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.

Discretization and solving of the transport equation has been an area of great research where many methods have been developed. Under the deterministic transport methods, the method of characteristics, MOC, is one such discretization and solution method that has been applied to large-scale problems. Although these MOC, specifically long characteristics, LC, have been thoroughly applied to discretize and solve transport problems in the spatial domain, there is a need for an equally adequate time-dependent discretization. A method has been developed that uses LC discretization of the time and space variables in solving the transport equation. This space-time long characteristic, STLC, method is a discrete ordinates method that applies LC discretization in space and time and employs a least-squares approximation of sources such as the scattering source in each cell. This method encounters the same problems that previous spatial LC methods have dealt with concerning achieving all of the following: particle conservation, exact solution along a ray, and smooth variation in reaction rate for specific problems. However, quantities that preserve conservation in each cell can also be produced with this method and compared to the non-conservative results from this method to determine the extent to which this STLC method addresses the previous problems. Results from several test problems show that this STLC method produces conservative and non-conservative solutions that are very similar for most cases and the difference between them vanishes as track spacing is refined. These quantities are also compared to the results produced from a traditional linear discontinuous spatial discretization with finite difference time discretization. It is found that this STLC method is more accurate for streaming-dominate and scattering-dominate test problems. Also, the solution from this STLC method approaches the steady-state diffusion limit solution from a traditional LD method. Through asymptotic analysis and test problems, this STLC method produces a time-dependent diffusion solution in the thick diffusive limit that is accurate to O(E) and is similar to a continuous linear FEM discretization method in space with time differencing. Application of this method in parallel looks promising, mostly due to the ray independence along which the solution is computed in this method.

This dissertation focuses on the development and implementation of a new method to solve the time-dependent form of the linear Boltzmann transport equation for reactor transients. This new method allows for a stable solution to the fully explicit form of the transport equation with delayed neutrons by employing an error-controlled, adaptive Runge-Kutta-Fehlberg (RKF) method to differentiate the time domain. Allowing for the time step size to vary adaptively and as needed to resolve the time-dependent behavior of the angular flux and neutron precursor concentrations. The RKF expansion of the time domain occurs at each point and is coupled with a Source Iteration to resolve the spatial behavior of the angular flux at the specified point in time. The decoupling of the space and time domains requires the application of a quasi-static iteration between solving the time domain using adaptive RKF with error control and resolving the space domain with a Source Iteration sweep. The research culminated with the development of the 1-D Adaptive Runge-Kutta Time-Dependent Transport code (ARKTRAN-TD), which successfully implemented the new method and applied it to a suite of reactor transient benchmarks.

No description available.

In this thesis we investigate coupling and preconditioning techniques for 19D hybrid neutronics calculations. Each problem is represented by two spatial regions with Sn in one region and either Diffusion (P1) or P3 in the other region. For each of these two cases we define one coupling scheme and two different preconditioned systems. These systems are solved with both fixed9point iteration and the GMRES Krylov method. The solution techniques are compared in terms of iteration count and computational cost. Preconditioning with a global diffusion operator is found to be very effective for the most difficult problems.

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.