Development of new source diagnostic methods and variance reduction techniques for Monte Carlo eigenvalue problems with a focus on high dominance ratio problems

Obtaining the solution to the linear Boltzmann equation is often is often a daunting task. The time-independent form is an equation of six independent variables which cannot be solved analytically in all but some special problems. Instead, numerical approaches have been devised. This work focuses on improving Monte Carlo methods for its solution in eigenvalue form.;First, a statistical method of stationarity detection called the KPSS test adapted as a Monte Carlo eigenvalue source convergence test. The KPSS test analyzes the source center of mass series which was chosen since it should be indicative of overall source behavior, and is physically easy to understand. A source center of mass plot alone serves as a good visual source convergence diagnostic. The KPSS test and three different information theoretic diagnostics were implemented into the well known KENOV.a code inside of the SCALE (version 5) code package from Oak Ridge National Laboratory and compared through analysis of a simple problem and several difficult source convergence benchmarks. Results showed that the KPSS test can add to the overall confidence by identifying more problematic simulations than without its usage. Not only this, the source center of mass information on hand visually aids in the understanding of the problem physics.;The second major focus of this dissertation concerned variance reduction methodologies for Monte Carlo eigenvalue problems. The CADIS methodology, based on importance sampling, was adapted to the eigenvalue problems. It was shown that the straight adaption of importance sampling can provide a significant variance reduction in determination of keff (in cases studied up to 30%?). A modified version of this methodology was developed which utilizes independent deterministic importance simulations. In this new methodology, each particle is simulated multiple times, once to every other discretized source region utilizing the importance for that region only. Since each particle is simulated multiple times, this methodology often slows down the final keff convergence, but an increase coupling between source zones with important yet low probability interaction is observed. This is an important finding for loosely coupled systems and may be useful in their analysis.;The third major focus of this dissertation concerns the use of the standard cumulative fission matrix methodology for high dominance ratio problems which results in high source correlation. Source eigenvector confidence is calculated utilizing a Monte Carlo iterated confidence approach and shown to be superior to the currently used plus and minus fission matrix methodology. Utilizing the fission matrix based approach with appropriately meshing and particle density, it is shown that the fission matrix elements tend to be independent. As a result, the keff and the source eigenvector can be calculated without bias, which is not the case for the standard methodology due to the source correlation. This approach was tested with a 1-D multigroup eigenvalue code developed for this work. A preliminary automatic mesh and particle population diagnostic were formulated to ensure independent and normal fission matrix elements. The algorithm was extended in parallel to show the favorable speedup possible with the fission matrix based approach. (Full text of this dissertation may be available via the University of Florida Libraries web site. Please check http://www.uflib.ufl.edu/etd.html)...