Directional Effects in Transitional Resonance Spectra and Group Constants

Abstract

Analytical exploratory investigations indicate that transition effects such as streaming cause a considerable spatial variation in the neutron spectra across resonances; streaming leads to opposite effects in the forward and backward directions. The neglect of this coupled spatial/angular variations of the transitory resonance spectra is an approximation that is common to all current group constant generation methodologies. This paper presents a description of the spatial/angular coupling of the neutron flux across isolated resonances. It appears to be necessary to differentiate between forward-and backward-directed neutron flux components or even to consider components in narrower angular cones. The effects are illustrated for an isolated actinide resonance in a simplified fast reactor blanket problem. The resonance spectra of the directional flux components {phi}{sup + } and {phi}{sup {minus}}, and even more so the 90-deg cone components, are shown to deviate significantly from the infinite medium approximation, and the differences increase with penetration. The charges in {phi}{sup + } lead to a decreasing scattering group constant that enhances neutron transmission; the changes in {phi}{sup {minus}} lead to an increasing group constant inhibiting backward scattering. Therefore, the changes in the forward-and backward-directed spectra both lead to increased neutron transmission. Conversely, the flux ({phi} = {phi}{supmore » + }+{phi}{sup {minus}}) is shown to agree closely with the infinite medium approximation both in the analytical formulas and in the numerical solution. The directional effect cancel in the summation. The forward-and backward-directed flux components are used as weighting spectra to illustrate the group constant changes for a single resonance.« less