Monte Carlo and deterministic computational methods for the calculation of the effective delayed neutron fraction

Abstract

The effective delayed neutron fraction βeff plays an important role in kinetics and static analysis of the reactor physics experiments. It is used as reactivity unit referred to as “dollar”. Usually, it is obtained by computer simulation due to the difficulty in measuring it experimentally. In 1965, Keepin proposed a method, widely used in the literature, for the calculation of the effective delayed neutron fraction βeff. This method requires calculation of the adjoint neutron flux as a weighting function of the phase space inner products and is easy to implement by deterministic codes. With Monte Carlo codes, the solution of the adjoint neutron transport equation is much more difficult because of the continuous-energy treatment of nuclear data. Consequently, alternative methods, which do not require the explicit calculation of the adjoint neutron flux, have been proposed. In 1997, Bretscher introduced the k-ratio method for calculating the effective delayed neutron fraction; this method is based on calculating the multiplication factor of a nuclear reactor core with and without the contribution of delayed neutrons. The multiplication factor set by the delayed neutrons (the delayed multiplication factor) is obtained as the difference between the total and the prompt multiplication factors. Using Monte Carlo calculation Bretscher evaluated the βeff as the ratio between the delayed and total multiplication factors (therefore the method is often referred to as the k-ratio method). In the present work, the k-ratio method is applied by Monte Carlo (MCNPX) and deterministic (PARTISN) codes. In the latter case, the ENDF/B nuclear data library of the fuel isotopes (235U and 238U) has been processed by the NJOY code with and without the delayed neutron data to prepare multi-group WIMSD neutron libraries for the lattice physics code DRAGON, which was used to generate the PARTISN macroscopic cross sections. In recent years Meulekamp and van der Marck in 2006 and Nauchi and Kameyama in 2005 proposed new methods for the effective delayed neutron fraction calculation with only one Monte Carlo computer simulation, compared with the k-ratio method which require two criticality calculations. In this paper, the Meulekamp/Marck and Nauchi/Kameyama methods are applied for the first time by the MCNPX computer code and the results obtained by all different methods are compared.