Neutron batch size optimisation methodology for Monte Carlo criticality calculations

• Published in: Annals of nuclear energy Vol. 75; pp. 620 - 626
• Main Authors: Tuttelberg, Kaur, Dufek, Jan
• Format: Journal Article
• Language: English
• Published: 01.01.2015
• Subjects: Computational efficiency; Computer simulation; Computing time; Dominance ratio; Error propagation; Fission; Mathematical analysis; Monte Carlo criticality; Monte Carlo methods; Nuclear power generation; Optimisation; Optimization; Source bias; Source convergence
• ISSN: 0306-4549; 1873-2100
• DOI: 10.1016/j.anucene.2014.09.011

We present a methodology that improves the efficiency of conventional power iteration based Monte Carlo criticality calculations by optimising the number of neutron histories simulated per criticality cycle (the so-called neutron batch size). The chosen neutron batch size affects both the rate of convergence (in computing time) and magnitude of bias in the fission source. Setting a small neutron batch size ensures a rapid simulation of criticality cycles, allowing the fission source to converge fast to its stationary state; however, at the same time, the small neutron batch size introduces a large systematic bias in the fission source. It follows that for a given allocated computing time, there is an optimal neutron batch size that balances these two effects. We approach this problem by studying the error in the cumulative fission source, i.e. the fission source combined over all simulated cycles, as all results are commonly combined over the simulated cycles. We have deduced a simplified formula for the error in the cumulative fission source, taking into account the neutron batch size, the dominance ratio of the system, the error in the initial fission source and the allocated computing time (in the form of the total number of simulated neutron histories). Knowing how the neutron batch size affects the error in the cumulative fission source allows us to find its optimal value. We demonstrate the benefits of the method on a number of numerical test calculations.