Nuclear Science and Engineering / Volume 156 / Number 2 / June 2007 / Pages 164-179
Three variance reduction techniques for the ongoing development of Monte Carlo isotopic inventory analysis are implemented as alternatives to improve the precision of Monte Carlo simulations. The Forced Reaction technique is designed to force an atom to undergo a predefined number of reactions in a given control volume. Biased Reaction Branching is primarily focused on improving statistical results of the isotopes that are produced from rare reaction pathways. Biased Source Sampling is aimed at increasing frequencies of sampling rare initial isotopes as the starting Monte Carlo particles. A variety of test problems is uniquely designed to demonstrate the validity and the improvement, relative to the analog problem, of each technique. The increases in precision due to the variance reduction techniques usually come at the expense of longer computing times per history.
A figure of merit (FOM) is developed as a tool to monitor the efficiency of Monte Carlo simulations with variance reduction schemes. A number of statistical characteristics of Monte Carlo isotopic inventory calculations are used to construct a variety of FOM formulations. Two of them offer robust FOMs: one based on the relative error of a known target isotope (1/R2T) and one based on the overall detection limit corrected by the relative error (1/DkR2T).
Figures of merit are later used to quantitatively assess the efficiencies of Monte Carlo simulations under different scopes of interest. Given a defined set of variance reduction parameters to produce desired effects, the efficiency measurements from an FOM agree with the expected performance.