Monte Carlo Methods for Reactor Kinetic Simulations

Abstract

The use of the Monte Carlo (MC) method for space-time reactor kinetics is expected to be much more accurate than the presently used deterministic methods largely based on few-group diffusion theory. However, the development of the MC method for space-time reactor kinetics poses challenges because of the vastly different timescales of neutrons and delayed neutron precursors and their vastly different populations that also change with time by several orders of magnitude. In order to meet these challenges in MC-based space kinetics, we propose various new schemes such as deterministic decay of precursors in each time step, adjustment of weights of neutrons and precursors for population control, use of mean number of secondaries per collision, and particle splitting/Russian roulette to reduce the variance in neutron power. The efficacy of these measures is first tested in a simpler point-kinetics version of the MC method against analytical or accurate numerical solutions of point-kinetics equations. The ideas are then extended to space-dependent MC kinetics and are validated against a transport theory/MC transient benchmark. We have also tested our methods by comparison with results of realistic space-time kinetics benchmarks/studies involving multiregion reactors, energy dependence, movement of control rods, and feedback—most of which are based on few-group diffusion theory treated by the finite difference method. To facilitate exact comparison with such benchmarks, we have implemented the schemes described above for space-time reactor kinetics based on finite difference diffusion MC, a method developed by us earlier in a different context.