During the investigation of particle transport with Monte Carlo methods one often faces tasks which need the estimation of coincidence of events or correlations between events. The problem becomes a transport problem when several detection events can originate from the same source event as the particle is transported in a multiplicative media between the source and the detection. A coincidence is when separate events (e.g. detection) occur during the same time period. Some examples for such problems are additive peaks in detectors or the dead-time effect. Correlation measures the interdependency of certain events. The estimation of correlation involves the higher moments of the distributions and typical examples are the different noise measurement techniques (e.g. Feynman-a, Rossi-a, etc.).

Such problems are often referenced as non-Boltzmann estimators as they depend on the collective effects of particle not described in the Boltzmann transport equation. Conventional non-analogous Monte Carlo is optimized to preserve the mean value of the distributions and is therefore not suited for non-Boltzmann problems. By using different variance reduction techniques it introduces artificial coincidences by splitting particle trajectories and biases the higher moments by the weighting of the events. Analogous Monte Carlo simulation avoids these problems but the computer time needed to arrive at acceptable statistics in full-scale problems may be overwhelming.

In order to circumvent the above problems the “history splitting” approach is presented. This method collects information about the non-analogous steps during transport and generates every possible history containing only analogous steps from the source to the detectors. Such “subhistories” are handled as independent ones originating from separate source events in order to remove the undesired artificial correlations. Unbiased estimation of the higher moments can be obtained by interpreting the weight of the subhistories as the probability of the realization of the given subhistory.

The method is implemented in a simple one-dimensional, monoenergetic Monte Carlo model of source and detector in a multiplicative media and verified against the analytical solution on problems involving coincidence and correlation. Further application of the method is planned in the investigation of neutron noise experiment in source driven subcritical systems.

For more information, please contact j.l.kloosterman@tudelft.nl.