A Stochastic Transport Model for the Cumulative Number of Fissions and Deposited Fission Energy

Abstract

The stochastic theory of neutron transport is extended to describe the cumulative distribution of fission numbers and deposited fission energy in a subvolume of a multiplying assembly. Solutions for the probability distributions are obtained using analytical approximations and Monte Carlo simulation in lumped geometry and in symmetric homogeneous and heterogeneous spheres. The results show the development of a power-law tail in the steady-state fission number and deposited energy distributions when the medium is critical, independent of the fission neutron multiplicity distribution and domain heterogeneity. In contrast, the asymptotic decay is faster than exponential in subcritical media due to rapid chain extinction and in supercritical media due to the increasing probability of chain divergence. A formal asymptotic analysis of the problem in lumped geometry with an arbitrary fission neutron multiplicity confirms the existence of power-law tails at critical.

Keywords:

• Stochastic fission number and energy deposition
• backward master equation
• power-law tails

Acknowledgments

This work was supported by the U.S. Department of Energy through the Los Alamos National Laboratory. Los Alamos National Laboratory is operated by Triad National Security, LLC, for the National Nuclear Security Administration of the U.S. Department of Energy (contract no. 89233218CNA000001). The work of the first author at the University of New Mexico was partially supported by the U.S. Department of Energy National Nuclear Security Administration through the Nuclear Science and Engineering Consortium for Nonproliferation under subaward number 00010833 with the University of California. The authors gratefully acknowledge helpful discussions with Scott Ramsey and Erin Davis.

Disclosure Statement

No potential conflict of interest was reported by the authors.