Comparing the time-eigenvalues of the natural mode equation by weight balancing and α-k methods

Abstract

The time–eigenvalues α of the natural mode equation are calculated for the CROCUS benchmark models corresponding to 11 water levels using suitable modifications of the power iteration of fission source in the MCNP-5 and TRIPOLI-4® codes. To model the time annihilation or source term in the natural mode equation, the weight balancing method has been implemented in MCNP-5, whereas the α-k method has been implemented in TRIPOLI-4®. For the calculations, thoroughly verified input models are prepared for the MCNP-5 and TRIPOLI-4® codes, so to have coherent effective multiplication factors keff. In the comparison of the time eigenvalues by the two methods, divergence and sign flip raise some issues for the configurations just near criticality. To overcome these problems, a novel estimator based on the shift of the eigenvalue from the minimum value is studied in this work. Here, the minimum value is taken as the opposite of the smallest decay constant of the delayed neutron precursors, λj. Based on our numerical simulations, we have verified the agreement of both methods, although all the tested estimators turn out to be possibly very sensitive to small discrepancies in the multiplication factor between the codes.