Eigenvalue-Dependent Neutron Energy Spectra: Definitions, Analyses, and Applications

An analysis of spectral effects that arise from solving the k-, α-, γ-, and δ-eigenvalue formulations of the neutron transport equation is presented. Hierarchies of neutron spectra softness are established and expressed in terms of spatial-dependent local indices that are defined for both the core and the reflector of nuclear system configurations. Conclusions regarding the general behavior of the spectrum-dependent integral spectral indices and initial conversion ratios given by the k-, α-, γ-, and δ-eigenvalue equations are also presented. Spectral effects in the core and in the reflector are distinguished by defining separate integral spectral indices for the core and for the reflector. It is shown that the relationship between the spectra given by the k-, α-, γ-, and δ-eigenvalue equations and the spectrum in a corresponding critical configuration depends on the specific physical process that causes deviation from criticality. Nevertheless, some general recommendations are offered regarding the use of a particular eigenvalue equation for specific applications. All conclusions are supported by numerical experiments performed for an idealized thermal system.