Thesis (Ph. D.)--University of Wisconsin--Madison, 1984. / Typescript. Vita. Description based on print version record. Includes bibliographies.

In this dissertation, we discuss an adaptive angular discretization scheme for the neutral-particle transport equation in three dimensions. We mesh the direction domain by dividing the faces of a regular octahedron into equilateral triangles and projecting these onto “spherical triangles” on the surface of the sphere. We choose four quadrature points per triangle, and we define interpolating basis functions that are linear in the direction cosines. The quadrature point’s weight is the integral of the point’s linear discontinuous finite element (LDFE) basis function over its local triangle. Variations in the locations of the four points produce variations in the quadrature set. The new quadrature sets are amenable to local refinement and coarsening, and hence can be used with an adaptive algorithm. If local refinement is requested, we use the LDFE basis functions to build an approximate angular flux, interpolated, by interpolation through the existing four points on a given triangle. We use a transport sweep to find the actual values, calc, at certain test directions in the triangle and compare against interpolated at those directions. If the results are not within a userdefined tolerance, the test directions are added to the quadrature set. The performance of our uniform sets (no local refinement) is dramatically better than that of commonly used sets (level-symmetric (LS), Gauss-Chebyshev (GC) and variants) and comparable to that of the Abu-Shumays Quadruple Range (QR) sets. On simple problems, the QR sets and the new sets exhibit 4th-order convergence in the scalar flux as the directional mesh is refined, whereas the LS and GC sets exhibit 1.5-order and 2nd-order convergence, respectively. On difficult problems (near discontinuities in the direction domain along directions that are not perpendicular to coordinate axes), these convergence orders diminish and the new sets outperform the others. We remark that the new LDFE sets have strictly positive weights and that arbitrarily refined sets can be generated without the numerical difficulties that plague the generation of high-order QR sets. Adapted LDFE sets are more efficient than uniform LDFE sets only in difficult problems. This is due partly to the high accuracy of the uniform sets, partly to basing refinement decisions on purely local information, and partly to the difficulty of mapping among differently refined sets. These results are promising and suggest interesting future work that could lead to more accurate solutions, lower memory requirements, and faster solutions for many transport problems.

Integral transport theory is used to compute transfer matrix elements for neutral particle streaming through r-z rectangular voids. The transfer matrix is utilized in a hybrid method; it interfaces with a conventional discrete ordinates calculation outside the void. Since the hybrid interface is accomplished within the inner iteration of an existing discrete ordinates code, standard sweeping schemes used in SN codes are not adversely affected. The resulting transfer matrix is independent of the multigroup energy structure used in a calculation. Further, the transfer matrix is not affected by changes in materials or cross sections outside the void. For these reasons, once a transfer matrix is calculated it can be used in a wide variety of problems containing a similar void. In this study, the transfer matrix hybrid, standard discrete ordinates, and Monte Carlo methods are applied to two sample problems to compare the accuracy of these methods. The Monte Carlo results are considered correct in order to compute errors in the deterministic calculations. The transfer matrix hybrid method is more accurate than conventional SN methods; the ray effect, persistent in discrete ordinates calculations, is substantially reduced. In addition, the transfer matrix hybrid executes faster than higher order SN calculations.

M.Phil. (Energy Studies) / SAFARI-1 is a 20 MW research reactor, which is over 45 years old, and is expected to reach the end of its operating life between 2020 and 2030. The aim of this work is to investigate various alternative conceptual core layouts of the SAFARI-1 reactor in order to facilitate more e ective utilization of the reactor, while potentially expanding its operating lifetime. The spatial and energy neutron distribution is one of the most signi cant parameters in the characterization of such an alternative core layout. This neutron distribution is a result of basic physics processes such as particle matter interactions, nuclear reactions, material properties, e ects of temperature and the time evolution of the system. This study focuses on the steady-state neutron distribution within the highly heterogeneous and complex geometry of the reactor core for the various alternative core layouts. This work has searched for and found a di erent inhomogeneous neutron distribution within the core, arising from a di erent core layout, which can nonetheless still achieve e ciency in the operation for various design purposes, but with a lower power output. Via numerical analysis with the OSCAR-4 code system, the safety and utilization requirements for the SAFARI-1 reactor are evaluated and quantied in terms of its steady-state neutron ux distribution. A SAFARI-1 reference core, obtained via an equilibrium cycle calculation, was used to generate a set of safety and utilization targets against which alternative designs may be measured. Alternative core layouts were developed by using a parametric study to scope the size and power level of potential candidate conceptual cores with the aim of minimizing the power level while adhering to the safety requirements. Utilization parameters of interest include isotope production capability, thermal ux levels in beam tubes and production levels in the silicon doping facility...

Radiation portal monitors are being deployed at border crossings throughout the world to prevent the smuggling of nuclear and radiological materials; however, a tension exists between security and the free-flow of commerce. Delays at ports-of-entry have major economic implications, so it is imperative to minimize portal monitor screening time. We have developed an algorithm to locate a radioactive source using a distributed array of detectors, specifically for use at border crossings. To locate the source, we formulated an optimization problem where the objective function describes the least-squares difference between the actual and predicted detector measurements. The predicted measurements are calculated by solving the 3-D deterministic neutron transport equation given an estimated source position. The source position is updated using the steepest descent method, where the gradient of the objective function with respect to the source position is calculated using adjoint transport calculations. If the objective function is smaller than a predetermined convergence criterion, then the source position has been identified. To test the algorithm, we first verified that the 3-D forward transport solver was working correctly by comparing to the code PARTISN (Parallel Time-Dependent SN). Then, we developed a baseline scenario to represent a typical border crossing. Test cases were run for various source positions within each vehicle and convergence criteria, which showed that the algorithm performed well in situations where we have perfect knowledge of parameters such as the material properties of the vehicles. We also ran a sensitivity analysis to determine how uncertainty in various parameters-the optical thickness of the vehicles, the fill level in the gas tank, the physical size of the vehicles, and the detector efficiencies-affects the results. We found that algorithm is most sensitive to the optical thickness of the vehicles. Finally, we tested the simplifying assumption of one energy group by using measurements obtained from MCNPX (Monte Carlo N-Particle Extended). These results showed that the one-energy-group assumption will not be sufficient if the code is deployed in a real-world scenario. While this work describes the application of the algorithm to a land border crossing, it has potential for use in a wide array of nuclear security problems.

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X-10, the genesis production reactor for the U.S. paved the way for all weapons material production. This feat offers a unique fundamental opportunity of nuclear forensic analysis and popular neutron code package evaluation. Production reactor nuclear forensic signatures and characteristics are emphasized throughout this work. These underlying production characteristics are reported and analyzed for potential in-core zone provenance and axial slug location coupled with how the nuclear data uncertainties affect these conclusions. Material attribution with respect to commercial versus military reactor applications is also featured in this study. Three nuclear code packages are examined including Scale 6.1 (Scale 6.2 beta-3 for nuclear data uncertainty reporting and evaluation), Monte Carlo N-Particle (MCNP) and Parallel Environment Neutral-particle TRANsport (PENTRAN). Each of these code packages employs different neutron transport methods and cross-section evaluation. These code results are compared and contrasted for the researcher to gain perspective into if and how nuclear forensic analysis is affected by these relative outcomes from the neutronics packages. Notably, Scale 6.2 beta-3 offers perspective on the nuclear data uncertainty and how it affects final conclusions on isotopic reporting and material provenance.

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Recent work by Yasseri and Rahnema has introduced a consistent spatial homogenization (CSH) method completely in transport theory. The CSH method can very accurately reproduce the heterogeneous flux shape and eigenvalue of a reactor, but at high computational cost. Other recent works for homogenization in diffusion or quasi-diffusion theory are accurate for problems with low heterogeneity, such as PWRs, but are not proven for more heterogeneous reactors such as BWRs or GCRs. To address these issues, a consistent hybrid diffusion-transport spatial homogenization (CHSH) method is developed as an extension of the CSH method that uses conventional flux weighted homogenized cross sections to calculate the heterogeneous solution. The whole-core homogenized transport calculation step of the CSH method has been replaced with a whole- core homogenized diffusion calculation. A whole-core diffusion calculation is a reasonable replacement for transport because the homogenization procedure tends to smear out transport effects at the core level. The CHSH solution procedure is to solve a core-level homogenized diffusion equation with the auxiliary source term and then to apply an on-the-fly transport-based re-homogenization at the assembly level to correct the homogenized and auxiliary cross sections. The method has been derived in general geometry with continuous energy, and it is implemented and tested in fine group, 1-D slab geometry on controlled and uncontrolled BWR and HTTR benchmark problems. The method converges to within 2% mean relative error for all four configurations tested and has computational efficiency 2 to 4 times faster than the reference calculation.