Analysis of the Eigenvalue Equations in k, λ, γ, and α Applied to Some Fast- and Thermal-Neutron Systems

The time-dependent Boltzmann equation for neutron transport is transformed into eigenvalue equations in k, λ, γ, and α, whose general properties are stated as hypotheses. Numerical solutions are obtained with the discrete-ordinates code DTF, where a direct λ eigenvalue calculation has been added. Eigenvalues and eigenfunctions are analyzed for idealized fast and thermal systems in both bare and reflected configurations. The differences found in these idealized cases provide some useful bases for estimating the behavior of the different eigenvalue solutions in specific applications.