| In this thesis two new methods of calculating the criticality of a nuclear system are introduced and verified.;The methods introduced in this thesis, including a direct leakage operator and an indirect multiple scattering leakage operator, obviate the need to know angular fluxes accurately at system boundaries. Instead, the system wide scalar flux, an integral quantity which is substantially easier to obtain with good precision, is sufficient to obtain production, absorption, scattering, and leakage rates.;Most methods of determining the criticality of a nuclear system depend implicitly upon knowledge of the angular flux, net currents, or moments of the angular flux, on the system surface in order to know the leakage. For small systems, leakage is the predominant element in criticality calculations. Unfortunately, in these methods the least accurate fluxes, currents, or moments are those occurring near system surfaces or interfaces. This is due to a mathematical inability to satisfy rigorously with a finite order angular polynomial expansion or angular difference technique the physical boundary conditions which occur on these surfaces. Consequently, one must accept large computational effort or less precise criticality calculations. |
