cavdar, S.
2009-01-01
The Homotopy Analysis Method (HAM), proposed in 1992 by Shi Jun Liao and has been developed since then, is based on a fundamental concept in differential geometry and topology, the homotopy. It has proved useful for problems involving algebraic, linear/non-linear, ordinary/partial differential and differential-integral equations being an analytic, recursive method that provides a series sum solution. It has the advantage of offering a certain freedom for the choice of its arguments such as the initial guess, the auxiliary linear operator and the convergence control parameter, and it allows us to effectively control the rate and region of convergence of the series solution. HAM is applied for the fixed source neutron diffusion equation in this work, which is a part of our research motivated by the question of whether methods for solving the neutron diffusion equation that yield straightforward expressions but able to provide a solution of reasonable accuracy exist such that we could avoid analytic methods that are widely used but either fail to solve the problem or provide solutions through many intricate expressions that are likely to contain mistakes or numerical methods that require powerful computational resources and advanced programming skills due to their very nature or intricate mathematical fundamentals. Fourier basis are employed for expressing the initial guess due to the structure of the problem and its boundary conditions. We present the results in comparison with other widely used methods of Adomian Decomposition and Variable Separation.
Finite difference solution of the time dependent neutron group diffusion equations
International Nuclear Information System (INIS)
Hendricks, J.S.; Henry, A.F.
1975-08-01
In this thesis two unrelated topics of reactor physics are examined: the prompt jump approximation and alternating direction checkerboard methods. In the prompt jump approximation it is assumed that the prompt and delayed neutrons in a nuclear reactor may be described mathematically as being instantaneously in equilibrium with each other. This approximation is applied to the spatially dependent neutron diffusion theory reactor kinetics model. Alternating direction checkerboard methods are a family of finite difference alternating direction methods which may be used to solve the multigroup, multidimension, time-dependent neutron diffusion equations. The reactor mesh grid is not swept line by line or point by point as in implicit or explicit alternating direction methods; instead, the reactor mesh grid may be thought of as a checkerboard in which all the ''red squares'' and '' black squares'' are treated successively. Two members of this family of methods, the ADC and NSADC methods, are at least as good as other alternating direction methods. It has been found that the accuracy of implicit and explicit alternating direction methods can be greatly improved by the application of an exponential transformation. This transformation is incompatible with checkerboard methods. Therefore, a new formulation of the exponential transformation has been developed which is compatible with checkerboard methods and at least as good as the former transformation for other alternating direction methods
International Nuclear Information System (INIS)
Kim, M.G.
1980-01-01
The multigroup neutron diffusion equations with the constraint of specified power distributions are investigated by the application of the straight-line method which can be considered as the limiting case of zero mesh space in the finite difference method. The standard partial differential form of the diffusion equation is reduced to sets of ordinary differential equations and then converted into sets of integral equations by using Green's functions defined on the pseudo straight lines. Coupling of each straight line to the adjacent lines arises from the application of a three-point central difference formula. The interfaces encountered between two regions are taken into account by imposing the continuity conditions for the grown fluxes and net currents with Taylor expansions of internal fluxes at the interface positions. A few sample problems are selected to test the validity of the method. It is found that the proposed method of solution is similar to the finite Fourier sine transform. Numerical results for the solutions obtained by the method of straight lines are compared with the results of the exact analytical solutions for simple geometries. These comparisons indicate that the proposed method is compatible with the analytical method, and in some problems considered the straight-line solutions are much more efficient than the exact solutions. The method is also extended to the reactor kinetics problem by expressing the kinetics parameters in terms of the basis functions which are used to obtain the solutions of the steady-state neutron diffusion equations
Multi-level methods for solving multigroup transport eigenvalue problems in 1D slab geometry
International Nuclear Information System (INIS)
Anistratov, D. Y.; Gol'din, V. Y.
2009-01-01
A methodology for solving eigenvalue problems for the multigroup neutron transport equation in 1D slab geometry is presented. In this paper we formulate and compare different variants of nonlinear multi-level iteration methods. They are defined by means of multigroup and effective one-group low-order quasi diffusion (LOQD) equations. We analyze the effects of utilization of the effective one-group LOQD problem for estimating the eigenvalue. We present numerical results to demonstrate the performance of the iteration algorithms in different types of reactor-physics problems. (authors)
International Nuclear Information System (INIS)
Jagannathan, V.
1985-01-01
A modular computer code system called FEMSYN has been developed to solve the multigroup diffusion theory equations. The various methods that are incorporated in FEMSYN are (i) finite difference method (FDM) (ii) finite element method (FEM) and (iii) single channel flux synthesis method (SCFS). These methods are described in detail in parts II, III and IV of the present report. In this report, a comparison of the accuracy and the speed of different methods of solution for some benchmark problems are reported. The input preparation and listing of sample input and output are included in the Appendices. The code FEMSYN has been used to solve a wide variety of reactor core problems. It can be used for both LWR and PHWR applications. (author)
International Nuclear Information System (INIS)
Jagannathan, V.
1985-01-01
For solving the multigroup diffusion theory equations in 3-D problems in which the material properties are uniform in large segments of axial direction, the synthesis method is known to give fairly accurate results, at very low computational cost. In the code system FEMSYN, the single channel continuous flux synthesis option has been incorporated. One can generate the radial trail functions by either finite difference method (FDM) or finite element method (FEM). The axial mixing functions can also be found by either FDM or FEM. Use of FEM for both radial and axial directions is found to reduce the calculation time considerably. One can determine eigenvalue, 3-D flux and power distributions with FEMSYN. In this report, a detailed discription of the synthesis module SYNTHD is given. (author)
International Nuclear Information System (INIS)
Nagaya, Yasunobu; Okumura, Keisuke; Sakurai, Takeshi; Mori, Takamasa
2017-03-01
In order to realize fast and accurate Monte Carlo simulation of neutron and photon transport problems, two Monte Carlo codes MVP (continuous-energy method) and GMVP (multigroup method) have been developed at Japan Atomic Energy Agency. The codes have adopted a vectorized algorithm and have been developed for vector-type supercomputers. They also support parallel processing with a standard parallelization library MPI and thus a speed-up of Monte Carlo calculations can be achieved on general computing platforms. The first and second versions of the codes were released in 1994 and 2005, respectively. They have been extensively improved and new capabilities have been implemented. The major improvements and new capabilities are as follows: (1) perturbation calculation for effective multiplication factor, (2) exact resonant elastic scattering model, (3) calculation of reactor kinetics parameters, (4) photo-nuclear model, (5) simulation of delayed neutrons, (6) generation of group constants. This report describes the physical model, geometry description method used in the codes, new capabilities and input instructions. (author)
International Nuclear Information System (INIS)
Nagaya, Yasunobu; Okumura, Keisuke; Sakurai, Takeshi; Mori, Takamasa
2017-03-01
In order to realize fast and accurate Monte Carlo simulation of neutron and photon transport problems, two Monte Carlo codes MVP (continuous-energy method) and GMVP (multigroup method) have been developed at Japan Atomic Energy Agency. The codes have adopted a vectorized algorithm and have been developed for vector-type supercomputers. They also support parallel processing with a standard parallelization library MPI and thus a speed-up of Monte Carlo calculations can be achieved on general computing platforms. The first and second versions of the codes were released in 1994 and 2005, respectively. They have been extensively improved and new capabilities have been implemented. The major improvements and new capabilities are as follows: (1) perturbation calculation for effective multiplication factor, (2) exact resonant elastic scattering model, (3) calculation of reactor kinetics parameters, (4) photo-nuclear model, (5) simulation of delayed neutrons, (6) generation of group constants. This report describes the physical model, geometry description method used in the codes, new capabilities and input instructions. (author)
Current trends in methods for neutron diffusion calculations
International Nuclear Information System (INIS)
Adams, C.H.
1977-01-01
Current work and trends in the application of neutron diffusion theory to reactor design and analysis are reviewed. Specific topics covered include finite-difference methods, synthesis methods, nodal calculations, finite-elements and perturbation theory
Program SITHA. New version of the multigroup system of the neutron cross section GR175-V1
International Nuclear Information System (INIS)
Daniehl', A.V.; Perov, V.Yu.; Sokol, E.A.
1991-01-01
Structure of the system of the group neutron constants with band description of the resonance field and program system is described. Results of the testing calculations, made by code SITHA, for number of integral experiments devoted to measurements of the neutron flux from H 2 O,C,N,O and Al spherical targets are discussed. 13 refs.; 8 figs.; 1 tab
Energy Technology Data Exchange (ETDEWEB)
Burns, Kimberly A. [Georgia Inst. of Technology, Atlanta, GA (United States)
2009-08-01
The accurate and efficient simulation of coupled neutron-photon problems is necessary for several important radiation detection applications. Examples include the detection of nuclear threats concealed in cargo containers and prompt gamma neutron activation analysis for nondestructive determination of elemental composition of unknown samples.
NUMERICAL MULTIGROUP TRANSIENT ANALYSIS OF SLAB NUCLEAR REACTOR WITH THERMAL FEEDBACK
Directory of Open Access Journals (Sweden)
Filip Osuský
2016-12-01
Full Text Available The paper describes a new numerical code for multigroup transient analyses with thermal feedback. The code is developed at Institute of Nuclear and Physical Engineering. It is necessary to carefully investigate transient states of fast neutron reactors, due to recriticality issues after accident scenarios. The code solves numerical diffusion equation for 1D problem with possible neutron source incorporation. Crank-Nicholson numerical method is used for the transient states. The investigated cases are describing behavior of PWR fuel assembly inside of spent fuel pool and with the incorporated neutron source for better illustration of thermal feedback.
Pulsed neutron method for diffusion, slowing down, and reactivity measurements
International Nuclear Information System (INIS)
Sjoestrand, N.G.
1985-01-01
An outline is given on the principles of the pulsed neutron method for the determination of thermal neutron diffusion parameters, for slowing-down time measurements, and for reactivity determinations. The historical development is sketched from the breakthrough in the middle of the nineteen fifties and the usefulness and limitations of the method are discussed. The importance for the present understanding of neutron slowing-down, thermalization and diffusion are point out. Examples are given of its recent use for e.g. absorption cross section measurements and for the study of the properties of heterogeneous systems
Parallel diffusion length on thermal neutrons in rod type lattices
International Nuclear Information System (INIS)
Ahmed, T.; Siddiqui, S.A.M.M.; Khan, A.M.
1981-11-01
Calculation of diffusion lengths of thermal neutrons in lead-water and aluminum water lattices in direction parallel to the rods are performed using one group diffusion equation together with Shevelev transport correction. The formalism is then applied to two practical cases, the Kawasaki (Hitachi) and the Douglas point (Candu) reactor lattices. Our results are in good agreement with the observed values. (author)
Derivation of a volume-averaged neutron diffusion equation; Atomos para el desarrollo de Mexico
Energy Technology Data Exchange (ETDEWEB)
Vazquez R, R.; Espinosa P, G. [UAM-Iztapalapa, Av. San Rafael Atlixco 186, Col. Vicentina, Mexico D.F. 09340 (Mexico); Morales S, Jaime B. [UNAM, Laboratorio de Analisis en Ingenieria de Reactores Nucleares, Paseo Cuauhnahuac 8532, Jiutepec, Morelos 62550 (Mexico)]. e-mail: rvr@xanum.uam.mx
2008-07-01
This paper presents a general theoretical analysis of the problem of neutron motion in a nuclear reactor, where large variations on neutron cross sections normally preclude the use of the classical neutron diffusion equation. A volume-averaged neutron diffusion equation is derived which includes correction terms to diffusion and nuclear reaction effects. A method is presented to determine closure-relationships for the volume-averaged neutron diffusion equation (e.g., effective neutron diffusivity). In order to describe the distribution of neutrons in a highly heterogeneous configuration, it was necessary to extend the classical neutron diffusion equation. Thus, the volume averaged diffusion equation include two corrections factor: the first correction is related with the absorption process of the neutron and the second correction is a contribution to the neutron diffusion, both parameters are related to neutron effects on the interface of a heterogeneous configuration. (Author)
Measurement of neutron diffusion length in heavy concrete
International Nuclear Information System (INIS)
Krejci, D.
2007-04-01
Using an aluminium sampler filled with heavy concrete the neutron diffusion length was determined, measuring thermal and fast neutrons over the whole beam hole with various threshold detectors using gold samples. These calculations should describe the neutron distribution in the whole concrete shield of the reactor and contribute to the investigation of the activation of the concrete shield using reactor parameters like operating time, power and neutron flux. Instrumentation, activation and positioning of the samples in the beam hole of the TRIGA Mark II reactor are described. (nevyjel)
Neutron spin-echo spectroscopy for diffusion in crystalline solids
International Nuclear Information System (INIS)
Kaisermayr, M.; Rennhofer, M.; Vogl, G.; Pappas, C.; Longeville, S.
2002-01-01
Neutron spin-echo spectroscopy (NSE) offers unprecedented opportunities in the investigation of diffusion in crystalline systems due to its outstanding energy resolution. NSE not only enables measurements at lower diffusivities than the established techniques of neutron spectroscopy, but it also gives a very immediate access to the different time scales involved in the diffusion process. This is demonstrated in detail on the example of the binary alloy NiGa where the Ni atoms hop between regular sites on the Ni sublattice and anti-sites on the Ga sublattice. Experiments on two different NSE instruments are compared to measurements using neutron backscattering spectroscopy. The potential of NSE for the investigation of jump diffusion and experimental requirements are discussed
International Nuclear Information System (INIS)
Nagaya, Yasunobu; Okumura, Keisuke; Mori, Takamasa; Nakagawa, Masayuki
2005-06-01
In order to realize fast and accurate Monte Carlo simulation of neutron and photon transport problems, two vectorized Monte Carlo codes MVP and GMVP have been developed at JAERI. MVP is based on the continuous energy model and GMVP is on the multigroup model. Compared with conventional scalar codes, these codes achieve higher computation speed by a factor of 10 or more on vector super-computers. Both codes have sufficient functions for production use by adopting accurate physics model, geometry description capability and variance reduction techniques. The first version of the codes was released in 1994. They have been extensively improved and new functions have been implemented. The major improvements and new functions are (1) capability to treat the scattering model expressed with File 6 of the ENDF-6 format, (2) time-dependent tallies, (3) reaction rate calculation with the pointwise response function, (4) flexible source specification, (5) continuous-energy calculation at arbitrary temperatures, (6) estimation of real variances in eigenvalue problems, (7) point detector and surface crossing estimators, (8) statistical geometry model, (9) function of reactor noise analysis (simulation of the Feynman-α experiment), (10) arbitrary shaped lattice boundary, (11) periodic boundary condition, (12) parallelization with standard libraries (MPI, PVM), (13) supporting many platforms, etc. This report describes the physical model, geometry description method used in the codes, new functions and how to use them. (author)
International Nuclear Information System (INIS)
Kim, Jung Do; Gil, Choong Sup.
1997-03-01
The KAFAX-F22 was developed from JEF-2.2, which is a MATXS format, multigroup library of fast reactor. The KAFAX-F22 has 80 and 24 energy group structures for neutron and photon, respectively. It includes 89 nuclide data processed by NJOY94.38. The TRANSX/TWODANT system was used for benchmark calculations of fast reactor and one- and two-dimensional calculations of ONEDANT and TWODANT were carried out with 80 group, P 3 S 16 and with 25 group, P 3 S 8 , respectively. The average values of multiplication factors are 0.99652 for MOX cores, 1.00538 for uranium cores and 1.00032 for total cores. Various central reaction rate ratios also give good agreements with the experimental values considering experimental uncertainties except for VERA-11A, VERA-1B, ZPR-6-7 and ZPR-6-6A cores of which experimental values seem to involve some problems. (author). 13 refs., 18 tabs., 2 figs
International Nuclear Information System (INIS)
Premuda, F.
1983-01-01
Two lines in improved neutron diffusion theory extending the efficiency of finite-difference diffusion codes to the field of optically small systems, are here reviewed. The firs involves the nodal solution for tensorial diffusion equation in slab geometry and tensorial formulation in parallelepiped and cylindrical gemometry; the dependence of critical eigenvalue from small slab thicknesses is also analitically investigated and finally a regularized tensorial diffusion equation is derived for slab. The other line refer to diffusion models formally unchanged with respect to the classical one, but where new size-dependent RTGB definitions for diffusion parameters are adopted, requiring that they allow to reproduce, in diffusion approach, the terms of neutron transport global balance; the trascendental equation for the buckling, arising in slab, sphere and parallelepiped geometry from the above requirement, are reported and the sizedependence of the new diffusion coefficient and extrapolated end point is investigated
A fast nodal neutron diffusion method for cartesian geometry
International Nuclear Information System (INIS)
Makai, M.; Maeder, C.
1983-01-01
A numerical method based on an analytical solution to the three-dimensional two-group diffusion equation has been derived assuming that the flux is a sum of the functions of one variable. In each mesh the incoming currents are used as boundary conditions. The final equations for the average flux and the outgoing currents are of the response matrix type. The method is presented in a form that can be extended to the general multigroup case. In the SEXI computer program developed on the basis of this method, the response matrix elements are recalculated in each outer iteration to minimize the data transfer between disk storage and central memory. The efficiency of the method is demonstrated for a light water reactor (LWR) benchmark problem. The SEXI program has been incorporated into the LWR simulator SILWER code as a possible option
International Nuclear Information System (INIS)
Gast, R.C.
1981-08-01
A procedure for defining diffusion coefficients from Monte Carlo calculations that results in suitable ones for use in neutron diffusion theory calculations is not readily obtained. This study provides a survey of the methods used to define diffusion coefficients from deterministic calculations and provides a discussion as to why such traditional methods cannot be used in Monte Carlo. This study further provides the empirical procedure used for defining diffusion coefficients from the RCP01 Monte Carlo program
3-DB, 3-D Multigroup Diffusion, X-Y-Z, R-Theta-Z, Triangular-Z Geometry, Fast Reactor Burnup
International Nuclear Information System (INIS)
Hardie, R.W.; Little, W.W. Jr.; Mroz, W.
1974-01-01
1 - Description of problem or function: 3DB is a three-dimensional (x-y-z, r-theta-z, triangular-z) multigroup diffusion code for use in detailed fast-reactor criticality and burnup analysis. The code can be used to - (a) compute k eff and perform criticality searches on time absorption, reactor composition, and reactor dimensions by means of either a flux or an adjoint model, (b) compute material burnup using a flexible material shuffling scheme, and (c) compute flux distributions for an arbitrary extraneous source. 2 - Method of solution: Eigenvalues are computed by standard source- iteration techniques. Group re-balancing and successive over-relaxation with line inversion are used to accelerate convergence. Adjoint solutions are obtained by inverting the input data and redefining the source terms. Material burnup is by reactor zone. The burnup rate is determined by the zone and energy-averaged cross sections which are recomputed after each time-step. The isotopic chains, which can contain any number of isotopes are formed by the user. The code does not contain built- in or internal chains. 3 - Restrictions on the complexity of the problem: Since variable dimensioning is employed, no simple bounds can be stated
Energy Technology Data Exchange (ETDEWEB)
Hosseini, Seyed Abolfaz [Dept. of Energy Engineering, Sharif University of Technology, Tehran (Iran, Islamic Republic of)
2017-02-15
The purpose of the present study is the presentation of the appropriate element and shape function in the solution of the neutron diffusion equation in two-dimensional (2D) geometries. To this end, the multigroup neutron diffusion equation is solved using the Galerkin finite element method in both rectangular and hexagonal reactor cores. The spatial discretization of the equation is performed using unstructured triangular and quadrilateral finite elements. Calculations are performed using both linear and quadratic approximations of shape function in the Galerkin finite element method, based on which results are compared. Using the power iteration method, the neutron flux distributions with the corresponding eigenvalue are obtained. The results are then validated against the valid results for IAEA-2D and BIBLIS-2D benchmark problems. To investigate the dependency of the results to the type and number of the elements, and shape function order, a sensitivity analysis of the calculations to the mentioned parameters is performed. It is shown that the triangular elements and second order of the shape function in each element give the best results in comparison to the other states.
Reflector modelization for neutronic diffusion and parameters identification
International Nuclear Information System (INIS)
Argaud, J.P.
1993-04-01
Physical parameters of neutronic diffusion equations can be adjusted to decrease calculations-measurements errors. The reflector being always difficult to modelize, we choose to elaborate a new reflector model and to use the parameters of this model as adjustment coefficients in the identification procedure. Using theoretical results, and also the physical behaviour of neutronic flux solutions, the reflector model consists then in its replacement by boundary conditions for the diffusion equations on the core only. This theoretical result of non-local operator relations leads then to some discrete approximations by taking into account the multiscaled behaviour, on the core-reflector interface, of neutronic diffusion solutions. The resulting model of this approach is then compared with previous reflector modelizations, and first results indicate that this new model gives the same representation of reflector for the core than previous. (author). 12 refs
Measurement of diffusion length of thermal neutrons in concrete
International Nuclear Information System (INIS)
Moser, M.
2007-04-01
The diffusion length of neutrons with a medium energy < 0.025 eV in concrete were determined using 4π-β detector and gamma detectors. Then it was possible to determine how deep can neutrons penetrate diverse concrete construction parts in a reactor in operation, with this method the dismantling process of a reactor can be planned in terms of what parts can be removed without danger and what parts can be assumed still are activated. (nevyjel)
Determination of thermal neutrons diffusion length in graphite
International Nuclear Information System (INIS)
Garcia Fite, J.
1959-01-01
The diffusion length of thermal neutrons in graphite using the less possible quantity of material has been determined. The proceeding used was the measurement in a graphite pile which has a punctual source of rapid neutrons inside surrounded by a reflector medium (paraffin or water). The measurement was done in the following conditions: a) introducing an aluminium plate between both materials. b) Introducing a cadmium plate between both materials. (Author) 91 refs
On the numerical solution of the neutron fractional diffusion equation
International Nuclear Information System (INIS)
Maleki Moghaddam, Nader; Afarideh, Hossein; Espinosa-Paredes, Gilberto
2014-01-01
Highlights: • The new version of neutron diffusion equation which established on the fractional derivatives is presented. • The Neutron Fractional Diffusion Equation (NFDE) is solved in the finite differences frame. • NFDE is solved using shifted Grünwald-Letnikov definition of fractional operators. • The results show that “K eff ” strongly depends on the order of fractional derivative. - Abstract: In order to core calculation in the nuclear reactors there is a new version of neutron diffusion equation which is established on the fractional partial derivatives, named Neutron Fractional Diffusion Equation (NFDE). In the NFDE model, neutron flux in each zone depends directly on the all previous zones (not only on the nearest neighbors). Under this circumstance, it can be said that the NFDE has the space history. We have developed a one-dimension code, NFDE-1D, which can simulate the reactor core using arbitrary exponent of differential operators. In this work a numerical solution of the NFDE is presented using shifted Grünwald-Letnikov definition of fractional derivative in finite differences frame. The model is validated with some numerical experiments where different orders of fractional derivative are considered (e.g. 0.999, 0.98, 0.96, and 0.94). The results show that the effective multiplication factor (K eff ) depends strongly on the order of fractional derivative
Chemical order-disorder in alloys. Study by neutrons diffuse diffusion
International Nuclear Information System (INIS)
Novion, C. de; Beuneu, B.
1993-01-01
Applications of neutrons diffuse diffusion for short distance chemical order in FCC transition metals solid solutions (Pd-V, Ni-V, Ni-Cr) and understoichiometric carbides or nitrides of transition metals (TiC 1-x , NbC 1-x , TiN 1-x ) are shortly presented with theoretical and experimental aspects. (A.B.)
Solving the uncommon nuclear reactor core neutronics problems
International Nuclear Information System (INIS)
Vondy, D.R.; Fowler, T.B.
1983-01-01
Calculational procedures have been implemented for solving importance and higher harmonic neutronics problems. Solutions are obtained routinely to support analysis of reactor core performance, treating up to three space coordinates with the multigroup diffusion theory approximation to neutron transport. The techniques used and some of the calculational difficulties are discussed
Generating and verification of ACE-multigroup library for MCNP
International Nuclear Information System (INIS)
Chen Chaobin; Hu Zehua; Chen Yixue; Wu Jun; Yang Shouhai
2012-01-01
The Monte Carlo code MCNP can handle multigroup calculations and a sample multigroup set based on ENDF/B-V, MGXSNP, is available for MCNP for coupled neutron-photon transport. However, this library is not suit- able for all problems, and there is a need for users to be able to generate multigroup libraries tailored to their specific applications. For these purposes CSPT (cross section processing tool) is created to generate multigroup library for MCNP from deterministic multigroup cross sections (GENDF or ANISN format at present). Several ACE-multigroup libraries based on ENDF/B-VII.0 converted and verified in this work, we drawn the conclusion that the CSPT code works correctly and the libraries produced are credible. (authors)
Energy Technology Data Exchange (ETDEWEB)
Costa da Silva, Adilson; Carvalho da Silva, Fernando [COPPE/UFRJ, Programa de Engenharia Nuclear, Caixa Postal 68509, 21941-914, Rio de Janeiro (Brazil); Senra Martinez, Aquilino, E-mail: aquilino@lmp.ufrj.br [COPPE/UFRJ, Programa de Engenharia Nuclear, Caixa Postal 68509, 21941-914, Rio de Janeiro (Brazil)
2011-07-15
Highlights: > We proposed a new neutron diffusion hybrid equation with external neutron source. > A coarse mesh finite difference method for the adjoint flux and reactivity calculation was developed. > 1/M curve to predict the criticality condition is used. - Abstract: We used the neutron diffusion hybrid equation, in cartesian geometry with external neutron sources to predict the subcritical multiplication of neutrons in a pressurized water reactor, using a 1/M curve to predict the criticality condition. A Coarse Mesh Finite Difference Method was developed for the adjoint flux calculation and to obtain the reactivity values of the reactor. The results obtained were compared with benchmark values in order to validate the methodology presented in this paper.
International Nuclear Information System (INIS)
Costa da Silva, Adilson; Carvalho da Silva, Fernando; Senra Martinez, Aquilino
2011-01-01
Highlights: → We proposed a new neutron diffusion hybrid equation with external neutron source. → A coarse mesh finite difference method for the adjoint flux and reactivity calculation was developed. → 1/M curve to predict the criticality condition is used. - Abstract: We used the neutron diffusion hybrid equation, in cartesian geometry with external neutron sources to predict the subcritical multiplication of neutrons in a pressurized water reactor, using a 1/M curve to predict the criticality condition. A Coarse Mesh Finite Difference Method was developed for the adjoint flux calculation and to obtain the reactivity values of the reactor. The results obtained were compared with benchmark values in order to validate the methodology presented in this paper.
Generalized diffusion theory for calculating the neutron transport scalar flux
International Nuclear Information System (INIS)
Alcouffe, R.E.
1975-01-01
A generalization of the neutron diffusion equation is introduced, the solution of which is an accurate approximation to the transport scalar flux. In this generalization the auxiliary transport calculations of the system of interest are utilized to compute an accurate, pointwise diffusion coefficient. A procedure is specified to generate and improve this auxiliary information in a systematic way, leading to improvement in the calculated diffusion scalar flux. This improvement is shown to be contingent upon satisfying the condition of positive calculated-diffusion coefficients, and an algorithm that ensures this positivity is presented. The generalized diffusion theory is also shown to be compatible with conventional diffusion theory in the sense that the same methods and codes can be used to calculate a solution for both. The accuracy of the method compared to reference S/sub N/ transport calculations is demonstrated for a wide variety of examples. (U.S.)
Diffuse neutron scattering from anion-excess strontium chloride
DEFF Research Database (Denmark)
Goff, J.P.; Clausen, K.N.; Fåk, B.
1992-01-01
The defect structure and diffusional processes have been studied in the anion-excess fluorite (Sr, Y)Cl2.03 by diffuse neutron scattering techniques. Static cuboctahedral clusters found at ambient temperature break up at temperatures below 1050 K, where the anion disorder is highly dynamic. The a...
Diffuse scattering of neutrons and X-rays
International Nuclear Information System (INIS)
Novion, C.H. de
1978-01-01
Diffuse scattering is used to study defect concentrations of about 10 -4 in the case of X-rays and 10 -3 in the case of neutrons. The foundations of diffuse scattering formalism are given, some experimental devices described and a few applications discussed: study by diffraction on powders of defects in CeOsub(2-x); short-range order study by X-rays on Cusub(0.75) Ausub(0.25); short-range order study by neutrons on Cusub(0.435)Nisub(0.565); short-range order study by electrons TiOx; study of irradiation-induced self-interstitials in Al; study of holes created by neutrons in Al [fr
Measurement of the diffusion length of thermal neutrons inside graphite
International Nuclear Information System (INIS)
Ertaud, A.; Beauge, R.; Fauquez, H.; De Laboulay, H.; Mercier, C.; Vautrey, L.
1948-11-01
The diffusion length of thermal neutrons inside a given industrial graphite is determined by measuring the neutron density inside a parallelepipedal piling up of graphite bricks (2.10 x 2.10 x 2.442 m). A 3.8 curies (Ra α → Be) source is placed inside the parallelepipedal block of graphite and thin manganese detectors are used. Corrections are added to the unweighted measurements to take into account the effects of the damping of supra-thermal neutrons in the measurement area. These corrections are experimentally deduced from the differential measurements made with a cadmium screen interposed between the source and the first plane of measurement. An error analysis completes the report. The diffusion length obtained is: L = 45.7 cm ± 0.3. The average density of the graphite used is 1.76 and the average apparent density of the piling up is 1.71. (J.S.)
Nodal spectrum method for solving neutron diffusion equation
International Nuclear Information System (INIS)
Sanchez, D.; Garcia, C. R.; Barros, R. C. de; Milian, D.E.
1999-01-01
Presented here is a new numerical nodal method for solving static multidimensional neutron diffusion equation in rectangular geometry. Our method is based on a spectral analysis of the nodal diffusion equations. These equations are obtained by integrating the diffusion equation in X, Y directions and then considering flat approximations for the current. These flat approximations are the only approximations that are considered in this method, as a result the numerical solutions are completely free from truncation errors. We show numerical results to illustrate the methods accuracy for coarse mesh calculations
An extension of diffusion theory for thermal neutrons near boundaries
International Nuclear Information System (INIS)
Alvarez Rivas, J. L.
1963-01-01
The distribution of thermal neutron flux has been measured inside and outside copper rods of several diameters, immersed in water. It has been found that these distributions can be calculated by means of elemental diffusion theory if the value of the coefficient of diffusion is changed. this parameter is truly a diffusion coefficient, which now also depends on the diameter of the rod. Through a model an expression of this coefficient is introduced which takes account of the measurements of the author and of those reported in PIGC P/928 (1995), ANL-5872 (1959), DEGR 319 (D) (1961). This model could be extended also to plane geometry. (Author) 19 refs
2-DB, 2-D Multigroup Diffusion, X-Y, R-Theta, Hexagonal Geometry Fast Reactor, Criticality Search
International Nuclear Information System (INIS)
Little, W.W. Jr.; Hardie, R.W.; Hirons, T.J.; O'Dell, R.D.
1969-01-01
1 - Description of problem or function: 2DB is a flexible, two- dimensional (x-y, r-z, r-theta, hex geometry) diffusion code for use in fast reactor analyses. The code can be used to: (a) Compute fuel burnup using a flexible material shuffling scheme. (b) Perform criticality searches on time absorption (alpha), material concentrations, and region dimensions using a regular or adjoint model. Criticality searches can be performed during burnup to compensate for fuel depletion. (c) Compute flux distributions for an arbitrary extraneous source. 2 - Method of solution: Standard source-iteration techniques are used. Group re-balancing and successive over-relaxation with line inversion are used to accelerate convergence. Material burnup is by reactor zone. The burnup rate is determined by the zone and energy (group) averaged cross sections which are recomputed after each time-step. The isotopic chains, which can contain any number of isotopes, are formed by the user. The code does not contain built-in or internal chains. 3 - Restrictions on the complexity of the problem: Since variable dimensioning is employed, no simple bounds can be stated. The current 1108 version, however, is nominally restricted to 50 energy groups in a 65 K memory. In the 6600 version the power fraction, average burnup rate, and breeding ratio calculations are limited to reactors with a maximum of 50 zones
System of adjoint P1 equations for neutron moderation
International Nuclear Information System (INIS)
Martinez, Aquilino Senra; Silva, Fernando Carvalho da; Cardoso, Carlos Eduardo Santos
2000-01-01
In some applications of perturbation theory, it is necessary know the adjoint neutron flux, which is obtained by the solution of adjoint neutron diffusion equation. However, the multigroup constants used for this are weighted in only the direct neutron flux, from the solution of direct P1 equations. In this work, this procedure is questioned and the adjoint P1 equations are derived by the neutron transport equation, the reversion operators rules and analogies between direct and adjoint parameters. (author)
International Nuclear Information System (INIS)
Keinert, J.
1982-06-01
In providing THERM-126 with cross section matrices for deuterium bound in heavy water the IKE phonon spectrum was reevaluated. The changes are modifications in the acoustic part and in the frequency of the second oscillator. Contrary to the phonon spectrum model for D in D 2 O in ENDF/B-IV the broad band of hindered rotations is assumed to be temperature dependent taking into account the diffusive motion of the molecule. With the new model scattering law data S (α, β) are generated in the temperature range 293.6 K-673.6 K. The THERM-126 scattering cross section matrices are calculated up to P 3 . As a validity check a lot of differential and integral cross sections are compared to experiments and benchmarks are recalculated. (orig.) [de
Energy Technology Data Exchange (ETDEWEB)
Martinez, Aquilino Senra; Silva, Fernando Carvalho da; Cardoso, Carlos Eduardo Santos [Universidade Federal, Rio de Janeiro, RJ (Brazil). Coordenacao dos Programas de Pos-graduacao de Engenharia. Programa de Engenharia Nuclear
2000-07-01
In some applications of perturbation theory, it is necessary know the adjoint neutron flux, which is obtained by the solution of adjoint neutron diffusion equation. However, the multigroup constants used for this are weighted in only the direct neutron flux, from the solution of direct P1 equations. In this work, this procedure is questioned and the adjoint P1 equations are derived by the neutron transport equation, the reversion operators rules and analogies between direct and adjoint parameters. (author)
Diffusion theory model for optimization calculations of cold neutron sources
International Nuclear Information System (INIS)
Azmy, Y.Y.
1987-01-01
Cold neutron sources are becoming increasingly important and common experimental facilities made available at many research reactors around the world due to the high utility of cold neutrons in scattering experiments. The authors describe a simple two-group diffusion model of an infinite slab LD 2 cold source. The simplicity of the model permits to obtain an analytical solution from which one can deduce the reason for the optimum thickness based solely on diffusion-type phenomena. Also, a second more sophisticated model is described and the results compared to a deterministic transport calculation. The good (particularly qualitative) agreement between the results suggests that diffusion theory methods can be used in parametric and optimization studies to avoid the generally more expensive transport calculations
Range calculations using multigroup transport methods
International Nuclear Information System (INIS)
Hoffman, T.J.; Robinson, M.T.; Dodds, H.L. Jr.
1979-01-01
Several aspects of radiation damage effects in fusion reactor neutron and ion irradiation environments are amenable to treatment by transport theory methods. In this paper, multigroup transport techniques are developed for the calculation of particle range distributions. These techniques are illustrated by analysis of Au-196 atoms recoiling from (n,2n) reactions with gold. The results of these calculations agree very well with range calculations performed with the atomistic code MARLOWE. Although some detail of the atomistic model is lost in the multigroup transport calculations, the improved computational speed should prove useful in the solution of fusion material design problems
DNS: Diffuse scattering neutron time-of-flight spectrometer
Directory of Open Access Journals (Sweden)
Yixi Su
2015-08-01
Full Text Available DNS is a versatile diffuse scattering instrument with polarisation analysis operated by the Jülich Centre for Neutron Science (JCNS, Forschungszentrum Jülich GmbH, outstation at the Heinz Maier-Leibnitz Zentrum (MLZ. Compact design, a large double-focusing PG monochromator and a highly efficient supermirror-based polarizer provide a polarized neutron flux of about 107 n cm-2 s-1. DNS is used for the studies of highly frustrated spin systems, strongly correlated electrons, emergent functional materials and soft condensed matter.
Neutron spectroscopy of fast hydrogen diffusion in BCC transition metals
International Nuclear Information System (INIS)
Richter, D.; Lottner, V.
1979-01-01
Quasielastic neutron scattering reveals microscopic details of both the time and space development of the H-diffusion process on an atomic scale. After outlining the method on the example of PdH/sub x/, new results on the jump geometry in bcc metals are surveyed. In particular, the anomalous diffusion behavior of H in Nb, Ta, and V at elevated temperature is emphasized, where correlated jump processes are important. The influence of impurities on the H-diffusion process is demonstrated by experiments performed on NbH/sub x/ doped with nitrogen impurities, which act as trapping centers for the diffusing hydrogen. The results are discussed in terms of a two-state random walk model which includes multiple trapping and detrapping processes. The concentration and temperature dependence of the capture and escape rates of traps are obtained
Asymptotic neutron scattering laws for anomalously diffusing quantum particles
Energy Technology Data Exchange (ETDEWEB)
Kneller, Gerald R. [Centre de Biophysique Moléculaire, CNRS, Rue Charles Sadron, 45071 Orléans (France); Université d’Orléans, Chateau de la Source-Ave. du Parc Floral, 45067 Orléans (France); Synchrotron-SOLEIL, L’Orme de Merisiers, 91192 Gif-sur-Yvette (France)
2016-07-28
The paper deals with a model-free approach to the analysis of quasielastic neutron scattering intensities from anomalously diffusing quantum particles. All quantities are inferred from the asymptotic form of their time-dependent mean square displacements which grow ∝t{sup α}, with 0 ≤ α < 2. Confined diffusion (α = 0) is here explicitly included. We discuss in particular the intermediate scattering function for long times and the Fourier spectrum of the velocity autocorrelation function for small frequencies. Quantum effects enter in both cases through the general symmetry properties of quantum time correlation functions. It is shown that the fractional diffusion constant can be expressed by a Green-Kubo type relation involving the real part of the velocity autocorrelation function. The theory is exact in the diffusive regime and at moderate momentum transfers.
Thermal diffuse scattering in angular-dispersive neutron diffraction
International Nuclear Information System (INIS)
Popa, N.C.; Willis, B.T.M.
1998-01-01
The theoretical treatment of one-phonon thermal diffuse scattering (TDS) in single-crystal neutron diffraction at fixed incident wavelength is reanalysed in the light of the analysis given by Popa and Willis [Acta Cryst. (1994), (1997)] for the time-of-flight method. Isotropic propagation of sound with different velocities for the longitudinal and transverse modes is assumed. As in time-of-flight diffraction, there exists, for certain scanning variables, a forbidden range in the one-phonon TDS of slower-than-sound neutrons, and this permits the determination of the sound velocity in the crystal. A fast algorithm is given for the TDS correction of neutron diffraction data collected at a fixed wavelength: this algorithm is similar to that reported earlier for the time-of-flight case. (orig.)
Domain decomposition method for solving the neutron diffusion equation
International Nuclear Information System (INIS)
Coulomb, F.
1989-03-01
The aim of this work is to study methods for solving the neutron diffusion equation; we are interested in methods based on a classical finite element discretization and well suited for use on parallel computers. Domain decomposition methods seem to answer this preoccupation. This study deals with a decomposition of the domain. A theoretical study is carried out for Lagrange finite elements and some examples are given; in the case of mixed dual finite elements, the study is based on examples [fr
SHREDI, Neutron Flux and Neutron Activation in 2-D Shields by Removal Diffusion
International Nuclear Information System (INIS)
Daneri, A.; Toselli, G.
1976-01-01
1 - Nature of physical problem solved: SHREDI is a removal - diffusion neutron shielding code. The program computes neutron fluxes and activations in bidimensional sections (x,y or r,z) of the shield. It is also possible to consider shielding points with the same y or z coordinate (mono-dimensional problems). 2 - Method of solution: The integrals which define the removal fluxes are computed in some shield points by means of a particular algorithm based on the Simpson's and trapezoidal rules. For the diffusion calculation the finite difference method is used. The removal sources are interpolated in all diffusion points by Chebyshev polynomials. 3 - Restrictions on the complexity of the problem: Maxima: number of removal energy groups NGR = 40; number of diffusion energy groups NGD = 40; number of the reactor core and shield materials NCMP = 50; number of core mesh points in r (or x) direction for integral calculation = 75; number of core mesh points in z (or y) direction for integral calculation = 75; number of core mesh points in theta (or z) direction for integral calculation = 75; number of shield mesh points for the neutron flux calculation in r (or x) direction NPX = 200; number of shield mesh points for the neutron flux calculation in z (or y) direction NPY = 200; n.b. (NPX * NPY) le 12000
Iterative schemes for obtaining dominant alpha-modes of the neutron diffusion equation
International Nuclear Information System (INIS)
Singh, K.P.; Modak, R.S.; Degweker, S.B.; Singh, Kanchhi
2009-01-01
Two new methods of obtaining dominant prompt alpha-modes (sometimes referred to as time-eigenfunctions) of the multigroup neutron diffusion equation are discussed. In the first of these, we initially compute the dominant K-eigenfunctions and K-eigenvalues (denoted by λ 1 , λ 2 , λ 3 ...λ 1 being equal to the K eff ) for the given nuclear reactor model, by existing method based on sub-space iteration (SSI) which is an improved version of power iteration method. Subsequently, a uniformly distributed (positive or negative) 1/v absorber of sufficient concentration is added so as to make a particular eigenvalue λ i equal to unity. This gives ith alpha-mode. This procedure is repeated to find all the required alpha-modes. In the second method, we solve the alpha-eigenvalue problem directly by SSI method. This is clearly possible for a sub-critical reactor for which the inverse of the dominant alpha-eigenvalues are also the largest in magnitude as required by the SSI method. Here, the procedure is made applicable even to a super-critical reactor by making the reactor model sub-critical by the addition of a 1/v absorber. Results of these calculations for a 3-D two group PHWR test-case are given. These results are validated against the results as obtained by a completely different approach based on Orthomin(1) algorithm published earlier. The direct method based on the sub-space iteration strategy is found to be a simple and reliable method for obtaining any number of alpha-modes. Also comments have been made on the relationship between fundamental α and k values.
Neutron diffuse scattering in magnetite due to molecular polarons
International Nuclear Information System (INIS)
Yamada, Y.; Wakabayashi, N.; Nicklow, R.M.
1980-01-01
A detailed neutron diffuse scattering study has been carried out in order to verify a model which describes the property of valence fluctuations in magnetite above T/sub V/. This model assumes the existence of a complex which is composed of two excess electrons and a local displacement mode of oxygens within the fcc primitive cell. The complex is called a molecular polaron. It is assumed that at sufficiently high temperatures there is a random distribution of molecular polarons, which are fluctuating independently by making hopping motions through the crystal or by dissociating into smaller polarons. The lifetime of each molecular polaron is assumed to be long enough to induce an instantaneous strain field around it. Based on this model, the neutron diffuse scattering cross section due to randomly distributed dressed molecular polarons has been calculated. A precise measurement of the quasielastic scattering of neutrons has been carried out at 150 K. The observed results definitely show the characteristics which are predicted by the model calculation and, thus, give evidence for the existence of the proposed molecular polarons. From this standpoint, the Verwey transition of magnetite may be viewed as the cooperative ordering process of dressed molecular polarons. Possible extensions of the model to describe the ordering and the dynamical behavior of the molecular polarons are discussed
Development of a polynomial nodal model to the multigroup transport equation in one dimension
International Nuclear Information System (INIS)
Feiz, M.
1986-01-01
A polynomial nodal model that uses Legendre polynomial expansions was developed for the multigroup transport equation in one dimension. The development depends upon the least-squares minimization of the residuals using the approximate functions over the node. Analytical expressions were developed for the polynomial coefficients. The odd moments of the angular neutron flux over the half ranges were used at the internal interfaces, and the Marshak boundary condition was used at the external boundaries. Sample problems with fine-mesh finite-difference solutions of the diffusion and transport equations were used for comparison with the model
Linear extended neutron diffusion theory for semi-in finites homogeneous means
International Nuclear Information System (INIS)
Vazquez R, R.; Vazquez R, A.; Espinosa P, G.
2009-10-01
Originally developed for heterogeneous means, the linear extended neutron diffusion theory is applied to the limit case of monoenergetic neutron diffusion in a semi-infinite homogeneous mean with a neutron source, located in the coordinate origin situated in the frontier of dispersive material. The monoenergetic neutron diffusion is studied taking into account the spatial deviations in the neutron flux to the interfacial current caused by the neutron source, as well as the influence of the spatial deviations in the absorption rate. The developed pattern is an unidimensional model for an energy group obtained of application of volumetric average diffusion equation in the moderator. The obtained results are compared against the classic diffusion theory and qualitatively against the neutron transport theory. (Author)
A comparison of certain variational solutions of neutron diffusion equation
International Nuclear Information System (INIS)
Altiparmakov, D.V.; Milgram, M.S.
1987-01-01
Using the R-function theory and the variational method of Kantorovich, an approximate solution of the neutron diffusion equation is constructed for a homogeneous spatial domain of arbitrary shape. Calculations have been carried out by five different types of trial functions for certain characteristic domains of polygonal shape (square, triangle, hexagon, rhombus nad L-shaped domain). In the case of non-convex polygons, the consequence of the R-function solution is very poor and a separate treatment of singularity seems to be necessary. Compared to the R-function solution, the singular function development is mathematically more complicated but superior in respect to convergence rate. (author)
Parallel preconditioned conjugate gradient algorithm applied to neutron diffusion problem
International Nuclear Information System (INIS)
Majumdar, A.; Martin, W.R.
1992-01-01
Numerical solution of the neutron diffusion problem requires solving a linear system of equations such as Ax = b, where A is an n x n symmetric positive definite (SPD) matrix; x and b are vectors with n components. The preconditioned conjugate gradient (PCG) algorithm is an efficient iterative method for solving such a linear system of equations. In this paper, the authors describe the implementation of a parallel PCG algorithm on a shared memory machine (BBN TC2000) and on a distributed workstation (IBM RS6000) environment created by the parallel virtual machine parallelization software
High order backward discretization of the neutron diffusion equation
Energy Technology Data Exchange (ETDEWEB)
Ginestar, D.; Bru, R.; Marin, J. [Universidad Politecnica de Valencia (Spain). Departamento de Matematica Aplicada; Verdu, G.; Munoz-Cobo, J.L. [Universidad Politecnica de Valencia (Spain). Departamento de Ingenieria Quimica y Nuclear; Vidal, V. [Universidad Politecnica de Valencia (Spain). Departamento de Sistemas Informaticos y Computacion
1997-11-21
Fast codes capable of dealing with three-dimensional geometries, are needed to be able to simulate spatially complicated transients in a nuclear reactor. We propose a new discretization technique for the time integration of the neutron diffusion equation, based on the backward difference formulas for systems of stiff ordinary differential equations. This method needs to solve a system of linear equations for each integration step, and for this purpose, we have developed an iterative block algorithm combined with a variational acceleration technique. We tested the algorithm with two benchmark problems, and compared the results with those provided by other codes, concluding that the performance and overall agreement are very good. (author).
MODICO, 1-D Time-Dependent 1 Group, 2 Group Neutron Diffusion with Delayed Neutron Precursors
International Nuclear Information System (INIS)
Camiciola, P.; Cundari, D.; Montagnini, B.
1992-01-01
1 - Description of program or function: The program solves the 1-D time-dependent one and two group coarse-mesh neutron diffusion equations, coupled with the equations for the delayed-neutron precursor, in plane geometry. 2 - Method of solution: The program is based on a simple coarse-mesh cubic approximation formula for the spatial behaviour of the flux inside each interval. An implicit scheme (the time-integrated method) is used for the advancement of the solution. The resulting (block three-diagonal) matrix is inverted at each time step by Thomas' method. 3 - Restrictions on the complexity of the problem: Number of coarse- mesh intervals LE 80; number of material regions LE 10; number of delayed-neutron precursor groups LE 10. Typical mesh sizes range from 5 cm to 20 cm; typical step length (non-prompt critical transients) ranges from 0.005 to 0.1 seconds
Nested element method in multidimensional neutron diffusion calculations
International Nuclear Information System (INIS)
Altiparmakov, D.V.
1983-01-01
A new numerical method is developed that is particularly efficient in solving the multidimensional neutron diffusion equation in geometrically complex systems. The needs for a generally applicable and fast running computer code have stimulated the inroad of a nonclassical (R-function) numerical method into the nuclear field. By using the R-functions, the geometrical components of the diffusion problem are a priori analytically implemented into the approximate solution. The class of functions, to which the approximate solution belongs, is chosen as close to the exact solution class as practically acceptable from the time consumption point of view. That implies a drastic reduction of the number of degrees of freedom, compared to the other methods. Furthermore, the reduced number of degrees of freedom enables calculation of large multidimensional problems on small computers
Three-group albedo method applied to the diffusion phenomenon with up-scattering of neutrons
International Nuclear Information System (INIS)
Terra, Andre M. Barge Pontes Torres; Silva, Jorge A. Valle da; Cabral, Ronaldo G.
2007-01-01
The main objective of this research is to develop a three-group neutron Albedo algorithm considering the up-scattering of neutrons in order to analyse the diffusion phenomenon in nonmultiplying media. The neutron Albedo method is an analytical method that does not try to solve describing explicit equations for the neutron fluxes. Thus the neutron Albedo methodology is very different from the conventional methodology, as the neutron diffusion theory model. Graphite is analyzed as a model case. One major application is in the determination of the nonleakage probabilities with more understandable results in physical terms than conventional radiation transport method calculations. (author)
Parallel solutions of the two-group neutron diffusion equations
International Nuclear Information System (INIS)
Zee, K.S.; Turinsky, P.J.
1987-01-01
Recent efforts to adapt various numerical solution algorithms to parallel computer architectures have addressed the possibility of substantially reducing the running time of few-group neutron diffusion calculations. The authors have developed an efficient iterative parallel algorithm and an associated computer code for the rapid solution of the finite difference method representation of the two-group neutron diffusion equations on the CRAY X/MP-48 supercomputer having multi-CPUs and vector pipelines. For realistic simulation of light water reactor cores, the code employees a macroscopic depletion model with trace capability for selected fission product transients and critical boron. In addition to this, moderator and fuel temperature feedback models are also incorporated into the code. The validity of the physics models used in the code were benchmarked against qualified codes and proved accurate. This work is an extension of previous work in that various feedback effects are accounted for in the system; the entire code is structured to accommodate extensive vectorization; and an additional parallelism by multitasking is achieved not only for the solution of the matrix equations associated with the inner iterations but also for the other segments of the code, e.g., outer iterations
Domain decomposition methods for the neutron diffusion problem
International Nuclear Information System (INIS)
Guerin, P.; Baudron, A. M.; Lautard, J. J.
2010-01-01
The neutronic simulation of a nuclear reactor core is performed using the neutron transport equation, and leads to an eigenvalue problem in the steady-state case. Among the deterministic resolution methods, simplified transport (SPN) or diffusion approximations are often used. The MINOS solver developed at CEA Saclay uses a mixed dual finite element method for the resolution of these problems. and has shown his efficiency. In order to take into account the heterogeneities of the geometry, a very fine mesh is generally required, and leads to expensive calculations for industrial applications. In order to take advantage of parallel computers, and to reduce the computing time and the local memory requirement, we propose here two domain decomposition methods based on the MINOS solver. The first approach is a component mode synthesis method on overlapping sub-domains: several Eigenmodes solutions of a local problem on each sub-domain are taken as basis functions used for the resolution of the global problem on the whole domain. The second approach is an iterative method based on a non-overlapping domain decomposition with Robin interface conditions. At each iteration, we solve the problem on each sub-domain with the interface conditions given by the solutions on the adjacent sub-domains estimated at the previous iteration. Numerical results on parallel computers are presented for the diffusion model on realistic 2D and 3D cores. (authors)
Performance modeling of parallel algorithms for solving neutron diffusion problems
International Nuclear Information System (INIS)
Azmy, Y.Y.; Kirk, B.L.
1995-01-01
Neutron diffusion calculations are the most common computational methods used in the design, analysis, and operation of nuclear reactors and related activities. Here, mathematical performance models are developed for the parallel algorithm used to solve the neutron diffusion equation on message passing and shared memory multiprocessors represented by the Intel iPSC/860 and the Sequent Balance 8000, respectively. The performance models are validated through several test problems, and these models are used to estimate the performance of each of the two considered architectures in situations typical of practical applications, such as fine meshes and a large number of participating processors. While message passing computers are capable of producing speedup, the parallel efficiency deteriorates rapidly as the number of processors increases. Furthermore, the speedup fails to improve appreciably for massively parallel computers so that only small- to medium-sized message passing multiprocessors offer a reasonable platform for this algorithm. In contrast, the performance model for the shared memory architecture predicts very high efficiency over a wide range of number of processors reasonable for this architecture. Furthermore, the model efficiency of the Sequent remains superior to that of the hypercube if its model parameters are adjusted to make its processors as fast as those of the iPSC/860. It is concluded that shared memory computers are better suited for this parallel algorithm than message passing computers
RASH D - A mercury programme for neutron shielding calculations
International Nuclear Information System (INIS)
Bendall, D.E.
1962-08-01
An improved version of an earlier neutron shielding programme (RASH B) is described. The new programme is also written in Mercury Autocode and solves a set of multigroup diffusion equations in one dimension. It differs from RASH B in that distributed source terms may be introduced into all the groups if required. Some other improvements are also included. (author)
An approach to neutronics analysis of candu reactors
International Nuclear Information System (INIS)
Gul, S.; Arshad, M.
1982-12-01
An attempt is made to tackle the problem of neutronics analysis of CANDU reactors. Until now CANDU reactors have been analysed by the methods developed at AECL and CGE using mainly receipe methods. Relying on multigroup transport codes GAM-GATHER in combination with diffusion code CITATION a package of codes is established to use it for survey as well as production purposes. (authors)
A comparison of Nodal methods in neutron diffusion calculations
Energy Technology Data Exchange (ETDEWEB)
Tavron, Barak [Israel Electric Company, Haifa (Israel) Nuclear Engineering Dept. Research and Development Div.
1996-12-01
The nuclear engineering department at IEC uses in the reactor analysis three neutron diffusion codes based on nodal methods. The codes, GNOMERl, ADMARC2 and NOXER3 solve the neutron diffusion equation to obtain flux and power distributions in the core. The resulting flux distributions are used for the furl cycle analysis and for fuel reload optimization. This work presents a comparison of the various nodal methods employed in the above codes. Nodal methods (also called Coarse-mesh methods) have been designed to solve problems that contain relatively coarse areas of homogeneous composition. In the nodal method parts of the equation that present the state in the homogeneous area are solved analytically while, according to various assumptions and continuity requirements, a general solution is sought out. Thus efficiency of the method for this kind of problems, is very high compared with the finite element and finite difference methods. On the other hand, using this method one can get only approximate information about the node vicinity (or coarse-mesh area, usually a feel assembly of a 20 cm size). These characteristics of the nodal method make it suitable for feel cycle analysis and reload optimization. This analysis requires many subsequent calculations of the flux and power distributions for the feel assemblies while there is no need for detailed distribution within the assembly. For obtaining detailed distribution within the assembly methods of power reconstruction may be applied. However homogenization of feel assembly properties, required for the nodal method, may cause difficulties when applied to fuel assemblies with many absorber rods, due to exciting strong neutron properties heterogeneity within the assembly. (author).
International Nuclear Information System (INIS)
Petrie, L.M.; Landers, N.F.
2001-01-01
1 - Description of problem or function: KENO is a multigroup, Monte Carlo criticality code containing a special geometry package which allows easy description of systems composed of cylinders, spheres, and cuboids (rectangular parallelepipeds) arranged in any order with only one restriction. They cannot be rotated or translated. Each geometrical region must be described as completely enclosing all regions interior to it. For systems not describable using this special geometry package, the program can use the generalized geometry package (GEOM) developed for the O5R Monte Carlo code. It allows any system that can be described by a collection of planes and/or quadratic surfaces, arbitrarily oriented and intersecting in arbitrary fashion. The entire problem can be mocked up in generalized geometry, or one generalized geometry unit or box type can be used alone or in combination with standard KENO units or box types. Rectangular arrays of fissile units are allowed with or without external reflector regions. Output from KENO consists of k eff for the system plus an estimate of its standard deviation and the leakage, absorption, and fissions for each energy group plus the totals for all groups. Flux as a function of energy group and region and fission densities as a function of region are optional output. KENO-4: Added features include a neutron balance edit, PICTURE routines to check the input geometry, and a random number sequencing subroutine written in FORTRAN-4. 2 - Method of solution: The scattering treatment used in KENO assumes that the differential neutron scattering cross section can be represented by a P1 Legendre polynomial. Absorption of neutrons in KENO is not allowed. Instead, at each collision point of a neutron tracking history the weight of the neutron is reduced by the absorption probability. When the neutron weight has been reduced below a specified point for the region in which the collision occurs, Russian roulette is played to determine if the
Development of neutron diffuse scattering analysis code by thin film and multilayer film
International Nuclear Information System (INIS)
Soyama, Kazuhiko
2004-01-01
To research surface structure of thin film and multilayer film by neutron, a neutron diffuse scattering analysis code using DWBA (Distorted-Wave Bron Approximation) principle was developed. Subjects using this code contain the surface and interface properties of solid/solid, solid/liquid, liquid/liquid and gas/liquid, and metal, magnetism and polymer thin film and biomembran. The roughness of surface and interface of substance shows fractal self-similarity and its analytical model is based on DWBA theory by Sinha. The surface and interface properties by diffuse scattering are investigated on the basis of the theoretical model. The calculation values are proved to be agreed with the experimental values. On neutron diffuse scattering by thin film, roughness of surface of thin film, correlation function, neutron propagation by thin film, diffuse scattering by DWBA theory, measurement model, SDIFFF (neutron diffuse scattering analysis program by thin film) and simulation results are explained. On neutron diffuse scattering by multilayer film, roughness of multilayer film, principle of diffuse scattering, measurement method and simulation examples by MDIFF (neutron diffuse scattering analysis program by multilayer film) are explained. (S.Y.)To research surface structure of thin film and multilayer film by neutron, a neutron diffuse scattering analysis code using DWBA (Distorted-Wave Bron Approximation) principle was developed. Subjects using this code contain the surface and interface properties of solid/solid, solid/liquid, liquid/liquid and gas/liquid, and metal, magnetism and polymer thin film and biomembran. The roughness of surface and interface of substance shows fractal self-similarity and its analytical model is based on DWBA theory by Sinha. The surface and interface properties by diffuse scattering are investigated on the basis of the theoretical model. The calculation values are proved to be agreed with the experimental values. On neutron diffuse scattering
International Nuclear Information System (INIS)
Ouisloumen, M.
1989-03-01
This research thesis reports an investigation of neutron diffusion by the fuel of a nuclear reactor while taking thermal agitation of diffusing nuclei into account. The author adopted the free gas model to describe the atom vibrations in the crystal network. He reports the elaboration of a diffusion law which gives the neutron energy spectrum after collision. Some particular theoretical cases are then studied in order to explain the observed physical phenomena, and to confirm the obtained results. The Monte Carlo method is also used to validate these results. The author presents the various physical criteria which must be met by an energetic grid in order to minimize errors in reaction rate calculations
Energy Technology Data Exchange (ETDEWEB)
Saint-James, D [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires
1962-02-15
General paramagnetic scattering of neutrons is investigated in the situation where the orbital moment of the magnetic scattering ions is not quenched. The general relevant expression of the cross-section is given. The proceeding results are applied to rare earths and iron group ions. It is shown that if crystalline actions lift the free ion ground state degeneracy the neutron may induce transitions between the various levels, the distances of which are typically of the order of several hundred cm{sup -1}. The various scattering cross-sections (elastic and inelastic) are calculated for the rare earths in a cubic crystal field, for the holmium and erbium sesquioxide and for the anhydrous iron chloride (Cl{sub 2}Fe). These cross-sections are high enough to allow for an experimental detection, thus providing a direct determination of the levels distances through the measurement of the neutron wave-length shift. Moreover it is shown that, for neodymium, holmium, erbium, the total cross-section for neutrons of one angstrom wave length is rather insensitive to the crystal field effects. The results are then compared with the available experimental studies. The influence of the orbital moment on the angular dependence of the scattering for polarised ions is then investigated. The well-known formula: I = I{sub 0}sin{sup 2}{beta} is only an approximation, the validity of which is discussed. (author) [French] On envisage le cas general de la diffusion paramagnetique de neutrons. Le moment orbital des ions magnetiques ne peut etre considere comme bloque. On donne l'expression generale de la section efficace. Les resultats obtenus sont appliques au cas des terres rares et des ions du groupe du fer. On montre que, si les actions cristallines levent la degenerescence du niveau fondamental de l'ion libre, le neutron peut induire des transitions entre les divers sous-niveaux, dont la distance est ordinairement de l'ordre de quelques centaines de cm{sup -1}. La section efficace des
Development and verification of the neutron diffusion solver for the GeN-Foam multi-physics platform
International Nuclear Information System (INIS)
Fiorina, Carlo; Kerkar, Nordine; Mikityuk, Konstantin; Rubiolo, Pablo; Pautz, Andreas
2016-01-01
Highlights: • Development and verification of a neutron diffusion solver based on OpenFOAM. • Integration in the GeN-Foam multi-physics platform. • Implementation and verification of acceleration techniques. • Implementation of isotropic discontinuity factors. • Automatic adjustment of discontinuity factors. - Abstract: The Laboratory for Reactor Physics and Systems Behaviour at the PSI and the EPFL has been developing in recent years a new code system for reactor analysis based on OpenFOAM®. The objective is to supplement available legacy codes with a modern tool featuring state-of-the-art characteristics in terms of scalability, programming approach and flexibility. As part of this project, a new solver has been developed for the eigenvalue and transient solution of multi-group diffusion equations. Several features distinguish the developed solver from other available codes, in particular: object oriented programming to ease code modification and maintenance; modern parallel computing capabilities; use of general unstructured meshes; possibility of mesh deformation; cell-wise parametrization of cross-sections; and arbitrary energy group structure. In addition, the solver is integrated into the GeN-Foam multi-physics solver. The general features of the solver and its integration with GeN-Foam have already been presented in previous publications. The present paper describes the diffusion solver in more details and provides an overview of new features recently implemented, including the use of acceleration techniques and discontinuity factors. In addition, a code verification is performed through a comparison with Monte Carlo results for both a thermal and a fast reactor system.
Parallel computation of multigroup reactivity coefficient using iterative method
Susmikanti, Mike; Dewayatna, Winter
2013-09-01
One of the research activities to support the commercial radioisotope production program is a safety research target irradiation FPM (Fission Product Molybdenum). FPM targets form a tube made of stainless steel in which the nuclear degrees of superimposed high-enriched uranium. FPM irradiation tube is intended to obtain fission. The fission material widely used in the form of kits in the world of nuclear medicine. Irradiation FPM tube reactor core would interfere with performance. One of the disorders comes from changes in flux or reactivity. It is necessary to study a method for calculating safety terrace ongoing configuration changes during the life of the reactor, making the code faster became an absolute necessity. Neutron safety margin for the research reactor can be reused without modification to the calculation of the reactivity of the reactor, so that is an advantage of using perturbation method. The criticality and flux in multigroup diffusion model was calculate at various irradiation positions in some uranium content. This model has a complex computation. Several parallel algorithms with iterative method have been developed for the sparse and big matrix solution. The Black-Red Gauss Seidel Iteration and the power iteration parallel method can be used to solve multigroup diffusion equation system and calculated the criticality and reactivity coeficient. This research was developed code for reactivity calculation which used one of safety analysis with parallel processing. It can be done more quickly and efficiently by utilizing the parallel processing in the multicore computer. This code was applied for the safety limits calculation of irradiated targets FPM with increment Uranium.
Fourier convergence analysis applied to neutron diffusion Eigenvalue problem
International Nuclear Information System (INIS)
Lee, Hyun Chul; Noh, Jae Man; Joo, Hyung Kook
2004-01-01
Fourier error analysis has been a standard technique for the stability and convergence analysis of linear and nonlinear iterative methods. Though the methods can be applied to Eigenvalue problems too, all the Fourier convergence analyses have been performed only for fixed source problems and a Fourier convergence analysis for Eigenvalue problem has never been reported. Lee et al proposed new 2-D/1-D coupling methods and they showed that the new ones are unconditionally stable while one of the two existing ones is unstable at a small mesh size and that the new ones are better than the existing ones in terms of the convergence rate. In this paper the convergence of method A in reference 4 for the diffusion Eigenvalue problem was analyzed by the Fourier analysis. The Fourier convergence analysis presented in this paper is the first one applied to a neutronics eigenvalue problem to the best of our knowledge
Time-of-flight and vector polarization analysis for diffuse neutron scattering
International Nuclear Information System (INIS)
Schweika, W.
2003-01-01
The potential of pulsed neutron sources for diffuse scattering including time-of-flight (TOF) and polarization analysis is discussed in comparison to the capabilities of the present instrument diffuse neutron scattering at the research center Juelich. We present first results of a new method for full polarization analysis using precessing neutron polarization. A proposal is made for a new type of instrument at pulsed sources, which allows for vector polarization analysis in TOF instruments with multi-detectors
Energy Technology Data Exchange (ETDEWEB)
Gennes, P.G. de [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires
1959-07-01
Certain statistical aspects of a large collection of electronic spins coupled by exchange forces are examined. The treatment is limited to substances where the orbital magnetic moment can be considered fixed, and where the effect of thermal agitation of the ions can be neglected. A system of this kind can be followed experimentally by elastic and inelastic diffusion of neutrons. At high temperatures, inelastic diffusion allows the microscopic aspect, reversible, and the macroscopic aspect, irreversible, to be studied simultaneously and these 2 fields to be linked. At temperatures around the Curie point, the average phenomenon is the appearance of a critical opalescence. At low temperatures, collective spin excitations can be observed. In the neighborhood of the Curie point, the spin coefficient {lambda}, which governs the relaxation of fluctuations of magnetization, is calculated. An intrinsic factor is discussed in {lambda}, bound to the microscopic frequency of the spin exchanges, and to a factor due to the damping of the diffusion by the magnetic field. At the transition point, {lambda} is cancelled. The spectrum of the spin excitations in metals is discussed. (author)
Parallel computing for homogeneous diffusion and transport equations in neutronics
International Nuclear Information System (INIS)
Pinchedez, K.
1999-06-01
Parallel computing meets the ever-increasing requirements for neutronic computer code speed and accuracy. In this work, two different approaches have been considered. We first parallelized the sequential algorithm used by the neutronics code CRONOS developed at the French Atomic Energy Commission. The algorithm computes the dominant eigenvalue associated with PN simplified transport equations by a mixed finite element method. Several parallel algorithms have been developed on distributed memory machines. The performances of the parallel algorithms have been studied experimentally by implementation on a T3D Cray and theoretically by complexity models. A comparison of various parallel algorithms has confirmed the chosen implementations. We next applied a domain sub-division technique to the two-group diffusion Eigen problem. In the modal synthesis-based method, the global spectrum is determined from the partial spectra associated with sub-domains. Then the Eigen problem is expanded on a family composed, on the one hand, from eigenfunctions associated with the sub-domains and, on the other hand, from functions corresponding to the contribution from the interface between the sub-domains. For a 2-D homogeneous core, this modal method has been validated and its accuracy has been measured. (author)
Diffuse neutron scattering study of metallic interstitial solid solutions
International Nuclear Information System (INIS)
Barberis, P.
1991-10-01
We studied two interstitial solid solutions (Ni-C(1at%) and Nb-O(2at%) and two stabilized zirconia (ZrO2-CaO(13.6mol%) and ZrO2-Y2O3(9.6mol%) by elastic diffuse neutron scattering. We used polarized neutron scattering in the case of the ferromagnetic Ni-based sample, in order to determine the magnetic perturbation induced by the C atoms. Measurements were made on single crystals in the Laboratoire Leon Brillouin (CEA-CNRS, Saclay, France). An original algorithm to deconvolve time-of-flight spectra improved the separation between elastically and inelastically scattered intensities. In the case of metallic solutions, we used a simple non-linear model, assuming that interstitials are isolated and located in octahedral sites. Results are: - in both compounds, nearest neighbours are widely displaced away from the interstitial, while next nearest neighbours come slightly closer. - the large magnetic perturbation induced by carbon in Nickel decreases with increasing distance on the three first neighbour shells and is in good agreement with the total magnetization variation. - no chemical order between solute atoms could be evidenced. Stabilized zirconia exhibit a strong correlation between chemical order and the large displacements around vacancies and dopants. (Author). 132 refs., 38 figs., 13 tabs
Calculation of the power factor using the neutron diffusion hybrid equation
International Nuclear Information System (INIS)
Costa da Silva, Adilson; Carvalho da Silva, Fernando; Senra Martinez, Aquilino
2013-01-01
Highlights: ► A neutron diffusion hybrid equation with an external neutron source was used. ► Nodal expansion method to obtain the neutron flux was used. ► Nuclear power factors in each fuel element in the reactor core were calculated. ► The results obtained were very accurate. -- Abstract: In this paper, we used a neutron diffusion hybrid equation with an external neutron source to calculate nuclear power factors in each fuel element in the reactor core. We used the nodal expansion method to obtain the neutron flux for a given control rods bank position. The results were compared with results obtained for eigenvalue problem near criticality condition and fixed source problem during the start-up of the reactor, where external neutron sources are extremely important for the stabilization of external neutron detectors.
Adjoint P1 equations solution for neutron slowing down
International Nuclear Information System (INIS)
Cardoso, Carlos Eduardo Santos; Martinez, Aquilino Senra; Silva, Fernando Carvalho da
2002-01-01
In some applications of perturbation theory, it is necessary know the adjoint neutron flux, which is obtained by the solution of adjoint neutron diffusion equation. However, the multigroup constants used for this are weighted in only the direct neutron flux, from the solution of direct P1 equations. In this work, the adjoint P1 equations are derived by the neutron transport equation, the reversion operators rules and analogies between direct and adjoint parameters. The direct and adjoint neutron fluxes resulting from the solution of P 1 equations were used to three different weighting processes, to obtain the macrogroup macroscopic cross sections. It was found out noticeable differences among them. (author)
Energy Technology Data Exchange (ETDEWEB)
Cardoso, Carlos Eduardo Santos; Martinez, Aquilino Senra; Silva, Fernando Carvalho da [Universidade Federal, Rio de Janeiro, RJ (Brazil). Coordenacao dos Programas de Pos-graduacao de Engenharia. Programa de Engenharia Nuclear
2002-07-01
In some applications of perturbation theory, it is necessary know the adjoint neutron flux, which is obtained by the solution of adjoint neutron diffusion equation. However, the multigroup constants used for this are weighted in only the direct neutron flux, from the solution of direct P1 equations. In this work, the adjoint P1 equations are derived by the neutron transport equation, the reversion operators rules and analogies between direct and adjoint parameters. The direct and adjoint neutron fluxes resulting from the solution of P{sub 1} equations were used to three different weighting processes, to obtain the macrogroup macroscopic cross sections. It was found out noticeable differences among them. (author)
3-D anisotropic neutron diffusion in optically thick media with optically thin channels
International Nuclear Information System (INIS)
Trahan, Travis J.; Larsen, Edward W.
2011-01-01
Standard neutron diffusion theory accurately approximates the neutron transport process for optically thick, scattering-dominated systems in which the angular neutron flux is a weak (nearly linear) function of angle. Therefore, standard diffusion theory is not directly applicable for Very High Temperature Reactor (VHTR) cores, which contain numerous narrow, axially-oriented, nearly-voided coolant channels. However, we have derived a new, accurate diffusion equation for such problems, which contains nonstandard anisotropic diffusion coefficients near and within the channels, but which reduces to the standard diffusion approximation away from the channels. The new diffusion approximation significantly improves the accuracy of VHTR diffusion simulations, while having lower computational cost than higher-order transport methods. (author)
Multi-Group Covariance Data Generation from Continuous-Energy Monte Carlo Transport Calculations
International Nuclear Information System (INIS)
Lee, Dong Hyuk; Shim, Hyung Jin
2015-01-01
The sensitivity and uncertainty (S/U) methodology in deterministic tools has been utilized for quantifying uncertainties of nuclear design parameters induced by those of nuclear data. The S/U analyses which are based on multi-group cross sections can be conducted by an simple error propagation formula with the sensitivities of nuclear design parameters to multi-group cross sections and the covariance of multi-group cross section. The multi-group covariance data required for S/U analysis have been produced by nuclear data processing codes such as ERRORJ or PUFF from the covariance data in evaluated nuclear data files. However in the existing nuclear data processing codes, an asymptotic neutron flux energy spectrum, not the exact one, has been applied to the multi-group covariance generation since the flux spectrum is unknown before the neutron transport calculation. It can cause an inconsistency between the sensitivity profiles and the covariance data of multi-group cross section especially in resolved resonance energy region, because the sensitivities we usually use are resonance self-shielded while the multi-group cross sections produced from an asymptotic flux spectrum are infinitely-diluted. In order to calculate the multi-group covariance estimation in the ongoing MC simulation, mathematical derivations for converting the double integration equation into a single one by utilizing sampling method have been introduced along with the procedure of multi-group covariance tally
Enhanced finite difference scheme for the neutron diffusion equation using the importance function
International Nuclear Information System (INIS)
Vagheian, Mehran; Vosoughi, Naser; Gharib, Morteza
2016-01-01
Highlights: • An enhanced finite difference scheme for the neutron diffusion equation is proposed. • A seven-step algorithm is considered based on the importance function. • Mesh points are distributed through entire reactor core with respect to the importance function. • The results all proved that the proposed algorithm is highly efficient. - Abstract: Mesh point positions in Finite Difference Method (FDM) of discretization for the neutron diffusion equation can remarkably affect the averaged neutron fluxes as well as the effective multiplication factor. In this study, by aid of improving the mesh point positions, an enhanced finite difference scheme for the neutron diffusion equation is proposed based on the neutron importance function. In order to determine the neutron importance function, the adjoint (backward) neutron diffusion calculations are performed in the same procedure as for the forward calculations. Considering the neutron importance function, the mesh points can be improved through the entire reactor core. Accordingly, in regions with greater neutron importance, density of mesh elements is higher than that in regions with less importance. The forward calculations are then performed for both of the uniform and improved non-uniform mesh point distributions and the results (the neutron fluxes along with the corresponding eigenvalues) for the two cases are compared with each other. The results are benchmarked against the reference values (with fine meshes) for Kang and Rod Bundle BWR benchmark problems. These benchmark cases revealed that the improved non-uniform mesh point distribution is highly efficient.
Continuous energy Monte Carlo method based homogenization multi-group constants calculation
International Nuclear Information System (INIS)
Li Mancang; Wang Kan; Yao Dong
2012-01-01
The efficiency of the standard two-step reactor physics calculation relies on the accuracy of multi-group constants from the assembly-level homogenization process. In contrast to the traditional deterministic methods, generating the homogenization cross sections via Monte Carlo method overcomes the difficulties in geometry and treats energy in continuum, thus provides more accuracy parameters. Besides, the same code and data bank can be used for a wide range of applications, resulting in the versatility using Monte Carlo codes for homogenization. As the first stage to realize Monte Carlo based lattice homogenization, the track length scheme is used as the foundation of cross section generation, which is straight forward. The scattering matrix and Legendre components, however, require special techniques. The Scattering Event method was proposed to solve the problem. There are no continuous energy counterparts in the Monte Carlo calculation for neutron diffusion coefficients. P 1 cross sections were used to calculate the diffusion coefficients for diffusion reactor simulator codes. B N theory is applied to take the leakage effect into account when the infinite lattice of identical symmetric motives is assumed. The MCMC code was developed and the code was applied in four assembly configurations to assess the accuracy and the applicability. At core-level, A PWR prototype core is examined. The results show that the Monte Carlo based multi-group constants behave well in average. The method could be applied to complicated configuration nuclear reactor core to gain higher accuracy. (authors)
Energy Technology Data Exchange (ETDEWEB)
Koechlin, J C; Martelly, J; Duggal, V P [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires
1955-07-01
The diffusion length of thermal neutrons in the beryllium oxide has been obtained while studying the spatial distribution of the neutrons in a massive parallelepiped of this matter placed before the thermal column of the reactor core of Saclay. The mean density of the beryllium oxide (BeO) is 2,95 gr/cm{sup 3}, the mean density of the massif is 2,92 gr/cm{sup 3}. The value of the diffusion length, deducted of the done measures, is: L = 32,7 {+-} 0,5 cm (likely gap). Some remarks are formulated about the influence of the spectral distribution of the neutrons flux used. (authors) [French] La longueur de diffusion des neutrons thermiques dans l'oxyde de beryllium a ete obtenue en etudiant la repartition spatiale des neutrons dans un massif parallelepipedique de cette matiere placee devant la colonne thermique de la Pile de Saclay. La densite moyenne de l'oxyde de beryllium (BeO) est de 2,95 gr/cm{sup 3}, la densite moyenne du massif de 2,92 gr/cm{sup 3}. La valeur de la longueur de diffusion, deduite des mesures effectuees est: L 32,7 {+-} 0,5 cm (ecart probable). Des remarques sont formulees quant a l'influence de la repartition spectrale du flux de neutrons utilise. (auteurs)
Energy Technology Data Exchange (ETDEWEB)
Parker, K [Atomic Weapons Research Establishment, Aldermaston (United Kingdom)
1962-03-15
The AWRE punched-card library of neutron cross-sections is described together with associated IBM-7090 programmes which process this data to give group-averaged cross-sections for use in Monte Carlo, Carlson S{sub n} and other multi-group neutronics calculations. The methods developed to deal with both isotropic and anisotropic elastic scattering are described. These include the multi-group transport approximation and the full treatment of anisotropic scattering using the Legendre polynomial moments of the scattering transfer matrix. The principles of group-constant formation are considered and illustrated by describing systems of group constants suitable for fast-reactor calculations. Practical problems such as the empirical adjustment of group constants to reproduce integral results and the collapsing of a many-group set of constants to give a few-group set are discussed. (author) [French] L'auteur decrit le fichier de cartes perforees sur lesquelles on enregistre a l'Atomic Weapons Research Establishment (AWRE) les sections efficaces neutroniques ainsi que les programmes IBM-7090 associes qui sont employes pour le traitement de ces informations, en vue d'obtenir des sections efficaces moyennes par groupe pouvant servir aux calculs de neutroniques a plusieurs groupes, effectues a l'aide des methodes de Monte-Carlo, S{sub n} de Carlson et autres methodes. L'auteur expose ensuite les methodes mises au point roda etudier la diffusion elastique, tant isotrope qu'anisotrope. Elles comprennent l'approximation de transport a plusieurs groupes, ainsi que le traitement complet de la diffusion anisotrope par les moments polynomiaux de Legendre de la matrice de transfert de la diffusion. L'auteur examine les principes de la formation des constantes de groupes; a titre d'illustration, il decrit les systemes de constantes de groupes qui se pretent aux calculs de reacteurs a neutrons rapides. Il expose quelques problemes pratiques, tels que l'ajustement empirique des
On the convergence of multigroup discrete-ordinates approximations
International Nuclear Information System (INIS)
Victory, H.D. Jr.; Allen, E.J.; Ganguly, K.
1987-01-01
Our analysis is divided into two distinct parts which we label for convenience as Part A and Part B. In Part A, we demonstrate that the multigroup discrete-ordinates approximations are well-defined and converge to the exact transport solution in any subcritical setting. For the most part, we focus on transport in two-dimensional Cartesian geometry. A Nystroem technique is used to extend the discrete ordinates multigroup approximates to all values of the angular and energy variables. Such an extension enables us to employ collectively compact operator theory to deduce stability and convergence of the approximates. In Part B, we perform a thorough convergence analysis for the multigroup discrete-ordinates method for an anisotropically-scattering subcritical medium in slab geometry. The diamond-difference and step-characteristic spatial approximation methods are each studied. The multigroup neutron fluxes are shown to converge in a Banach space setting under realistic smoothness conditions on the solution. This is the first thorough convergence analysis for the fully-discretized multigroup neutron transport equations
On the calculation of multi-group fission spectrum vectors
International Nuclear Information System (INIS)
Mueller, E.Z.
1984-05-01
In this report, the problem of calculating fission spectrum vectors in a consistent manner is formulated. The practical implications of using fission spectrum vectors in multi-group transport calculations are also addressed. The significance of the weighting spectra used for the calculation of fission spectrum vectors is illustrated for the case of a simple neutronic assembly
Calculation of multigroup reaction rates for the Ghana Research ...
African Journals Online (AJOL)
The discrete ordinate spatial model, which pro-vides solution to the differential form of the transport equation by the Carlson-SN (N=4) approach was adopted to solve the Ludwig-Boltzmann multigroup neutron transport equation for this analysis. The results show that for any fissile resonance absorber, the reaction rates ...
Cooperative learning of neutron diffusion and transport theories
International Nuclear Information System (INIS)
Robinson, Michael A.
1999-01-01
A cooperative group instructional strategy is being used to teach a unit on neutron transport and diffusion theory in a first-year-graduate level, Reactor Theory course that was formerly presented in the traditional lecture/discussion style. Students are divided into groups of two or three for the duration of the unit. Class meetings are divided into traditional lecture/discussion segments punctuated by cooperative group exercises. The group exercises were designed to require the students to elaborate, summarize, or practice the material presented in the lecture/discussion segments. Both positive interdependence and individual accountability are fostered by adjusting individual grades on the unit exam by a factor dependent upon group achievement. Group collaboration was also encouraged on homework assignments by assigning each group a single grade on each assignment. The results of the unit exam have been above average in the two classes in which the cooperative group method was employed. In particular, the problem solving ability of the students has shown particular improvement. Further,the students felt that the cooperative group format was both more educationally effective and more enjoyable than the lecture/discussion format
Energy Technology Data Exchange (ETDEWEB)
Capdebosq, Y
1999-09-01
In order to study and simulate nuclear reactor cores, one needs to access the neutron distribution in the core. In practice, the description of this density of neutrons is given by a system of diffusion equations, coupled by non differential exchange terms. The strong heterogeneity of the medium constitutes a major obstacle to the numerical computation of this models at reasonable cost. Homogenization appears as compulsory. Heuristic methods have been developed since the origin by nuclear physicists, under a periodicity assumption on the coefficients. They consist in doing a fine computation one a single periodicity cell, to solve the system on the whole domain with homogeneous coefficients, and to reconstruct the neutron density by multiplying the solutions of the two computations. The objectives of this work are to provide mathematically rigorous basis to this factorization method, to obtain the exact formulas of the homogenized coefficients, and to start on geometries where two periodical medium are placed side by side. The first result of this thesis concerns eigenvalue problem models which are used to characterize the state of criticality of the reactor, under a symmetry assumption on the coefficients. The convergence of the homogenization process is proved, and formulas of the homogenized coefficients are given. We then show that without symmetry assumptions, a drift phenomenon appears. It is characterized by the mean of a real Bloch wave method, which gives the homogenized limit in the general case. These results for the critical problem are then adapted to the evolution model. Finally, the homogenization of the critical problem in the case of two side by side periodic medium is studied on a one dimensional on equation model. (authors)
International Nuclear Information System (INIS)
Hursin, Mathieu; Xiao Shanjie; Jevremovic, Tatjana
2006-01-01
This paper summarizes the theoretical and numerical aspects of the AGENT code methodology accurately applied for detailed three-dimensional (3D) multigroup steady-state modeling of neutron interactions in complex heterogeneous reactor domains. For the first time we show the fine-mesh neutron scalar flux distribution in Purdue research reactor (that was built over forty years ago). The AGENT methodology is based on the unique combination of the three theories: the method of characteristics (MOC) used to simulate the neutron transport in two-dimensional (2D) whole core heterogeneous calculation, the theory of R-functions used as a mathematical tool to describe the true geometry and fuse with the MOC equations, and one-dimensional (1D) higher-order diffusion correction of 2D transport model to account for full 3D heterogeneous whole core representation. The synergism between the radial 2D transport and the 1D axial transport (to take into account the axial neutron interactions and leakage), called the 2D/1D method (used in DeCART and CHAPLET codes), provides a 3D computational solution. The unique synergism between the AGENT geometrical algorithm capable of modeling any current or future reactor core geometry and 3D neutron transport methodology is described in details. The 3D AGENT accuracy and its efficiency are demonstrated showing the eigenvalues, point-wise flux and reaction rate distributions in representative reactor geometries. The AGENT code, comprising this synergism, represents a building block of the computational system, called the virtual reactor. Its main purpose is to perform 'virtual' experiments and demonstrations of various mainly university research reactor experiments
Energy Technology Data Exchange (ETDEWEB)
Garcia Fite, J
1959-07-01
The diffusion length of thermal neutrons in graphite using the less possible quantity of material has been determined. The proceeding used was the measurement in a graphite pile which has a punctual source of rapid neutrons inside surrounded by a reflector medium (paraffin or water). The measurement was done in the following conditions: a) introducing an aluminium plate between both materials. b) Introducing a cadmium plate between both materials. (Author) 91 refs.
A method to measure the diffusion coefficient by neutron wave propagation for limited samples
International Nuclear Information System (INIS)
Woznicka, U.
1986-03-01
A study has been made of the use of the neutron wave and pulse propagation method for measurement of thermal neutron diffusion parameters. Earlier works an homogenous and heterogeneous media are reviewed. A new method is sketched for the determination of the diffusion coefficient for samples of limited size. The principle is to place a relatively thin slab of the material between two blocks of a medium with known properties. The advantages and disadvantages of the method are discussed. (author)
Ohmic ion temperature and thermal diffusivity profiles from the JET neutron emission profile monitor
Energy Technology Data Exchange (ETDEWEB)
Esposito, B. (ENEA, Frascati (Italy). Centro Ricerche Energia); Marcus, F.B.; Conroy, S.; Jarvis, O.N.; Loughlin, M.J.; Sadler, G.; Belle, P. van (Commission of the European Communities, Abingdon (United Kingdom). JET Joint Undertaking); Adams, J.M.; Watkins, N. (AEA Industrial Technology, Harwell (United Kingdom))
1993-10-01
The JET neutron emission profile monitor was used to study ohmically heated deuterium discharges. The radial profile of the neutron emissivity is deduced from the line-integral data. The profiles of ion temperature, T[sub i], and ion thermal diffusivity, [chi][sub i], are derived under steady-state conditions. The ion thermal diffusivity is higher than, and its scaling with plasma current opposite to, that predicted by neoclassical theory. (author).
Ohmic ion temperature and thermal diffusivity profiles from the JET neutron emission profile monitor
International Nuclear Information System (INIS)
Esposito, B.
1993-01-01
The JET neutron emission profile monitor was used to study ohmically heated deuterium discharges. The radial profile of the neutron emissivity is deduced from the line-integral data. The profiles of ion temperature, T i , and ion thermal diffusivity, χ i , are derived under steady-state conditions. The ion thermal diffusivity is higher than, and its scaling with plasma current opposite to, that predicted by neoclassical theory. (author)
International Nuclear Information System (INIS)
Zalan, T.A.
1988-01-01
Multi-energy-group neutron diffusion theory is used to numerically evaluate the utility of two different dual-detector neutron porosity logging devices, a 14 MeV (accelerator) neutron source - epithermal neutron detector device and a 4 MeV neutron source - capture gamma-ray detector device, relative to the traditional 4 MeV neutron source - thermal neutron detector device. Fast and epithermal neutron diffusion parameters are calculated using Monte Carlo - derived neutron flux distributions. Thermal parameters are calculated from tabulated cross sections. An existing analytical method to describe the transport of gamma-rays through common earth materials is modified in order to accommodate the modeling of the 4 MeV neutron - capture gamma-ray device. The 14 MeV neutron - epithermal neutron device is found to be less sensitive to porosity than the 4 MeV neutron - capture gamma-ray device, which in turn is found to be less sensitive to porosity than the traditional 4 MeV neutron - thermal neutron device. Salinity effects are found to be comparable for the 4 MeV neutron - capture gamma-ray and 4 MeV neutron - thermal neutron devices. The 4 MeV neutron capture gamma-ray measurement is found to be deepest investigating
Fe and N diffusion in nitrogen-rich FeN measured using neutron ...
Indian Academy of Sciences (India)
E-mail: mgupta@csr.ernet.in. Abstract. Grazing incidence neutron reflectometry provides an opportunity to measure the depth profile of a thin film sample with a resolution <1 nm, in a non-destructive way. In this way the diffusion across the interfaces can also be measured. In addition, neutrons have contrast among the ...
Review of multigroup nuclear cross-section processing
Energy Technology Data Exchange (ETDEWEB)
Trubey, D.K.; Hendrickson, H.R. (comps.)
1978-10-01
These proceedings consist of 18 papers given at a seminar--workshop on ''Multigroup Nuclear Cross-Section Processing'' held at Oak Ridge, Tennessee, March 14--16, 1978. The papers describe various computer code systems and computing algorithms for producing multigroup neutron and gamma-ray cross sections from evaluated data, and experience with several reference data libraries. Separate abstracts were prepared for 13 of the papers. The remaining five have already been cited in ERA, and may be located by referring to the entry CONF-780334-- in the Report Number Index. (RWR)
Albedo-adjusted fast-neutron diffusion coefficients in reactor reflectors
International Nuclear Information System (INIS)
Terney, W.B.
1975-01-01
In the newer, larger pressurized-water reactor cores, the calculated power distributions are fairly sensitive to the number of neutron groups used and to the treatment of the reflector cross sections. Comparisons between transport and diffusion calculations show that the latter substantially underpredict the reflector albedos in the fast (top) group and that the power distribution is shifted toward the core center when compared to 4-group transport theory results. When the fast-neutron diffusion coefficients are altered to make the transport- and diffusion-theory albedos agree, the power distributions are also brought into agreement. An expression for the fast-neutron diffusion coefficients in reflector regions has been derived such that the diffusion calculation reproduces the albedo obtained from a transport solution. In addition, a correction factor for mesh effects applicable to coarse mesh problems is presented. The use of the formalism gives the correct albedos and improved power distributions. (U.S.)
Finite element method for neutron diffusion problems in hexagonal geometry
International Nuclear Information System (INIS)
Wei, T.Y.C.; Hansen, K.F.
1975-06-01
The use of the finite element method for solving two-dimensional static neutron diffusion problems in hexagonal reactor configurations is considered. It is investigated as a possible alternative to the low-order finite difference method. Various piecewise polynomial spaces are examined for their use in hexagonal problems. The central questions which arise in the design of these spaces are the degree of incompleteness permissible and the advantages of using a low-order space fine-mesh approach over that of a high-order space coarse-mesh one. There is also the question of the degree of smoothness required. Two schemes for the construction of spaces are described and a number of specific spaces, constructed with the questions outlined above in mind, are presented. They range from a complete non-Lagrangian, non-Hermite quadratic space to an incomplete ninth order space. Results are presented for two-dimensional problems typical of a small high temperature gas-cooled reactor. From the results it is concluded that the space used should at least include the complete linear one. Complete spaces are to be preferred to totally incomplete ones. Once function continuity is imposed any additional degree of smoothness is of secondary importance. For flux shapes typical of the small high temperature gas-cooled reactor the linear space fine-mesh alternative is to be preferred to the perturbation quadratic space coarse-mesh one and the low-order finite difference method is to be preferred over both finite element schemes
Measurement of the diffusion length of thermal neutrons in the beryllium oxide
International Nuclear Information System (INIS)
Koechlin, J.C.; Martelly, J.; Duggal, V.P.
1955-01-01
The diffusion length of thermal neutrons in the beryllium oxide has been obtained while studying the spatial distribution of the neutrons in a massive parallelepiped of this matter placed before the thermal column of the reactor core of Saclay. The mean density of the beryllium oxide (BeO) is 2,95 gr/cm 3 , the mean density of the massif is 2,92 gr/cm 3 . The value of the diffusion length, deducted of the done measures, is: L = 32,7 ± 0,5 cm (likely gap). Some remarks are formulated about the influence of the spectral distribution of the neutrons flux used. (authors) [fr
Diffuse neutron scattering study of Cu2−xSe
DEFF Research Database (Denmark)
Cava, R. J.; Andersen, Niels Hessel; Clausen, Kurt Nørgaard
1986-01-01
We have measured the diffuse neutron scattering in the hkk plane for Cu2Se and Cu1.8Se at 180°C and 51°C, respectively, in the cubic antifluorite type phase. The diffuse scattering shows significant structure, indicative of correlated short range mobile ion ordering. The short range order is foun...
Energy Technology Data Exchange (ETDEWEB)
Ertaud, A; Beauge, R; Fauquez, H; De Laboulay, H; Mercier, C; Vautrey, L
1948-11-01
The diffusion length of thermal neutrons inside a given industrial graphite is determined by measuring the neutron density inside a parallelepipedal piling up of graphite bricks (2.10 x 2.10 x 2.442 m). A 3.8 curies (Ra {alpha} {yields} Be) source is placed inside the parallelepipedal block of graphite and thin manganese detectors are used. Corrections are added to the unweighted measurements to take into account the effects of the damping of supra-thermal neutrons in the measurement area. These corrections are experimentally deduced from the differential measurements made with a cadmium screen interposed between the source and the first plane of measurement. An error analysis completes the report. The diffusion length obtained is: L = 45.7 cm {+-} 0.3. The average density of the graphite used is 1.76 and the average apparent density of the piling up is 1.71. (J.S.)
Energy Technology Data Exchange (ETDEWEB)
Fernandes, Julio Cesar L.; Vilhena, Marco Tullio, E-mail: julio.lombaldo@ufrgs.b, E-mail: vilhena@pq.cnpq.b [Universidade Federal do Rio Grande do Sul (DMPA/UFRGS), Porto Alegre, RS (Brazil). Dept. de Matematica Pura e Aplicada. Programa de Pos Graduacao em Matematica Aplicada; Borges, Volnei; Bodmann, Bardo Ernest, E-mail: bardo.bodmann@ufrgs.b, E-mail: borges@ufrgs.b [Universidade Federal do Rio Grande do Sul (PROMEC/UFRGS), Porto Alegre, RS (Brazil). Programa de Pos-Graduacao em Engenharia Mecanica
2011-07-01
The principal idea of this work, consist on formulate an analytical method to solved problems for diffusion of neutrons with isotropic scattering in one-dimensional cylindrical geometry. In this area were develop many works that study the same problem in different system of coordinates as well as cartesian system, nevertheless using numerical methods to solve the shielding problem. In view of good results in this works, we starting with the idea that we can represent a source in the origin of the cylindrical system by a Delta Dirac distribution, we describe the physical modeling and solved the neutron diffusion equation inside of cylinder of radius R. For the case of transport equation, the formulation of discrete ordinates S{sub N} consists in discretize the angular variables in N directions and in using a quadrature angular set for approximate the sources of scattering, where the Diffusion equation consist on S{sub 2} approximated transport equation in discrete ordinates. We solved the neutron diffusion equation with an analytical form by the finite Hankel transform. Was presented also the build-up factor for the case that we have neutron flux inside the cylinder. (author)
International Nuclear Information System (INIS)
Fernandes, Julio Cesar L.; Vilhena, Marco Tullio; Borges, Volnei; Bodmann, Bardo Ernest
2011-01-01
The principal idea of this work, consist on formulate an analytical method to solved problems for diffusion of neutrons with isotropic scattering in one-dimensional cylindrical geometry. In this area were develop many works that study the same problem in different system of coordinates as well as cartesian system, nevertheless using numerical methods to solve the shielding problem. In view of good results in this works, we starting with the idea that we can represent a source in the origin of the cylindrical system by a Delta Dirac distribution, we describe the physical modeling and solved the neutron diffusion equation inside of cylinder of radius R. For the case of transport equation, the formulation of discrete ordinates S N consists in discretize the angular variables in N directions and in using a quadrature angular set for approximate the sources of scattering, where the Diffusion equation consist on S 2 approximated transport equation in discrete ordinates. We solved the neutron diffusion equation with an analytical form by the finite Hankel transform. Was presented also the build-up factor for the case that we have neutron flux inside the cylinder. (author)
Incoherent neutron scattering functions for random jump diffusion in bounded and infinite media
International Nuclear Information System (INIS)
Hall, P.L.; Ross, D.K.
1981-01-01
The incoherent neutron scattering function for unbounded jump diffusion is calculated from random walk theory assuming a gaussian distribution of jump lengths. The method is then applied to calculate the scattering function for spatially bounded random jumps in one dimension. The dependence on momentum transfer of the quasi-elastic energy broadenings predicted by this model and a previous model for bounded one-dimensional continuous diffusion are calculated and compared with the predictions of models for diffusion in unbounded media. The one-dimensional solutions can readily be generalized to three dimensions to provide a description of quasi-elastic scattering of neutrons by molecules undergoing localized random motions. (author)
Solution of two energy-group neutron diffusion equation by triangular elements
International Nuclear Information System (INIS)
Correia Filho, A.
1981-01-01
The application of the triangular finite elements of first order in the solution of two energy-group neutron diffusion equation in steady-state conditions is aimed at. The EFTDN (triangular finite elements in neutrons diffusion) computer code in FORTRAN IV language is developed. The discrete formulation of the diffusion equation is obtained applying the Galerkin method. The power method is used to solve the eigenvalues' problem and the convergence is accelerated through the use of Chebshev polynomials. For the equation systems solution the Gauss method is applied. The results of the analysis of two test-problems are presented. (Author) [pt
NDS multigroup cross section libraries
International Nuclear Information System (INIS)
DayDay, N.
1981-12-01
A summary description and documentation of the multigroup cross section libraries which exist at the IAEA Nuclear Data Section are given in this report. The libraries listed are available either on tape or in printed form. (author)
Energy Technology Data Exchange (ETDEWEB)
Beyster, J. R.; Young, J. C.; Neill, J. M.; Mowry, W. R. [General Atomic Division of General Dynamics Corporation, John Jay Hopkins Laboratory for Pure and Applied Science, San Diego, CA (United States)
1965-08-15
experiments, which are sensitive mainly to P{sub 0} scattering. In particular one may test the P{sub 1} scattering kernel appropriate to a given molecular model. Third, the transport cross-section may be calculated directly from the experiments for use in multigroup reactor analysis. (author) [French] On mesure par les methodes du temps de vol les sections efficaces differentielles de diffusion simple (d{sigma}/d {Omega}) pour les ralentisseurs usuels. On utilise des neutrons thermiques produits par une source puisee intense (accelerateur lineaire de la General Atomic) avec un parcours de vol de 12 m a l'extremite duquel est place un echantillon mince du ralentisseur a l*etude. En outre, on a egalement prevu un petit parcours de vol terminal pour les neutrons diffuses, entre l'echantillon et plusieurs detecteurs de neutrons entierement absorbants. Cette methode permet de mesurer simultanement la distribution angulaire de diffusion pour plus de 50 energies des neutrons incidents. Les intensites sont-elevees, le bruit de fond est faible et bien defini et on peut proceder a des mesures rapides pour tous les angles de diffusion compris entre 10 et 155 degres. Les auteurs presentent des mesures de la section efficace differentielle de diffusion pour le vanadium, H{sub 2}O, D{sub 2}O et ZrH. On a etudie le vanadium pour controler le dispositif experimental. On a fait des mesures avec H{sub 2}O pour diverses epaisseurs et orientations des echantillons en vue de les comparer aux calculs fondes sur divers modeles de diffusion par l'hydrogene lie et aux resultats obtenus par Springer et Reinsch. Toutes les mesures experimentales ont ete corrigees pour tenir compte des effets importants de la diffusion multiple dans les echantillons. Pour l'instant, on n'a pas observe experimentalement la variation accusee que fait prevoir le modele de diffusion de Nelkin lorsque l'energie des neutrons est d'environ 0,06 eV; ceci est du au fait que l'hypothese du rotateur unique inhibe a 0,06 eV n'a pas
Energy Technology Data Exchange (ETDEWEB)
Coote, G E; Haywood, B C [Atomic Energy of Canada Ltd., Chalk River, Ontario (Canada)
1963-01-15
Neutrons of 0.037 eV and 0.0088 eV were scattered from a thin sample of liquid bromine at room temperature, and the energy distributions of the scattered neutrons measured at angles from 10{sup o} to 160{sup o} by the time-of-flight method. The angular distribution confirms the results of a previous study by Caglioti. Spectra were expressed in the form of the ''scattering law'' S({alpha},{beta}) of Egelstaff and analysed to derive the generalized frequency distribution p({beta}) of atomic motions in the liquid. The function p({beta}) has a broad smooth peak centred at {beta}{approx}0.3, and shows no evidence for discrete levels in the measured range 0<{beta}< 0.8: the general shape of the curve supports the 'quasi-crystalline' picture of the liquid. Difficulty in the absolute normalization of p({beta}) is discussed. (author) [French] Des neutrons de 0,037 eV et 0,0088 eV ont ete dissuses par un echantillon mince de brome liquide a la temperature ambiante; on a mesure, par la methode du temps de vol, les distributions d'energies des neutrons diffuses, pour des angles compris entre 10{sup o} et 160{sup o}. La distribution angulaire confirme les resultats d'une etude anterieure faite par Caglioti. Les spectres ont ete exprimes d'apres la ''loi de dispersion'' S({alpha},{beta}) d'Egelstaff et analyses pour determiner la distribution generalisee des frequences p({beta}) des mouvements atomiques dans le liquide. La fonction p({beta}) comporte un pic large et a faible pente dont le centre est a {beta} {approx} 0,3 et ne presente aucune indication de niveaux discrets dans la gamme mesuree 0 < {beta} < 0,8; la forme generale de la courbe confirme l'image ''quasi cristalline'' du liquide. Les auteurs examinent les difficultes qui s'opposent a la normalisation absolue de p({beta}). (author) [Spanish] Los autores han estudiado la dispersion de neutrones de 0,037 eV y 0,0088 eV en una muestra de bromo liquido de espesor reducido, a temperatura ambiente. La distribucion
International Nuclear Information System (INIS)
Schwenk-Ferrero, A.
1986-11-01
GANTRAS is a system of codes for neutron transport calculations in which the anisotropy of elastic and inelastic (including (n,n'x)-reactions) scattering is fully taken into account. This is achieved by employing a rigorous method, so-called I * -method, to represent the scattering term of the transport equation and with the use of double-differential cross-sections for the description of the emission of secondary neutrons. The I * -method was incorporated into the conventional transport code ONETRAN. The ONETRAN subroutines were modified for the new purpose. An implementation of the updated version ANTRA1 was accomplished for plane and spherical geometry. ANTRA1 was included in GANTRAS and linked to another modules which prepare angle-dependent transfer matrices. The GANTRAS code consists of three modules: 1. The CROMIX code which calculates the macroscopic transfer matrices for mixtures on the base of microscopic nuclide-dependent data. 2. The ATP code which generates discretized angular transfer probabilities (i.e. discretizes the I * -function). 3. The ANTRA1 code to perform S N transport calculations in one-dimensional plane and spherical geometries. This structure of GANTRAS allows to accommodate the system to various transport problems. (orig.) [de
Fast solution of neutron diffusion problem by reduced basis finite element method
International Nuclear Information System (INIS)
Chunyu, Zhang; Gong, Chen
2018-01-01
Highlights: •An extremely efficient method is proposed to solve the neutron diffusion equation with varying the cross sections. •Three orders of speedup is achieved for IAEA benchmark problems. •The method may open a new possibility of efficient high-fidelity modeling of large scale problems in nuclear engineering. -- Abstract: For the important applications which need carry out many times of neutron diffusion calculations such as the fuel depletion analysis and the neutronics-thermohydraulics coupling analysis, fast and accurate solutions of the neutron diffusion equation are demanding but necessary. In the present work, the certified reduced basis finite element method is proposed and implemented to solve the generalized eigenvalue problems of neutron diffusion with variable cross sections. The order reduced model is built upon high-fidelity finite element approximations during the offline stage. During the online stage, both the k eff and the spatical distribution of neutron flux can be obtained very efficiently for any given set of cross sections. Numerical tests show that a speedup of around 1100 is achieved for the IAEA two-dimensional PWR benchmark problem and a speedup of around 3400 is achieved for the three-dimensional counterpart with the fission cross-sections, the absorption cross-sections and the scattering cross-sections treated as parameters.
Energy Technology Data Exchange (ETDEWEB)
Galula, M; Jacrot, B; Mangin, J P [Commissariat a l' Energie Atomique, Saclay (France)
1959-07-01
The critical scattering of very slow neutrons by iron near critical point is measured by time of flight techniques. The VAN HOVE formula is verified and the geometrical parameters K{sub 1} et r{sub 1} introduced in this theory are determined. (author) [French] On etudie la diffusion critique des neutrons tres lents par le fer dans la region du point de Curie par une methode de temps de vol. On verifie la formule de VAN HOVE et on determine les parametres geometriques K{sub 1} et r{sub 1} introduit par ce dernier. (auteur)
Interpretation of the quasi-elastic neutron scattering on PAA by rotational diffusion models
International Nuclear Information System (INIS)
Bata, L.; Vizi, J.; Kugler, S.
1974-10-01
First the most important data determined by other methods for para azoxy anisolon (PAA) are collected. This molecule makes a rotational oscillational motion around the mean molecular direction. The details of this motion can be determined by inelastic neutron scattering. Quasielastic neutron scattering measurements were carried out without orienting magnetic field on a time-of-flight facility with neutron beam of 4.26 meV. For the interpretation of the results two models, the spherical rotation diffusion model and the circular random walk model are investigated. The comparison shows that the circular random walk model (with N=8 sites, d=4A diameter and K=10 10 s -1 rate constant) fits very well with the quasi-elastic neutron scattering, while the spherical rotational diffusion model seems to be incorrect. (Sz.N.Z.)
International Nuclear Information System (INIS)
Drozdowicz, K.
1999-01-01
Macroscopic parameters for a description of the thermal neutron transport in finite volumes are considered. A very good correspondence between the theoretical and experimental parameters of hydrogenous media is attained. Thermal neutrons in the medium possess an energy distribution, which is dependent on the size (characterized by the geometric buckling) and on the neutron transport properties of the medium. In a hydrogenous material the thermal neutron transport is dominated by the scattering cross section which is strongly dependent on energy. A monoenergetic treatment of the thermal neutron group (admissible for other materials) leads in this case to a discrepancy between theoretical and experimental results. In the present paper the theoretical definitions of the pulsed thermal neutron parameters (the absorption rate, the diffusion coefficient, and the diffusion cooling coefficient) are based on Nelkin's analysis of the decay of a neutron pulse. Problems of the experimental determination of these parameters for a hydrogenous medium are discussed. A theoretical calculation of the pulsed parameters requires knowledge of the scattering kernel. For thermal neutrons it is individual for each hydrogenous material because neutron scattering on hydrogen nuclei bound in a molecule is affected by the molecular dynamics (characterized with internal energy modes which are comparable to the incident neutron energy). Granada's synthetic model for slow-neutron scattering is used. The complete up-dated formalism of calculation of the energy transfer scattering kernel after this model is presented in the paper. An influence of some minor variants within the model on the calculated differential and integral neutron parameters is shown. The theoretical energy-dependent scattering cross section (of Plexiglas) is compared to experimental results. A particular attention is paid to the calculation of the diffusion cooling coefficient. A solution of an equation, which determines the
Energy Technology Data Exchange (ETDEWEB)
Wright, R.Q.; Renier, J.P.; Bucholz, J.A.
1995-08-01
The original ANSL-V cross-section libraries (ORNL-6618) were developed over a period of several years for the physics analysis of the ANS reactor, with little thought toward including the materials commonly needed for shielding applications. Materials commonly used for shielding applications include calcium barium, sulfur, phosphorous, and bismuth. These materials, as well as {sup 6}Li, {sup 7}Li, and the naturally occurring isotopes of hafnium, have been added to the ANSL-V libraries. The gamma-ray production and gamma-ray interaction cross sections were completely regenerated for the ANSL-V 99n/44g library which did not exist previously. The MALOCS module was used to collapse the 99n/44g coupled library to the 39n/44g broad- group library. COMET was used to renormalize the two-dimensional (2- D) neutron matrix sums to agree with the one-dimensional (1-D) averaged values. The FRESH module was used to adjust the thermal scattering matrices on the 99n/44g and 39n/44g ANSL-V libraries. PERFUME was used to correct the original XLACS Legendre polynomial fits to produce acceptable distributions. The final ANSL-V 99n/44g and 39n/44g cross-section libraries were both checked by running RADE. The AIM module was used to convert the master cross-section libraries from binary coded decimal to binary format (or vice versa).
International Nuclear Information System (INIS)
Chakraverty, S.; Nayak, S.
2013-01-01
Highlights: • Uncertain neutron diffusion equation of bare square homogeneous reactor is studied. • Proposed interval arithmetic is extended for fuzzy numbers. • The developed fuzzy arithmetic is used to handle uncertain parameters. • Governing differential equation is modelled by modified fuzzy finite element method. • Fuzzy critical eigenvalues and effective multiplication factors are investigated. - Abstract: The scattering of neutron collision inside a reactor depends upon geometry of the reactor, diffusion coefficient and absorption coefficient etc. In general these parameters are not crisp and hence we get uncertain neutron diffusion equation. In this paper we have investigated the above equation for a bare square homogeneous reactor. Here the uncertain governing differential equation is modelled by a modified fuzzy finite element method. Using modified fuzzy finite element method, obtained eigenvalues and effective multiplication factors are studied. Corresponding results are compared with the classical finite element method in special cases and various uncertain results have been discussed
Pulsed neutron determination of anisotropic diffusion constants in multi-layered slabs
International Nuclear Information System (INIS)
Sri Ram, K.
1978-01-01
Anisotropic neutron diffusion parameters for graphite and plexiglas slab assemblies were calculated using one-dimensional discrete ordinates code ANISN, and also Case's eigenfunction expansion technique as suggested by Leonard. These calculated values were checked with the pulsed neutron experimental results as well as simple diffusion theory calculations of Spinrad. Relatively little experimental work has been done with heterogeneous assemblies which do not contain voids. The present comparison shows that the experimental results agree well with transport theory calculations. It appears from the results and inter-comparison of this work in simple geometries, that the pulsed neutron method can yield accurate experimental anisotropic diffusion constants, and can therefore be applied to more complicated geometries which may be difficult to calculate. (author)
International Nuclear Information System (INIS)
Kobayashi, Keisuke; Ishibashi, Hideo
1978-01-01
A two-dimensional neutron diffusion equation for a triangular region is shown to be solved by the finite Fourier transformation. An application of the Fourier transformation to the diffusion equation for triangular region yields equations whose unknowns are the expansion coefficients of the neutron flux and current in Fourier series or Legendre polynomials expansions only at the region boundary. Some numerical calculations have revealed that the present technique gives accurate results. It is shown also that the solution using the expansion in Legendre polynomials converges with relatively few terms even if the solution in Fourier series exhibits the Gibbs' phenomenon. (auth.)
Study on neutron diffusion and time dependence heat ina fluidized bed nuclear reactor
International Nuclear Information System (INIS)
Vilhena, M.T. de.
1988-01-01
The purpose of this work is to model the neutron diffusion and heat transfer for a Fluidized Bed Nuclear Reactor and its solution by Laplace Transform Technique with numerical inversion using Fourier Series. Also Gaussian quadrature and residues techniques were applied for numerical inversion. The neutron transport, diffusion, and point Kinetic equation for this nuclear reactor concept are developed. A matricial and Taylor Series methods are proposed for the solution of the point Kinetic equation which is a time scale problem of Stiff type
Neuro-diffuse algorithm for neutronic power identification of TRIGA Mark III reactor
International Nuclear Information System (INIS)
Rojas R, E.; Benitez R, J. S.; Segovia de los Rios, J. A.; Rivero G, T.
2009-10-01
In this work are presented the results of design and implementation of an algorithm based on diffuse logic systems and neural networks like method of neutronic power identification of TRIGA Mark III reactor. This algorithm uses the punctual kinetics equation as data generator of training, a cost function and a learning stage based on the descending gradient algorithm allow to optimize the parameters of membership functions of a diffuse system. Also, a series of criteria like part of the initial conditions of training algorithm are established. These criteria according to the carried out simulations show a quick convergence of neutronic power estimated from the first iterations. (Author)
An analytical solution for the two-group kinetic neutron diffusion equation in cylindrical geometry
International Nuclear Information System (INIS)
Fernandes, Julio Cesar L.; Vilhena, Marco Tullio; Bodmann, Bardo Ernst
2011-01-01
Recently the two-group Kinetic Neutron Diffusion Equation with six groups of delay neutron precursor in a rectangle was solved by the Laplace Transform Technique. In this work, we report on an analytical solution for this sort of problem but in cylindrical geometry, assuming a homogeneous and infinite height cylinder. The solution is obtained applying the Hankel Transform to the Kinetic Diffusion equation and solving the transformed problem by the same procedure used in the rectangle. We also present numerical simulations and comparisons against results available in literature. (author)
Energy Technology Data Exchange (ETDEWEB)
Ghrayeb, S. Z. [Dept. of Mechanical and Nuclear Engineering, Pennsylvania State Univ., 230 Reber Building, Univ. Park, PA 16802 (United States); Ouisloumen, M. [Westinghouse Electric Company, 1000 Westinghouse Drive, Cranberry Township, PA 16066 (United States); Ougouag, A. M. [Idaho National Laboratory, MS-3860, PO Box 1625, Idaho Falls, ID 83415 (United States); Ivanov, K. N.
2012-07-01
A multi-group formulation for the exact neutron elastic scattering kernel is developed. This formulation is intended for implementation into a lattice physics code. The correct accounting for the crystal lattice effects influences the estimated values for the probability of neutron absorption and scattering, which in turn affect the estimation of core reactivity and burnup characteristics. A computer program has been written to test the formulation for various nuclides. Results of the multi-group code have been verified against the correct analytic scattering kernel. In both cases neutrons were started at various energies and temperatures and the corresponding scattering kernels were tallied. (authors)
Neutron diffusion in spheroidal, bispherical, and toroidal systems
International Nuclear Information System (INIS)
Williams, M.M.R.
1986-01-01
The neutron flux has been studied around absorbing bodies of spheroidal, bispherical, and toroidal shapes in an infinite nonabsorbing medium. Exact solutions have been obtained by using effective boundary conditions at the surfaces of the absorbing bodies. The problems considered are as follows: 1. Neutron flux and current distributions around prolate and oblate spheroids. It is shown that an equivalent sphere approximation can lead to accurate values for the rate of absorption. 2. Neutron flux and current in a bispherical system of unequal spheres. Three separate situations arise here: (a) two absorbing spheres, (b) two spherical sources, and (c) one spherical source and one absorbing sphere. It is shown how the absorption rate in the two spheres depends on their separation. 3. Neutron flux and current in a toroidal system: (a) an absorbing toroid and (b) a toroidal source. The latter case simulates the flux distribution from a thermonuclear reactor vessel. Finally, a brief description of how these techniques can be extended to multiregion problems is given
International Nuclear Information System (INIS)
Bussac, J.; Reuss, P.
1985-01-01
This book presents the main physical bases of neutron theory and nuclear reactor calculation. 1) Interactions of neutrons with matter and basic principles of neutron transport; 2) Neutron transport in homogeneous medium and the neutron field: kinetic behaviour, slowing-down, resonance absorption, diffusion equation, processing methods; 3) Theory of a reactor constituted with homogeneous zones: critical condition, kinetics, separation of variables, calculation and neutron balance of the fundamental mode, one-group and multigroup theories; 4) Study of heterogeneous cell lattices: fast fission factor, resonance absorption, thermal output factor, diffusion coefficient, computer codes; 5) Operation and control of reactors: perturbation theory, reactivity, fuel properties evolution, poisoning by fission products, calculation of a reactor and fuel management; 6) Study of some types of reactors: PWR and fast breeder reactors, the main reactor types of the present French program [fr
International Nuclear Information System (INIS)
Koch, R.; Findeisen, A.
1986-04-01
The multigroup neutron diffusion theory code SNAP-3D has been used to perform time independent neutron flux and power calculations of the 10 MW Rossendorf research reactor of the type WWR-SM. The report describes these calculations, as well as the actual reactor configuration, some details of the code SNAP-3D, and two- and three-dimensional reactor models. For evaluating the calculations some flux values and control rod worths have been compared with those of measurements. (author)
International Nuclear Information System (INIS)
Czubek, J.A.; Woznicka, U.
1997-01-01
A solution of the neutron diffusion equation is given for a three layer cylindrical coaxial geometry. The calculation is performed in two neutron-energy groups which distinguish the thermal and epithermal neutron fluxes in the media irradiated by the fast point neutron source. The aim of the calculation is to define the neutron slowing down and migration lengths which are observed at a given point of the system. Generally, the slowing down and migration lengths are defined for an infinite homogenous medium (irradiated by the point neutron source) as a quotient of the neutron flux moment of the (2n + 2)-order to the moment of the 2n-order. Czubek(1992) introduced in the same manner the apparent neutron slowing down length and the apparent migration length for a given multi-region cylindrical geometry. The solutions in the present paper are applied to the method of semi-empirical calibration of neutron well-logging tools. The three-region cylindrical geometry corresponds to the borehole of radius R 1 surrounded by the intermediate region (e.g. mud cake) of thickness (R 2 -R 1 ) and finally surrounded by the geological formation which spreads from R 2 up to infinity. The cylinders of an infinite length are considered. The paper gives detailed solutions for the 0-th, 2-nd and 4-th neutron moments of the neutron fluxes for each neutron energy group and in each cylindrical layer. A comprehensive list of the solutions for integrals containing Bessel functions or their derivatives, which are absent in common tables of integrals, is also included. (author)
Energy Technology Data Exchange (ETDEWEB)
Czubek, J.A.; Woznicka, U. [The H. Niewodniczanski Inst. of Nuclear Physics, Cracow (Poland)
1997-12-31
A solution of the neutron diffusion equation is given for a three layer cylindrical coaxial geometry. The calculation is performed in two neutron-energy groups which distinguish the thermal and epithermal neutron fluxes in the media irradiated by the fast point neutron source. The aim of the calculation is to define the neutron slowing down and migration lengths which are observed at a given point of the system. Generally, the slowing down and migration lengths are defined for an infinite homogenous medium (irradiated by the point neutron source) as a quotient of the neutron flux moment of the (2n{sup +}2)-order to the moment of the 2n-order. Czubek(1992) introduced in the same manner the apparent neutron slowing down length and the apparent migration length for a given multi-region cylindrical geometry. The solutions in the present paper are applied to the method of semi-empirical calibration of neutron well-logging tools. The three-region cylindrical geometry corresponds to the borehole of radius R{sub 1} surrounded by the intermediate region (e.g. mud cake) of thickness (R{sub 2}-R{sub 1}) and finally surrounded by the geological formation which spreads from R{sub 2} up to infinity. The cylinders of an infinite length are considered. The paper gives detailed solutions for the 0-th, 2-nd and 4-th neutron moments of the neutron fluxes for each neutron energy group and in each cylindrical layer. A comprehensive list of the solutions for integrals containing Bessel functions or their derivatives, which are absent in common tables of integrals, is also included. (author) 6 refs, 2 figs
Elastic neutron diffuse scattering in Zr(Ca, Y)O2-x
International Nuclear Information System (INIS)
Barberis, P.; Beuneu, B.; Novion, C.H. de.
1990-01-01
Elastic neutron diffuse scattering has been measured in cubic Zr(Ca, Y)O 2-x at room temperature. The very high diffuse scattering (up to 70 Laue) is explained mostly by the oxygen displacements along directions, and by Ca displacements along . The weak short-range order contribution strongly suggests that oxygen vacancies tend to place as second rather than at first neighbours of a Ca stabilizing ion
Optimal calculational schemes for solving multigroup photon transport problem
International Nuclear Information System (INIS)
Dubinin, A.A.; Kurachenko, Yu.A.
1987-01-01
A scheme of complex algorithm for solving multigroup equation of radiation transport is suggested. The algorithm is based on using the method of successive collisions, the method of forward scattering and the spherical harmonics method, and is realized in the FORAP program (FORTRAN, BESM-6 computer). As an example the results of calculating reactor photon transport in water are presented. The considered algorithm being modified may be used for solving neutron transport problems
Estimating anisotropic diffusion of neutrons near the boundary of a pebble bed random system
International Nuclear Information System (INIS)
Vasques, R.
2013-01-01
Due to the arrangement of the pebbles in a Pebble Bed Reactor (PBR) core, if a neutron is located close to a boundary wall, its path length probability distribution function in directions of flight parallel to the wall is significantly different than in other directions. Hence, anisotropic diffusion of neutrons near the boundaries arises. We describe an analysis of neutron transport in a simplified 3-D pebble bed random system, in which we investigate the anisotropic diffusion of neutrons born near one of the system's boundary walls. While this simplified system does not model the actual physical process that takes place near the boundaries of a PBR core, the present work paves the road to a formulation that may enable more accurate diffusion simulations of such problems to be performed in the future. Monte Carlo codes have been developed for (i) deriving realizations of the 3-D random system, and (ii) performing 3-D neutron transport inside the heterogeneous model; numerical results are presented for three different choices of parameters. These numerical results are used to assess the accuracy of estimates for the mean-squared displacement of neutrons obtained with the diffusion approximations of the Atomic Mix Model and of the recently introduced [1] Non-Classical Theory with angular-dependent path length distribution. The Non-Classical Theory makes use of a Generalized Linear Boltzmann Equation in which the locations of the scattering centers in the system are correlated and the distance to collision is not exponentially distributed. We show that the results predicted using the Non-Classical Theory successfully model the anisotropic behavior of the neutrons in the random system, and more closely agree with experiment than the results predicted by the Atomic Mix Model. (authors)
Estimating anisotropic diffusion of neutrons near the boundary of a pebble bed random system
Energy Technology Data Exchange (ETDEWEB)
Vasques, R. [Department of Mathematics, Center for Computational Engineering Science, RWTH Aachen University, Schinkel Strasse 2, D-52062 Aachen (Germany)
2013-07-01
Due to the arrangement of the pebbles in a Pebble Bed Reactor (PBR) core, if a neutron is located close to a boundary wall, its path length probability distribution function in directions of flight parallel to the wall is significantly different than in other directions. Hence, anisotropic diffusion of neutrons near the boundaries arises. We describe an analysis of neutron transport in a simplified 3-D pebble bed random system, in which we investigate the anisotropic diffusion of neutrons born near one of the system's boundary walls. While this simplified system does not model the actual physical process that takes place near the boundaries of a PBR core, the present work paves the road to a formulation that may enable more accurate diffusion simulations of such problems to be performed in the future. Monte Carlo codes have been developed for (i) deriving realizations of the 3-D random system, and (ii) performing 3-D neutron transport inside the heterogeneous model; numerical results are presented for three different choices of parameters. These numerical results are used to assess the accuracy of estimates for the mean-squared displacement of neutrons obtained with the diffusion approximations of the Atomic Mix Model and of the recently introduced [1] Non-Classical Theory with angular-dependent path length distribution. The Non-Classical Theory makes use of a Generalized Linear Boltzmann Equation in which the locations of the scattering centers in the system are correlated and the distance to collision is not exponentially distributed. We show that the results predicted using the Non-Classical Theory successfully model the anisotropic behavior of the neutrons in the random system, and more closely agree with experiment than the results predicted by the Atomic Mix Model. (authors)
Nuclear data and multigroup methods in fast reactor calculations
International Nuclear Information System (INIS)
Gur, Y.
1975-03-01
The work deals with fast reactor multigroup calculations, and the efficient treatment of basic nuclear data, which serves as raw material for the calculations. Its purpose is twofold: to build a computer code system that handles a large, detailed library of basic neutron cross section data, (such as ENDF/B-III) and yields a compact set of multigroup cross sections for reactor calculations; to use the code system for comparative analysis of different libraries, in order to discover basic uncertainties that still exist in the measurement of neutron cross sections, and to determine their influence upon uncertainties in nuclear calculations. A program named NANICK which was written in two versions is presented. The first handles the American basic data library, ENDF/B-III, while the second handles the German basic data library, KEDAK. The mathematical algorithm is identical in both versions, and only the file management is different. This program calculates infinitely diluted multigroup cross sections and scattering matrices. It is complemented by the program NASIF that calculates shielding factors from resonance parameters. Different versions of NASIF were written to handle ENDF/B-III or KEDAK. New methods for evaluating in reactor calculations the long term behavior of the neutron flux as well as its fine structure are described and an efficient calculation of the shielding factors from resonance parameters is offered. (B.G.)
Energy Technology Data Exchange (ETDEWEB)
Gerhard Strydom; Cristian Rabiti; Andrea Alfonsi
2012-10-01
PHISICS is a neutronics code system currently under development at the Idaho National Laboratory (INL). Its goal is to provide state of the art simulation capability to reactor designers. The different modules for PHISICS currently under development are a nodal and semi-structured transport core solver (INSTANT), a depletion module (MRTAU) and a cross section interpolation (MIXER) module. The INSTANT module is the most developed of the mentioned above. Basic functionalities are ready to use, but the code is still in continuous development to extend its capabilities. This paper reports on the effort of coupling the nodal kinetics code package PHISICS (INSTANT/MRTAU/MIXER) to the thermal hydraulics system code RELAP5-3D, to enable full core and system modeling. This will enable the possibility to model coupled (thermal-hydraulics and neutronics) problems with more options for 3D neutron kinetics, compared to the existing diffusion theory neutron kinetics module in RELAP5-3D (NESTLE). In the second part of the paper, an overview of the OECD/NEA MHTGR-350 MW benchmark is given. This benchmark has been approved by the OECD, and is based on the General Atomics 350 MW Modular High Temperature Gas Reactor (MHTGR) design. The benchmark includes coupled neutronics thermal hydraulics exercises that require more capabilities than RELAP5-3D with NESTLE offers. Therefore, the MHTGR benchmark makes extensive use of the new PHISICS/RELAP5-3D coupling capabilities. The paper presents the preliminary results of the three steady state exercises specified in Phase I of the benchmark using PHISICS/RELAP5-3D.
TRITON, 3-D Multi-Region Neutron Diffusion Burnup with Criticality Search
International Nuclear Information System (INIS)
1974-01-01
1 - Nature of physical problem solved: TRITON is a multigroup diffusion depletion program in three dimensions (x,y,z). In addition to the straight K eff calculation, three types of criticality searches are possible - diluted control isotope search, region-wise smeared control isotope search, region-wise smeared control isotope search, region-wise smeared control isotope boundary search (the control isotope can be smeared over one region or over a group of regions called a control bank). The depletion equations are solved region-wise. More than one microscopic cross section library can be used in the various regions of the reactor. The same is true for self-shielding factors. Such sets of data can be changed at pre-determined time steps. 2 - Method of solution: The mathematical model employed for the solution of the finite difference equations, which is derived from a seven-point approximation of diffusion equations, is an on-line Chebyshev semi- iterative method. 3 - Restrictions on the complexity of the problem: Maximum number of: library sets: 1; self-shielding sets: 10; compositions: 100; self-shielding coefficients: 6000; groups: 10; fuel isotopes: 30; fission products: 29; isotopes: 50; burnable isotopes: 40; control banks: 100; mesh points: 15000; regions: 400; time steps: 100; control areas: 100; small time steps: 200; elements in the control list: 400; x planes: 100; y planes: 100; z planes: 100
Study by neutron diffusion of local order liquid sulfur around the polymerization transition
International Nuclear Information System (INIS)
Descotes, L.
1994-05-01
We studied the liquid sulfur according to the temperature. The sulfur is one of the most complicated elementary liquid. We experimented the neutron diffusion by the powder orthorhombic sulfur. The complexity at the polymerization transition are only accompanied by weak local structural transfer. 231 refs., 48 figs., 8 tabs., 3 annexes
International Nuclear Information System (INIS)
Buckel, G.; Wouters, R. de; Pilate, S.
1977-01-01
The synthesis code KASY for an approximate solution of the three-dimensional neutron diffusion equation is described; the state of the art as well as envisaged program extensions and the application to tasks from the field of reactor designing are dealt with. (RW) [de
ARGO, 1-D Neutron Diffusion in Slab, Cylindrical, Spherical Geometry from JAERI Fast-Set, ABBN, RCBN
International Nuclear Information System (INIS)
Ikawa, Koji
1971-01-01
1 - Nature of physical problem solved: ARGO is a one-dimensional (slab, cylinder or sphere), multigroup diffusion code for use in fast reactor criticality and kinetic parameter analysis. Three cross section sets, i.e., JAERI-Fast-Set, ABBN-Set and RCBN-Set, of 25 groups are prepared for the code as its library tapes. 2 - Method of solution: Eigenvalues are computed by ordinary source-iteration techniques with ordinary acceleration methods for convergence. 3 - Restrictions on the complexity of the problem: Sphere geometry
Inter-atomic force constants of BaF{sub 2} by diffuse neutron scattering measurement
Energy Technology Data Exchange (ETDEWEB)
Sakuma, Takashi, E-mail: sakuma@mx.ibaraki.ac.jp; Makhsun,; Sakai, Ryutaro [Institute of Applied Beam Science, Ibaraki University, Mito 310-8512 (Japan); Xianglian [College of Physics and Electronics Information, Inner Mongolia University for the Nationalities, Tongliao 028043 (China); Takahashi, Haruyuki [Institute of Applied Beam Science, Ibaraki University, Hitachi 316-8511 (Japan); Basar, Khairul [Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Bandung 40132 (Indonesia); Igawa, Naoki [Quantum Beam Science Directorate, Japan Atomic Energy Agency, Tokai 319-1195 (Japan); Danilkin, Sergey A. [Bragg Institute, Australian Nuclear Science and Technology Organisation, Kirrawee DC NSW 2232 (Australia)
2015-04-16
Diffuse neutron scattering measurement on BaF{sub 2} crystals was performed at 10 K and 295 K. Oscillatory form in the diffuse scattering intensity of BaF{sub 2} was observed at 295 K. The correlation effects among thermal displacements of F-F atoms were obtained from the analysis of oscillatory diffuse scattering intensity. The force constants among neighboring atoms in BaF{sub 2} were determined and compared to those in ionic crystals and semiconductors.
Chapter 9: Experimental measurements of the diffusion area of neutrons in graphite
International Nuclear Information System (INIS)
Brown, G.; McCulloch, D.B.
1963-01-01
This report describes measurements of the diffusion area of neutrons in a solid graphite exponential stack, and in a stack containing cylindrical air channels of 4.5 in. diameter, arranged on a square lattice of 8 in. pitch. The resulting diffusion area ratios are compared with the theoretical predictions of a number of authors. The diffusion area ratios deduced from a pair of experiments in which the orientation of the air channels with respect to the source-plane is changed are found to be in agreement with those deduced from experiments in which the stack size is changed but a constant air channel orientation maintained. (author)
Diffusive instability of a kaon condensate in neutron star matter
International Nuclear Information System (INIS)
Kubis, Sebastian
2004-01-01
The beta equilibrated dense matter with kaon condensate is analyzed with respect to extended stability conditions, including charge fluctuations. This kind of the diffusive instability appeared to be common property in the kaon condensation case. Results for three different nuclear models are presented
Diffusion of water adsorbed in hydrotalcite: neutron scattering Study
Energy Technology Data Exchange (ETDEWEB)
Mitra, S [Solid State Physics Division, Bhabha Atomic Research Centre, Mumbai (India); Pramanik, A [Unilever Research India, Bangalore 500 066 (India); Chakrabarty, D [Godrej Sara Lee Limited, Research and Development Centre, Mumbai 400 079 (India); Juranyi, F [Laboratory for Neutron Scattering, ETHZ and PSI, CH-5232 Villigen PSI (Switzerland); Gautam, S [Solid State Physics Division, Bhabha Atomic Research Centre, Mumbai (India); Mukhopadhyay, R [Solid State Physics Division, Bhabha Atomic Research Centre, Mumbai (India)
2007-12-15
Layered double hydroxides (LDH) are a class of ionic lamellar solids with positively charged layers of two kinds of metallic cations and exchangeable hydrated anions. Quasi-elastic neutron scattering (QENS) measurements are performed in this type of LDH structured hydrated hydrotalcite sample to study the dynamical behaviour of the water in geometric confinement within the layers. Dynamical parameters correspond to the confined water molecules revealed that depending on the amount of excess water present, behaves differently and approaches bulk values at high concentration. Both translational and rotational dynamical parameters showed that at very low concentration of excess water, water molecules are attached to the surfaces and show the confinement effect.
A scatter model for fast neutron beams using convolution of diffusion kernels
International Nuclear Information System (INIS)
Moyers, M.F.; Horton, J.L.; Boyer, A.L.
1988-01-01
A new model is proposed to calculate dose distributions in materials irradiated with fast neutron beams. Scattered neutrons are transported away from the point of production within the irradiated material in the forward, lateral and backward directions, while recoil protons are transported in the forward and lateral directions. The calculation of dose distributions, such as for radiotherapy planning, is accomplished by convolving a primary attenuation distribution with a diffusion kernel. The primary attenuation distribution may be quickly calculated for any given set of beam and material conditions as it describes only the magnitude and distribution of first interaction sites. The calculation of energy diffusion kernels is very time consuming but must be calculated only once for a given energy. Energy diffusion distributions shown in this paper have been calculated using a Monte Carlo type of program. To decrease beam calculation time, convolutions are performed using a Fast Fourier Transform technique. (author)
International Nuclear Information System (INIS)
Ceolin, Celina; Vilhena, Marco T.; Petersen, Claudio Z.
2009-01-01
In this work we report an analytical solution for the monoenergetic neutron diffusion kinetic equation in cartesian geometry. Bearing in mind that the equation for the delayed neutron precursor concentration is a first order linear differential equation in the time variable, to make possible the application of the GITT approach to the kinetic equation, we introduce a fictitious diffusion term multiplied by a positive small value ε. By this procedure, we are able to solve this set of equations. Indeed, applying the GITT technique to the modified diffusion kinetic equation, we come out with a matrix differential equation which has a well known analytical solution when ε goes to zero. We report numerical simulations as well study of numerical convergence of the results attained. (author)
Application of a numerical transport correction in diffusion calculations
International Nuclear Information System (INIS)
Tomatis, Daniele; Dall'Osso, Aldo
2011-01-01
Full core calculations by ordinary transport methods can demand considerable computational time, hardly acceptable in the industrial work frame. However, the trend of next generation nuclear cores goes toward more heterogeneous systems, where transport phenomena of neutrons become very important. On the other hand, using diffusion solvers is more practical allowing faster calculations, but a specific formulation of the diffusion coefficient is requested to reproduce the scalar flux with reliable physical accuracy. In this paper, the Ronen method is used to evaluate numerically the diffusion coefficient in the slab reactor. The new diffusion solution is driven toward the solution of the integral neutron transport equation by non linear iterations. Better estimates of currents are computed and diffusion coefficients are corrected at node interfaces, still assuming Fick's law. This method enables obtaining closer results to the transport solution by a common solver in multigroup diffusion. (author)
A multigroup treatment of radiation transport
International Nuclear Information System (INIS)
Tahir, N.A.; Laing, E.W.; Nicholas, D.J.
1980-12-01
A multi-group radiation package is outlined which will accurately handle radiation transfer problems in laser-produced plasmas. Bremsstrahlung, recombination and line radiation are included as well as fast electron Bremsstrahlung radiation. The entire radiation field is divided into a large number of groups (typically 20), which diffuse radiation energy in real space as well as in energy space, the latter occurring via electron-radiation interaction. Using this model a radiation transport code will be developed to be incorporated into MEDUSA. This modified version of MEDUSA will be used to study radiative preheat effects in laser-compression experiments at the Central Laser Facility, Rutherford Laboratory. The model is also relevant to heavy ion fusion studies. (author)
Nuclear data processing and multigroup cross section generation
International Nuclear Information System (INIS)
Kim, Jeong Do; Kil, Chung Sub
1996-01-01
The multigroup constants for WIMS/CASMO were updated with ENDF/B-VI and were tested. The continuous energy MCNP library developed last year was validated against the LWR-simulated critical experiments. The MCNP library will be used to design and analyze nuclear and shielding facilities. The system for generation of MATXS multigroup library and TRANSX code, which is able to prepare the data for the discrete ordinates and diffusion codes from the MATXS library, was established. The MATXS libraries for analyses of thermal and fast critical experiments were generated and tested. The MATXS/TRANSX system for the discrete ordinates and diffusion codes will be useful for nuclear analyses. 10 tabs., 5 figs., 17 refs. (Author)
Multigroup neutron data base for nuclear geophysics
International Nuclear Information System (INIS)
Dworak, D.; Loskiewicz, J.
1989-01-01
The average group constants for the total, elastic, inelastic and capture cross sections as well as the average cosine of the scattering angle for elastic scattering and the average logarithmic energy decrement for elastic scattering have been obtained at two temperatures (300 and 400 deg K), using the ENDF/B-4 data and the IAEA-NDS pre-processing codes. The extended Abagyan group structure and the weighting spectrum of type 1/E were applied in course of the calculations. Self-shielding effect was not taken into account. All cross sections were Doppler broadened for both, 300 and 400 deg K temperatures. Under above assumptions, the average group constants were obtained for exactly 22 ENDF materials, which are of special importance for nuclear geophysics applications. 10 refs., 15 figs., 44 tabs. (author)
Neutrons in a highly diffusive medium a new propulsion tool for deep space exploration?
Rubbia, Carlo
1998-01-01
The recently completed TARC Experiment at the CERN-PS has shown how it is possible to confine neutrons by diffusion in a limited volume of a highly transparent medium for very long times (tens of milliseconds), with correspondingly very long diffusive paths (> 60 m neutron path ÒwoundÓ within a ~ 60 cm effective radius). Assume an empty cavity is introduced inside the previous volume of diffusing medium. The inner walls of the cavity are covered with a thin layer of highly fissionable material, which acts as a neutron multiplying source. This configuration, called Òn-HohlraumÓ, is reminiscent of a classic black-body radiator, with the exception that now neutrons rather than photons are propagated. The flux can be sufficiently enhanced as to permit to reach criticality with a ~ 1 mm thick Americium deposit, corresponding to a mere 1100 atomic layers. Such a layer is so thin that the Fission Fragments (FF) exit freely into the cavity. The energy carried by FF can be recovered directly, thus making use of th...
Kalpakkam multigroup cross section set for fast reactor applications - status and performance
International Nuclear Information System (INIS)
Ramanadhan, M.M.; Gopalakrishnan, M.M.
1986-01-01
This report documents the status of the presently created set of multigroup constants at Kalpakkam. The list of nuclides processed and the details of multigroup structure are given. Also included are the particulars of dilutions and temperatures for each nuclide in the multigroup cross section set for which self shielding factors have been calculated. Using this new multigroup cross section set, measured integral quantities such as K-eff, central reaction rate ratios, central reactivity worths etc. were calculated for a few fast critical benchmark assemblies and the calculated values of neutronic parameters obtained were compared with those obtained using the available Cadarache cross section library and those published in literature for ENDF/B-IV based set and Japanese evaluated nuclear data library (JENDL). The details of analyses are documented along with the conclusions. (author). 17 refs., 12 tabs
Interpretation of active neutron measurements by the heterogeneous theory
International Nuclear Information System (INIS)
Birkhoff, G.; Depraz, J.; Descieux, J.P.
1979-01-01
In this paper are presented results from a study on the application of the heterogeneous method for the interpretation of active neutron measurements. The considered apparatus consists out of a cylindrical lead pile, which is provided with two axial channels: a central channel incorporates an antimony beryllium photoneutron source and an excentric channel serves for the insertion of the sample to be assayed for fissionable materials contents. The mathematical model of this apparatus is the heterogeneous group diffusion theory. Sample and source channel are described by multigroup monopolar and dipolar sources and sinks. Monopolar sources take account of neutron production within energy group and in-scatter from upper groups. Monopolar sinks represent neutron removal by absorption within energy group and outscatter to lower groups. Dipol sources describe radial streaming of neutrons across the sample channel. Multigroup diffusion theory is applied throughout the lead pile. The strengths of the monopolar and dipolar sources and sinks are determined by linear extrapolation distances of azimuthal mean and first harmonic flux values at the channels' surface. In an experiment we may measure the neutrons leaking out of the lead pile and linear extrapolation distances at the channels' surface. Such informations are utilized for interpretation in terms of fission neutron source strengh and mean neutron flux values in the sample. In this paper we summarized the theoretical work in course
POW3D-Neutron diffusion module of the AUS system. A user's manual
International Nuclear Information System (INIS)
Harrington, B.V.; Pollard, J.P.; Barry, J.M.
1996-11-01
POW3D is a three-dimensional neutron diffusion module of the AUS modular neutronics code system. It performs eigenvalue, source of feedback-free kinetics calculations. The module includes general criticality search options and extensive editing facilities including perturbation calculations. Output options include flux or reaction rate plot files. The code permits selection from one of a variety of different solution methods (MINI, ICCG or SLOR) for inner iterations with region re balance to enhance convergence. A MINI accelerated Gauss-Siedel method is used for upscatter iterations with group rebalance to enhance a convergence. Chebyshev source extrapolation is applied for outer iterations. A detailed index is included
International Nuclear Information System (INIS)
Herzig, C.
1995-01-01
For examining the connection between the diffusion systematics and the lattice dynamics of the body-centered cubic metals, the temperature dependence of the self-diffusion (radiotracer technique) and the phonon dispersion (neutron scattering) have been measured in selected systems. In continuation of previous studies, the goal of the examinations reported was to put the earlier developed phonon-related diffusion model on a broader experimental basis, in order to perform verifying analyses. The phonon dispersion of the group 5 metal Nb has been measured up to high temperatures. In contrast to the values measured for the group 4 (β-Zr) and group 6 (Cr) metals, the dispersion in Nb revealed an only very weak temperature dependence. The exceptional case of the bcc β-Tl has been examined by measuring the diffusion and the dispersion in the β-T 83 In 17 alloy. Significant deviations from the conditions in the bcc transition metals have been found. Self-diffusion has been measured for the first time in Ba and β-Sc. Their diffusion systematics correlate with electron configuration. The influence of the d-electron concentration on the diffusion systematics has been measured in Ti-Mo and Hf-Nb alloys, the results backing the predictions of the phonon-related diffusion model. (orig.) [de
Diffusion Parameters of BeO by the Pulsed Neutron Method
International Nuclear Information System (INIS)
Joshi, B.V.; Nargundkar, V.R.; Subbarao, K.
1965-01-01
The use of the pulsed neutron method for the precise determination of the diffusion parameters of moderators is described. The diffusion parameters of BeO have been obtained by this method. The neutron bursts were produced from a cascade accelerator by pulsing the ion source and using the Be (d, n) reaction. The detector was an enriched boron trifluoride proportional counter. It is shown that by a proper choice of the counter position arid length, and the source position, most of the space harmonics can be eliminated. Any constant background can be accounted for in the calculation of the decay constant. Very large bucklings were not used to avoid time harmonics. Any remaining harmonic content was rendered ineffective by the use of adequate time delay. The decay constant of the fundamental mode of the thermal neutron population was determined for several bucklings. Conditions to be satisfied for an accurate determination of the diffusion cooling constant C are discussed. The following values are obtained for BeO: λ 0 = absorption constant = 156.02 ± 4.37 s -1 D = diffusion coefficient = (1.3334 ± 0.0128) x 10 5 cm 2 /s C = diffusion cooling constant = (-4.8758 ± 0.5846) x 10 5 cm 4 /s. The effect of neglecting the contribution of the B 6 term on the determination of the diffusion parameters was estimated and is shown to be considerable. The reason for the longstanding discrepancy between the values of C obtained for the same moderator by different workers is attributed to this. (author) [fr
DEFF Research Database (Denmark)
Bai, M.; Miskowiec, A.; Hansen, F. Y.
2012-01-01
High-energy-resolution quasielastic neutron scattering has been used to elucidate the diffusion of water molecules in proximity to single bilayer lipid membranes supported on a silicon substrate. By varying sample temperature, level of hydration, and deuteration, we identify three different types...... of diffusive water motion: bulk-like, confined, and bound. The motion of bulk-like and confined water molecules is fast compared to those bound to the lipid head groups (7-10 H2O molecules per lipid), which move on the same nanosecond time scale as H atoms within the lipid molecules. Copyright (C) EPLA, 2012...
Asymptotic equivalence of neutron diffusion and transport in time-independent reactor systems
International Nuclear Information System (INIS)
Borysiewicz, M.; Mika, J.; Spiga, G.
1982-01-01
Presented in this paper is the asymptotic analysis of the time-independent neutron transport equation in the second-order variational formulation. The small parameter introduced into the equation is an estimate of the ratio of absorption and leakage to scattering in the system considered. When the ratio tends to zero, the weak solution to the transport problem tends to the weak solution of the diffusion problem, including properly defined boundary conditions. A formula for the diffusion coefficient different from that based on averaging the transport mean-free-path is derived
Derivation of Inter-Atomic Force Constants of Cu2O from Diffuse Neutron Scattering Measurement
Directory of Open Access Journals (Sweden)
T. Makhsun
2013-04-01
Full Text Available Neutron scattering intensity from Cu2O compound has been measured at 10 K and 295 K with High Resolution Powder Diffractometer at JRR-3 JAEA. The oscillatory diffuse scattering related to correlations among thermal displacements of atoms was observed at 295 K. The correlation parameters were determined from the observed diffuse scattering intensity at 10 and 295 K. The force constants between the neighboring atoms in Cu2O were estimated from the correlation parameters and compared to those of Ag2O
Generalization of the Fourier Convergence Analysis in the Neutron Diffusion Eigenvalue Problem
International Nuclear Information System (INIS)
Lee, Hyun Chul; Noh, Jae Man; Joo, Hyung Kook
2005-01-01
Fourier error analysis has been a standard technique for the stability and convergence analysis of linear and nonlinear iterative methods. Lee et al proposed new 2- D/1-D coupling methods and demonstrated several advantages of the new methods by performing a Fourier convergence analysis of the methods as well as two existing methods for a fixed source problem. We demonstrated the Fourier convergence analysis of one of the 2-D/1-D coupling methods applied to a neutron diffusion eigenvalue problem. However, the technique cannot be used directly to analyze the convergence of the other 2-D/1-D coupling methods since some algorithm-specific features were used in our previous study. In this paper we generalized the Fourier convergence analysis technique proposed and analyzed the convergence of the 2-D/1-D coupling methods applied to a neutron diffusion Eigenvalue problem using the generalized technique
Determination of the ion thermal diffusivity from neutron emission profiles in decay
Energy Technology Data Exchange (ETDEWEB)
Sasao, M. (National Inst. for Fusion Science, Nagoya (Japan)); Adams, J.M. (AEA Industrial Technology, Harwell (United Kingdom)); Conroy, S.; Jarvis, O.N.; Marcus, F.B.; Sadler, G.; Belle, P. van (Commission of the European Communities, Abingdon (United Kingdom). JET Joint Undertaking)
1994-01-01
Spatial profiles of the neutron emission from deuterium plasmas are routinely obtained at the Joint European Torus (JET) using the line-integrated signals measured with a multichannel instrument. It is shown that the manner in which these profiles relax following the termination of strong heating with neutral beam injection (NBI) permits the local thermal diffusivity ([chi][sub i]) to be obtained with an accuracy of about 20%. (author).
Determination of the ion thermal diffusivity from neutron emission profiles in decay
International Nuclear Information System (INIS)
Sasao, M.; Adams, J.M.; Conroy, S.; Jarvis, O.N.; Marcus, F.B.; Sadler, G.; Belle, P. van
1994-01-01
Spatial profiles of the neutron emission from deuterium plasmas are routinely obtained at the Joint European Torus (JET) using the line-integrated signals measured with a multichannel instrument. It is shown that the manner in which these profiles relax following the termination of strong heating with neutral beam injection (NBI) permits the local thermal diffusivity (χ i ) to be obtained with an accuracy of about 20%. (author)
DWARF, 1-D Few-Group Neutron Diffusion with Thermal Feedback for Burnup and Xe Oscillation
International Nuclear Information System (INIS)
Anderson, E.C.; Putnam, G.E.
1975-01-01
1 - Description of problem or function: DWARF allows one-dimensional simulation of reactor burnup and xenon oscillation problems in slab, cylindrical, or spherical geometry using a few-group diffusion theory model. 2 - Method of solution: The few-group, neutron diffusion theory equations are reduced to a system of finite-difference equations that are solved for each group by the Gauss method at each time point. Fission neutron source iteration can be accelerated with Chebyshev extrapolation. A thermal feedback iterative loop is used to obtain consistent solutions for the distributions of reactor power, neutron flux, and fuel and coolant properties with the neutron group constants functions of the latter. Solutions for the new nuclide concentrations of a time-point are made with the flux assumed constant in the time interval. 3 - Restrictions on the complexity of the problem - Maxima of: 4 groups; 40 regions; 50 macroscopic materials (Only 10 are functions of the feedback variables); 50 nuclides per region; 250 mesh points
International Nuclear Information System (INIS)
Guerin, P.
2007-12-01
The neutronic simulation of a nuclear reactor core is performed using the neutron transport equation, and leads to an eigenvalue problem in the steady-state case. Among the deterministic resolution methods, diffusion approximation is often used. For this problem, the MINOS solver based on a mixed dual finite element method has shown his efficiency. In order to take advantage of parallel computers, and to reduce the computing time and the local memory requirement, we propose in this dissertation two domain decomposition methods for the resolution of the mixed dual form of the eigenvalue neutron diffusion problem. The first approach is a component mode synthesis method on overlapping sub-domains. Several Eigenmodes solutions of a local problem solved by MINOS on each sub-domain are taken as basis functions used for the resolution of the global problem on the whole domain. The second approach is a modified iterative Schwarz algorithm based on non-overlapping domain decomposition with Robin interface conditions. At each iteration, the problem is solved on each sub domain by MINOS with the interface conditions deduced from the solutions on the adjacent sub-domains at the previous iteration. The iterations allow the simultaneous convergence of the domain decomposition and the eigenvalue problem. We demonstrate the accuracy and the efficiency in parallel of these two methods with numerical results for the diffusion model on realistic 2- and 3-dimensional cores. (author)
A diffuse neutron scattering study of clustering in copper-nickel alloys
International Nuclear Information System (INIS)
Vrijen, J.
1977-01-01
The amount of clustering in Cu-Ni alloys in thermal equilibrium at several temperatures between 400degC and 700degC and ranging in composition between 20 and 80 atomic percent Ni has been determined by means of diffuse neutron scattering. A rough calculation of the excess elastic energy due to alloying Cu with Ni shows that the contribution of size effects to the configurational energy is asymmetric in the composition with its maximum located between 60 and 70 atomic percent Ni. This asymmetry is caused by different elastic constants for Cu and Ni and it might explain part of the asymmetry of clustering in Cu-Ni and its temperature dependence. With the help of the measured cluster parameters, the magnetic diffuse neutron scattering cross-sections of several differently clustered compositions in Cu-Ni could be interpreted, both well inside the ferromagnetic phase and in the transition region between ferromagnetism and superparamagnetism. Giants moments have been observed. Non-equilibrium distributions and their changes during relaxing towards equilibrium have been investigated by measuring the time-evolution of the diffuse scattering. The relaxation of the null matrix (composition without Bragg reflections for neutron scattering) has been measured at five temperatures between 320degC and 450degC. The results of these relaxations were compared with a few available kinetic models
Simulation of a parallel processor on a serial processor: The neutron diffusion equation
International Nuclear Information System (INIS)
Honeck, H.C.
1981-01-01
Parallel processors could provide the nuclear industry with very high computing power at a very moderate cost. Will we be able to make effective use of this power. This paper explores the use of a very simple parallel processor for solving the neutron diffusion equation to predict power distributions in a nuclear reactor. We first describe a simple parallel processor and estimate its theoretical performance based on the current hardware technology. Next, we show how the parallel processor could be used to solve the neutron diffusion equation. We then present the results of some simulations of a parallel processor run on a serial processor and measure some of the expected inefficiencies. Finally we extrapolate the results to estimate how actual design codes would perform. We find that the standard numerical methods for solving the neutron diffusion equation are still applicable when used on a parallel processor. However, some simple modifications to these methods will be necessary if we are to achieve the full power of these new computers. (orig.) [de
Fast diffusion in the intermetallics Ni3Sb and Fe3Si: a neutron scattering study
International Nuclear Information System (INIS)
Randl, O.G.
1994-02-01
We present the results of neutron scattering experiments designed to elucidate the reason for the extraordinarily fast majority component diffusion in two intermetallic alloys of DO 3 structure, Fe 3 Si and Ni 3 Sb: We have performed diffraction measurements in order to determine the crystal structure and the state of order of both alloys as a function of composition and temperature. The results on Fe 3 Si essentially confirm the classical phase diagram: The alloys of a composition between 16 and 25 at % Si are DO 3 -ordered at room temperature and disorder at high temperatures. The high-temperature phase Ni 3 Sb also crystallizes in the DO 3 structure. Vacancies are created in one Ni sublattice at Sb contents beyond 25 at %. In a second step the diffusion mechanism in Ni 3 Sb has been studied by means of quasielastic neutron scattering. The results are reconcileable with a very simple NN jump model between the two different Ni sublattices. Finally, the lattice dynamics of Fe 3 Si and Ni 3 Sb has been studied by inelastic neutron scattering in dependence of temperature (both alloys) and alloy composition (Fe 3 Si only). The results on Fe 3 Si indicate clearly that phonon enhancement is not the main reason for fast diffusion in this alloy. In Ni 3 Sb no typical signs of phonon-enhanced diffusion have been found either. As a conclusion, fast diffusion in DO 3 intermetallics is explained by extraordinarily high vacancy concentrations (several atomic percent) in the majority component sublattices. (author)
CASTRO: A NEW COMPRESSIBLE ASTROPHYSICAL SOLVER. III. MULTIGROUP RADIATION HYDRODYNAMICS
International Nuclear Information System (INIS)
Zhang, W.; Almgren, A.; Bell, J.; Howell, L.; Burrows, A.; Dolence, J.
2013-01-01
We present a formulation for multigroup radiation hydrodynamics that is correct to order O(v/c) using the comoving-frame approach and the flux-limited diffusion approximation. We describe a numerical algorithm for solving the system, implemented in the compressible astrophysics code, CASTRO. CASTRO uses a Eulerian grid with block-structured adaptive mesh refinement based on a nested hierarchy of logically rectangular variable-sized grids with simultaneous refinement in both space and time. In our multigroup radiation solver, the system is split into three parts: one part that couples the radiation and fluid in a hyperbolic subsystem, another part that advects the radiation in frequency space, and a parabolic part that evolves radiation diffusion and source-sink terms. The hyperbolic subsystem and the frequency space advection are solved explicitly with high-order Godunov schemes, whereas the parabolic part is solved implicitly with a first-order backward Euler method. Our multigroup radiation solver works for both neutrino and photon radiation.
International Nuclear Information System (INIS)
Mi Aijun; Li Junjie
2010-01-01
In this paper the multi-group libraries were constructed by processing ENDF/B-VII neutron incident files into multi-group structure, and the application of the multi-group libraries in the pressurized-water reactor(PWR) design was studied. The construction of the multi-group library is realized by using the NJOY nuclear data processing system. The code can process the neutron cross section files form ENDF format to MATXS format which was required in SN code. Two dimension transport theory code of discrete ordinates DORT was used to verify the multi-group libraries and the method of the construction by comparing calculations for some representative benchmarks. We made the PWR shielding calculation by using the multi-group libraries and studied the influence of the parameters involved during the construction of the libraries such as group structure, temperatures and weight functions on the shielding design of the PWR. This work is the preparation for the construction of the multi-group library which will be used in PWR shielding design in engineering. (authors)
International Nuclear Information System (INIS)
Zou Jun; He Zhaozhong; Zeng Qin; Qiu Yuefeng; Wang Minghuang
2010-01-01
A multigroup library HENDL2.1/SS (Hybrid Evaluated Nuclear Data Library/Self-Shielding) based on ENDF/B-VII.0 evaluate data has been generated using Bondarenko and flux calculator method for the correction of self-shielding effect of neutronics analyses. To validate the reliability of the multigroup library HENDL2.1/SS, transport calculations for fusion-fission hybrid system FDS-I were performed in this paper. It was verified that the calculations with the HENDL2.1/SS gave almost the same results with MCNP calculations and were better than calculations with the HENDL2.0/MG which is another multigroup library without self-shielding correction. The test results also showed that neglecting resonance self-shielding caused underestimation of the K eff , neutron fluxes and waste transmutation ratios in the multigroup calculations of FDS-I.
Thermal diffuse scattering in time-of-flight neutron diffraction studied on SBN single crystals
International Nuclear Information System (INIS)
Prokert, F.; Savenko, B.N.; Balagurov, A.M.
1994-01-01
At time-of-flight (TOF) diffractometer D N-2, installed at the pulsed reactor IBR-2 in Dubna, Sr x Ba 1-x Nb 2 O 6 mixed single crystals (SBN-x) of different compositions (0.50 < x< 0.75) were investigated between 15 and 773 K. The diffraction patterns were found to be strongly influenced by the thermal diffuse scattering (TDS). The appearance of the TDS from the long wavelength acoustic models of vibration in single crystals is characterized by the ratio of the velocity of sound to the velocity of neutron. Due to the nature of the TOF Laue diffraction technique used on D N-2, the TDS around Bragg peaks has rather a complex profile. An understanding of the TDS close to Bragg peaks is essential in allowing the extraction of the diffuse scattering occurring at the diffuse ferroelectric phase transition in SBN crystals. 11 refs.; 9 figs.; 1 tab. (author)
A diffuse neutron scattering study of clustering kinetics in Cu-Ni alloys
International Nuclear Information System (INIS)
Vrijen, J.; Radelaar, S.; Schwahn, D.
1977-01-01
Diffuse scattering of thermal neutrons was used to investigate the kinetics of clustering in Cu-Ni alloys. In order to optimize the experimental conditions the isotopes 65 Cu and 62 Ni were alloyed. The time evolution of the diffuse scattered intensity at 400 0 C has been measured for eight Cu-Ni alloys, varying in composition between 30 and 80 at. pour cent Ni. The relaxation of the so called null matrix, containing 56.5 at. pour cent Ni has also been investigated at 320, 340, 425 and 450 0 C. Using Cook's model from all these measurements information has been deduced about diffusion at low temperatures and about thermodynamic properties of the Cu-Ni system. It turns out that Cook's model is not sufficiently detailed for an accurate description of the initial stages of these relaxations
International Nuclear Information System (INIS)
Drozdowicz, K.; Woznicka, U.
1982-01-01
The program in FORTRAN for the ODRA-1305 computer is described. The dependence of the decay constant of the thermal neutron flux upon the dimensions of the two-region concentric cylindrical system is the result of the program. The solution (with a constant neutron flux in the inner medium assumed) is generally obtained in the one-group diffusion approximation by the method of the perturbation calculation. However, the energy distribution of the thermal neutron flux and the diffusion cooling are taken into account. The program is written for the case when the outer medium is hydrogenous. The listing of the program and an example of calculation results are included. (author)
Directory of Open Access Journals (Sweden)
Holmes Jesse
2017-01-01
Full Text Available The neutron scattering properties of water ice are of interest to the nuclear criticality safety community for the transport and storage of nuclear materials in cold environments. The common hexagonal phase ice Ih has locally ordered, but globally disordered, H2O molecular orientations. A 96-molecule supercell is modeled using the VASP ab initio density functional theory code and PHONON lattice dynamics code to calculate the phonon vibrational spectra of H and O in ice Ih. These spectra are supplied to the LEAPR module of the NJOY2012 nuclear data processing code to generate thermal neutron scattering laws for H and O in ice Ih in the incoherent approximation. The predicted vibrational spectra are optimized to be representative of the globally averaged ice Ih structure by comparing theoretically calculated and experimentally measured total cross sections and inelastic neutron scattering spectra. The resulting scattering kernel is then supplied to the MC21 Monte Carlo transport code to calculate time eigenvalues for the fundamental mode decay in ice cylinders at various temperatures. Results are compared to experimental flux decay measurements for a pulsed-neutron die-away diffusion benchmark.
One-velocity neutron diffusion calculations based on a two-group reactor model
Energy Technology Data Exchange (ETDEWEB)
Bingulac, S; Radanovic, L; Lazarevic, B; Matausek, M; Pop-Jordanov, J [Boris Kidric Institute of Nuclear Sciences, Vinca, Belgrade (Yugoslavia)
1965-07-01
Many processes in reactor physics are described by the energy dependent neutron diffusion equations which for many practical purposes can often be reduced to one-dimensional two-group equations. Though such two-group models are satisfactory from the standpoint of accuracy, they require rather extensive computations which are usually iterative and involve the use of digital computers. In many applications, however, and particularly in dynamic analyses, where the studies are performed on analogue computers, it is preferable to avoid iterative calculations. The usual practice in such situations is to resort to one group models, which allow the solution to be expressed analytically. However, the loss in accuracy is rather great particularly when several media of different properties are involved. This paper describes a procedure by which the solution of the two-group neutron diffusion. equations can be expressed analytically in the form which, from the computational standpoint, is as simple as the one-group model, but retains the accuracy of the two-group treatment. In describing the procedure, the case of a multi-region nuclear reactor of cylindrical geometry is treated, but the method applied and the results obtained are of more general application. Another approach in approximate solution of diffusion equations, suggested by Galanin is applicable only in special ideal cases.
Study of accelerated diffusion in gold and aluminium under neutron irradiation
International Nuclear Information System (INIS)
Acker, Denis.
1977-09-01
The speed-up of diffusion under neutron irradiation was studied. The experiments concern the self-diffusion of gold as a function of temperature and the heterodiffusion of copper and gold in aluminium against flux and temperature. In each of these systems the coefficients measured were 10 6 times higher than the expected extra-irradiation values for a flux of 6.10 12 n/cm 2 /s and at a temperature 0.33 Tsub(f), Tsub(f) being the matting point of the matrix expressed in Kelvins. The results obtained can be explained satisfactorily by assuming that, under irradiation: the activation energy of the diffusion coefficient is equal to half the hole migration energy (corrected for the hole-impurity interaction terms in the case of heterodiffusion); the diffusion coefficient under irradiation varies with the square root of the flux; defect wells eliminate interstitials much more efficient by than holes. The first two points agree well with theoretical predictions if the holes and interstitials are assumed to disappear essentially by mutual recombination, whereas the third can be interpreted in terms of a low efficiency of wells for holes and by supposing that the interstitial elimination reaction is limited only by the diffusion rate of these interstitials [fr
Multi-level iteration optimization for diffusive critical calculation
International Nuclear Information System (INIS)
Li Yunzhao; Wu Hongchun; Cao Liangzhi; Zheng Youqi
2013-01-01
In nuclear reactor core neutron diffusion calculation, there are usually at least three levels of iterations, namely the fission source iteration, the multi-group scattering source iteration and the within-group iteration. Unnecessary calculations occur if the inner iterations are converged extremely tight. But the convergence of the outer iteration may be affected if the inner ones are converged insufficiently tight. Thus, a common scheme suit for most of the problems was proposed in this work to automatically find the optimized settings. The basic idea is to optimize the relative error tolerance of the inner iteration based on the corresponding convergence rate of the outer iteration. Numerical results of a typical thermal neutron reactor core problem and a fast neutron reactor core problem demonstrate the effectiveness of this algorithm in the variational nodal method code NODAL with the Gauss-Seidel left preconditioned multi-group GMRES algorithm. The multi-level iteration optimization scheme reduces the number of multi-group and within-group iterations respectively by a factor of about 1-2 and 5-21. (authors)
Performance of a parallel algorithm for solving the neutron diffusion equation on the hypercube
International Nuclear Information System (INIS)
Kirk, B.L.; Azmy, Y.Y.
1989-01-01
The one-group, steady state neutron diffusion equation in two- dimensional Cartesian geometry is solved using the nodal method technique. By decoupling sets of equations representing the neutron current continuity along the length of rows and columns of computational cells a new iterative algorithm is derived that is more suitable to solving large practical problems. This algorithm is highly parallelizable and is implemented on the Intel iPSC/2 hypercube in three versions which differ essentially in the total size of communicated data. Even though speedup was achieved, the efficiency is very low when many processors are used leading to the conclusion that the hypercube is not as well suited for this algorithm as shared memory machines. 10 refs., 1 fig., 3 tabs
Exact and approximate interior corner problem in neutron diffusion by integral transform methods
International Nuclear Information System (INIS)
Bareiss, E.H.; Chang, K.S.J.; Constatinescu, D.A.
1976-09-01
The mathematical solution of the neutron diffusion equation exhibits singularities in its derivatives at material corners. A mathematical treatment of the nature of these singularities and its impact on coarse network approximation methods in computational work is presented. The mathematical behavior is deduced from Green's functions, based on a generalized theory for two space dimensions, and the resulting systems of integral equations, as well as from the Kontorovich--Lebedev Transform. The effect on numerical calculations is demonstrated for finite difference and finite element methods for a two-region corner problem
Energy Technology Data Exchange (ETDEWEB)
Silva, Davi J.M.; Nunes, Carlos E.A.; Alves Filho, Hermes; Barros, Ricardo C., E-mail: davijmsilva@yahoo.com.br, E-mail: ceanunes@yahoo.com.br, E-mail: rcbarros@pq.cnpq.br [Secretaria Municipal de Educacao de Itaborai, RJ (Brazil); Universidade Estacio de Sa (UNESA), Rio de Janeiro, RJ (Brazil); Universidade do Estado do Rio de Janeiro (UERJ), Novra Friburgo, RJ (Brazil). Instituto Politecnico. Departamento de Modelagem Computacional
2017-11-01
Discussed here is the accuracy of approximate albedo boundary conditions for energy multigroup discrete ordinates (S{sub N}) eigenvalue problems in two-dimensional rectangular geometry for criticality calculations in neutron fission reacting systems, such as nuclear reactors. The multigroup (S{sub N}) albedo matrix substitutes approximately the non-multiplying media around the core, e.g., baffle and reflector, as we neglect the transverse leakage terms within these non-multiplying regions. Numerical results to a typical model problem are given to illustrate the accuracy versus the computer running time. (author)
International Nuclear Information System (INIS)
Huang, Mi; Yi, Ce; Manalo, Kevin L.; Sjoden, Glenn E.
2011-01-01
Multigroup optimization is performed on a neutron detector assembly to examine the validity of transport response in forward and adjoint modes. For SN transport simulations, we discuss the multigroup collapse of an 80 group library to 40, 30, and 16 groups, constructed from using the 3-D parallel PENTRAN and macroscopic cross section collapsing with YGROUP contribution weighting. The difference in using P_1 and P_3 Legendre order in scattering cross sections is investigated; also, associated forward and adjoint transport responses are calculated. We conclude that for the block analyzed, a 30 group cross section optimizes both computation time and accuracy relative to the 80 group transport calculations. (author)
DEFF Research Database (Denmark)
Blanchard, Didier; Riktor, M.D.; Maronsson, Jon Bergmann
2010-01-01
Hydrogen dynamics in crystalline calcium borohydride can be initiated by long-range diffusion or localized motion such as rotations, librations, and vibrations. Herein, the rotational and translational diffusion were studied by quasielastic neutron scattering (QENS) by using two instruments...... with different time scales in combination with density functional theory (DFT) calculations. Two thermally activated reorientational motions were observed, around the 2-fold (C2) and 3-fold (C3) axes of the BH4− units, at temperature from 95 to 280K. The experimental energy barriers (EaC2 = 0.14 eV and EaC3 = 0...... of the interstitial H2 might come from the synthesis of the compound or a side reaction with trapped synthesis residue leading to the partial oxidation of the compound and hydrogen release....
Quasi-elastic neutron scattering studies of the diffusion of hydrogen in metals
Energy Technology Data Exchange (ETDEWEB)
Ross, D K [Birmingham Univ. (UK). School of Physics and Space Research
1989-01-01
Quasi-elastic neutron scattering provides a uniquely detailed way of investigating microscopic models for diffusion in lattice gases. In the present paper we discuss extensions of the original Chudley-Elliott model to cover systems containing high concentrations of interacting particles for both the incoherent and coherent cases. In the former case, the peak width is changed by site blocking and by interactions and its shape is altered by correlation effects between successive jumps. In the coherent case, although interactions introduce different correlation effects, the most important changes are due to the short-range order caused by the interactions. A simple Mean Field theory is described which predicts peak narrowing where the diffuse scattering is at a maximum. Experimental tests of both coherent and incoherent theories are described for the case of {alpha}'NbD{sub x}. (orig.).
Quasi-elastic neutron scattering studies of the diffusion of hydrogen in metals
International Nuclear Information System (INIS)
Ross, D.K.
1989-01-01
Quasi-elastic neutron scattering provides a uniquely detailed way of investigating microscopic models for diffusion in lattice gases. In the present paper we discuss extensions of the original Chudley-Elliott model to cover systems containing high concentrations of interacting particles for both the incoherent and coherent cases. In the former case, the peak width is changed by site blocking and by interactions and its shape is altered by correlation effects between successive jumps. In the coherent case, although interactions introduce different correlation effects, the most important changes are due to the short-range order caused by the interactions. A simple Mean Field theory is described which predicts peak narrowing where the diffuse scattering is at a maximum. Experimental tests of both coherent and incoherent theories are described for the case of α'NbD x . (orig.)
A digital data acquisition system for a time of flight neutron diffuse scattering instrument
International Nuclear Information System (INIS)
Venegas, Rafael; Bacza, Lorena; Navarro, Gustavo
1998-01-01
Full text. We describe the design of a digital data acquisition system built for acquiring and storing the information produced by a neutron diffuse scattering apparatus. This instrument is based on the analysis of pulsed subthermal neutron which are scattered by a solid or liquid sample, measured as function of the scattered neutron wavelength and momentum direction. The time of flight neutron intensities on 14 different angular detector positions and two fission chambers must be analyzed simultaneously for each neutron burst. A PC controlled data acquisition board system was built based on two parallel multiscannning units, each with its own add-one counting unit, and a common base time generator. The unit plugs onto the ISA bus through an interface card. Two separate counting units were designed, to avoid possible access competition between low counting rate counters at off-axis positions and the higher rate frontal 0 deg and beam monitoring counters. the first unit contains logic for 14 independent and simultaneous multi scaling inputs, with 128 time channels and dwell time per channel of 5, 10 or 20 microseconds. Sweep trigger is synchronized with an electric signal from a coil sensing the rotor. The second unit contains logic for four additional multi scalers using the same external synchronizing signal, similar in all others details to the previously described multi scalers. Basic control routines for the acquisitions were written in C and a program for spectrum display and user interface was written in C ++ for a Windows 3.1 OS. A block diagram of the system is presented
International Nuclear Information System (INIS)
Kutner, R.; Sosnowska, I.
1977-01-01
A Multi-Sublattice Jump Diffusion Model (MSJD) for hydrogen diffusion through interstitial-site lattices is presented. The MSJD approach may, in principle, be considered as an extension of the Rowe et al (J. Phys. Chem. Solids; 32:41 (1971)) model. Jump diffusion to any neighbours with different jump times which may be asymmetric in space is discussed. On the basis of the model a new method of calculating the diffusion tensor is advanced. The quasielastic, double differential cross section for thermal neutron scattering is obtained in terms of the MSJD model. The model can be used for systems in which interstitial jump diffusion of impurity particles occurs. In Part II the theoretical results are compared with those for quasielastic neutron scattering from the αNbHsub(x) system. (author)
Study of the diffusion movements of water by quasi-elastic scattering of slow neutrons
International Nuclear Information System (INIS)
Yamazaki, Ione Makiko
1980-01-01
The diffusion movements of water at three different temperatures in the liquid state have been studied by slow neutron quasi-elastic scattering. The measurements have been performed using the IPEN Triple Axis Spectrometer. Broadening and integrated intensity of the quasi-elastic line have been determined for several momentum transfer (K) in the range 0,7627 ≤ K ≤ 2,993 A -1 . The broadening of the quasi-elastic peaks as function of momentum transfer (K) observed at various temperatures has been interpreted in terms of globular diffusion models. The results obtained at 30 deg C have been explained in a consistent way considering the translational and rotational globular diffusion movements. To describe the results obtained at 55 deg and 70 deg C only the translational globular diffusion model was sufficient. This analysis indicates the existence in water of globules with distance of the farest proton position to the center of gravity of the globule 4,5 A, corroborating the idea of quasi-crystalline structure for water. The Debye-Waller factor has been obtained through the analysis of the integrated intensity of quasi-elastic scattering peaks over the K 2 measured range. From this analysis an estimative of the mean square displacement was obtained. (author)
International Nuclear Information System (INIS)
Azmy, Y. Y.
2004-01-01
An approach is developed for solving the neutron diffusion equation on combinatorial geometry computational cells, that is computational cells composed by combinatorial operations involving simple-shaped component cells. The only constraint on the component cells from which the combinatorial cells are assembled is that they possess a legitimate discretization of the underlying diffusion equation. We use the Finite Difference (FD) approximation of the x, y-geometry diffusion equation in this work. Performing the same combinatorial operations involved in composing the combinatorial cell on these discrete-variable equations yields equations that employ new discrete variables defined only on the combinatorial cell's volume and faces. The only approximation involved in this process, beyond the truncation error committed in discretizing the diffusion equation over each component cell, is a consistent-order Legendre series expansion. Preliminary results for simple configurations establish the accuracy of the solution to the combinatorial geometry solution compared to straight FD as the system dimensions decrease. Furthermore numerical results validate the consistent Legendre-series expansion order by illustrating the second order accuracy of the combinatorial geometry solution, the same as standard FD. Nevertheless the magnitude of the error for the new approach is larger than FD's since it incorporates the additional truncated series approximation. (authors)
X-ray and neutron diffuse scattering in LiNbO3 from 38 to 1200 K
International Nuclear Information System (INIS)
Zotov, N.; Mayer, H.M.; Guethoff, F.; Hohlwein, D.
1995-01-01
A semi-quantitative description of X-ray and neutron diffuse scattering from congruent lithium niobate, LiNbO 3 , is given. The diffuse scattering is concentrated in three sets of diffuse planes perpendicular to the pseudo-cubic symmetry-related [221], [241] and [ anti 4 anti 21] directions and can be attributed to one-dimensional displacive and chemical disorder along these directions. The variation of the X-ray and neutron diffuse intensities with the scattering vector, as well as the comparison between X-ray and neutron data, indicate that more than one type of atom is involved. Temperature variations are followed from 38 to 1200 K. Different disorder models are discussed. The increase of the integrated intensities of the diffuse lines along the [0 1k 2l] * and [0 anti 1k 4l] * directions (i.e. sections of the diffuse planes) up to 800 K followed by a slight decrease at higher temperatures may be interpreted either by static disorder related to temperature-dependent variation of disorder/defect clusters or by dynamic disorder. Inelastic neutron scattering experiments do not show any anomaly of the transversal acoustic (TA) modes. (orig.)
Conjugate Gradient like methods and their application to fixed source neutron diffusion problems
International Nuclear Information System (INIS)
Suetomi, Eiichi; Sekimoto, Hiroshi
1989-01-01
This paper presents a number of fast iterative methods for solving systems of linear equations appearing in fixed source problems for neutron diffusion. We employed the conjugate gradient and conjugate residual methods. In order to accelerate the conjugate residual method, we proposed the conjugate residual squared method by transforming the residual polynomial of the conjugate residual method. Since the convergence of these methods depends on the spectrum of coefficient matrix, we employed the incomplete Choleski (IC) factorization and the modified IC (MIC) factorization as preconditioners. These methods were applied to some neutron diffusion problems and compared with the successive overrelaxation (SOR) method. The results of these numerical experiments showed superior convergence characteristics of the conjugate gradient like method with MIC factorization to the SOR method, especially for a problem involving void region. The CPU time of the MICCG, MICCR and MICCRS methods showed no great difference. In order to vectorize the conjugate gradient like methods based on (M)IC factorization, the hyperplane method was used and implemented on the vector computers, the HITAC S-820/80 and ETA10-E (one processor mode). Significant decrease of the CPU times was observed on the S-820/80. Since the scaled conjugate gradient (SCG) method can be vectorized with no manipulation, it was also compared with the above methods. It turned out the SCG method was the fastest with respect to the CPU times on the ETA10-E. These results suggest that one should implement suitable algorithm for different vector computers. (author)
Energy Technology Data Exchange (ETDEWEB)
Park, Ho Jin; Cho, Jin Young [KAERI, Daejeon (Korea, Republic of); Kim, Kang Seog [Oak Ridge National Laboratory, Oak Ridge (United States); Hong, Ser Gi [Kyung Hee University, Yongin (Korea, Republic of)
2016-05-15
In this study, multi-group cross section libraries for the DeCART code were generated using a new procedure. The new procedure includes generating the RI tables based on the MC calculations, correcting the effective fission product yield calculations, and considering most of the fission products as resonant nuclides. KAERI (Korea Atomic Energy Research Institute) has developed the transport lattice code KARMA (Kernel Analyzer by Ray-tracing Method for fuel Assembly) and DeCART (Deterministic Core Analysis based on Ray Tracing) for a multi-group neutron transport analysis of light water reactors (LWRs). These codes adopt the method of characteristics (MOC) to solve the multi-group transport equation and resonance fixed source problem, the subgroup and the direct iteration method with resonance integral tables for resonance treatment. With the development of the DeCART and KARMA code, KAERI has established its own library generation system for a multi-group transport calculation. In the KAERI library generation system, the multi-group average cross section and resonance integral (RI) table are generated and edited using PENDF (point-wise ENDF) and GENDF (group-wise ENDF) produced by the NJOY code. The new method does not need additional processing because the MC method can handle any geometry information and material composition. In this study, the new method is applied to the dominant resonance nuclide such as U{sup 235} and U{sup 238} and the conventional method is applied to the minor resonance nuclides. To examine the newly generated multi-group cross section libraries, various benchmark calculations such as pin-cell, FA, and core depletion problem are performed and the results are compared with the reference solutions. Overall, the results by the new method agree well with the reference solution. The new procedure based on the MC method were verified and provided the multi-group library that can be used in the SMR nuclear design analysis.
International Nuclear Information System (INIS)
Kirk, B.L.; Azmy, Y.Y.
1992-01-01
In this paper the one-group, steady-state neutron diffusion equation in two-dimensional Cartesian geometry is solved using the nodal integral method. The discrete variable equations comprise loosely coupled sets of equations representing the nodal balance of neutrons, as well as neutron current continuity along rows or columns of computational cells. An iterative algorithm that is more suitable for solving large problems concurrently is derived based on the decomposition of the spatial domain and is accelerated using successive overrelaxation. This algorithm is very well suited for parallel computers, especially since the spatial domain decomposition occurs naturally, so that the number of iterations required for convergence does not depend on the number of processors participating in the calculation. Implementation of the authors' algorithm on the Intel iPSC/2 hypercube and Sequent Balance 8000 parallel computer is presented, and measured speedup and efficiency for test problems are reported. The results suggest that the efficiency of the hypercube quickly deteriorates when many processors are used, while the Sequent Balance retains very high efficiency for a comparable number of participating processors. This leads to the conjecture that message-passing parallel computers are not as well suited for this algorithm as shared-memory machines
International Nuclear Information System (INIS)
Itagaki, Masafumi; Sahashi, Naoki.
1997-01-01
The multiple reciprocity boundary element method has been applied to three-dimensional two-group neutron diffusion problems. A matrix-type boundary integral equation has been derived to solve the first and the second group neutron diffusion equations simultaneously. The matrix-type fundamental solutions used here satisfy the equation which has a point source term and is adjoint to the neutron diffusion equations. A multiple reciprocity method has been employed to transform the matrix-type domain integral related to the fission source into an equivalent boundary one. The higher order fundamental solutions required for this formulation are composed of a series of two types of analytic functions. The eigenvalue itself is also calculated using only boundary integrals. Three-dimensional test calculations indicate that the present method provides stable and accurate solutions for criticality problems. (author)
Energy Technology Data Exchange (ETDEWEB)
Alvarez Rivas, J L
1963-07-01
The distribution of thermal neutron flux has been measured inside and outside copper rods of several diameters, immersed in water. It has been found that these distributions can be calculated by means of elemental diffusion theory if the value of the coefficient of diffusion is changed. this parameter is truly a diffusion coefficient, which now also depends on the diameter of the rod. Through a model an expression of this coefficient is introduced which takes account of the measurements of the author and of those reported in PUGC P/928 (1995), ANL-5872 (1959), DEGR 319 (D) (1961). This model could be extended also to plane geometry. (Author) 19 refs.
Study by neutron diffusion of magnetic fluctuations in iron in the curie temperature region
International Nuclear Information System (INIS)
Ericson-Galula, M.
1958-12-01
The critical diffusion of neutrons in iron is due to the magnetisation fluctuations which occur in ferromagnetic substances in the neighbourhood of the Curie temperature. The fluctuations can be described in correlation terms; a correlation function γ R vector (t) is defined, γ R vector (t) = 0 vector (0) S R vector (t)> mean value of the scalar product of a reference spin and a spin situated at a distance (R) from the first and considered at the instant t. In chapter I we recall the generalities on neutron diffusion cross-sections; a brief summary is given of the theory of VAN HOVE, who has shown that the magnetic diffusion cross section of neutrons is the Fourier transformation of the correlation function. In chapter Il we study the spatial dependence of the correlation function, assumed to be independent of time. It can then be characterised by two parameters K 1 and r 1 , by means of which the range and intensity of the correlations can be calculated respectively. After setting out the principle of the measurement of these parameters, we shall describe the experimental apparatus. The experimental values obtained are in good agreement with the calculations, and the agreement is better if it is supposed that the second and not the first neighbours of an iron atom are magnetically active, as proposed by Neel. In chapter III we study the evolution with time of the correlation function; this evolution is characterised by a parameter Λ depending on the temperature, which occurs in the diffusion equation obeyed by the magnetisation fluctuations: δM vector /δt = Λ ∇ 2 M vector . The principle of the measurement of Λ is given, after which the modifications carried out on the experimental apparatus mentioned in chapter II are described. The results obtained are then discussed and compared with the theoretical forecasts of De Gennes, mode by using the Heinsenberg model and a simple band model; our values in good agreement with those calculated in the Heisenberg
A Laplace transform method for energy multigroup hybrid discrete ordinates
International Nuclear Information System (INIS)
Segatto, C.F.; Vilhena, M.T.; Barros, R.C.
2010-01-01
In typical lattice cells where a highly absorbing, small fuel element is embedded in the moderator, a large weakly absorbing medium, high-order transport methods become unnecessary. In this work we describe a hybrid discrete ordinates (S N) method for energy multigroup slab lattice calculations. This hybrid S N method combines the convenience of a low-order S N method in the moderator with a high-order S N method in the fuel. The idea is based on the fact that in weakly absorbing media whose physical size is several neutron mean free paths in extent, even the S 2 method (P 1 approximation), leads to an accurate result. We use special fuel-moderator interface conditions and the Laplace transform (LTS N ) analytical numerical method to calculate the two-energy group neutron flux distributions and the thermal disadvantage factor. We present numerical results for a range of typical model problems.
International Nuclear Information System (INIS)
Greene, N.M.; Arwood, J.W.; Wright, R.Q.; Parks, C.V.
1994-08-01
The 238-group LAW Library is a new multigroup neutron cross-section library based on ENDF/B-V data, with five sets of data taken from ENDF/B-VI ( 14 N 7 , 15 N 7 , 16 O 8 , 154Eu 63 , and 155 Eu 63 ). These five nuclides are included because the new evaluations are thought to be superior to those in Version 5. The LAW Library contains data for over 300 materials and will be distributed by the Radiation Shielding Information Center, located at Oak Ridge National Laboratory. It was generated for use in neutronics calculations required in radioactive waste analyses, although it has equal utility in any study requiring multigroup neutron cross sections
International Nuclear Information System (INIS)
Mansur, Ralph S.; Barros, Ricardo C.
2011-01-01
We describe a method to determine the neutron scalar flux in a slab using monoenergetic diffusion model. To achieve this goal we used three ingredients in the computational code that we developed on the Scilab platform: a spectral nodal method that generates numerical solution for the one-speed slab-geometry fixed source diffusion problem with no spatial truncation errors; a spatial reconstruction scheme to yield detailed profile of the coarse-mesh solution; and an angular reconstruction scheme to yield approximately the neutron angular flux profile at a given location of the slab migrating in a given direction. Numerical results are given to illustrate the efficiency of the offered code. (author)
International Nuclear Information System (INIS)
Aufiero, Manuele; Brovchenko, Mariya; Cammi, Antonio; Clifford, Ivor; Geoffroy, Olivier; Heuer, Daniel; Laureau, Axel; Losa, Mario; Luzzi, Lelio; Merle-Lucotte, Elsa; Ricotti, Marco E.; Rouch, Hervé
2014-01-01
Highlights: • Calculation of effective delayed neutron fraction in circulating-fuel reactors. • Extension of the Monte Carlo SERPENT-2 code for delayed neutron precursor tracking. • Forward and adjoint multi-group diffusion eigenvalue problems in OpenFOAM. • Analytical approach for β eff calculation in simple geometries and flow conditions. • Good agreement among the three proposed approaches in the MSFR test-case. - Abstract: This paper deals with the calculation of the effective delayed neutron fraction (β eff ) in circulating-fuel nuclear reactors. The Molten Salt Fast Reactor is adopted as test case for the comparison of the analytical, deterministic and Monte Carlo methods presented. The Monte Carlo code SERPENT-2 has been extended to allow for delayed neutron precursors drift, according to the fuel velocity field. The forward and adjoint eigenvalue multi-group diffusion problems are implemented and solved adopting the multi-physics tool-kit OpenFOAM, by taking into account the convective and turbulent diffusive terms in the precursors balance. These two approaches show good agreement in the whole range of the MSFR operating conditions. An analytical formula for the circulating-to-static conditions β eff correction factor is also derived under simple hypotheses, which explicitly takes into account the spatial dependence of the neutron importance. Its accuracy is assessed against Monte Carlo and deterministic results. The effects of in-core recirculation vortex and turbulent diffusion are finally analysed and discussed
Crystal structure and ion-diffusion pathway of inorganic materials through neutron diffraction
International Nuclear Information System (INIS)
Yashima, Masatomo
2012-01-01
The present brief review describes the application of neutron powder diffractometry and maximum-entropy method to the studies of crystal structure and diffusional pathways of mobile ions in ionic conducting ceramic materials. La 0.62 Li 0.16 TiO 3 and L i0.6 FePO 4 exhibit two- and one-dimensional networks of Li cation diffusional pathways, respectively. In the fluorite-structure ionic conductors such as celia solid solution Ce 0.93 Y 0.07 O 1.96 , bismuth oxide solid solution δ-Bi 1.4 Yb 0.6 O 3 and copper iodide CuI, a similar curved diffusion pathway along the directions is observed. In the cubic ABO 3 perovskite-type ionic conductor, lanthanum gallate solid solution, the mobile ions diffuse along a curved line keeping the interatomic distance between the B cation and O 2- anion. We have experimentally confirmed that the anisotropic thermal motions of the apex O2 atom and the interstitial O3 atoms are essential for the high oxygen permeability of the K 2 NiF 4 -type mixed conductor. Diffusion paths of proton are visualized along c axis in hexagonal hydroxyapatite. (author)
Natural equilibria in steady-state neutron diffusion with temperature feedback
International Nuclear Information System (INIS)
Pounders, J. M.; Ingram, R.
2013-01-01
The critical diffusion equation with feedback is investigated within the context of steady-state multiphysics. It is proposed that for critical configurations there is no need to include the multiplication factor k in the formulation of the diffusion equation. This is notable because exclusion of k from the coupled system of equations precludes the mathematically tenuous notion of a nonlinear eigenvalue problem. On the other hand, it is shown that if the factor k is retained in the diffusion equation, as is currently common practice, then the resulting problem is equivalent to the constrained minimization of a functional representing the critical equilibrium of neutron and temperature distributions. The unconstrained solution corresponding to k = 1 represents the natural equilibrium of a critical system at steady-state. Computational methods for solving the constrained problem (with k) are briefly reviewed from the literature and a method for the unconstrained problem (without k) is outlined. A numerical example is studied to examine the effects of the constraint in the nonlinear system. (authors)
Analysis of diffuse scattering in neutron powder diagrams. Application to glassy carbon
International Nuclear Information System (INIS)
Boysen, H.
1985-01-01
From the quantitative analysis of the diffuse scattered intensity in powder diagrams valuable information about the disorder in crystals may be obtained. According to the dimensionality of this disorder (0D, 1D, 2D or 3D corresponding to diffuse peaks, streaks, planes or volume in reciprocal space) a characteristic modulation of the background is observed, which is described by specific functions. These are derived by averaging the appropriate cross sections over all crystallite orientations in the powder and folding with the resolution function of the instrument. If proper account is taken of all proportionality factors different components of the background can be put on one relative scale. The results are applied to two samples of glassy carbon differing in their degree of disorder. The neutron powder patterns contain contributions from 0D (00l peaks due to the stacking of graphitic layers), 1D (hkzeta streaks caused by the random orientation of these layers) and 3D (incoherent scattering, averaged thermal diffuse scattering, multiple scattering). From the fit to the observed data various parameters of the disorder like domain sizes, strains, interlayer distances, amount of incorporated hydrogen, pore sizes etc. are determined. It is shown that the omission of resolution corrections leads to false parameters. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Descotes, L
1994-05-01
We studied the liquid sulfur according to the temperature. The sulfur is one of the most complicated elementary liquid. We experimented the neutron diffusion by the powder orthorhombic sulfur. The complexity at the polymerization transition are only accompanied by weak local structural transfer. 231 refs., 48 figs., 8 tabs., 3 annexes.
MC^{2}-3: Multigroup Cross Section Generation Code for Fast Reactor Analysis
Energy Technology Data Exchange (ETDEWEB)
Lee, C. H. [Argonne National Lab. (ANL), Argonne, IL (United States); Yang, W. S. [Argonne National Lab. (ANL), Argonne, IL (United States)
2013-11-08
The MC^{2}-3 code is a Multigroup Cross section generation Code for fast reactor analysis, developed by improving the resonance self-shielding and spectrum calculation methods of MC^{2}-2 and integrating the one-dimensional cell calculation capabilities of SDX. The code solves the consistent P1 multigroup transport equation using basic neutron data from ENDF/B data files to determine the fundamental mode spectra for use in generating multigroup neutron cross sections. A homogeneous medium or a heterogeneous slab or cylindrical unit cell problem is solved in ultrafine (~2000) or hyperfine (~400,000) group levels. In the resolved resonance range, pointwise cross sections are reconstructed with Doppler broadening at specified isotopic temperatures. The pointwise cross sections are directly used in the hyperfine group calculation whereas for the ultrafine group calculation, self-shielded cross sections are prepared by numerical integration of the pointwise cross sections based upon the narrow resonance approximation. For both the hyperfine and ultrafine group calculations, unresolved resonances are self-shielded using the analytic resonance integral method. The ultrafine group calculation can also be performed for two-dimensional whole-core problems to generate region-dependent broad-group cross sections. Multigroup cross sections are written in the ISOTXS format for a user-specified group structure. The code is executable on UNIX, Linux, and PC Windows systems, and its library includes all isotopes of the ENDF/BVII. 0 data.
Energy Technology Data Exchange (ETDEWEB)
Jacrot, B [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires
1964-07-01
Inelastic scattering of cold neutrons can be used to study some aspects of magnetism: spins waves, exchange integrals, vicinity of Curie point. After description of the experimental set-up, several experiments, in the fields mentioned above, are analysed. (author) [French] La technique de diffusion inelastique des neutrons froids est utilisee pour etudier certains aspects du magnetisme: ondes de spins, integrales d'echange, etude au voisinage du point de Curie, etc. Apres une description de l'appareillage, on analyse diverses experiences effectuees dans les domaines enumeres plus haut. (auteur)
Applying the response matrix method for solving coupled neutron diffusion and transport problems
International Nuclear Information System (INIS)
Sibiya, G.S.
1980-01-01
The numerical determination of the flux and power distribution in the design of large power reactors is quite a time-consuming procedure if the space under consideration is to be subdivided into very fine weshes. Many computing methods applied in reactor physics (such as the finite-difference method) require considerable computing time. In this thesis it is shown that the response matrix method can be successfully used as an alternative approach to solving the two-dimension diffusion equation. Furthermore it is shown that sufficient accuracy of the method is achieved by assuming a linear space dependence of the neutron currents on the boundaries of the geometries defined for the given space. (orig.) [de
Solution of two group neutron diffusion equation by using homotopy analysis method
International Nuclear Information System (INIS)
Cavdar, S.
2010-01-01
The Homotopy Analysis Method (HAM), proposed in 1992 by Shi Jun Liao and has been developed since then, is based on differential geometry as well as homotopy which is a fundamental concept in topology. It has proved to be useful for obtaining series solutions of many such problems involving algebraic, linear/non-linear, ordinary/partial differential equations, differential-integral equations, differential-difference equations, and coupled equations of them. Briefly, through HAM, it is possible to construct a continuous mapping of an initial guess approximation to the exact solution of the equation of concern. An auxiliary linear operator is chosen to construct such kind of a continuous mapping and an auxiliary parameter is used to ensure the convergence of series solution. We present the solutions of two-group neutron diffusion equation through HAM in this work. We also compare the results with that obtained by other well-known solution analytical and numeric methods.
A numerical study of the eigenvalues in the neutron diffusion theory
International Nuclear Information System (INIS)
Lima Bezerra, J. de.
1982-12-01
A systematic numerical study for the eigenvalue problem in one dimension was carried out. A computer code RED2G was developed to obtain and to discuss a number of numerical solutions concerning eigenvalues problems originating from the discretization of the two groups neutron diffusion equation in one dimension and steady state. The problem of eigenvalues was created from the discretization by the method of finite differences. The solutions were obtained by four different iterative methods, i.e. Power, Wielandt-1, Wielandt-2 and accelerated Power with the Chebyshev polinomials. The numerical results given by the solution of the two test-problems indicate that the RED2G code is fast and efficient in these calculations and the Wielandt-2 method has been found to be the best both in respect of rapidity of calculations as well as programation effort required. (E.G.) [pt
Use of diffusion bonded SS-Al composite material in the development of neutron detectors
International Nuclear Information System (INIS)
Alex, Mary; Prasad, K.R.; Pappachan, A.L.; Grover, A.K.; Krishnan, J.; Derose, D.J.; Bhanumurthy, K.; Kale, G.B.
2005-01-01
The present paper describes the development of a SS-Al composite plate in-house at BARC by diffusion bonding technique. Details of the several tests carried out on the composite material and the use of the plate in the development of a boron lined neutron chamber for Dhruva reactor control instrumentation has been described. The bonded sample has withstood tensile strength test, leak test and thermal cycling test and the leak rate was observed to be less than 3 x 10 -10 stdcc/sec. The chamber with the composite material has been installed in Dhruva Basket C location and connected to the log rate safety channel. It has been working successfully for the past two years. The use of SS-Al composite material has improved the reliability and long-term performance of the detector. (author)
International Nuclear Information System (INIS)
Itagaki, Masafumi; Sahashi, Naoki.
1996-01-01
The multiple reciprocity method (MRM) in conjunction with the boundary element method has been employed to solve one-group eigenvalue problems described by the three-dimensional (3-D) neutron diffusion equation. The domain integral related to the fission source is transformed into a series of boundary-only integrals, with the aid of the higher order fundamental solutions based on the spherical and the modified spherical Bessel functions. Since each degree of the higher order fundamental solutions in the 3-D cases has a singularity of order (1/r), the above series of boundary integrals requires additional terms which do not appear in the 2-D MRM formulation. The critical eigenvalue itself can be also described using only boundary integrals. Test calculations show that Wielandt's spectral shift technique guarantees rapid and stable convergence of 3-D MRM computations. (author)
Determination of the ion thermal diffusivity from neutron emission profiles in decay
International Nuclear Information System (INIS)
Sasao, M.; Adam, J.M.; Conroy, S.; Jarvis, O.N.; Marcus, F.B.; Sadler, G.; Belle, P. van
1992-01-01
Spatial profiles of neutron emission are routinely obtained at the Joint European Torus (JET) from line-integrated emissivities measured with a multi-channel instrument. It is shown that the manner in which the emission profiles relax following termination of strong heating with Neutral Beam Injection (NBI) permits the local thermal diffusivity (χ i ) to be obtained with an accuracy of about 20%. The radial profiles of χ i for small minor radius (r/a 2 /s for H-mode plasmas with plasma current I p = 3.1 MA and toroidal field B T = 2.3T. The experimental value of χ i is smallest for Z eff = 2.2 and increases weakly with increasing Z eff . The experimental results disagree by two orders of magnitude with predictions from an ion temperature gradient driven turbulence model. (author) 6 refs., 3 figs
International Nuclear Information System (INIS)
Cvikl, B.; Dahlborg, U.; Calvo-Dahlborg, M.
1999-01-01
Based upon the model of particles diffusion within the sphere of partially absorbing boundaries, the possibilities of the detection, by the incoherent cold neutron scattering method, of particle precipitation on the boundary walls, has been investigated. The calculated scattering law as a function of the boundary absorption properties exhibits distinct characteristic which might, under favorable conditions, make such an experimental attempt feasible.(author)
A method of precise profile analysis of diffuse scattering for the KENS pulsed neutrons
International Nuclear Information System (INIS)
Todate, Y.; Fukumura, T.; Fukazawa, H.
2001-01-01
An outline of our profile analysis method, which is now of practical use for the asymmetric KENS pulsed thermal neutrons, are presented. The analysis of the diffuse scattering from a single crystal of D 2 O is shown as an example. The pulse shape function is based on the Ikeda-Carpenter function adjusted for the KENS neutron pulses. The convoluted intensity is calculated by a Monte-Carlo method and the precision of the calculation is controlled. Fitting parameters in the model cross section can be determined by the built-in nonlinear least square fitting procedure. Because this method is the natural extension of the procedure conventionally used for the triple-axis data, it is easy to apply with generality and versatility. Most importantly, furthermore, this method has capability of precise correction of the time shift of the observed peak position which is inevitably caused in the case of highly asymmetric pulses and broad scattering function. It will be pointed out that the accurate determination of true time-of-flight is important especially in the single crystal inelastic experiments. (author)
Parareal in time 3D numerical solver for the LWR Benchmark neutron diffusion transient model
Energy Technology Data Exchange (ETDEWEB)
Baudron, Anne-Marie, E-mail: anne-marie.baudron@cea.fr [Laboratoire de Recherche Conventionné MANON, CEA/DEN/DANS/DM2S and UPMC-CNRS/LJLL (France); CEA-DRN/DMT/SERMA, CEN-Saclay, 91191 Gif sur Yvette Cedex (France); Lautard, Jean-Jacques, E-mail: jean-jacques.lautard@cea.fr [Laboratoire de Recherche Conventionné MANON, CEA/DEN/DANS/DM2S and UPMC-CNRS/LJLL (France); CEA-DRN/DMT/SERMA, CEN-Saclay, 91191 Gif sur Yvette Cedex (France); Maday, Yvon, E-mail: maday@ann.jussieu.fr [Sorbonne Universités, UPMC Univ Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions and Institut Universitaire de France, F-75005, Paris (France); Laboratoire de Recherche Conventionné MANON, CEA/DEN/DANS/DM2S and UPMC-CNRS/LJLL (France); Brown Univ, Division of Applied Maths, Providence, RI (United States); Riahi, Mohamed Kamel, E-mail: riahi@cmap.polytechnique.fr [Laboratoire de Recherche Conventionné MANON, CEA/DEN/DANS/DM2S and UPMC-CNRS/LJLL (France); CMAP, Inria-Saclay and X-Ecole Polytechnique, Route de Saclay, 91128 Palaiseau Cedex (France); Salomon, Julien, E-mail: salomon@ceremade.dauphine.fr [CEREMADE, Univ Paris-Dauphine, Pl. du Mal. de Lattre de Tassigny, F-75016, Paris (France)
2014-12-15
In this paper we present a time-parallel algorithm for the 3D neutrons calculation of a transient model in a nuclear reactor core. The neutrons calculation consists in numerically solving the time dependent diffusion approximation equation, which is a simplified transport equation. The numerical resolution is done with finite elements method based on a tetrahedral meshing of the computational domain, representing the reactor core, and time discretization is achieved using a θ-scheme. The transient model presents moving control rods during the time of the reaction. Therefore, cross-sections (piecewise constants) are taken into account by interpolations with respect to the velocity of the control rods. The parallelism across the time is achieved by an adequate use of the parareal in time algorithm to the handled problem. This parallel method is a predictor corrector scheme that iteratively combines the use of two kinds of numerical propagators, one coarse and one fine. Our method is made efficient by means of a coarse solver defined with large time step and fixed position control rods model, while the fine propagator is assumed to be a high order numerical approximation of the full model. The parallel implementation of our method provides a good scalability of the algorithm. Numerical results show the efficiency of the parareal method on large light water reactor transient model corresponding to the Langenbuch–Maurer–Werner benchmark.
International Nuclear Information System (INIS)
Chiba, Gou; Tsuji, Masashi; Shimazu, Yoichiro
2001-01-01
A hierarchical domain decomposition boundary element method (HDD-BEM) that was developed to solve a two-dimensional neutron diffusion equation has been modified to deal with three-dimensional problems. In the HDD-BEM, the domain is decomposed into homogeneous regions. The boundary conditions on the common inner boundaries between decomposed regions and the neutron multiplication factor are initially assumed. With these assumptions, the neutron diffusion equations defined in decomposed homogeneous regions can be solved respectively by applying the boundary element method. This part corresponds to the 'lower level' calculations. At the 'higher level' calculations, the assumed values, the inner boundary conditions and the neutron multiplication factor, are modified so as to satisfy the continuity conditions for the neutron flux and the neutron currents on the inner boundaries. These procedures of the lower and higher levels are executed alternately and iteratively until the continuity conditions are satisfied within a convergence tolerance. With the hierarchical domain decomposition, it is possible to deal with problems composing a large number of regions, something that has been difficult with the conventional BEM. In this paper, it is showed that a three-dimensional problem even with 722 regions can be solved with a fine accuracy and an acceptable computation time. (author)
Diffusion of Hydrogen in the beta-Phase of Pd-H Studied by Small Energy Transfer Neutron Scattering
Energy Technology Data Exchange (ETDEWEB)
Nelin, G; Skoeld, K
1974-07-01
The diffusion of hydrogen in beta-PdH has been studied by quasielastic neutron scattering. It is shown that the diffusion occurs through jumps between adjacent octahedral interstitial sites. The observed integrated quasielastic intensities cannot be described by a simple Debye-Waller factor. The phase transition from the beta-phase to the alpha-phase has also been studied. No dramatic changes in the scattering patterns were observed. It is concluded that the diffusion mechanism is remarkably similar between the low concentration alpha-phase and the high concentration beta-phase
The analytical solution to the 1D diffusion equation in heterogeneous media
International Nuclear Information System (INIS)
Ganapol, B.D.; Nigg, D.W.
2011-01-01
The analytical solution to the time-independent multigroup diffusion equation in heterogeneous plane cylindrical and spherical media is presented. The solution features the simplicity of the one-group formulation while addressing the complication of multigroup diffusion in a fully heterogeneous medium. Beginning with the vector form of the diffusion equation, the approach, based on straightforward mathematics, resolves a set of coupled second order ODEs. The analytical form is facilitated through matrix diagonalization of the neutron interaction matrix rendering the multigroup solution as a series of one-group solutions which, when re-assembled, gives the analytical solution. Customized Eigenmode solutions of the one-group diffusion operator then represent the homogeneous solution in a uniform spatial domain. Once the homogeneous solution is known, the particular solution naturally emerges through variation of parameters. The analytical expression is then numerically implemented through recurrence. Finally, we apply the theory to assess the accuracy of a second order finite difference scheme and to a 1D slab BWR reactor in the four-group approximation. (author)
International Nuclear Information System (INIS)
Lee, Jeong Hun; Park, Tong Kyu; Jeon, Seong Su
2014-01-01
The Rhodium SPND is accurate in steady-state conditions but responds slowly to changes in neutron flux. The slow response time of Rhodium SPND precludes its direct use for control and protection purposes specially when nuclear power plant is used for load following. To shorten the response time of Rhodium SPND, there were some acceleration methods but they could not reflect neutron flux distribution in reactor core. On the other hands, some methods for core power distribution monitoring could not consider the slow response time of Rhodium SPND and noise effect. In this paper, time dependent neutron diffusion equation is directly used to estimate reactor power distribution and extended Kalman filter method is used to correct neutron flux with Rhodium SPND's and to shorten the response time of them. Extended Kalman filter is effective tool to reduce measurement error of Rhodium SPND's and even simple FDM to solve time dependent neutron diffusion equation can be an effective measure. This method reduces random errors of detectors and can follow reactor power level without cross-section change. It means monitoring system may not calculate cross-section at every time steps and computing time will be shorten. To minimize delay of Rhodium SPND's conversion function h should be evaluated in next study. Neutron and Rh-103 reaction has several decay chains and half-lives over 40 seconds causing delay of detection. Time dependent neutron diffusion equation will be combined with decay chains. Power level and distribution change corresponding movement of control rod will be tested with more complicated reference code as well as xenon effect. With these efforts, final result is expected to be used as a powerful monitoring tool of nuclear reactor core
Energy Technology Data Exchange (ETDEWEB)
Lee, Jeong Hun; Park, Tong Kyu; Jeon, Seong Su [FNC Technology Co., Ltd., Yongin (Korea, Republic of)
2014-05-15
The Rhodium SPND is accurate in steady-state conditions but responds slowly to changes in neutron flux. The slow response time of Rhodium SPND precludes its direct use for control and protection purposes specially when nuclear power plant is used for load following. To shorten the response time of Rhodium SPND, there were some acceleration methods but they could not reflect neutron flux distribution in reactor core. On the other hands, some methods for core power distribution monitoring could not consider the slow response time of Rhodium SPND and noise effect. In this paper, time dependent neutron diffusion equation is directly used to estimate reactor power distribution and extended Kalman filter method is used to correct neutron flux with Rhodium SPND's and to shorten the response time of them. Extended Kalman filter is effective tool to reduce measurement error of Rhodium SPND's and even simple FDM to solve time dependent neutron diffusion equation can be an effective measure. This method reduces random errors of detectors and can follow reactor power level without cross-section change. It means monitoring system may not calculate cross-section at every time steps and computing time will be shorten. To minimize delay of Rhodium SPND's conversion function h should be evaluated in next study. Neutron and Rh-103 reaction has several decay chains and half-lives over 40 seconds causing delay of detection. Time dependent neutron diffusion equation will be combined with decay chains. Power level and distribution change corresponding movement of control rod will be tested with more complicated reference code as well as xenon effect. With these efforts, final result is expected to be used as a powerful monitoring tool of nuclear reactor core.
A New Method for Predicting the Penetration and Slowing-Down of Neutrons in Reactor Shields
International Nuclear Information System (INIS)
Hjaerne, L.; Leimdoerfer, M.
1965-05-01
A new approach is presented in the formulation of removal-diffusion theory. The 'removal cross-section' is redefined and the slowing-down between the multigroup diffusion equations is treated with a complete energy transfer matrix rather than in an age theory approximation. The method, based on the new approach contains an adjustable parameter. Examples of neutron spectra and thermal flux penetrations are given in a number of differing shield configurations and the results compare favorably with experiments and Moments Method calculations
A New Method for Predicting the Penetration and Slowing-Down of Neutrons in Reactor Shields
Energy Technology Data Exchange (ETDEWEB)
Hjaerne, L; Leimdoerfer, M
1965-05-15
A new approach is presented in the formulation of removal-diffusion theory. The 'removal cross-section' is redefined and the slowing-down between the multigroup diffusion equations is treated with a complete energy transfer matrix rather than in an age theory approximation. The method, based on the new approach contains an adjustable parameter. Examples of neutron spectra and thermal flux penetrations are given in a number of differing shield configurations and the results compare favorably with experiments and Moments Method calculations.
International Nuclear Information System (INIS)
Tayloe, R.W. Jr.; Brown, A.S.; Dobelbower, M.C.; Woollard, J.E.
1997-03-01
Neutron-sensitive radiation detectors are used in the Portsmouth Gaseous Diffusion Plant's (PORTS) criticality accident alarm system (CAAS). The CAAS is composed of numerous detectors, electronics, and logic units. It uses a telemetry system to sound building evacuation horns and to provide remote alarm status in a central control facility. The ANSI Standard for a CAAS uses a free-in-air dose rate to define the detection criteria for a minimum accident-of-concern. Previously, the free-in-air absorbed dose rate from neutrons was used for determining the areal coverge of criticality detection within PORTS buildings handling fissile materials. However, the free-in-air dose rate does not accurately reflect the response of the neutron detectors in use at PORTS. Because the cost of placing additional CAAS detectors in areas of questionable coverage (based on a free-in-air absorbed dose rate) is high, the actual response function for the CAAS neutron detectors was determined. This report, which is organized into three major sections, discusses how the actual response function for the PORTS CAAS neutron detectors was determined. The CAAS neutron detectors are described in Section 2. The model of the detector system developed to facilitate calculation of the response function is discussed in Section 3. The results of the calculations, including confirmatory measurements with neutron sources, are given in Section 4
Water diffusion through compacted clays analyzed by neutron scattering and tracer experiments
International Nuclear Information System (INIS)
Gonzalez Sanchez, F.
2007-11-01
/cm 3 , in order to reduce the pore sizes and to better study the dynamic properties of water close to the water-clay interface. We compared the water dynamics in fully hydrated compacted clays, at two significantly different time-space scales, in an attempt to distinguish the relevant features of the water transport. A fundamental microscopic investigation, tracing down to the atomic level was carried out, by neutron scattering, using time-of-flight and backscattering techniques. A classical macroscopic study was performed by using tracer through-diffusion methods. At the macroscopic level (time/spatial scale of about hours/mm to cm) the water diffusion depends strongly on the clay pore size and arrangement of the particles. However, at the microscopic level (time/spatial scale of about ten to hundred picosecond/10 -8 cm) the diffusion is governed by the local environment, which concerns to cations and clay surfaces and less to the particle arrangement. For a further understanding of this local environment, the water diffusion in clays was also measured at different hydration states, to vary the fraction of interlayer or external layer water, as compared to free pore water. The large difference in the diffusion paths of the two selected techniques makes a direct comparison of water diffusivities impossible. Therefore, two possibilities were established: An indirect comparison by connecting the results for diffusion coefficient at the two different scales through pure geometrical and electrostatic factors; and a direct comparison through the activation energy E a which was estimated from the dependence of the diffusion coefficients on the temperature. In contrast to the macroscopic diffusion coefficients, the activation energy is probably less influenced by geometrical factors and more by microscopic interactions, and thus could possibly be directly compared at the two different scales. The research was accomplished by a detailed characterization of the clay samples
Water diffusion through compacted clays analyzed by neutron scattering and tracer experiments
Energy Technology Data Exchange (ETDEWEB)
Gonzalez Sanchez, F
2007-11-15
/cm{sup 3}, in order to reduce the pore sizes and to better study the dynamic properties of water close to the water-clay interface. We compared the water dynamics in fully hydrated compacted clays, at two significantly different time-space scales, in an attempt to distinguish the relevant features of the water transport. A fundamental microscopic investigation, tracing down to the atomic level was carried out, by neutron scattering, using time-of-flight and backscattering techniques. A classical macroscopic study was performed by using tracer through-diffusion methods. At the macroscopic level (time/spatial scale of about hours/mm to cm) the water diffusion depends strongly on the clay pore size and arrangement of the particles. However, at the microscopic level (time/spatial scale of about ten to hundred picosecond/10{sup -8} cm) the diffusion is governed by the local environment, which concerns to cations and clay surfaces and less to the particle arrangement. For a further understanding of this local environment, the water diffusion in clays was also measured at different hydration states, to vary the fraction of interlayer or external layer water, as compared to free pore water. The large difference in the diffusion paths of the two selected techniques makes a direct comparison of water diffusivities impossible. Therefore, two possibilities were established: An indirect comparison by connecting the results for diffusion coefficient at the two different scales through pure geometrical and electrostatic factors; and a direct comparison through the activation energy E{sub a} which was estimated from the dependence of the diffusion coefficients on the temperature. In contrast to the macroscopic diffusion coefficients, the activation energy is probably less influenced by geometrical factors and more by microscopic interactions, and thus could possibly be directly compared at the two different scales. The research was accomplished by a detailed characterization of the clay
Verification and validation of multi-group library MUSE1.0 created from ENDF/B-VII.0
International Nuclear Information System (INIS)
Chen Yixue; Wu Jun; Yang Shouhai; Zhang Bin; Lu Daogang; Chen Chaobin
2010-01-01
A multi-group library set named MUSE1.0 with 172-neutron group and 42-photon group is produced based on ENDF/B-VII.0 using NJOY code. Weight function of the multi-group library set is taken from the Vitanim-e library and the max legendre order of scattering matrix is six. All the nuclides have thermal scattering data created using free-gas scattering law and 10 Bondarenko background cross sections se lected to generate the self-shielded multi-group cross sections. The final libraries have GENDF-format, MATXS-format and ACE-multi-group sub-libraries and each sub-library generated under 4 temperatures(293 K,600 K,800 K and 900 K). This paper provides a summary of the procedure to produce the library set and a detail description of the validation of the multi-group library set by several critical benchmark devices and shielding benchmark devices using MCNP code. The ability to handle the thermal neutron transport and resonance self-shielding problems are investigated specially. In the end, we draw the conclusion that the multi-group libraries produced is credible and can be used in the R and D process of Supercritical Water Reactor Design. (authors)
A code system to generate multigroup cross-sections using basic data
International Nuclear Information System (INIS)
Garg, S.B.; Kumar, Ashok
1978-01-01
For the neutronic studies of nuclear reactors, multigroup cross-sections derived from the basic energy point data are needed. In order to carry out the design based studies, these cross-sections should also incorporate the temperature and fuel concentration effects. To meet these requirements, a code system comprising of RESRES, UNRES, FIGERO, INSCAT, FUNMO, AVER1 and BGPONE codes has been adopted. The function of each of these codes is discussed. (author)
Survey of computer codes which produce multigroup data from ENDF/B-IV
International Nuclear Information System (INIS)
Greene, N.M.
1975-01-01
The features of three code systems that produce multigroup neutron data are contrasted. This includes the ETOE-2/MC 2 -2/SDX, MINX/SPHINX and AMPX code packages. These systems all contain a fairly extensive set of processing capabilities with the current evaluated nuclear data files--ENDF/B. They were designed with different goals and applications in mind. This paper discusses some of their differences and the implications for particular situations
Multigroup P8 - elastic scattering matrices of main reactor elements
International Nuclear Information System (INIS)
Garg, S.B.; Shukla, V.K.
1979-01-01
To study the effect of anisotropic scattering phenomenon on shielding and neutronics of nuclear reactors multigroup P8-elastic scattering matrices have been generated for H, D, He, 6 Li, 7 Li, 10 B, C, N, O, Na, Cr, Fe, Ni, 233 U, 235 U, 238 U, 239 Pu, 240 Pu, 241 Pu and 242 Pu using their angular distribution, Legendre coefficient and elastic scattering cross-section data from the basic ENDF/B library. Two computer codes HSCAT and TRANS have been developed to complete this task for BESM-6 and CDC-3600 computers. These scattering matrices can be directly used as input to the transport theory codes ANISN and DOT. (auth.)
TVEDIM, 2-D Homogeneous and Inhomogeneous Neutron Diffusion for X-Y, R-Z, R-Theta Geometry
International Nuclear Information System (INIS)
Kristiansen, G.K.
1987-01-01
1 - Nature of physical problem solved: The two-dimensional neutron diffusion equation (x-y, r-z, or r-theta geometry is solved, either in the inhomogeneous (source calculation) or the homogeneous form (K eff calculation or absorber adjustment). The boundary conditions specify each group current as a linear homogeneous function of the group fluxes (gamma matrix concept). For each material, the fission matrix is assumed to by dyadic. 2 - Method of solution: Finite difference formulation (5 point scheme, mesh corner variant) is used. Solution technique: multi-line SOR. Eigenvalue estimate by neutron balance
Fast resolution of the neutron diffusion equation through public domain Ode codes
Energy Technology Data Exchange (ETDEWEB)
Garcia, V.M.; Vidal, V.; Garayoa, J. [Universidad Politecnica de Valencia, Departamento de Sistemas Informaticos, Valencia (Spain); Verdu, G. [Universidad Politecnica de Valencia, Departamento de Ingenieria Quimica y Nuclear, Valencia (Spain); Gomez, R. [I.E.S. de Tavernes Blanques, Valencia (Spain)
2003-07-01
The time-dependent neutron diffusion equation is a partial differential equation with source terms. The resolution method usually includes discretizing the spatial domain, obtaining a large system of linear, stiff ordinary differential equations (ODEs), whose resolution is computationally very expensive. Some standard techniques use a fixed time step to solve the ODE system. This can result in errors (if the time step is too large) or in long computing times (if the time step is too little). To speed up the resolution method, two well-known public domain codes have been selected: DASPK and FCVODE that are powerful codes for the resolution of large systems of stiff ODEs. These codes can estimate the error after each time step, and, depending on this estimation can decide which is the new time step and, possibly, which is the integration method to be used in the next step. With these mechanisms, it is possible to keep the overall error below the chosen tolerances, and, when the system behaves smoothly, to take large time steps increasing the execution speed. In this paper we address the use of the public domain codes DASPK and FCVODE for the resolution of the time-dependent neutron diffusion equation. The efficiency of these codes depends largely on the preconditioning of the big systems of linear equations that must be solved. Several pre-conditioners have been programmed and tested; it was found that the multigrid method is the best of the pre-conditioners tested. Also, it has been found that DASPK has performed better than FCVODE, being more robust for our problem.We can conclude that the use of specialized codes for solving large systems of ODEs can reduce drastically the computational work needed for the solution; and combining them with appropriate pre-conditioners, the reduction can be still more important. It has other crucial advantages, since it allows the user to specify the allowed error, which cannot be done in fixed step implementations; this, of course
Energy Technology Data Exchange (ETDEWEB)
Calloo, A.; Vidal, J.F.; Le Tellier, R.; Rimpault, G., E-mail: ansar.calloo@cea.fr, E-mail: jean-francois.vidal@cea.fr, E-mail: romain.le-tellier@cea.fr, E-mail: gerald.rimpault@cea.fr [CEA, DEN, DER/SPRC/LEPh, Saint-Paul-lez-Durance (France)
2011-07-01
This paper deals with the solving of the multigroup integro-differential form of the transport equation for fine energy group structure. In that case, multigroup transfer cross sections display strongly peaked shape for light scatterers and the current Legendre polynomial expansion is not well-suited to represent them. Furthermore, even if considering an exact scattering cross sections representation, the scattering source in the discrete ordinates method (also known as the Sn method) being calculated by sampling the angular flux at given directions, may be wrongly computed due to lack of angular support for the angular flux. Hence, following the work of Gerts and Matthews, an angular finite volume solver has been developed for 2D Cartesian geometries. It integrates the multigroup transport equation over discrete volume elements obtained by meshing the unit sphere with a product grid over the polar and azimuthal coordinates and by considering the integrated flux per solid angle element. The convergence of this method has been compared to the S{sub n} method for a highly anisotropic benchmark. Besides, piecewise-average scattering cross sections have been produced for non-bound Hydrogen atoms using a free gas model for thermal neutrons. LWR lattice calculations comparing Legendre representations of the Hydrogen scattering multigroup cross section at various orders and piecewise-average cross sections for this same atom are carried out (while keeping a Legendre representation for all other isotopes). (author)
International Nuclear Information System (INIS)
Calloo, A.; Vidal, J.F.; Le Tellier, R.; Rimpault, G.
2011-01-01
This paper deals with the solving of the multigroup integro-differential form of the transport equation for fine energy group structure. In that case, multigroup transfer cross sections display strongly peaked shape for light scatterers and the current Legendre polynomial expansion is not well-suited to represent them. Furthermore, even if considering an exact scattering cross sections representation, the scattering source in the discrete ordinates method (also known as the Sn method) being calculated by sampling the angular flux at given directions, may be wrongly computed due to lack of angular support for the angular flux. Hence, following the work of Gerts and Matthews, an angular finite volume solver has been developed for 2D Cartesian geometries. It integrates the multigroup transport equation over discrete volume elements obtained by meshing the unit sphere with a product grid over the polar and azimuthal coordinates and by considering the integrated flux per solid angle element. The convergence of this method has been compared to the S_n method for a highly anisotropic benchmark. Besides, piecewise-average scattering cross sections have been produced for non-bound Hydrogen atoms using a free gas model for thermal neutrons. LWR lattice calculations comparing Legendre representations of the Hydrogen scattering multigroup cross section at various orders and piecewise-average cross sections for this same atom are carried out (while keeping a Legendre representation for all other isotopes). (author)
Energy Technology Data Exchange (ETDEWEB)
Chiang, Min-Han; Wang, Jui-Yu [Institute of Nuclear Engineering and Science, National Tsing Hua University, 101, Section 2, Kung-Fu Road, Hsinchu 30013, Taiwan (China); Sheu, Rong-Jiun, E-mail: rjsheu@mx.nthu.edu.tw [Institute of Nuclear Engineering and Science, National Tsing Hua University, 101, Section 2, Kung-Fu Road, Hsinchu 30013, Taiwan (China); Department of Engineering System and Science, National Tsing Hua University, 101, Section 2, Kung-Fu Road, Hsinchu 30013, Taiwan (China); Liu, Yen-Wan Hsueh [Institute of Nuclear Engineering and Science, National Tsing Hua University, 101, Section 2, Kung-Fu Road, Hsinchu 30013, Taiwan (China); Department of Engineering System and Science, National Tsing Hua University, 101, Section 2, Kung-Fu Road, Hsinchu 30013, Taiwan (China)
2014-05-01
The High Temperature Engineering Test Reactor (HTTR) in Japan is a helium-cooled graphite-moderated reactor designed and operated for the future development of high-temperature gas-cooled reactors. Two detailed full-core models of HTTR have been established by using SCALE6 and MCNP5/X, respectively, to study its neutronic properties. Several benchmark problems were repeated first to validate the calculation models. Careful code-to-code comparisons were made to ensure that two calculation models are both correct and equivalent. Compared with experimental data, the two models show a consistent bias of approximately 20–30 mk overestimation in effective multiplication factor for a wide range of core states. Most of the bias could be related to the ENDF/B-VII.0 cross-section library or incomplete modeling of impurities in graphite. After that, a series of systematic analyses was performed to investigate the effects of cross sections on the HTTR criticality and burnup calculations, with special interest in the comparison between continuous-energy and multigroup results. Multigroup calculations in this study were carried out in 238-group structure and adopted the SCALE double-heterogeneity treatment for resonance self-shielding. The results show that multigroup calculations tend to underestimate the system eigenvalue by a constant amount of ∼5 mk compared to their continuous-energy counterparts. Further sensitivity studies suggest the differences between multigroup and continuous-energy results appear to be temperature independent and also insensitive to burnup effects.
International Nuclear Information System (INIS)
Chiang, Min-Han; Wang, Jui-Yu; Sheu, Rong-Jiun; Liu, Yen-Wan Hsueh
2014-01-01
The High Temperature Engineering Test Reactor (HTTR) in Japan is a helium-cooled graphite-moderated reactor designed and operated for the future development of high-temperature gas-cooled reactors. Two detailed full-core models of HTTR have been established by using SCALE6 and MCNP5/X, respectively, to study its neutronic properties. Several benchmark problems were repeated first to validate the calculation models. Careful code-to-code comparisons were made to ensure that two calculation models are both correct and equivalent. Compared with experimental data, the two models show a consistent bias of approximately 20–30 mk overestimation in effective multiplication factor for a wide range of core states. Most of the bias could be related to the ENDF/B-VII.0 cross-section library or incomplete modeling of impurities in graphite. After that, a series of systematic analyses was performed to investigate the effects of cross sections on the HTTR criticality and burnup calculations, with special interest in the comparison between continuous-energy and multigroup results. Multigroup calculations in this study were carried out in 238-group structure and adopted the SCALE double-heterogeneity treatment for resonance self-shielding. The results show that multigroup calculations tend to underestimate the system eigenvalue by a constant amount of ∼5 mk compared to their continuous-energy counterparts. Further sensitivity studies suggest the differences between multigroup and continuous-energy results appear to be temperature independent and also insensitive to burnup effects
International Nuclear Information System (INIS)
Valdes Parra, J.J.
1986-01-01
One of the main problems in reactor physics is to determine the neutron distribution in reactor core, since knowing that, it is possible to calculate the rapidity of occurrence of different nuclear reaction inside the reactor core. Within different theories existing in nuclear reactor physics, is neutron transport the one in which equation who govern the exact behavior of neutronic distribution are developed even inside the proper neutron transport theory, there exist different methods of solution which are approximations to exact solution; still more, with the purpose to reach a more precise solution, the majority of methods have been approached to the obtention of solutions in numerical form with the aim of take the advantages of modern computers, and for this reason a great deal of effort is dedicated to numerical solution of the equations of neutron transport. In agreement with the above mentioned, in this work has been developed a computer program which uses a relatively new techniques known as 'acceleration of synthetic diffusion' which has been applied to solve the neutron transport equation with 'classical schemes of spatial integration' obtaining results with a smaller quantity of interactions, if they compare to done without using such equation (Author)
International Nuclear Information System (INIS)
Ozgener, B.; Azgener, H.A.
1991-01-01
In finite element formulations for the solution of the within-group neutron diffusion equation, two different treatments are possible for the group source term: the consistent source approximation (CSA) and the lumped source approximation (LSA). CSA results in intra-group scattering and fission matrices which have the same nondiagonal structure as the global coefficient matrix. This situation might be regarded as a disadvantage, compared to the conventional (i.e. finite difference) methods where the intra-group scattering and fission matrices are diagonal. To overcome this disadvantage, LSA could be used to diagonalize these matrices. LSA is akin to the lumped mass approximation of continuum mechanics. We concentrate on two different aspects of the source approximations. Although it has been reported that LSA does not modify the asymptotic h 2 convergence behaviour for linear elements, the effect of LSA on convergence of higher degree elements has not been investigated. Thus, we would be interested in determining, p, the asymptotic order of convergence, in: Δk |k eff (analytical) -k eff (finite element)| = Ch p (1) for finite element approximations of varying degree (N) with both of the source approximations. Since (1) is valid in the asymptotic limit, we must use ultra-fine meshes and quadruple precision arithmetic. For our order of convergence study, we used infinite cylindrical geometry with azimuthal symmetry. Hence, the effects of singularities remain uninvestigated. The second aspect we dwell on is the performance of LSA in bilinear 3-D finite element calculations, compared to CSA. LSA has been used quite extensively in 1- and 2-D even-parity transport and diffusion calculations. In this work, we will try to assess the relative merits of LSA and CSA in 3-D problems. (author)
CARMEN-SYSTEM, Programs System for Thermal Neutron Diffusion and Burnup with Feedback
International Nuclear Information System (INIS)
Ahnert, Carol; Aragones, Jose M.
1983-01-01
1 - Description of problem or function: CARMEN is a system of programs developed for the neutronic calculation of PWR cycles. It includes the whole chain of analysis from cell calculations to core calculations with burnup. The core calculations are based on diffusion theory with cross sections depending on the relevant space-dependent feedback effects which are present at each moment along the cycles. The diffusion calculations are in one, two or three dimensions and in two energy groups. The feedback effects which are treated locally are: burnup, water density, power density and fission products. In order to study in detail these parameters the core should be divided into as many zones as different cross section sets are expected to be required in order to reproduce reality correctly. A relevant difference in any feedback parameter between zones produces different cross section sets for the corresponding zones. CARMEN is also capable to perform the following calculations: - Multiplication factor by burnup step with fixed boron concentration - Buckling and control rod insertion - Buckling search by burnup step - Boron search by burnup step - Control rod insertion search by burnup step. 2 - Method of solution: The cell code (LEOPARD-TRACA) generates the fuel assembly cross sections versus burnup. This is the basic library to be used in the CARMEN code proper. With a planar distribution guess for power density, water density and fluxes, the macroscopic cross sections by zone are calculated by CARMEN, and then a diffusion calculation is done in the whole geometry. With the distribution of power density, heat accumulated in the coolant and the thermal and fast fluxes determined in the diffusion calculation, CARMEN calculates the values of the most relevant parameters that influence the macroscopic cross sections by zone: burnup, water density, effective fuel temperature and fission product concentrations. If these parameters by zone are different from the reference
International Nuclear Information System (INIS)
Kubaschewski, O.
1983-01-01
The diffusion rate values of titanium, its compounds and alloys are summarized and tabulated. The individual chemical diffusion coefficients and self-diffusion coefficients of certain isotopes are given. Experimental methods are listed which were used for the determination of diffusion coefficients. Some values have been taken over from other studies. Also given are graphs showing the temperature dependences of diffusion and changes in the diffusion coefficient with concentration changes
Energy Technology Data Exchange (ETDEWEB)
Guerin, P
2007-12-15
The neutronic simulation of a nuclear reactor core is performed using the neutron transport equation, and leads to an eigenvalue problem in the steady-state case. Among the deterministic resolution methods, diffusion approximation is often used. For this problem, the MINOS solver based on a mixed dual finite element method has shown his efficiency. In order to take advantage of parallel computers, and to reduce the computing time and the local memory requirement, we propose in this dissertation two domain decomposition methods for the resolution of the mixed dual form of the eigenvalue neutron diffusion problem. The first approach is a component mode synthesis method on overlapping sub-domains. Several Eigenmodes solutions of a local problem solved by MINOS on each sub-domain are taken as basis functions used for the resolution of the global problem on the whole domain. The second approach is a modified iterative Schwarz algorithm based on non-overlapping domain decomposition with Robin interface conditions. At each iteration, the problem is solved on each sub domain by MINOS with the interface conditions deduced from the solutions on the adjacent sub-domains at the previous iteration. The iterations allow the simultaneous convergence of the domain decomposition and the eigenvalue problem. We demonstrate the accuracy and the efficiency in parallel of these two methods with numerical results for the diffusion model on realistic 2- and 3-dimensional cores. (author)
International Nuclear Information System (INIS)
Najera H, M.C.; Benitez R, J.S.
2003-01-01
The results of a comparative study are presented of: to) A denominated diffuse controller 'exact', designed by means of an innovative method that determines analytically so much the group of exit resultant in the aggregation stage like the de fuzzy process, and b) a diffuse controller denominated 'discreet' based on the discretization of the variable of having left as much for the aggregation as for the de fuzzy. These stages incorporated to the control algorithms whose objective is the ascent and regulation of the neutron power, carrying out an analysis of its performance. (Author)
Energy Technology Data Exchange (ETDEWEB)
Millot, J P [Commissariat a l' Energie Atomique, Fontenay-aux-Roses (France). Centre d' Etudes Nucleaires
1962-07-01
We propose a method for calculating the biological efficiency of fast neutrons emitted by in-pile fission sources. This method justifies the empirical theory of Albert and Welton. In making simple assumptions concerning the cross-sections, we have supposed that the propagation can ben reduced to a mono-kinetic problem. A system of orthonormal functions is then set up making it possible to calculate the flux leaving a planar source. This method generalises the results obtained by Platzek to the case where the elastic cross-sections are not isotropic, and make it possible in particular to define a displacement cross-section: extension of the diffusion coefficient. This method can be generalised to the case of neutron diffraction as a function of time, and to the study of slowing-down. Numerical results are given in an appendix for the following: H{sub 2}O, D{sub 2}O, Fe, Be, Pb, CH, CH{sub 2}. These cross-sections have been verified experimentally in water and in graphite for neutrons of 2.5 and 14 MeV using a SAMES accelerator and a 2 MeV Van De Graaff. (author) [French] Nous proposons une methode permettant de calculer l'efficacite biologique des neutrons rapides issus des sources de fission dans la protection d'une pile. Cette methode justifie la theorie empirique d'Albert et Welton. En faisant des hypotheses simples sur les sections efficaces, nous avons suppose que la propagation pouvait etre ramenee a un probleme monocinetique. Nous construisons alors un systeme de fonctions orthonormales qui permet de calculer le flux issu d'une source plane. Cette methode generalise les resultats obtenus par Platzek au cas ou les sections efficaces elastiques ne sont pas isotropes et en particulier permet de definir une section efficace de deplacement: extension du coefficient de diffusion. Cette methode peut etre generalisee a la diffusion des neutrons en fonction du temps et a l'etude du ralentissement. Les resultats numeriques sont donnes en annexe pour les corps. H{sub 2
Iterative Two- and One-Dimensional Methods for Three-Dimensional Neutron Diffusion Calculations
International Nuclear Information System (INIS)
Lee, Hyun Chul; Lee, Deokjung; Downar, Thomas J.
2005-01-01
Two methods are proposed for solving the three-dimensional neutron diffusion equation by iterating between solutions of the two-dimensional (2-D) radial and one-dimensional (1-D) axial solutions. In the first method, the 2-D/1-D equations are coupled using a current correction factor (CCF) with the average fluxes of the lower and upper planes and the axial net currents at the plane interfaces. In the second method, an analytic expression for the axial net currents at the interface of the planes is used for planar coupling. A comparison of the new methods is made with two previously proposed methods, which use interface net currents and partial currents for planar coupling. A Fourier convergence analysis of the four methods was performed, and results indicate that the two new methods have at least three advantages over the previous methods. First, the new methods are unconditionally stable, whereas the net current method diverges for small axial mesh size. Second, the new methods provide better convergence performance than the other methods in the range of practical mesh sizes. Third, the spectral radii of the new methods asymptotically approach zero as the mesh size increases, while the spectral radius of the partial current method approaches a nonzero value as the mesh size increases. Of the two new methods proposed here, the analytic method provides a smaller spectral radius than the CCF method, but the CCF method has several advantages over the analytic method in practical applications
Boundary element methods applied to two-dimensional neutron diffusion problems
International Nuclear Information System (INIS)
Itagaki, Masafumi
1985-01-01
The Boundary element method (BEM) has been applied to two-dimensional neutron diffusion problems. The boundary integral equation and its discretized form have been derived. Some numerical techniques have been developed, which can be applied to critical and fixed-source problems including multi-region ones. Two types of test programs have been developed according to whether the 'zero-determinant search' or the 'source iteration' technique is adopted for criticality search. Both programs require only the fluxes and currents on boundaries as the unknown variables. The former allows a reduction in computing time and memory in comparison with the finite element method (FEM). The latter is not always efficient in terms of computing time due to the domain integral related to the inhomogeneous source term; however, this domain integral can be replaced by the equivalent boundary integral for a region with a non-multiplying medium or with a uniform source, resulting in a significant reduction in computing time. The BEM, as well as the FEM, is well suited for solving irregular geometrical problems for which the finite difference method (FDM) is unsuited. The BEM also solves problems with infinite domains, which cannot be solved by the ordinary FEM and FDM. Some simple test calculations are made to compare the BEM with the FEM and FDM, and discussions are made concerning the relative merits of the BEM and problems requiring future solution. (author)
Coarse-grain parallel solution of few-group neutron diffusion equations
International Nuclear Information System (INIS)
Sarsour, H.N.; Turinsky, P.J.
1991-01-01
The authors present a parallel numerical algorithm for the solution of the finite difference representation of the few-group neutron diffusion equations. The targeted architectures are multiprocessor computers with shared memory like the Cray Y-MP and the IBM 3090/VF, where coarse granularity is important for minimizing overhead. Most of the work done in the past, which attempts to exploit concurrence, has concentrated on the inner iterations of the standard outer-inner iterative strategy. This produces very fine granularity. To coarsen granularity, the authors introduce parallelism at the nested outer-inner level. The problem's spatial domain was partitioned into contiguous subregions and assigned a processor to solve for each subregion independent of all other subregions, hence, processors; i.e., each subregion is treated as a reactor core with imposed boundary conditions. Since those boundary conditions on interior surfaces, referred to as internal boundary conditions (IBCs), are not known, a third iterative level, the recomposition iterations, is introduced to communicate results between subregions
Nodal integral method for the neutron diffusion equation in cylindrical geometry
International Nuclear Information System (INIS)
Azmy, Y.Y.
1987-01-01
The nodal methodology is based on retaining a higher a higher degree of analyticity in the process of deriving the discrete-variable equations compared to conventional numerical methods. As a result, extensive numerical testing of nodal methods developed for a wide variety of partial differential equations and comparison of the results to conventional methods have established the superior accuracy of nodal methods on coarse meshes. Moreover, these tests have shown that nodal methods are more computationally efficient than finite difference and finite-element methods in the sense that they require shorter CPU times to achieve comparable accuracy in the solutions. However, nodal formalisms and the final discrete-variable equations they produce are, in general, more complicated than their conventional counterparts. This, together with anticipated difficulties in applying the transverse-averaging procedure in curvilinear coordinates, has limited the applications of nodal methods, so far, to Cartesian geometry, and with additional approximations to hexagonal geometry. In this paper the authors report recent progress in deriving and numerically implementing a nodal integral method (NIM) for solving the neutron diffusion equation in cylindrical r-z geometry. Also, presented are comparisons of numerical solutions to two test problems with those obtained by the Exterminator-2 code, which indicate the superior accuracy of the nodal integral method solutions on much coarser meshes
International Nuclear Information System (INIS)
Priem, Thierry
1988-01-01
Short-range order in non-stoichiometric transition metal carbides and nitrides (TiN 0.82 , TiC 0.64 , TiC 0.76 , NbC 0.73 and NbC 0.83 ) was investigated by thermal neutron diffuse scattering on G4-4 (L.L.B - Saclay) and D10 (I.L.L. Grenoble) spectrometers. From experimental measurements, we have found that metalloid vacancies (carbon or nitrogen) prefer the f.c.c. third neighbour positions. Ordering interaction energies were calculated within the Ising model framework by three approximations: mean field (Clapp and Moss formula), Monte-Carlo simulation, Cluster variation Method. The energies obtained by the two latter methods are very close, and in qualitative agreement with theoretical values calculated from the band structure. Theoretical phase diagrams were calculated from these ordering energies for TiN x and TiC x ; three ordered structures were predicted, corresponding to compositions Ti 6 N 5 Ti 2 C and Ti 3 C 2 . On the other hand, atomic displacements are induced by vacancies. The metal first neighbours were found to move away from a vacancy, whereas the second neighbours move close to it. Near neighbour atomic displacements were theoretically determined by the lattice statics formalism with results in good agreement with experiment. (author) [fr
Determination of the ion thermal diffusivity from neutron emission profiles in decay
Energy Technology Data Exchange (ETDEWEB)
Sasao, M. (National Inst. for Fusion Science, Nagoya (Japan)); Adam, J.M. (AEA Industrial Technology, Harwell (United Kingdom)); Conroy, S.; Jarvis, O.N.; Marcus, F.B.; Sadler, G.; Belle, P. van (Commission of the European Communities, Abingdon (United Kingdom). JET Joint Undertaking)
1992-01-01
Spatial profiles of neutron emission are routinely obtained at the Joint European Torus (JET) from line-integrated emissivities measured with a multi-channel instrument. It is shown that the manner in which the emission profiles relax following termination of strong heating with Neutral Beam Injection (NBI) permits the local thermal diffusivity ([chi][sub i]) to be obtained with an accuracy of about 20%. The radial profiles of [chi][sub i] for small minor radius (r/a < 0.6) were found to be flat and to take values between 0.3 and 1.1 m[sup 2]/s for H-mode plasmas with plasma current I[sub p] = 3.1 MA and toroidal field B[sub T] = 2.3T. The experimental value of [chi][sub i] is smallest for Z[sub eff] = 2.2 and increases weakly with increasing Z[sub eff]. The experimental results disagree by two orders of magnitude with predictions from an ion temperature gradient driven turbulence model. (author) 6 refs., 3 figs.
International Nuclear Information System (INIS)
Ceolin, C.; Schramm, M.; Bodmann, B.E.J.; Vilhena, M.T.
2015-01-01
Recently the stationary neutron diffusion equation in heterogeneous rectangular geometry was solved by the expansion of the scalar fluxes in polynomials in terms of the spatial variables (x; y), considering the two-group energy model. The focus of the present discussion consists in the study of an error analysis of the aforementioned solution. More specifically we show how the spatial subdomain segmentation is related to the degree of the polynomial and the Lipschitz constant. This relation allows to solve the 2-D neutron diffusion problem for second degree polynomials in each subdomain. This solution is exact at the knots where the Lipschitz cone is centered. Moreover, the solution has an analytical representation in each subdomain with supremum and infimum functions that shows the convergence of the solution. We illustrate the analysis with a selection of numerical case studies. (author)
Energy Technology Data Exchange (ETDEWEB)
Ceolin, C., E-mail: celina.ceolin@gmail.com [Universidade Federal de Santa Maria (UFSM), Frederico Westphalen, RS (Brazil). Centro de Educacao Superior Norte; Schramm, M.; Bodmann, B.E.J.; Vilhena, M.T., E-mail: celina.ceolin@gmail.com [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Programa de Pos-Graduacao em Engenharia Mecanica
2015-07-01
Recently the stationary neutron diffusion equation in heterogeneous rectangular geometry was solved by the expansion of the scalar fluxes in polynomials in terms of the spatial variables (x; y), considering the two-group energy model. The focus of the present discussion consists in the study of an error analysis of the aforementioned solution. More specifically we show how the spatial subdomain segmentation is related to the degree of the polynomial and the Lipschitz constant. This relation allows to solve the 2-D neutron diffusion problem for second degree polynomials in each subdomain. This solution is exact at the knots where the Lipschitz cone is centered. Moreover, the solution has an analytical representation in each subdomain with supremum and infimum functions that shows the convergence of the solution. We illustrate the analysis with a selection of numerical case studies. (author)
International Nuclear Information System (INIS)
Bernal, A.; Roman, J.E.; Miró, R.; Verdú, G.
2016-01-01
Highlights: • A method is proposed to solve the eigenvalue problem of the Neutron Diffusion Equation in BWR. • The Neutron Diffusion Equation is discretized with the Finite Volume Method. • The currents are calculated by using a polynomial expansion of the neutron flux. • The current continuity and boundary conditions are defined implicitly to reduce the size of the matrices. • Different structured and unstructured meshes were used to discretize the BWR. - Abstract: The neutron flux spatial distribution in Boiling Water Reactors (BWRs) can be calculated by means of the Neutron Diffusion Equation (NDE), which is a space- and time-dependent differential equation. In steady state conditions, the time derivative terms are zero and this equation is rewritten as an eigenvalue problem. In addition, the spatial partial derivatives terms are transformed into algebraic terms by discretizing the geometry and using numerical methods. As regards the geometrical discretization, BWRs are complex systems containing different components of different geometries and materials, but they are usually modelled as parallelepiped nodes each one containing only one homogenized material to simplify the solution of the NDE. There are several techniques to correct the homogenization in the node, but the most commonly used in BWRs is that based on Assembly Discontinuity Factors (ADFs). As regards numerical methods, the Finite Volume Method (FVM) is feasible and suitable to be applied to the NDE. In this paper, a FVM based on a polynomial expansion method has been used to obtain the matrices of the eigenvalue problem, assuring the accomplishment of the ADFs for a BWR. This eigenvalue problem has been solved by means of the SLEPc library.
WIMSD5, Deterministic Multigroup Reactor Lattice Calculations
International Nuclear Information System (INIS)
2004-01-01
1 - Description of program or function: The Winfrith improved multigroup scheme (WIMS) is a general code for reactor lattice cell calculation on a wide range of reactor systems. In particular, the code will accept rod or plate fuel geometries in either regular arrays or in clusters and the energy group structure has been chosen primarily for thermal calculations. The basic library has been compiled with 14 fast groups, 13 resonance groups and 42 thermal groups, but the user is offered the choice of accurate solutions in many groups or rapid calculations in few groups. Temperature dependent thermal scattering matrices for a variety of scattering laws are included in the library for the principal moderators which include hydrogen, deuterium, graphite, beryllium and oxygen. WIMSD5 is a successor version of WIMS-D/4. 2 - Method of solution: The treatment of resonances is based on the use of equivalence theorems with a library of accurately evaluated resonance integrals for equivalent homogeneous systems at a variety of temperatures. The collision theory procedure gives accurate spectrum computations in the 69 groups of the library for the principal regions of the lattice using a simplified geometric representation of complicated lattice cells. The computed spectra are then used for the condensation of cross-sections to the number of groups selected for solution of the transport equation in detailed geometry. Solution of the transport equation is provided either by use of the Carlson DSN method or by collision probability methods. Leakage calculations including an allowance for streaming asymmetries may be made using either diffusion theory or the more elaborate B1-method. The output of the code provides Eigenvalues for the cases where a simple buckling mode is applicable or cell-averaged parameters for use in overall reactor calculations. Various reaction rate edits are provided for direct comparison with experimental measurements. 3 - Restrictions on the complexity of
3-D Deep Penetration Neutron Imaging of Thick Absorgin and Diffusive Objects Using Transport Theory
Energy Technology Data Exchange (ETDEWEB)
Ragusa, Jean; Bangerth, Wolfgang
2011-08-01
here explores the inverse problem of optical tomography applied to heterogeneous domains. The neutral particle transport equation was used as the forward model for how neutral particles stream through and interact within these heterogeneous domains. A constrained optimization technique that uses Newtons method served as the basis of the inverse problem. Optical tomography aims at reconstructing the material properties using (a) illuminating sources and (b) detector readings. However, accurate simulations for radiation transport require that the particle (gamma and/or neutron) energy be appropriate discretize in the multigroup approximation. This, in turns, yields optical tomography problems where the number of unknowns grows (1) about quadratically with respect to the number of energy groups, G, (notably to reconstruct the scattering matrix) and (2) linearly with respect to the number of unknown material regions. As pointed out, a promising approach could rely on algorithms to appropriately select a material type per material zone rather than G2 values. This approach, though promising, still requires further investigation: (a) when switching from cross-section values unknowns to material type indices (discrete integer unknowns), integer programming techniques are needed since derivative information is no longer available; and (b) the issue of selecting the initial material zoning remains. The work reported here proposes an approach to solve the latter item, whereby a material zoning is proposed using one-group or few-groups transport approximations. The capabilities and limitations of the presented method were explored; they are briefly summarized next and later described in fuller details in the Appendices. The major factors that influenced the ability of the optimization method to reconstruct the cross sections of these domains included the locations of the sources used to illuminate the domains, the number of separate experiments used in the reconstruction, the
Energy Technology Data Exchange (ETDEWEB)
Duerigen, Susan
2013-05-15
The superior advantage of a nodal method for reactor cores with hexagonal fuel assemblies discretized as cells consisting of equilateral triangles is its mesh refinement capability. In this thesis, a diffusion and a simplified P{sub 3} (or SP{sub 3}) neutron transport nodal method are developed based on trigonal geometry. Both models are implemented in the reactor dynamics code DYN3D. As yet, no other well-established nodal core analysis code comprises an SP{sub 3} transport theory model based on trigonal meshes. The development of two methods based on different neutron transport approximations but using identical underlying spatial trigonal discretization allows a profound comparative analysis of both methods with regard to their mathematical derivations, nodal expansion approaches, solution procedures, and their physical performance. The developed nodal approaches can be regarded as a hybrid NEM/AFEN form. They are based on the transverse-integration procedure, which renders them computationally efficient, and they use a combination of polynomial and exponential functions to represent the neutron flux moments of the SP{sub 3} and diffusion equations, which guarantees high accuracy. The SP{sub 3} equations are derived in within-group form thus being of diffusion type. On this basis, the conventional diffusion solver structure can be retained also for the solution of the SP{sub 3} transport problem. The verification analysis provides proof of the methodological reliability of both trigonal DYN3D models. By means of diverse hexagonal academic benchmark and realistic detailed-geometry full-transport-theory problems, the superiority of the SP{sub 3} transport over the diffusion model is demonstrated in cases with pronounced anisotropy effects, which is, e.g., highly relevant to the modeling of fuel assemblies comprising absorber material.
International Nuclear Information System (INIS)
Fanaro, L.C.C.B.
1984-01-01
It was developed the BLINDAGE computer code for the radiation transport (neutrons and gammas) calculation. The code uses the removal - diffusion method for neutron transport and point-kernel technique with buil-up factors for gamma-rays. The results obtained through BLINDAGE code are compared with those obtained with the ANISN and SABINE computer codes. (Author) [pt
Neutron kinetics of fluid-fuel systems by the quasi-static method
International Nuclear Information System (INIS)
Dulla, S.; Ravetto, P.; Rostagno, M.M.
2004-01-01
The quasi-static method for the neutron kinetics of nuclear reactors is generalized for application to neutron multiplying systems fueled by a fluid multiplying material, typically a mixture of fissile molten salts. The method is derived by the application of factorization formulae for both the neutron density and the delayed precursor concentrations and the projection of the balance equations upon a weighting function. A physically meaningful weight can be assumed as the solution of the adjoint model, which is constructed for the situation considered, including delayed neutrons. The quasi-static scheme is then applied to calculations of some transients for a typical configuration of a molten-salt reactor, in a multigroup diffusion model with a one-dimensional slug-flow velocity field. The physical features associated to the motion of the fissile material are highlighted
International Nuclear Information System (INIS)
Alonso-Vargas, G.
1991-01-01
A computer program has been developed which uses a technique of synthetic acceleration by diffusion by analytical schemes. Both in the diffusion equation as in that of transport, analytical schemes were used which allowed a substantial time saving in the number of iterations required by source iteration method to obtain the K e ff. The program developed ASD (Synthetic Diffusion Acceleration) by diffusion was written in FORTRAN and can be executed on a personal computer with a hard disc and mathematical O-processor. The program is unlimited as to the number of regions and energy groups. The results obtained by the ASD program for K e ff is nearly completely concordant with those of obtained utilizing the ANISN-PC code for different analytical type problems in this work. The ASD program allowed obtention of an approximate solution of the neutron transport equation with a relatively low number of internal reiterations with good precision. One of its applications would be in the direct determinations of axial distribution neutronic flow in a fuel assembly as well as in the obtention of the effective multiplication factor. (Author)
International Nuclear Information System (INIS)
Gastaldi, B.
1986-07-01
This study intends to improve then to check on integral experiments, the calculation of the main neutronic parameters in light water moderated lattices: Uranium 238 capture and consequently Plutonium 239 build-up, multiplication factor, temperature coefficient. The first part of this work concerns the resonant reaction rate calculation method implemented in the APOLLO code, the so-called LIVOLANT and JEANPIERRE formalism. The errors introduced by the corresponding assumptions are quantified and we propose substitution methods which avoid large biases and supply satisfactory results. The second part is dedicated to the cross-section evaluation of uranium major isotopes and to the achievement of APOLLO multigroup cross-sections. This cross-section set takes into considerations on the one hand the recent differential information and the other hand the various integral information obtained in the French Atomic Energy Commission facilities. The nuclear data file (JEF abd ENDF/B5) processing, for multigroup and self-shielded cross-sections achieving enable us to check the new THEMIS computer code. In the last part, the experimental validation of the proposed procedure (accurate formalism mutuel shielding and new multigroup library) is presented. This qualification is based on the reinterpretation of critical experiments performed in the EOLE reactor at Cadarache and spent fuel analysis. The corresponding results demonstrate that our propositions provide improvements on the computation of the PWR neutronic parameters; calculation-experiment discrepancies are now consistent with experimental uncertainty margins. 46 refs; 31 figs; 23 tabl [fr
Two-dimensional finite element neutron diffusion analysis using hierarchic shape functions
International Nuclear Information System (INIS)
Carpenter, D.C.
1997-01-01
Recent advances have been made in the use of p-type finite element method (FEM) for structural and fluid dynamics problems that hold promise for reactor physics problems. These advances include using hierarchic shape functions, element-by-element iterative solvers and more powerful mapping techniques. Use of the hierarchic shape functions allows greater flexibility and efficiency in implementing energy-dependent flux expansions and incorporating localized refinement of the solution space. The irregular matrices generated by the p-type FEM can be solved efficiently using element-by-element conjugate gradient iterative solvers. These solvers do not require storage of either the global or local stiffness matrices and can be highly vectorized. Mapping techniques based on blending function interpolation allow exact representation of curved boundaries using coarse element grids. These features were implemented in a developmental two-dimensional neutron diffusion program based on the use of hierarchic shape functions (FEM2DH). Several aspects in the effective use of p-type analysis were explored. Two choices of elemental preconditioning were examined--the proper selection of the polynomial shape functions and the proper number of functions to use. Of the five shape function polynomials tested, the integral Legendre functions were the most effective. The serendipity set of functions is preferable over the full tensor product set. Two global preconditioners were also examined--simple diagonal and incomplete Cholesky. The full effectiveness of the finite element methodology was demonstrated on a two-region, two-group cylindrical problem but solved in the x-y coordinate space, using a non-structured element grid. The exact, analytic eigenvalue solution was achieved with FEM2DH using various combinations of element grids and flux expansions
Vectorized and multitasked solution of the few-group neutron diffusion equations
International Nuclear Information System (INIS)
Zee, S.K.; Turinsky, P.J.; Shayer, Z.
1989-01-01
A numerical algorithm with parallelism was used to solve the two-group, multidimensional neutron diffusion equations on computers characterized by shared memory, vector pipeline, and multi-CPU architecture features. Specifically, solutions were obtained on the Cray X/MP-48, the IBM-3090 with vector facilities, and the FPS-164. The material-centered mesh finite difference method approximation and outer-inner iteration method were employed. Parallelism was introduced in the inner iterations using the cyclic line successive overrelaxation iterative method and solving in parallel across lines. The outer iterations were completed using the Chebyshev semi-iterative method that allows parallelism to be introduced in both space and energy groups. For the three-dimensional model, power, soluble boron, and transient fission product feedbacks were included. Concentrating on the pressurized water reactor (PWR), the thermal-hydraulic calculation of moderator density assumed single-phase flow and a closed flow channel, allowing parallelism to be introduced in the solution across the radial plane. Using a pinwise detail, quarter-core model of a typical PWR in cycle 1, for the two-dimensional model without feedback the measured million floating point operations per second (MFLOPS)/vector speedups were 83/11.7. 18/2.2, and 2.4/5.6 on the Cray, IBM, and FPS without multitasking, respectively. Lower performance was observed with a coarser mesh, i.e., shorter vector length, due to vector pipeline start-up. For an 18 x 18 x 30 (x-y-z) three-dimensional model with feedback of the same core, MFLOPS/vector speedups of --61/6.7 and an execution time of 0.8 CPU seconds on the Cray without multitasking were measured. Finally, using two CPUs and the vector pipelines of the Cray, a multitasking efficiency of 81% was noted for the three-dimensional model
Energy Technology Data Exchange (ETDEWEB)
Raievski, V; Horowitz, J [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires
1955-07-01
The further method is the outcome of a technique used in the study of neutrons in scattering and slowing-down environment. In this technique, we replace the constant sources used in the classic experiences by modulated sources with a variable frequency. The object of this article is to describe the extension of the method for the mean free path for transport of thermal neutrons and also to indicate the possible applications for other sizes, as the slowing length, or the absolute value of the cross-section of the boron. (M.B.) [French] La methode qui va etre decrite est l'aboutissement d'une technique utilisee dans l'etude des milieux ou diffusent et se ralentissent des neutrons. Dans cette technique, on remplace les sources constantes utilisees dans les experiences classiques par des sources modulees, a frequence variable. L'objet de cet article est de decrire l'extension de la methode a la mesure du libre parcours moyen de transport des neutrons thermiques et egalement d'indiquer les applications possibles a la mesure d'autres grandeurs, telles que la longueur de ralentissement, ou la valeur absolue de la section de capture du bore. (M.B.)
Multigroup perturbation model for kinetic analysis of nuclear reactors
International Nuclear Information System (INIS)
Souza, G.M.
1989-01-01
The scope of this work is the development of a multigroup perturbation theory for the purpose of Kinetic and dynamic analysis of nuclear reactors. The equations that describe the reactor behavior were presented in all generality and written in the shorthand notation of matrices and vectors. In the derivation of those equations indetermined operators and discretizing factors were introduced and then determined by comparision with conventional equations. Fick's Law was developed in higher orders for neutron and importance current density. The solution of the direct and adjoint fields were represented by combination of the eigenfunctions of the B and B* operators and the eigenvalue modulus equality was established mathematically. In the derivation of the reactivity expression the B operator perturbation was split in two non coupled to the flux form and level. The prompt neutrons effective mean life was derived from reactor equations and importance conservation. The establishment of the Nordheim's equation, although modified, was based on Gandini. Finally, a mathematical interpretation of the flux-trap region was avented. (author)
International Nuclear Information System (INIS)
Correia Filho, A.
1981-04-01
The Neutron Diffusion Equation at two groups of energy is solved with the use of the Finite - Element Method with first order triangular elements. The program EFTDN (Triangular Finite Elements on Neutron Diffusion) was developed using the language FORTRAN IV. The discrete formulation of the Diffusion Equation is obtained with the application of the Galerkin's Method. In order to solve the eigenvalue - problem, the Method of the Power is applied and, with the purpose of the convergence of the results, Chebshev's polynomial expressions are applied. On the solution of the systems of equations Gauss' Method is applied, divided in two different parts: triangularization of the matrix of coeficients and retrosubstitution taking in account the sparsity of the system. Several test - problems are solved, among then two P.W.R. type reactors, the ZION-1 with 1300 MWe and the 2D-IAEA - Benchmark. Comparision of results with standard solutions show the validity of application of the EFM and precision of the results. (Author) [pt
International Nuclear Information System (INIS)
Zee, S.K.
1987-01-01
A numeric algorithm and an associated computer code were developed for the rapid solution of the finite-difference method representation of the few-group neutron-diffusion equations on parallel computers. Applications of the numeric algorithm on both SIMD (vector pipeline) and MIMD/SIMD (multi-CUP/vector pipeline) architectures were explored. The algorithm was successfully implemented in the two-group, 3-D neutron diffusion computer code named DIFPAR3D (DIFfusion PARallel 3-Dimension). Numerical-solution techniques used in the code include the Chebyshev polynomial acceleration technique in conjunction with the power method of outer iteration. For inner iterations, a parallel form of red-black (cyclic) line SOR with automated determination of group dependent relaxation factors and iteration numbers required to achieve specified inner iteration error tolerance is incorporated. The code employs a macroscopic depletion model with trace capability for selected fission products' transients and critical boron. In addition to this, moderator and fuel temperature feedback models are also incorporated into the DIFPAR3D code, for realistic simulation of power reactor cores. The physics models used were proven acceptable in separate benchmarking studies
Energy Technology Data Exchange (ETDEWEB)
Harris, D; Cocking, S J; Egelstaff, P A; Webb, F J [Nuclear Physics Division, Aere, Harwell, Didcot, Berks (United Kingdom)
1963-01-15
A narrow band of neutron wavelengths (4 A and greater) is selected from a collimated neutron beam obtained from the Dido reactor at Harwell. These neutrqps are scattered by various samples and the energy transfer of the scattered neutrons measured using time-of-flight techniques. The neutrons, moderated by a liquid hydrogen source in the reactor pass through first a liquid nitrogen- cooled filter, then a single crystal of bismuth and finally they are ''chopped'' by a magnesium-cadmium high- speed curved slot rotor. In this apparatus the wavelength spread of 0. 3 A at 4 . 1 A is determined primarily by the Be-Bi filter, while the time spread (8 {mu}s) is determined by the rotor. The monochromated neutron bursts from this rotor are scattered by a sample and detected in one of two counter arrays. When studying liquid or polycrystalline samples an array of six BF{sub 3}, counter assemblies (each 2 inches x 24 inches in area)are used covering scatter angles from 20{sup o} to 90{sup o}. This array is placed below the neutron beam. Above the line of the neutron beam is a second array consisting of three scintillators 2 inches in diameter, which is used for the study of single crystal samples. The output of each counter is fed into a tape recording system which has 500 time channels available for each counter. This apparatus has been used to study neutron scattering from several gaseous, liquid and crystalline samples and the most recent measurements are presented in other papers in these proceedings. [French] Les auteurs extraient une bande etroite de neutrons ( 4 A et plus) d'un faisceau collimate de neutrons produits par le reacteur Dido de Harwell. On fait diffuser ces neutrons au moyen de divers echantillons et on mesure le transfert d'energie des neutrons diffuses par la methode du temps de vol. Les neutrons ralentis par de l'hydrogene liquide place dans le reacteur passent d'abord dans un filtre refroidi a l'azote liquide, puis dans un monocristal de bismuth
International Nuclear Information System (INIS)
Costa, Danilo Leite
2013-01-01
This work aims to present a study about the power distribution behavior in a PWR type reactor, considering both intensity and migration of power peaks due to insertion of control rods into the core. Employing the multidimensional steady-state neutron diffusion equation in order to simulate the neutron flux, and using the Finite Difference Method. Furthermore, based on the axial power distribution on the largest heat flux rod, is carried out thermal analysis of this rod and associated coolant channel. For this purpose is employed the FueLRod 3 D code, it uses the Finite Element Method to model the fuel rod and the associated coolant channel, allowing the thermohydraulics simulation of a single rod discretized in three dimensions, considering the heat flux from the pellet, crossing the gap and the cladding until it reaches the coolant. (author)
Energy Technology Data Exchange (ETDEWEB)
Golikov, V V; Shapiro, F L; Shkatula, A; Yanik, E A [Ob' edinennyj institut yadernykh issledovanij, Dubna, Union of Soviet Socialist Republics (Russian Federation)
1963-01-15
Using the pulsed fut reactor in the Joint Institute for Nuclear Research, an installation was set up to investigate the spectrometry of cold neutrons. The moderator, adjoining the reactor reflector, and the beryllium filter were at the temperature of liquid nitrogen. The scatterer, located at a distance of about 0. 6 m from the moderator, was irradiated by flashes of cold neutrons, whose duration was determined by the lifetime of the neutrons in the moderator and the dispersion of the times-of-flight over a distance of 0. 6 m. The frequency of the flashes was 8/s. The steep beryllium edge of the spectrum, lying around 200 {mu}s, was used for spectrometry in the quasi-elastic range. The energy of the scattered neutrons was determined by the time-of-flight over the distance between scatterer and detector, which was about 10-40 m. ZnS + 10{sub 2}{sup 10} O{sub 3} scintillation detectors with surfaces of 300 and 2 000 cm{sup 2} were used and the efficiency, for fast neutrons, was about 60%. (author) [French] A l'aide du reacteur a flux pulse de neutrons rapides de l'Institut unifie de recherches nucleaires, les auteurs ont mis au point une installation pour la spectrometrie des neutrons thermiques. Le ralentisseur contigu au reflecteur du reacteur et le filtre deberyllium sont maintenus a la temperature de l'azote liquide. Le diffuseur, place a environ 60 cm du ralentisseur, est irradie par une bouffee de neutrons thermiques dont la duree est determinee par la vie moyenne des neutrons dans le ralentisseur et par l'etalement des temps de vol necessaires pour parcourir la distance de 60 cm. La frequence des bouffees est de 8/s. Pour la spectrometrie dans la region quasi-elastique, on utilise la bande en bordure du spectre qui correspond au beryllium et s'etale sur environ 200 {mu}s. L'energie des neutrons diffuses est determinee par la duree du parcours entre le diffuseur et le detecteur. Les auteurs ont utilise des detecteurs a scintillation a ZnS + 10{sub 2}{sup 10} O
FEMB, 2-D Homogeneous Neutron Diffusion in X-Y Geometry with Keff Calculation, Dyadic Fission Matrix
International Nuclear Information System (INIS)
Misfeldt, I.B.
1987-01-01
1 - Nature of physical problem solved: The two-dimensional neutron diffusion equation (xy geometry) is solved in the homogeneous form (K eff calculation). The boundary conditions specify each group current as a linear homogeneous function of the group fluxes (gamma matrix concept). For each material, the fission matrix is assumed to be dyadic. 2 - Method of solution: Finite element formulation with Lagrange type elements. Solution technique: SOR with extrapolation. 3 - Restrictions on the complexity of the problem: Maximum order of the Lagrange elements is 6
DEFF Research Database (Denmark)
Hansen, Flemming Yssing; Criswell, L.; Fuhrmann, D
2004-01-01
Molecular dynamics simulations of a tetracosane (n-C24H50) monolayer adsorbed on a graphite basal-plane surface show that there are diffusive motions associated with the creation and annihilation of gauche defects occurring on a time scale of similar to0.1-4 ns. We present evidence...... that these relatively slow motions are observable by high-energy-resolution quasielastic neutron scattering (QNS) thus demonstrating QNS as a technique, complementary to nuclear magnetic resonance, for studying conformational dynamics on a nanosecond time scale in molecular monolayers....
CLUB - a multigroup integral transport theory code for lattice calculations of PHWR cells
International Nuclear Information System (INIS)
Krishnani, P.D.
1992-01-01
The computer code CLUB has been developed to calculate lattice parameters as a function of burnup for a pressurised heavy water reactor (PHWR) lattice cell containing fuel in the form of cluster. It solves the multigroup integral transport equation by the method based on combination of small scale collision probability (CP) method and large scale interface current technique. The calculations are performed by using WIMS 69 group cross section library or its condensed versions of 27 or 28 group libraries. It can also compute Keff from the given geometrical buckling in the input using multigroup diffusion theory in fundamental mode. The first order differential burnup equations can be solved by either Trapezoidal rule or Runge-Kutta method. (author). 17 refs., 2 figs
Energy Technology Data Exchange (ETDEWEB)
Moreau, G [Commissariat a l' Energie Atomique, Fontenay-aux-Roses (France). Centre d' Etudes Nucleaires
1969-06-01
Examination of bulky diffusion couples Al (Mg) - Al and Mg (Al) - Mg handled in same thermal conditions (between 200 and 440 C) out of pile and under fast neutron irradiation show, in the latter case: 1 - An increase of the growth kinetics of {beta} phase which can be explained with KIDSON' s formula. 2 - An apparent increase of solubility caused by migration of a part of excess vacancies as complexes (vacancy - solute atom) to sinks (stacking faults, grain boundaries) or to sub-microscopical clusters. 3 - An enhancement of chemical diffusion at low temperature. At infinite dilution, chemical diffusion coefficient of Mg in Al can be expressed in normal conditions as: D = 1 exp(- 31000/RT {+-} 1200/RT cal/mole) cm{sup 2}.s{sup -1} and under irradiation as: D = 8.10{sup -3} exp(-24500/RT {+-} 1200/RT cal/mole) cm{sup 2}.s{sup -1}. Interpretation can be carried out by DIENES and Damask's theory. Excess defects (vacancies and interstitials generated in equal numbers by radiation) annihilate by migration to sinks and by direct recombination. Sinks density varies with temperature and irradiation time. The part of complexes (vacancy-solute atom) is important in the vacancies annealing kinetics. (author) [French] L'examen de couples de diffusion massifs Al (Mg) - Al et Mg (Al) - Mg traites dans les memes conditions thermiques (entre 200 et 440 C) hors pile et sous flux de neutrons rapides montre dans le dernier cas: 1 - Une acceleration de la cinetique de croissance de la phase {beta} a basse temperature dont on peut rendre compte a l'aide de la formule de KIDSON. 2 - Une augmentation apparente de la solubilite due a l'elimination d'une partie des lacunes en exces sous forme de complexes (lacune -solute) sur des pieges (dislocations, joints) ou sous forme d'amas sub-microscopiques. 3 - Une acceleration de la diffusion a basse temperature. A dilution infinie la diffusion (en cm{sup 2}/s) du Mg dans l'Al passe de: 1 exp(- 31000/RT {+-} 1200/RT cal/mole) a 8.10{sup -3} exp
Neutron Diffusion in a Space Lattice of Fissionable and Absorbing Materials
Feynman, R. P.; Welton, T. A.
1946-08-27
Methods are developed for estimating the effect on a critical assembly of fabricating it as a lattice rather than in the more simply interpreted homogeneous manner. An idealized case is discussed supposing an infinite medium in which fission, elastic scattering and absorption can occur, neutrons of only one velocity present, and the neutron m.f.p. independent of position and equal to unity with the unit of length used.
Boron Neutron Capture Therapy activity of diffused tumors at TRIGA Mark II in Pavia
Energy Technology Data Exchange (ETDEWEB)
Bortolussi, S.; Stella, S.; De Bari, A.; Altieri, S. [Department of Nuclear and Theoretical Physics, University of Pavia, Pavia (Italy)]|[National Institute of Nuclear Physics (INFN), Pavia (Italy); Bruschi, P.; Bakeine, J.G. [Department of Nuclear and Theoretical Physics, University of Pavia, Pavia (Italy); Clerici, A.; Ferrari, C.; Zonta, C.; Zonta, A. [Department of Surgery, University of Pavia, Pavia (Italy); Nano, R. [Department of Animal Biology, University of Pavia, Pavia (Italy)
2008-10-29
The Boron neutron Capture Therapy research in Pavia has a long tradition: it begun more than 20 years ago at the TRIGA Mark II reactor of the University. A technique for the treatment of the hepatic metastases was developed, consisting in explanting the liver treated with {sup 10}B, irradiating it in the thermal column of the reactor, and re-implanting the organ in the patient. In the last years, the possibility of applying BNCT to the lung tumours using epithermal collimated neutron beams and without explanting the organ, is being explored. The principal obtained results of the BNCT research will be presented, with particular emphasis on the following aspects: a) the project of a new thermal column configuration to make the thermal neutron flux more uniform inside the explanted liver, b) the Monte Carlo study by means of the MCNP code of the thermal neutron flux distribution inside a patient's thorax irradiated with epithermal neutrons, and c) the measurement of the boron concentration in tissues by (n,{alpha}) spectroscopy and neutron autoradiography. (authors)
Boron Neutron Capture Therapy activity of diffused tumors at TRIGA Mark II in Pavia
International Nuclear Information System (INIS)
Bortolussi, S.; Stella, S.; De Bari, A.; Altieri, S.; Bruschi, P.; Bakeine, J.G.; Clerici, A.; Ferrari, C.; Zonta, C.; Zonta, A.; Nano, R.
2008-01-01
The Boron neutron Capture Therapy research in Pavia has a long tradition: it begun more than 20 years ago at the TRIGA Mark II reactor of the University. A technique for the treatment of the hepatic metastases was developed, consisting in explanting the liver treated with 10 B, irradiating it in the thermal column of the reactor, and re-implanting the organ in the patient. In the last years, the possibility of applying BNCT to the lung tumours using epithermal collimated neutron beams and without explanting the organ, is being explored. The principal obtained results of the BNCT research will be presented, with particular emphasis on the following aspects: a) the project of a new thermal column configuration to make the thermal neutron flux more uniform inside the explanted liver, b) the Monte Carlo study by means of the MCNP code of the thermal neutron flux distribution inside a patient's thorax irradiated with epithermal neutrons, and c) the measurement of the boron concentration in tissues by (n,α) spectroscopy and neutron autoradiography. (authors)
International Nuclear Information System (INIS)
Fujimura, Toichiro; Okumura, Keisuke
2002-11-01
A prototype version of a diffusion code has been developed to analyze the hexagonal core as reduced moderation reactor and the applicability of some acceleration methods have been investigated to accelerate the convergence of the iterative solution method. The hexagonal core is divided into regular triangular prisms in the three-dimensional code MOSRA-Prism and a polynomial expansion nodal method is applied to approximate the neutron flux distribution by a cubic polynomial. The multi-group diffusion equation is solved iteratively with ordinal inner and outer iterations and the effectiveness of acceleration methods is ascertained by applying an adaptive acceleration method and a neutron source extrapolation method, respectively. The formulation of the polynomial expansion nodal method is outlined in the report and the local and global effectiveness of the acceleration methods is discussed with various sample calculations. A new general expression of vacuum boundary condition, derived in the formulation is also described. (author)
Energy Technology Data Exchange (ETDEWEB)
Pinchedez, K
1999-06-01
Parallel computing meets the ever-increasing requirements for neutronic computer code speed and accuracy. In this work, two different approaches have been considered. We first parallelized the sequential algorithm used by the neutronics code CRONOS developed at the French Atomic Energy Commission. The algorithm computes the dominant eigenvalue associated with PN simplified transport equations by a mixed finite element method. Several parallel algorithms have been developed on distributed memory machines. The performances of the parallel algorithms have been studied experimentally by implementation on a T3D Cray and theoretically by complexity models. A comparison of various parallel algorithms has confirmed the chosen implementations. We next applied a domain sub-division technique to the two-group diffusion Eigen problem. In the modal synthesis-based method, the global spectrum is determined from the partial spectra associated with sub-domains. Then the Eigen problem is expanded on a family composed, on the one hand, from eigenfunctions associated with the sub-domains and, on the other hand, from functions corresponding to the contribution from the interface between the sub-domains. For a 2-D homogeneous core, this modal method has been validated and its accuracy has been measured. (author)
Energy Technology Data Exchange (ETDEWEB)
Benoist, P [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires
1964-01-15
In an previous publication, a simple and general formulation of the diffusion coefficient, which defines the mode of weighting of the mean free paths of the various media, in introducing the collision probabilities in each medium, was established. This expression is demonstrated again here through a more direct method, and the velocity is introduced; new terms are emphasised, the existence of which implies that the representation of the diffusion area as the mean square of the straight line distance from source to absorption is not correct in a lattice. However these terms are of small enough an order of magnitude to he treated as a correction. The general expression also shows the existence, for the radial coefficient, of the series of angular correlation terms, which is seen to converge very slowly for large channels. The term by term computation which was initiated in the first work was then interrupted and a global formulation, which emphasize a resemblance with the problem of the thermal utilisation factor, was adopted. An integral method, analogous to that use for the computation of this factor, gives the possibility to establish new and simple practical formulae, which require the use of a few basic functions only. These formulae are very accurate, as seen from the results of a variational method which was studied as a reference. Various correction effects are reviewed. Expressions which allow the exact treatment of fuel rod clusters are presented. The theory is confronted with various experimental results, and a new method of measuring the radial coefficient is proposed. (author) [French] Dans une publication anterieure, on a etablie une formulation simple et generale du coefficient de diffusion, qui definit le mode de ponderation des libres parcours des differents milieux constituants en faisant apparaitre les probabilites de collision dans chaque milieu. On redemontre ici cette expression d'une maniere plus directe, tout en introduisant la variable
Energy Technology Data Exchange (ETDEWEB)
Benoist, P. [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires
1964-01-15
In an previous publication, a simple and general formulation of the diffusion coefficient, which defines the mode of weighting of the mean free paths of the various media, in introducing the collision probabilities in each medium, was established. This expression is demonstrated again here through a more direct method, and the velocity is introduced; new terms are emphasised, the existence of which implies that the representation of the diffusion area as the mean square of the straight line distance from source to absorption is not correct in a lattice. However these terms are of small enough an order of magnitude to he treated as a correction. The general expression also shows the existence, for the radial coefficient, of the series of angular correlation terms, which is seen to converge very slowly for large channels. The term by term computation which was initiated in the first work was then interrupted and a global formulation, which emphasize a resemblance with the problem of the thermal utilisation factor, was adopted. An integral method, analogous to that use for the computation of this factor, gives the possibility to establish new and simple practical formulae, which require the use of a few basic functions only. These formulae are very accurate, as seen from the results of a variational method which was studied as a reference. Various correction effects are reviewed. Expressions which allow the exact treatment of fuel rod clusters are presented. The theory is confronted with various experimental results, and a new method of measuring the radial coefficient is proposed. (author) [French] Dans une publication anterieure, on a etablie une formulation simple et generale du coefficient de diffusion, qui definit le mode de ponderation des libres parcours des differents milieux constituants en faisant apparaitre les probabilites de collision dans chaque milieu. On redemontre ici cette expression d'une maniere plus directe, tout en introduisant la variable
International Nuclear Information System (INIS)
Hall, S.K.; Eaton, M.D.; Williams, M.M.R.
2012-01-01
Highlights: ► Isogeometric analysis used to obtain solutions to the neutron diffusion equation. ► Exact geometry captured for a circular fuel pin within a square moderator. ► Comparisons are made between the finite element method and isogeometric analysis. ► Error and observed order of convergence found using an analytic solution. -- Abstract: In this paper the neutron diffusion equation is solved using Isogeometric Analysis (IGA), which is an attempt to generalise Finite Element Analysis (FEA) to include exact geometries. In contrast to FEA, the basis functions are rational functions instead of polynomials. These rational functions, called non-uniform rational B-splines, are used to capture both the geometry and approximate the solution. The method of manufactured solutions is used to verify a MatLab implementation of IGA, which is then applied to a pincell problem. This is a circular uranium fuel pin within a square block of graphite moderator. A new method is used to compute an analytic solution to a simplified version of this problem, and is then used to observe the order of convergence of the numerical scheme. Comparisons are made against quadratic finite elements for the pincell problem, and it is found that the disadvantage factor computed using IGA is less accurate. This is due to a cancellation of errors in the FEA solution. A modified pincell problem with vacuum boundary conditions is then considered. IGA is shown to outperform FEA in this situation.
SYNTH-C, Steady-State and Time-Dependent 3-D Neutron Diffusion with Thermohydraulic Feedback
Energy Technology Data Exchange (ETDEWEB)
Brega, E [ENEL-CRTN, Bastioni di Porta Volta 10, Milan (Italy); Salina, E [A.R.S. Spa, Viale Maino 35, Milan (Italy)
1980-04-01
1 - Description of problem or function: SYNTH-C-STEADY and SYNTH-C- TRANS solve respectively the steady-state and time-dependent few- group neutron diffusion equations in three dimensions x,y,z in the presence of fuel temperature and thermal-hydraulic feedback. The neutron diffusion and delayed precursor equations are approximated by a space-time (z,t) synthesis method with axially discontinuous trial functions. Three thermal-hydraulic and fuel heat transfer models are available viz. COBRA-3C/MIT model, lumped parameter (WIGL) model and adiabatic fuel heat-up model. 2 - Method of solution: The steady-state and time-dependent synthesis equations are solved respectively by the Wielandt's power method and by the theta-difference method (in time), both coupled with a block factorization technique and double precision arithmetic. The thermal-hydraulic model equations are solved by fully implicit finite differences (WIGL) or explicit-implicit difference techniques with iterations (COBRA-EC/MIT). 3 - Restrictions on the complexity of the problem: Except for the few- group limitation, the programs have no other fixed limitation so the ability to run a problem depends only on the available computer storage.
International Nuclear Information System (INIS)
Nemkovski, K; Ioffe, A; Su, Y; Babcock, E; Schweika, W; Brückel, Th
2017-01-01
We present the concept and the results of the simulations of a new polarizer for the diffuse neutron scattering spectrometer DNS at MLZ. The concept of the polarizer is based on the idea of a bender made from the stack of the silicon wafers with a double-side supermirror polarizing coating and absorbing spacers in between. Owing to its compact design, such a system provides more free space for the arrangement of other instrument components. To reduce activation of the polarizer in the high intensity neutron beam of the DNS spectrometer we plan to use the Fe/Si supermirrors instead of currently used FeCoV/Ti:N ones. Using the VITESS simulation package we have performed simulations for horizontally focusing polarizing benders with different geometries in the combination with the double-focusing crystal monochromator of DNS. Neutron transmission and polarization efficiency as well as the effects of the focusing for convergent conventional C-benders and S-benders have been analyzed both for wedge-like and plane-parallel convergent geometries of the channels. The results of these simulations and the advantages/disadvantages of the various configurations are discussed. (paper)
Nemkovski, K.; Ioffe, A.; Su, Y.; Babcock, E.; Schweika, W.; Brückel, Th
2017-06-01
We present the concept and the results of the simulations of a new polarizer for the diffuse neutron scattering spectrometer DNS at MLZ. The concept of the polarizer is based on the idea of a bender made from the stack of the silicon wafers with a double-side supermirror polarizing coating and absorbing spacers in between. Owing to its compact design, such a system provides more free space for the arrangement of other instrument components. To reduce activation of the polarizer in the high intensity neutron beam of the DNS spectrometer we plan to use the Fe/Si supermirrors instead of currently used FeCoV/Ti:N ones. Using the VITESS simulation package we have performed simulations for horizontally focusing polarizing benders with different geometries in the combination with the double-focusing crystal monochromator of DNS. Neutron transmission and polarization efficiency as well as the effects of the focusing for convergent conventional C-benders and S-benders have been analyzed both for wedge-like and plane-parallel convergent geometries of the channels. The results of these simulations and the advantages/disadvantages of the various configurations are discussed.
Energy Technology Data Exchange (ETDEWEB)
Ryu, Eun Hyun; Song, Yong Mann; Park, Joo Hwan [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)
2013-05-15
If time-dependent equation is solved with the FEM, the limitation of the input geometry will disappear. It has often been pointed out that the numerical methods implemented in the RFSP code are not state-of-the-art. Although an acceleration method such as the Coarse Mesh Finite Difference (CMFD) for Finite Difference Method (FDM) does not exist for the FEM, one should keep in mind that the number of time steps for the transient simulation is not large. The rigorous formulation in this study will richen the theoretical basis of the FEM and lead to an extension of the dynamics code to deal with a more complicated problem. In this study, the formulation for the 1-D, 1-G Time Dependent Neutron Diffusion Equation (TDNDE) without consideration of the delay neutron will first be done. A problem including one multiplying medium will be solved. Also several conclusions from a comparison between the numerical and analytic solutions, a comparison between solutions with various element orders, and a comparison between solutions with different time differencing will be made to be certain about the formulation and FEM solution. By investigating various cases with different values of albedo, theta, and the order of elements, it can be concluded that the finite element solution is agree well with the analytic solution. The higher the element order used, the higher the accuracy improvements are obtained.
Vacik, J.; Hnatowicz, V.; Attar, F. M. D.; Mathakari, N. L.; Dahiwale, S. S.; Dhole, S. D.; Bhoraskar, V. N.
2014-10-01
Diffusion of lithium from a LiCl aqueous solution into polyether ether ketone (PEEK) and polyimide (PI) assisted by in situ irradiation with 6.5 MeV electrons was studied by the neutron depth profiling method. The number of the Li atoms was found to be roughly proportional to the diffusion time. Regardless of the diffusion time, the measured depth profiles in PEEK exhibit a nearly exponential form, indicating achievement of a steady-state phase of a diffusion-reaction process specified in the text. The form of the profiles in PI is more complex and it depends strongly on the diffusion time. For the longer diffusion time, the profile consists of near-surface bell-shaped part due to Fickian-like diffusion and deeper exponential part.
Using the probability method for multigroup calculations of reactor cells in a thermal energy range
International Nuclear Information System (INIS)
Rubin, I.E.; Pustoshilova, V.S.
1984-01-01
The possibility of using the transmission probability method with performance inerpolation for determining spatial-energy neutron flux distribution in cells of thermal heterogeneous reactors is considered. The results of multigroup calculations of several uranium-water plane and cylindrical cells with different fuel enrichment in a thermal energy range are given. A high accuracy of results is obtained with low computer time consumption. The use of the transmission probability method is particularly reasonable in algorithms of the programmes compiled computer with significant reserve of internal memory
Mining the multigroup-discrete ordinates algorithm for high quality solutions
International Nuclear Information System (INIS)
Ganapol, B.D.; Kornreich, D.E.
2005-01-01
A novel approach to the numerical solution of the neutron transport equation via the discrete ordinates (SN) method is presented. The new technique is referred to as 'mining' low order (SN) numerical solutions to obtain high order accuracy. The new numerical method, called the Multigroup Converged SN (MGCSN) algorithm, is a combination of several sequence accelerators: Romberg and Wynn-epsilon. The extreme accuracy obtained by the method is demonstrated through self consistency and comparison to the independent semi-analytical benchmark BLUE. (authors)
Specifications for a two-dimensional multi-group scattering code: ALCI
International Nuclear Information System (INIS)
Bayard, J.P.; Guillou, A.; Lago, B.; Bureau du Colombier, M.J.; Guillou, G.; Vasseur, Ch.
1965-02-01
This report describes the specifications of the ALCI programme. This programme resolves the system of difference equations similar to the homogeneous problem of multigroup neutron scattering, with two dimensions in space, in the three geometries XY, RZ, RΘ. It is possible with this method to calculate geometric and composition criticalities and also to calculate the accessory problem on demand. The maximum number of points dealt with is 6000. The maximum permissible number of groups is 12. The internal iterations are treated by the method of alternating directions. The external iterations are accelerated using the extrapolation method due to Tchebychev. (authors) [fr
Iterative solutions of finite difference diffusion equations
International Nuclear Information System (INIS)
Menon, S.V.G.; Khandekar, D.C.; Trasi, M.S.
1981-01-01
The heterogeneous arrangement of materials and the three-dimensional character of the reactor physics problems encountered in the design and operation of nuclear reactors makes it necessary to use numerical methods for solution of the neutron diffusion equations which are based on the linear Boltzmann equation. The commonly used numerical method for this purpose is the finite difference method. It converts the diffusion equations to a system of algebraic equations. In practice, the size of this resulting algebraic system is so large that the iterative methods have to be used. Most frequently used iterative methods are discussed. They include : (1) basic iterative methods for one-group problems, (2) iterative methods for eigenvalue problems, and (3) iterative methods which use variable acceleration parameters. Application of Chebyshev theorem to iterative methods is discussed. The extension of the above iterative methods to multigroup neutron diffusion equations is also considered. These methods are applicable to elliptic boundary value problems in reactor design studies in particular, and to elliptic partial differential equations in general. Solution of sample problems is included to illustrate their applications. The subject matter is presented in as simple a manner as possible. However, a working knowledge of matrix theory is presupposed. (M.G.B.)
Energy Technology Data Exchange (ETDEWEB)
Petersen, Claudio Zen
2008-07-01
In this dissertation we use the Laplace transform to derive expressions for nonstandard albedo boundary conditions for one and two non-multiplying regions at the ends of one dimensional domains. In practice, the fuel regions of reactor cores are surrounded by reflector regions that reduce neutron leakage. In order to exclude the reflector regions from the calculations, we introduce a reflection coefficient or albedo. We use the present albedo boundary conditions to solve numerically slab-geometry monoenergetic and multigroup diffusion equations using the conventional finite difference method. Numerical results are generated for fixed source and eigenvalue diffusion problems in slab geometry(author)
International Nuclear Information System (INIS)
Mendonca, A.G.
1980-01-01
Two computer codes that are available at IPEN for analyses of static neutron diffusion problems are studied and applied. The CITATION code is animed at analyses of criticality, fuel burnup, flux and power distributions etc, in one, two, and three spatial dimensions in multigroup. The EXTERMINATOR code can be used for the same purposes as for CITATION with a limitation to one or two spatial dimensions. Basic theories and numerical techniques used in the codes are studied and summarized. Benchmark problems have been solved using the codes. Comparisons of the results show that both codes can be used with confidence in the analyses of nuclear reactor problems. (author) [pt
Macroscopic multigroup constants for accelerator driven system core calculation
International Nuclear Information System (INIS)
Heimlich, Adino; Santos, Rubens Souza dos
2011-01-01
The high-level wastes stored in facilities above ground or shallow repositories, in close connection with its nuclear power plant, can take almost 106 years before the radiotoxicity became of the order of the background. While the disposal issue is not urgent from a technical viewpoint, it is recognized that extended storage in the facilities is not acceptable since these ones cannot provide sufficient isolation in the long term and neither is it ethical to leave the waste problem to future generations. A technique to diminish this time is to transmute these long-lived elements into short-lived elements. The approach is to use an Accelerator Driven System (ADS), a sub-critical arrangement which uses a Spallation Neutron Source (SNS), after separation the minor actinides and the long-lived fission products (LLFP), to convert them to short-lived isotopes. As an advanced reactor fuel, still today, there is a few data around these type of core systems. In this paper we generate macroscopic multigroup constants for use in calculations of a typical ADS fuel, take into consideration, the ENDF/BVI data file. Four energy groups are chosen to collapse the data from ENDF/B-VI data file by PREPRO code. A typical MOX fuel cell is used to validate the methodology. The results are used to calculate one typical subcritical ADS core. (author)
Energy Technology Data Exchange (ETDEWEB)
Ericson-Galula, M [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires
1958-12-15
The critical diffusion of neutrons in iron is due to the magnetisation fluctuations which occur in ferromagnetic substances in the neighbourhood of the Curie temperature. The fluctuations can be described in correlation terms; a correlation function {gamma}{sub R{sub vector}} (t) is defined, {gamma}{sub R{sub vector}} (t) = mean value of the scalar product of a reference spin and a spin situated at a distance (R) from the first and considered at the instant t. In chapter I we recall the generalities on neutron diffusion cross-sections; a brief summary is given of the theory of VAN HOVE, who has shown that the magnetic diffusion cross section of neutrons is the Fourier transformation of the correlation function. In chapter Il we study the spatial dependence of the correlation function, assumed to be independent of time. It can then be characterised by two parameters K{sub 1} and r{sub 1}, by means of which the range and intensity of the correlations can be calculated respectively. After setting out the principle of the measurement of these parameters, we shall describe the experimental apparatus. The experimental values obtained are in good agreement with the calculations, and the agreement is better if it is supposed that the second and not the first neighbours of an iron atom are magnetically active, as proposed by Neel. In chapter III we study the evolution with time of the correlation function; this evolution is characterised by a parameter {lambda} depending on the temperature, which occurs in the diffusion equation obeyed by the magnetisation fluctuations: {delta}M{sub vector}/{delta}t = {lambda} {nabla}{sup 2} M{sub vector}. The principle of the measurement of {lambda} is given, after which the modifications carried out on the experimental apparatus mentioned in chapter II are described. The results obtained are then discussed and compared with the theoretical forecasts of De Gennes, mode by using the
International Nuclear Information System (INIS)
Raskach, K. F.
2012-01-01
In multigroup calculations of reactivity and sensitivity coefficients, methodical errors can appear if the interdependence of multigroup constants is not taken into account. For this effect to be taken into account, so-called implicit components of the aforementioned values are introduced. A simple technique for computing these values is proposed. It is based on the use of subgroup parameters.
Energy Technology Data Exchange (ETDEWEB)
Belicev, P [Vojnotehnicki Inst., Belgrade (Yugoslavia)
1988-07-01
An outline of the problems encountered in the multigroup calculations of the neutron transport in the resonance region is given. The difference between subgroup and multigroup approximation is described briefly. The features of the Monte Carlo code SUBGR are presented. The results of the calculations of the neutron transmission and albedo for infinite iron slabs are given. (author)
Energy Technology Data Exchange (ETDEWEB)
Ott, F
1998-11-26
Theoretical (Zeeman energy effects) and experimental (beam polarisation problems) progress have been made in the understanding of polarized neutron reflectivity with polarisation analysis. It has been shown that modelization and numerical simulations makes it possible to avoid to have to systematically measure a full set of reflectivity curves for each field and temperature condition. It has been possible to determine a magnetic profile as a function of the field in a magnetic bilayer system by using only a few points in the reciprocal space. This technique allows to considerable reduce the experiment time. In single nickel layer systems, we have shown that it is possible to induce magnetic rotation inhomogeneities when these systems are subjects to deformation strains. The effect are related to magneto-elastic constants gradients. In trilayer systems, with a ME constant modulation, we have been able to induce large magnetic rotation gradients. A new magneto-optic technique to measure the magnetization direction without rotating the magnetic field has been developed. The field of neutron reflectivity has been extended to off-specular studies. It has been possible to account quantitatively of the off-specular diffusion on 2-D model systems (prepared by optical lithography). This new technique should make it possible in the future to determine magnetic structures with a in-depth as well as lateral resolution. (author)
Energy Technology Data Exchange (ETDEWEB)
Bally, D; Tarina, V; Todireanu, S [Institute of Atomic Physics, Bucharest (Romania)
1963-01-15
The angular distribution of 1.61 A wavelength neutrons scattered from hydrogen and ethylene has been measured. For ethylene the pressure was varied from 15 to 60 atm and for hydrogen from 60 to 110 atm. The investigated angular range was between 5''o and 90{sup o}. The experimental results obtained have been compared with the differential cross-section calculated using the Krieger-Nelkin formulae. (author) [French] Les auteurs ont mesure la distribution angulaire des neutrons ayant une longueur d'onde de 1,61 A diffuses par de l'hydrogene et par l'ethylene. Ils ont fait varier la pression de l'ethylene de 15 a 60 atm et celle de l'hydrogene de 60 a 110 atm. Le domaine angulaire etudie etait compris entre 5{sup o} et 90{sup o}. Les resultats des experiences ont ete compares aux sections efficaces differentielles calculees au moyen des formules de Krieger-Nelkin. (author) [Spanish] Los autores han medido la distribucion angular de neutrones de longitud de onda igual a 1,61 A, despersados por hidrogeno y etileno. En el caso del etileno, la presion vario de 15 a 60 atm y en el del higrogeno, de 60 a 110 atm. Los autores han explorado angulos comprendidos entre 5{sup o} y 90{sup o}. comparan los resultados experimentales obtenidos con el valor de la seccion eficaz diferencial calculado con ayuda de las formulas de Kriger-Nelkin. (author)
Neutron-proton elastic diffusion study at low transfer between 400-1000 MeV
International Nuclear Information System (INIS)
Wellers, F.
1986-01-01
This thesis presents the first complete results of forward differential cross-section, over the entire range of the intermediate energies, in the neutron-proton system. The neutron beam is produced with the synchrotron Saturne II, using the reaction of deuteron break-up, which gives it a relatively high intensity and a small energy dispersion. The experimental apparatus is a drift ionization chamber, IKAR, filled with high pressure gas which plays the double role of target and detector of the recoil proton. The use of a neutral beam requires new procedures in the analysis, more elaborate than in the case of charged projectiles, where scattered particles were detected in coincidence in wire chambers. The results are then normalized and discussed, using a phenomenological parametrization, and integrated in a continuously energy-dependent phase-shifts analysis. An entirely analytic Glauber calculation allows us to estimate the validity of the normalization method [fr
Travelling Wave Solutions in Multigroup Age-Structured Epidemic Models
Ducrot, Arnaut; Magal, Pierre; Ruan, Shigui
2010-01-01
Age-structured epidemic models have been used to describe either the age of individuals or the age of infection of certain diseases and to determine how these characteristics affect the outcomes and consequences of epidemiological processes. Most results on age-structured epidemic models focus on the existence, uniqueness, and convergence to disease equilibria of solutions. In this paper we investigate the existence of travelling wave solutions in a deterministic age-structured model describing the circulation of a disease within a population of multigroups. Individuals of each group are able to move with a random walk which is modelled by the classical Fickian diffusion and are classified into two subclasses, susceptible and infective. A susceptible individual in a given group can be crisscross infected by direct contact with infective individuals of possibly any group. This process of transmission can depend upon the age of the disease of infected individuals. The goal of this paper is to provide sufficient conditions that ensure the existence of travelling wave solutions for the age-structured epidemic model. The case of two population groups is numerically investigated which applies to the crisscross transmission of feline immunodeficiency virus (FIV) and some sexual transmission diseases.
Importance estimation in Monte Carlo modelling of neutron and photon transport
International Nuclear Information System (INIS)
Mickael, M.W.
1992-01-01
The estimation of neutron and photon importance in a three-dimensional geometry is achieved using a coupled Monte Carlo and diffusion theory calculation. The parameters required for the solution of the multigroup adjoint diffusion equation are estimated from an analog Monte Carlo simulation of the system under investigation. The solution of the adjoint diffusion equation is then used as an estimate of the particle importance in the actual simulation. This approach provides an automated and efficient variance reduction method for Monte Carlo simulations. The technique has been successfully applied to Monte Carlo simulation of neutron and coupled neutron-photon transport in the nuclear well-logging field. The results show that the importance maps obtained in a few minutes of computer time using this technique are in good agreement with Monte Carlo generated importance maps that require prohibitive computing times. The application of this method to Monte Carlo modelling of the response of neutron porosity and pulsed neutron instruments has resulted in major reductions in computation time. (Author)
Energy Technology Data Exchange (ETDEWEB)
Verdu, G.; Miro, R. [Departamento de Ingenieria Quimica y Nuclear, Universidad Politecnica de Valencia, Valencia (Spain); Ginestar, D. [Departamento de Matematica Aplicada, Universidad Politecnica de Valencia, Valencia (Spain); Vidal, V. [Departamento de Sistemas Informaticos y Computacion, Universidad Politecnica de Valencia, Valencia (Spain)
1999-05-01
To calculate the neutronic steady state of a nuclear power reactor core and its subcritical modes, it is necessary to solve a partial eigenvalue problem. In this paper, an implicit restarted Arnoldi method is presented as an advantageous alternative to classical methods as the Power Iteration method and the Subspace Iteration method. The efficiency of these methods, has been compared calculating the dominant Lambda modes of several configurations of the Three Mile Island reactor core.
Multigroup cross section library; WIMS library
International Nuclear Information System (INIS)
Kannan, Umasankari
2000-01-01
The WIMS library has been extensively used in thermal reactor calculations. This multigroup constants library was originally developed from the UKNDL in the late 60's and has been updated in 1986. This library has been distributed with the WIMS-D code by NEA data bank. The references to WIMS library in literature are the 'old' which is the original as developed by the AEA Winfrith and the 'new' which is the current 1986 WIMS library. IAEA has organised a CRP where a new and fully updated WIMS library will soon be available. This paper gives an overview of the definitions of the group constants that go into any basic nuclear data library used for reactor calculations. This paper also outlines the contents of the WIMS library and some of its shortcomings
International Nuclear Information System (INIS)
Schuerrer, F.
1980-01-01
For characterizing heterogene configurations of pebble-bed reactors the fine structure of the flux distribution as well as the determination of the macroscopic neutronphysical quantities are of interest. When calculating system parameters of Wigner-Seitz-cells the usual codes for neutron spectra calculation always neglect the modulation of the neutron flux by the influence of neighbouring spheres. To judge the error arising from that procedure it is necessary to determinate the flux distribution in the surrounding of a spherical fuel element. In the present paper an approximation method to calculate the flux distribution in the two-sphere model is developed. This method is based on the exactly solvable problem of the flux determination of a point source of neutrons in an infinite medium, which contains a spherical perturbation zone eccentric to the point source. An iteration method allows by superposing secondary fields and alternately satisfying the conditions of continuity on the surface of each of the two fuel elements to advance to continually improving approximations. (orig.) 891 RW/orig. 892 CKA [de
International Nuclear Information System (INIS)
Volino, F.
1976-01-01
After a short review of the main concepts concerning the neutron and its interaction with matter, the authors focus their attention on the study of molecular systems by means of neutron scattering. Instead of reviewing the subject yet again, they limit themselves to the new kind of work which can be done now, with the combined help of high flux reactors and novel instruments. As examples, a few experiments performed at the Institut Laue-Langevin in Grenoble are described: a neutron diffraction study of liquid acetonitrile using a powder diffractometer installed at the hot source; three high-resolution quasi-elastic studies of molecular motions - in an organic solid, (PAA), an organic liquid (C 3 H 6 ) and a liquid crystal (TBBA) - made by combining measurements with high and ultra-high energy resolution spectrometers installed at the cold source. The concept of elastic incoherent structure factor (EISF) is extensively used for the analysis. Finally some prospects on possible future developments are presented. (orig./HK) [de
International Nuclear Information System (INIS)
Takamatsu, Kuniyoshi; Shimakawa, Satoshi; Nojiri, Naoki; Fujimoto, Nozomu
2003-10-01
In the case of evaluations for the highest temperature of the fuels in the HTTR, it is very important to expect the power density distributions accurately; therefore, it is necessary to improve the analytical model with the neutron diffusion and the burn-up theory. The power density distributions are analyzed in terms of two models, the one mixing the fuels and the burnable poisons homogeneously and the other modeling them heterogeneously. Moreover these analytical power density distributions are compared with the ones derived from the gross gamma-ray measurements and the Monte Carlo calculational code with continuous energy. As a result the homogeneous mixed model isn't enough to expect the power density distributions of the core in the axial direction; on the other hand, the heterogeneous model improves the accuracy. (author)
Energy Technology Data Exchange (ETDEWEB)
Sagot, M; Tellier, H [Commissariat a l' Energie Atomique. Centre d' Etudes Nucleaires de Saclay, 91 - Gif-sur-Yvette (France)
1963-07-01
The diffusion coefficient, cooling coefficient, and anisotropy of graphite were determined to be (2.19 {+-} 0.03) x 10{sup 5} cm{sup 2} sec{sup -1}, (37.9 {+-} 4) x 10{sup 5} cm{sup 4} sec{sup -1}, and 1.017 {+-} 0.008, respectively. The range of geometrical buckling was from 7 to 155 m{sup -2}. The values obtained are compared with published values. (authors) [French] Un programme experimental utilisant la methode de la source pulsee de neutrons a ete realise sur le graphite. La gamme des laplaciens couverte est de 7 m{sup -2} a 155 m{sup -2}. Les resultats en sont presentes dans ce rapport: - coefficient de diffusion D{sub 0} = (2,19 {+-} 0,03) x 10{sup 5} cm{sup 2} s{sup -1} - coefficient de refroidissement C = (37,9 {+-} 4) x 10{sup 5} cm{sup 4} s{sup -1} - anisotropie du graphite (D parall./D perp.) = 1,017 {+-} 0,008. Ils sont compares aux valeurs deja publiees. (auteurs)
International Nuclear Information System (INIS)
Charlton, J.S.
1986-01-01
The way in which neutrons interact with matter such as slowing-down, diffusion, neutron absorption and moderation are described. The use of neutron techniques in industry, in moisture gages, level and interface measurements, the detection of blockages, boron analysis in ore feedstock and industrial radiography are discussed. (author)
Czech Academy of Sciences Publication Activity Database
Vacík, Jiří; Hnatowicz, Vladimír; Attar, F. M. D.; Mathakari, N. L.; Dahiwale, S. S.; Dhole, S. D.; Bhoraskar, V. N.
2014-01-01
Roč. 169, č. 10 (2014), s. 885-891 ISSN 1042-0150 R&D Projects: GA ČR(CZ) GBP108/12/G108; GA MŠk(XE) LM2011019 Institutional support: RVO:61389005 Keywords : diffusion * lithium * neutron depth profiling * polymers Subject RIV: BG - Nuclear, Atomic and Molecular Physics, Colliders Impact factor: 0.513, year: 2014
International Nuclear Information System (INIS)
Esquivel E, J.; Del Valle G, E.
2014-10-01
The system called NodHex3D is a graphical application that allows the solution of the neutron diffusion equation. The system considers fuel assemblies of hexagonal cross section. This application arose from the idea of expanding the development of neutron own codes, used primarily for academic purposes. The advantage associated with the use of NodHex3D, is that the kernel configuration and fuel batches is dynamically without affecting directly the base source code of the solution of the neutron diffusion equation. In addition to the kernel configuration to use, specify the values for the cross sections for each batch of fuel used, these values are: diffusion coefficient, removal cross section, absorption cross section, fission cross section and dispersion cross section. Important also, considering that the system is able to perform calculations for various energy groups. As evidence of the operation of NodHex3D, was proposed to model three-dimensional core of a nuclear reactor VVER-1000, based on the reference problem AER-FCM-101. The configuration of the reactor core consists of fuel assemblies (25 batches), composed of seven distinct materials, one of which reflector material, vacuum boundary conditions on the surface delimiting the reactor core. The diffusion equation for two energy groups solves, obtaining the value of the effective neutron multiplication factor. The obtained results are compared to those documented in the reference problem and by 3-DNT codes. (Author)
International Nuclear Information System (INIS)
Silva A, L.; Del Valle G, E.
2012-10-01
This work shows an application of the program COMSOL Multi physics Ver. 4.2a in the solution of the neutron diffusion equations for several energy groups in nuclear reactors whose core is formed by assemblies of hexagonal transversal cut as is the cas of fast reactors. A reference problem of 4 energy groups is described of which takes the cross sections which are processed by means of a program that prepares the definition of the constants utilized in COMSOL for the generic partial differential equations that this uses. The considered solution domain is the sixth part of the core which is applied frontier conditions of reflection and incoming flux zero. The discretization mesh is elaborated in automatic way by COMSOL and the solution method is one of finite elements of Lagrange grade two. The reference problem is known as the Knk with and without control rod which led to propose the calculation of the effective multiplication factor in function of the control rod fraction from a value 0 (completely inserted control rod) until the value 1 (completely extracted control rod). Besides this the reactivity was determined as well as the change of this in function of control rod fraction. The neutrons scalar flux for each energy group with and without control rod is proportioned. The reported results show a behavior similar to the one reported in other works but using the discreet ordinates S 2 approximation. (Author)
International Nuclear Information System (INIS)
Turgut, M.H.
1985-01-01
A fast calculation program ''BRIDGE'' was developed for the calculation of a Cold Neutron Source (CNS) at a radial beam tube of the FRG-I reactor, which couples a total assembly diffusion calculation to a transport calculation for a certain subregion. For the coupling flux and current boundary values at the common surfaces are taken from the diffusion calculation and are used as driving conditions in the transport calculation. 'Equivalence Theorie' is used for the transport feedback effect on the diffusion calculation to improve the consistency of the boundary values. The optimization of a CNS for maximizing the subthermal flux in the wavelength range 4 - 6 A is discussed. (orig.) [de
International Nuclear Information System (INIS)
Oka, Y.; Kodama, T.; Akiyama, M.; Hashikura, H.; Kondo, S.
1987-01-01
The reaction rates in the multi-layers containing depleted uranium were measured by activation foils and micro-fission chambers. The analysis of the experiment was carried out by using the multi-group transport calculation code, DOT 3.5 and the continuous energy Monte Carlo code, MCNP. The multi-group calculation overpredicted the low energy reaction rates in the DU layers, while the continuous energy calculation agreed well. The multi-group and continuous energy calculation was compared for the one-dimensional transmission of iron spheres. The results revealed overprediction of the multi-group calculation near the fast neutron source. The averaging of the resonance shapes in generating the multi-group cross sections made minima of the resonance valleys higher than that of the pointwise cross section. This increased the scattering of the neutrons inside and caused the overprediction of the multi-group calculation
International Nuclear Information System (INIS)
Kirk, B.L.; Azmy, Y.
1994-01-01
A modified scheme is developed for solving the two-dimensional nodal diffusion equations on distributed memory computers. The scheme is aimed at minimizing the volume of communication among processors while maximizing the tasks in parallel. Results show a significant improvement in parallel efficiency on the Intel iPSC/860 hypercube compared to previous algorithms
International Nuclear Information System (INIS)
Ahnert, C.; Aragones, J.M.
1982-01-01
The Carmen code (theory and user's manual) is described. This code for assembly and core calculations uses diffusion theory (Citation), with feedback in the cross sections by zone due to the effects of burnup, water density, fuel temperature, Xenon and Samarium. The burnup calculation of a full cycle is solved in only an execution of Carmen, and in a reduced computer time. (auth.)
Neutron and Proton Diffusion in Fusion Reactions for the Synthesis of Superheavy Nuclei
International Nuclear Information System (INIS)
Ming-Hui, Huang; Zai-Guo, Gan; Zhao-Qing, Feng; Xiao-Hong, Zhou; Jun-Qing, Li
2008-01-01
The restriction of the one dimensional (1D) master equation (ME) with the mass number of the projectile-like fragment as a variable is studied, and a two-dimensional (2D) master equation with the neutron and proton numbers as independent variables is set up, and solved numerically. Our study showed that the 2D ME can describe the fusion process well in all projectile-target combinations. Therefore the possible channels to synthesize super-heavy nuclei can be studied correctly in wider possibilities. The available condition for employing 1D ME is pointed out
Energy Technology Data Exchange (ETDEWEB)
Lawrence, R.D.
1983-03-01
A nodal method is developed for the solution of the neutron-diffusion equation in two- and three-dimensional hexagonal geometries. The nodal scheme has been incorporated as an option in the finite-difference diffusion-theory code DIF3D, and is intended for use in the analysis of current LMFBR designs. The nodal equations are derived using higher-order polynomial approximations to the spatial dependence of the flux within the hexagonal-z node. The final equations, which are cast in the form of inhomogeneous response-matrix equations for each energy group, involved spatial moments of the node-interior flux distribution plus surface-averaged partial currents across the faces of the node. These equations are solved using a conventional fission-source iteration accelerated by coarse-mesh rebalance and asymptotic source extrapolation. This report describes the mathematical development and numerical solution of the nodal equations, as well as the use of the nodal option and details concerning its programming structure. This latter information is intended to supplement the information provided in the separate documentation of the DIF3D code.
International Nuclear Information System (INIS)
Lawrence, R.D.
1983-03-01
A nodal method is developed for the solution of the neutron-diffusion equation in two- and three-dimensional hexagonal geometries. The nodal scheme has been incorporated as an option in the finite-difference diffusion-theory code DIF3D, and is intended for use in the analysis of current LMFBR designs. The nodal equations are derived using higher-order polynomial approximations to the spatial dependence of the flux within the hexagonal-z node. The final equations, which are cast in the form of inhomogeneous response-matrix equations for each energy group, involved spatial moments of the node-interior flux distribution plus surface-averaged partial currents across the faces of the node. These equations are solved using a conventional fission-source iteration accelerated by coarse-mesh rebalance and asymptotic source extrapolation. This report describes the mathematical development and numerical solution of the nodal equations, as well as the use of the nodal option and details concerning its programming structure. This latter information is intended to supplement the information provided in the separate documentation of the DIF3D code
International Nuclear Information System (INIS)
Azmy, Y.Y.; Kirk, B.L.
1990-01-01
Modern parallel computer architectures offer an enormous potential for reducing CPU and wall-clock execution times of large-scale computations commonly performed in various applications in science and engineering. Recently, several authors have reported their efforts in developing and implementing parallel algorithms for solving the neutron diffusion equation on a variety of shared- and distributed-memory parallel computers. Testing of these algorithms for a variety of two- and three-dimensional meshes showed significant speedup of the computation. Even for very large problems (i.e., three-dimensional fine meshes) executed concurrently on a few nodes in serial (nonvector) mode, however, the measured computational efficiency is very low (40 to 86%). In this paper, the authors present a highly efficient (∼85 to 99.9%) algorithm for solving the two-dimensional nodal diffusion equations on the Sequent Balance 8000 parallel computer. Also presented is a model for the performance, represented by the efficiency, as a function of problem size and the number of participating processors. The model is validated through several tests and then extrapolated to larger problems and more processors to predict the performance of the algorithm in more computationally demanding situations
International Nuclear Information System (INIS)
Butland, A.T.D.; Putney, J.; Sweet, D.W.
1980-04-01
This report describes work performed to compare two UK neutron diffusion theory codes, TIGAR and SNAP, with published results for eight other codes available abroad. Both mesh edge and mesh centred finite difference diffusion theory codes as well as one axial synthesis code are included in the comparison and a range of iteration procedures are used by them. Comparison is made of calculations for a model of the sodium cooled fast reactor SNR-300 in both triangular and rectangular geometry and for a range of spatial meshes, enabling extrapolations to infinite mesh to be made. Calculated values of the effective multiplication constant, keff, for all the codes, agree very well when extrapolated to infinite mesh, indicating that no significant errors arising from the finite difference approximation but independent of mesh spacing are present in the calculations. The variation of keff with mesh area is found to be linear for the small meshes considered here, with the gradients for the mesh centred and mesh edged codes being of opposite sign. The results obtained using the mesh centred codes TIGAR, SNAP and CITATION agree closely with one another for all the meshes considered; the mesh edge codes agree less closely. (author)
Development of multi-group spectral code TVS-M
International Nuclear Information System (INIS)
Lazarenko, A. P.; Pryanichnikov, A. V.; Kalugin, M. A.; Gurevich, M. I.
2011-01-01
This paper is dedicated to the latest version of TVS-M code - TVS-M 2007, which allows the neutron flux distribution inside fuel assemblies to be calculated without using the diffusion approximation. The new spatial calculation module PERST introduced in TBS-M code is based on the first collisions probability method and allows the scattering anisotropy to be accounted for. This paper presents some preliminary results calculated with the use of the new version of TVS-M code. (Authors)
Measurement of Diffusion Parameters and of Anisotropy of Graphite with a Pulsed Source of Neutrons
International Nuclear Information System (INIS)
Sagot, M.; Tellier, H.
1963-01-01
The diffusion coefficient, cooling coefficient, and anisotropy of graphite were determined to be (2.19 ± 0.03) x 10 5 cm 2 sec -1 , (37.9 ± 4) x 10 5 cm 4 sec -1 , and 1.017 ± 0.008, respectively. The range of geometrical buckling was from 7 to 155 m -2 . The values obtained are compared with published values. (authors) [fr
International Nuclear Information System (INIS)
Van Geemert, Rene
2008-01-01
For satisfaction of future global customer needs, dedicated efforts are being coordinated internationally and pursued continuously at AREVA NP. The currently ongoing CONVERGENCE project is committed to the development of the ARCADIA R next generation core simulation software package. ARCADIA R will be put to global use by all AREVA NP business regions, for the entire spectrum of core design processes, licensing computations and safety studies. As part of the currently ongoing trend towards more sophisticated neutronics methodologies, an SP 3 nodal transport concept has been developed for ARTEMIS which is the steady-state and transient core simulation part of ARCADIA R . For enabling a high computational performance, the SP N calculations are accelerated by applying multi-level coarse mesh re-balancing. In the current implementation, SP 3 is about 1.4 times as expensive computationally as SP 1 (diffusion). The developed SP 3 solution concept is foreseen as the future computational workhorse for many-group 3D pin-by-pin full core computations by ARCADIA R . With the entire numerical workload being highly parallelizable through domain decomposition techniques, associated CPU-time requirements that adhere to the efficiency needs in the nuclear industry can be expected to become feasible in the near future. The accuracy enhancement obtainable by using SP 3 instead of SP 1 has been verified by a detailed comparison of ARTEMIS 16-group pin-by-pin SP N results with KAERI's DeCart reference results for the 2D pin-by-pin Purdue UO 2 /MOX benchmark. This article presents the accuracy enhancement verification and quantifies the achieved ARTEMIS-SP 3 computational performance for a number of 2D and 3D multi-group and multi-box (up to pin-by-pin) core computations. (authors)
EDEF: a program for solving the neutron diffusion equation using microcomputers
International Nuclear Information System (INIS)
Fernandes, A.; Maiorino, J.R.
1990-01-01
This work presents the development of a program to solve the two-group two-dimensional diffusion equation (with a buckling option to simulate axial leakage) applying the finite element method. It has been developed to microcomputers compatibles to the IBM-PC. Among the facilities of the program, we can mention the simplicity to represent two-dimensional complex domains, the input through a pre-processor and the output in which the fluxes are presented graphically. The program also calculates the multiplication factor, the peaking factor and the power distribution. (author) [pt
International Nuclear Information System (INIS)
Filio Lopez, Carlos.
1979-01-01
A calculation program (URA 6.F4) was elaborated on FORTRAN IV language, that through finite differences solves the unidimensional scalar Helmholtz equation, assuming only one energy group, in spherical cylindrical or plane geometry. The purpose is the determination of the flow distribution in a reactor of spherical cylindrical or plane geometry and the critical dimensions. Feeding as entrance datas to the program the geometry, diffusion coefficients and macroscopic transversals cross sections of absorption and fission for each region. The differential diffusion equation is converted with its boundary conditions, to one system of homogeneous algebraic linear equations using the box integration technique. The investigation on criticality is converted then in a succession of eigenvalue problems for the critical eigenvalue. In general, only is necessary to solve the first eigenvalue and its corresponding eigenvector, employing the power method. The obtained results by the program for the critical dimensions of the clean reactors are admissible, the existing error as respect to the analytic is less of 0.5%; by the analysed reactors of three regions, the relative error with respect to the semianalytic result is less of 0.2%. With this program is possible to obtain one quantitative description of one reactor if the transversal sections that appears in the monoenergetic model are adequatedly averaged by the energy group used. (author)
International Nuclear Information System (INIS)
Couto, Nozimar do
2003-01-01
Diffusion theory is traditionally applied to nuclear reactor global calculations. Based on the good results generated by the one-dimensional spectral nodal diffusion (SND) method for benchmark problems, we offer the SND method for nuclear reactor global calculations in X,Y geometry. In this method, the continuity equation and Flick law are transverse integrated in each spatial direction leading to a system of two 'one-dimensional' equations coupled by the transverse leakage terms. We then apply the SND method to numerically solve this system with constant approximations for the transverse leakage terms. We perform a spectral analysis to determine the local general solution of each 'one-dimensional' nodal equation with flat approximation for the transverse leakages. We used special auxiliary equations with parameters that are to be determined in order to preserve the analytical general solutions in the numerical algorithm. By considering continuity conditions at the node interfaces and appropriate boundary conditions, we obtain a solvable system of discretized equations involving the node-edge average scalar fluxes at each estimate of the dominant eigenvalue (k eff ) in the outer power iterations. As we considered approximations to the transverse leakages, the SND method is not free of spatial truncation errors. Nevertheless, it generated good results for the typical model problems that we considered. (author)
International Nuclear Information System (INIS)
Gupta, I.J.; Trikha, S.K.
1977-01-01
Calculations are presented of the diffusion of thermal neutrons (2.5 x 10 -4 to 7 x 10 -1 eV) across an absorption discontinuity in a water assembly, consisting of pure water on one side and aqueous solutions of three different non-1/V absorbers on the other, which were obtained by solving the Boltzmann transport equation in the diffusion approximation using the multigroup formalism. The gradual appearance and disappearance of the depletion region in the neutron spectra (caused by the resonance absorption peaks at energies 0.096 and 0.179 eV for samarium and cadmium respectively), as one moves from the pure water assembly to the poisoned water assembly and vice versa, have also been studied. The minimum concentrations of Sm and Cd atoms in water for which the depletion region in the spectra just starts building up are found to be 60 x 10 18 Sm atom cm -3 and 125 x 10 18 Cd atom cm -3 respectively. However no such depletion region is observed in gadolinium-poisoned water assembly. At the boundary, the equilibrium neutron distribution gets disturbed and is re-established to the equilibrium distribution of the second medium at some distance from the interface. The diffusion lengths so calculated from the total neutron density curves are in good agreement with the experimental results of Goddard and Johnson (Nucl. Sci. Eng.; 37:127 (1969)) at various concentrations of Gd and Cd atoms in water. (author)
Energy Technology Data Exchange (ETDEWEB)
Tardy-Joubert, P [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires
1966-03-01
The cascade induced in protective screens by a 3 GeV proton beam has been studied using activation detectors; the results have been compared with the cosmic neutron spectrum in the atmosphere. A study of the secondary neutron spectrum has made, it possible to obtain the distribution of the dose and to determine the maximum permissible fluxes expressed in terms of the energy, taking into account all the daughter products present. The dose calculated has been checked experimentally. The proportion of cascade neutrons has been studied using the idea of an imaginary source. The parameters which have to be introduced into the general equations to take into account scattering in the the air have been determined. (author) [French] La cascade induite dans les ecrans de protection par un faisceau de protons de 3 GeV a ete etudiee au moyen de detecteurs a activation et la comparaison a ete faite avec le spectre des neutrons cosmiques dans l'atmosphere. L'etude du spectre des neutrons secondaires a permis de preciser la distribution de la dose et de determiner les flux maximaux admissibles qui sont exprimes en fonction de l'energie, en tenant compte de l'ensemble des descendants presents. La dose calculee a ete verifiee experimentalement. La propagation des neutrons de cascade a ete etudiee en introduisant la notion de source fictive. Les parametres a introduire dans les equations generales pour rendre compte de la diffusion dans l'air ont ete determines. (auteur)
Theory of the diffusion coefficient of neutrons in a lattice containing cavities
International Nuclear Information System (INIS)
Benoist, P.
1964-01-01
In an previous publication, a simple and general formulation of the diffusion coefficient, which defines the mode of weighting of the mean free paths of the various media, in introducing the collision probabilities in each medium, was established. This expression is demonstrated again here through a more direct method, and the velocity is introduced; new terms are emphasised, the existence of which implies that the representation of the diffusion area as the mean square of the straight line distance from source to absorption is not correct in a lattice. However these terms are of small enough an order of magnitude to he treated as a correction. The general expression also shows the existence, for the radial coefficient, of the series of angular correlation terms, which is seen to converge very slowly for large channels. The term by term computation which was initiated in the first work was then interrupted and a global formulation, which emphasize a resemblance with the problem of the thermal utilisation factor, was adopted. An integral method, analogous to that use for the computation of this factor, gives the possibility to establish new and simple practical formulae, which require the use of a few basic functions only. These formulae are very accurate, as seen from the results of a variational method which was studied as a reference. Various correction effects are reviewed. Expressions which allow the exact treatment of fuel rod clusters are presented. The theory is confronted with various experimental results, and a new method of measuring the radial coefficient is proposed. (author) [fr
Energy Technology Data Exchange (ETDEWEB)
Mousavi Shirazi, Seyed Alireza [Islamic Azad Univ. (I.A.U.), Dept. of Physics, Tehran (Iran, Islamic Republic of)
2015-07-15
In this symbolic investigation, a cylindrical cell in a LWR, which consists of one fuel pin and moderator (water), is considered. The width of this cylindrical cell is divided into 100 equal units. Since the neutron flux in a cylindrical fuel pin is resulting from the diffusion equation: -(1)/(r)(d)/(dr)Dr(d)/(dr)φ(r) + Σ{sub a}φ(r) = S(r), the amount of fast neutron fluxes are obtained on the basis of the numeric solution of this equation, and the applied boundary conditions are considered: φ'(0) = φ'(1) = 0. This differential equation is solved by the tridiagonal method for variant enrichments of uranium. Neutron fluxes are obtained in variant radii of fuel pin and moderator and are finally compared with each other. There are some interesting outcomes resulting from this investigation. It can be inferred that because of the fuel enrichment increment, the fast neutron flux increases significantly at the centre of core, while many of the fast neutrons produced are absorbed after entering the water region, moderation of lots of them causes the reduced neutron flux to get improved in this region.
Application of Trotter approximation for solving time dependent neutron transport equation
International Nuclear Information System (INIS)
Stancic, V.
1987-01-01
A method is proposed to solve multigroup time dependent neutron transport equation with arbitrary scattering anisotropy. The recurrence relation thus obtained is simple, numerically stable and especially suitable for treatment of complicated geometries. (author)
International Nuclear Information System (INIS)
Williams, M.M.R.
1985-01-01
A multigroup formalism is developed for the backward-forward-isotropic scattering model of neutron transport. Some exact solutions are obtained in two-group theory for slab and spherical geometry. The results are useful for benchmark problems involving multigroup anisotropic scattering. (author)
Energy Technology Data Exchange (ETDEWEB)
Abramson - Szteinsznaider, D [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires
1961-07-01
- The aim of this work is to see if this reaction occurs only by compound nucleus formation or involves some contribution of direct interaction. In the first case, the angular distribution of inelastic neutrons is symmetric about 90 degree. In the second case, this distribution must be asymmetric and must change slowly with energy of incident neutrons. The neutrons corresponding at the excitation of a given level of the residual nucleus are selected by their coincidence with the {gamma} rays of deexcitation of this level. From the results of our measurements on iron, iodine and bismuth and of other laboratories on different elements, we can conclude that generally, the inelastic scattering of neutrons of some MeV occurs only by compound nucleus. (author) [French] - Le but de ce travail est de determiner si cette reaction s'effectue uniquement par passage par un noyau compose ou fait intervenir un processus d'interaction directe. Dans le premier cas, la distribution angulaire des neutrons inelastiques est symetrique par rapport a 90 degree. Dans le deuxieme cas, cette distribution doit etre asymetrique et doit varier lentement avec l'energie des neutrons incidents. Les neutrons correspondant a l'excitation d'un niveau determine du residuel sont selectionnes par leur cofncidence avec les rayonnements {gamma} de desexcitation de ce niveau. D'apres les resultats de nos mesures sur le fer, l'iode et le bismuth et de celles des autres laboratoires sur differents elements, nous pouvons conclure que, en general, la diffusion inelastique des neutrons de quelques MeV s'effectue uniquement par noyau compose. (auteur)
Neutron cross section libraries for analysis of fusion neutronics experiments
International Nuclear Information System (INIS)
Kosako, Kazuaki; Oyama, Yukio; Maekawa, Hiroshi; Nakamura, Tomoo
1988-03-01
We have prepared two computer code systems producing neutron cross section libraries to analyse fusion neutronics experiments. First system produces the neutron cross section library in ANISN format, i.e., the multi-group constants in group independent format. This library can be obtained by using the multi-group constant processing code system MACS-N and the ANISN format cross section compiling code CROKAS. Second system is for the continuous energy cross section library for the MCNP code. This library can be obtained by the nuclear data processing system NJOY which generates pointwise energy cross sections and the cross section compiling code MACROS for the MCNP library. In this report, we describe the production procedures for both types of the cross section libraries, and show six libraries with different conditions in ANISN format and a library for the MCNP code. (author)
International Nuclear Information System (INIS)
Boufraqech, A.
1991-01-01
Two methods for determining the diffusion parameters of thermal neutrons for non-moderator and non-multiplicator media have been developped: The first one, which is a pulsed method, is based on thermal neutrons relaxation coefficients measurement in a moderator, with and without the medium of interest that plays the role of reflector. For the experimental results interpretation using the diffusion theory, a corrective factor which takes into account the neutron cooling by diffusion has been introduced. Its dependence on the empirically obtained relaxation coefficients is in a good agreement with the calculations made in P3L2 approximation. The difference between linear extrapolation lengths of the moderator and the reflector has been taken into account, by developping the scalar fluxes in Bessel function series which automatically satisfy the boundary conditions at the extra-polated surfaces of the two media. The obtained results for Iron are in a good agreement with those in the literature. The second method is time independent, based on the 'flux albedo' measurements interpretation (Concept introduced by Amaldi and Fermi) by P3 approximation in the one group trans-port theory. The independent sources are introduced in the Marshak boundary conditions. An angular albedo matrix has been used to deal with multiple reflections and to take into account the distortion of the current vector when entring a medium, after being reflected by this latter. The results obtained by this method are slightly different from those given in the literature. The analysis of the possible sources causing this discrepancy, particulary the radial distribution of flux in cylindrical geometry and the flux depression at medium-black body interface, has shown that the origin of this discrepancy is the neutron heating by diffusion. 47 figs., 20 tabs., 39 refs. (author)
Deuterium short-range order in Pd0.975Ag0.025D0.685 by diffuse neutron scattering
DEFF Research Database (Denmark)
Blaschko, O.; Klemencic, R.; Fratzl, P.
1983-01-01
By diffuse neutron scattering the D short-range order in a Pd0.975Ag0.025D0.685 crystal was investigated at 50 and 70K. The results are compared with the D ordering in the PdDx system previously investigated, and it is shown that the isointensity contours around the (1/2,1,0) point are similar...