Conservation of the Adjoint Neutron Spectrum by Use of Bilinear-Weighted Cross Sections and Its Effect on Fast Reactor Calculations

Flux weighting for the generation of broad-group cross sections is designed to preserve eigenvalue, flux spectrum, and reaction rates; however, it will not preserve adjoint spectrum and reactivity worths. Bilinear (flux-adjoint) weighting preserves all of the above quantities except reaction rates. Bilinear weighting also makes the eigenvalue of the broad-group calculation less sensitive to distortions of the spectrum away from the fundamental mode over which the cross sections were collapsed than is the case when flux weighting is used. A series of 29- and 11-group numerical tests has been made to assess the size of errors (relative to a fine-group standard) in eigenvalue, reaction rate ratios, isotopic worth components, and spectral shapes resulting from the use of the two energy collapse procedures. The errors in adjoint spectrum and calculated worth of scattering materials are found to be large when flux weighting is used.