Monte Carlo Direct Simulation Method for Initiation Probability Problems

Abstract

During the early period of a supercritical system, the growth of fission chains shows a significant stochastic feature. In multiplying medium, it is a probability issue of fail-pass type for a single neutron to sponsor a divergent fission chain, and the probability of success is named as single neutron initiation probability. Meanwhile, in the presence of a weak neutron source, the time at which fission burst occurs also exhibits a stochastic nature, which can be observed on experiments of pulsed reactors such as GODIVA I and GODIVA II. The initiation probability and burst waiting time reflect the dynamic feature of a supercritical system, which are very important for nuclear criticality safety concerns. It is desirable that a supercritical system has an initiation probability very close to zero and releases limited energy in case of criticality accidents. The stochastic process of neutron population evolution in early age in a multiplying system is governed by Bell's equation in the form of an adjoint neutron transport equation with a non-linear fission term. In order to solve this stochastic neutron transport equation, the deterministic method discretizing the phase space was proposed long ago and has been implemented in several SN codes such as Partisn, Ardra and PANDA. However, the deterministic method is of limited usage, due to its poor ability to precisely describe real-world 3D complex geometries and continuous energy neutron spectrum. Recently, Monte Carlo methods have gradually gained attention for solving Bell's equation. Greenman from LLNL proposed an analog Monte Carlo forward-transport method for calculating initiation probability in 2007. He implemented this method by introducing the maximum age parameter, the time sub-interval and the neutron progenitor tag into Mercury in time-dependent fixed-source simulation mode. This method is only suitable for initiation probability calculations, however not for analyzing the randomness of burst waiting time. Later, GANG in 2011 developed the GSMP (Generalized Semi-Markov Process method) Monte Carlo method according to Bell's equation. While the GSMP method, which can deal with both initiation probability and burst waiting time, is flexible and powerful for zero-dimensional problems, it is not favorable when extended to 3D and continuous energy problems due to severe lack of computational efficiency. In 2015, a direct Monte Carlo simulation method for stochastic systems problems was implemented in MCATK, yet this method has not been applied specifically to the burst waiting time. In this work, a new and efficient 3D Monte Carlo direct simulation method for calculating both the initiation probability and the burst waiting time is developed. By taking random factors during evolvement of fission chains into account in dynamic Monte Carlo simulation, this new method has the potential of simulating the whole process from source neutron injection to exponential growth of the neutron population, and finally to extinction of the neutron pulse. This capability is useful in criticality accidents evaluation and pulsed reactor experiments explanation. (authors)