Derivation of the Two-Exponential Probability Density Function for Rossi-Alpha Measurements of Reflected Assemblies and Validation for the Special Case of Shielded Measurements

Rossi-alpha measurements of fissionable assemblies are used to estimate the prompt neutron decay constant α. Reactivity can be inferred from α if the values of the neutron generation time and effective delayed neutron fraction are assumed. If multiple measurements are performed on an assembly near delayed critical, one can determine α at delayed critical and directly infer reactivity (without needing to assume values for the neutron generation time or effective delayed neutron fraction). Previous works have demonstrated that two-exponential fits for Rossi-alpha measurements of reflected assemblies have better fit metrics than those of one-exponential fits; however, the two-exponential probability density function that is needed to obtain α from the fit parameters has not been derived. This paper derives the two-exponential fit based on a two-region point kinetics model for Rossi-alpha measurements of reflected assemblies, a generalization of the current, one-region model (one-exponential fit). The new model is validated for shielded assemblies, a special case of reflected assemblies where the reflector-to-core leakage is negligibly small. The validation is performed using shielded, fissionable assemblies (highly enriched uranium with k_eff ≈ 0.95 and weapons-grade plutonium with k_eff > 0.77). The results show that the two-exponential model can (1) predict the constant α within two standard deviations, and (2) deconvolve α and the time a neutron spends in the reflector region, neither of which is possible with the one-exponential model.