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9-Zoom : A One-Dimensional, Multigroup, Neutron Diffusion Theory Reactor Code for the IBM 709

Description: The following document describes the usage and purpose of the neutron diffusion theory reactor program 9-Zoom, a memory-contained program that takes advantage of 709 features such as, for example, preferential order of multiply by zero, and for small problems approaches input-output limitations with excellent convergence properties.
Date: August 25, 1959
Creator: Stone, S. P.; Collins, E. T. & Lenihan, S. R..
Partner: UNT Libraries Government Documents Department

Multigroup Methods for Neutron Diffusion Problems

Description: Abstract: "The age-diffusion is adequate to describe the neutron behavior of a very large class of nonthermal reactors (all except those whose dimensions are comparable to the neutron mean free path). Thus, a convenient means of obtaining an accurate solution to this equation is very useful for general reactor calculations. Methods for reducing the age-diffusion equation to a finite set of coupled ordinary differential equations, called multigroup equations, are described. The relative merits of several alternate schemes are discussed. The multigroup equations may be solved by iterative procedures based on an assumed spatial distribution of the fission source neutrons. In practice the initially assumed source shape is accurate enough so that additional iterations are unnecessary. Analytical and numerical methods for solving the multigroup equations with the assumed source are discussed. The adjoint equations are also reduced to multigroup form, and examples of the adjoint function in obtaining improved reactivity values are given."
Date: August 20, 1953
Creator: Hurwitz, H. & Ehrlich, R.
Partner: UNT Libraries Government Documents Department

Corn Pone: A Multigroup, Multiregion Reactor Code

Description: Report covering the development of a set of difference equations for machine solution. In addition, this report serves as user's manual for Corn Pone, which is a code for the Oracle, the Oak Ridge National Laboratory computer.
Date: 1961?
Creator: Kinney, W. E. & Coveyou, R. R.
Partner: UNT Libraries Government Documents Department

Automated Approach to Quantitative Error Analysis in Neutron Transport Calculations

Description: A method is described how a quantitative measure for the robustness of a given transport theory code for coarse network calculations can be obtained. A code, that performs this task automatically and at only nominal cost, is described and has been implemented for slab geometry. This code generates also user oriented benchmark problems which exhibit the analytic behavior at interfaces.
Date: September 1976
Creator: Bareiss, Erwin H. & Derstine, Keith L.
Partner: UNT Libraries Government Documents Department

Slow Neutron Leakage Spectra from Spallation Neutron Sources

Description: An efficient technique is described for Monte Carlo simulation of neutron beam spectra from target-moderator-reflector assemblies typical of pulsed spallation neutron sources. The technique involves the scoring of the transport-theoretical probability that a neutron will emerge from the moderator surface in the direction of interest, at each collision. An angle-biasing probability is also introduced which further enhances efficiency in simple problems.
Date: February 1980
Creator: Das, Shashikala G.; Carpenter, J. M. & Prael, R. E.
Partner: UNT Libraries Government Documents Department

Time-Independent One-Speed Neutron Transport Equation with Anisotropic Scattering in Absorbing Media

Description: This report treats the time-independent, one-speed neutron transport equation with anisotropic scattering in absorbing media. For nuclear gain operators existence and uniqueness of solutions to the half-space and finite-slab problems are proved in L₂-space. The formulas needed for explicit calculations are derived by the use of perturbation theory techniques.
Date: June 1980
Creator: Hangelbroek, Rutger Jan
Partner: UNT Libraries Government Documents Department

IBM Multigroup Numerical Procedures

Description: Introduction: "This paper presents in formula form IBM computational procedure for averaging cross-section data and for calculating reflected spherical reactors by the linear by the linear multigroup numerical method developed by the Physics Section of the ANP Central Design Group. The adjoint reactor numerical procedural is included."
Date: November 28, 1950
Creator: Holmes, David K. & Schulze, O. A.
Partner: UNT Libraries Government Documents Department

Technical Foundations of TRIGA

Description: From foreword: The TRIGA is a novel and unusually safe training, research, and isotope-production reactor that contains solid homogeneous uranium-zirconium-hydride-moderator fuel elements and operates at power levels in the range of from 10 kw to 250 kw.
Date: August 27, 1958
Creator: General Dynamics Corporation. General Atomic Division.
Partner: UNT Libraries Government Documents Department

Variational correction to the FERMI beam solution

Description: We consider the time-independent, monoenergetic searchlight problem for a purely scattering, homogeneous slab with a pencil beam of nuclear particles impinging upon one surface. The scattering process is assumed sufficiently peaked in the forward direction so that the Fokker-Planck differential scattering operator can be used. Further, the slab is assumed sufficiently thin so that backscattering is negligibly small. Generally, this problem is approximated by the classic Fermi solution. A number of modifications of Fermi theory, aiming at improved accuracy, have been proposed. Here, we show that the classic Fermi solution (or any approximate solution) can I be improved via a variational formalism.
Date: October 1, 1996
Creator: Su, Bingjing & Pomraning, G.C.
Partner: UNT Libraries Government Documents Department

The planar Green`s function in an infinite multiplying medium

Description: Throughout the history of neutron transport theory, the study of simplified problems that have analytical or semi-analytical solutions has been a foundation for more complicated analyses. Analytical transport results are often used as benchmarks or in pedagogical settings. Benchmark problems in infinite homogeneous media have been studied continually, beginning with the monograph by Case, DeHoffmann, and Placzek. A fundamental problem considered in this work is the Green`s function in an infinite medium. The Green`s function problem considers an infinite planar source emitting neutral particles in the single directions`. Recently, this Green`s function has been used to obtain solutions for finite media. These solutions, which hinge on accurate and fast evaluation of the infinite medium Green`s function, use Fourier and Laplace transform inversion techniques for the evaluation. Until now, only absorbing media have been considered, and applications were therefore limited to non-multiplying media. In an effort to relax this limitation, the infinite medium Green`s function is numerically evaluated for an infinite multiplying medium using the double-sided Laplace transform inversion. Of course, no steady-state mathematical solution exists for an infinite multiplying medium with a source present; however, the non-physical solution in an infinite medium can be used in finite media problems where the solution is physically realizable.
Date: October 1, 1996
Creator: Kornreich, D.E. & Ganapol, B.D.
Partner: UNT Libraries Government Documents Department

The Green`s function method for critical heterogeneous slabs

Description: Recently, the Green`s Function Method (GFM) has been employed to obtain benchmark-quality results for nuclear engineering and radiative transfer calculations. This was possible because of fast and accurate calculations of the Green`s function and the associated Fourier and Laplace transform inversions. Calculations have been provided in one-dimensional slab geometries for both homogeneous and heterogeneous media. A heterogeneous medium is analyzed as a series of homogeneous slabs, and Placzek`s lemma is used to extend each slab to infinity. This allows use of the infinite medium Green`s function (the anisotropic plane source in an infinite homogeneous medium) in the solution. To this point, a drawback of the GFM has been the limitation to media with c < 1, where c is the number of secondary particles produced in a collision. Clearly, no physical steady-state solution exists for an infinite medium that contains an infinite source and is described by c >1; however, mathematical solutions exist which result in oscillating Green`s functions. Such calculations are briefly discussing. The limitation to media with c < 1 has been relaxed so that the Green`s function may also be calculated for media with c {ge} 1. Thus, materials that contain fissionable isotopes may be modeled.
Date: October 1, 1996
Creator: Kornreich, D.E.
Partner: UNT Libraries Government Documents Department

Singular perturbation analysis of the neutron transport equation

Description: A singular perturbation technique is applied to the one-speed, one- dimensional neutron transport equation with isotropic scattering. Our technique extends previous singular perturbation applications to higher-order and reduces the transport problem to a series of diffusion theory problems in the interior medium and a series of analytically solvable transport problems in the boundary layers. Asymptotic matching links the two solutions, yielding boundary conditions and a composite expansion valid throughout the media. Our formulation generates an accurate correction for the material interface condition used in global diffusion theory calculations.
Date: July 1, 1996
Creator: Losey, D.C. & Lee, J.C.
Partner: UNT Libraries Government Documents Department

A portable, parallel, object-oriented Monte Carlo neutron transport code in C++

Description: 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 {alpha}-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 {alpha}-eigenvalues in seconds to minutes rather than hours to days. Future plans and the implementation of a general transport physics framework are also discussed.
Date: May 1, 1997
Creator: Lee, S.R.; Cummings, J.C. & Nolen, S.D.
Partner: UNT Libraries Government Documents Department