One-run Monte Carlo Calculation of Effective Delayed Neutron Fraction and Area-ratio Reactivity

The Monte Carlo code MCNPX has been utilized to calculate the effective delayed neutron fraction and reactivity by using the area-ratio method. The effective delayed neutron fraction eff has been calculated with the fission probability method proposed by Meulekamp and van der Marck. MCNPX was used to calculate separately the fission probability of the delayed and the prompt neutrons by using the TALLYX user subroutine of MCNPX. In this way, eff was obtained from the one criticality (k-code) calculation without performing an adjoint calculation. The traditional k-ratio method requires two criticality calculations to calculate eff, while this approach utilizes only one MCNPX criticality calculation. Therefore, the approach described here is referred to as a one-run method. In subcritical systems driven by a pulsed neutron source, the area-ratio method is used to calculate reactivity (in dollar units) as the ratio between the prompt and delayed areas. These areas represent the integral of the reaction rates induced from the prompt and delayed neutrons during the pulse period. Traditionally, application of the area-ratio method requires two separate fixedsource MCNPX simulations: one with delayed neutrons and the other without. The number of source particles in these two simulations must be extremely high in order to obtain accurate results with low statistical errors because the values of the total and prompt areas are very close. Consequently, this approach is time consuming and suffers from the statistical errors of the two simulations. The present paper introduces a more efficient method for estimating the reactivity calculated with the area method by taking advantage of the TALLYX user subroutine of MCNPX. This subroutine has been developed for separately scoring the reaction rates caused by the delayed and the prompt neutrons during a single simulation. Therefore the method is referred to as a onerun calculation. These methodologies have been utilized for several published benchmark cases, and a comparison of the results shows good agreement.