A Method of Transforming the Prompt Decay Constants α_l into the Static Reactivity ρs

Abstract

This report describes an analytical method of transforming the prompt decay constants α_l into the static reactivity ρ_s. It has been developed through the use of the time-dependent, two-group diffusion theory ignoring delayed neutrons under several assumptions. A generalized characteristic equation which relates the prompt decay constants to the effective multiplication constant can in general be derived by expanding the static fluxes into kinetic fluxes containing the fundamental and higher modes, and several approximated formulas for this equation have been obtained with the ap-plication of certain conditions. In particular, a formula that takes into account the change in the generation time -ρ_d2, =(β_eff/α_c){α_c-(G_α/G_αc)α}- is proposed as a most useful method for reactiv-ity measurement. Error evaluation has been performed in regard to several approximate formulas, and some problems involved in numerical calculation have been examined.