Calculation of the Effective Delayed Neutron Fraction by Deterministic and Monte Carlo Methods

Abstract

The studies on Accelerator-Driven Systems (ADSs) have renewed the interest in the theoretical and computational evaluation of the main integral parameters characterizing subcritical systems (e.g., reactivity, effective delayed neutron fractionβeff, and mean prompt neutron generation time). In particular, some kinetic parameters, as the effective delayed neutron fraction, are evaluated in Monte Carlo codes by formulations which do not require the calculation of the adjoint flux. This paper is focused on a theoretical and computational analysis about how the differentβeffdefinitions are connected and which are the approximations inherent to the Monte Carlo definition with respect to the standard definition involving weighted integrals. By means of a refined transport computational analysis carried out in a coherent and consistent way, that is, using the same deterministic code and neutron data library for theβeffevaluation in different ways, the theoretical analysis is numerically confirmed. Both theoretical and numerical results confirm the effectiveness of the Monte Carloβeffevaluation, at least in cases where spectral differences between total and prompt fluxes are negligible with respect to the value of the functionals entering the classicalβeffformulation.