Monte and Usha Ahuja Distinguished Lecture Series - Speaker: Anil Prinja

Modeling Stochastic Neutron Populations with Branching Markov Process Theory

Abstract 

Representation of neutrons as discrete point particles and the probabilistic laws governing neutron-nucleus interactions (capture, scattering and fission) ensures that the neutron population in a nuclear assembly is fundamentally stochastic with at best stationary statistics. Truly deterministic behavior is never realized in practice, especially in fissile materials where neutron multiplication can rapidly grow the population. In particular, situations arise, whether by design or accident, where random uctuations in the neutron number dominate the mean trend and therefore necessitate special and explicit consideration. Potential supercritical excursions during nuclear reactor operations and in fuel processing, preinitiation phenomena in burst or pulsed reactors, and neutron signature analysis in nuclear safeguards highlight instances where the neutron population is strongly stochastic and a knowledge of just the low order statistical moments (mean, variance) is not useful. A common theme in these seemingly disparate applications is that of neutron populations in multiplying media evolving over time in the presence of weak intrinsic, random sources (spontaneous fission). Characterizing neutron populations under these conditions perforce requires a modeling approach that is grounded in branching Markov stochastic process theory.

In this talk we review the stochastic theory of neutron transport, emphasize under-appreciated facts associated with stochastic populations, and generalize the theory to describe the probability distribution of the cumulative amount of deposited fission energy. Analytical and numerical solutions for key probabilities characterizing the evolution of the neutron population are presented. Recent advances in extending this approach to compute detailed neutron multiplicity distributions, of interest in nuclear safeguards, using deterministic methods will also be presented.

About the Speaker

Dr. Anil K. Prinja is currently Distinguished Professor and Immediate Past Chair
(2014 –2019) in the Department of Nuclear Engineering at the University of New Mexico. He obtained his B.Sc. (1976) and Ph.D. (1980) in Nuclear Engineering from Queen Mary College, University of London, UK, and was a Research Faculty in Nuclear Engineering at UCLA prior to joining UNM in 1987. Dr. Prinja’s overarching research focus is deterministic and stochastic particle transport theory, with specific interests in: modeling stochastic neutron populations for nuclear security applications; radiation transport on stochastic geometries; high energy charged particle transport; and uncertainty quantification. Dr. Prinja is a Fellow of the American Nuclear Society and recipient of the 2015 American Nuclear Society “Gerald C. Pomraning Award”.

Host: Richard Vasques