The purpose of this thesis is to examine the accuracy of the RAPID (Real-Time Analysis for Particle Transport and In-situ Detection) eigenvalue algorithm based on a few problems from the ICSBEP (International Criticality Safety Benchmark Evaluation Project) Handbook. RAPID is developed based on the MRT (Multi-Stage Response-Function Transport) methodology and it uses the fission matrix (FM) method for performing eigenvalue calculations. RAPID has already been benchmarked based on several real-world problems including spent fuel pools and casks, and reactor cores. This thesis examines the accuracy of the RAPID eigenvalue algorithm for modeling the physics of problems with unique geometric configurations. Four problems were selected from the ICSBEP Handbook; these problems differ by their unique configurations which can effectively examine the capability of the RAPID code system. For each problem, a reference Serpent Monte Carlo calculation has been performed. Using the same Serpent model in the pRAPID (pre- and post-processing for RAPID) utility code, a series of fixed-source Serpent calculations are performed to determine spatially-dependent FM coefficients. RAPID calculations are performed using these FM coefficients to obtain the axially-dependent, pin-wise fission density distribution and system eigenvalue for each problem. It is demonstrated that the eigenvalues calculated by RAPID and Serpent agree with the experimental data within the given experimental uncertainty. Further, the detailed 3-D pin-wise fission density distribution obtained by RAPID agrees with the reference prediction by Serpent which itself has converged to less than 1% weighted uncertainty. While achieving accurate results, RAPID calculations are significantly faster than the reference Serpent calculations, with a calculation time speed-up of between 4x and 34x demonstrated in this thesis. In addition to examining the accuracy of the RAPID algorithm, this thesis provides useful information on the use of the FM method for simulation of nuclear systems. / Master of Science / In the modeling and simulation of nuclear systems, two parameters are of key importance: the system eigenvalue and the fission distribution. The system eigenvalue, known as kef f , is the ratio of neutron production from fission in the current neutron generation compared with the absorption and leakage of neutrons from the system in the previous neutron generation. When this ratio is equal to one, the system is critical and is a self-sustaining chain reaction. Knowledge of the fission distribution is important in the nuclear power industry, as it enables engineers to determine the best reactor core assembly configuration to maintain an even power distribution. Several methods have been developed over the years to effectively solve for a nuclear systems fission distribution and system eigenvalue. Aspects of both Monte Carlo and deterministic transport methods have been combined into RAPID’s MRT methodology. It is capable of accurately determining the system eigenvalue and fission distribution in real time. This thesis examines the accuracy of the RAPID algorithm using four unique problems from the ICSBEP handbook. These problems help us to test the limits of the FM method in RAPID through the modeling of small, unique geometric configurations not seen in large, uniformly configured power reactor cores and spent fuel pools. For comparison, each problem is modeled using the Serpent Monte Carlo code, an accurate code meant to serve as the industry standard for determination of the fission distribution of each problem. This model is then used to generate a set of FM coefficients for use in RAPID calculations. It is demonstrated that the eigenvalues calculated by RAPID and Serpent agree with the experimental data within the given experimental uncertainty. The fission distribution obtained by RAPID is also in agreement with the Serpent reference model. Finally, the RAPID eigenvalue calculation is significantly faster than the corresponding Serpent reference model, with speed-ups ranging from 4x to 34x demonstrated.

A novel collision source method has been developed to solve the Linear Boltzmann Equation (LBE) more efficiently by adaptation of the angular quadrature order. The angular adaptation method is unique in that the flux from each scattering source iteration is obtained, with potentially a different quadrature order used for each. Traditionally, the flux from every iteration is combined, with the same quadrature applied to the combined flux. Since the scattering process tends to distribute the radiation more evenly over angles (i.e., make it more isotropic), the quadrature requirements generally decrease with each iteration. This method allows for an optimal use of processing power, by using a high order quadrature for the first few iterations that need it, before shifting to lower order quadratures for the remaining iterations. This is essentially an extension of the first collision source method, and is referred to as the adaptive collision source (ACS) method. The ACS methodology has been implemented in the 3-D, parallel, multigroup discrete ordinates code TITAN. This code was tested on a variety of test problems including fixed-source and eigenvalue problems. The ACS implementation in TITAN has shown a reduction in computation time by a factor of 1.5-4 on the fixed-source test problems, for the same desired level of accuracy, as compared to the standard TITAN code. / Ph. D.

Thesis: Sc. D., Massachusetts Institute of Technology, Department of Nuclear Engineering, 1977 / Vita. / Includes bibliographical references. / Sc. D. / Sc. D. Massachusetts Institute of Technology, Department of Nuclear Engineering

Transport of low energy neutrons associated with the galactic cosmic ray cascade is analyzed in this dissertation. A benchmark quality analytical algorithm is demonstrated for use with B scRYNTRN, a computer program written by the High Energy Physics Division of N scASA Langley Research Center, which is used to design and analyze shielding against the radiation created by the cascade. B scRYNTRN uses numerical methods to solve the integral transport equations for baryons with the straight-ahead approximation, and numerical and empirical methods to generate the interaction probabilities. The straight-ahead approximation is adequate for charged particles, but not for neutrons. As N scASA Langley improves B scRYNTRN to include low energy neutrons, a benchmark quality solution is needed for comparison. The neutron transport algorithm demonstrated in this dissertation uses the closed-form Green's function solution to the galactic cosmic ray cascade transport equations to generate a source of neutrons. A basis function expansion for finite heterogeneous and semi-infinite homogeneous slabs with multiple energy groups and isotropic scattering is used to generate neutron fluxes resulting from the cascade. This method, called the F(N) method, is used to solve the neutral particle linear Boltzmann transport equation. As a demonstration of the algorithm coded in the programs M scGSLAB and M scGSEMI, neutron and ion fluxes are shown for a beam of fluorine ions at 1000 MeV per nucleon incident on semi-infinite and finite aluminum slabs. Also, to demonstrate that the shielding effectiveness against the radiation from the galactic cosmic ray cascade is not directly proportional to shield thickness, a graph of transmitted total neutron scalar flux versus slab thickness is shown. A simple model based on the nuclear liquid drop assumption is used to generate cross sections for the galactic cosmic ray cascade. The E scNDF/B V database is used to generate the total and scattering cross sections for neutrons in aluminum. As an external verification, the results from M scGSLAB and M scGSEMI were compared to A scNISN/P scC, a routinely used neutron transport code, showing excellent agreement. In an application to an aluminum shield, the F(N) method seems to generate reasonable results.

Thesis (Ph. D.)--University of Washington, 1984. / Vita. Includes bibliographical references.

No description available.

Thesis (Ph. D.)--University of Missouri-Columbia, 2007. / The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file (viewed on March 11, 2008) Includes bibliographical references.

Thesis (doctoral)--Helsinki University of Technology, 2007. / Includes bibliographical references (p. 219-228). Also available on the World Wide Web.

Thesis (M. S.)--Nuclear and Radiological Engineering and Medical Physics, Georgia Institute of Technology, 2010. / Committee Chair: Rahnema, Farzad; Committee Member: Wang, Chris; Committee Member: Zhang, Dingkang. Part of the SMARTech Electronic Thesis and Dissertation Collection.

Thesis (Ph. D.)--University of Missouri-Columbia, 2007. / The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file (viewed on September 27, 2007) Vita. Includes bibliographical references.