Creation of problem-dependent Doppler-broadened cross sections in the KENO Monte Carlo code

Abstract

This paper introduces a quick method for improving the accuracy of Monte Carlo simulations by generating one-and twodimensional cross sections at a user-defined temperature before performing transport calculations. A finite difference method is used to Doppler-broaden cross sections to the desired temperature, and unit-base interpolation is done to generate the probability distributions for double differential two-dimensional thermal moderator cross sections at any arbitrarily user-defined temperature. The accuracy of these methods is tested using a variety of contrived problems. In addition, various benchmarks at elevated temperatures are modeled, and results are compared with benchmark results. The problem-dependent cross sections are observed to produce eigenvalue estimates that are closer to the benchmark results than those without the problem-dependent cross sections.

Resonance Scattering Treatment with the Windowed Multipole Formalism

“…The Doppler Broadening Rejection Correction (DBRC) [4] was one of the early proposed techniques to treat the effect of strong variations of the interaction cross section within the energetic vicinity of a scattering neutron, whereas S(α, β) tables had been used prior [11]. The method has since been implemented in numerous continuous energy Monte Carlo neutron transport programs [4,39,35,18], and has shown to successfully model the resonance upscatter effect. However, DBRC suffers from rejection probabilities as high as 99.995% [31] for neutron energies in the vicinity of a resonance.…”

Comparison of Temperature-Dependent Cross Section Treatments within the Shift Monte Carlo Radiation Transport Code

“…Additionally, the computational performance and trade-offs in memory and run time for each of the methods are quantified. Four methods are compared: the traditional method of storing cross section data at a select few temperatures (the Library method), calculating all the interpolated cross sections in a 1D and a 2D space before radiation transport is simulated (the 1D Preprocess and 2D Preprocess methods) Hart et al 2016, and an on-the-fly method using a WMP technique (the WMP method) Josey et al 2016. These methods were used in three radiation transport problems, and the results were compared with respect to accuracy, run time, and memory usage.…”

Implementation of the direct S(α,β) method in the KENO Monte Carlo code

“…ENDF files provide the thermal moderating data at a fixed number of temperatures. In order to to obtain temperatures at intermediate values, an interpolation scheme 40 implemented using a unit-based interpolation scheme similiar to that described in (Hart et al, 2014). The S(α, β) data are only used for inelastic scattering.…”

“…To test the accuracy of the temperature intperolation, 295 benchmarks were chosen to be consistent with those in previous Doppler broadening work. (Hart et al, 2016)…”