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
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)
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)
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)
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)
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)
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
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
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
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)
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
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
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
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
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
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
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)
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
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)
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)
Clancy, B.E.
1982-05-01
ANAUSN is a general purpose, one-dimensional discrete ordinate transport theory program which has access to AUS datapools. Fixed source, reactivity and a variety of criticality search calculations can be performed. The program can be operated as a module in the AUS scheme or as a stand-alone program
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)
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
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.
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)
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)
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
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.
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)
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)
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
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)
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)
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
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)
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
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)
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)
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
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
International Nuclear Information System (INIS)
Berthoud, Georges; Ducros, Gerard; Feron, Damien; Guerin, Yannick; Latge, Christian; Limoge, Yves; Santarini, Gerard; Seiler, Jean-Marie; Vernaz, Etienne; Coste-Delclaux, Mireille; M'Backe Diop, Cheikh; Nicolas, Anne; Andrieux, Catherine; Archier, Pascal; Baudron, Anne-Marie; Bernard, David; Biaise, Patrick; Blanc-Tranchant, Patrick; Bonin, Bernard; Bouland, Olivier; Bourganel, Stephane; Calvin, Christophe; Chiron, Maurice; Damian, Frederic; Dumonteil, Eric; Fausser, Clement; Fougeras, Philippe; Gabriel, Franck; Gagnier, Emmanuel; Gallo, Daniele; Hudelot, Jean-Pascal; Hugot, Francois-Xavier; Dat Huynh, Tan; Jouanne, Cedric; Lautard, Jean-Jacques; Laye, Frederic; Lee, Yi-Kang; Lenain, Richard; Leray, Sylvie; Litaize, Olivier; Magnaud, Christine; Malvagi, Fausto; Mijuin, Dominique; Mounier, Claude; Naury, Sylvie; Nicolas, Anne; Noguere, Gilles; Palau, Jean-Marc; Le Pallec, Jean-Charles; Peneliau, Yannick; Petit, Odile; Poinot-Salanon, Christine; Raepsaet, Xavier; Reuss, Paul; Richebois, Edwige; Roque, Benedicte; Royer, Eric; Saint-Jean, Cyrille de; Santamarina, Alain; Serot, Olivier; Soldevila, Michel; Tommasi, Jean; Trama, Jean-Christophe; Tsilanizara, Aime; Behar, Christophe; Provitina, Olivier; Lecomte, Michael; Forestier, Alain; Bender, Alexandra; Parisot, Jean-Francois; Finot, Pierre
2013-10-01
This bibliographical note presents a reference book which addresses the study of neutron transport in matter, the study of conditions for a chain reaction and the study of modifications of matter composition due to nuclear reactions. This book presents the main nuclear data, their measurement, assessment and processing, and the spallation. It proposes an overview of methods applied for the study of neutron transport: basic equations and their derived forms, deterministic methods and Monte Carlo method of resolution of the Boltzmann equation, methods of resolution of generalized Bateman equations, methods of time resolution of space kinetics coupled equations. It presents the main calculation codes, discusses the qualification and experimental aspects, and gives an overview of neutron transport applications: neutron transport calculation of reactors, neutron transport coupled with other disciplines, physics of fuel cycle, criticality
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%
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)
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
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)
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
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
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
From Fourier Transforms to Singular Eigenfunctions for Multigroup Transport
International Nuclear Information System (INIS)
Ganapol, B.D.
2001-01-01
A new Fourier transform approach to the solution of the multigroup transport equation with anisotropic scattering and isotropic source is presented. Through routine analytical continuation, the inversion contour is shifted from the real line to produce contributions from the poles and cuts in the complex plane. The integrand along the branch cut is then recast in terms of matrix continuum singular eigenfunctions, demonstrating equivalence of Fourier transform inversion and the singular eigenfunction expansion. The significance of this paper is that it represents the initial step in revealing the intimate connection between the Fourier transform and singular eigenfunction approaches as well as serves as a basis for a numerical algorithm
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.
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
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
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
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
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)
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.)
Discrete formulation for two-dimensional multigroup neutron diffusion equations
Energy Technology Data Exchange (ETDEWEB)
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
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
Energy Technology Data Exchange (ETDEWEB)
Coste-Delclaux, M
2006-03-15
This document describes the improvements carried out for modelling the self-shielding phenomenon in the multigroup transport code APOLLO2. They concern the space and energy treatment of the slowing-down equation, the setting up of quadrature formulas to calculate reaction rates, the setting-up of a method that treats directly a resonant mixture and the development of a sub-group method. We validate these improvements either in an elementary or in a global way. Now, we obtain, more accurate multigroup reaction rates and we are able to carry out a reference self-shielding calculation on a very fine multigroup mesh. To end, we draw a conclusion and give some prospects on the remaining work. (author)
Energy Technology Data Exchange (ETDEWEB)
Coste-Delclaux, M
2006-03-15
This document describes the improvements carried out for modelling the self-shielding phenomenon in the multigroup transport code APOLLO2. They concern the space and energy treatment of the slowing-down equation, the setting up of quadrature formulas to calculate reaction rates, the setting-up of a method that treats directly a resonant mixture and the development of a sub-group method. We validate these improvements either in an elementary or in a global way. Now, we obtain, more accurate multigroup reaction rates and we are able to carry out a reference self-shielding calculation on a very fine multigroup mesh. To end, we draw a conclusion and give some prospects on the remaining work. (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)
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)
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
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)
Benchmark calculations in multigroup and multidimensional time-dependent transport
International Nuclear Information System (INIS)
Ganapol, B.D.; Musso, E.; Ravetto, P.; Sumini, M.
1990-01-01
It is widely recognized that reliable benchmarks are essential in many technical fields in order to assess the response of any approximation to the physics of the problem to be treated and to verify the performance of the numerical methods used. The best possible benchmarks are analytical solutions to paradigmatic problems where no approximations are actually introduced and the only error encountered is connected to the limitations of computational algorithms. Another major advantage of analytical solutions is that they allow a deeper understanding of the physical features of the model, which is essential for the intelligent use of complicated codes. In neutron transport theory, the need for benchmarks is particularly great. In this paper, the authors propose to establish accurate numerical solutions to some problems concerning the migration of neutron pulses. Use will be made of the space asymptotic theory, coupled with a Laplace transformation inverted by a numerical technique directly evaluating the inversion integral
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)
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
Multigroup calculations of low-energy neutral transport in tokamak plasmas
International Nuclear Information System (INIS)
Gilligan, J.G.; Gralnick, S.L.; Price, W.G. Jr.; Kammash, T.
1978-01-01
Multigroup discrete ordinates methods avoid many of the approximations that have been used in previous neutral transport analyses. Of particular interest are the neutral profiles generated as an integral part of larger plasma system simulation codes. To determine the appropriateness of utilizing a particular multigroup code, ANISN, for this purpose, results are compared with the neutral transport module of the Duechs code. For a typical TFTR plasma, predicted neutral densities differ by a maximum factor of three on axis and outfluxes at the plasma boundary by approximately 40%. This is found to be significant for a neutral transport module. Possible sources of the observed discrepancies are indicated from an analysis of the approximations used in the Duechs model. Recommendations are made concerning the future application of the multigroup method. (author)
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.
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.
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)
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)
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)
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)
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.
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)
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)
International Nuclear Information System (INIS)
Kobayashi, Keisuke; Kikuchi, Hirohiko; Tsutsuguchi, Ken
1993-01-01
A neutron multigroup transport equation in x-y-z geometry is solved by the spherical harmonics method using finite Fourier transformation. Using the first term of the Fourier series for the space variables of spherical harmonics moments, three-point finite difference like equations are derived for x-, y- and z-axis directions, which are more consistent and accurate than those derived using the usual finite difference approximation, and these equations are solved by the iteration method in each axis direction alternatively. A method to find an optimum acceleration factor for this inner iteration is described. It is shown in the numerical examples that the present method gives higher accuracy with less mesh points that the usual finite difference method. (author)
International Nuclear Information System (INIS)
Yamano, Naoki; Minami, Kazuyoshi; Koyama, Kinji; Naito, Yoshitaka.
1989-03-01
A modular code system RADHEAT-V4 has been developed for performing precisely neutron and photon transport analyses, and shielding safety evaluations. The system consists of the functional modules for producing coupled multi-group neutron and photon cross section sets, for analyzing the neutron and photon transport, and for calculating the atom displacement and the energy deposition due to radiations in nuclear reactor or shielding material. A precise method named Direct Angular Representation (DAR) has been developed for eliminating an error associated with the method of the finite Legendre expansion in evaluating angular distributions of cross sections and radiation fluxes. The DAR method implemented in the code system has been described in detail. To evaluate the accuracy and applicability of the code system, some test calculations on strong anisotropy problems have been performed. From the results, it has been concluded that RADHEAT-V4 is successfully applicable to evaluating shielding problems accurately for fission and fusion reactors and radiation sources. The method employed in the code system is very effective in eliminating negative values and oscillations of angular fluxes in a medium having an anisotropic source or strong streaming. Definitions of the input data required in various options of the code system and the sample problems are also presented. (author)
Neutron transportation simulator
International Nuclear Information System (INIS)
Uenohara, Yuzo.
1995-01-01
In the present invention, problems in an existent parallelized monte carlo method is solved, and behaviors of neutrons in a large scaled system are accurately simulated at a high speed. Namely, a neutron transportation simulator according to the monte carlo method simulates movement of each of neutrons by using a parallel computer. In this case, the system to be processed is divided based on a space region and an energy region to which neutrons belong. Simulation of neutrons in the divided regions is allotted to each of performing devices of the parallel computer. Tarry data and nuclear data of the neutrons in each of the regions are memorized dispersedly to memories of each of the performing devices. A transmission means for simulating the behaviors of the neutrons in the region by each of the performing devices, as well as transmitting the information of the neutrons, when the neutrons are moved to other region, to the performing device in a transported portion are disposed to each of the performing devices. With such procedures, simulation for the neutrons in the allotted region can be conducted with small capacity of memories. (I.S.)
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)
Olson, Gordon L.
2016-01-01
One-dimensional models for the transport of radiation through binary stochastic media do not work in multi-dimensions. Authors have attempted to modify or extend the 1D models to work in multidimensions without success. Analytic one-dimensional models are successful in 1D only when assuming greatly simplified physics. State of the art theories for stochastic media radiation transport do not address multi-dimensions and temperature-dependent physics coefficients. Here, the concept of effective opacities and effective heat capacities is found to well represent the ensemble averaged transport solutions in cases with gray or multigroup temperature-dependent opacities and constant or temperature-dependent heat capacities. In every case analyzed here, effective physics coefficients fit the transport solutions over a useful range of parameter space. The transport equation is solved with the spherical harmonics method with angle orders of n=1 and 5. Although the details depend on what order of solution is used, the general results are similar, independent of angular order. - Highlights: • Gray and multigroup radiation transport is done through 2D stochastic media. • Approximate models for the mean radiation field are found for all test problems. • Effective opacities are adjusted to fit the means of stochastic media transport. • Test problems include temperature dependent opacities and heat capacities • Transport solutions are done with angle orders n=1 and 5.
International Nuclear Information System (INIS)
Mosca, P.
2009-12-01
The deterministic transport codes solve the stationary Boltzmann equation in a discretized energy formalism called multigroup. The transformation of continuous data in a multigroup form is obtained by averaging the highly variable cross sections of the resonant isotopes with the solution of the self-shielding models and the remaining ones with the coarse energy spectrum of the reactor type. So far the error of such an approach could only be evaluated retrospectively. To remedy this, we studied in this thesis a set of methods to control a priori the accuracy and the cost of the multigroup transport computation. The energy mesh optimisation is achieved using a two step process: the creation of a reference mesh and its optimized condensation. In the first stage, by refining locally and globally the energy mesh, we seek, on a fine energy mesh with subgroup self-shielding, a solution equivalent to a reference solver (Monte Carlo or pointwise deterministic solver). In the second step, once fixed the number of groups, depending on the acceptable computational cost, and chosen the most appropriate self-shielding models to the reactor type, we look for the best bounds of the reference mesh minimizing reaction rate errors by the particle swarm optimization algorithm. This new approach allows us to define new meshes for fast reactors as accurate as the currently used ones, but with fewer groups. (author)
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
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)
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
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.)
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)
The transport of neutrons and gamma-rays in the air
International Nuclear Information System (INIS)
Adamski, J.
1980-01-01
The transport of neutrons and gamma rays in the infinite homogeneous air has been investigated. For the calculations has been used the Multigroup One Dimensional Discrete Ordinates Transport Code ANISN-W. The calculations have been performed for three types of neutron sources. The neutrons and gamma ray doses in the air have been analyzed, and comparison to the other authors' results has been given. (author)
Multigroup adjoint transport solution using the method of cyclic characteristics
International Nuclear Information System (INIS)
Assawaroongruengchot, M.; Marleau, G.
2005-01-01
The adjoint transport solution algorithm based on the method of cyclic characteristics (MOCC) is developed for the heterogeneous 2-dimensional geometries. The adjoint characteristics equation associated with a cyclic tracking line is formulated, then a closed form for adjoint angular flux can be determined. The acceleration techniques are implemented using the group-reduction and group-splitting techniques. To demonstrate the efficacy of the algorithm, the calculations are performed on the 17*17 PWR and Watanabe-Maynard benchmark problems. Comparisons of adjoint flux and k eff results obtained by MOCC and collision probability (CP) methods are performed. The mathematical relationship between pseudo-adjoint flux obtained by CP method and adjoint flux by MOCC method is presented. It appears that the pseudo-adjoint flux by CP method is equivalent to the adjoint flux by MOCC method and that the MOCC method requires lower computing time than the CP method for a single adjoint flux calculation
Multigroup adjoint transport solution using the method of cyclic characteristics
Energy Technology Data Exchange (ETDEWEB)
Assawaroongruengchot, M.; Marleau, G. [Ecole Polytechnique de Montreal, Institut de Genie Nucleaire, Montreal, Quebec (Canada)
2005-07-01
The adjoint transport solution algorithm based on the method of cyclic characteristics (MOCC) is developed for the heterogeneous 2-dimensional geometries. The adjoint characteristics equation associated with a cyclic tracking line is formulated, then a closed form for adjoint angular flux can be determined. The acceleration techniques are implemented using the group-reduction and group-splitting techniques. To demonstrate the efficacy of the algorithm, the calculations are performed on the 17*17 PWR and Watanabe-Maynard benchmark problems. Comparisons of adjoint flux and k{sub eff} results obtained by MOCC and collision probability (CP) methods are performed. The mathematical relationship between pseudo-adjoint flux obtained by CP method and adjoint flux by MOCC method is presented. It appears that the pseudo-adjoint flux by CP method is equivalent to the adjoint flux by MOCC method and that the MOCC method requires lower computing time than the CP method for a single adjoint flux calculation.
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
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.
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.
Hydrogen transport in a toroidal plasma using multigroup discrete-ordinates methodology
International Nuclear Information System (INIS)
Wienke, B.R.; Miller, W.F. Jr.; Seed, T.J.
1979-01-01
Neutral hydrogen transport in a fully ionized two-dimensional tokamak plasma was examined using discrete ordinates and contrasted with earlier analyses. In particular, curvature effects induced by toroidal geometries and ray effects caused by possible source localization were investigated. From an overview of the multigroup discrete-ordinates approximation, methodology in two-dimensional cylindrical geometry is detailed, mesh and plasma zoning procedures are sketched, and the piecewise polynomial solution algorithm on a triangular domain is obtained. Toroidal effects and comparisons as related to reaction rates and perticle spectra are examined for various model and source configurations
Energy Technology Data Exchange (ETDEWEB)
Stancic, V [Institut za nuklearne nauke Boris Kidric, Vinca, Beograd (Yugoslavia)
1987-07-01
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)
Stankovski, Z.; Zmijarevic, I.
1987-06-01
This paper presents two approximations used in multigroup two-dimensional transport calculations in large, very homogeneous media: isotropic reflection together with recently proposed group-dependent spatial representations. These approximations are implemented as standard options in APOLLO 2 assembly transport code. Presented example calculations show that significant savings in computational costs are obtained while preserving the overall accuracy
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
Variational P1 approximations of general-geometry multigroup transport problems
International Nuclear Information System (INIS)
Rulko, R.P.; Tomasevic, D.; Larsen, E.W.
1995-01-01
A variational approximation is developed for general-geometry multigroup transport problems with arbitrary anisotropic scattering. The variational principle is based on a functional that approximates a reaction rate in a subdomain of the system. In principle, approximations that result from this functional ''optimally'' determine such reaction rates. The functional contains an arbitrary parameter α and requires the approximate solutions of a forward and an adjoint transport problem. If the basis functions for the forward and adjoint solutions are chosen to be linear functions of the angular variable Ω, the functional yields the familiar multigroup P 1 equations for all values of α. However, the boundary conditions that result from the functional depend on α. In particular, for problems with vacuum boundaries, one obtains the conventional mixed boundary condition, but with an extrapolation distance that depends continuously on α. The choice α = 0 yields a generalization of boundary conditions derived earlier by Federighi and Pomraning for a more limited class of problems. The choice α = 1 yields a generalization of boundary conditions derived previously by Davis for monoenergetic problems. Other boundary conditions are obtained by choosing different values of α. The authors discuss this indeterminancy of α in conjunction with numerical experiments
Neutron stochastic transport theory with delayed neutrons
International Nuclear Information System (INIS)
Munoz-Cobo, J.L.; Verdu, G.
1987-01-01
From the stochastic transport theory with delayed neutrons, the Boltzmann transport equation with delayed neutrons for the average flux emerges in a natural way without recourse to any approximation. From this theory a general expression is obtained for the Feynman Y-function when delayed neutrons are included. The single mode approximation for the particular case of a subcritical assembly is developed, and it is shown that Y-function reduces to the familiar expression quoted in many books, when delayed neutrons are not considered, and spatial and source effects are not included. (author)
Energy Technology Data Exchange (ETDEWEB)
Wilcox, T. P.
1973-09-20
The code ANISN-L solves the one-dimensional, multigroup, time-independent Boltzmann transport equation by the method of discrete ordinates. In problems involving a fissionable system, it can calculate the system multiplication or alpha. In such cases, it is also capable of determining isotopic concentrations, radii, zone widths, or buckling in order to achieve a given multiplication or alpha. The code may also calculate fluxes caused by a specified fixed source. Neutron, gamma, and coupled neutron--gamma problems may be solved in either the forward or adjoint (backward) modes. Cross sections describing upscatter, as well as the usual downscatter, may be employed. This report describes the use of ANISN-L; this is a revised version of ANISN which handles both large and small problems efficiently on CDC-7600 computers. (RWR)
International Nuclear Information System (INIS)
Ching, J.; Oblow, E.M.; Goldstein, H.
1976-01-01
An algebraic equivalence between the point-energy and multigroup forms of the Boltzmann transport equation is demonstrated that allows the development of a discrete energy, discrete ordinates method for the solution of radiation transport problems. In the discrete energy method, the group averaging required in the cross-section processing for multigroup calculations is replaced by a faster numerical quadrature scheme capable of generating transfer cross sections describing all the physical processes of interest on a fine point-energy grid. Test calculations in which the discrete energy method is compared with the multigroup method show that, for the same energy grid, the discrete energy method is much faster, although somewhat less accurate, than the multigroup method. However, the accuracy of the discrete energy method increases rapidly as the spacing between energy grid points is decreased, approaching that of multigroup calculations. For problems requiring great detail in the energy spectrum, the discrete energy method is therefore expected to be far more economical than the multigroup technique for equivalent accuracy solutions. This advantage of the point method is demonstrated by application to the study of neutron transport in a thick iron slab
Program to solve the multigroup discrete ordinates transport equation in (x,y,z) geometry
International Nuclear Information System (INIS)
Lathrop, K.D.
1976-04-01
Numerical formulations and programming algorithms are given for the THREETRAN computer program which solves the discrete ordinates, multigroup transport equation in (x,y,z) geometry. An efficient, flexible, and general data-handling strategy is derived to make use of three hierarchies of storage: small core memory, large core memory, and disk file. Data management, input instructions, and sample problem output are described. A six-group, S 4 , 18 502 mesh point, 2 800 zone, k/sub eff/ calculation of the ZPPR-4 critical assembly required 144 min of CDC-7600 time to execute to a convergence tolerance of 5 x 10 -4 and gave results in good qualitative agreement with experiment and other calculations. 6 references
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
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
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 ...
A New Monte Carlo Neutron Transport Code at UNIST
International Nuclear Information System (INIS)
Lee, Hyunsuk; Kong, Chidong; Lee, Deokjung
2014-01-01
Monte Carlo neutron transport code named MCS is under development at UNIST for the advanced reactor design and research purpose. This MC code can be used for fixed source calculation and criticality calculation. Continuous energy neutron cross section data and multi-group cross section data can be used for the MC calculation. This paper presents the overview of developed MC code and its calculation results. The real time fixed source calculation ability is also tested in this paper. The calculation results show good agreement with commercial code and experiment. A new Monte Carlo neutron transport code is being developed at UNIST. The MC codes are tested with several benchmark problems: ICSBEP, VENUS-2, and Hoogenboom-Martin benchmark. These benchmarks covers pin geometry to 3-dimensional whole core, and results shows good agreement with reference results
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
International Nuclear Information System (INIS)
Koyama, Kinji; Taji, Yukichi; Miyasaka, Shun-ichi; Minami, Kazuyoshi.
1977-07-01
The modular code system RADHEAT is for producing coupled multigroup neutron and gamma-ray cross section sets, analyzing the neutron and gamma-ray transport, and calculating the energy deposition and atomic displacements due to these radiations in a nuclear reactor or shield. The basic neutron cross sections and secondary gamma-ray production data are taken from ENDF/B and POPOP4 libraries respectively. The system (1) generates multigroup neutron cross sections, energy deposition coefficients and atomic displacement factors due to neutron reactions, (2) generates multigroup gamma-ray cross sections and energy transfer coefficients, (3) generates secondary gamma-ray production cross sections, (4) combines these cross sections into the coupled set, (5) outputs and updates the multigroup cross section libraries in convenient formats for other transport codes, (6) analyzes the neutron and gamma-ray transport and calculates the energy deposition and the number density of atomic displacements in a medium, (7) collapses the cross sections to a broad-group structure, by option, using the weighting functions obtained by one-dimensional transport calculation, and (8) plots, by option, multigroup cross sections, and neutron and gamma-ray distributions. Definitions of the input data required in various options of the code system are also given. (auth.)
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
MINARET: Towards a time-dependent neutron transport parallel solver
International Nuclear Information System (INIS)
Baudron, A.M.; Lautard, J.J.; Maday, Y.; Mula, O.
2013-01-01
We present the newly developed time-dependent 3D multigroup discrete ordinates neutron transport solver that has recently been implemented in the MINARET code. The solver is the support for a study about computing acceleration techniques that involve parallel architectures. In this work, we will focus on the parallelization of two of the variables involved in our equation: the angular directions and the time. This last variable has been parallelized by a (time) domain decomposition method called the para-real in time algorithm. (authors)
Criticality problems in energy dependent neutron transport theory
International Nuclear Information System (INIS)
Victory, H.D. Jr.
1979-01-01
The criticality problem is considered for energy dependent neutron transport in an isotropically scattering, homogeneous slab. Under a positivity assumption on the scattering kernel, an expression can be found relating the thickness of the slab to a parameter characterizing production by fission. This is accomplished by exploiting the Perron-Frobenius-Jentsch characterization of positive operators (i.e. those leaving invariant a normal, reproducing cone in a Banach space). It is pointed out that those techniques work for classes of multigroup problems were the Case singular eigenfunction approach is not as feasible as in the one-group theory, which is also analyzed
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
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)
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
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)
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
An introduction to neutron transport
International Nuclear Information System (INIS)
Wiesenfeld, Bernard
2015-01-01
Neutron transport science is the study of neutron transport in a nuclear reactor and of associated nuclear reactions, notably fission reactions. Heat released by these reactions can be used for several purposes: electricity production, hydrogen production, sea water desalination, urban heating, naval propulsion, space propulsion, and so on. This publication contains the course proposed at Mines ParisTech and at the Arts et Metiers ParisTech. It is an introduction to neutron transport science and aims at presenting fundamental physical principles of this original branch of nuclear physics, a so called 'low energies' branch whereas 'high energy' nuclear physics focuses on elementary particles. It addresses complex computation methods which have been developed during the last decades with computation codes of always higher performance. The first part presents elements of atom physics: origin of matter, properties of nuclei and atoms, notion of quantum mechanics, interaction between radiation and matter (ray absorption, Compton Effect and scattering, photoelectric effect). The second part introduces neutron transport by addressing the following issues: nuclear structure, the various aspects of the interaction between neutrons and matter, the evolution of the reactivity of a reactor in normal operation, the chain fission reaction kinetics, and neutron slowing down. The third part addresses various aspects of neutron transport calculation: expression of neutron assessment, scattering approximation, critical condition of a nuclear reactor, introduction to transport theory, peculiarities of fast breeder reactors. The last chapter 'from theory to practice' addresses the approach of the neutron scientist, proposes an overview of the main calculation codes, and presents fields of application (within or without nuclear fission)
3-D neutron transport benchmarks
International Nuclear Information System (INIS)
Takeda, T.; Ikeda, H.
1991-03-01
A set of 3-D neutron transport benchmark problems proposed by the Osaka University to NEACRP in 1988 has been calculated by many participants and the corresponding results are summarized in this report. The results of K eff , control rod worth and region-averaged fluxes for the four proposed core models, calculated by using various 3-D transport codes are compared and discussed. The calculational methods used were: Monte Carlo, Discrete Ordinates (Sn), Spherical Harmonics (Pn), Nodal Transport and others. The solutions of the four core models are quite useful as benchmarks for checking the validity of 3-D neutron transport codes
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
A method for solving neutron transport equation
International Nuclear Information System (INIS)
Dimitrijevic, Z.
1993-01-01
The procedure for solving the transport equation by directly integrating for case one-dimensional uniform multigroup medium is shown. The solution is expressed in terms of linear combination of function H n (x,μ), and the coefficient is determined from given conditions. The solution is applied for homogeneous slab of critical thickness. (author)
International Nuclear Information System (INIS)
Mori, Takamasa; Nakagawa, Masayuki; Sasaki, Makoto.
1988-11-01
We have developed a group of computer codes to realize the accurate transport calculation by using the multi-group double-differential form cross section. This type of cross section can correctly take account of the energy-angle correlated reaction kinematics. Accordingly, the transport phenomena in materials with highly anisotropic scattering are accurately calculated by using this cross section. They include the following four codes or code systems: PROF-DD : a code system to generate the multi-group double-differential form cross section library by processing basic nuclear data file compiled in the ENDF / B-IV or -V format, ANISN-DD : a one-dimensional transport code based on the discrete ordinate method, DOT-DD : a two-dimensional transport code based on the discrete ordinate method, MORSE-DD : a three-dimensional transport code based on the Monte Carlo method. In addition to these codes, several auxiliary codes have been developed to process calculated results. This report describes the calculation algorithm employed in these codes and how to use them. (author)
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)
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)
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)
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
Linear stochastic neutron transport theory
International Nuclear Information System (INIS)
Lewins, J.
1978-01-01
A new and direct derivation of the Bell-Pal fundamental equation for (low power) neutron stochastic behaviour in the Boltzmann continuum model is given. The development includes correlation of particle emission direction in induced and spontaneous fission. This leads to generalizations of the backward and forward equations for the mean and variance of neutron behaviour. The stochastic importance for neutron transport theory is introduced and related to the conventional deterministic importance. Defining equations and moment equations are derived and shown to be related to the backward fundamental equation with the detector distribution of the operational definition of stochastic importance playing the role of an adjoint source. (author)
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.
GAPER-1D, 1-D Multigroup 1. Order Perturbation Transport Theory for Reactivity Coefficient
International Nuclear Information System (INIS)
Koch, P.K.
1976-01-01
1 - Description of problem or function: Reactivity coefficients are computed using first-order transport perturbation theory for one- dimensional multi-region reactor assemblies. The number of spatial mesh-points and energy groups is arbitrary. An elementary synthesis scheme is employed for treatment of two- and three-dimensional problems. The contributions to the change in inverse multiplication factor, delta(1/k), from perturbations in the individual capture, net fission, total scattering, (n,2n), inelastic scattering, and leakage cross sections are computed. A multi-dimensional prompt neutron lifetime calculation is also available. 2 - Method of solution: Broad group cross sections for the core and perturbing or sample materials are required as input. Scalar neutron fluxes and currents, as computed by SN transport calculations, are then utilized to solve the first-order transport perturbation theory equations. A synthesis scheme is used, along with independent SN calculations in two or three dimensions, to treat a multi- dimensional assembly. Spherical harmonics expansions of the angular fluxes and scattering source terms are used with leakage and anisotropic scattering treated in a P1 approximation. The angular integrations in the perturbation theory equations are performed analytically. Various reactivity coefficients and material worths are then easily computed at specified positions in the assembly. 3 - Restrictions on the complexity of the problem: The formulation of the synthesis scheme used for two- and three-dimensional problems assumes that the fluxes and currents were computed by the DTF4 code (NESC Abstract 209). Therefore, fluxes and currents from two- or three-dimensional transport or diffusion theory codes cannot be used
International Nuclear Information System (INIS)
Rubin, I.E.; Dneprovskaya, N.M.
2005-01-01
A technique for calculation of reactor lattices by means of the transmission probabilities with taking into account the scattering anisotropy is generalized for the multigroup case. The errors of the calculated multiplication coefficients and energy release distributions do noe exceed practically the errors, of these values, obtained by the Monte Carlo method. The proposed method is most effective when determining the small difference effects [ru
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)
Ching, J.T.
1975-01-01
An algebraic equivalence between the point-energy and multigroup forms of the Boltzmann transport equation is demonstrated which allows the development of a discrete-energy, discrete-ordinates method for the solution of radiation transport problems. The method utilizes a modified version of a cross section processing scheme devised for the moments method code BMT and the transport equation solution algorithm from the one-dimensional discrete-ordinates transport code ANISN. The combined system, identified as MOMANS, computes fluxes directly from point cross sections in a single operation. In the cross-section processing, the group averaging required for multigroup calculations is replaced by a fast numerical scheme capable of generating a set of transfer cross sections containing all the physical features of interest, thereby increasing the detail in the calculated results. Test calculations in which the discrete-energy method was compared with the multigroup method have shown that for the same energy grid (number of points = number of groups), the discrete-energy method is faster but somewhat less accurate than the multigroup method. However, the accuracy of the discrete-energy method increases rapidly as the spacing between energy points is decreased, approaching that of multigroup calculations. For problems requiring great detail in the energy spectrum the discrete-energy method has therefore proven to be as accurate as, and more economical than, the multigroup technique. This was demonstrated by the application of the method to the study of the transport of neutrons in an iron sphere. Using the capability of the discrete-energy method for rapidly treating changes in cross-section sets, the propagation of neutrons from a 14 MeV source in a 22 cm radius sphere of iron was analyzed for sensitivity to changes in the microscopic scattering mechanisms
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
Energy Technology Data Exchange (ETDEWEB)
Barcellos, Luiz Felipe F.C.; Bodmann, Bardo E.J.; Vilhena, Marco T.M.B., E-mail: luizfelipe.fcb@gmail.com, E-mail: bardo.bodmann@ufrgs.br, E-mail: mtmbvilhena@gmail.com [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Grupo de Estudos Nucleares; Leite, Sergio Q. Bogado, E-mail: sbogado@ibest.com.br [Comissao Nacional de Energia Nuclear (CNEN), Rio de Janeiro, RJ (Brazil)
2017-07-01
In this work a Monte Carlo simulator with continuous energy is used. This simulator distinguishes itself by using the sum of three probability distributions to represent the neutron spectrum. Two distributions have known shape, but have varying population of neutrons in time, and these are the fission neutron spectrum (for high energy neutrons) and the Maxwell-Boltzmann distribution (for thermal neutrons). The third distribution has an a priori unknown and possibly variable shape with time and is determined from parametrizations of Monte Carlo simulation. It is common practice in neutron transport calculations, e.g. multi-group transport, to consider that the neutrons only lose energy with each scattering reaction and then to use a thermal group with a Maxwellian distribution. Such an approximation is valid due to the fact that for fast neutrons up-scattering occurrence is irrelevant, being only appreciable at low energies, i.e. in the thermal energy region, in which it can be regarded as a Maxwell-Boltzmann distribution for thermal equilibrium. In this work the possible neutron-matter interactions are simulated with exception of the up-scattering of neutrons. In order to preserve the thermal spectrum, neutrons are selected stochastically as being part of the thermal population and have an energy attributed to them taken from a Maxwellian distribution. It is then shown how this procedure can emulate the up-scattering effect by the increase in the neutron population kinetic energy. Since the simulator uses tags to identify the reactions it is possible not only to plot the distributions by neutron energy, but also by the type of interaction with matter and with the identification of the target nuclei involved in the process. This work contains some preliminary results obtained from a Monte Carlo simulator for neutron transport that is being developed at Federal University of Rio Grande do Sul. (author)
International Nuclear Information System (INIS)
Hoogenboom, J. Eduard
2003-01-01
Adjoint Monte Carlo may be a useful alternative to regular Monte Carlo calculations in cases where a small detector inhibits an efficient Monte Carlo calculation as only very few particle histories will cross the detector. However, in general purpose Monte Carlo codes, normally only the multigroup form of adjoint Monte Carlo is implemented. In this article the general methodology for continuous-energy adjoint Monte Carlo neutron transport is reviewed and extended for photon and coupled neutron-photon transport. In the latter cases the discrete photons generated by annihilation or by neutron capture or inelastic scattering prevent a direct application of the general methodology. Two successive reaction events must be combined in the selection process to accommodate the adjoint analog of a reaction resulting in a photon with a discrete energy. Numerical examples illustrate the application of the theory for some simplified problems
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.
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.
Neutron measurement by transportable spectrometer
International Nuclear Information System (INIS)
Anon.
1990-01-01
Two levels of neutron spectrometry are in regular use at nuclear power plants: some techniques used in the laboratory produce detailed spectra but require specialist operators, while simple instruments used by non-specialists to measure the neutron dose-rate to operators provide little spectral information. The standard portable instruments are therefore of no use when anomalous readings are obtained which require further investigation. AEA Technology at Winfrith has developed a Transportable Neutron Spectrometer (TNS) which is designed to produce reasonable spectra in routine use by staff with no specialist skill in spectroscopy, and high-quality spectra in the hands of skilled staff. The TNS provides a level of information intermediate between those currently available, and is also designed to solve the problem of imperfect dose response which is common in portable dosimeters. The TNS system consists of a power supply, a probe and a signal processing and data acquisition unit. (author)
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
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
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)
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)
International Nuclear Information System (INIS)
Devillers, C.
1973-01-01
1 - Nature of physical problem solved: The ANISN system treats neutron and gamma transport in one-dimensional plane, spherical and cylinder geometry. The multigroup cross sections prepared by the programs LIANE and SUPERTOG are processed by the program RETTOG, which produces a binary library with Legendre expansions. The binary library can be updated and edited with the program LGR/B. The photon multigroup cross sections are created with the program GAMLEG/A. If the bulk of the data is too large, the program TAPEMA produces a special group-by-group library. The volume sources are calculated from a reduced set of input data and punched in a format suitable for input to ANISN, using the program PRESOU. The program ANISN calculates fluxes by groups, space intervals, angle and any number of reaction rates. The energy and space dependent fluxes are stored on tape and can be reprocessed, edited and plotted with the program ANISEX, which also permits to calculate supplementary reaction rates. The program ANISN can condense cross sections into a reduced number of groups. The ANISN system is used as a reference system for the evaluation of approximation methods (space-diffusion or point- kernel) or for the preparation of multigroup libraries for 2- dimensional transport codes (DOT). In particular it is used for shielding problems with high attenuation in water reactors and fast reactors. 2 - Method of solution: Method of discrete ordinates. The program has been designed to treat deep penetration with detailed calculation of spectrum as function of angle. Tests for pointwise convergence have also been introduced. 3 - Restrictions on the complexity of the problem: The complexity of the problem is limited by the storage size
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.
Monte Carlo simulation of neutron transport phenomena
International Nuclear Information System (INIS)
Srinivasan, P.
2009-01-01
Neutron transport is one of the central problems in nuclear reactor related studies and other applied sciences. Some of the major applications of neutron transport include nuclear reactor design and safety, criticality safety of fissile material handling, neutron detector design and development, nuclear medicine, assessment of radiation damage to materials, nuclear well logging, forensic analysis etc. Most reactor and dosimetry studies assume that neutrons diffuse from regions of high to low density just like gaseous molecules diffuse to regions of low concentration or heat flow from high to low temperature regions. However while treatment of gaseous or heat diffusion is quite accurately modeled, treatment of neutron transport as simple diffusion is quite limited. In simple diffusion, the neutron trajectories are irregular, random and zigzag - where as in neutron transport low reaction cross sections (1 barn- 10 -24 cm 2 ) lead to long mean free paths which again depend on the nature and irregularities of the medium. Hence a more accurate representation of the neutron transport evolved based on the Boltzmann equation of kinetic gas theory. In fact the neutron transport equation is a linearized version of the Boltzmann gas equation based on neutron conservation with seven independent variables. The transport equation is difficult to solve except in simple cases amenable to numerical methods. The diffusion (equation) approximation follows from removing the angular dependence of the neutron flux
Killing symmetries in neutron transport
International Nuclear Information System (INIS)
Lukacs, B.; Racz, A.
1992-10-01
Although inside the reactor zone there is no exact continuous spatial symmetry, in certain configurations neutron flux distribution is close to a symmetrical one. In such cases the symmetrical solution could provide a good starting point to determine the non-symmetrical power distribution. All possible symmetries are determined in the 3-dimensional Euclidean space, and the form of the transport equation is discussed in such a coordinate system which is adapted to the particular symmetry. Possible spontaneous symmetry breakings are pointed out. (author) 6 refs
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.
ZZ AIRFEWG, Gamma, Neutron Transport Calculation in Air Using FEWG1 Cross-Section
International Nuclear Information System (INIS)
1985-01-01
1 - Description of program or function: Format: ANISN; Number of groups: 37 neutron / 21 gamma-ray; Nuclides: air (79% N and 21% O); Origin: DLC-0031/FEWG1 cross sections (ENDF/B-IV). Weighting spectrum: 1/E. The AIRFEWG library has been generated by an ANISN multigroup calculation of gamma-ray, neutron, and secondary gamma-ray transport in infinite homogeneous air using DLC-0031/FEWG1 cross sections. 2 - Method of solution: The results were generated with a P3, ANISN run with a source in a single energy group. Thus, 58 such runs were required. For sources in the 37 neutron groups, both neutron and secondary gamma-ray fluence results were calculated. For gamma-ray sources only gamma-ray fluences were calculated
MC++: A parallel, portable, Monte Carlo neutron transport code in C++
International Nuclear Information System (INIS)
Lee, S.R.; Cummings, J.C.; Nolen, S.D.
1997-01-01
MC++ is an implicit multi-group Monte Carlo neutron transport code written in C++ and based on the Parallel Object-Oriented Methods and Applications (POOMA) class library. MC++ runs in parallel on and is portable to a wide variety of platforms, including MPPs, SMPs, and clusters of UNIX workstations. MC++ is being developed to provide transport capabilities to the Accelerated Strategic Computing Initiative (ASCI). It is also intended to form the basis of the first transport physics framework (TPF), which is a C++ class library containing appropriate abstractions, objects, and methods for the particle transport problem. The transport problem is briefly described, as well as the current status and algorithms in MC++ for solving the transport equation. The alpha version of the POOMA class library is also discussed, along with the implementation of the transport solution algorithms using POOMA. Finally, a simple test problem is defined and performance and physics results from this problem are discussed on a variety of platforms
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)
Some improved methods in neutron transport theory
Energy Technology Data Exchange (ETDEWEB)
Pop-Jordanov, J; Stefanovic, D; Kocic, A; Matausek, M; Bosevski, T [Boris Kidric Institute of Nuclear Sciences Vinca, Beograd (Yugoslavia)
1973-07-01
The methods described in this paper are: analytical approach to neutron spectra in case of energy dependent anisotropy of elastic scattering; Monte Carlo estimations of neutron absorption reaction rate during slowing down process; spherical harmonics treatment of space-angle-lethargy dependent slowing down transport equation; integral transport theory based on point-wise representation of variables.
International Nuclear Information System (INIS)
Hong, Ser Gi; Lee, Deokjung
2015-01-01
A highly accurate S 4 eigenfunction-based nodal method has been developed to solve multi-group discrete ordinate neutral particle transport problems with a linearly anisotropic scattering in slab geometry. The new method solves the even-parity form of discrete ordinates transport equation with an arbitrary S N order angular quadrature using two sub-cell balance equations and the S 4 eigenfunctions of within-group transport equation. The four eigenfunctions from S 4 approximation have been chosen as basis functions for the spatial expansion of the angular flux in each mesh. The constant and cubic polynomial approximations are adopted for the scattering source terms from other energy groups and fission source. A nodal method using the conventional polynomial expansion and the sub-cell balances was also developed to be used for demonstrating the high accuracy of the new methods. Using the new methods, a multi-group eigenvalue problem has been solved as well as fixed source problems. The numerical test results of one-group problem show that the new method has third-order accuracy as mesh size is finely refined and it has much higher accuracies for large meshes than the diamond differencing method and the nodal method using sub-cell balances and polynomial expansion of angular flux. For multi-group problems including eigenvalue problem, it was demonstrated that the new method using the cubic polynomial approximation of the sources could produce very accurate solutions even with large mesh sizes. (author)
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.
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
TWOTRAN-2, 2-D Multigroup Transport in X-Y, R-Z, R-Theta Geometry with Anisotropic Scattering
International Nuclear Information System (INIS)
Lathrop, K.D.; Brinkley, F.W.
1995-01-01
1 - Description of problem or function: TWOTRAN2 solves the two-dimensional multigroup transport equation in (x,y), (r,theta), and (r,z) geometries. Both regular and adjoint, inhomogeneous and homogeneous (k eff and eigenvalue searches) problems subject to vacuum, reflective, periodic, white or input-specified 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 in finite difference form which is solved with the central (diamond) difference approximation. Negative fluxes are eliminated by a local set-to zero and correct algorithm. Standard inner (within-group) and outer iterative cycles are accelerated by a coarse-mesh re-balancing on a coarse mesh which may be independent of the material mesh. 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 MAXLEN can be accommodated. On IBM machines, TWOTRAN2 will execute in the 4-byte mode so that any combination of problem parameters leading to a container array less than MAXLEN can be accommodated. MAXLEN can be several hundred thousand and most problems can be core-contained. On the CDC machines MAXLEN can be slightly greater than 40,000 words and peripheral storage is used for most group-dependent data
Multigroup Boltzmann-Fokker-Planck approach for ion transport in amorphous media
Energy Technology Data Exchange (ETDEWEB)
Keen, N.D.; Prinja, A.K.; Dunham, G.D. [New Mexico Univ., Albuquerque, NM (United States). Chemical and Nuclear Engineering Dept.
2001-07-01
We present a MGMC approach for the transport of arbitrary mass ions having energies up to a few MeV. Specifically, we consider interactions with target atoms through Coulomb mediated elastic nuclear and inelastic electronic collisions and restrict considerations to ion implantation and energy deposition of primary ions in amorphous media. (orig.)
RTk/SN Solutions of the Two-Dimensional Multigroup Transport Equations in Hexagonal Geometry
International Nuclear Information System (INIS)
Valle, Edmundo del; Mund, Ernest H.
2004-01-01
This paper describes an extension to the hexagonal geometry of some weakly discontinuous nodal finite element schemes developed by Hennart and del Valle for the two-dimensional discrete ordinates transport equation in quadrangular geometry. The extension is carried out in a way similar to the extension to the hexagonal geometry of nodal element schemes for the diffusion equation using a composite mapping technique suggested by Hennart, Mund, and del Valle. The combination of the weakly discontinuous nodal transport scheme and the composite mapping is new and is detailed in the main section of the paper. The algorithm efficiency is shown numerically through some benchmark calculations on classical problems widely referred to in the literature
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)
Garcia, R.D.M.
1985-01-01
The generalization of a semi-analytical technique for the evaluation of angular integrals that appear in the generation of elastic and discrete inelastic tranfer matrices for transport codes is carried out. In contrast to the generalized series expansions which are found to be too complex and thus of little practical value, when compared to the Gaussian quadrature technique, the recursion relations developed in this work are superior to the quadrature scheme, for those cases where the round-off error propagation is not significant. (Author) [pt
A portable, parallel, object-oriented Monte Carlo neutron transport code in C++
International Nuclear Information System (INIS)
Lee, S.R.; Cummings, J.C.; Nolen, S.D.
1997-01-01
We have developed a multi-group Monte Carlo neutron transport code using C++ and the Parallel Object-Oriented Methods and Applications (POOMA) class library. This transport code, called MC++, currently computes k and α-eigenvalues and is portable to and runs parallel on a wide variety of platforms, including MPPs, clustered SMPs, and individual workstations. It contains appropriate classes and abstractions for particle transport and, through the use of POOMA, for portable parallelism. Current capabilities of MC++ are discussed, along with physics and performance results on a variety of hardware, including all Accelerated Strategic Computing Initiative (ASCI) hardware. Current parallel performance indicates the ability to compute α-eigenvalues in seconds to minutes rather than hours to days. Future plans and the implementation of a general transport physics framework are also discussed
Exact solution of the neutron transport equation in spherical geometry
Energy Technology Data Exchange (ETDEWEB)
Anli, Fikret; Akkurt, Abdullah; Yildirim, Hueseyin; Ates, Kemal [Kahramanmaras Suetcue Imam Univ. (Turkey). Faculty of Sciences and Letters
2017-03-15
Solution of the neutron transport equation in one dimensional slab geometry construct a basis for the solution of neutron transport equation in a curvilinear geometry. Therefore, in this work, we attempt to derive an exact analytical benchmark solution for both neutron transport equations in slab and spherical medium by using P{sub N} approximation which is widely used in neutron transport theory.
Solving the multigroup adjoint transport equations using the method of cyclic characteristics
Energy Technology Data Exchange (ETDEWEB)
Assawaroongruengchot, M.; Marleau, G. [Ecole Polytechnique de Montreal, Inst. de genie nucleaire, Montreal, Quebec (Canada)]. E-mail: monchai.assawar@polymtl.ca
2005-07-01
The adjoint transport solution algorithm based on the method of cyclic characteristics (MOCC) is developed for the heterogeneous 2D geometries. The adjoint characteristics equation associated with a cyclic tracking line is formulated, then a closed form for adjoint angular flux can be determined. The acceleration techniques are implemented using the group-reduction and group-splitting techniques. To demonstrate the efficacy of the algorithm, the calculations are performed on the 37 pin CANDU cell and on the Watanabe-Maynard benchmark problem. Comparisons of adjoint flux and k{sub eff} results obtained by MOCC and collision probability (CP) methods are performed. The mathematical relationship between pseudo-adjoint flux obtained by CP method and adjoint flux by MOCC method is presented. (author)
Solving the multigroup adjoint transport equations using the method of cyclic characteristics
International Nuclear Information System (INIS)
Assawaroongruengchot, M.; Marleau, G.
2005-01-01
The adjoint transport solution algorithm based on the method of cyclic characteristics (MOCC) is developed for the heterogeneous 2D geometries. The adjoint characteristics equation associated with a cyclic tracking line is formulated, then a closed form for adjoint angular flux can be determined. The acceleration techniques are implemented using the group-reduction and group-splitting techniques. To demonstrate the efficacy of the algorithm, the calculations are performed on the 37 pin CANDU cell and on the Watanabe-Maynard benchmark problem. Comparisons of adjoint flux and k eff results obtained by MOCC and collision probability (CP) methods are performed. The mathematical relationship between pseudo-adjoint flux obtained by CP method and adjoint flux by MOCC method is presented. (author)
International Nuclear Information System (INIS)
Koch, K.R.
1985-01-01
A new analysis method specially suited for the inherent difficulties of fusion neutronics was developed to provide detailed studies of the fusion neutron transport physics. These studies should provide a better understanding of the limitations and accuracies of typical fusion neutronics calculations. The new analysis method is based on the direct integration of the integral form of the neutron transport equation and employs a continuous energy formulation with the exact treatment of the energy angle kinematics of the scattering process. In addition, the overall solution is analyzed in terms of uncollided, once-collided, and multi-collided solution components based on a multiple collision treatment. Furthermore, the numerical evaluations of integrals use quadrature schemes that are based on the actual dependencies exhibited in the integrands. The new DITRAN computer code was developed on the Cyber 205 vector supercomputer to implement this direct integration multiple-collision fusion neutronics analysis. Three representative fusion reactor models were devised and the solutions to these problems were studied to provide suitable choices for the numerical quadrature orders as well as the discretized solution grid and to understand the limitations of the new analysis method. As further verification and as a first step in assessing the accuracy of existing fusion-neutronics calculations, solutions obtained using the new analysis method were compared to typical multigroup discrete ordinates calculations
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
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
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)
Cai, Li
2014-01-01
In the framework of the Generation IV reactors neutronic research, new core calculation tools are implemented in the code system APOLLO3 for the deterministic part. These calculation methods are based on the discretization concept of nuclear energy data (named multi-group and are generally produced by deterministic codes) and should be validated and qualified with respect to some Monte-Carlo reference calculations. This thesis aims to develop an alternative technique of producing multi-group nuclear properties by a Monte-Carlo code (TRIPOLI-4). At first, after having tested the existing homogenization and condensation functionalities with better precision obtained nowadays, some inconsistencies are revealed. Several new multi-group parameters estimators are developed and validated for TRIPOLI-4 code with the aid of itself, since it has the possibility to use the multi-group constants in a core calculation. Secondly, the scattering anisotropy effect which is necessary for handling neutron leakage case is studied. A correction technique concerning the diagonal line of the first order moment of the scattering matrix is proposed. This is named the IGSC technique and is based on the usage of an approximate current which is introduced by Todorova. An improvement of this IGSC technique is then presented for the geometries which hold an important heterogeneity property. This improvement uses a more accurate current quantity which is the projection on the abscissa X. The later current can represent the real situation better but is limited to 1D geometries. Finally, a B1 leakage model is implemented in the TRIPOLI-4 code for generating multi-group cross sections with a fundamental mode based critical spectrum. This leakage model is analyzed and validated rigorously by the comparison with other codes: Serpent and ECCO, as well as an analytical case.The whole development work introduced in TRIPOLI-4 code allows producing multi-group constants which can then be used in the core
International Nuclear Information System (INIS)
Nahavandi, N.; Minuchehr, A.; Zolfaghari, A.; Abbasi, M.
2015-01-01
Highlights: • Powerful hp-SEM refinement approach for P N neutron transport equation has been presented. • The method provides great geometrical flexibility and lower computational cost. • There is a capability of using arbitrary high order and non uniform meshes. • Both posteriori and priori local error estimation approaches have been employed. • High accurate results are compared against other common adaptive and uniform grids. - Abstract: In this work we presented the adaptive hp-SEM approach which is obtained from the incorporation of Spectral Element Method (SEM) and adaptive hp refinement. The SEM nodal discretization and hp adaptive grid-refinement for even-parity Boltzmann neutron transport equation creates powerful grid refinement approach with high accuracy solutions. In this regard a computer code has been developed to solve multi-group neutron transport equation in one-dimensional geometry using even-parity transport theory. The spatial dependence of flux has been developed via SEM method with Lobatto orthogonal polynomial. Two commonly error estimation approaches, the posteriori and the priori has been implemented. The incorporation of SEM nodal discretization method and adaptive hp grid refinement leads to high accurate solutions. Coarser meshes efficiency and significant reduction of computer program runtime in comparison with other common refining methods and uniform meshing approaches is tested along several well-known transport benchmarks
A Green function of neutron transport equation
International Nuclear Information System (INIS)
Simovic, R.
1993-01-01
In this paper the angularly dependent Green function of the neutron transport equation is derived analytically and approximately. By applying the analytical FDPN approximation up to eighth order, numerical values of the Green functions are obtained with the accuracy of six significant figures in the whole range of parameter c, angle cosine μ and distances x up to the ten optical lengths from the neutron source. (author)
International Nuclear Information System (INIS)
Matausek, M.
1972-01-01
A new proposed method for solving the space-energy dependent spherical harmonics equations represents a methodological contribution to neutron transport theory. The proposed method was applied for solving the problem of spec-energy transport of fast and resonance neutrons in multi-zone, cylindrical y symmetric infinite reactor cell and is related to previously developed procedure for treating the thermal energy region. The advantages of this method are as follows: a unique algorithm was obtained for detailed determination of spatial and energy distribution of neutrons (from thermal to fast) in the reactor cell; these detailed distributions enable more precise calculations of criticality conditions, obtaining adequate multigroup data and better interpretation of experimental data; computing time is rather short
Heterogeneity effects in neutron transport computations
International Nuclear Information System (INIS)
Gelbard, E.M.
1975-01-01
A nuclear reactor is, generally, an intricate heterogeneous structure whose adjacent components may differ radically in their neutronic properties. The heterogeneities in the structure of the reactor complicate the work of the reactor analyst and tend to degrade the efficiency of the numerical methods used in reactor computations. Two types of heterogeneity effects are considered. First, certain singularities in the solution of the neutron transport equation, induced by heterogeneities, are briefly described. Second, the effect of heterogeneities on neutron leakage rates, and consequently on effective diffusion coefficients, are discussed. (5 figures) (U.S.)
Study of a transportable neutron radiography system
International Nuclear Information System (INIS)
Souza, S.N.A. de.
1991-05-01
This work presents a study a transportable neutron radiography system for a 185 GBq 241 Am-Be (α, η) source with a neutron yield roughly 1,25 x 10 7 n/s. Studies about moderation, collimation and shielding are showed. In these studies, a calculation using Transport Theory was carried out by means of transport codes ANISN and DOT (3.5). Objectives were: to obtain a maximum and more homogeneous thermal neutron flux in the collimator outlet to the image plain, and an adequate radiation shielding to attend radiological protection rules. With the presented collimator, it was possible to obtain for the thermal neutron flux, at the collimator outlet and next to the image plain, a L/D ratio of 14, for neutron fluxes up to 4,09 x 10 2 n.cm -2 .s -1 . Considering the low intensity of the source, it is a good value. Studies have also been carried out for L/D ratios of 22 and 30, giving thermal neutron fluxes at the image plain of 1,27 x 10 2 n.cm -2 .s -1 and 2,65 x 10 2 n.cm -2 .s -1 , respectively. (author). 30 refs, 39 figs, 9 tabs
Transportable type neutron level indicators
International Nuclear Information System (INIS)
Khatskevich, M.V.; Kalinin, O.V.; Moskovkin, V.N.; Molchanov, A.V.; Bobkov, A.D.; Rabotnov, Yu.A.
1979-01-01
Some peculiarities of designing level neutron converters (LNC) for portable indicators or level neutron relays are considered. The effect of the LNC geometry and other factors on measurement errors has been studied. Calibration results of the LNC with a neutron reflector and without it are presented. It is shown that the problem of level monitoring with the help of portable indicators can be solved practically for any volume, provided two LNC modifications with reflectors are available: the NPU-G modification with horizontal location of a counter for large volumes and the NPU-V with vertical location of a counter for lesser volumes. A possibility of perfecting LNC performances by shielding the counter with thermal neutron absorbers has been studied. The design of the NPU-V modification for the NIUP-2 level indicator is described. It is intended for tubes and cylinders 30-100 mm in diameter. Measurements carried out on different steel and aluminium vessels with a diameter ranging from 300 to 100 mm and a wall thickness of up to 16 mm with the help of the NPU-V and NPU-G modifications proved the efficiency of the LNC to control a variety of products (kerosine, gasoline, oils, acids, alkalis) [ru
Discrete-ordinates electron transport calculations using standard neutron transport codes
International Nuclear Information System (INIS)
Morel, J.E.
1979-01-01
The primary purpose of this work was to develop a method for using standard neutron transport codes to perform electron transport calculations. The method is to develop approximate electron cross sections which are sufficiently well-behaved to be treated with standard S/sub n/ methods, but which nonetheless yield flux solutions which are very similar to the exact solutions. The main advantage of this approach is that, once the approximate cross sections are constructed, their multigroup Legendre expansion coefficients can be calculated and input to any standard S/sub n/ code. Discrete-ordinates calculations were performed to determine the accuracy of the flux solutions for problems corresponding to 1.0-MeV electrons incident upon slabs of aluminum and gold. All S/sub n/ calculations were compared with similar calculations performed with an electron Monte Carlo code, considered to be exact. In all cases, the discrete-ordinates solutions for integral flux quantities (i.e., scalar flux, energy deposition profiles, etc.) are generally in agreement with the Monte Carlo solutions to within approximately 5% or less. The central conclusion is that integral electron flux quantities can be efficiently and accurately calculated using standard S/sub n/ codes in conjunction with approximate cross sections. Furthermore, if group structures and approximate cross section construction are optimized, accurate differential flux energy spectra may also be obtainable without having to use an inordinately large number of energy groups. 1 figure
Lectures on neutron transport theory
International Nuclear Information System (INIS)
Benoist, P.
1986-02-01
This note is divided in two parts. In the first one the basis of transport theory, that is, the principal forms of the transport equation and the resulting theorems, are presented. The second part is particularly devoted to the applications of integral transport theory to reactor lattice problems [fr
Energy Technology Data Exchange (ETDEWEB)
Silva, Davi Jose M.; Alves Filho, Hermes; Barros, Ricardo C., E-mail: davijmsilva@yahoo.com.br, E-mail: halves@iprj.uerj.br, E-mail: rcbarros@pq.cnpq.br [Universidade do Estado do Rio de Janeiro (UERJ), Nova Friburgo, RJ (Brazil). Programa de Pos-Graduacao em Modelagem Computacional
2015-07-01
A spectral nodal method is developed for multigroup x,y-geometry discrete ordinates (S{sub N}) eigenvalue problems for nuclear reactor global calculations. This method uses the conventional multigroup SN discretized spatial balance nodal equations with two non-standard auxiliary equations: the spectral diamond (SD) auxiliary equations for the discretization nodes inside the fuel regions, and the spectral Green's function (SGF) auxiliary equations for the non-multiplying regions, such as the baffle and the reactor. This spectral nodal method is derived from the analytical general solution of the SN transverse integrated nodal equations with constant approximations for the transverse leakage terms within each discretization node. The SD and SGF auxiliary equations have parameters, which are determined to preserve the homogeneous and the particular components of these local general solutions. Therefore, we refer to the offered method as the hybrid SD-SGF-Constant Nodal (SD-SGF-CN) method. The S{sub N} discretized spatial balance equations, together with the SD and the SGF auxiliary equations form the SD-SGF-CN equations. We solve the SD-SGF-CN equations by using the one-node block inversion inner iterations (NBI), wherein the most recent estimates for the incoming group node-edge average or prescribed boundary conditions are used to evaluate the outgoing group node-edge average fluxes in the directions of the S{sub N} transport sweeps, for each estimate of the dominant eigenvalue in the conventional Power outer iterations. We show in numerical calculations that the SD-SGF-CN method is very accurate for coarse-mesh multigroup S{sub N} eigenvalue problems, even though the transverse leakage terms are approximated rather simply. (author)
International Nuclear Information System (INIS)
Silva, Davi Jose M.; Alves Filho, Hermes; Barros, Ricardo C.
2015-01-01
A spectral nodal method is developed for multigroup x,y-geometry discrete ordinates (S N ) eigenvalue problems for nuclear reactor global calculations. This method uses the conventional multigroup SN discretized spatial balance nodal equations with two non-standard auxiliary equations: the spectral diamond (SD) auxiliary equations for the discretization nodes inside the fuel regions, and the spectral Green's function (SGF) auxiliary equations for the non-multiplying regions, such as the baffle and the reactor. This spectral nodal method is derived from the analytical general solution of the SN transverse integrated nodal equations with constant approximations for the transverse leakage terms within each discretization node. The SD and SGF auxiliary equations have parameters, which are determined to preserve the homogeneous and the particular components of these local general solutions. Therefore, we refer to the offered method as the hybrid SD-SGF-Constant Nodal (SD-SGF-CN) method. The S N discretized spatial balance equations, together with the SD and the SGF auxiliary equations form the SD-SGF-CN equations. We solve the SD-SGF-CN equations by using the one-node block inversion inner iterations (NBI), wherein the most recent estimates for the incoming group node-edge average or prescribed boundary conditions are used to evaluate the outgoing group node-edge average fluxes in the directions of the S N transport sweeps, for each estimate of the dominant eigenvalue in the conventional Power outer iterations. We show in numerical calculations that the SD-SGF-CN method is very accurate for coarse-mesh multigroup S N eigenvalue problems, even though the transverse leakage terms are approximated rather simply. (author)
CACTUS, a characteristics solution to the neutron transport equations in complicated geometries
International Nuclear Information System (INIS)
Halsall, M.J.
1980-04-01
CACTUS has been written to solve the multigroup neutron transport equation in a general two-dimensional geometry. The method is based upon a characteristics formulation for the problem in which the transport equation is integrated explicitly along straight line tracks that are suitably distributed throughout the problem. Source distributions and scattering are assumed to be isotropic, but the only restriction on geometry is that the outer boundary should be rectangular. Within this rectangular boundary the user is free to build his problem geometry using any combination of intersecting straight lines and circular arcs. The theory of the method is described, followed by some details of a coding, a sensitivity study on the number of tracks required to integrate fluxes in a particular problem, a user's guide, and a few test cases. (author)
Uncertainty analysis of neutron transport calculation
International Nuclear Information System (INIS)
Oka, Y.; Furuta, K.; Kondo, S.
1987-01-01
A cross section sensitivity-uncertainty analysis code, SUSD was developed. The code calculates sensitivity coefficients for one and two-dimensional transport problems based on the first order perturbation theory. Variance and standard deviation of detector responses or design parameters can be obtained using cross section covariance matrix. The code is able to perform sensitivity-uncertainty analysis for secondary neutron angular distribution(SAD) and secondary neutron energy distribution(SED). Covariances of 6 Li and 7 Li neutron cross sections in JENDL-3PR1 were evaluated including SAD and SED. Covariances of Fe and Be were also evaluated. The uncertainty of tritium breeding ratio, fast neutron leakage flux and neutron heating was analysed on four types of blanket concepts for a commercial tokamak fusion reactor. The uncertainty of tritium breeding ratio was less than 6 percent. Contribution from SAD/SED uncertainties are significant for some parameters. Formulas to estimate the errors of numerical solution of the transport equation were derived based on the perturbation theory. This method enables us to deterministically estimate the numerical errors due to iterative solution, spacial discretization and Legendre polynomial expansion of transfer cross-sections. The calculational errors of the tritium breeding ratio and the fast neutron leakage flux of the fusion blankets were analysed. (author)
Neutron radiography using a transportable superconducting cyclotron
Energy Technology Data Exchange (ETDEWEB)
Allen, D.A. (School of Physics and Space Research, University of Birmingham, Birmingham, B15 2TT (United Kingdom)); Hawkesworth, M.R. (School of Physics and Space Research, University of Birmingham, Birmingham, B15 2TT (United Kingdom)); Beynon, T.D. (School of Physics and Space Research, University of Birmingham, Birmingham, B15 2TT (United Kingdom)); Green, S. (School of Physics and Space Research, University of Birmingham, Birmingham, B15 2TT (United Kingdom)); Rogers, J.D. (Rolls-Royce, Derby (United Kingdom)); Allen, M.J. (Rolls-Royce, Derby (United Kingdom)); Plummer, H.C. (Rolls-Royce, MatEval, Derby (United Kingdom)); Boulding, N.J. (Oxford Instruments (United Kingdom)); Cox, M. (Oxford Instruments (United Kingdom)); McDougall, I. (Oxford Instruments (United Kingdom))
1994-12-30
A thermal neutron radiography system based on a compact 12 MeV superconducting proton cyclotron is described. Neutrons are generated using a thick beryllium target and moderated in high density polyethylene. Monte Carlo computer simulations have been used to model the neutron and photon transport in order to optimise the performance of the system. With proton beam currents in excess of 100 [mu]A, it can provide high thermal neutron fluxes with L/D ratios of between 50 and 300 for various applications. Both film and electronic imaging are used to produce radiographs. The electronic imaging system consists of a [sup 6]Li-loaded ZnS intensifier screen, and a low light CCD or SIT camera. High resolution images can be recorded and computer-controlled data processing, analysis and display are possible. ((orig.))
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
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)
3D neutron transport modelization
International Nuclear Information System (INIS)
Warin, X.
1996-12-01
Some nodal methods to solve the transport equation in 3D are presented. Two nodal methods presented at an OCDE congress are described: a first one is a low degree one called RTN0; a second one is a high degree one called BDM1. The two methods can be made faster with a totally consistent DSA. Some results of parallelization show that: 98% of the time is spent in sweeps; transport sweeps are easily parallelized. (K.A.)
3D neutron transport modelization
Energy Technology Data Exchange (ETDEWEB)
Warin, X.
1996-12-01
Some nodal methods to solve the transport equation in 3D are presented. Two nodal methods presented at an OCDE congress are described: a first one is a low degree one called RTN0; a second one is a high degree one called BDM1. The two methods can be made faster with a totally consistent DSA. Some results of parallelization show that: 98% of the time is spent in sweeps; transport sweeps are easily parallelized. (K.A.). 10 refs.
International Nuclear Information System (INIS)
Ganapol, B.D.; Kornreich, D.E.
1997-01-01
Because of the requirement of accountability and quality control in the scientific world, a demand for high-quality analytical benchmark calculations has arisen in the neutron transport community. The intent of these benchmarks is to provide a numerical standard to which production neutron transport codes may be compared in order to verify proper operation. The overall investigation as modified in the second year renewal application includes the following three primary tasks. Task 1 on two dimensional neutron transport is divided into (a) single medium searchlight problem (SLP) and (b) two-adjacent half-space SLP. Task 2 on three-dimensional neutron transport covers (a) point source in arbitrary geometry, (b) single medium SLP, and (c) two-adjacent half-space SLP. Task 3 on code verification, includes deterministic and probabilistic codes. The primary aim of the proposed investigation was to provide a suite of comprehensive two- and three-dimensional analytical benchmarks for neutron transport theory applications. This objective has been achieved. The suite of benchmarks in infinite media and the three-dimensional SLP are a relatively comprehensive set of one-group benchmarks for isotropically scattering media. Because of time and resource limitations, the extensions of the benchmarks to include multi-group and anisotropic scattering are not included here. Presently, however, enormous advances in the solution for the planar Green's function in an anisotropically scattering medium have been made and will eventually be implemented in the two- and three-dimensional solutions considered under this grant. Of particular note in this work are the numerical results for the three-dimensional SLP, which have never before been presented. The results presented were made possible only because of the tremendous advances in computing power that have occurred during the past decade
Solving the equation of neutron transport
International Nuclear Information System (INIS)
Nasfi, Rim
2009-01-01
This work is devoted to the study of some numerical methods of resolution of the problem of transport of the neutrons. We started by introducing the equation integro-differential transport of the neutrons. Then we applied the finite element method traditional for stationary and nonstationary linear problems in 2D. A great part is reserved for the presentation of the mixed numerical diagram and mixed hybrid with two types of uniform grids: triangular and rectangular. Thereafter we treated some numerical examples by implementations in Matlab in order to test the convergence of each method. To finish, we had results of simulation by the Monte Carlo method on a problem of two-dimensional transport with an aim of comparing them with the results resulting from the finite element method mixed hybrids. Some remarks and prospects conclude this work.
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)
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.
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
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
Monte Carlo method for neutron transport problems
International Nuclear Information System (INIS)
Asaoka, Takumi
1977-01-01
Some methods for decreasing variances in Monte Carlo neutron transport calculations are presented together with the results of sample calculations. A general purpose neutron transport Monte Carlo code ''MORSE'' was used for the purpose. The first method discussed in this report is the method of statistical estimation. As an example of this method, the application of the coarse-mesh rebalance acceleration method to the criticality calculation of a cylindrical fast reactor is presented. Effective multiplication factor and its standard deviation are presented as a function of the number of histories and comparisons are made between the coarse-mesh rebalance method and the standard method. Five-group neutron fluxes at core center are also compared with the result of S4 calculation. The second method is the method of correlated sampling. This method was applied to the perturbation calculation of control rod worths in a fast critical assembly (FCA-V-3) Two methods of sampling (similar flight paths and identical flight paths) are tested and compared with experimental results. For every cases the experimental value lies within the standard deviation of the Monte Carlo calculations. The third method is the importance sampling. In this report a biased selection of particle flight directions discussed. This method was applied to the flux calculation in a spherical fast neutron system surrounded by a 10.16 cm iron reflector. Result-direction biasing, path-length stretching, and no biasing are compared with S8 calculation. (Aoki, K.)
Cosmic-ray neutron transport at a forest field site
DEFF Research Database (Denmark)
Andreasen, Mie; Jensen, Karsten Høgh; Desilets, Darin
2017-01-01
-ray neutron intensity is essential (e.g., the effect of vegetation, litter layer and soil type). In this study the environmental effect is examined by performing a sensitivity analysis using neutron transport modeling. We use a neutron transport model with various representations of the forest and different...
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.
Numerical solution of neutron transport equations in discrete ordinates and slab geometry
International Nuclear Information System (INIS)
Serrano Pedraza, F.
1985-01-01
An unified formalism to solve numerically, between other equation, the neutron transport in discrete ordinates, slab geometry, several energy groups and independents of time, has been developed recently. Such a formalism cover some of the conventional schemes as diamond difference, (WDD) characteristic step (SC) lineal characteristic (LC), quadratic characteristic (QC) and lineal discontinuous. Unified formation gives before hand the convergence order of the previously selected scheme. In fact it allows besides to generate a big amount of numerical schemes, with which is also possible to solve numerical equations as soon as neutron transport. The essential purpose of this work was to solve the neutron transport equations in slab geometry and discrete ordinates considering several energy groups without to take under advisement time dependence based in the above mentioned unified formalism. To reach this purpose it was necesary to design a computer code with the name TNOD1 (Neutron transport in discrete ordinates and 1 dimension) which includes each one of the schemes already pointed out. there exist two numerical schemes, also recently developed, quadratic continuous (QC) and cubic continuous (CN), although covered by unified formalism, it has been possible to include them inside this computer code without make substantial changes in its structure. In chapter I, derivative of neutron transport equation independent of time is taken, for angular flux, including boundary conditions and discontinuity. In chapter II the neutron transport equations are obtained in multigroups, independents of time, for approximation of discrete ordinates. Description of theory related with unified formalism and its relationship with mentioned discretization schemes is presented in chapter III. Chapter IV describes the computer code developed and finally, in chapter V different numerical results obtained with TNOD1 program are shown. In Appendix A theorems and mathematical arguments used
Progress in multidimensional neutron transport computation
International Nuclear Information System (INIS)
Lewis, E.E.
1977-01-01
The methods available for solution of the time-independent neutron transport problems arising in the analysis of nuclear systems are examined. The merits of deterministic and Monte Carlo methods are briefly compared. The capabilities of deterministic computational methods derived from the first-order form of the transport equation, from the second-order even-parity form of this equation, and from integral transport formulations are discussed in some detail. Emphasis is placed on the approaches for dealing with the related problems of computer memory requirements, computational cost, and achievable accuracy. Attention is directed to some areas where problems exist currently and where the need for further work appears to be particularly warranted
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
Some results on the neutron transport and the coupling of equations
International Nuclear Information System (INIS)
Bal, G.
1997-01-01
Neutron transport in nuclear reactors is well modeled by the linear Boltzmann transport equation. Its resolution is relatively easy but very expensive. To achieve whole core calculations, one has to consider simpler models, such as diffusion or homogeneous transport equations. However, the solutions may become inaccurate in particular situations (as accidents for instance). That is the reason why we wish to solve the equations on small area accurately and more coarsely on the remaining part of the core. It is than necessary to introduce some links between different discretizations or modelizations. In this note, we give some results on the coupling of different discretizations of all degrees of freedom of the integral-differential neutron transport equation (two degrees for the angular variable, on for the energy component, and two or three degrees for spatial position respectively in 2D (cylindrical symmetry) and 3D). Two chapters are devoted to the coupling of discrete ordinates methods (for angular discretization). The first one is theoretical and shows the well posing of the coupled problem, whereas the second one deals with numerical applications of practical interest (the results have been obtained from the neutron transport code developed at the R and D, which has been modified for introducing the coupling). Next, we present the nodal scheme RTN0, used for the spatial discretization. We show well posing results for the non-coupled and the coupled problems. At the end, we deal with the coupling of energy discretizations for the multigroup equations obtained by homogenization. Some theoretical results of the discretization of the velocity variable (well-posing of problems), which do not deal directly with the purposes of coupling, are presented in the annexes. (author)
Discrete elements method of neutron transport
International Nuclear Information System (INIS)
Mathews, K.A.
1988-01-01
In this paper a new neutron transport method, called discrete elements (L N ) is derived and compared to discrete ordinates methods, theoretically and by numerical experimentation. The discrete elements method is based on discretizing the Boltzmann equation over a set of elements of angle. The discrete elements method is shown to be more cost-effective than discrete ordinates, in terms of accuracy versus execution time and storage, for the cases tested. In a two-dimensional test case, a vacuum duct in a shield, the L N method is more consistently convergent toward a Monte Carlo benchmark solution
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)
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)
Asymptotic time dependent neutron transport in multidimensional systems
International Nuclear Information System (INIS)
Nagy, M.E.; Sawan, M.E.; Wassef, W.A.; El-Gueraly, L.A.
1983-01-01
A model which predicts the asymptotic time behavior of the neutron distribution in multi-dimensional systems is presented. The model is based on the kernel factorization method used for stationary neutron transport in a rectangular parallelepiped. The accuracy of diffusion theory in predicting the asymptotic time dependence is assessed. The use of neutron pulse experiments for predicting the diffusion parameters is also investigated
Minaret, a deterministic neutron transport solver for nuclear core calculations
International Nuclear Information System (INIS)
Moller, J-Y.; Lautard, J-J.
2011-01-01
We present here MINARET a deterministic transport solver for nuclear core calculations to solve the steady state Boltzmann equation. The code follows the multi-group formalism to discretize the energy variable. It uses discrete ordinate method to deal with the angular variable and a DGFEM to solve spatially the Boltzmann equation. The mesh is unstructured in 2D and semi-unstructured in 3D (cylindrical). Curved triangles can be used to fit the exact geometry. For the curved elements, two different sets of basis functions can be used. Transport solver is accelerated with a DSA method. Diffusion and SPN calculations are made possible by skipping the transport sweep in the source iteration. The transport calculations are parallelized with respect to the angular directions. Numerical results are presented for simple geometries and for the C5G7 Benchmark, JHR reactor and the ESFR (in 2D and 3D). Straight and curved finite element results are compared. (author)
Minaret, a deterministic neutron transport solver for nuclear core calculations
Energy Technology Data Exchange (ETDEWEB)
Moller, J-Y.; Lautard, J-J., E-mail: jean-yves.moller@cea.fr, E-mail: jean-jacques.lautard@cea.fr [CEA - Centre de Saclay , Gif sur Yvette (France)
2011-07-01
We present here MINARET a deterministic transport solver for nuclear core calculations to solve the steady state Boltzmann equation. The code follows the multi-group formalism to discretize the energy variable. It uses discrete ordinate method to deal with the angular variable and a DGFEM to solve spatially the Boltzmann equation. The mesh is unstructured in 2D and semi-unstructured in 3D (cylindrical). Curved triangles can be used to fit the exact geometry. For the curved elements, two different sets of basis functions can be used. Transport solver is accelerated with a DSA method. Diffusion and SPN calculations are made possible by skipping the transport sweep in the source iteration. The transport calculations are parallelized with respect to the angular directions. Numerical results are presented for simple geometries and for the C5G7 Benchmark, JHR reactor and the ESFR (in 2D and 3D). Straight and curved finite element results are compared. (author)
Neutron transport on the connection machine
International Nuclear Information System (INIS)
Robin, F.
1991-12-01
Monte Carlo methods are heavily used at CEA and account for a a large part of the total CPU time of industrial codes. In the present work (done in the frame of the Parallel Computing Project of the CEL-V Applied Mathematics Department) we study and implement on the Connection Machine an optimised Monte Carlo algorithm for solving the neutron transport equation. This allows us to investigate the suitability of such an architecture for this kind of problem. This report describes the chosen methodology, the algorithm and its performances. We found that programming the CM-2 in CM Fortran is relatively easy and we got interesting performances as, on a 16 k, CM-2 they are the same level as those obtained on one processor of a CRAY X-MP with a well optimized vector code
SAM-CE, Time-Dependent 3-D Neutron Transport, Gamma Transport in Complex Geometry by Monte-Carlo
International Nuclear Information System (INIS)
2003-01-01
1 - Nature of physical problem solved: The SAM-CE system comprises two Monte Carlo codes, SAM-F and SAM-A. SAM-F supersedes the forward Monte Carlo code, SAM-C. SAM-A is an adjoint Monte Carlo code designed to calculate the response due to fields of primary and secondary gamma radiation. The SAM-CE system is a FORTRAN Monte Carlo computer code designed to solve the time-dependent neutron and gamma-ray transport equations in complex three-dimensional geometries. SAM-CE is applicable for forward neutron calculations and for forward as well as adjoint primary gamma-ray calculations. In addition, SAM-CE is applicable for the gamma-ray stage of the coupled neutron-secondary gamma ray problem, which may be solved in either the forward or the adjoint mode. Time-dependent fluxes, and flux functionals such as dose, heating, count rates, etc., are calculated as functions of energy, time and position. Multiple scoring regions are permitted and these may be either finite volume regions or point detectors or both. Other scores of interest, e.g., collision and absorption densities, etc., are also made. 2 - Method of solution: A special feature of SAM-CE is its use of the 'combinatorial geometry' technique which affords the user geometric capabilities exceeding those available with other commonly used geometric packages. All nuclear interaction cross section data (derived from the ENDF for neutrons and from the UNC-format library for gamma-rays) are tabulated in point energy meshes. The energy meshes for neutrons are internally derived, based on built-in convergence criteria and user- supplied tolerances. Tabulated neutron data for each distinct nuclide are in unique and appropriate energy meshes. Both resolved and unresolved resonance parameters from ENDF data files are treated automatically, and extremely precise and detailed descriptions of cross section behaviour is permitted. Such treatment avoids the ambiguities usually associated with multi-group codes, which use flux
An optimized ultra-fine energy group structure for neutron transport calculations
International Nuclear Information System (INIS)
Huria, Harish; Ouisloumen, Mohamed
2008-01-01
This paper describes an optimized energy group structure that was developed for neutron transport calculations in lattices using the Westinghouse lattice physics code PARAGON. The currently used 70-energy group structure results in significant discrepancies when the predictions are compared with those from the continuous energy Monte Carlo methods. The main source of the differences is the approximations employed in the resonance self-shielding methodology. This, in turn, leads to ambiguous adjustments in the resonance range cross-sections. The main goal of developing this group structure was to bypass the self-shielding methodology altogether thereby reducing the neutronic calculation errors. The proposed optimized energy mesh has 6064 points with 5877 points spanning the resonance range. The group boundaries in the resonance range were selected so that the micro group cross-sections matched reasonably well with those derived from reaction tallies of MCNP for a number of resonance absorbers of interest in reactor lattices. At the same time, however, the fast and thermal energy range boundaries were also adjusted to match the MCNP reaction rates in the relevant ranges. The resulting multi-group library was used to obtain eigenvalues for a wide variety of reactor lattice numerical benchmarks and also the Doppler reactivity defect benchmarks to establish its adequacy. (authors)
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.)
Generic programming for deterministic neutron transport codes
International Nuclear Information System (INIS)
Plagne, L.; Poncot, A.
2005-01-01
This paper discusses the implementation of neutron transport codes via generic programming techniques. Two different Boltzmann equation approximations have been implemented, namely the Sn and SPn methods. This implementation experiment shows that generic programming allows us to improve maintainability and readability of source codes with no performance penalties compared to classical approaches. In the present implementation, matrices and vectors as well as linear algebra algorithms are treated separately from the rest of source code and gathered in a tool library called 'Generic Linear Algebra Solver System' (GLASS). Such a code architecture, based on a linear algebra library, allows us to separate the three different scientific fields involved in transport codes design: numerical analysis, reactor physics and computer science. Our library handles matrices with optional storage policies and thus applies both to Sn code, where the matrix elements are computed on the fly, and to SPn code where stored matrices are used. Thus, using GLASS allows us to share a large fraction of source code between Sn and SPn implementations. Moreover, the GLASS high level of abstraction allows the writing of numerical algorithms in a form which is very close to their textbook descriptions. Hence the GLASS algorithms collection, disconnected from computer science considerations (e.g. storage policy), is very easy to read, to maintain and to extend. (authors)
International Nuclear Information System (INIS)
Prinja, A.K.
1995-08-01
We have developed and successfully implemented a two-dimensional bilinear discontinuous in space and time, used in conjunction with the S N angular approximation, to numerically solve the time dependent, one-dimensional, one-speed, slab geometry, (ion) transport equation. Numerical results and comparison with analytical solutions have shown that the bilinear-discontinuous (BLD) scheme is third-order accurate in the space ad time dimensions independently. Comparison of the BLD results with diamond-difference methods indicate that the BLD method is both quantitavely and qualitatively superior to the DD scheme. We note that the form of the transport operator is such that these conclusions carry over to energy dependent problems that include the constant-slowing-down-approximation term, and to multiple space dimensions or combinations thereof. An optimized marching or inversion scheme or a parallel algorithm should be investigated to determine if the increased accuracy can compensate for the extra overhead required for a BLD solution, and then could be compared to other discretization methods such as nodal or characteristic schemes
The TORT three-dimensional discrete ordinates neutron/photon transport code (TORT version 3)
Energy Technology Data Exchange (ETDEWEB)
Rhoades, W.A.; Simpson, D.B.
1997-10-01
TORT calculates the flux or fluence of neutrons and/or photons throughout three-dimensional systems due to particles incident upon the system`s external boundaries, due to fixed internal sources, or due to sources generated by interaction with the system materials. The transport process is represented by the Boltzman transport equation. The method of discrete ordinates is used to treat the directional variable, and a multigroup formulation treats the energy dependence. Anisotropic scattering is treated using a Legendre expansion. Various methods are used to treat spatial dependence, including nodal and characteristic procedures that have been especially adapted to resist numerical distortion. A method of body overlay assists in material zone specification, or the specification can be generated by an external code supplied by the user. Several special features are designed to concentrate machine resources where they are most needed. The directional quadrature and Legendre expansion can vary with energy group. A discontinuous mesh capability has been shown to reduce the size of large problems by a factor of roughly three in some cases. The emphasis in this code is a robust, adaptable application of time-tested methods, together with a few well-tested extensions.
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)
International Nuclear Information System (INIS)
Valle G, E. del; Mugica R, C.A.
2005-01-01
In our country, in last congresses, Gomez et al carried out reactivity calculations based on the solution of the diffusion equation for an energy group using nodal methods in one dimension and the TPL approach (Lineal Perturbation Theory). Later on, Mugica extended the application to the case of multigroup so much so much in one as in two dimensions (X Y geometry) with excellent results. Presently work is carried out similar calculations but this time based on the solution of the neutron transport equation in X Y geometry using nodal methods and again the TPL approximation. The idea is to provide a calculation method that allows to obtain in quick form the reactivity solving the direct problem as well as the enclosed problem of the not perturbed problem. A test problem for the one that results are provided for the effective multiplication factor is described and its are offered some conclusions. (Author)
Comparison of neutron transport calculations with NRC test results
International Nuclear Information System (INIS)
Koban, J.; Hofmann, W.
1981-02-01
For an exactly defined reactor arrangement (PCA = Pool Critical Assembly) neutron fluxes, neutron spectra and reaction rates for several neutron detectors were calculated by means of one and two dimensional transport codes. An international comparison proved the methods applied at KWU to be adequate. There were difficulties, however, in considering the three dimensions of the assembly which result mainly from its small dimension. This fact applies to all participants who didn't use three dimensional codes. (orig.) [de
Concise four-vector scheme for neutron transport calculations
International Nuclear Information System (INIS)
Kulacsy, K.; Lukacs, B.; Racz, A.
1995-01-01
An explicit Riemannian geometrical form or the vectorial Neutron Streaming Term is presented. The method applies the full Riemannian technique of general covariance. There are cases when the symmetry of the neutron flux must be smaller than that of the arrangement. However, in coordinate space there are always solutions of the Neutron Transport Equation as symmetric as the arrangement, if the latter's symmetry is at least an affine collineation of the Euclidian 3-space. (author). 7 refs
Energy Technology Data Exchange (ETDEWEB)
Maldonado-Velázquez, M. [Posgrado en Ciencias Físicas, Universidad Nacional Autónoma de México, 04510 (Mexico); Barrón-Palos, L., E-mail: libertad@fisica.unam.mx [Instituto de Física, Universidad Nacional Autónoma de México, Apartado Postal 20-364, 01000 (Mexico); Crawford, C. [University of Kentucky, Lexington, KY 40506 (United States); Snow, W.M. [Indiana University, Bloomington, IN 47405 (United States)
2017-05-11
The neutron spin is a critical degree of freedom for many precision measurements using low-energy neutrons. Fundamental symmetries and interactions can be studied using polarized neutrons. Parity-violation (PV) in the hadronic weak interaction and the search for exotic forces that depend on the relative spin and velocity, are two questions of fundamental physics that can be studied via the neutron spin rotations that arise from the interaction of polarized cold neutrons and unpolarized matter. The Neutron Spin Rotation (NSR) collaboration developed a neutron polarimeter, capable of determining neutron spin rotations of the order of 10{sup −7} rad per meter of traversed material. This paper describes two key components of the NSR apparatus, responsible for the transport and manipulation of the spin of the neutrons before and after the target region, which is surrounded by magnetic shielding and where residual magnetic fields need to be below 100 μG. These magnetic field devices, called input and output coils, provide the magnetic field for adiabatic transport of the neutron spin in the regions outside the magnetic shielding while producing a sharp nonadiabatic transition of the neutron spin when entering/exiting the low-magnetic-field region. In addition, the coils are self contained, forcing the return magnetic flux into a compact region of space to minimize fringe fields outside. The design of the input and output coils is based on the magnetic scalar potential method.
International Nuclear Information System (INIS)
Moriakov, A.; Vasyukhno, V.; Netecha, M.; Khacheresov, G.
2003-01-01
Powerful supercomputers are available today. MBC-1000M is one of Russian supercomputers that may be used by distant way access. Programs LUCKY and LUCKY C were created to work for multi-processors systems. These programs have algorithms created especially for these computers and used MPI (message passing interface) service for exchanges between processors. LUCKY may resolved shielding tasks by multigroup discreet ordinate method. LUCKY C may resolve critical tasks by same method. Only XYZ orthogonal geometry is available. Under little space steps to approximate discreet operator this geometry may be used as universal one to describe complex geometrical structures. Cross section libraries are used up to P8 approximation by Legendre polynomials for nuclear data in GIT format. Programming language is Fortran-90. 'Vector' processors may be used that lets get a time profit up to 30 times. But unfortunately MBC-1000M has not these processors. Nevertheless sufficient value for efficiency of parallel calculations was obtained under 'space' (LUCKY) and 'space and energy' (LUCKY C ) paralleling. AUTOCAD program is used to control geometry after a treatment of input data. Programs have powerful geometry module, it is a beautiful tool to achieve any geometry. Output results may be processed by graphic programs on personal computer. (authors)
Neutron transport in Eulerian coordinates with bulk material motion
Energy Technology Data Exchange (ETDEWEB)
Baker, Randal S., E-mail: rsb@lanl.gov [Los Alamos National Laboratory, Computational Physics Group, Los Alamos, NM (United States); Dahl, Jon A., E-mail: dahl@lanl.gov [Los Alamos National Laboratory, Computational Physics Group, Los Alamos, NM (United States); Fichtl, Erin J., E-mail: efichtl@lanl.gov [Los Alamos National Laboratory, Computational Physics Group, Los Alamos, NM (United States); Morel, Jim E., E-mail: morel@tamu.edu [Department of Nuclear Engineering, Texas A& M University, College Station, TX (United States)
2015-12-15
A consistent, numerically stable algorithm for the solution of the neutron transport equation in the presence of a moving material background is presented for one-dimensional spherical geometry. Manufactured solutions are used to demonstrate the correctness and stability of our numerical algorithm. The importance of including moving material corrections is shown for the r-process in proto-neutron stars.
International Nuclear Information System (INIS)
Pillon, M.; Martone, M.; Verschuur, K.A.; Jarvis, O.N.; Kaellne, J.
1989-01-01
Neutron transport calculations have been performed using fluence ray tracing (FURNACE code) and Monte Carlo particle trajectory sampling methods (MCNP code) in order to determine the neutron fluence and energy distributions at different locations in the JET tokamak. These calculations were used to calibrate the activation measurements used in the determination of the absolute fusion neutron yields from the JET plasma. We present here the neutron activation response coefficients calculated for three different materials. Comparison of the MCNP and FURNACE results helps identify the sources of error in these neutron transport calculations. The accuracy of these calculations was tested by comparing the total 2.5 MeV neutron yields derived from the activation measurements with those obtained with calibrated fission chambers; agreement at the ±15% level was demonstrate. (orig.)
A random walk approach to stochastic neutron transport
International Nuclear Information System (INIS)
Mulatier, Clelia de
2015-01-01
One of the key goals of nuclear reactor physics is to determine the distribution of the neutron population within a reactor core. This population indeed fluctuates due to the stochastic nature of the interactions of the neutrons with the nuclei of the surrounding medium: scattering, emission of neutrons from fission events and capture by nuclear absorption. Due to these physical mechanisms, the stochastic process performed by neutrons is a branching random walk. For most applications, the neutron population considered is very large, and all physical observables related to its behaviour, such as the heat production due to fissions, are well characterised by their average values. Generally, these mean quantities are governed by the classical neutron transport equation, called linear Boltzmann equation. During my PhD, using tools from branching random walks and anomalous diffusion, I have tackled two aspects of neutron transport that cannot be approached by the linear Boltzmann equation. First, thanks to the Feynman-Kac backward formalism, I have characterised the phenomenon of 'neutron clustering' that has been highlighted for low-density configuration of neutrons and results from strong fluctuations in space and time of the neutron population. Then, I focused on several properties of anomalous (non-exponential) transport, that can model neutron transport in strongly heterogeneous and disordered media, such as pebble-bed reactors. One of the novel aspects of this work is that problems are treated in the presence of boundaries. Indeed, even though real systems are finite (confined geometries), most of previously existing results were obtained for infinite systems. (author) [fr
Scattered Neutron Tomography Based on A Neutron Transport Inverse Problem
International Nuclear Information System (INIS)
William Charlton
2007-01-01
Neutron radiography and computed tomography are commonly used techniques to non-destructively examine materials. Tomography refers to the cross-sectional imaging of an object from either transmission or reflection data collected by illuminating the object from many different directions
TDTORT: Time-Dependent, 3-D, Discrete Ordinates, Neutron Transport Code System with Delayed Neutrons
International Nuclear Information System (INIS)
2002-01-01
1 - Description of program or function: TDTORT solves the time-dependent, three-dimensional neutron transport equation with explicit representation of delayed neutrons to estimate the fission yield from fissionable material transients. This release includes a modified version of TORT from the C00650MFMWS01 DOORS3.1 code package plus the time-dependent TDTORT code. GIP is also included for cross-section preparation. TORT calculates the flux or fluence of particles due to particles incident upon the system from extraneous sources or generated internally as a result of interaction with the system in two- or three-dimensional geometric systems. The principle application is to the deep-penetration transport of neutrons and photons. Reactor eigenvalue problems can also be solved. Numerous printed edits of the results are available, and results can be transferred to output files for subsequent analysis. TDTORT reads ANISN-format cross-section libraries, which are not included in the package. Users may choose from several available in RSICC's data library collection which can be identified by the keyword 'ANISN FORMAT'. 2 - Methods:The time-dependent spatial flux is expressed as a product of a space-, energy-, and angle-dependent shape function, which is usually slowly varying in time and a purely time-dependent amplitude function. The shape equation is solved for the shape using TORT; and the result is used to calculate the point kinetics parameters (e.g., reactivity) by using their inner product definitions, which are then used to solve the time-dependent amplitude and precursor equations. The amplitude function is calculated by solving the kinetics equations using the LSODE solver. When a new shape calculation is needed, the flux is calculated using the newly computed amplitude function. The Boltzmann transport equation is solved using the method of discrete ordinates to treat the directional variable and weighted finite-difference methods, in addition to Linear Nodal
A finite element method for neutron transport
International Nuclear Information System (INIS)
Ackroyd, R.T.
1978-01-01
A variational treatment of the finite element method for neutron transport is given based on a version of the even-parity Boltzmann equation which does not assume that the differential scattering cross-section has a spherical harmonic expansion. The theory of minimum and maximum principles is based on the Cauchy-Schwartz equality and the properties of a leakage operator G and a removal operator C. For systems with extraneous sources, two maximum and one minimum principles are given in boundary free form, to ease finite element computations. The global error of an approximate variational solution is given, the relationship of one the maximum principles to the method of least squares is shown, and the way in which approximate solutions converge locally to the exact solution is established. A method for constructing local error bounds is given, based on the connection between the variational method and the method of the hypercircle. The source iteration technique and a maximum principle for a system with extraneous sources suggests a functional for a variational principle for a self-sustaining system. The principle gives, as a consequence of the properties of G and C, an upper bound to the lowest eigenvalue. A related functional can be used to determine both upper and lower bounds for the lowest eigenvalue from an inspection of any approximate solution for the lowest eigenfunction. The basis for the finite element is presented in a general form so that two modes of exploitation can be undertaken readily. The model can be in phase space, with positional and directional co-ordinates defining points of the model, or it can be restricted to the positional co-ordinates and an expansion in orthogonal functions used for the directional co-ordinates. Suitable sets of functions are spherical harmonics and Walsh functions. The latter set is appropriate if a discrete direction representation of the angular flux is required. (author)
DTF4-J, 1-D Neutron Transport with Anisotropic Scattering by Sn Method
International Nuclear Information System (INIS)
Nishimura, Hideo
1971-01-01
Nature of physical problem solved: DTF-4-J solves the one-dimensional multi-group transport equation with anisotropic scattering by Sn method. It is a FORTRAN adaptation of the Los Alamos DTF-IV program written by K.D. Lathrop, and it is combined with the JAERI SIMPLED-4 program written by H. Nishimura
Energy Technology Data Exchange (ETDEWEB)
Bal, G. [Electricite de France (EDF), Direction des Etudes et Recherches, 92 - Clamart (France)
1997-12-31
Neutron transport in nuclear reactors is well modeled by the linear Boltzmann transport equation. Its resolution is relatively easy but very expensive. To achieve whole core calculations, one has to consider simpler models, such as diffusion or homogeneous transport equations. However, the solutions may become inaccurate in particular situations (as accidents for instance). That is the reason why we wish to solve the equations on small area accurately and more coarsely on the remaining part of the core. It is than necessary to introduce some links between different discretizations or modelizations. In this note, we give some results on the coupling of different discretizations of all degrees of freedom of the integral-differential neutron transport equation (two degrees for the angular variable, on for the energy component, and two or three degrees for spatial position respectively in 2D (cylindrical symmetry) and 3D). Two chapters are devoted to the coupling of discrete ordinates methods (for angular discretization). The first one is theoretical and shows the well posing of the coupled problem, whereas the second one deals with numerical applications of practical interest (the results have been obtained from the neutron transport code developed at the R and D, which has been modified for introducing the coupling). Next, we present the nodal scheme RTN0, used for the spatial discretization. We show well posing results for the non-coupled and the coupled problems. At the end, we deal with the coupling of energy discretizations for the multigroup equations obtained by homogenization. Some theoretical results of the discretization of the velocity variable (well-posing of problems), which do not deal directly with the purposes of coupling, are presented in the annexes. (author). 34 refs.
Charged-particle calculations using Boltzmann transport methods
International Nuclear Information System (INIS)
Hoffman, T.J.; Dodds, H.L. Jr.; Robinson, M.T.; Holmes, D.K.
1981-01-01
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 charged particle range distributions, reflection coefficients, and sputtering yields. The Boltzmann transport approach can be implemented, with minor changes, in standard neutral particle computer codes. With the multigroup discrete ordinates code, ANISN, determination of ion and target atom distributions as functions of position, energy, and direction can be obtained without the stochastic error associated with atomistic computer codes such as MARLOWE and TRIM. With the multigroup Monte Carlo code, MORSE, charged particle effects can be obtained for problems associated with very complex geometries. Results are presented for several charged particle problems. Good agreement is obtained between quantities calculated with the multigroup approach and those obtained experimentally or by atomistic computer codes
International Nuclear Information System (INIS)
Wienke, H.; Herman, M.
1998-01-01
Evaluated neutron reaction data and photon-atom interaction cross sections for materials contained in the general purpose Fusion Evaluated Nuclear Data Library (FENDL/E2.0) have been processed with the NJOY code system into VITAMIN-J multigroup structure, for use in discrete-ordinates transport codes, and into continuous energy ACE format, for use in the Monte Carlo transport code MCNP. This document summarizes the resulting data libraries FENDL/MG-2.0 version 1 and FENDL/MC-2.0 version 1. The data are available costfree from the IAEA Nuclear Data Section online or on magnetic tape. (author)
Transport coefficients in superfluid neutron stars
Energy Technology Data Exchange (ETDEWEB)
Tolos, Laura [Instituto de Ciencias del Espacio (IEEC/CSIC) Campus Universitat Autònoma de Barcelona, Facultat de Ciències, Torre C5, E-08193 Bellaterra (Barcelona) (Spain); Frankfurt Institute for Advances Studies. Johann Wolfgang Goethe University, Ruth-Moufang-Str. 1, 60438 Frankfurt am Main (Germany); Manuel, Cristina [Instituto de Ciencias del Espacio (IEEC/CSIC) Campus Universitat Autònoma de Barcelona, Facultat de Ciències, Torre C5, E-08193 Bellaterra (Barcelona) (Spain); Sarkar, Sreemoyee [Tata Institute of Fundamental Research, Homi Bhaba Road, Mumbai-400005 (India); Tarrus, Jaume [Physik Department, Technische Universität München, D-85748 Garching (Germany)
2016-01-22
We study the shear and bulk viscosity coefficients as well as the thermal conductivity as arising from the collisions among phonons in superfluid neutron stars. We use effective field theory techniques to extract the allowed phonon collisional processes, written as a function of the equation of state and the gap of the system. The shear viscosity due to phonon scattering is compared to calculations of that coming from electron collisions. We also comment on the possible consequences for r-mode damping in superfluid neutron stars. Moreover, we find that phonon collisions give the leading contribution to the bulk viscosities in the core of the neutron stars. We finally obtain a temperature-independent thermal conductivity from phonon collisions and compare it with the electron-muon thermal conductivity in superfluid neutron stars.
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)
Neutron transport from targets to moderators
International Nuclear Information System (INIS)
Taylor, A.D.
1981-06-01
By appropriately choosing parameters such as temperature, decoupler, thickness and effective size it is possible to tailor the moderators of a pulsed spallation neutron source in such a way that the different characteristics regarding time structure and spectral distribution as requested for the different instruments can be met very closely. This enables a unique flexibility in the design of neutron spectrometers to be used at such a source. (author)
Effect of granulation of geological samples in neutron transport measurements
International Nuclear Information System (INIS)
Woznicka, Urszula; Drozdowicz, Krzysztof; Gabanska, Barbara; Krynicka, Ewa; Igielski, Andrzej
2001-01-01
The thermal neutron absorption cross section is one of the parameters describing the transport of thermal neutrons in a medium. Theoretical descriptions and experiments which determine the absorption cross section have a wide literature for homogeneous media. The situation comes true e.g. for fluids or amorphous solids. There are many other media which should be treated as heterogeneous. Among others - geological materials. The material heterogeneity for the thermal neutron transport in a considered volume is understood here as an existence of many small regions which differ significantly in their macroscopic neutron diffusion parameters (defined by the absorption and transport cross sections). The final difference, which influences the neutron transport, comes from a combination of the absolute differences between the parameters and of sizes of regions (related to the neutron mean free paths). A rock can be naturally heterogeneous in the above meaning. Besides, it can happen that a preparation of the rock sample for a neutron measurement can increase its natural heterogeneity. (For example, when the rock material is crushed and the measured sample consists of the obtained grains). The question is which granulation is allowed to treat the sample material as still homogeneous, and from which size of the rock grains we have to consider a two-component medium. It has been experimentally proved that the effective absorption of thermal neutrons in a heterogeneous two-component material can significantly differ from the absorption in a homogeneous one which consists of the same elements. The final effect is dependent on a few factors: the macroscopic absorption cross sections of the components, their total mass contributions, and the size of the grains. The ratio of the effective absorption cross section of the heterogeneous material to the cross section of the equivalent homogeneous, is a measure of the heterogeneity effect on the thermal neutron absorption
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.)
MUXS: a code to generate multigroup cross sections for sputtering calculations
International Nuclear Information System (INIS)
Hoffman, T.J.; Robinson, M.T.; Dodds, H.L. Jr.
1982-10-01
This report documents MUXS, a computer code to generate multigroup cross sections for charged particle transport problems. Cross sections generated by MUXS can be used in many multigroup transport codes, with minor modifications to these codes, to calculate sputtering yields, reflection coefficients, penetration distances, etc
Energy Technology Data Exchange (ETDEWEB)
Boyarinov, V.F.; Davidenko, V.D.; Polismakov, A.A.; Tsybulsky, V.F. [RRC Kurchatov Institute, Moscow (Russian Federation)
2005-07-01
At the present time, the new code system SUHAM-U for calculation of the neutron-physical processes in nuclear reactor core with triangular and square lattices based both on the modern micro-group (about 7000 groups) cross-sections library of code system UNK and on solving the multigroup (up to 89 groups) neutron transport equation by Surface Harmonics Method is elaborated. In this paper the procedure for generation of multigroup cross-sections from micro-group ones for calculation of VVER-1000 reactor core with MOX loading is described. The validation has consisted in computing VVER-1000 fuel assemblies with uranium and MOX fuel and has shown enough high accuracy under corresponding selection of the number and boundaries of the energy groups. This work has been fulfilled in the frame of ISTC project 'System Analyses of Nuclear Safety for VVER Reactors with MOX Fuels'.
Neutron transport from targets to moderators
International Nuclear Information System (INIS)
Taylor, A.D.
1980-01-01
The title of this meeting is 'Targets for Neutron Beam Spallation Sources', but so far all the emphasis in the talks has been on how to produce the fast neutron flux. I would like to stress that that is just the beginning of the story. What we are required to produce are beams of thermal and epithermal neutrons with time and spectral characteristics tailored to the instrumental requirements. The real source of our neutrons is not uranium arrays or thorium cylinders but a small volume of hydrogenous material, some 10 x 10 x 5 cm 3 . This is really what the whole thing is about - the target produces a copious field of fast neutrons, but if we fail to moderate them with the right energy and time characteristics, we will not match to what is happening downstream. In this talk, I am going to deal specifically with what we have done for SNS to optimise the target-moderator-reflector and decoupler system in this respect. (orig.)
Neutron and gamma-ray transport experiments in liquid air
International Nuclear Information System (INIS)
Farley, W.E.
1976-01-01
Accurate estimates of neutron and gamma radiations from a nuclear explosion and their subsequent transport through the atmosphere are vital to nuclear-weapon employment studies: i.e., for determining safety radii for aircraft crews, casualty and collateral-damage risk radii for tactical weapons, and the kill range from a high-yield defensive burst for a maneuvering reentry vehicle. Radiation transport codes, such as the Laboratory's TARTNP, are used to calculate neutron and gamma fluences. Experiments have been performed to check and update these codes. Recently, a 1.3-m-radius liquid-air (21 percent oxygen) sphere, with a pulsed source of 14-MeV neutrons at its center, was used to measure the fluence and spectra of emerging neutrons and secondary gamma rays. Comparison of measured radiation dose with TARTNP showed agreement within 10 percent
Transport of accelerator produced high energy neutrons though concrete
International Nuclear Information System (INIS)
Prabhakar Rao, G.; Sarkar, P.K.
1996-01-01
Development of a computational system for estimating the production and transport of high energy neutrons in particle accelerators is reported. The energy-angle distribution of neutrons from accelerated ions bombarding thick targets is calculated by a hybrid nuclear reaction model code, ALICE-91, modified to suit the purpose. Subsequent transmission of these neutrons through concrete slabs is treated using the anisotropic source-flux iteration technique (ASFIT) in the framework of a coupled neutron-gamma transport. Several parameters of both the codes have been optimized to obtain the transmitted dose through concrete. The calculations are found to be accurate and at the same time faster compared to the detailed Monte Carlo calculations. (author). 8 refs., 2 figs
Energy Technology Data Exchange (ETDEWEB)
Gleicher, Frederick N.; Williamson, Richard L.; Ortensi, Javier; Wang, Yaqi; Spencer, Benjamin W.; Novascone, Stephen R.; Hales, Jason D.; Martineau, Richard C.
2014-10-01
The MOOSE neutron transport application RATTLESNAKE was coupled to the fuels performance application BISON to provide a higher fidelity tool for fuel performance simulation. This project is motivated by the desire to couple a high fidelity core analysis program (based on the self-adjoint angular flux equations) to a high fidelity fuel performance program, both of which can simulate on unstructured meshes. RATTLESNAKE solves self-adjoint angular flux transport equation and provides a sub-pin level resolution of the multigroup neutron flux with resonance treatment during burnup or a fast transient. BISON solves the coupled thermomechanical equations for the fuel on a sub-millimeter scale. Both applications are able to solve their respective systems on aligned and unaligned unstructured finite element meshes. The power density and local burnup was transferred from RATTLESNAKE to BISON with the MOOSE Multiapp transfer system. Multiple depletion cases were run with one-way data transfer from RATTLESNAKE to BISON. The eigenvalues are shown to agree well with values obtained from the lattice physics code DRAGON. The one-way data transfer of power density is shown to agree with the power density obtained from an internal Lassman-style model in BISON.
Transportable, Low-Dose Active Fast-Neutron Imaging
Energy Technology Data Exchange (ETDEWEB)
Mihalczo, John T. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Wright, Michael C. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); McConchie, Seth M. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Archer, Daniel E. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Palles, Blake A. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
2017-08-01
This document contains a description of the method of transportable, low-dose active fast-neutron imaging as developed by ORNL. The discussion begins with the technique and instrumentation and continues with the image reconstruction and analysis. The analysis discussion includes an example of how a gap smaller than the neutron production spot size and detector size can be detected and characterized depending upon the measurement time.
On generating neutron transport tables with the NJOY system
International Nuclear Information System (INIS)
Caldeira, Alexandre D.; Claro, Luiz H.
2013-01-01
Incorrect values for the product of the average number of neutrons released per fission and the fission microscopic cross-section were detected in several energy groups of a neutron transport table generated with the most updated version of the NJOY system. It was verified that the problem persists when older versions of this system are utilized. Although this problem exists for, at least, ten years, it is still an open question. (author)
Considerations in the design of an improved transportable neutron spectrometer
Williams, A M; Brushwood, J M; Beeley, P A
2002-01-01
The Transportable Neutron Spectrometer (TNS) has been used by the Ministry of Defence for over 15 years to characterise neutron fields in workplace environments and provide local correction factors for both area and personal dosimeters. In light of advances in neutron spectrometry, a programme to evaluate and improve TNS has been initiated. This paper describes TNS, presents its operation in known radioisotope fields and in a reactor environment. Deficiencies in the operation of the instrument are highlighted, together with proposals for updating the response functions and spectrum unfolding methodologies.
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)
Measurements of anomalous neutron transport in bulk graphite
International Nuclear Information System (INIS)
Bowman, C.D.; Smith, G.A.; Vogelaar, B.; Howell, C.R.; Bilpuch, E.G.; Tornow, W.
2003-01-01
The neutron absorption of bulk granular graphite has been measured in a classical exponential diffusion experiment. Our first measurements of April 2002 implementing both exponential decay and pulsed die-away experiments and using the TUNL pulsed accelerator at Duke University as a neutron source indicated a capture cross section for graphite a striking factor of three lower than the measured value for carbon of 3.4 millibarns. Therefore a new exponential experiment with an improved geometry enabling greater accuracy has been performed giving an apparent cross section for carbon in the form of bulk granular graphite of less than 0.5 millibarns. This result confirms our first result and is also consistent with less than one part per million of boron in our graphite. The bulk density of the graphite is 1.02 compared with the actual particle density of 1.60 indicating a packing fraction of 0.64 or a void fraction of 0.36. We suspect that the apparent suppression of absorption in bulk graphite may be associated with the strong coherent diffraction of neutrons that dominates neutron transport in graphite. Coherent diffraction has never been taken into account in graphite reactor design and no neutron transport code including general use codes such as MCNP incorporate diffraction effects even though diffraction dominates many practical thermal neutron transport problems. (orig.)
Measurements of anomalous neutron transport in bulk graphite
Energy Technology Data Exchange (ETDEWEB)
Bowman, C.D.; Smith, G.A. [ADNA Corp., Los Alamos, NM (United States); Vogelaar, B. [Virginia Tech., Blacksburg, VA (United States); Howell, C.R.; Bilpuch, E.G.; Tornow, W. [Triangle Univ. Nuclear Lab., Duke Univ., Durham, NC (United States)
2003-07-01
The neutron absorption of bulk granular graphite has been measured in a classical exponential diffusion experiment. Our first measurements of April 2002 implementing both exponential decay and pulsed die-away experiments and using the TUNL pulsed accelerator at Duke University as a neutron source indicated a capture cross section for graphite a striking factor of three lower than the measured value for carbon of 3.4 millibarns. Therefore a new exponential experiment with an improved geometry enabling greater accuracy has been performed giving an apparent cross section for carbon in the form of bulk granular graphite of less than 0.5 millibarns. This result confirms our first result and is also consistent with less than one part per million of boron in our graphite. The bulk density of the graphite is 1.02 compared with the actual particle density of 1.60 indicating a packing fraction of 0.64 or a void fraction of 0.36. We suspect that the apparent suppression of absorption in bulk graphite may be associated with the strong coherent diffraction of neutrons that dominates neutron transport in graphite. Coherent diffraction has never been taken into account in graphite reactor design and no neutron transport code including general use codes such as MCNP incorporate diffraction effects even though diffraction dominates many practical thermal neutron transport problems. (orig.)
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
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)
The Lattice Boltzmann Method applied to neutron transport
International Nuclear Information System (INIS)
Erasmus, B.; Van Heerden, F. A.
2013-01-01
In this paper the applicability of the Lattice Boltzmann Method to neutron transport is investigated. One of the main features of the Lattice Boltzmann method is the simultaneous discretization of the phase space of the problem, whereby particles are restricted to move on a lattice. An iterative solution of the operator form of the neutron transport equation is presented here, with the first collision source as the starting point of the iteration scheme. A full description of the discretization scheme is given, along with the quadrature set used for the angular discretization. An angular refinement scheme is introduced to increase the angular coverage of the problem phase space and to mitigate lattice ray effects. The method is applied to a model problem to investigate its applicability to neutron transport and the results are compared to a reference solution calculated, using MCNP. (authors)
A modular spherical harmonics approach to the neutron transport equation
International Nuclear Information System (INIS)
Inanc, F.; Rohach, A.F.
1989-01-01
A modular nodal method was developed for solving the neutron transport equation in 2-D xy coordinates. The spherical harmonic expansion was used for approximating the second-order even-parity form of the neutron transport equation. The boundary conditions of the spherical harmonics approximation were derived in a form to have forms analogous to the partial currents in the neutron diffusion equation. Relations were developed for generating both the second-order spherical harmonic equations and the boundary conditions in an automated computational algorithm. Nodes using different orders of the spherical harmonics approximation to the transport equation were interfaced through mixed-type boundary conditions. The determination of spherical harmonic orders implemented in the nodes were determined by the scheme in an automated manner. Results of the method compared favorably to benchmark problems. (author)
Energy Technology Data Exchange (ETDEWEB)
Fernandes, Julio C.L.; Vilhena, Marco T.; Bodmann, Bardo E.J., E-mail: julio.lombaldo@ufrgs.br, E-mail: mtmbvilhena@gmail.com, E-mail: bardo.bodmann@ufrgs.br [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Dept. de Matematica Pura e Aplicada; Dulla, Sandra; Ravetto, Piero, E-mail: sandra.dulla@polito.it, E-mail: piero.ravetto@polito.it [Dipartimento di Energia, Politecnico di Torino, Piemonte (Italy)
2015-07-01
In this work we generalize the solution of the one-dimensional neutron transport equation to a multi- group approach in planar geometry. The basic idea of this work consists in consider the hierarchical construction of a solution for a generic number G of energy groups, starting from a mono-energetic solution. The hierarchical method follows the reasoning of the decomposition method. More specifically, the additional terms from adding energy groups is incorporated into the recursive scheme as source terms. This procedure leads to an analytical representation for the solution with G energy groups. The recursion depth is related to the accuracy of the solution, that may be evaluated after each recursion step. The authors present a heuristic analysis of stability for the results. Numerical simulations for a specific example with four energy groups and a localized pulsed source. (author)
Calculated characteristics of subcritical assembly with anisotropic transport of neutrons
International Nuclear Information System (INIS)
Gorin, N.V.; Lipilina, E.N.; Lyutov, V.D.; Saukov, A.I.
2003-01-01
There was considered possibility of creating enough sub-critical system that multiply neutron fluence from a primary source by many orders. For assemblies with high neutron tie between parts, it is impossible. That is why there was developed a construction consisting of many units (cascades) having weak feedback with preceding cascades. The feedback attenuation was obtained placing layers of slow neutron absorber and moderators between the cascades of fission material. Anisotropy of fast neutron transport through the layers was used. The system consisted of many identical cascades aligning one by another. Each cascade consists of layers of moderator, fissile material and absorber of slow neutrons. The calculations were carried out using the code MCNP.4a with nuclear data library ENDF/B5. In this construction neutrons spread predominantly in one direction multiplying in each next fissile layer, and they attenuate considerably in the opposite direction. In a calculated construction, multiplication factor of one cascade is about 1.5 and multiplication factor of whole construction composed of n cascades is 1.5 n . Calculated keff value is 0.9 for one cascade and does not exceed 0.98 for a system containing any number of cascades. Therefore the assembly is always sub-critical and therefore it is safe in respect of criticality. There was considered using such a sub-critical assembly to create a powerful neutron fluence for neutron boron-capturing therapy. The system merits and demerits were discussed. (authors)
Neutronics equations: Positiveness; compactness; spectral theory; time asymptotic behavior
International Nuclear Information System (INIS)
Mokhtar-Kharroubi, M.
1987-12-01
Neutronics equations are studied: the continuous model (with and without delayed neutrons) and the multigroup model. Asymptotic descriptions of these equations (t→+∞) are obtained, either by the Dunford method or by using semigroup perturbation techniques, after deriving the spectral theory for the equations. Compactness problems are reviewed, and a general theory of compact injection in neutronic functional space is derived. The effects of positiveness in neutronics are analyzed: the irreducibility of the transport semigroup, and the properties of the main eigenvalue (existence, nonexistence, frame, strict dominance, strict monotony in relation to all the parameters). A class of transport operators whose real spectrum can be completely described is shown [fr
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)
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 new multigrid schemes for the method of characteristics in neutron transport theory
International Nuclear Information System (INIS)
Grassi, G.
2006-01-01
This dissertation is based upon our doctoral research that dealt with the conception and development of new non-linear multigrid techniques for the Method of the Characteristics (MOC) within the TDT code. Here we focus upon a two-level scheme consisting of a fine level on which the neutron transport equation is iteratively solved using the MOC algorithm, and a coarse level defined by a more coarsely discretized phase space on which a low-order problem is considered. The solution of this problem is then used in order to correct the angular flux moments resulting from the previous transport iteration. A flux-volume homogenization procedure is employed to evaluate the coarse-level material properties after each transport iteration. This entails the non-linearity of the methods. According to the Generalised Equivalence Theory (GET), additional degrees of freedom are introduced for the low-order problem so that the convergence of the acceleration scheme can be ensured. We present two classes of non-linear methods: transport-like methods and discussion-like methods. Transport-like methods consider a homogenized low-order transport problem on the coarse level. This problem is iteratively solved using the same MOC algorithm as for the transport problem on the fine level. Discontinuity factors are then employed, per region or per surface, in order to reconstruct the currents evaluated by the low-order operator, which ensure the convergence of the acceleration scheme. On the other hand, discussion-like methods consider a low-order problem inspired by diffusion. We studied the non-linear Coarse Mesh Finite Difference (CMFD) method, already present in literature, in the perspective of integrating it into TDT code. Then, we developed a new non-linear method on the model of CMFD. From the latter, we borrowed the idea to establish a simple relation between currents and fluxes in order to obtain a problem involving only coarse fluxes. Finally, those non-linear methods have been
Implementation of the quasi-static method for neutron transport
International Nuclear Information System (INIS)
Alcaro, Fabio; Dulla, Sandra; Ravetto, Piero; Le Tellier, Romain; Suteau, Christophe
2011-01-01
The study of the dynamic behavior of next generation nuclear reactors is a fundamental aspect for safety and reliability assessments. Despite the growing performances of modern computers, the full solution of the neutron Boltzmann equation in the time domain is still an impracticable task, thus several approximate dynamic models have been proposed for the simulation of nuclear reactor transients; the quasi-static method represents the standard tool currently adopted for the space-time solution of neutron transport problems. All the practical applications of this method that have been proposed contain a major limit, consisting in the use of isotropic quantities, such as scalar fluxes and isotropic external neutron sources, being the only data structures available in most deterministic transport codes. The loss of the angular information produces both inaccuracies in the solution of the kinetic model and the inconsistency of the quasi-static method itself. The present paper is devoted to the implementation of a consistent quasi-static method. The computational platform developed by CEA in Cadarache has been used for the creation of a kinetic package to be coupled with the existing SNATCH solver, a discrete-ordinate multi-dimensional neutron transport solver, employed for the solution of the steady-state Boltzmann equation. The work aims at highlighting the effects of the angular treatment of the neutron flux on the transient analysis, comparing the results with those produced by the previous implementations of the quasi-static method. (author)
International Nuclear Information System (INIS)
Stefanovic, D.
1975-09-01
The research work of this contract was oriented towards the study of different methods in neutron transport theory. Authors studied analytical solution of the neutron slowing down transport equation and extension of this solution to include the energy dependence of the anisotropy of neutron scattering. Numerical solution of the fast and resonance transport equation for the case of mixture of scatterers including inelastic effects were also reviewed. They improved the existing formalism for treating the scattering of neutrons on water molecules; Identifying modal analysis as the Galerkin method, general conditions for modal technique applications have been investigated. Inverse problems in transport theory were considered. They obtained the evaluation of an advanced level distribution function, made improvement of the standard formalism for treating the inelastic scattering and development of a cluster nuclear model for this evaluation. Authors studied the neutron transport treatment in space energy groups for criticality calculation of a reactor core, and development of the Monte Carlo sampling scheme from the neutron transport equation
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)
Finite element method for solving neutron transport problems
International Nuclear Information System (INIS)
Ferguson, J.M.; Greenbaum, A.
1984-01-01
A finite element method is introduced for solving the neutron transport equations. Our method falls into the category of Petrov-Galerkin solution, since the trial space differs from the test space. The close relationship between this method and the discrete ordinate method is discussed, and the methods are compared for simple test problems
Neutron transport in two dissimilar media anisotropic scattering
International Nuclear Information System (INIS)
Burkart, A.R.; Ishiguro, Y.; Siewert, C.E.
1976-01-01
The elementary solution of the one-speed neutron-transport equation with linearly anisotropic scattering are used in conjunction with Chandrasekhar's invariance principles to solve in a concise manner the Milne problem for two adjoining half-spaces and the critical reactor problem for a reflected slab
Neutron transport calculations of some fast critical assemblies
Energy Technology Data Exchange (ETDEWEB)
Martinez-Val Penalosa, J A
1976-07-01
To analyse the influence of the input variables of the transport codes upon the neutronic results (eigenvalues, generation times, . . . ) four Benchmark calculations have been performed. Sensitivity analysis have been applied to express these dependences in a useful way, and also to get an unavoidable experience to carry out calculations achieving the required accuracy and doing them in practical computing times. (Author) 29 refs.
Neutron transport calculations of some fast critical assemblies
International Nuclear Information System (INIS)
Martinez-Val Penalosa, J. A.
1976-01-01
To analyse the influence of the input variables of the transport codes upon the neutronic results (eigenvalues, generation times, . . . ) four Benchmark calculations have been performed. Sensitivity analysis have been applied to express these dependences in a useful way, and also to get an unavoidable experience to carry out calculations achieving the required accuracy and doing them in practical computing times. (Author) 29 refs
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.
Optimization of a neutron detector design using adjoint transport simulation
International Nuclear Information System (INIS)
Yi, C.; Manalo, K.; Huang, M.; Chin, M.; Edgar, C.; Applegate, S.; Sjoden, G.
2012-01-01
A synthetic aperture approach has been developed and investigated for Special Nuclear Materials (SNM) detection in vehicles passing a checkpoint at highway speeds. SNM is postulated to be stored in a moving vehicle and detector assemblies are placed on the road-side or in chambers embedded below the road surface. Neutron and gamma spectral awareness is important for the detector assembly design besides high efficiencies, so that different SNMs can be detected and identified with various possible shielding settings. The detector assembly design is composed of a CsI gamma-ray detector block and five neutron detector blocks, with peak efficiencies targeting different energy ranges determined by adjoint simulations. In this study, formulations are derived using adjoint transport simulations to estimate detector efficiencies. The formulations is applied to investigate several neutron detector designs for Block IV, which has its peak efficiency in the thermal range, and Block V, designed to maximize the total neutron counts over the entire energy spectrum. Other Blocks detect different neutron energies. All five neutron detector blocks and the gamma-ray block are assembled in both MCNP and deterministic simulation models, with detector responses calculated to validate the fully assembled design using a 30-group library. The simulation results show that the 30-group library, collapsed from an 80-group library using an adjoint-weighting approach with the YGROUP code, significantly reduced the computational cost while maintaining accuracy. (authors)
International Nuclear Information System (INIS)
Thiagu Supramaniam
2007-01-01
The aim of this research was to propose a new neutron collimator design for thermal neutron radiography facility using tangential beam port of PUSPATI TRIGA Mark II reactor, Malaysia Institute of Nuclear Technology Research (MINT). Best geometry and materials for neutron collimator were chosen in order to obtain a uniform beam with maximum thermal neutron flux, high L/ D ratio, high neutron to gamma ratio and low beam divergence with high resolution. Monte Carlo N-particle Transport Code version 5 (MCNP 5) was used to optimize six neutron collimator components such as beam port medium, neutron scatterer, neutron moderator, gamma filter, aperture and collimator wall. The reactor and tangential beam port setup in MCNP5 was plotted according to its actual sizes. A homogeneous reactor core was assumed and population control method of variance reduction technique was applied by using cell importance. The comparison between experimental results and simulated results of the thermal neutron flux measurement of the bare tangential beam port, shows that both graph obtained had similar pattern. This directly suggests the reliability of MCNP5 in order to obtained optimal neutron collimator parameters. The simulated results of the optimal neutron medium, shows that vacuum was the best medium to transport neutrons followed by helium gas and air. The optimized aperture component was boral with 3 cm thickness. The optimal aperture center hole diameter was 2 cm which produces 88 L/ D ratio. Simulation also shows that graphite neutron scatterer improves thermal neutron flux while reducing fast neutron flux. Neutron moderator was used to moderate fast and epithermal neutrons in the beam port. Paraffin wax with 90 cm thick was bound to be the best neutron moderator material which produces the highest thermal neutron flux at the image plane. Cylindrical shape high density polyethylene neutron collimator produces the highest thermal neutron flux at the image plane rather than divergent
Analysis and development of spatial hp-refinement methods for solving the neutron transport equation
International Nuclear Information System (INIS)
Fournier, D.
2011-01-01
The different neutronic parameters have to be calculated with a higher accuracy in order to design the 4. generation reactor cores. As memory storage and computation time are limited, adaptive methods are a solution to solve the neutron transport equation. The neutronic flux, solution of this equation, depends on the energy, angle and space. The different variables are successively discretized. The energy with a multigroup approach, considering the different quantities to be constant on each group, the angle by a collocation method called SN approximation. Once the energy and angle variable are discretized, a system of spatially-dependent hyperbolic equations has to be solved. Discontinuous finite elements are used to make possible the development of hp-refinement methods. Thus, the accuracy of the solution can be improved by spatial refinement (h-refinement), consisting into subdividing a cell into sub-cells, or by order refinement (p-refinement), by increasing the order of the polynomial basis. In this thesis, the properties of this methods are analyzed showing the importance of the regularity of the solution to choose the type of refinement. Thus, two error estimators are used to lead the refinement process. Whereas the first one requires high regularity hypothesis (analytical solution), the second one supposes only the minimal hypothesis required for the solution to exist. The comparison of both estimators is done on benchmarks where the analytic solution is known by the method of manufactured solutions. Thus, the behaviour of the solution as a regard of the regularity can be studied. It leads to a hp-refinement method using the two estimators. Then, a comparison is done with other existing methods on simplified but also realistic benchmarks coming from nuclear cores. These adaptive methods considerably reduces the computational cost and memory footprint. To further improve these two points, an approach with energy-dependent meshes is proposed. Actually, as the
Homogenization of the critically spectral equation in neutron transport
Energy Technology Data Exchange (ETDEWEB)
Allaire, G. [CEA Saclay, 91 - Gif-sur-Yvette (France). Dept. de Mecanique et de Technologie]|[Paris-6 Univ., 75 (France). Lab. d' Analyse Numerique; Bal, G. [Electricite de France (EDF), 92 - Clamart (France). Direction des Etudes et Recherches
1998-07-01
We address the homogenization of an eigenvalue problem for the neutron transport equation in a periodic heterogeneous domain, modeling the criticality study of nuclear reactor cores. We prove that the neutron flux, corresponding to the first and unique positive eigenvector, can be factorized in the product of two terms, up to a remainder which goes strongly to zero with the period. On terms is the first eigenvector of the transport equation in the periodicity cell. The other term is the first eigenvector of a diffusion equation in the homogenized domain. Furthermore, the corresponding eigenvalue gives a second order corrector for the eigenvalue of the heterogeneous transport problem. This result justifies and improves the engineering procedure used in practice for nuclear reactor cores computations. (author)
Application of Walsh functions to neutron transport problems. I. Theory
International Nuclear Information System (INIS)
Seed, T.J.; Albrecht, R.W.
1976-01-01
An approximation to the neutron transport equation is made by representing the angular flux with an expansion of the angular dependence in the orthogonal, complete, and binary valued sets of Walsh function. The Walsh approximation is applied to the one-speed, isotropic-scattering, rectangular-geometry form of the neutron transport equation. Sets of partial differential equations for the expansion coefficients are derived along with appropriate boundary conditions for their solution. The sets of the Walsh expansion to one- and two-dimensional forms of the transport equation are also obtained. The two-dimensional expansion coefficient equations are shown to be not only hyperbolic but also transformable to a set of S/sub N/-like equations that are coupled only through the scattering term. Such transformal sets of equations are termed Walsh-derived quadrature sets
Homogenization of the critically spectral equation in neutron transport
International Nuclear Information System (INIS)
Allaire, G.; Paris-6 Univ., 75; Bal, G.
1998-01-01
We address the homogenization of an eigenvalue problem for the neutron transport equation in a periodic heterogeneous domain, modeling the criticality study of nuclear reactor cores. We prove that the neutron flux, corresponding to the first and unique positive eigenvector, can be factorized in the product of two terms, up to a remainder which goes strongly to zero with the period. On terms is the first eigenvector of the transport equation in the periodicity cell. The other term is the first eigenvector of a diffusion equation in the homogenized domain. Furthermore, the corresponding eigenvalue gives a second order corrector for the eigenvalue of the heterogeneous transport problem. This result justifies and improves the engineering procedure used in practice for nuclear reactor cores computations. (author)
Rapid Measurement of Neutron Dose Rate for Transport Index
International Nuclear Information System (INIS)
Morris, R.L.
2000-01-01
A newly available neutron dose equivalent remmeter with improved sensitivity and energy response has been put into service at Rocky Flats Environmental Technology Site (RFETS). This instrument is being used to expedite measurement of the Transport Index and as an ALARA tool to identify locations where slightly elevated neutron dose equivalent rates exist. The meter is capable of measuring dose rates as low as 0.2 μSv per hour (20 μrem per hour). Tests of the angular response and energy response of the instrument are reported. Calculations of the theoretical instrument response made using MCNPtrademark are reported for materials typical of those being shipped
Discontinuous nodal schemes applied to the bidimensional neutron transport equation
International Nuclear Information System (INIS)
Delfin L, A.; Valle G, E. Del; Hennart B, J.P.
1996-01-01
In this paper several strong discontinuous nodal schemes are described, starting from the one that has only two interpolation parameters per cell to the one having ten. Their application to the spatial discretization of the neutron transport equation in X-Y geometry is also described, giving, for each one of the nodal schemes, the approximation for the angular neutron flux that includes the set of interpolation parameters and the corresponding polynomial space. Numerical results were obtained for several test problems presenting here the problem with the highest degree of difficulty and their comparison with published results 1,2 . (Author)
MCNP4C2, Coupled Neutron, Electron Gamma 3-D Time-Dependent Monte Carlo Transport Calculations
International Nuclear Information System (INIS)
2002-01-01
1 - Description of program or function: MCNP is a general-purpose, continuous-energy, generalized geometry, time-dependent, coupled neutron-photon-electron Monte Carlo transport code system. MCNP4C2 is an interim release of MCNP4C with distribution restricted to the Criticality Safety community and attendees of the LANL MCNP workshops. The major new features of MCNP4C2 include: - Photonuclear physics; - Interactive plotting; - Plot superimposed weight window mesh; - Implement remaining macro-body surfaces; - Upgrade macro-bodies to surface sources and other capabilities; - Revised summary tables; - Weight window improvements. See the MCNP home page more information http://www-xdiv.lanl.gov/XCI/PROJECTS/MCNP with a link to the MCNP Forum. See the Electronic Notebook at http://www-rsicc.ornl.gov/rsic.html for information on user experiences with MCNP. 2 - Methods:MCNP treats an arbitrary three-dimensional configuration of materials in geometric cells bounded by first- and second-degree surfaces and some special fourth-degree surfaces. Pointwise continuous-energy cross section data are used, although multigroup data may also be used. Fixed-source adjoint calculations may be made with the multigroup data option. For neutrons, all reactions in a particular cross-section evaluation are accounted for. Both free gas and S(alpha, beta) thermal treatments are used. Criticality sources as well as fixed and surface sources are available. For photons, the code takes account of incoherent and coherent scattering with and without electron binding effects, the possibility of fluorescent emission following photoelectric absorption, and absorption in pair production with local emission of annihilation radiation. A very general source and tally structure is available. The tallies have extensive statistical analysis of convergence. Rapid convergence is enabled by a wide variety of variance reduction methods. Energy ranges are 0-60 MeV for neutrons (data generally only available up to
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)
Fournier, D.; Le Tellier, R.; Suteau, C.; Herbin, R.
2011-01-01
The solution of the time-independent neutron transport equation in a deterministic way invariably consists in the successive discretization of the three variables: energy, angle and space. In the SNATCH solver used in this study, the energy and the angle are respectively discretized with a multigroup approach and the discrete ordinate method. A set of spatial coupled transport equations is obtained and solved using the Discontinuous Galerkin Finite Element Method (DGFEM). Within this method, the spatial domain is decomposed into elements and the solution is approximated by a hierarchical polynomial basis in each one. This approach is time and memory consuming when the mesh becomes fine or the basis order high. To improve the computational time and the memory footprint, adaptive algorithms are proposed. These algorithms are based on an error estimation in each cell. If the error is important in a given region, the mesh has to be refined (h−refinement) or the polynomial basis order increased (p−refinement). This paper is related to the choice between the two types of refinement. Two ways to estimate the error are compared on different benchmarks. Analyzing the differences, a hp−refinement method is proposed and tested. (author)
International Nuclear Information System (INIS)
Fujimura, T.; Nakahara, Y.; Matsumura, M.
1983-01-01
A double finite element method (DFEM), in which both the space-and-angle finite elements are employed, has been formulated and computer codes have been developed to solve the static multigroup neutron transport problems in the three-dimensional geometry. Two methods, Galerkin's weighted residual and variational are used to apply the DFEM to the transport equation. The variational principle requires complicated formulation than the Galerkin method, but the boundary conditions can be automatically incorporated and each plane equation becomes symmetric. The system equations are solved over the planar layers which we call plane iteration. The coarse mesh rebalancing technique is used for the inner iteration and the outer iteration is accelerated by extra-polation. Numerical studies of these two DFEM algorithms have been done in comparison between them and also with THe CITATION and TWOTRAN-II results. It has been confirmed that in the case of variational formulation an adaptive acceleration method of the SSOR iteration works effectively and the ray effects are mitigated in both DFEM algorithms. (author)
International Nuclear Information System (INIS)
Masiello, Emiliano; Martin, Brunella; Do, Jean-Michel
2011-01-01
A new development for the IDT solver is presented for large reactor core applications in XYZ geometries. The multigroup discrete-ordinate neutron transport equation is solved using a Domain-Decomposition (DD) method coupled with the Coarse-Mesh Finite Differences (CMFD). The later is used for accelerating the DD convergence rate. In particular, the external power iterations are preconditioned for stabilizing the oscillatory behavior of the DD iterative process. A set of critical 2-D and 3-D numerical tests on a single processor will be presented for the analysis of the performances of the method. The results show that the application of the CMFD to the DD can be a good candidate for large 3D full-core parallel applications. (author)
International Nuclear Information System (INIS)
Kobayashi, K.
1979-03-01
TP1, a FORTRAN-IV program based on transport theory, has been developed to determine reactivity effects and kinetic parameters such as effective delayed neutron fractions and mean generation time by applying the usual perturbation formalism for one-dimensional geometry. Direct and adjoint angular dependent neutron fluxes are read from an interface file prepared by using the one-dimensional Ssub(n)-code DTK which provides options for slab, cylindrical and spherical geometry. Multigroup cross sections which are equivalent to those of the DTK-calculations are supplied in the SIGM-block which is also read from an interface file. This block which is usually produced by the code GRUCAL should contain the necessary delayed neutron data, which can be added to the original SIGMN-block by using the code SIGMUT. Two perturbation options are included in TP1: a) the usual first oder perturbation theory can be applied to determine probe reactivities, b) assuming that there are available direct fluxes for the unperturbed reactor system and adjoint fluxes for the perturbed system, the exact reactivity effect induced by the perturbation can be determined by an exact perturbation calculation. According to the input specifications, the output lists the reactivity contributions for each neutron reaction process in the desired detailed spatial and energy group resolution. (orig./RW) [de
KAMCCO, a reactor physics Monte Carlo neutron transport code
International Nuclear Information System (INIS)
Arnecke, G.; Borgwaldt, H.; Brandl, V.; Lalovic, M.
1976-06-01
KAMCCO is a 3-dimensional reactor Monte Carlo code for fast neutron physics problems. Two options are available for the solution of 1) the inhomogeneous time-dependent neutron transport equation (census time scheme), and 2) the homogeneous static neutron transport equation (generation cycle scheme). The user defines the desired output, e.g. estimates of reaction rates or neutron flux integrated over specified volumes in phase space and time intervals. Such primary quantities can be arbitrarily combined, also ratios of these quantities can be estimated with their errors. The Monte Carlo techniques are mostly analogue (exceptions: Importance sampling for collision processes, ELP/MELP, Russian roulette and splitting). Estimates are obtained from the collision and track length estimators. Elastic scattering takes into account first order anisotropy in the center of mass system. Inelastic scattering is processed via the evaporation model or via the excitation of discrete levels. For the calculation of cross sections, the energy is treated as a continuous variable. They are computed by a) linear interpolation, b) from optionally Doppler broadened single level Breit-Wigner resonances or c) from probability tables (in the region of statistically distributed resonances). (orig.) [de
Energy Technology Data Exchange (ETDEWEB)
Zwermann, W.; Aures, A.; Bernnat, W.; and others
2013-06-15
This report documents the status of the research and development goals reached within the reactor safety research project RS1503 ''Development and Application of Neutron Transport Methods and Uncertainty Analyses for Reactor Core Calculations'' as of the 1{sup st} quarter of 2013. The superordinate goal of the project is the development, validation, and application of neutron transport methods and uncertainty analyses for reactor core calculations. These calculation methods will mainly be applied to problems related to the core behaviour of light water reactors and innovative reactor concepts. The contributions of this project towards achieving this goal are the further development, validation, and application of deterministic and stochastic calculation programmes and of methods for uncertainty and sensitivity analyses, as well as the assessment of artificial neutral networks, for providing a complete nuclear calculation chain. This comprises processing nuclear basis data, creating multi-group data for diffusion and transport codes, obtaining reference solutions for stationary states with Monte Carlo codes, performing coupled 3D full core analyses in diffusion approximation and with other deterministic and also Monte Carlo transport codes, and implementing uncertainty and sensitivity analyses with the aim of propagating uncertainties through the whole calculation chain from fuel assembly, spectral and depletion calculations to coupled transient analyses. This calculation chain shall be applicable to light water reactors and also to innovative reactor concepts, and therefore has to be extensively validated with the help of benchmarks and critical experiments.
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)
Spatial domain decomposition for neutron transport problems
International Nuclear Information System (INIS)
Yavuz, M.; Larsen, E.W.
1989-01-01
A spatial Domain Decomposition method is proposed for modifying the Source Iteration (SI) and Diffusion Synthetic Acceleration (DSA) algorithms for solving discrete ordinates problems. The method, which consists of subdividing the spatial domain of the problem and performing the transport sweeps independently on each subdomain, has the advantage of being parallelizable because the calculations in each subdomain can be performed on separate processors. In this paper we describe the details of this spatial decomposition and study, by numerical experimentation, the effect of this decomposition on the SI and DSA algorithms. Our results show that the spatial decomposition has little effect on the convergence rates until the subdomains become optically thin (less than about a mean free path in thickness)
Symmetrized neutron transport equation and the fast Fourier transform method
International Nuclear Information System (INIS)
Sinh, N.Q.; Kisynski, J.; Mika, J.
1978-01-01
The differential equation obtained from the neutron transport equation by the application of the source iteration method in two-dimensional rectangular geometry is transformed into a symmetrized form with respect to one of the angular variables. The discretization of the symmetrized equation leads to finite difference equations based on the five-point scheme and solved by use of the fast Fourier transform method. Possible advantages of the approach are shown on test calculations
Deterministic methods to solve the integral transport equation in neutronic
International Nuclear Information System (INIS)
Warin, X.
1993-11-01
We present a synthesis of the methods used to solve the integral transport equation in neutronic. This formulation is above all used to compute solutions in 2D in heterogeneous assemblies. Three kinds of methods are described: - the collision probability method; - the interface current method; - the current coupling collision probability method. These methods don't seem to be the most effective in 3D. (author). 9 figs
Mathematical models for volume rendering and neutron transport
International Nuclear Information System (INIS)
Max, N.
1994-09-01
This paper reviews several different models for light interaction with volume densities of absorbing, glowing, reflecting, or scattering material. They include absorption only, glow only, glow and absorption combined, single scattering of external illumination, and multiple scattering. The models are derived from differential equations, and illustrated on a data set representing a cloud. They are related to corresponding models in neutron transport. The multiple scattering model uses an efficient method to propagate the radiation which does not suffer from the ray effect
Complex eigenvalues for neutron transport equation with quadratically anisotropic scattering
International Nuclear Information System (INIS)
Sjoestrand, N.G.
1981-01-01
Complex eigenvalues for the monoenergetic neutron transport equation in the buckling approximation have been calculated for various combinations of linearly and quadratically anisotropic scattering. The results are discussed in terms of the time-dependent case. Tables are given of complex bucklings for real decay constants and of complex decay constants for real bucklings. The results fit nicely into the pattern of real and purely imaginary eigenvalues obtained earlier. (author)
Sensitivity of neutron air transport to nitrogen cross section uncertainties
International Nuclear Information System (INIS)
Niiler, A.; Beverly, W.B.; Banks, N.E.
1975-01-01
The sensitivity of the transport of 14-MeV neutrons in sea level air to uncertainties in the ENDF/B-III values of the various Nitrogen cross sections has been calculated using the correlated sampling Monte Carlo neutron transport code SAMCEP. The source consisted of a 14.0- to 14.9-MeV band of isotropic neutrons and the fluences (0.5 to 15.0 MeV) were calculated at radii from 50 to 1500 metres. The maximum perturbations, assigned to the ENDF/B-III or base cross section set in the 6.0- to 14.5-MeV energy range were; (1) 2 percent to the total, (2) 10 percent to the total elastic, (3) 40 percent to the inelastic and absorption and (4) 20 percent to the first Legendre coefficient and 10 percent to the second Legendre coefficient of the elastic angular distribtuions. Transport calculations were carried out using various physically realistic sets of perturbed cross sections, bounded by evaluator-assigned uncertainties, as well as the base set. Results show that in some energy intervals at 1500 metres, the differential fluence level with a perturbed set differed by almost a factor of two from the differential fluence level with the base set. 5 figures
Transport of D-D fusion neutrons in thick concrete
International Nuclear Information System (INIS)
Ku, L.P.; Kolibal, J.G.
1982-07-01
By altering the collision mechanism in the numerical transport calculations, and by constructing an analytical model based on age-diffusion theory, the outstanding feature in the life history of D-D fusion neutrons penetrating deeply into ordinary concrete is shown to be the transport in the 2.3 MeV oxygen anti-resonance. This result is used to assess the impact of the cross-section uncertainties and the uncertainties due to variations in the D-D fusion spectrum and temperature
Toward whole-core neutron transport without spatial homogenization
International Nuclear Information System (INIS)
Lewis, E. E.
2009-01-01
Full text of publication follows: A long-term goal of computational reactor physics is the deterministic analysis of power reactor core neutronics without incurring significant discretization errors in the energy, spatial or angular variables. In principle, given large enough parallel configurations with unlimited CPU time and memory, this goal could be achieved using existing three-dimensional neutron transport codes. In practice, however, solving the Boltzmann equation for neutrons over the six-dimensional phase space is made intractable by the nature of neutron cross-sections and the complexity and size of power reactor cores. Tens of thousands of energy groups would be required for faithful cross section representation. Likewise, the numerous material interfaces present in power reactor lattices require exceedingly fine spatial mesh structures; these ubiquitous interfaces preclude effective implementation of adaptive grid, mesh-less methods and related techniques that have been applied so successfully in other areas of engineering science. These challenges notwithstanding, substantial progress continues in the pursuit for more robust deterministic methods for whole-core neutronics analysis. This paper examines the progress over roughly the last decade, emphasizing the space-angle variables and the quest to eliminate errors attributable to spatial homogenization. As prolog we briefly assess 1990's methods used in light water reactor analysis and review the lessons learned from the C5G7 benchmark exercises which were originated in 1999 to appraise the ability of transport codes to perform core calculations without homogenization. We proceed by examining progress over the last decade much of which falls into three areas. These may be broadly characterized as reduced homogenization, dynamic homogenization and planar-axial synthesis. In the first, homogenization in three-dimensional calculations is reduced from the fuel assembly to the pin-cell level. In the second
Directory of Open Access Journals (Sweden)
Shane Stimpson
2017-09-01
Full Text Available An essential component of the neutron transport solver is the resonance self-shielding calculation used to determine equivalence cross sections. The neutron transport code, MPACT, is currently using the subgroup self-shielding method, in which the method of characteristics (MOC is used to solve purely absorbing fixed-source problems. Recent efforts incorporating multigroup kernels to the MOC solvers in MPACT have reduced runtime by roughly 2×. Applying the same concepts for self-shielding and developing a novel lumped parameter approach to MOC, substantial improvements have also been made to the self-shielding computational efficiency without sacrificing any accuracy. These new multigroup and lumped parameter capabilities have been demonstrated on two test cases: (1 a single lattice with quarter symmetry known as VERA (Virtual Environment for Reactor Applications Progression Problem 2a and (2 a two-dimensional quarter-core slice known as Problem 5a-2D. From these cases, self-shielding computational time was reduced by roughly 3–4×, with a corresponding 15–20% increase in overall memory burden. An azimuthal angle sensitivity study also shows that only half as many angles are needed, yielding an additional speedup of 2×. In total, the improvements yield roughly a 7–8× speedup. Given these performance benefits, these approaches have been adopted as the default in MPACT.
International Nuclear Information System (INIS)
Stimpson, Shane G.; Liu, Yuxuan; Collins, Benjamin S.; Clarno, Kevin T.
2017-01-01
An essential component of the neutron transport solver is the resonance self-shielding calculation used to determine equivalence cross sections. The neutron transport code, MPACT, is currently using the subgroup self-shielding method, in which the method of characteristics (MOC) is used to solve purely absorbing fixed-source problems. Recent efforts incorporating multigroup kernels to the MOC solvers in MPACT have reduced runtime by roughly 2×. Applying the same concepts for self-shielding and developing a novel lumped parameter approach to MOC, substantial improvements have also been made to the self-shielding computational efficiency without sacrificing any accuracy. These new multigroup and lumped parameter capabilities have been demonstrated on two test cases: (1) a single lattice with quarter symmetry known as VERA (Virtual Environment for Reactor Applications) Progression Problem 2a and (2) a two-dimensional quarter-core slice known as Problem 5a-2D. From these cases, self-shielding computational time was reduced by roughly 3–4×, with a corresponding 15–20% increase in overall memory burden. An azimuthal angle sensitivity study also shows that only half as many angles are needed, yielding an additional speedup of 2×. In total, the improvements yield roughly a 7–8× speedup. Furthermore given these performance benefits, these approaches have been adopted as the default in MPACT.
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.)
AMPX: a modular system for multigroup cross-section generation and manipulation
International Nuclear Information System (INIS)
Greene, N.M.; Ford, W.E. III; Petrie, L.M.; Diggs, B.R.; Webster, C.C.; Lucius, J.L.; White, J.E.; Wright, R.Q.; Westfall, R.M.
1978-01-01
The AMPX system, developed at the Oak Ridge National Laboratory over the past seven years, is a collection of computer programs in a modular arrangement. Starting with ENDF-formatted nuclear data files, the system includes a full range of features needed to produce and use multigroup neutron, gamma-ray production, and gamma-ray interaction cross-section data. The balance between production and analysis is roughly even; thus, the system serves a wide variety of needs. The modularity is particularly attractive, since it allows the user to choose an arbitrary execution sequence from the approximately 40 to 50 modules available in the system. The modularity also allows selection from different treatments; e.g., the Nordheim method, a full-blown integral transport calculation, the Bondarenko method, or other alternative can be selected for resonance shielding. 2 figures
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.)
Beam-transport optimization for cold-neutron spectrometer
Directory of Open Access Journals (Sweden)
Nakajima Kenji
2015-01-01
Full Text Available We report the design of the beam-transport system (especially the vertical geometry for a cold-neutron disk-chopper spectrometer AMATERAS at J-PARC. Based on the elliptical shape, which is one of the most effective geometries for a ballistic mirror, the design was optimized to obtain, at the sample position, a neutron beam with high flux without serious degrading in divergence and spacial homogeneity within the boundary conditions required from actual spectrometer construction. The optimum focal point was examined. An ideal elliptical shape was modified to reduce its height without serious loss of transmission. The final result was adapted to the construction requirements of AMATERAS. Although the ideas studied in this paper are considered for the AMATERAS case, they can be useful also to other spectrometers in similar situations.
Energy Technology Data Exchange (ETDEWEB)
Valle G, E. del; Mugica R, C.A. [IPN, ESFM, Departamento de Ingenieria Nuclear, 07738 Mexico D.F. (Mexico)]. e-mail: cmugica@ipn.mx
2005-07-01
In our country, in last congresses, Gomez et al carried out reactivity calculations based on the solution of the diffusion equation for an energy group using nodal methods in one dimension and the TPL approach (Lineal Perturbation Theory). Later on, Mugica extended the application to the case of multigroup so much so much in one as in two dimensions (X Y geometry) with excellent results. Presently work is carried out similar calculations but this time based on the solution of the neutron transport equation in X Y geometry using nodal methods and again the TPL approximation. The idea is to provide a calculation method that allows to obtain in quick form the reactivity solving the direct problem as well as the enclosed problem of the not perturbed problem. A test problem for the one that results are provided for the effective multiplication factor is described and its are offered some conclusions. (Author)
A three-dimensional neutron transport benchmark solution
International Nuclear Information System (INIS)
Ganapol, B.D.; Kornreich, D.E.
1993-01-01
For one-group neutron transport theory in one dimension, several powerful analytical techniques have been developed to solve the neutron transport equation, including Caseology, Wiener-Hopf factorization, and Fourier and Laplace transform methods. In addition, after a Fourier transform in the transverse plane and formulation of a pseudo problem, two-dimensional (2-D) and three-dimensional (3-D) problems can be solved using the techniques specifically developed for the one-dimensional (1-D) case. Numerical evaluation of the resulting expressions requiring an inversion in the transverse plane have been successful for 2-D problems but becomes exceedingly difficult in the 3-D case. In this paper, we show that by using the symmetry along the beam direction, a 2-D problem can be transformed into a 3-D problem in an infinite medium. The numerical solution to the 3-D problem is then demonstrated. Thus, a true 3-D transport benchmark solution can be obtained from a well-established numerical solution to a 2-D problem
Error reduction techniques for Monte Carlo neutron transport calculations
International Nuclear Information System (INIS)
Ju, J.H.W.
1981-01-01
Monte Carlo methods have been widely applied to problems in nuclear physics, mathematical reliability, communication theory, and other areas. The work in this thesis is developed mainly with neutron transport applications in mind. For nuclear reactor and many other applications, random walk processes have been used to estimate multi-dimensional integrals and obtain information about the solution of integral equations. When the analysis is statistically based such calculations are often costly, and the development of efficient estimation techniques plays a critical role in these applications. All of the error reduction techniques developed in this work are applied to model problems. It is found that the nearly optimal parameters selected by the analytic method for use with GWAN estimator are nearly identical to parameters selected by the multistage method. Modified path length estimation (based on the path length importance measure) leads to excellent error reduction in all model problems examined. Finally, it should be pointed out that techniques used for neutron transport problems may be transferred easily to other application areas which are based on random walk processes. The transport problems studied in this dissertation provide exceptionally severe tests of the error reduction potential of any sampling procedure. It is therefore expected that the methods of this dissertation will prove useful in many other application areas
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)
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
Novel Parallel Numerical Methods for Radiation and Neutron Transport
International Nuclear Information System (INIS)
Brown, P N
2001-01-01
In many of the multiphysics simulations performed at LLNL, transport calculations can take up 30 to 50% of the total run time. If Monte Carlo methods are used, the percentage can be as high as 80%. Thus, a significant core competence in the formulation, software implementation, and solution of the numerical problems arising in transport modeling is essential to Laboratory and DOE research. In this project, we worked on developing scalable solution methods for the equations that model the transport of photons and neutrons through materials. Our goal was to reduce the transport solve time in these simulations by means of more advanced numerical methods and their parallel implementations. These methods must be scalable, that is, the time to solution must remain constant as the problem size grows and additional computer resources are used. For iterative methods, scalability requires that (1) the number of iterations to reach convergence is independent of problem size, and (2) that the computational cost grows linearly with problem size. We focused on deterministic approaches to transport, building on our earlier work in which we performed a new, detailed analysis of some existing transport methods and developed new approaches. The Boltzmann equation (the underlying equation to be solved) and various solution methods have been developed over many years. Consequently, many laboratory codes are based on these methods, which are in some cases decades old. For the transport of x-rays through partially ionized plasmas in local thermodynamic equilibrium, the transport equation is coupled to nonlinear diffusion equations for the electron and ion temperatures via the highly nonlinear Planck function. We investigated the suitability of traditional-solution approaches to transport on terascale architectures and also designed new scalable algorithms; in some cases, we investigated hybrid approaches that combined both
An application of reactor noise techniques to neutron transport problems in a random medium
International Nuclear Information System (INIS)
Sahni, D.C.
1989-01-01
Neutron transport problems in a random medium are considered by defining a joint Markov process describing the fluctuations of one neutron population and the random changes in the medium. Backward Chapman-Kolmogorov equations are derived which yield an adjoint transport equation for the average neutron density. It is shown that this average density also satisfied the direct transport equation as given by the phenomenological model. (author)
Reliability analysis of neutron transport simulation using Monte Carlo method
International Nuclear Information System (INIS)
Souza, Bismarck A. de; Borges, Jose C.
1995-01-01
This work presents a statistical and reliability analysis covering data obtained by computer simulation of neutron transport process, using the Monte Carlo method. A general description of the method and its applications is presented. Several simulations, corresponding to slowing down and shielding problems have been accomplished. The influence of the physical dimensions of the materials and of the sample size on the reliability level of results was investigated. The objective was to optimize the sample size, in order to obtain reliable results, optimizing computation time. (author). 5 refs, 8 figs
Structures of the fractional spaces generated by the difference neutron transport operator
International Nuclear Information System (INIS)
Ashyralyev, Allaberen; Taskin, Abdulgafur
2015-01-01
The initial boundary value problem for the neutron transport equation is considered. The first, second and third order of accuracy difference schemes for the approximate solution of this problem are presented. Highly accurate difference schemes for neutron transport equation based on Padé approximation are constructed. In applications, stability estimates for solutions of difference schemes for the approximate solution of the neutron transport equation are obtained.The positivity of the neutron transport operator in Slobodeckij spaces is proved. Numerical techniques are developed and algorithms are tested on an example in MATLAB
Two-dimensional time dependent Riemann solvers for neutron transport
International Nuclear Information System (INIS)
Brunner, Thomas A.; Holloway, James Paul
2005-01-01
A two-dimensional Riemann solver is developed for the spherical harmonics approximation to the time dependent neutron transport equation. The eigenstructure of the resulting equations is explored, giving insight into both the spherical harmonics approximation and the Riemann solver. The classic Roe-type Riemann solver used here was developed for one-dimensional problems, but can be used in multidimensional problems by treating each face of a two-dimensional computation cell in a locally one-dimensional way. Several test problems are used to explore the capabilities of both the Riemann solver and the spherical harmonics approximation. The numerical solution for a simple line source problem is compared to the analytic solution to both the P 1 equation and the full transport solution. A lattice problem is used to test the method on a more challenging problem
Criticality of neutron transport in a slab with finite reflectors
International Nuclear Information System (INIS)
Pao, C.V.
1978-01-01
The purpose of this paper is to investigate the subcriticality and the supercriticality for the neutron transport in a slab which is surrounded by two finite reflectors. The mathematical problem is to determine when the coupled boundary-value problem has or has no positive solution. It is shown under some explicit conditions on the material properties of the transport mediums and the size of the slab length that the coupled problem has a unique solution which insures the subcriticality of the system. It is also shown under some different conditions on the same physical quantities that the system cannot have a nonnegative solution when there is an external source, and it only has the trivial solution when there is no source in the system. This conclusion leads to the supercriticality of the system. Both upper and lower bounds for the critical length of the slab are explicitly given
SUSD, Sensitivity and Uncertainty in Neutron Transport and Detector Response
International Nuclear Information System (INIS)
Furuta, Lazuo; Kondo, Shunsuke; Oka, Yoshika
1991-01-01
1 - Description of program or function: SUSD calculates sensitivity coefficients for one and two-dimensional transport problems. Variance and standard deviation of detector responses or design parameters can be obtained using cross-section covariance matrices. In neutron transport problems, this code is able to perform sensitivity-uncertainty analysis for secondary angular distribution (SAD) or secondary energy distribution (SED). 2 - Method of solution: The first-order perturbation theory is used to obtain sensitivity coefficients. The method described in the distributed report is employed to consider SAD/SED effect. 3 - Restrictions on the complexity of the problem: Variable dimension is used so that there is no limitation in each array size but the total core size
MPI version of NJOY and its application to multigroup cross-section generation
Energy Technology Data Exchange (ETDEWEB)
Alpan, A.; Haghighat, A.
1999-07-01
Multigroup cross-section libraries are needed in performing neutronics calculations. These libraries are referred to as broad-group libraries. The number of energy groups and group structure are highly dependent on the application and/or user's objectives. For example, for shielding calculations, broad-group libraries such as SAILOR and BUGLE with 47-neutron and 20-gamma energy groups are used. The common procedure to obtain a broad-group library is a three-step process: (1) processing pointwise ENDF (PENDF) format cross sections; (2) generating fine-group cross sections; and (3) collapsing fine-group cross sections to broad-group. The NJOY code is used to prepare fine-group cross sections by processing pointwise ENDF data. The code has several modules, each one performing a specific task. For instance, the module RECONR performs linearization and reconstruction of the cross sections, and the module GROUPR generates multigroup self-shielded cross sections. After fine-group, i.e., groupwise ENDF (GENDF), cross sections are produced, cross sections are self-shielded, and a one-dimensional transport calculation is performed to obtain flux spectra at specific regions in the model. These fluxes are then used as weighting functions to collapse the fine-group cross sections to obtain a broad-group cross-section library. The third step described is commonly performed by the AMPX code system. SMILER converts NJOY GENDF filed to AMPX master libraries, AJAX collects the master libraries. BONAMI performs self-shielding calculations, NITAWL converts the AMPX master library to a working library, XSDRNPM performs one-dimensional transport calculations, and MALOCS collapses fine-group cross sections to broad-group. Finally, ALPO is used to generate ANISN format libraries. In this three-step procedure, generally NJOY requires the largest amount of CPU time. This time varies depending on the user's specified parameters for each module, such as reconstruction tolerances
MPI version of NJOY and its application to multigroup cross-section generation
International Nuclear Information System (INIS)
Alpan, A.; Haghighat, A.
1999-01-01
Multigroup cross-section libraries are needed in performing neutronics calculations. These libraries are referred to as broad-group libraries. The number of energy groups and group structure are highly dependent on the application and/or user's objectives. For example, for shielding calculations, broad-group libraries such as SAILOR and BUGLE with 47-neutron and 20-gamma energy groups are used. The common procedure to obtain a broad-group library is a three-step process: (1) processing pointwise ENDF (PENDF) format cross sections; (2) generating fine-group cross sections; and (3) collapsing fine-group cross sections to broad-group. The NJOY code is used to prepare fine-group cross sections by processing pointwise ENDF data. The code has several modules, each one performing a specific task. For instance, the module RECONR performs linearization and reconstruction of the cross sections, and the module GROUPR generates multigroup self-shielded cross sections. After fine-group, i.e., groupwise ENDF (GENDF), cross sections are produced, cross sections are self-shielded, and a one-dimensional transport calculation is performed to obtain flux spectra at specific regions in the model. These fluxes are then used as weighting functions to collapse the fine-group cross sections to obtain a broad-group cross-section library. The third step described is commonly performed by the AMPX code system. SMILER converts NJOY GENDF filed to AMPX master libraries, AJAX collects the master libraries. BONAMI performs self-shielding calculations, NITAWL converts the AMPX master library to a working library, XSDRNPM performs one-dimensional transport calculations, and MALOCS collapses fine-group cross sections to broad-group. Finally, ALPO is used to generate ANISN format libraries. In this three-step procedure, generally NJOY requires the largest amount of CPU time. This time varies depending on the user's specified parameters for each module, such as reconstruction tolerances, temperatures
Study of influence of transport performance of the neutron guide
International Nuclear Information System (INIS)
Li Xinxi; Wang Yan; Huang Chaoqiang; Chen Bo; Chen Liang
2009-01-01
For the sake of improving the performance of the neutron scattering instrument, usually we need use the neutron guide, it's very important to select the right type and optimizing of neutron guide. The papers calculate the focus neutron guide and the single channel neutron guide by numeric method. The results shows that the choice of neutron guide should consult the resolution requirement of neutron scattering instrument, and the length of the neutron guide should be optimized. The calculation results can be the theoretical reference for the design of neutron scattering instrument. (authors)
International Nuclear Information System (INIS)
Pashchenko, A.B.; Wienke, H.
1997-01-01
This document summarizes the libraries of neutron activation cross-section data processed into the following three formats: continuous energy format as used by the Monte Carlo neutron/photon transport code MCNP4A; VITAMIN-J 175 multigroup format weighted with the VITAMIN-E weighting spectrum as used by the transmutation codes REAC*2/3 and FOUR ACES; VITAMIN-J 175 multigroup ENDF-6 format, with a flat weighting spectrum. The data are available from the IAEA Nuclear Data Section online via INTERNET by FTP command, or on magnetic tape. (author)
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
Transport calculations for a 14.8 MeV neutron beam in a water phantom
International Nuclear Information System (INIS)
Goetsch, S.J.
1981-01-01
A coupled neutron/photon Monte Carlo radiation transport code (MORSE-CG) has been used to calculate neutron and photon doses in a water phantom irradiated by 14.8 MeV neutrons from the Gas Target Neutron Source. The source-collimator-phantom geometry was carefully simulated. Results of calculations utilizing two different statistical estimators (next-collision and track-length) are presented
Simulations of neutron transport at low energy: a comparison between GEANT and MCNP.
Colonna, N; Altieri, S
2002-06-01
The use of the simulation tool GEANT for neutron transport at energies below 20 MeV is discussed, in particular with regard to shielding and dose calculations. The reliability of the GEANT/MICAP package for neutron transport in a wide energy range has been verified by comparing the results of simulations performed with this package in a wide energy range with the prediction of MCNP-4B, a code commonly used for neutron transport at low energy. A reasonable agreement between the results of the two codes is found for the neutron flux through a slab of material (iron and ordinary concrete), as well as for the dose released in soft tissue by neutrons. These results justify the use of the GEANT/MICAP code for neutron transport in a wide range of applications, including health physics problems.
International Nuclear Information System (INIS)
Sallah, M.; Margeanu, C. A.
2016-01-01
The space-fractional neutron transport equation is used to describe the neutrons transport in finite disturbed reactors. It is approximated using the Pomraning-Eddington technique to yield two space-fractional differential equations, in terms of neutron density and net neutron flux. These resultant equations are coupled into a fractional diffusion-like equation for the neutron density whose solution is obtained by using Laplace transformation method. The solution is represented in terms of the Mittag-Leffler function and its different orders. The scattering is considered as quadratic scattering to offer a more realistic, compact representation of the system, and to increase the accuracy of the estimated neutronic parameters. The results are presented graphically to illustrate the fractional parameter effect in addition to the effect of radiative-transfer properties on the physical parameters of interest (reflection coefficient, transmission coefficient, neutron energy, and net neutron flux). The neutron transport problem in finite disturbed reactor with quadratic scattering is considered in investigating the shielding effectiveness, by using MAVRIC shielding module from SCALE6 programs package. The fractional parameter can be used to adjust the analysed data on neutron energy and flux, both for the theoretical model and the neutron transport application. (authors)
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)
Finite element based composite solution for neutron transport problems
International Nuclear Information System (INIS)
Mirza, A.N.; Mirza, N.M.
1995-01-01
A finite element treatment for solving neutron transport problems is presented. The employs region-wise discontinuous finite elements for the spatial representation of the neutron angular flux, while spherical harmonics are used for directional dependence. Composite solutions has been obtained by using different orders of angular approximations in different parts of a system. The method has been successfully implemented for one dimensional slab and two dimensional rectangular geometry problems. An overall reduction in the number of nodal coefficients (more than 60% in some cases as compared to conventional schemes) has been achieved without loss of accuracy with better utilization of computational resources. The method also provides an efficient way of handling physically difficult situations such as treatment of voids in duct problems and sharply changing angular flux. It is observed that a great wealth of information about the spatial and directional dependence of the angular flux is obtained much more quickly as compared to Monte Carlo method, where most of the information in restricted to the locality of immediate interest. (author)
Nodal methods for problems in fluid mechanics and neutron transport
International Nuclear Information System (INIS)
Azmy, Y.Y.
1985-01-01
A new high-accuracy, coarse-mesh, nodal integral approach is developed for the efficient numerical solution of linear partial differential equations. It is shown that various special cases of this general nodal integral approach correspond to several high efficiency nodal methods developed recently for the numerical solution of neutron diffusion and neutron transport problems. The new approach is extended to the nonlinear Navier-Stokes equations of fluid mechanics; its extension to these equations leads to a new computational method, the nodal integral method which is implemented for the numerical solution of these equations. Application to several test problems demonstrates the superior computational efficiency of this new method over previously developed methods. The solutions obtained for several driven cavity problems are compared with the available experimental data and are shown to be in very good agreement with experiment. Additional comparisons also show that the coarse-mesh, nodal integral method results agree very well with the results of definitive ultra-fine-mesh, finite-difference calculations for the driven cavity problem up to fairly high Reynolds numbers
Neutron transport and Montecarlo method: analysis and revision
International Nuclear Information System (INIS)
Perlado, J.M.
1982-01-01
The resolution of the neutron transport equation by the Montecarlo method is presented. Coming from an extensive discussion on the best formulation of that equation in order to be treated through the mentioned method, the theoretical bases of the estimator and random-walk generation is extensively explained. The most general expression for the estimators in different physical situations, each with a diverse random-walk, is included in this basical theoretical part. Furthemore, a large revision on the variance reduction methods is made. Its theoretical presentation is claimed to be in connection with the need for each one of them. The use of the adjoint equation, as a part of the importance sampling, Russian Roulette, splitting, exponential transform, conditional and correlated Montecarlo, and one-collision and next-event extimators, are discussed. Finally, come comments in the presentation of the last works on the theoretical prediction of errors in the generation of estimators-random walks are made. (author)
Approximate solution to neutron transport equation with linear anisotropic scattering
International Nuclear Information System (INIS)
Coppa, G.; Ravetto, P.; Sumini, M.
1983-01-01
A method to obtain an approximate solution to the transport equation, when both sources and collisions show a linearly anisotropic behavior, is outlined and the possible implications for numerical calculations in applied neutronics as well as shielding evaluations are investigated. The form of the differential system of equations taken by the method is quite handy and looks simpler and more manageable than any other today available technique. To go deeper into the efficiency of the method, some typical calculations concerning critical dimension of multiplying systems are then performed and the results are compared with the ones coming from the classical Ssub(N) approximations. The outcome of such calculations leads us to think of interesting developments of the method which could be quite useful in alternative to other today widespread approximate procedures, for any geometry, but especially for curved ones. (author)
Numerical method for solving integral equations of neutron transport. II
International Nuclear Information System (INIS)
Loyalka, S.K.; Tsai, R.W.
1975-01-01
In a recent paper it was pointed out that the weakly singular integral equations of neutron transport can be quite conveniently solved by a method based on subtraction of singularity. This previous paper was devoted entirely to the consideration of simple one-dimensional isotropic-scattering and one-group problems. The present paper constitutes interesting extensions of the previous work in that in addition to a typical two-group anisotropic-scattering albedo problem in the slab geometry, the method is also applied to an isotropic-scattering problem in the x-y geometry. These results are compared with discrete S/sub N/ (ANISN or TWOTRAN-II) results, and for the problems considered here, the proposed method is found to be quite effective. Thus, the method appears to hold considerable potential for future applications. (auth)
Massively parallel performance of neutron transport response matrix algorithms
International Nuclear Information System (INIS)
Hanebutte, U.R.; Lewis, E.E.
1993-01-01
Massively parallel red/black response matrix algorithms for the solution of within-group neutron transport problems are implemented on the Connection Machines-2, 200 and 5. The response matrices are dericed from the diamond-differences and linear-linear nodal discrete ordinate and variational nodal P 3 approximations. The unaccelerated performance of the iterative procedure is examined relative to the maximum rated performances of the machines. The effects of processor partitions size, of virtual processor ratio and of problems size are examined in detail. For the red/black algorithm, the ratio of inter-node communication to computing times is found to be quite small, normally of the order of ten percent or less. Performance increases with problems size and with virtual processor ratio, within the memeory per physical processor limitation. Algorithm adaptation to courser grain machines is straight-forward, with total computing time being virtually inversely proportional to the number of physical processors. (orig.)
On the Solution of the Neutron Transport Equation
Energy Technology Data Exchange (ETDEWEB)
Depken, S
1962-12-15
The neutron transport equation has occupied the attention of many authors since Placzek, Wick and others made their first attempts to solve it, Even in the simple case of energy independent cross-sections, and disregarding the motion of the scattering nucleons, it is difficult to find a solution in an analytical form which is easily surveyable and fitted for numerical calculations. In Part I of this paper some new viewpoints will be introduced which enable the solution to be presented in its simplest possible form. Part II is devoted to an investigation of some functions introduced in Part I. In Part III the results are applied to the case of large energy lethargy, and the validity of derived formulas is discussed.
Parallel processing of neutron transport in fuel assembly calculation
International Nuclear Information System (INIS)
Song, Jae Seung
1992-02-01
Group constants, which are used for reactor analyses by nodal method, are generated by fuel assembly calculations based on the neutron transport theory, since one or a quarter of the fuel assembly corresponds to a unit mesh in the current nodal calculation. The group constant calculation for a fuel assembly is performed through spectrum calculations, a two-dimensional fuel assembly calculation, and depletion calculations. The purpose of this study is to develop a parallel algorithm to be used in a parallel processor for the fuel assembly calculation and the depletion calculations of the group constant generation. A serial program, which solves the neutron integral transport equation using the transmission probability method and the linear depletion equation, was prepared and verified by a benchmark calculation. Small changes from the serial program was enough to parallelize the depletion calculation which has inherent parallel characteristics. In the fuel assembly calculation, however, efficient parallelization is not simple and easy because of the many coupling parameters in the calculation and data communications among CPU's. In this study, the group distribution method is introduced for the parallel processing of the fuel assembly calculation to minimize the data communications. The parallel processing was performed on Quadputer with 4 CPU's operating in NURAD Lab. at KAIST. Efficiencies of 54.3 % and 78.0 % were obtained in the fuel assembly calculation and depletion calculation, respectively, which lead to the overall speedup of about 2.5. As a result, it is concluded that the computing time consumed for the group constant generation can be easily reduced by parallel processing on the parallel computer with small size CPU's
A spin-transport system for a longitudinally polarized epithermal neutron beam
International Nuclear Information System (INIS)
Crawford, B.E.; Bowman, J.D.; Penttilae, S.I.; Roberson, N.R.
2001-01-01
The TRIPLE (Time Reversal and Parity at Low Energies) collaboration uses a polarized epithermal neutron beam and a capture γ-ray detector to study parity violation in neutron-nucleus reactions. In order to preserve the spin polarization of the neutrons as they travel the 60-m path to the target, the beam pipes are wrapped with wire to produce a solenoidal magnetic field of about 10 G along the beam direction. The flanges and bellows between sections of the beam pipe cause gaps in the windings which in turn produce radial fields that can depolarize the neutron spins. A computer code has been developed that numerically evaluates the effect of these gaps on the polarization. A measurement of the neutron depolarization for neutrons in the actual spin-transport system agrees with a calculation of the neutron depolarization for the TRIPLE system. Features that will aid in designing similar spin-transport systems are discussed
Transport calculation of medium-energy protons and neutrons by Monte Carlo method
International Nuclear Information System (INIS)
Ban, Syuuichi; Hirayama, Hideo; Katoh, Kazuaki.
1978-09-01
A Monte Carlo transport code, ARIES, has been developed for protons and neutrons at medium energy (25 -- 500 MeV). Nuclear data provided by R.G. Alsmiller, Jr. were used for the calculation. To simulate the cascade development in the medium, each generation was represented by a single weighted particle and an average number of emitted particles was used as the weight. Neutron fluxes were stored by the collisions density method. The cutoff energy was set to 25 MeV. Neutrons below the cutoff were stored to be used as the source for the low energy neutron transport calculation upon the discrete ordinates method. Then transport calculations were performed for both low energy neutrons (thermal -- 25 MeV) and secondary gamma-rays. Energy spectra of emitted neutrons were calculated and compared with those of published experimental and calculated results. The agreement was good for the incident particles of energy between 100 and 500 MeV. (author)
Neutron transport in structural materials and shielding design
International Nuclear Information System (INIS)
Salvatores, M.
1979-01-01
In this paper recent development in integral Benchmark experiments and their analysis is reviewed. The main problems related to data and method assesment are also briefly reviewed. In particular, the basic data processing and multigroup structure optimization and the effects of the basic data uncertainty evaluation are stressed. The representativity of an integral experiment from the designer point of view is indicated. Moreover a procedure to deduce design oriented bias factors is outlined. Cross section adjustments are indicated as a useful tool to reduce these bias factors and their uncertainties
Safety improvement of start-up neutron source handling work by preparing new transport containers
International Nuclear Information System (INIS)
Shimazaki, Yosuke; Sawahata, Hiroaki; Yanagida, Yoshinori; Shinohara, Masanori; Kawamoto, Taiki; Takada, Shoji
2016-01-01
The conventional transport containers that have been used in HTTR start-up neutron source replacement work are not specialized type for HTTR start-up neutron source. As the risks associated with the safe handling of neutron source holders due to the above fact, the following three risks have been confirmed: (1) exposure risk due to leakage of neutron source or gamma rays, (2) risk of erroneous fall of neutron source holders, and (3) accident due to incorrect handling of transport containers. This paper reports the risks confirmed in the handling of neutron source holders associated with transport containers and the risk reduction measures, as well as the fabrication of new transport containers. By employing the size-reduction and simple structure, new transport containers have been completed at the same level of costs compared with the continuous use of the conventional transport containers, while satisfying the criteria of Type A transport materials and serving as risk preventive measures. Thus, new transport containers aimed at the risk prevention measures for the handling work of neutron source holders have been completed, and the safety of operation has been improved. (A.O.)
Experimental validation of GADRAS's coupled neutron-photon inverse radiation transport solver
International Nuclear Information System (INIS)
Mattingly, John K.; Mitchell, Dean James; Harding, Lee T.
2010-01-01
Sandia National Laboratories has developed an inverse radiation transport solver that applies nonlinear regression to coupled neutron-photon deterministic transport models. The inverse solver uses nonlinear regression to fit a radiation transport model to gamma spectrometry and neutron multiplicity counting measurements. The subject of this paper is the experimental validation of that solver. This paper describes a series of experiments conducted with a 4.5 kg sphere of α-phase, weapons-grade plutonium. The source was measured bare and reflected by high-density polyethylene (HDPE) spherical shells with total thicknesses between 1.27 and 15.24 cm. Neutron and photon emissions from the source were measured using three instruments: a gross neutron counter, a portable neutron multiplicity counter, and a high-resolution gamma spectrometer. These measurements were used as input to the inverse radiation transport solver to evaluate the solver's ability to correctly infer the configuration of the source from its measured radiation signatures.
Development of a transportable neutron radiography system for non-destructive tests application
International Nuclear Information System (INIS)
Silva, Ademir X. da; Crispim, Verginia R.
1999-01-01
This paper presents a study of a transportable neutron radiography system utilizing californium-252. Studies about moderation, collimation and shielding are showed. A Monte Carlo Code, MCNP3b, has been used to obtain a maximum and more homogeneous thermal neutron flux in the collimator outlet next to the image plain, and an adequate radiation shielding to attend radiological protection rules. With the presented collimator, it was possible to obtain for the thermal neutron flux, at the collimator outlet and next to the image plain, a L/D ratio 7,5, for neutron flux up to 6 X 10 -6 cm -2 .s -1 per neutron source. (author)
International Nuclear Information System (INIS)
Kotegawa, Hiroshi; Sasamoto, Nobuo; Tanaka, Shun-ichi
1987-02-01
Both ''measured radioactive inventory due to neutron activation in the shield concrete of JPDR'' and ''measured intermediate and low energy neutron spectra penetrating through a graphite sphere'' are analyzed using a continuous energy model Monte Carlo code MCNP so as to estimate calculational accuracy of the code for neutron transport in thermal and epithermal energy regions. Analyses reveal that MCNP calculates thermal neutron spectra fairly accurately, while it apparently over-estimates epithermal neutron spectra (of approximate 1/E distribution) as compared with the measurements. (author)
International Nuclear Information System (INIS)
Masahiro, Tatsumi; Akio, Yamamoto
2003-01-01
A production code SCOPE2 was developed based on the fine-grained parallel algorithm by the red/black iterative method targeting parallel computing environments such as a PC-cluster. It can perform a depletion calculation in a few hours using a PC-cluster with the model based on a 9-group nodal-SP3 transport method in 3-dimensional pin-by-pin geometry for in-core fuel management of commercial PWRs. The present algorithm guarantees the identical convergence process as that in serial execution, which is very important from the viewpoint of quality management. The fine-mesh geometry is constructed by hierarchical decomposition with introduction of intermediate management layer as a block that is a quarter piece of a fuel assembly in radial direction. A combination of a mesh division scheme forcing even meshes on each edge and a latency-hidden communication algorithm provided simplicity and efficiency to message passing to enhance parallel performance. Inter-processor communication and parallel I/O access were realized using the MPI functions. Parallel performance was measured for depletion calculations by the 9-group nodal-SP3 transport method in 3-dimensional pin-by-pin geometry with 340 x 340 x 26 meshes for full core geometry and 170 x 170 x 26 for quarter core geometry. A PC cluster that consists of 24 Pentium-4 processors connected by the Fast Ethernet was used for the performance measurement. Calculations in full core geometry gave better speedups compared to those in quarter core geometry because of larger granularity. Fine-mesh sweep and feedback calculation parts gave almost perfect scalability since granularity is large enough, while 1-group coarse-mesh diffusion acceleration gave only around 80%. The speedup and parallel efficiency for total computation time were 22.6 and 94%, respectively, for the calculation in full core geometry with 24 processors. (authors)
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)
AUS, Neutron Transport and Gamma Transport System for Fission Reactors and Fusion Reactors
International Nuclear Information System (INIS)
1990-01-01
1 - Description of program or function: AUS is a neutronics code system which may be used for calculations of a wide range of fission reactors, fusion blankets and other neutron applications. The present version, AUS98, has a nuclear cross section library based on ENDF/B-VI and includes modules which provide for reactor lattice calculations, one-dimensional transport calculations, multi-dimensional diffusion calculations, cell and whole reactor burnup calculations, and flexible editing of results. Calculations of multi-region resonance shielding, coupled neutron and photon transport, energy deposition, fission product inventory and neutron diffusion are combined within the one code system. The major changes from the previous release, AUS87, are the inclusion of a cross-section library based on ENDF/B-VI, the addition of the POW3D multi-dimensional diffusion module, the addition of the MICBURN module for controlling whole reactor burnup calculations, and changes to the system as a consequence of moving from IBM mainframe computers to UNIX workstations. 2 - Method of solution: AUS98 is a modular system in which the modules are complete programs linked by a path given in the input stream. A simple path is simply a sequence of modules, but the path is actually pre-processed and compiled using the Fortran 77 compiler. This provides for complex module linking if required. Some of the modules included in AUS98 are: MIRANDA Cross-section generation in a multi-region resonance subgroup calculation and preliminary group condensation. ANAUSN One-dimensional discrete ordinates calculation. ICPP Isotropic collision probability calculation in one dimension and for rod clusters. POW3D Multi-dimensional neutron diffusion calculation including feedback-free kinetics. AUSIDD One-dimensional diffusion calculation. EDITAR Reaction-rate editing and group collapsing following a transport calculation. CHAR Lattice and global burnup calculation. MICBURN Control of global burnup
Numerical study of the particle transport in fast neutron detectors with conversion layer
International Nuclear Information System (INIS)
Sedlackova, K.; Zatko, B.; Necas, V.
2012-01-01
This paper deals with fast neutron and recoil proton transport simulation using statistical analysis of Monte Carlo radiation transport code (MCNPX). Its possibilities in the detector design and optimization are presented. MCNPX proved as a very advantageous self-contained simulation program for fast neutron and secondary proton tracking. Simulations of respective particle transport through conversion layer of HDPE and further in the active volume of detector let us to follow important characteristics as neutron/proton flux density, reaction rate of elastic scattering on hydrogen nuclei and deposited energy as well as their dependencies on incident neutron energy and conversion layer/active region thickness. The efficiency of neutrons to protons conversion has been calculated and its maximum was reached for 500 μm thick conversion layer. The minimum active region thickness has been estimated to be about 300 μm.(authors)
Monte Carlo study of the mechanisms of transport of fast neutrons in various media
International Nuclear Information System (INIS)
Ku, L.
1976-01-01
The technique of analyzing Monte Carlo histories was used to study the details of neutron transport and slowing down mechanisms. The statistical properties of life histories of ''exceptional'' neutrons, i.e., those staying closer to the source or penetrating to larger distances from the source, were compared to those of the general population. The macroscopic behavior of ''exceptional'' neutrons was also related to the interaction mechanics and to the microscopic properties of the medium
International Nuclear Information System (INIS)
Alpan, F. Arzu; Haghighat, Alireza
2008-01-01
Multigroup (i.e., broad-group) libraries play a significant role in the accuracy of transport calculations. There are several broad-group libraries available for particular applications. For example the 47-neutron (26 fast groups), 20-gamma-group BUGLE libraries are commonly used for light water reactor shielding and pressure vessel dosimetry problems. However, there is no publicly available methodology to construct group structures for a problem and objective of interest. Therefore, we have developed the Contribution and Point-wise Cross-Section Driven (CPXSD) methodology, which constructs effective fine-and broad-group structures. In this paper, we use the CPXSD methodology to construct broad-group structures for fast neutron dosimetry problems. It is demonstrated that the broad-group libraries generated from CPXSD constructed group structures, while only 14 groups (rather than 26 groups) in the fast energy range are in good agreement (similar to 1 %-2 %) with the fine-group library from which they were derived, in reaction rate calculations.
Transport calculation of neutron flux distribution in reflector of PW reactor
International Nuclear Information System (INIS)
Remec, I.
1982-01-01
Two-dimensional transport calculation of the neutron flux and spectrum in the equatorial plain of PW reactor, using computer program DOT 3, is presented. Results show significant differences between neutron fields in which test samples and reactor vessel are exposed. (author)
International Nuclear Information System (INIS)
Bareiss, E.H.
1975-01-01
The objectives of the research remain the same as outlined in the original proposal. They are in short as follows: Develop mathematically and computationally founded criteria for the design of highly efficient and reliable multi-dimensional neutron transport codes to solve a variety of neutron migration and radiation problems and analyze existing and new methods for performance. (U.S.)
FMCEIR: a Monte Carlo program for solving the stationary neutron and gamma transport equation
International Nuclear Information System (INIS)
Taormina, A.
1978-05-01
FMCEIR is a three-dimensional Monte Carlo program for solving the stationary neutron and gamma transport equation. It is used to study the problem of neutron and gamma streaming in the GCFR and HHT reactor channels. (G.T.H.)
On the reciprocity-like relations in linear neutron transport theory
International Nuclear Information System (INIS)
Modak, R.S.; Sahni, D.C.
1997-01-01
The existence of certain reciprocity-like relations in neutron transport theory was shown earlier under some quite restrictive conditions. Here, these relations are shown to be valid in more general situations by using a different approach based on individual neutron trajectories. (author)
International Nuclear Information System (INIS)
Bareiss, E.H.
1977-08-01
The objectives of this research are to develop mathematically and computationally founded criteria for the design of highly efficient and reliable multidimensional neutron transport codes to solve a variety of neutron migration and radiation problems, and to analyze existing and new methods for performance
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
Neutron and photon transport calculations in fusion system. 2
Energy Technology Data Exchange (ETDEWEB)
Sato, Satoshi [Japan Atomic Energy Research Inst., Naka, Ibaraki (Japan). Naka Fusion Research Establishment
1998-03-01
On the application of MCNP to the neutron and {gamma}-ray transport calculations for fusion reactor system, the wide range design calculation has been carried out in the engineering design activities for the international thermonuclear fusion experimental reactor (ITER) being developed jointly by Japan, USA, EU and Russia. As the objects of shielding calculation for fusion reactors, there are the assessment of dose equivalent rate for living body shielding and the assessment of the nuclear response for the soundness of in-core structures. In the case that the detailed analysis of complicated three-dimensional shapes is required, the assessment using MCNP has been carried out. Also when the nuclear response of peripheral equipment due to the gap streaming between blanket modules is evaluated with good accuracy, the calculation with MCNP has been carried out. The analyses of the shieldings for blanket modules and NBI port are explained, and the examples of the results of analyses are shown. In the blanket modules, there are penetrating holes and continuous gap. In the case of the NBI port, shielding plug cannot be installed. These facts necessitate the MCNP analysis with high accuracy. (K.I.)
Energy Technology Data Exchange (ETDEWEB)
Bal, G. [Departement MMN, Service IMA, Direction des Etudes et Recherches, Electricite de France (EDF), 92 - Clamart (France)
1995-10-01
Neutron transport in nuclear reactors is quite well modelled by the linear Boltzmann transport equation. Its solution is relatively easy, but unfortunately too expensive to achieve whole core computations. Thus, we have to simplify it, for example by homogenizing some physical characteristics. However, the solution may then be inaccurate. Moreover, in strongly homogeneous areas, the error may be too big. Then we would like to deal with such an inconvenient by solving the equation accurately on this area, but more coarsely away from it, so that the computation is not too expensive. This problem is the subject of a thesis. We present here some results obtained for slab geometry. The couplings between the fine and coarse discretization regions could be conceived in a number of approaches. Here, we only deal with the coupling at crossing the interface between two sub-domains. In the first section, we present the coupling of discrete ordinate methods for solving the homogeneous, isotropic and mono-kinetic equation. Coupling operators are defined and shown to be optimal. The second and the third sections are devoted to an extension of the previous results when the equation is non-homogeneous, anisotropic and multigroup (under some restrictive assumptions). Some numerical results are given in the case of isotropic and mono-kinetic equations. (author) 15 refs.
TEMPS, 1-Group Time-Dependent Pulsed Source Neutron Transport
International Nuclear Information System (INIS)
Ganapol, B.D.
1988-01-01
1 - Description of program or function: TEMPS numerically determines the scalar flux as given by the one-group neutron transport equation with a pulsed source in an infinite medium. Standard plane, point, and line sources are considered as well as a volume source in the negative half-space in plane geometry. The angular distribution of emitted neutrons can either be isotropic or mono-directional (beam) in plane geometry and isotropic in spherical and cylindrical geometry. A general anisotropic scattering Kernel represented in terms of Legendre polynomials can be accommodated with a time- dependent number of secondaries given by c(t)=c 0 (t/t 0 ) β , where β is greater than -1 and less than infinity. TEMPS is designed to provide the flux to a high degree of accuracy (4-5 digits) for use as a benchmark to which results from other numerical solutions or approximations can be compared. 2 - Method of solution: A semi-analytic Method of solution is followed. The main feature of this approach is that no discretization of the transport or scattering operators is employed. The numerical solution involves the evaluation of an analytical representation of the solution by standard numerical techniques. The transport equation is first reformulated in terms of multiple collisions with the flux represented by an infinite series of collisional components. Each component is then represented by an orthogonal Legendre series expansion in the variable x/t where the distance x and time t are measured in terms of mean free path and mean free time, respectively. The moments in the Legendre reconstruction are found from an algebraic recursion relation obtained from Legendre expansion in the direction variable mu. The multiple collision series is evaluated first to a prescribed relative error determined by the number of digits desired in the scalar flux. If the Legendre series fails to converge in the plane or point source case, an accelerative transformation, based on removing the
Simulation of neutron transport equation using parallel Monte Carlo for deep penetration problems
International Nuclear Information System (INIS)
Bekar, K. K.; Tombakoglu, M.; Soekmen, C. N.
2001-01-01
Neutron transport equation is simulated using parallel Monte Carlo method for deep penetration neutron transport problem. Monte Carlo simulation is parallelized by using three different techniques; direct parallelization, domain decomposition and domain decomposition with load balancing, which are used with PVM (Parallel Virtual Machine) software on LAN (Local Area Network). The results of parallel simulation are given for various model problems. The performances of the parallelization techniques are compared with each other. Moreover, the effects of variance reduction techniques on parallelization are discussed
Calculation of neutron and gamma transport at the FOA:type of problems and calculation methods
International Nuclear Information System (INIS)
Lefvert, T.
1975-11-01
Protection against the effects of nuclear warfare involves the analysis of the forms of results of a nuclear charge explosion producing neutron and gamma radiation. It brings out problems leading to the calculation of criticality, leakage, and deep transmission. Methods have been developed for various kinds of particle transport problems. Applications to radiation therapy, storage of fissile materials, and fast reactors are discussed. A list (with brief description) of all neutron and gamma transport programmes of the FOA is given. (J.S.)
Transport calculation of thermal and cold neutrons using NMTC/JAERI-MCNP4A code system
International Nuclear Information System (INIS)
Iga, Kiminori; Takada, Hiroshi; Nagao, Tadashi.
1998-01-01
In order to investigate the applicability of the NMTC/JAERI-MCNP4A code system to the neutronics design study in the neutron science research project of JAERI, transport calculations of thermal and cold neutrons are performed with the code system on a spallation neutron source composed of light water cooled tantalum target with a moderator and a reflector system. The following neutronic characteristics are studied in the calculation : the variation of the intensity of neutrons emitted from a light water moderator or a liquid hydrogen with/without the B 4 C decoupler, which are installed to produce sharp pulse, and that dependent on the position of external source neutrons in the tantalum target. The calculated neutron energy spectra are reproduced well by the semi-empirical formula with the parameter values reliable in physical meanings. It is found to be necessary to employ proper importance sampling technique in the statistics. It is confirmed from this work that the NMTC/JAERI-MCNP4A code system is applicable to the neutronics design study of spallation neutron sources proposed for the neutron science research project. (author)
Transport calculation of thermal and cold neutrons using NMTC/JAERI-MCNP4A code system
Energy Technology Data Exchange (ETDEWEB)
Iga, Kiminori [Kyushu Univ., Fukuoka (Japan); Takada, Hiroshi; Nagao, Tadashi
1998-01-01
In order to investigate the applicability of the NMTC/JAERI-MCNP4A code system to the neutronics design study in the neutron science research project of JAERI, transport calculations of thermal and cold neutrons are performed with the code system on a spallation neutron source composed of light water cooled tantalum target with a moderator and a reflector system. The following neutronic characteristics are studied in the calculation : the variation of the intensity of neutrons emitted from a light water moderator or a liquid hydrogen with/without the B{sub 4}C decoupler, which are installed to produce sharp pulse, and that dependent on the position of external source neutrons in the tantalum target. The calculated neutron energy spectra are reproduced well by the semi-empirical formula with the parameter values reliable in physical meanings. It is found to be necessary to employ proper importance sampling technique in the statistics. It is confirmed from this work that the NMTC/JAERI-MCNP4A code system is applicable to the neutronics design study of spallation neutron sources proposed for the neutron science research project. (author)
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
Continuous energy adjoint Monte Carlo for coupled neutron-photon transport
Energy Technology Data Exchange (ETDEWEB)
Hoogenboom, J.E. [Delft Univ. of Technology (Netherlands). Interfaculty Reactor Inst.
2001-07-01
Although the theory for adjoint Monte Carlo calculations with continuous energy treatment for neutrons as well as for photons is known, coupled neutron-photon transport problems present fundamental difficulties because of the discrete energies of the photons produced by neutron reactions. This problem was solved by forcing the energy of the adjoint photon to the required discrete value by an adjoint Compton scattering reaction or an adjoint pair production reaction. A mathematical derivation shows the exact procedures to follow for the generation of an adjoint neutron and its statistical weight. A numerical example demonstrates that correct detector responses are obtained compared to a standard forward Monte Carlo calculation. (orig.)
International Nuclear Information System (INIS)
Singleterry, R.C. Jr.; Wilson, J.W.
1997-01-01
Extension of the high charge and energy (HZE) transport computer program HZETRN for angular transport of neutrons is considered. For this paper, only light ion transport, He 4 and lighter, will be analyzed using a pure solar proton source. The angular transport calculator is the ANISN/PC program which is being controlled by the HZETRN program. The neutron flux values are compared for straight-ahead transport and angular transport in one dimension. The shield material is aluminum and the target material is water. The thickness of these materials is varied; however, only the largest model calculated is reported which is 50 gm/cm 2 of aluminum and 100 gm/cm 2 of water. The flux from the ANISN/PC calculation is about two orders of magnitude lower than the flux from HZETRN for very low energy neutrons. It is only a magnitude lower for the neutrons in the 10 to 20 MeV range in the aluminum and two orders lower in the water. The major reason for this difference is in the transport modes: straight-ahead versus angular. The angular treatment allows a longer path length than the straight-ahead approximation. Another reason is the different cross section sets used by the ANISN/PC-BUGLE-80 mode and the HZETRN mode. The next step is to investigate further the differences between the two codes and isolate the differences to just the angular versus straight-ahead transport mode. Then, create a better coupling between the angular neutron transport and the charged particle transport
The Application of Neutron Transport Green's Functions to Threat Scenario Simulation
Thoreson, Gregory G.; Schneider, Erich A.; Armstrong, Hirotatsu; van der Hoeven, Christopher A.
2015-02-01
Radiation detectors provide deterrence and defense against nuclear smuggling attempts by scanning vehicles, ships, and pedestrians for radioactive material. Understanding detector performance is crucial to developing novel technologies, architectures, and alarm algorithms. Detection can be modeled through radiation transport simulations; however, modeling a spanning set of threat scenarios over the full transport phase-space is computationally challenging. Previous research has demonstrated Green's functions can simulate photon detector signals by decomposing the scenario space into independently simulated submodels. This paper presents decomposition methods for neutron and time-dependent transport. As a result, neutron detector signals produced from full forward transport simulations can be efficiently reconstructed by sequential application of submodel response functions.
Neutron transport simulation in high speed moving media using Geant4
Li, G.; Ciungu, B.; Harrisson, G.; Rogge, R. B.; Tun, Z.; van der Ende, B. M.; Zwiers, I.
2017-12-01
A method using Geant4 to simulate neutron transport in moving media is described. The method is implanted in the source code of the software since Geant4 does not intrinsically support a moving object. The simulation utilizes the existing physical model and data library in Geant4, combined with frame transformations to account for the effect of relative velocity between neutrons and the moving media. An example is presented involving a high speed rotating cylinder to verify this method and show the effect of moving media on neutron transport.
Parallel computing solution of Boltzmann neutron transport equation
International Nuclear Information System (INIS)
Ansah-Narh, T.
2010-01-01
The focus of the research was on developing parallel computing algorithm for solving Eigen-values of the Boltzmam Neutron Transport Equation (BNTE) in a slab geometry using multi-grid approach. In response to the problem of slow execution of serial computing when solving large problems, such as BNTE, the study was focused on the design of parallel computing systems which was an evolution of serial computing that used multiple processing elements simultaneously to solve complex physical and mathematical problems. Finite element method (FEM) was used for the spatial discretization scheme, while angular discretization was accomplished by expanding the angular dependence in terms of Legendre polynomials. The eigenvalues representing the multiplication factors in the BNTE were determined by the power method. MATLAB Compiler Version 4.1 (R2009a) was used to compile the MATLAB codes of BNTE. The implemented parallel algorithms were enabled with matlabpool, a Parallel Computing Toolbox function. The option UseParallel was set to 'always' and the default value of the option was 'never'. When those conditions held, the solvers computed estimated gradients in parallel. The parallel computing system was used to handle all the bottlenecks in the matrix generated from the finite element scheme and each domain of the power method generated. The parallel algorithm was implemented on a Symmetric Multi Processor (SMP) cluster machine, which had Intel 32 bit quad-core x 86 processors. Convergence rates and timings for the algorithm on the SMP cluster machine were obtained. Numerical experiments indicated the designed parallel algorithm could reach perfect speedup and had good stability and scalability. (au)
National Research Council Canada - National Science Library
Labowski, Kristofer
2001-01-01
The Linear Characteristic (LC) method on rectangular boxoid meshes is a discrete ordinate neutron transport technique that uses both zeroth and first moments of the angular neutron flux to construct a relatively accurate...
International Nuclear Information System (INIS)
Brenner, D.J.; Prael, R.E.; Little, R.C.
1987-01-01
Realistic simulations of the passage of fast neutrons through tissue require a large quantity of cross-sectional data. What are needed are differential (in particle type, energy and angle) cross sections. A computer code is described which produces such spectra for neutrons above ∼14 MeV incident on light nuclei such as carbon and oxygen. Comparisons have been made with experimental measurements of double-differential secondary charged-particle production on carbon and oxygen at energies from 27 to 60 MeV; they indicate that the model is adequate in this energy range. In order to utilize fully the results of these calculations, they should be incorporated into a neutron transport code. This requires defining a generalized format for describing charged-particle production, putting the calculated results in this format, interfacing the neutron transport code with these data, and charged-particle transport. The design and development of such a program is described. 13 refs., 3 figs
Optimization of multi-group cross sections for fast reactor analysis
International Nuclear Information System (INIS)
Chin, M. R.; Manalo, K. L.; Edgar, C. A.; Paul, J. N.; Molinar, M. P.; Redd, E. M.; Yi, C.; Sjoden, G. E.
2013-01-01
The selection of the number of broad energy groups, collapsed broad energy group boundaries, and their associated evaluation into collapsed macroscopic cross sections from a general 238-group ENDF/B-VII library dramatically impacted the k eigenvalue for fast reactor analysis. An analysis was undertaken to assess the minimum number of energy groups that would preserve problem physics; this involved studies using the 3D deterministic transport parallel code PENTRAN, the 2D deterministic transport code SCALE6.1, the Monte Carlo based MCNP5 code, and the YGROUP cross section collapsing tool on a spatially discretized MOX fuel pin comprised of 21% PUO 2 -UO 2 with sodium coolant. The various cases resulted in a few hundred pcm difference between cross section libraries that included the 238 multi-group reference, and cross sections rendered using various reaction and adjoint weighted cross sections rendered by the YGROUP tool, and a reference continuous energy MCNP case. Particular emphasis was placed on the higher energies characteristic of fission neutrons in a fast spectrum; adjoint computations were performed to determine the average per-group adjoint fission importance for the MOX fuel pin. This study concluded that at least 10 energy groups for neutron transport calculations are required to accurately predict the eigenvalue for a fast reactor system to within 250 pcm of the 238 group case. In addition, the cross section collapsing/weighting schemes within YGROUP that provided a collapsed library rendering eigenvalues closest to the reference were the contribution collapsed, reaction rate weighted scheme. A brief analysis on homogenization of the MOX fuel pin is also provided, although more work is in progress in this area. (authors)
Energy Technology Data Exchange (ETDEWEB)
Fournier, D.
2011-10-10
The different neutronic parameters have to be calculated with a higher accuracy in order to design the 4. generation reactor cores. As memory storage and computation time are limited, adaptive methods are a solution to solve the neutron transport equation. The neutronic flux, solution of this equation, depends on the energy, angle and space. The different variables are successively discretized. The energy with a multigroup approach, considering the different quantities to be constant on each group, the angle by a collocation method called SN approximation. Once the energy and angle variable are discretized, a system of spatially-dependent hyperbolic equations has to be solved. Discontinuous finite elements are used to make possible the development of hp-refinement methods. Thus, the accuracy of the solution can be improved by spatial refinement (h-refinement), consisting into subdividing a cell into sub-cells, or by order refinement (p-refinement), by increasing the order of the polynomial basis. In this thesis, the properties of this methods are analyzed showing the importance of the regularity of the solution to choose the type of refinement. Thus, two error estimators are used to lead the refinement process. Whereas the first one requires high regularity hypothesis (analytical solution), the second one supposes only the minimal hypothesis required for the solution to exist. The comparison of both estimators is done on benchmarks where the analytic solution is known by the method of manufactured solutions. Thus, the behaviour of the solution as a regard of the regularity can be studied. It leads to a hp-refinement method using the two estimators. Then, a comparison is done with other existing methods on simplified but also realistic benchmarks coming from nuclear cores. These adaptive methods considerably reduces the computational cost and memory footprint. To further improve these two points, an approach with energy-dependent meshes is proposed. Actually, as the
Comparison of 2D and 3D Neutron Transport Analyses on Yonggwang Unit 3 Reactor
International Nuclear Information System (INIS)
Maeng, Aoung Jae; Kim, Byoung Chul; Lim, Mi Joung; Kim, Kyung Sik; Jeon, Young Kyou; Yoo, Choon Sung
2012-01-01
10 CFR Part 50 Appendix H requires periodical surveillance program in the reactor vessel (RV) belt line region of light water nuclear power plant to check vessel integrity resulting from the exposure to neutron irradiation and thermal environment. Exact exposure analysis of the neutron fluence based on right modeling and simulations is the most important in the evaluation. Traditional 2 dimensional (D) and 1D synthesis methodologies have been widely applied to evaluate the fast neutron (E > 1.0 MeV) fluence exposure to RV. However, 2D and 1D methodologies have not provided accurate fast neutron fluence evaluation at elevations far above or below the active core region. RAPTOR-M3G (RApid Parallel Transport Of Radiation - Multiple 3D Geometries) program for 3D geometries calculation was therefore developed both by Westinghouse Electronic Company, USA and Korea Reactor Integrity Surveillance Technology (KRIST) for the analysis of In-Vessel Surveillance Test and Ex-Vessel Neutron Dosimetry (EVND). Especially EVND which is installed at active core height between biological shielding material and concrete also evaluates axial neutron fluence by placing three dosimetries each at Top, Middle and Bottom part of the angle representing maximum neutron fluence. The EVND programs have been applied to the Korea Nuclear Plants. The objective of this study is therefore to compare the 3D and the 2D Neutron Transport Calculations and Analyses on the Yonggwang unit 3 Reactor as an example
Special Features of the Air to Space Neutron Transport Problem
2017-09-14
an atmosphere model. Radioactive Decay Free neutrons are not stable elementary particles. They decay radioactively with a half- life of around ten...milliseconds to seconds, so that radioactive decay of neutrons is negligible. (The probability of decay in 100 milliseconds with a 10 minute half- life is...the bottom and top of a layer are 1bZ - and bZ respectively. The methods developed here apply to any planet with an atmosphere and an orbiting
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.
Resolution of the neutron transport equation by massively parallel computer in the Cronos code
International Nuclear Information System (INIS)
Zardini, D.M.
1996-01-01
The feasibility of neutron transport problems parallel resolution by CRONOS code's SN module is here studied. In this report we give the first data about the parallel resolution by angular variable decomposition of the transport equation. Problems about parallel resolution by spatial variable decomposition and memory stage limits are also explained here. (author)
The infinite medium Green's function for neutron transport in plane geometry 40 years later
International Nuclear Information System (INIS)
Ganapol, B.D.
1993-01-01
In 1953, the first of what was supposed to be two volumes on neutron transport theory was published. The monograph, entitled open-quotes Introduction to the Theory of Neutron Diffusionclose quotes by Case et al., appeared as a Los Alamos National Laboratory report and was to be followed by a second volume, which never appeared as intended because of the death of Placzek. Instead, Case and Zweifel collaborated on the now classic work entitled Linear Transport Theory 2 in which the underlying mathematical theory of linear transport was presented. The initial monograph, however, represented the coming of age of neutron transport theory, which had its roots in radiative transfer and kinetic theory. In addition, it provided the first benchmark results along with the mathematical development for several fundamental neutron transport problems. In particular, one-dimensional infinite medium Green's functions for the monoenergetic transport equation in plane and spherical geometries were considered complete with numerical results to be used as standards to guide code development for applications. Unfortunately, because of the limited computational resources of the day, some numerical results were incorrect. Also, only conventional mathematics and numerical methods were used because the transport theorists of the day were just becoming acquainted with more modern mathematical approaches. In this paper, Green's function solution is revisited in light of modern numerical benchmarking methods with an emphasis on evaluation rather than theoretical results. The primary motivation for considering the Green's function at this time is its emerging use in solving finite and heterogeneous media transport problems
Application of neutron/gamma transport codes for the design of explosive detection systems
International Nuclear Information System (INIS)
Elias, E.; Shayer, Z.
1994-01-01
Applications of neutron and gamma transport codes to the design of nuclear techniques for detecting concealed explosives material are discussed. The methodology of integrating radiation transport computations in the development, optimization and analysis phases of these new technologies is discussed. Transport and Monte Carlo codes are used for proof of concepts, guide the system integration, reduce the extend of experimental program and provide insight into the physical problem involved. The paper concentrates on detection techniques based on thermal and fast neutron interactions in the interrogated object. (authors). 6 refs., 1 tab., 5 figs
International Nuclear Information System (INIS)
Jahshan, S.N.; Wemple, C.A.; Ganapol, B.D.
1993-01-01
A comparison of the numerical solutions of the transport equation describing the steady neutron slowing down in an infinite medium with constant cross sections is made with stochastic solutions obtained from tracking successive neutron histories in the same medium. The transport equation solution is obtained using a numerical Laplace transform inversion algorithm. The basis for the algorithm is an evaluation of the Bromwich integral without analytical continuation. Neither the transport nor the stochastic solution is limited in the number of scattering species allowed. The medium may contain an absorption component as well. (orig.)
International Nuclear Information System (INIS)
Bareiss, E.H.
1976-05-01
The objectives of the work are to develop mathematically and computationally founded for the design of highly efficient and reliable multidimensional neutron transport codes to solve a variety of neutron migration and radiation problems, and to analyze existing and new methods for performance. As new analytical insights are gained, new numerical methods are developed and tested. Significant results obtained include implementation of the integer-preserving Gaussian elimination method (two-step method) in a CDC 6400 computer code, modes analysis for one-dimensional transport solutions, and a new method for solving the 1-T transport equation. Some of the work dealt with the interface and corner problem in diffusion theory
Study on MPI/OpenMP hybrid parallelism for Monte Carlo neutron transport code
International Nuclear Information System (INIS)
Liang Jingang; Xu Qi; Wang Kan; Liu Shiwen
2013-01-01
Parallel programming with mixed mode of messages-passing and shared-memory has several advantages when used in Monte Carlo neutron transport code, such as fitting hardware of distributed-shared clusters, economizing memory demand of Monte Carlo transport, improving parallel performance, and so on. MPI/OpenMP hybrid parallelism was implemented based on a one dimension Monte Carlo neutron transport code. Some critical factors affecting the parallel performance were analyzed and solutions were proposed for several problems such as contention access, lock contention and false sharing. After optimization the code was tested finally. It is shown that the hybrid parallel code can reach good performance just as pure MPI parallel program, while it saves a lot of memory usage at the same time. Therefore hybrid parallel is efficient for achieving large-scale parallel of Monte Carlo neutron transport. (authors)
Design studies for a high-resolution, transportable neutron radiography/radioscopy system
International Nuclear Information System (INIS)
Gillespie, G.H.; Micklich, B.J.; McMichael, G.E.
1996-01-01
A preliminary design has been developed for a high-resolution, transportable neutron radiology system (TNRS) concept. The primary system requirement is taken to be a thermal neutron flux of 10[sup 6] n/(cm[sup 2]-sec) with a L/D ratio of 100. The approach is to use an accelerator-driven neutron source, with a radiofrequency quadrupole (RFQ) as the primary accelerator component. Initial concepts for all of the major components of the system have been developed,and selected key parts have been examined further. An overview of the system design is presented, together with brief summaries of the concepts for the ion source, low energy beam transport (LEBT), RFQ, high energy beam transport (HEBT), target, moderator, collimator, image collection, power, cooling, vacuum, structure, robotics, control system, data analysis, transport vehicle, and site support. The use of trade studies for optimizing the TNRS concept are also described
International Nuclear Information System (INIS)
Both, J.P.; Mazzolo, A.; Petit, O.; Peneliau, Y.; Roesslinger, B.
2008-01-01
1 - Description of program or function: TRIPOLI-4 is a general purpose radiation transport code. It uses the Monte Carlo method to simulate neutron and photon behaviour in three-dimensional geometries. The main areas of applications include but are not restricted to: radiation protection and shielding, nuclear criticality safety, fission and fusion reactor design, nuclear instrumentation. In addition, it can simulate electron-photon cascade showers. It computes particle fluxes and currents and several related physical quantities such as, reaction rates, dose rates, heating, energy deposition, effective multiplication factor, perturbation effects due to density, concentration or partial cross-section variations. The summary precises the types of particles, the nuclear data format and cross sections, the energy ranges, the geometry, the sources, the calculated physical quantities and estimators, the biasing, the time-dependant transport for neutrons, the perturbation, the coupled particle transport and the qualification benchmarks. Data libraries distributed with the TRIPOLI-4: ENDFB6R4, ENDL, JEF2, Mott-Rutherford and Qfission. NEA-1716/04: TRIPOLI-4.4 does not contain the source programs. New features available in TRIPOLI-4 version 4 concern the following points: New biasing features, neutron collision in multigroup homogenized mode, display of the collision sites, ENDF format evaluations, computation of the gamma source produced by neutrons, output format for all results, Verbose level for output warnings, photons reactions rates, XML format output, ENDF format evaluations, combinatorial geometry checks, Green's functions files, and neutronics-shielding coupling. 2 - Methods: The geometry package allows the user to describe a three dimensional configuration by means of surfaces (as in the MCNP code) and also through predefined shapes combine with operators (union, intersection, subtraction...). It is also possible to repeat a pattern to built a network of networks
Transport synthetic acceleration scheme for multi-dimensional neutron transport problems
Energy Technology Data Exchange (ETDEWEB)
Modak, R S; Kumar, Vinod; Menon, S V.G. [Theoretical Physics Div., Bhabha Atomic Research Centre, Mumbai (India); Gupta, Anurag [Reactor Physics Design Div., Bhabha Atomic Research Centre, Mumbai (India)
2005-09-15
The numerical solution of linear multi-energy-group neutron transport equation is required in several analyses in nuclear reactor physics and allied areas. Computer codes based on the discrete ordinates (Sn) method are commonly used for this purpose. These codes solve external source problem and K-eigenvalue problem. The overall solution technique involves solution of source problem in each energy group as intermediate procedures. Such a single-group source problem is solved by the so-called Source Iteration (SI) method. As is well-known, the SI-method converges very slowly for optically thick and highly scattering regions, leading to large CPU times. Over last three decades, many schemes have been tried to accelerate the SI; the most prominent being the Diffusion Synthetic Acceleration (DSA) scheme. The DSA scheme, however, often fails and is also rather difficult to implement. In view of this, in 1997, Ramone and others have developed a new acceleration scheme called Transport Synthetic Acceleration (TSA) which is much more robust and easy to implement. This scheme has been recently incorporated in 2-D and 3-D in-house codes at BARC. This report presents studies on the utility of TSA scheme for fairly general test problems involving many energy groups and anisotropic scattering. The scheme is found to be useful for problems in Cartesian as well as Cylindrical geometry. (author)
Transport synthetic acceleration scheme for multi-dimensional neutron transport problems
International Nuclear Information System (INIS)
Modak, R.S.; Vinod Kumar; Menon, S.V.G.; Gupta, Anurag
2005-09-01
The numerical solution of linear multi-energy-group neutron transport equation is required in several analyses in nuclear reactor physics and allied areas. Computer codes based on the discrete ordinates (Sn) method are commonly used for this purpose. These codes solve external source problem and K-eigenvalue problem. The overall solution technique involves solution of source problem in each energy group as intermediate procedures. Such a single-group source problem is solved by the so-called Source Iteration (SI) method. As is well-known, the SI-method converges very slowly for optically thick and highly scattering regions, leading to large CPU times. Over last three decades, many schemes have been tried to accelerate the SI; the most prominent being the Diffusion Synthetic Acceleration (DSA) scheme. The DSA scheme, however, often fails and is also rather difficult to implement. In view of this, in 1997, Ramone and others have developed a new acceleration scheme called Transport Synthetic Acceleration (TSA) which is much more robust and easy to implement. This scheme has been recently incorporated in 2-D and 3-D in-house codes at BARC. This report presents studies on the utility of TSA scheme for fairly general test problems involving many energy groups and anisotropic scattering. The scheme is found to be useful for problems in Cartesian as well as Cylindrical geometry. (author)
Interfacing MCNPX and McStas for simulation of neutron transport
DEFF Research Database (Denmark)
Klinkby, Esben Bryndt; Lauritzen, Bent; Nonbøl, Erik
2013-01-01
Stas[4, 5, 6, 7]. The coupling between the two simulation suites typically consists of providing analytical fits of MCNPX neutron spectra to McStas. This method is generally successful but has limitations, as it e.g. does not allow for re-entry of neutrons into the MCNPX regime. Previous work to resolve......Simulations of target-moderator-reflector system at spallation sources are conventionally carried out using Monte Carlo codes such as MCNPX[1] or FLUKA[2, 3] whereas simulations of neutron transport from the moderator and the instrument response are performed by neutron ray tracing codes such as Mc...... geometries, backgrounds, interference between beam-lines as well as shielding requirements along the neutron guides....
How to polarise all neutrons in one beam: a high performance polariser and neutron transport system
Rodriguez, D. Martin; Bentley, P. M.; Pappas, C.
2016-09-01
Polarised neutron beams are used in disciplines as diverse as magnetism,soft matter or biology. However, most of these applications often suffer from low flux also because the existing neutron polarising methods imply the filtering of one of the spin states, with a transmission of 50% at maximum. With the purpose of using all neutrons that are usually discarded, we propose a system that splits them according to their polarisation, flips them to match the spin direction, and then focuses them at the sample. Monte Carlo (MC) simulations show that this is achievable over a wide wavelength range and with an outstanding performance at the price of a more divergent neutron beam at the sample position.
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)
Nobuhara, Fumiyoshi; Kuroyanagi, Makoto; Masumoto, Kazuyoshi; Nakamura, Hajime; Toyoda, Akihiro; Takahashi, Katsuhiko
2017-09-01
In order to evaluate the state of activation in a cyclotron facility used for the radioisotope production of PET diagnostics, we measured the neutron flux by using gold foils and TLDs. Then, the spatial distribution of neutrons and induced activity inside the cyclotron vault were simulated with the Monte Calro calculation code for neutron transport and DCHAIN-SP for activation calculation. The calculated results are in good agreement with measured values within factor 3. Therefore, the adaption of the advanced evaluation procedure for activation level is proved to be important for the planning of decommissioning of these facilities.
A domian Decomposition Method for Transient Neutron Transport with Pomrning-Eddington Approximation
International Nuclear Information System (INIS)
Hendi, A.A.; Abulwafa, E.E.
2008-01-01
The time-dependent neutron transport problem is approximated using the Pomraning-Eddington approximation. This approximation is two-flux approximation that expands the angular intensity in terms of the energy density and the net flux. This approximation converts the integro-differential Boltzmann equation into two first order differential equations. The A domian decomposition method that used to solve the linear or nonlinear differential equations is used to solve the resultant two differential equations to find the neutron energy density and net flux, which can be used to calculate the neutron angular intensity through the Pomraning-Eddington approximation
Energy Technology Data Exchange (ETDEWEB)
Souza, S N.A. de
1991-05-01
This work presents a study a transportable neutron radiography system for a 185 GBq {sup 241} Am-Be ({alpha}, {eta}) source with a neutron yield roughly 1,25 x 10{sup 7} n/s. Studies about moderation, collimation and shielding are showed. In these studies, a calculation using Transport Theory was carried out by means of transport codes ANISN and DOT (3.5). Objectives were: to obtain a maximum and more homogeneous thermal neutron flux in the collimator outlet to the image plain, and an adequate radiation shielding to attend radiological protection rules. With the presented collimator, it was possible to obtain for the thermal neutron flux, at the collimator outlet and next to the image plain, a L/D ratio of 14, for neutron fluxes up to 4,09 x 10{sup 2} n.cm{sup -2}.s{sup -1}. Considering the low intensity of the source, it is a good value. Studies have also been carried out for L/D ratios of 22 and 30, giving thermal neutron fluxes at the image plain of 1,27 x 10{sup 2} n.cm{sup -2}.s{sup -1} and 2,65 x 10{sup 2} n.cm{sup -2}.s{sup -1}, respectively. (author). 30 refs, 39 figs, 9 tabs.
International Nuclear Information System (INIS)
Jewer, S.; Buchan, A.G.; Pain, C.C.; Cacuci, D.G.
2014-01-01
Highlights: • A new method of coupled radiation transport, heat and momentum exchanges on fluids, and heat transfer simulations. • Simulation of the thermal hydraulics and radiative properties within whole PWR assemblies. • An immersed body method for modelling complex solid domains on practical computational meshes. - Abstract: A recently developed immersed body method is adapted and used to model a typical pressurised water reactor (PWR) fuel assembly. The approach is implemented with the numerical framework of the finite element, transient criticality code, FETCH which is composed of the neutron transport code, EVENT, and the CFD code, FLUIDITY. Within this framework the neutron transport equation, Navier–Stokes equations and a fluid energy conservation equation are solved in a coupled manner on a coincident structured or unstructured mesh. The immersed body method has been used to model the solid fuel pins. The key feature of this method is that the fluid/neutronic domain and the solid domain are represented by overlapping and non-conforming meshes. The main difficulty of this approach, for which a solution is proposed in this work, is the conservative mapping of the energy and momentum exchange between the fluid/neutronic mesh and the solid fuel pin mesh. Three numerical examples are presented which include a validation of the fuel pin submodel against an analytical solution; an uncoupled (no neutron transport solution) PWR fuel assembly model with a specified power distribution which was validated against the COBRA-EN subchannel analysis code; and finally a coupled model of a PWR fuel assembly with reflective neutron boundary conditions. Coupling between the fluid and neutron transport solutions is through the nuclear cross sections dependence on Doppler fuel temperature, coolant density and temperature, which was taken into account by using pre-calculated cross-section lookup tables generated using WIMS9a. The method was found to show good agreement
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)
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
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
Solution and study of nodal neutron transport equation applying the LTSN-DiagExp method
International Nuclear Information System (INIS)
Hauser, Eliete Biasotto; Pazos, Ruben Panta; Vilhena, Marco Tullio de; Barros, Ricardo Carvalho de
2003-01-01
In this paper we report advances about the three-dimensional nodal discrete-ordinates approximations of neutron transport equation for Cartesian geometry. We use the combined collocation method of the angular variables and nodal approach for the spatial variables. By nodal approach we mean the iterated transverse integration of the S N equations. This procedure leads to the set of one-dimensional averages angular fluxes in each spatial variable. The resulting system of equations is solved with the LTS N method, first applying the Laplace transform to the set of the nodal S N equations and then obtained the solution by symbolic computation. We include the LTS N method by diagonalization to solve the nodal neutron transport equation and then we outline the convergence of these nodal-LTS N approximations with the help of a norm associated to the quadrature formula used to approximate the integral term of the neutron transport equation. (author)
Least-squares finite element discretizations of neutron transport equations in 3 dimensions
Energy Technology Data Exchange (ETDEWEB)
Manteuffel, T.A [Univ. of Colorado, Boulder, CO (United States); Ressel, K.J. [Interdisciplinary Project Center for Supercomputing, Zurich (Switzerland); Starkes, G. [Universtaet Karlsruhe (Germany)
1996-12-31
The least-squares finite element framework to the neutron transport equation introduced in is based on the minimization of a least-squares functional applied to the properly scaled neutron transport equation. Here we report on some practical aspects of this approach for neutron transport calculations in three space dimensions. The systems of partial differential equations resulting from a P{sub 1} and P{sub 2} approximation of the angular dependence are derived. In the diffusive limit, the system is essentially a Poisson equation for zeroth moment and has a divergence structure for the set of moments of order 1. One of the key features of the least-squares approach is that it produces a posteriori error bounds. We report on the numerical results obtained for the minimum of the least-squares functional augmented by an additional boundary term using trilinear finite elements on a uniform tesselation into cubes.
Spallation neutron production and the current intra-nuclear cascade and transport codes
International Nuclear Information System (INIS)
Filges, D.; Goldenbaum, F.
2001-01-01
A recent renascent interest in energetic proton-induced production of neutrons originates largely from the inception of projects for target stations of intense spallation neutron sources, like the planned European Spallation Source (ESS), accelerator-driven nuclear reactors, nuclear waste transmutation, and also from the application for radioactive beams. In the framework of such a neutron production, of major importance is the search for ways for the most efficient conversion of the primary beam energy into neutron production. Although the issue has been quite successfully addressed experimentally by varying the incident proton energy for various target materials and by covering a huge collection of different target geometries --providing an exhaustive matrix of benchmark data-- the ultimate challenge is to increase the predictive power of transport codes currently on the market. To scrutinize these codes, calculations of reaction cross-sections, hadronic interaction lengths, average neutron multiplicities, neutron multiplicity and energy distributions, and the development of hadronic showers are confronted with recent experimental data of the NESSI collaboration. Program packages like HERMES, LCS or MCNPX master the prevision of reaction cross-sections, hadronic interaction lengths, averaged neutron multiplicities and neutron multiplicity distributions in thick and thin targets for a wide spectrum of incident proton energies, geometrical shapes and materials of the target generally within less than 10% deviation, while production cross-section measurements for light charged particles on thin targets point out that appreciable distinctions exist within these models. (orig.)
Spallation neutron production and the current intra-nuclear cascade and transport codes
Filges, D.; Goldenbaum, F.; Enke, M.; Galin, J.; Herbach, C.-M.; Hilscher, D.; Jahnke, U.; Letourneau, A.; Lott, B.; Neef, R.-D.; Nünighoff, K.; Paul, N.; Péghaire, A.; Pienkowski, L.; Schaal, H.; Schröder, U.; Sterzenbach, G.; Tietze, A.; Tishchenko, V.; Toke, J.; Wohlmuther, M.
A recent renascent interest in energetic proton-induced production of neutrons originates largely from the inception of projects for target stations of intense spallation neutron sources, like the planned European Spallation Source (ESS), accelerator-driven nuclear reactors, nuclear waste transmutation, and also from the application for radioactive beams. In the framework of such a neutron production, of major importance is the search for ways for the most efficient conversion of the primary beam energy into neutron production. Although the issue has been quite successfully addressed experimentally by varying the incident proton energy for various target materials and by covering a huge collection of different target geometries --providing an exhaustive matrix of benchmark data-- the ultimate challenge is to increase the predictive power of transport codes currently on the market. To scrutinize these codes, calculations of reaction cross-sections, hadronic interaction lengths, average neutron multiplicities, neutron multiplicity and energy distributions, and the development of hadronic showers are confronted with recent experimental data of the NESSI collaboration. Program packages like HERMES, LCS or MCNPX master the prevision of reaction cross-sections, hadronic interaction lengths, averaged neutron multiplicities and neutron multiplicity distributions in thick and thin targets for a wide spectrum of incident proton energies, geometrical shapes and materials of the target generally within less than 10% deviation, while production cross-section measurements for light charged particles on thin targets point out that appreciable distinctions exist within these models.
Analytical benchmarks for nuclear engineering applications. Case studies in neutron transport theory
International Nuclear Information System (INIS)
2008-01-01
The developers of computer codes involving neutron transport theory for nuclear engineering applications seldom apply analytical benchmarking strategies to ensure the quality of their programs. A major reason for this is the lack of analytical benchmarks and their documentation in the literature. The few such benchmarks that do exist are difficult to locate, as they are scattered throughout the neutron transport and radiative transfer literature. The motivation for this benchmark compendium, therefore, is to gather several analytical benchmarks appropriate for nuclear engineering applications under one cover. We consider the following three subject areas: neutron slowing down and thermalization without spatial dependence, one-dimensional neutron transport in infinite and finite media, and multidimensional neutron transport in a half-space and an infinite medium. Each benchmark is briefly described, followed by a detailed derivation of the analytical solution representation. Finally, a demonstration of the evaluation of the solution representation includes qualified numerical benchmark results. All accompanying computer codes are suitable for the PC computational environment and can serve as educational tools for courses in nuclear engineering. While this benchmark compilation does not contain all possible benchmarks, by any means, it does include some of the most prominent ones and should serve as a valuable reference. (author)
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
The spectral element approach for the solution of neutron transport problems
International Nuclear Information System (INIS)
Barbarino, A.; Dulla, S.; Ravetto, P.; Mund, E.H.
2011-01-01
In this paper a possible application of the Spectral Element Method to neutron transport problems is presented. The basic features of the numerical scheme on the one-dimensional diffusion equation are illustrated. Then, the AN model for neutron transport is introduced, and the basic steps for the construction of a bi-dimensional solver are described. The AN equations are chosen for their structure, involving a system of coupled elliptic-type equations. Some calculations are carried out on typical benchmark problems and results are compared with the Finite Element Method, in order to evaluate their performances. (author)
International Nuclear Information System (INIS)
Tewari, S.P.
1975-01-01
A method of studying neutron transport properties in H 2 O-D 2 O mixtures, both liquid and solid, which extrapolates the neutron thermalization parameters of H 2 O is described. The decay of pulsed neutrons in the media has been investigated as an example of the application of the method. The results of the calcutions agree with the experiment for concentrations up to 50 percent D 2 O. (1 figure) (U.S.)
International Nuclear Information System (INIS)
Mika, J.
1975-09-01
Originally the work was oriented towards two main topics: a) difference and integral methods in neutron transport theory. Two computers were used for numerical calculations GIER and CYBER-72. During the first year the main effort was shifted towards basic theoretical investigations. At the first step the ANIS code was adopted and later modified to check various finite difference approaches against each other. Then the general finite element method and the singular perturbation method were developed. The analysis of singularities of the one-dimensional neutron transport equation in spherical geometry has been done and presented. Later the same analysis for the case of cylindrical symmetry has been carried out. The second and the third year programme included the following topics: 1) finite difference methods in stationary neutron transport theory; 2)mathematical fundamentals of approximate methods for solving the transport equation; 3) singular perturbation method for the time-dependent transport equation; 4) investigation of various iterative procedures in reactor calculations. This investigation will help to better understanding of the mathematical basis for existing and developed numerical methods resulting in more effective algorithms for reactor computer codes
Effects of fuel particle size distributions on neutron transport in stochastic media
International Nuclear Information System (INIS)
Liang, Chao; Pavlou, Andrew T.; Ji, Wei
2014-01-01
Highlights: • Effects of fuel particle size distributions on neutron transport are evaluated. • Neutron channeling is identified as the fundamental reason for the effects. • The effects are noticeable at low packing and low optical thickness systems. • Unit cells of realistic reactor designs are studied for different size particles. • Fuel particle size distribution effects are not negligible in realistic designs. - Abstract: This paper presents a study of the fuel particle size distribution effects on neutron transport in three-dimensional stochastic media. Particle fuel is used in gas-cooled nuclear reactor designs and innovative light water reactor designs loaded with accident tolerant fuel. Due to the design requirements and fuel fabrication limits, the size of fuel particles may not be perfectly constant but instead follows a certain distribution. This brings a fundamental question to the radiation transport computation community: how does the fuel particle size distribution affect the neutron transport in particle fuel systems? To answer this question, size distribution effects and their physical interpretations are investigated by performing a series of neutron transport simulations at different fuel particle size distributions. An eigenvalue problem is simulated in a cylindrical container consisting of fissile fuel particles with five different size distributions: constant, uniform, power, exponential and Gaussian. A total of 15 parametric cases are constructed by altering the fissile particle volume packing fraction and its optical thickness, but keeping the mean chord length of the spherical fuel particle the same at different size distributions. The tallied effective multiplication factor (k eff ) and the spatial distribution of fission power density along axial and radial directions are compared between different size distributions. At low packing fraction and low optical thickness, the size distribution shows a noticeable effect on neutron
Obtaining incremental multigroup cross sections for CANDU super cells with reactivity devices
International Nuclear Information System (INIS)
Balaceanu, V.; Constantin, M.
2001-01-01
In the last 20 years a multigroup methodology WIMS - PIJXYZ (WP) was developed and validated at INR Pitesti for obtaining incremental cross sections for reactivity devices in CANDU reactors. This is an alternate methodology to the CANDU classic methodology (experimentally adjusted) based on the POWDERPUFS and MULTICELL computer codes. The 2D supercell calculation performed with the WIMS code, that is a NEA Data Bank transport code, and which produces multigroup cross sections (on 18 energy groups) for CANDU supercell material (standard and perturbed, with and without reactivity devices). To obtain an as correct as possible 3D modelling for the CANDU supercells containing reactivity devices, the WIMS cross sections are used as input data for the PIJXYZ code, thus obtaining homogenized cross sections for CANDU supercells. PIJXYZ is an integral transport code based on the formalism of the first collision probabilities. It is analogue to the SHETAN code and it was created for neutron analyzes at cell level for CANDU type reactors were the reactivity devices are perpendicular to the fuel channels. The coordinate system used in PIJXYZ is a mixed one, namely a rectangular-cylindrical system. The geometric model used in PIJXYZ is presented. The fuel beam is represented by a horizontal cylinder and the reactivity device by a vertical one both cylinders being immersed in the moderator. Two supercell types were considered: a perturbed supercell (containing a reactivity device) and the standard supercell were the place of reactivity device is occupied by the moderator. The incremental cross sections for reactivity device are obtained as differences between the homogenized over supercell cross sections (with reactivity device) and homogenized over standards supercell (without device) cross sections. The PIJXYZ computation may be done on an energy cutting with 2 up to 18 groups. The validation of VIMS - PIJXYZ was done on the basis of several benchmark and by comparison with
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
Neutron Transport Methods for Accelerator-Driven Systems
International Nuclear Information System (INIS)
Nicholas Tsoulfanidis; Elmer Lewis
2005-01-01
The objective of this project has been to develop computational methods that will enable more effective analysis of Accelerator Driven Systems (ADS). The work is centered at the University of Missouri at Rolla, with a subcontract at Northwestern University, and close cooperation with the Nuclear Engineering Division at Argonne National Laboratory. The work has fallen into three categories. First, the treatment of the source for neutrons originating from the spallation target which drives the neutronics calculations of the ADS. Second, the generalization of the nodal variational method to treat the R-Z geometry configurations frequently needed for scoping calculations in Accelerator Driven Systems. Third, the treatment of void regions within variational nodal methods as needed to treat the accelerator beam tube
A Monte Carlo Green's function method for three-dimensional neutron transport
International Nuclear Information System (INIS)
Gamino, R.G.; Brown, F.B.; Mendelson, M.R.
1992-01-01
This paper describes a Monte Carlo transport kernel capability, which has recently been incorporated into the RACER continuous-energy Monte Carlo code. The kernels represent a Green's function method for neutron transport from a fixed-source volume out to a particular volume of interest. This method is very powerful transport technique. Also, since kernels are evaluated numerically by Monte Carlo, the problem geometry can be arbitrarily complex, yet exact. This method is intended for problems where an ex-core neutron response must be determined for a variety of reactor conditions. Two examples are ex-core neutron detector response and vessel critical weld fast flux. The response is expressed in terms of neutron transport kernels weighted by a core fission source distribution. In these types of calculations, the response must be computed for hundreds of source distributions, but the kernels only need to be calculated once. The advance described in this paper is that the kernels are generated with a highly accurate three-dimensional Monte Carlo transport calculation instead of an approximate method such as line-of-sight attenuation theory or a synthesized three-dimensional discrete ordinates solution
The study of neutron transport by oscillation method
International Nuclear Information System (INIS)
Raievski, V.
1959-01-01
The oscillation method is of very general use for studying the behavior of thermal neutrons in media. The main experiments are described and a general theory of them is given. This theory, which is presented in the first part, is established using the two-group approximation which has proved its efficiency in the case of thermal neutron piles. The validity of the two-group approximation is recalled. This allows definition of the meaning of the parameters used in the theory and which are measured in these experiments. The experiments carried out by this method are described, especially those performed at the Centre d'Etudes Nucleaires de Saclay where the method has been extensively used. These experiments are interpreted by means of the general theory given previously. In this way, the identity of parameters measured by this method and those given by the theory is proved. This is particularly conclusive is the case of the mean life of neutrons in a pile. (author) [fr
PELAN - a transportable, neutron-based UXO identification technique
International Nuclear Information System (INIS)
Vourvopoulos, G.
1998-01-01
An elemental characterization method is used to differentiate between inert projectiles and UXO's. This method identifies in a non-intrusive, nondestructive manner, the elemental composition of the projectile contents. Most major and minor chemical elements within the interrogated object (hydrogen, carbon, nitrogen, oxygen, fluorine, phosphorus, chlorine, arsenic, etc.) are identified and quantified. The method is based on PELAN - Pulsed Elemental Analysis with Neutrons. PELAN uses pulsed neutrons produced from a compact, sealed tube neutron generator. Using an automatic analysis computer program, the quantities of each major and minor chemical element are determined. A decision-making tree identifies the object by comparing its elemental composition with stored elemental composition libraries of substances that could be contained within the projectile. In a series of blind tests, PELAN was able to identify without failure, the contents of each shell placed in front of it. The PELAN probe does not need to be in contact with the interrogated projectile. If the object is buried, the interrogation can take place in situ provided the probe can be inserted a few centimeters from the object's surface. (author)
International Nuclear Information System (INIS)
Sanchez, J.
2010-10-01
A standard numerical procedure for the solution of singular integral equations is applied to the one-dimensional transport equation for monoenergetic neutrons. As is usual in quadrature methods, the procedure yields an Eigen system whose solution provide, for the critical slab, both the eigenvalue which is proportional to the number of secondary neutrons per collision, and the density as a function of position. The results obtained with two versions of the procedure, differing only in the extent of the basic region to which they are applied, are compared with analytically derived results available for benchmarking. The procedures considered yield consistent results for the calculated neutron densities and eigenvalues. Since the one-dimensional transport kernel and its spatial moments are integrable and their integrals can be put in terms of exponential integral functions, the resulting approximations to the neutron density yield somewhat lengthy but closed, forms. These approximate expressions of the neutron density can be used to render, after they are operated on, closed-form formulas for build-up factors, extrapolation distances or angular densities or employed for other purposes that require an analytical expression of the neutron density. As an example of this latter capability, the results of the calculation of the angular density at the surface of the slab are provided. (Author)
International Nuclear Information System (INIS)
Zazula, J.M.
1984-01-01
This work concerns calculation of a neutron response, caused by a neutron field perturbed by materials surrounding the source or the detector. Solution of a problem is obtained using coupling of the Monte Carlo radiation transport computation for the perturbed region and the discrete ordinates transport computation for the unperturbed system. (author). 62 refs
Quantifying moisture transport in cementitious materials using neutron radiography
Lucero, Catherine L.
A portion of the concrete pavements in the US have recently been observed to have premature joint deterioration. This damage is caused in part by the ingress of fluids, like water, salt water, or deicing salts. The ingress of these fluids can damage concrete when they freeze and expand or can react with the cementitious matrix causing damage. To determine the quality of concrete for assessing potential service life it is often necessary to measure the rate of fluid ingress, or sorptivity. Neutron imaging is a powerful method for quantifying fluid penetration since it can describe where water has penetrated, how quickly it has penetrated and the volume of water in the concrete or mortar. Neutrons are sensitive to light atoms such as hydrogen and thus clearly detect water at high spatial and temporal resolution. It can be used to detect small changes in moisture content and is ideal for monitoring wetting and drying in mortar exposed to various fluids. This study aimed at developing a method to accurately estimate moisture content in mortar. The common practice is to image the material dry as a reference before exposing to fluid and normalizing subsequent images to the reference. The volume of water can then be computed using the Beer-Lambert law. This method can be limiting because it requires exact image alignment between the reference image and all subsequent images. A model of neutron attenuation in a multi-phase cementitious composite was developed to be used in cases where a reference image is not available. The attenuation coefficients for water, un-hydrated cement, and sand were directly calculated from the neutron images. The attenuation coefficient for the hydration products was then back-calculated. The model can estimate the degree of saturation in a mortar with known mixture proportions without using a reference image for calculation. Absorption in mortars exposed to various fluids (i.e., deionized water and calcium chloride solutions) were investigated
International Nuclear Information System (INIS)
McGill, B.L.; Roussin, R.W.; Trubey, D.K.; Maskewitz, B.F.
1980-01-01
The Radiation Shielding Information Center (RSIC), established in 1962 to collect, package, analyze, and disseminate information, computer codes, and data in the area of radiation transport related to fission, is now being utilized to support fusion neutronics technology. The major activities include: (1) answering technical inquiries on radiation transport problems, (2) collecting, packaging, testing, and disseminating computing technology and data libraries, and (3) reviewing literature and operating a computer-based information retrieval system containing material pertinent to radiation transport analysis. The computer codes emphasize methods for solving the Boltzmann equation such as the discrete ordinates and Monte Carlo techniques, both of which are widely used in fusion neutronics. The data packages include multigroup coupled neutron-gamma-ray cross sections and kerma coefficients, other nuclear data, and radiation transport benchmark problem results
Radiation transport calculations for the ANS [Advanced Neutron Source] beam tubes
International Nuclear Information System (INIS)
Engle, W.W. Jr.; Lillie, R.A.; Slater, C.O.
1988-01-01
The Advanced Neutron Source facility (ANS) will incorporate a large number of both radial and no-line-of-sight (NLS) beam tubes to provide very large thermal neutron fluxes to experimental facilities. The purpose of this work was to obtain comparisons for the ANS single- and split-core designs of the thermal and damage neutron and gamma-ray scalar fluxes in these beams tubes. For experimental locations far from the reactor cores, angular flux data are required; however, for close-in experimental locations, the scalar fluxes within each beam tube provide a credible estimate of the various signal to noise ratios. In this paper, the coupled two- and three-dimensional radiation transport calculations employed to estimate the scalar neutron and gamma-ray fluxes will be described and the results from these calculations will be discussed. 6 refs., 2 figs
TMCC: a transient three-dimensional neutron transport code by the direct simulation method - 222
International Nuclear Information System (INIS)
Shen, H.; Li, Z.; Wang, K.; Yu, G.
2010-01-01
A direct simulation method (DSM) is applied to solve the transient three-dimensional neutron transport problems. DSM is based on the Monte Carlo method, and can be considered as an application of the Monte Carlo method in the specific type of problems. In this work, the transient neutronics problem is solved by simulating the dynamic behaviors of neutrons and precursors of delayed neutrons during the transient process. DSM gets rid of various approximations which are always necessary to other methods, so it is precise and flexible in the requirement of geometric configurations, material compositions and energy spectrum. In this paper, the theory of DSM is introduced first, and the numerical results obtained with the new transient analysis code, named TMCC (Transient Monte Carlo Code), are presented. (authors)
International Nuclear Information System (INIS)
Sanchez G, J.
2007-01-01
A standard procedure for the solution of singular integral equations is applied to the one-dimensional transport equation for monoenergetic neutrons. The results obtained with two versions of the procedure, differing only in the extent of the basic region to which they are applied, are compared with analytically derived results available for benchmarking. The procedures considered yield consistent results for the calculated neutron densities and eigenvalues. Several approximate expressions of the neutron density are used to render closed-form formulas for the densities which can then be analytically operated on to obtain expressions for extrapolation distances or angular densities or serve other purposes that require an analytical expression of the neutron density. (Author)
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
International Nuclear Information System (INIS)
Ganapol, B.D.
1987-01-01
For almost 20 yr, the main thrust of the author's research has been the generation of as many benchmark solutions to the time-dependent monoenergetic neutron transport equation as possible. The major motivation behind this effort has been to provide code developers with highly accurate numerical solutions to serve as standards in the assessment of numerical transport algorithms. In addition, these solutions provide excellent educational tools since the important physical features of neutron transport are still present even though the problems solved are idealized. A secondary motivation, though of equal importance, is the intellectual stimulation and understanding provided by the combination of the analytical, numerical, and computational techniques required to obtain these solutions. Therefore, to further the benchmark development, the added complication of time-dependent cross sections in the one-group transport equation is considered here
Energy Technology Data Exchange (ETDEWEB)
Raievski, V
1959-07-01
The oscillation method is of very general use for studying the behavior of thermal neutrons in media. The main experiments are described and a general theory of them is given. This theory, which is presented in the first part, is established using the two-group approximation which has proved its efficiency in the case of thermal neutron piles. The validity of the two-group approximation is recalled. This allows definition of the meaning of the parameters used in the theory and which are measured in these experiments. The experiments carried out by this method are described, especially those performed at the Centre d'Etudes Nucleaires de Saclay where the method has been extensively used. These experiments are interpreted by means of the general theory given previously. In this way, the identity of parameters measured by this method and those given by the theory is proved. This is particularly conclusive is the case of the mean life of neutrons in a pile. (author) [French] La methode de modulation est un procede tres general d'etude des proprietes neutroniques des milieux contenant des neutrons thermiques. Le present rapport a pour but de decrire les principales de ces experiences et d'en donner une theorie generale. Cette theorie, exposee dans la premiere partie, est etablie dons le cadre de l'approximation a deux groupes de vitesse qui a prouve son efficacite dons le cas des piles a neutrons thermiques. Le domaine de validite de l'approximation a deux groupes est rappele au debut, ce qui permet de definir avec precision la signification des parametres qui entrent dons la theorie et qui font l'objet de ces mesures. La deuxieme partie decrit les experiences realisees, en particulier celles effectuees au Centre d'Etudes Nucleaires de Saclay ou la methode a ete considerablement developpee. Ces experiences sont interpretees dans le cadre de la theorie generale exposee precedemment. On prouve ainsi l'identite des parametres mesures par cette methode et de ceux figurant
Monte Carlo simulations of the particle transport in semiconductor detectors of fast neutrons
International Nuclear Information System (INIS)
Sedlačková, Katarína; Zaťko, Bohumír; Šagátová, Andrea; Nečas, Vladimír
2013-01-01
Several Monte Carlo all-particle transport codes are under active development around the world. In this paper we focused on the capabilities of the MCNPX code (Monte Carlo N-Particle eXtended) to follow the particle transport in semiconductor detector of fast neutrons. Semiconductor detector based on semi-insulating GaAs was the object of our investigation. As converter material capable to produce charged particles from the (n, p) interaction, a high-density polyethylene (HDPE) was employed. As the source of fast neutrons, the 239 Pu–Be neutron source was used in the model. The simulations were performed using the MCNPX code which makes possible to track not only neutrons but also recoiled protons at all interesting energies. Hence, the MCNPX code enables seamless particle transport and no other computer program is needed to process the particle transport. The determination of the optimal thickness of the conversion layer and the minimum thickness of the active region of semiconductor detector as well as the energy spectra simulation were the principal goals of the computer modeling. Theoretical detector responses showed that the best detection efficiency can be achieved for 500 μm thick HDPE converter layer. The minimum detector active region thickness has been estimated to be about 400 μm. -- Highlights: ► Application of the MCNPX code for fast neutron detector design is demonstrated. ► Simulations of the particle transport through conversion film of HDPE are presented. ► Simulations of the particle transport through detector active region are presented. ► The optimal thickness of the HDPE conversion film has been calculated. ► Detection efficiency of 0.135% was reached for 500 μm thick HDPE conversion film
Applications of the 3-D Deterministic Transport Attila(regsign) for Core Safety Analysis
International Nuclear Information System (INIS)
Lucas, D.S.; Gougar, D.; Roth, P.A.; Wareing, T.; Failla, G.; McGhee, J.; Barnett, A.
2004-01-01
An LDRD (Laboratory Directed Research and Development) project is ongoing at the Idaho National Engineering and Environmental Laboratory (INEEL) for applying the three-dimensional multi-group deterministic neutron transport code (Attila(reg s ign)) to criticality, flux and depletion calculations of the Advanced Test Reactor (ATR). This paper discusses the model development, capabilities of Attila, generation of the cross-section libraries, and comparisons to an ATR MCNP model and future
International Nuclear Information System (INIS)
Shafii, Mohammad Ali; Meidianti, Rahma; Wildian,; Fitriyani, Dian; Tongkukut, Seni H. J.; Arkundato, Artoto
2014-01-01
Theoretical analysis of integral neutron transport equation using collision probability (CP) method with quadratic flux approach has been carried out. In general, the solution of the neutron transport using the CP method is performed with the flat flux approach. In this research, the CP method is implemented in the cylindrical nuclear fuel cell with the spatial of mesh being conducted into non flat flux approach. It means that the neutron flux at any point in the nuclear fuel cell are considered different each other followed the distribution pattern of quadratic flux. The result is presented here in the form of quadratic flux that is better understanding of the real condition in the cell calculation and as a starting point to be applied in computational calculation
International Nuclear Information System (INIS)
Talamo, Alberto
2013-01-01
This study presents three numerical algorithms to solve the time dependent neutron transport equation by the method of the characteristics. The algorithms have been developed taking into account delayed neutrons and they have been implemented into the novel MCART code, which solves the neutron transport equation for two-dimensional geometry and an arbitrary number of energy groups. The MCART code uses regular mesh for the representation of the spatial domain, it models up-scattering, and takes advantage of OPENMP and OPENGL algorithms for parallel computing and plotting, respectively. The code has been benchmarked with the multiplication factor results of a Boiling Water Reactor, with the analytical results for a prompt jump transient in an infinite medium, and with PARTISN and TDTORT results for cross section and source transients. The numerical simulations have shown that only two numerical algorithms are stable for small time steps
Energy Technology Data Exchange (ETDEWEB)
Talamo, Alberto, E-mail: alby@anl.gov [Nuclear Engineering Division, Argonne National Laboratory, 9700 South Cass Avenue, Lemont, IL 60439 (United States)
2013-05-01
This study presents three numerical algorithms to solve the time dependent neutron transport equation by the method of the characteristics. The algorithms have been developed taking into account delayed neutrons and they have been implemented into the novel MCART code, which solves the neutron transport equation for two-dimensional geometry and an arbitrary number of energy groups. The MCART code uses regular mesh for the representation of the spatial domain, it models up-scattering, and takes advantage of OPENMP and OPENGL algorithms for parallel computing and plotting, respectively. The code has been benchmarked with the multiplication factor results of a Boiling Water Reactor, with the analytical results for a prompt jump transient in an infinite medium, and with PARTISN and TDTORT results for cross section and source transients. The numerical simulations have shown that only two numerical algorithms are stable for small time steps.
Energy Technology Data Exchange (ETDEWEB)
Shafii, Mohammad Ali, E-mail: mashafii@fmipa.unand.ac.id; Meidianti, Rahma, E-mail: mashafii@fmipa.unand.ac.id; Wildian,, E-mail: mashafii@fmipa.unand.ac.id; Fitriyani, Dian, E-mail: mashafii@fmipa.unand.ac.id [Department of Physics, Andalas University Padang West Sumatera Indonesia (Indonesia); Tongkukut, Seni H. J. [Department of Physics, Sam Ratulangi University Manado North Sulawesi Indonesia (Indonesia); Arkundato, Artoto [Department of Physics, Jember University Jember East Java Indonesia (Indonesia)
2014-09-30
Theoretical analysis of integral neutron transport equation using collision probability (CP) method with quadratic flux approach has been carried out. In general, the solution of the neutron transport using the CP method is performed with the flat flux approach. In this research, the CP method is implemented in the cylindrical nuclear fuel cell with the spatial of mesh being conducted into non flat flux approach. It means that the neutron flux at any point in the nuclear fuel cell are considered different each other followed the distribution pattern of quadratic flux. The result is presented here in the form of quadratic flux that is better understanding of the real condition in the cell calculation and as a starting point to be applied in computational calculation.
Guideline of Monte Carlo calculation. Neutron/gamma ray transport simulation by Monte Carlo method
2002-01-01
This report condenses basic theories and advanced applications of neutron/gamma ray transport calculations in many fields of nuclear energy research. Chapters 1 through 5 treat historical progress of Monte Carlo methods, general issues of variance reduction technique, cross section libraries used in continuous energy Monte Carlo codes. In chapter 6, the following issues are discussed: fusion benchmark experiments, design of ITER, experiment analyses of fast critical assembly, core analyses of JMTR, simulation of pulsed neutron experiment, core analyses of HTTR, duct streaming calculations, bulk shielding calculations, neutron/gamma ray transport calculations of the Hiroshima atomic bomb. Chapters 8 and 9 treat function enhancements of MCNP and MVP codes, and a parallel processing of Monte Carlo calculation, respectively. An important references are attached at the end of this report.
The importance of anisotropic scattering in high energy neutron transport problems
International Nuclear Information System (INIS)
Prillinger, G.; Mattes, M.
1984-01-01
To describe the highly anisotropic scattering of very fast neutrons adequately the transport code ANISN has been improved. Fokker-Planck terms have been introduced into the transport equation which accurately describe the small changes in energy and angle. The new code has been tested for a d(50)-Be neutron source in a deep penetration iron problem. The influence of the forward peaked elastic scattering on the fast neutron spectrum is shown to be significant and can be handled efficiently in the new ANISN version. Since common cross-section libraries are limited by Legendre expansion, or by their upper energy boundary, or exclude elastic scattering above 20 MeV a special library has been created. (Auth.)
Radiation Transport Simulation for Boron Neutron Capture Therapy (BNCT)
Energy Technology Data Exchange (ETDEWEB)
Ziegner, M.; Blaickner, M. [AIT Austrian Institute of Technology GmbH, Health and Environment Department, Molecular Medicine, Muthgasse 11, 1190 Wien (Austria); Ziegner, M.; Khan, R.; Boeck, H. [Vienna University of Technology, Institute of Atomic and Subatomic Physics, Stadionallee 2, 1020 Wien (Austria); Bortolussi, S.; Altieri, S. [Department of Nuclear and Theoretical Physics, University of Pavia, National Institute of Nuclear Physics (INFN) Pavia Section, Pavia (Italy); Schmitz, T.; Hampel, G. [Nuclear Chemistry, University of Mainz, Fritz Strassmann Weg 2, 55099 Mainz (Germany)
2011-07-01
This work is part of a larger project initiated by the University of Mainz and aiming to use the university's TRIGA reactor to develop a treatment for liver metastases based on Boron Neutron Capture Therapy (BNCT). Diffuse distribution of cancerous cells within the organ makes complete resection difficult and the vicinity to radiosensitive organs impedes external irradiation. Therefore the method of 'autotransplantation', first established at the University of Pavia, is used. The liver is taken out of the body, irradiated in the thermal column of the reactor, therewith purged of metastases and then reimplanted. A highly precise dosimetry system is to be developed by means of measurements at the University of Mainz and computational calculations at the AIT. The stochastic MCNP-5 Monte Carlo-Code, developed by Los Alamos Laboratories, is applied. To verify the calculations of the flux and the absorbed dose in matter a number of measurements are performed irradiating different phantoms and liver sections in a 20cm x 20cm beam tube, which was created by removing graphite blocks from the thermal column of the reactor. The detector material consists of L- {alpha} -alanine pellets which are thought to be the most suitable because of their good tissue equivalence, small size and their wide response range. Another experiment focuses on the determination of the relative biological effectiveness (RBE-factor) of the neutron and photon dose for liver cells. Therefore cell culture plates with the cell medium enriched with {sup 157}Gd and {sup 10}B at different concentrations are irradiated. With regard to the alanine pellets MCNP-5 calculations give stable results. Nevertheless the absorbed dose is underestimated compared to the measurements, a phenomenon already observed in previous works. The cell culture calculations showed the enormous impact of the added isotopes with high thermal neutron cross sections, especially {sup 157}Gd, on the absorbed dose
Two-group neutron transport theory in adjacent space with lineary anisotropic scattering
International Nuclear Information System (INIS)
Maiorino, J.R.
1978-01-01
A solution method for two-group neutron transport theory with anisotropic scattering is introduced by the combination of case method (expansion method of self singular function) and the invariant imbedding (invariance principle). The numerical results for the Milne problem in light water and borated water is presented to demonstrate the avalibility of the method [pt
The neutron transport code DTF-Traca users manual and input data
Energy Technology Data Exchange (ETDEWEB)
Ahnert, C
1979-07-01
This is a users manual of the neutron transport code DTF-TRACA, which is a version of the original DTF-IV with some modifications made at JEN. A detailed input data descriptions is given. The new options developed at JEN are included too. (Author) 18 refs.
General-purpose Monte Carlo codes for neutron and photon transport calculations. MVP version 3
International Nuclear Information System (INIS)
Nagaya, Yasunobu
2017-01-01
JAEA has developed a general-purpose neutron/photon transport Monte Carlo code MVP. This paper describes the recent development of the MVP code and reviews the basic features and capabilities. In addition, capabilities implemented in Version 3 are also described. (author)
In situ neutron depth profiling: A powerful method to probe lithium transport in micro-batteries
Oudenhoven, J.F.M.; Labohm, F.; Mulder, M.; Niessen, R.A.H.; Mulder, F.M.; Notten, P.H.L.
2011-01-01
In situ neutron depth profiling (NDP) offers the possibility to observe lithium transport inside micro-batteries during battery operation. It is demonstrated that NDP results are consistent with the results of electrochemical measurements, and that the use of an enriched6LiCoO2 cathode offers more
The neutron transport code DTF-Traca users manual and input data
International Nuclear Information System (INIS)
Ahnert, C.
1979-01-01
This is a users manual of the neutron transport code DTF-TRACA, which is a version of the original DTF-IV with some modifications made at JEN. A detailed input data descriptions is given. The new options developed at JEN are included too. (Author) 18 refs
The neutron transport code DTF-TRACA. User's manual and input data
International Nuclear Information System (INIS)
Anhert, C.
1979-01-01
A user's manual of the neutron transport code DTF-TRACA, which is a version of the original DTF-IV with some modifications made at JEN. A detailed input data description is given. The new options developped at JEN are included too. (author)
International Nuclear Information System (INIS)
Trukhanov, G.Ya.
2005-01-01
Time-dependent neutron transport theory of G.Ya. Trukhanov and S.A. Podosenov is developed. Errors of calculating of power series expansion coefficients, γ k , in this theory were estimated. It has been found that power series convergence radius R=|χ 1,2 |= 0.9595. Power series convergence speed were estimated [ru
Normal and adjoint integral and integrodifferential neutron transport equations. Pt. 1
International Nuclear Information System (INIS)
Velarde, G.
1976-01-01
Using some simplifying hypotheses, different expressions of the Boltzmann integrodifferential equation are obtained. Posteriorly, they are applied to some particular cases: slowing down, thermalization, multigroups, critical reactors and virtual critical reactors with k, α and lambda. (author)
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
Energy Technology Data Exchange (ETDEWEB)
Dumazert, Jonathan; Coulon, Romain; Carrel, Frédérick; Corre, Gwenolé; Normand, Stéphane [CEA, LIST, Laboratoire Capteurs Architectures Electroniques, 91191 Gif-sur-Yvette (France); Méchin, Laurence [CNRS, UCBN, Groupe de Recherche en Informatique, Image, Automatique et Instrumentation de Caen, 14050 Caen (France); Hamel, Matthieu [CEA, LIST, Laboratoire Capteurs Architectures Electroniques, 91191 Gif-sur-Yvette (France)
2016-08-21
Neutron detection forms a critical branch of nuclear-related issues, currently driven by the search for competitive alternative technologies to neutron counters based on the helium-3 isotope. The deployment of plastic scintillators shows a high potential for efficient detectors, safer and more reliable than liquids, more easily scalable and cost-effective than inorganic. In the meantime, natural gadolinium, through its 155 and mostly 157 isotopes, presents an exceptionally high interaction probability with thermal neutrons. This paper introduces a dual system including a metal gadolinium core inserted at the center of a high-scale plastic scintillator sphere. Incident fast neutrons are thermalized by the scintillator shell and then may be captured with a significant probability by gadolinium 155 and 157 nuclei in the core. The deposition of a sufficient fraction of the capture high-energy prompt gamma signature inside the scintillator shell will then allow discrimination from background radiations by energy threshold, and therefore neutron detection. The scaling of the system with the Monte Carlo MCNPX2.7 code was carried out according to a tradeoff between the moderation of incident fast neutrons and the probability of slow neutron capture by a moderate-cost metal gadolinium core. Based on the parameters extracted from simulation, a first laboratory prototype for the assessment of the detection method principle has been synthetized. The robustness and sensitivity of the neutron detection principle are then assessed by counting measurement experiments. Experimental results confirm the potential for a stable, highly sensitive, transportable and cost-efficient neutron detector and orientate future investigation toward promising axes.
International Nuclear Information System (INIS)
Dumazert, Jonathan; Coulon, Romain; Carrel, Frédérick; Corre, Gwenolé; Normand, Stéphane; Méchin, Laurence; Hamel, Matthieu
2016-01-01
Neutron detection forms a critical branch of nuclear-related issues, currently driven by the search for competitive alternative technologies to neutron counters based on the helium-3 isotope. The deployment of plastic scintillators shows a high potential for efficient detectors, safer and more reliable than liquids, more easily scalable and cost-effective than inorganic. In the meantime, natural gadolinium, through its 155 and mostly 157 isotopes, presents an exceptionally high interaction probability with thermal neutrons. This paper introduces a dual system including a metal gadolinium core inserted at the center of a high-scale plastic scintillator sphere. Incident fast neutrons are thermalized by the scintillator shell and then may be captured with a significant probability by gadolinium 155 and 157 nuclei in the core. The deposition of a sufficient fraction of the capture high-energy prompt gamma signature inside the scintillator shell will then allow discrimination from background radiations by energy threshold, and therefore neutron detection. The scaling of the system with the Monte Carlo MCNPX2.7 code was carried out according to a tradeoff between the moderation of incident fast neutrons and the probability of slow neutron capture by a moderate-cost metal gadolinium core. Based on the parameters extracted from simulation, a first laboratory prototype for the assessment of the detection method principle has been synthetized. The robustness and sensitivity of the neutron detection principle are then assessed by counting measurement experiments. Experimental results confirm the potential for a stable, highly sensitive, transportable and cost-efficient neutron detector and orientate future investigation toward promising axes.
Available computer codes and data for radiation transport analysis
International Nuclear Information System (INIS)
Trubey, D.K.; Maskewitz, B.F.; Roussin, R.W.
1975-01-01
The Radiation Shielding Information Center (RSIC), sponsored and supported by the Energy Research and Development Administration (ERDA) and the Defense Nuclear Agency (DNA), is a technical institute serving the radiation transport and shielding community. It acquires, selects, stores, retrieves, evaluates, analyzes, synthesizes, and disseminates information on shielding and ionizing radiation transport. The major activities include: (1) operating a computer-based information system and answering inquiries on radiation analysis, (2) collecting, checking out, packaging, and distributing large computer codes, and evaluated and processed data libraries. The data packages include multigroup coupled neutron-gamma-ray cross sections and kerma coefficients, other nuclear data, and radiation transport benchmark problem results
International Nuclear Information System (INIS)
Mikata, Y.
2014-01-01
Highlights: • An exact solution for the one-speed neutron transport equation is obtained. • This solution as well as its derivation are believed to be new. • Neutron flux for a purely absorbing material with a point neutron source off the origin is obtained. • Spherically as well as cylindrically piecewise constant cross sections are studied. • Neutron flux expressions for a point neutron source off the origin are believed to be new. - Abstract: An exact analytical solution of the time-independent monoenergetic neutron transport equation is obtained in this paper. The solution is applied to systems with a point source. Systematic analysis of the solution of the time-independent neutron transport equation, and its applications represent the primary goal of this paper. To the best of the author’s knowledge, certain key results on the scalar neutron flux as well as their derivations are new. As an application of these results, a scalar neutron flux for a purely absorbing medium with a spherically piecewise constant cross section and an isotropic point neutron source off the origin as well as that for a cylindrically piecewise constant cross section with a point neutron source off the origin are obtained. Both of these results are believed to be new
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
Removal, transportation and disposal of the Millstone 2 neutron thermal shield
International Nuclear Information System (INIS)
Snedeker, D.F.; Thomas, L.S.; Schmoker, D.S.; Cade, M.S.
1985-01-01
Some PWR reactors equipped with neutron thermal shields (NTS) have experienced severe neutron shield degradation to the extent that removal and disposal of these shields has become necessary. Due to the relative size and activation levels of the thermal shield, disposal techniques, remote material handling and transportation equipment must be carefully evaluated to minimize plant down time and maintain disposal costs at a minimum. This paper describes the techniques, equipment and methodology employed in the removal, transportation and disposal of the NTS at the Millstone 2 Nuclear Generating Station, a PWR facility owned and operated by Northeast Utilities of Hartford, CT. Specific areas addressed include: (1) remote underwater equipment and tooling for use in segmenting and loading the thermal shield in a disposal liner; (2) adaptation of the General Electric IF-300 Irradiated Fuel Cask for transportation of the NTS for disposal; (3) equipment and techniques used for cask handling and liner burial at the Low Level Radioactive Waste (LLRW) disposal facility
Hybrid variational principles and synthesis method for finite element neutron transport calculations
International Nuclear Information System (INIS)
Ackroyd, R.T.; Nanneh, M.M.
1990-01-01
A family of hybrid variational principles is derived using a generalised least squares method. Neutron conservation is automatically satisfied for the hybrid principles employing two trial functions. No interfaces or reflection conditions need to be imposed on the independent even-parity trial function. For some hybrid principles a single trial function can be employed by relating one parity trial function to the other, using one of the parity transport equation in relaxed form. For other hybrid principles the trial functions can be employed sequentially. Synthesis of transport solutions, starting with the diffusion theory approximation, has been used as a way of reducing the scale of the computation that arises with established finite element methods for neutron transport. (author)
Development of a CAD-based neutron transport code with the method of characteristics
International Nuclear Information System (INIS)
Chen Zhenping; Wang Dianxi; He Tao; Wang Guozhong; Zheng Huaqing
2012-01-01
The main problem determining whether the method of characteristics (MOC) can be used in complicated and highly heterogeneous geometry is how to combine an effective geometry processing method with MOC. In this study, a new idea making use of MCAM, which is a Mutlti-Calculation Automatic Modeling for Neutronics and Radiation Transport program developed by FDS Team, for geometry description and ray tracing of particle transport was brought forward to solve the geometry problem mentioned above. Based on the theory and approach as the foregoing statement, a two dimensional neutron transport code was developed which had been integrated into VisualBUS, developed by FDS Team. Several benchmarks were used to verify the validity of the code and the numerical results were coincident with the reference values very well, which indicated the accuracy and feasibility of the method and the MOC code. (authors)
Energy Technology Data Exchange (ETDEWEB)
Saha Ray, S., E-mail: santanusaharay@yahoo.com; Patra, A.
2014-10-15
Highlights: • A stationary transport equation has been solved using the technique of Haar wavelet collocation method. • This paper intends to provide the great utility of Haar wavelets to nuclear science problem. • In the present paper, two-dimensional Haar wavelets are applied. • The proposed method is mathematically very simple, easy and fast. - Abstract: In this paper the numerical solution for the fractional order stationary neutron transport equation is presented using Haar wavelet Collocation Method (HWCM). Haar wavelet collocation method is efficient and powerful in solving wide class of linear and nonlinear differential equations. This paper intends to provide an application of Haar wavelets to nuclear science problems. This paper describes the application of Haar wavelets for the numerical solution of fractional order stationary neutron transport equation in homogeneous medium with isotropic scattering. The proposed method is mathematically very simple, easy and fast. To demonstrate about the efficiency and applicability of the method, two test problems are discussed.
International Nuclear Information System (INIS)
Chen, G.S.
1997-01-01
We apply and compare the preconditioned generalized conjugate gradient methods to solve the linear system equation that arises in the two-dimensional neutron and photon transport equation in this paper. Several subroutines are developed on the basis of preconditioned generalized conjugate gradient methods for time-independent, two-dimensional neutron and photon transport equation in the transport theory. These generalized conjugate gradient methods are used. TFQMR (transpose free quasi-minimal residual algorithm), CGS (conjuage gradient square algorithm), Bi-CGSTAB (bi-conjugate gradient stabilized algorithm) and QMRCGSTAB (quasi-minimal residual variant of bi-conjugate gradient stabilized algorithm). These sub-routines are connected to computer program DORT. Several problems are tested on a personal computer with Intel Pentium CPU. (author)
OECD/NEA benchmark for time-dependent neutron transport calculations without spatial homogenization
Energy Technology Data Exchange (ETDEWEB)
Hou, Jason, E-mail: jason.hou@ncsu.edu [Department of Nuclear Engineering, North Carolina State University, Raleigh, NC 27695 (United States); Ivanov, Kostadin N. [Department of Nuclear Engineering, North Carolina State University, Raleigh, NC 27695 (United States); Boyarinov, Victor F.; Fomichenko, Peter A. [National Research Centre “Kurchatov Institute”, Kurchatov Sq. 1, Moscow (Russian Federation)
2017-06-15
Highlights: • A time-dependent homogenization-free neutron transport benchmark was created. • The first phase, known as the kinetics phase, was described in this work. • Preliminary results for selected 2-D transient exercises were presented. - Abstract: A Nuclear Energy Agency (NEA), Organization for Economic Co-operation and Development (OECD) benchmark for the time-dependent neutron transport calculations without spatial homogenization has been established in order to facilitate the development and assessment of numerical methods for solving the space-time neutron kinetics equations. The benchmark has been named the OECD/NEA C5G7-TD benchmark, and later extended with three consecutive phases each corresponding to one modelling stage of the multi-physics transient analysis of the nuclear reactor core. This paper provides a detailed introduction of the benchmark specification of Phase I, known as the “kinetics phase”, including the geometry description, supporting neutron transport data, transient scenarios in both two-dimensional (2-D) and three-dimensional (3-D) configurations, as well as the expected output parameters from the participants. Also presented are the preliminary results for the initial state 2-D core and selected transient exercises that have been obtained using the Monte Carlo method and the Surface Harmonic Method (SHM), respectively.
The spectral element method for static neutron transport in AN approximation. Part I
International Nuclear Information System (INIS)
Barbarino, A.; Dulla, S.; Mund, E.H.; Ravetto, P.
2013-01-01
Highlights: ► Spectral elements methods (SEMs) are extended for the neutronics of nuclear reactor cores. ► The second-order, A N formulation of neutron trasport is adopted. ► Results for classical benchmark cases in 2D are presented and compared to finite elements. ► The advantages of SEM in terms of precision and convergence rate are illustrated. ► SEM consitutes a promising approach for the solution of neutron transport problems. - Abstract: Spectral elements methods provide very accurate solutions of elliptic problems. In this paper we apply the method to the A N (i.e. SP 2N−1 ) approximation of neutron transport. Numerical results for classical benchmark cases highlight its performance in comparison with finite element computations, in terms of accuracy per degree of freedom and convergence rate. All calculations presented in this paper refer to two-dimensional problems. The method can easily be extended to three-dimensional cases. The results illustrate promising features of the method for more complex transport problems
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
International Nuclear Information System (INIS)
Hoogenboom, J.E.
1981-01-01
An adjoint Monte Carlo technique is described for the solution of neutron transport problems. The optimum biasing function for a zero-variance collision estimator is derived. The optimum treatment of an analog of a non-velocity thermal group has also been derived. The method is extended to multiplying systems, especially for eigenfunction problems to enable the estimate of averages over the unknown fundamental neutron flux distribution. A versatile computer code, FOCUS, has been written, based on the described theory. Numerical examples are given for a shielding problem and a critical assembly, illustrating the performance of the FOCUS code. 19 refs
UN Method For The Critical Slab Problem In One-Speed Neutron Transport Theory
International Nuclear Information System (INIS)
Oeztuerk, Hakan; Guengoer, Sueleyman
2008-01-01
The Chebyshev polynomial approximation (U N method) is used to solve the critical slab problem in one-speed neutron transport theory using Marshak boundary condition. The isotropic scattering kernel with the combination of forward and backward scattering is chosen for the neutrons in a uniform finite slab. Numerical results obtained by the U N method are presented in the tables together with the results obtained by the well-known P N method for comparison. It is shown that the method converges rapidly with its easily executable equations.
The neutron transport with general boundary conditions (II)
International Nuclear Information System (INIS)
Boulanouar, Mohamed
2012-01-01
This Note deals with the one-dimensional transport operator, on an unbounded domain, endowed with general boundary conditions. We show the generation of a strongly continuous semigroup and we study its spectral properties. In particular, we prove the existence of a leading eigenvalue. (author)
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.
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)
An integral equation arising in two group neutron transport theory
International Nuclear Information System (INIS)
Cassell, J S; Williams, M M R
2003-01-01
An integral equation describing the fuel distribution necessary to maintain a flat flux in a nuclear reactor in two group transport theory is reduced to the solution of a singular integral equation. The formalism developed enables the physical aspects of the problem to be better understood and its relationship with the corresponding diffusion theory model is highlighted. The integral equation is solved by reducing it to a non-singular Fredholm equation which is then evaluated numerically
Comparison of neutronic transport equation resolution nodal methods
International Nuclear Information System (INIS)
Zamonsky, O.M.; Gho, C.J.
1990-01-01
In this work, some transport equation resolution nodal methods are comparatively studied: the constant-constant (CC), linear-nodal (LN) and the constant-quadratic (CQ). A nodal scheme equivalent to finite differences has been used for its programming, permitting its inclusion in existing codes. Some bidimensional problems have been solved, showing that linear-nodal (LN) are, in general, obtained with accuracy in CPU shorter times. (Author) [es
Methodology for coupling computational fluid dynamics and integral transport neutronics
International Nuclear Information System (INIS)
Thomas, J. W.; Zhong, Z.; Sofu, T.; Downar, T. J.
2004-01-01
The CFD code STAR-CD was coupled to the integral transport code DeCART in order to provide high-fidelity, full physics reactor simulations. An interface program was developed to perform the tasks of mapping the STAR-CD mesh to the DeCART mesh, managing all communication between STAR-CD and DeCART, and monitoring the convergence of the coupled calculations. The interface software was validated by comparing coupled calculation results with those obtained using an independently developed interface program. An investigation into the convergence characteristics of coupled calculations was performed using several test models on a multiprocessor LINUX cluster. The results indicate that the optimal convergence of the coupled field calculation depends on several factors, to include the tolerance of the STAR-CD solution and the number of DeCART transport sweeps performed before exchanging data between codes. Results for a 3D, multi-assembly PWR problem on 12 PEs of the LINUX cluster indicate the best performance is achieved when the STAR-CD tolerance and number of DeCART transport sweeps are chosen such that the two fields converge at approximately the same rate. (authors)
International Nuclear Information System (INIS)
Miller, W.F. Jr.
1975-10-01
The coarse-mesh rebalance method, based on neutron conservation, is used in discrete ordinates neutron transport codes to accelerate convergence of the within-group scattering source. Though very powerful for this application, the method is ineffective in accelerating the iteration on the discrete-ordinates-to-spherical-harmonics fictitious sources used for ray-effect elimination. This is largely because this source makes a minimum contribution to the neutron balance equation. The traditional rebalance approach is derived in a variational framework and compared with new rebalance approaches tailored to be compatible with the fictitious source. The new approaches are compared numerically to determine their relative advantages. It is concluded that there is little incentive to use the new methods. (3 tables, 5 figures)
A time-dependent neutron transport model and its coupling to thermal-hydraulics
International Nuclear Information System (INIS)
Pautz, A.
2001-01-01
A new neutron transport code for time-dependent analyses of nuclear systems has been developed. The code system is based on the well-known Discrete Ordinates code DORT, which solves the steady-state neutron/photon transport equation in two dimensions for an arbitrary number of energy groups and the most common regular geometries. For the implementation of time-dependence a fully implicit first-order scheme was employed to minimize errors due to temporal discretization. This requires various modifications to the transport equation as well as the extensive use of elaborated acceleration mechanisms. The convergence criteria for fluxes, fission rates etc. had to be strongly tightened to ensure the reliability of results. To perform coupled analyses, an interface to the GRS system code ATHLET has been developed. The nodal power densities from the neutron transport code are passed to ATHLET to calculate thermal-hydraulic system parameters, e.g. fuel and coolant temperatures. These are in turn used to generate appropriate nuclear cross sections by interpolation of pre-calculated data sets for each time step. Finally, to demonstrate the transient capabilities of the coupled code system, the research reactor FRM-II has been analysed. Several design basis accidents were modelled, like the loss of off site power, loss of secondary heat sink and unintended control rod withdrawal. (author)
Energy Technology Data Exchange (ETDEWEB)
Bernal, A.; Abarca, A.; Barrachina, T.; Miro, R.; Verdu, G.
2013-07-01
The resolution of the neutron transport equation in steady state in pool-type nuclear reactors, is normally achieved through 2 different numerical methods: Monte Carlo (stochastic) and discrete ordinates (deterministic). The discrete ordinates method solves the neutron transport equation for a set of specific addresses, obtaining a set of equations and solutions for each direction, where the solution for each direction is the angular flux. With the aim of treating energy dependence, used energy multigroup approximation, thus obtaining a set of equations that depends on the number of energy groups considered.
Neutron scattering and muon spin rotation as probes of light interstitial transport
International Nuclear Information System (INIS)
Brown, D.W.
1985-01-01
The transport of light interstitials, specifically of hydrogen isotopes and the positive muon, is studied with the help of microscopic transport models. The principal observables are the differential neutron scattering cross section of the hydrogen isotopes and the muon spin rotation signal of the positive muon. The transport feature of primary interest is coherence arising as a result of persistence of quantum mechanical phase memory. Evaluation of observables is based on the generalized master equation, or alternatively, the stochastic Liouville equation. The latter is applied to obtain the neutron scattering lineshapes for local tunneling systems as well as for extended Bravais and non-Bravais lattices. It is found that the usual form of the stochastic Liouville equation does not address adequately transport among non-degenerate site-states. An appropriate modification is suggested and employed to obtain scattering lineshapes applicable to recent experiments on impurity-trapped hydrogen. The muon spin rotation signal is formulated under the assumption that spin interactions constitute a negligible source of scattering for muon transport. The depolarization function is evaluated for the cases of local tunneling systems and simple models of spatially extended transport. The former addresses consequences of coherence and both address the consequences of the spatial extent of the muon wavefunction. It is found that the depolarization function is sensitive to the wave function extent, and the detail attributable to it is characterized
Anisotropic kernel p(μ → μ') for transport calculations of elastically scattered neutrons
International Nuclear Information System (INIS)
Stevenson, B.
1985-01-01
Literature in the area of anisotropic neutron scattering is by no means lacking. Attention, however, is usually devoted to solution of some particular neutron transport problem and the model employed is at best approximate. The present approach to the problem in general is classically exact and may be of some particular value to individuals seeking exact numerical results in transport calculations. For attempts neutrons originally directed toward the unit vector Omega, it attempts the evaluation of p(theta'), defined such that p(theta') d theta' is that fraction of scattered neutrons that emerges in the vicinity of a cone i.e., having been scattered to between angles theta' and theta' + d theta' with the axis of preferred orientation i; Omega makes an angle theta with i. The relative simplicity of the final form of the solution for hydrogen, in spite of the complicated nature of the limits involved, is a trade-off that truly is not necessary. The exact general solution presented here in integral form, has exceedingly simple limits, i.e., 0 ≤ theta' ≤ π regardless of the material involved; but the form of the final solution is extraordinarily complicated
Neutron transport by collision probability method in complicated geometries
International Nuclear Information System (INIS)
Constantin, Marin
2000-01-01
For the first flight collision probability (FFCP) method a rapidly increasing of the memory requirements and execution time with the number of discrete regions occurs. Generally, the use of the method is restricted at cell/supercell level. However, the amazing developments both in computer hardware and computer architecture allow a real extending of the problems' domain and a more detailed treatment of the geometry. Two ways are discussed into the paper: the direct design of new codes and the improving of the mainframe old versions. The author's experience is focused on the performances' improving of the 3D integral transport code PIJXYZ (from an old version to a modern one) and on the design and developing of the 2D transport code CP 2 D in the last years. In the first case an optimization process have been performed before the parallelization. In the second a modular design and the newest techniques (factorization of the geometry, the macrobands method, the mobile set of chords, the automatic calculation of the integration error, optimal algorithms for the innermost programming level, the mixed method for tracking process and CPs calculation, etc.) were adopted. In both cases the parallelization uses a PCs network system. Some short examples for CP 2 D and PIJXYZ calculation are presented: reactivity void effect in typical CANDU cells using a multistratified coolant model, a problem of some adjacent fuel assemblies, CANDU reactivity devices 3D simulation. (author)
Resolution of the neutron transport equation by a three-dimensional least square method
International Nuclear Information System (INIS)
Varin, Elisabeth
2001-01-01
The knowledge of space and time distribution of neutrons with a certain energy or speed allows the exploitation and control of a nuclear reactor and the assessment of the irradiation dose about an irradiated nuclear fuel storage site. The neutron density is described by a transport equation. The objective of this research thesis is to develop a software for the resolution of this stationary equation in a three-dimensional Cartesian domain by means of a deterministic method. After a presentation of the transport equation, the author gives an overview of the different deterministic resolution approaches, identifies their benefits and drawbacks, and discusses the choice of the Ressel method. The least square method is precisely described and then applied. Numerical benchmarks are reported for validation purposes
Monte Carlo method for neutron transport calculations in graphics processing units (GPUs)
International Nuclear Information System (INIS)
Pellegrino, Esteban
2011-01-01
Monte Carlo simulation is well suited for solving the Boltzmann neutron transport equation in an inhomogeneous media for complicated geometries. However, routine applications require the computation time to be reduced to hours and even minutes in a desktop PC. The interest in adopting Graphics Processing Units (GPUs) for Monte Carlo acceleration is rapidly growing. This is due to the massive parallelism provided by the latest GPU technologies which is the most promising solution to the challenge of performing full-size reactor core analysis on a routine basis. In this study, Monte Carlo codes for a fixed-source neutron transport problem were developed for GPU environments in order to evaluate issues associated with computational speedup using GPUs. Results obtained in this work suggest that a speedup of several orders of magnitude is possible using the state-of-the-art GPU technologies. (author) [es
A coordinate transform method for one-speed neutron transport in composite slabs
International Nuclear Information System (INIS)
Haidar, N.H.S.
1988-01-01
The optical path transformation is applied to reduce the one-speed neutron transport equation for a class of composite subcritical slabs to single-region problems. The class idealises, within the uncertainty of the one-speed model, a variety of practical situations such as U-D 2 O-C-Zr-Pb or Pu-U-Na-Fe symmetric reactor assemblies; which may possibly contain a symmetrically anisotropic neutron source. A closed form double series solution, which turns out to be quite convenient for design and optimisation purposes, has been obtained, in terms of discontinuous functions for the multi-regional angular flux by application of a double finite Legendre transform. Disadvantage factor evaluations for a U-C lattice cell resulting from a low-order P 0 P 1 approximation of this method are found to be in full agreement with hybrid diffusion-transport estimates. (author)
Effect of Fast Neutron Irradiation on Current Transport Properties of HTS Materials
Ballarino, A; Kruglov, V S; Latushkin, S T; Lubimov, A N; Ryazanov, A I; Shavkin, S V; Taylor, T M; Volkov, P V
2004-01-01
The effect of fast neutron irradiation with energy up to 35 MeV and integrated fluence of up to 5 x 10**15 cm-2 on the current transport properties of HTS materials Bi-2212 and Bi-2223 has been studied, both at liquid nitrogen and at room temperatures. The samples irradiated were selected after verification of the stability of their superconducting properties after temperature cycling in the range of 77 K - 293 K. It has been found that the irradiation by fast neutrons up to the above dose does not produce a significant degradation of critical current. The effect of room temperature annealing on the recovery of transport properties of the irradiated samples is also reported, as is a preliminary microstructure investigation of the effect of irradiation on the soldered contacts.
International Nuclear Information System (INIS)
Bosevski, T.
1971-01-01
The polynomial interpolation of neutron flux between the chosen space and energy variables enabled transformation of the integral transport equation into a system of linear equations with constant coefficients. Solutions of this system are the needed values of flux for chosen values of space and energy variables. The proposed improved method for solving the neutron transport problem including the mathematical formalism is simple and efficient since the number of needed input data is decreased both in treating the spatial and energy variables. Mathematical method based on this approach gives more stable solutions with significantly decreased probability of numerical errors. Computer code based on the proposed method was used for calculations of one heavy water and one light water reactor cell, and the results were compared to results of other very precise calculations. The proposed method was better concerning convergence rate, decreased computing time and needed computer memory. Discretization of variables enabled direct comparison of theoretical and experimental results
Presentation of some methods for the solution of the monoenergetic neutrons transport equation
International Nuclear Information System (INIS)
Valle G, E. del.
1978-01-01
The neutrons transport theory problems whose solution has been reached were collected in order to show that the transport equation is so complicated that different techniques were developed so as to give approximative numerical solutions to problems concerning the practical application. Such a technique, which had not been investigated in the literature dealing with these problems, is described here. The results which were obtained through this technique in undimensional problems of criticity are satisfactory and speaking in a conceptual way this method is extremely simple because it times. There is no limitation to deal with problems related neutrons sources with an arbitrary distribution and in principle the application of this technique can be extended to unhomogeneous environments. (author)
International Nuclear Information System (INIS)
Asadzadeh, M.; Thevenot, L.
2010-01-01
The objective of this paper is to give a mathematical framework for a fully discrete numerical approach for the study of the neutron transport equation in a cylindrical domain (container model,). More specifically, we consider the discontinuous Galerkin (D G) finite element method for spatial approximation of the mono-energetic, critical neutron transport equation in an infinite cylindrical domain ??in R3 with a polygonal convex cross-section ? The velocity discretization relies on a special quadrature rule developed to give optimal estimates in discrete ordinate parameters compatible with the quasi-uniform spatial mesh. We use interpolation spaces and derive optimal error estimates, up to maximal available regularity, for the fully discrete scalar flux. Finally we employ a duality argument and prove superconvergence estimates for the critical eigenvalue.
Neutron transport solver parallelization using a Domain Decomposition method
International Nuclear Information System (INIS)
Van Criekingen, S.; Nataf, F.; Have, P.
2008-01-01
A domain decomposition (DD) method is investigated for the parallel solution of the second-order even-parity form of the time-independent Boltzmann transport equation. The spatial discretization is performed using finite elements, and the angular discretization using spherical harmonic expansions (P N method). The main idea developed here is due to P.L. Lions. It consists in having sub-domains exchanging not only interface point flux values, but also interface flux 'derivative' values. (The word 'derivative' is here used with quotes, because in the case considered here, it in fact consists in the Ω.∇ operator, with Ω the angular variable vector and ∇ the spatial gradient operator.) A parameter α is introduced, as proportionality coefficient between point flux and 'derivative' values. This parameter can be tuned - so far heuristically - to optimize the method. (authors)
Normal and adjoint integral and integrodifferential neutron transport equations. Pt. 2
International Nuclear Information System (INIS)
Velarde, G.
1976-01-01
Using the simplifying hypotheses of the integrodifferential Boltzmann equations of neutron transport, given in JEN 334 report, several integral equations, and theirs adjoint ones, are obtained. Relations between the different normal and adjoint eigenfunctions are established and, in particular, proceeding from the integrodifferential Boltzmann equation it's found out the relation between the solutions of the adjoint equation of its integral one, and the solutions of the integral equation of its adjoint one (author)
Systems guide to MCNP (Monte Carlo Neutron and Photon Transport Code)
International Nuclear Information System (INIS)
Kirk, B.L.; West, J.T.
1984-06-01
The subject of this report is the implementation of the Los Alamos National Laboratory Monte Carlo Neutron and Photon Transport Code - Version 3 (MCNP) on the different types of computer systems, especially the IBM MVS system. The report supplements the documentation of the RSIC computer code package CCC-200/MCNP. Details of the procedure to follow in executing MCNP on the IBM computers, either in batch mode or interactive mode, are provided
Modular, object-oriented redesign of a large-scale Monte Carlo neutron transport program
International Nuclear Information System (INIS)
Moskowitz, B.S.
2000-01-01
This paper describes the modular, object-oriented redesign of a large-scale Monte Carlo neutron transport program. This effort represents a complete 'white sheet of paper' rewrite of the code. In this paper, the motivation driving this project, the design objectives for the new version of the program, and the design choices and their consequences will be discussed. The design itself will also be described, including the important subsystems as well as the key classes within those subsystems
Post-merger evolution of a neutron star-black hole binary with neutrino transport
Foucart, Francois; O'Connor, Evan; Roberts, Luke; Duez, Matthew D.; Haas, Roland; Kidder, Lawrence E.; Ott, Christian D.; Pfeiffer, Harald P.; Scheel, Mark A.; Szilagyi, Bela
2015-06-01
We present a first simulation of the post-merger evolution of a black hole-neutron star binary in full general relativity using an energy-integrated general-relativistic truncated moment formalism for neutrino transport. We describe our implementation of the moment formalism and important tests of our code, before studying the formation phase of an accretion disk after a black hole-neutron star merger. We use as initial data an existing general-relativistic simulation of the merger of a neutron star of mass 1.4 M⊙ with a black hole of mass 7 M⊙ and dimensionless spin χBH=0.8 . Comparing with a simpler leakage scheme for the treatment of the neutrinos, we find noticeable differences in the neutron-to-proton ratio in and around the disk, and in the neutrino luminosity. We find that the electron neutrino luminosity is much lower in the transport simulations, and that both the disk and the disk outflows are less neutron rich. The spatial distribution of the neutrinos is significantly affected by relativistic effects, due to large velocities and curvature in the regions of strongest emission. Over the short time scale evolved, we do not observe purely neutrino-driven outflows. However, a small amount of material (3 ×10-4M⊙ ) is ejected in the polar region during the circularization of the disk. Most of that material is ejected early in the formation of the disk, and is fairly neutron rich (electron fraction Ye˜0.15 - 0.25 ). Through r-process nucleosynthesis, that material should produce high-opacity lanthanides in the polar region, and could thus affect the light curve of radioactively powered electromagnetic transients. We also show that by the end of the simulation, while the bulk of the disk remains neutron rich (Ye˜0.15 - 0.2 and decreasing), its outer layers have a higher electron fraction: 10% of the remaining mass has Ye>0.3 . As that material would be the first to be unbound by disk outflows on longer time scales, and as composition evolution is
Solution to the monoenergetic time-dependent neutron transport equation with a time-varying source
International Nuclear Information System (INIS)
Ganapol, B.D.
1986-01-01
Even though fundamental time-dependent neutron transport problems have existed since the inception of neutron transport theory, it has only been recently that a reliable numerical solution to one of the basic problems has been obtained. Experience in generating numerical solutions to time-dependent transport equations has indicated that the multiple collision formulation is the most versatile numerical technique for model problems. The formulation coupled with a moment reconstruction of each collided flux component has led to benchmark-quality (four- to five-digit accuracy) numerical evaluation of the neutron flux in plane infinite geometry for any degree of scattering anisotropy and for both pulsed isotropic and beam sources. As will be shown in this presentation, this solution can serve as a Green's function, thus extending the previous results to more complicated source situations. Here we will be concerned with a time-varying source at the center of an infinite medium. If accurate, such solutions have both pedagogical and practical uses as benchmarks against which other more approximate solutions designed for a wider class of problems can be compared
Advances in the solution of three-dimensional nodal neutron transport equation
International Nuclear Information System (INIS)
Pazos, Ruben Panta; Hauser, Eliete Biasotto; Vilhena, Marco Tullio de
2003-01-01
In this paper we study the three-dimensional nodal discrete-ordinates approximations of neutron transport equation in a convex domain with piecewise smooth boundaries. We use the combined collocation method of the angular variables and nodal approach for the spatial variables. By nodal approach we mean the iterated transverse integration of the S N equations. This procedure leads to the set of one-dimensional averages angular fluxes in each spatial variable. The resulting system of equations is solved with the LTS N method, first applying the Laplace transform to the set of the nodal S N equations and then obtaining the solution by symbolic computation. We include the LTS N method by diagonalization to solve the nodal neutron transport equation and then we outline the convergence of these nodal-LTS N approximations with the help of a norm associated to the quadrature formula used to approximate the integral term of the neutron transport equation. We give numerical results obtained with an algebraic computer system (for N up to 8) and with a code for higher values of N. We compare our results for the geometry of a box with a source in a vertex and a leakage zone in the opposite with others techniques used in this problem. (author)
Synergism of the method of characteristics and CAD technology for neutron transport calculation
International Nuclear Information System (INIS)
Chen, Z.; Wang, D.; He, T.; Wang, G.; Zheng, H.
2013-01-01
The method of characteristics (MOC) is a very popular methodology in neutron transport calculation and numerical simulation in recent decades for its unique advantages. One of the key problems determining whether the MOC can be applied in complicated and highly heterogeneous geometry is how to combine an effective geometry processing method with MOC. Most of the existing MOC codes describe the geometry by lines and arcs with extensive input data, such as circles, ellipses, regular polygons and combination of them. Thus they have difficulty in geometry modeling, background meshing and ray tracing for complicated geometry domains. In this study, a new idea making use of a CAD solid modeler MCAM which is a CAD/Image-based Automatic Modeling Program for Neutronics and Radiation Transport developed by FDS Team in China was introduced for geometry modeling and ray tracing of particle transport to remove these geometrical limitations mentioned above. The diamond-difference scheme was applied to MOC to reduce the spatial discretization error of the flat flux approximation in theory. Based on MCAM and MOC, a new MOC code was developed and integrated into SuperMC system, which is a Super Multi-function Computational system for neutronics and radiation simulation. The numerical testing results demonstrated the feasibility and effectiveness of the new idea for geometry treatment in SuperMC. (authors)
Verification of KARMA GEOM/TRPT Module with Given Multi-group Cross Sections
International Nuclear Information System (INIS)
Koo, Bon Seung; Hong, Ser Gi; Song, Jae Seung
2009-01-01
KAERI has developed a two-dimensional multigroup transport theory code KARMA (Kernel Analyzer by Ray-tracing Method for Fuel Assembly). KARMA uses CMFD (Coarse Mesh Finite Difference) accelerated MOC (Method of Characteristics) method for burnup calculation on a single fuel pin, a fuel assembly and a core consisting of rectangular array of fuel pins. KARMA code intends to be employed as a nuclear design tool for the Korean commercial pressurizer water reactor. Prior to the application to actual assembly designs, the code has to be approved by regularity agency. Therefore, it is essential that the reliability of KARMA code should be sufficiently evaluated against well-defined benchmark problems. In this paper, verification of GEOM/TRPT modules of KARMA was performed to confirm a reliability of the KARMA transport solution via comparisons with Monte Carlo calculations by using a consistent set of multi-group macroscopic cross-sections
Criticality problems for slabs and spheres in energy dependent neutron transport theory
International Nuclear Information System (INIS)
Victory, H.D. Jr.
1980-01-01
The steady-state equation for energy-dependent neutron transport in isotropically scattering slabs and spheres is formulated as an integral equation. The Perron-Frobenius-Jentzsch theory of positive operators is used to analyze criticality problems for transport in slab and spherical media consisting of core and reflector. In addition, with an adroit selection of diffusion-like solutions, this theory is used to obtain an expression relating the critical radius of a homogeneous sphere to a parameter characterizing fission production. 21 refs
Neutron transport study based on assembly modular ray tracing MOC method
International Nuclear Information System (INIS)
Tian Chao; Zheng Youqi; Li Yunzhao; Li Shuo; Chai Xiaoming
2015-01-01
It is difficulty for the MOC method based on Cell Modular Ray Tracing to deal with the irregular geometry such as the water gap between the PWR lattices. Hence, the neutron transport code NECP-Medlar based on Assembly Modular Ray Tracing is developed. CMFD method is used to accelerate the transport calculation. The numerical results of the 2D C5G7 benchmark and typical PWR lattice prove that NECP-Medlar has an excellent performance in terms of accuracy and efficiency. Besides, NECP-Medlar can describe clearly the flux distribution of the lattice with water gap. (authors)
Neutron and gamma ray transport calculations in shielding system
Energy Technology Data Exchange (ETDEWEB)
Masukawa, Fumihiro; Sakamoto, Hiroki [Japan Atomic Energy Research Inst., Tokai, Ibaraki (Japan). Tokai Research Establishment
1998-03-01
In the shields for radiation in nuclear facilities, the penetrating holes of various kinds and irregular shapes are made for the reasons of operation, control and others. These penetrating holes and gaps are filled with air or the substances with relatively small shielding performance, and radiation flows out through them, which is called streaming. As the calculation techniques for the shielding design or analysis related to the streaming problem, there are the calculations by simplified evaluation, transport calculation and Monte Carlo method. In this report, the example of calculation by Monte Carlo method which is represented by MCNP code is discussed. A number of variance reduction techniques which seem effective for the analysis of streaming problem were tried. As to the investigation of the applicability of MCNP code to streaming analysis, the object of analysis which are the concrete walls without hole and with horizontal hole, oblique hole and bent oblique hole, the analysis procedure, the composition of concrete, and the conversion coefficient of dose equivalent, and the results of analysis are reported. As for variance reduction technique, cell importance was adopted. (K.I.)
TRIMARAN: a three dimensional multigroup P1 Monte Carlo code for criticality studies
International Nuclear Information System (INIS)
Ermumcu, G.; Gonnord, J.; Nimal, J.C.
1980-01-01
TRIMARAN is developed for safety analysis of nuclear components containing fissionable materials: shipping casks, storage and cooling pools, manufacture and reprocessing plants. It solves the transport equation by Monte Carlo method, in general three dimensional geometry with multigroup P1 approximation. A special representation of cross sections and numbers has been developed in order to reduce considerably the computing cost and allow this three dimensional code to compete with standard numerical program used in parametric studies
TRIMARAN: a three dimensional multigroup P1 Monte Carlo code for criticallity studies
International Nuclear Information System (INIS)
Ermuncu, G.; Gonnord, J.; Nimal, J.C.
1980-04-01
TRIMARAN is developed for safety analysis of nuclar components containing fissionnable materials: shipping casks, storage and cooling pools, manufacture and reprocessing plants. It solves the transport equation by Monte Carlo method in general three dimensional geometry with multigroup P1 approximation. A special representation of cross sections and numbers has been developed in order to reduce considerably the computing cost and allow this three dimensional code to compete with standard numerical program used in parametric studies
Andreasen, M.; Looms, M. C.; Bogena, H. R.; Desilets, D.; Zreda, M. G.; Sonnenborg, T. O.; Jensen, K. H.
2014-12-01
The water stored in the various compartments of the terrestrial ecosystem (in snow, canopy interception, soil and litter) controls the exchange of the water and energy between the land surface and the atmosphere. Therefore, measurements of the water stored within these pools are critical for the prediction of e.g. evapotranspiration and groundwater recharge. The detection of cosmic-ray neutron intensity is a novel non-invasive method for the quantification of continuous intermediate-scale soil moisture. The footprint of the cosmic-ray neutron probe is a hemisphere of a few hectometers and subsurface depths of 10-70 cm depending on wetness. The cosmic-ray neutron method offers measurements at a scale between the point-scale measurements and large-scale satellite retrievals. The cosmic-ray neutron intensity is inversely correlated to the hydrogen stored within the footprint. Overall soil moisture represents the largest pool of hydrogen and changes in the soil moisture clearly affect the cosmic-ray neutron signal. However, the neutron intensity is also sensitive to variations of hydrogen in snow, canopy interception and biomass offering the potential to determine water content in such pools from the signal. In this study we tested the potential of determining canopy interception and biomass using cosmic-ray neutron intensity measurements within the framework of the Danish Hydrologic Observatory (HOBE) and the Terrestrial Environmental Observatories (TERENO). Continuous measurements at the ground and the canopy level, along with profile measurements were conducted at towers at forest field sites. Field experiments, including shielding the cosmic-ray neutron probes with cadmium foil (to remove lower-energy neutrons) and measuring reference intensity rates at complete water saturated conditions (on the sea close to the HOBE site), were further conducted to obtain an increased understanding of the physics controlling the cosmic-ray neutron transport and the equipment used
Žukauskaite, A; Plukiene, R; Plukis, A
2007-01-01
Particle accelerators and other high energy facilities produce penetrating ionizing radiation (neutrons and γ-rays) that must be shielded. The objective of this work was to model photon and neutron transport in various materials, usually used as shielding, such as concrete, iron or graphite. Monte Carlo method allows obtaining answers by simulating individual particles and recording some aspects of their average behavior. In this work several nuclear experiments were modeled: AVF 65 – γ-ray beams (1-10 MeV), HIMAC and ISIS-800 – high energy neutrons (20-800 MeV) transport in iron and concrete. The results were then compared with experimental data.
International Nuclear Information System (INIS)
Takahashi, A.; Rusch, D.
1979-07-01
Some recent neutronics experiments for fusion reactor blankets show that the precise treatment of anisotropic secondary emissions for all types of neutron scattering is needed for neutron transport calculations. In the present work new rigorous methods, i.e. based on non-approximative microscopic neutron balance equations, are applied to treat the anisotropic collision source term in transport equations. The collision source calculation is free from approximations except for the discretization of energy, angle and space variables and includes the rigorous treatment of nonelastic collisions, as far as nuclear data are given. Two methods are presented: first the Ii-method, which relies on existing nuclear data files and then, as an ultimate goal, the I*-method, which aims at the use of future double-differential cross section data, but which is also applicable to the present single-differential data basis to allow a smooth transition to the new data type. An application of the Ii-method is given in the code system NITRAN which employs the Ssub(N)-method to solve the transport equations. Both rigorous methods, the Ii- and the I*-method, are applicable to all radiation transport problems and they can be used also in the Monte-Carlo-method to solve the transport problem. (orig./RW) [de
Calculation of neutron spectra for a 252Cf transport cask using ANISN running on a PC
International Nuclear Information System (INIS)
West, L.; Akin, B.P.; Lemley, E.C.
1995-01-01
Neutron spectra have been calculated using the ANISN one-dimensional discrete ordinates code for the case of a 152 Cf source in a transport cask of a particular design. All computations were done on personal computers (PCs) (mostly 486 models) with the ANISN-ORNL (486 version) computer code. With a source of 252 Cf fission neutrons, the neutron flux spectrum in the cask cannot be characterized as open-quotes moderated.close quotes Concern about an appropriate choice for the cross-section data set has led to a comparison, for this application, of three different cross-section libraries: DABL, HILO, and BUGLE-80. Although the cross-section sets were not originally designed for PC use, the libraries have been successfully employed for PC computations. Work with yet another data library, BUGLE-93, is incomplete at this stage. From neutron flux spectra on the surface of the cask, personnel dosimetric quantities (such as dose equivalent) have been determined for the DABL, HILO, and BUGLE-80 ANISN calculations
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)
Positive solution of a time and energy dependent neutron transport problem
International Nuclear Information System (INIS)
Pao, C.V.
1975-01-01
A constructive method is given for the determination of a solution and an existence--uniqueness theorem for some nonlinear time and energy dependent neutron transport problems, including the linear transport system. The geometry of the medium under consideration is allowed to be either bounded or unbounded which includes the geometry of a finite or infinite cylinder, a half-space and the whole space R/subm/ (m=1,2,center-dotcenter-dotcenter-dot). Our approach to the problem is by successive approximation which leads to various recursion formulas for the approximations in terms of explicit integrations. It is shown under some Lipschitz conditions on the nonlinear functions, which describe the process of neutrons absorption, fission, and scattering, that the sequence of approximations converges to a unique positive solution. Since these conditions are satisfied by the linear transport equation, all the results for the nonlinear system are valid for the linear transport problem. In the general nonlinear problem, the existence of both local and global solutions are discussed, and an iterative process for the construction of the solution is given