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

Journal Article · Thu Aug 25 00:00:00 EDT 2022 · Nuclear Science and Engineering

DOI:https://doi.org/10.1080/00295639.2022.2087830· OSTI ID:1895133

Prinja, Anil K. ^[1]; O’Rourke, Patrick F. ^[2]

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1. Univ. of New Mexico, Albuquerque, NM (United States); University of New Mexico
2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

The stochastic theory of neutron transport is extended to describe the cumulative distribution of fission numbers and deposited fission energy in 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. Here, 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.

• Research Organization: Univ. of New Mexico, Albuquerque, NM (United States)
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA)
• Grant/Contract Number: NA0003996
• OSTI ID: 1895133
• Journal Information: Nuclear Science and Engineering, Journal Name: Nuclear Science and Engineering Journal Issue: 2 Vol. 197; ISSN 0029-5639
• Publisher: Taylor & Francis
• Country of Publication: United States
• Language: English

Related Subjects

73 NUCLEAR PHYSICS AND RADIATION PHYSICS
97 MATHEMATICS AND COMPUTING
Stochastic fission number and energy deposition
backward master equation
power-law tails