Time Evolving Fission Chain Theory and Fast Neutron and Gamma-Ray Counting Distributions
Abstract
Here, we solve a simple theoretical model of time evolving fission chains due to Feynman that generalizes and asymptotically approaches the point model theory. The point model theory has been used to analyze thermal neutron counting data. This extension of the theory underlies fast counting data for both neutrons and gamma rays from metal systems. Fast neutron and gamma-ray counting is now possible using liquid scintillator arrays with nanosecond time resolution. For individual fission chains, the differential equations describing three correlated probability distributions are solved: the time-dependent internal neutron population, accumulation of fissions in time, and accumulation of leaked neutrons in time. Explicit analytic formulas are given for correlated moments of the time evolving chain populations. The equations for random time gate fast neutron and gamma-ray counting distributions, due to randomly initiated chains, are presented. Correlated moment equations are given for both random time gate and triggered time gate counting. There are explicit formulas for all correlated moments are given up to triple order, for all combinations of correlated fast neutrons and gamma rays. The nonlinear differential equations for probabilities for time dependent fission chain populations have a remarkably simple Monte Carlo realization. A Monte Carlo code was developed formore »
- Authors:
-
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- Publication Date:
- Research Org.:
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1377778
- Report Number(s):
- LLNL-JRNL-658859
Journal ID: ISSN 0029-5639; TRN: US1702573
- Grant/Contract Number:
- AC52-07NA27344
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Nuclear Science and Engineering
- Additional Journal Information:
- Journal Volume: 181; Journal Issue: 3; Journal ID: ISSN 0029-5639
- Publisher:
- American Nuclear Society - Taylor & Francis
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 22 GENERAL STUDIES OF NUCLEAR REACTORS; 46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND TECHNOLOGY; 73 NUCLEAR PHYSICS AND RADIATION PHYSICS
Citation Formats
Kim, K. S., Nakae, L. F., Prasad, M. K., Snyderman, N. J., and Verbeke, J. M. Time Evolving Fission Chain Theory and Fast Neutron and Gamma-Ray Counting Distributions. United States: N. p., 2015.
Web. doi:10.13182/NSE14-120.
Kim, K. S., Nakae, L. F., Prasad, M. K., Snyderman, N. J., & Verbeke, J. M. Time Evolving Fission Chain Theory and Fast Neutron and Gamma-Ray Counting Distributions. United States. https://doi.org/10.13182/NSE14-120
Kim, K. S., Nakae, L. F., Prasad, M. K., Snyderman, N. J., and Verbeke, J. M. Sun .
"Time Evolving Fission Chain Theory and Fast Neutron and Gamma-Ray Counting Distributions". United States. https://doi.org/10.13182/NSE14-120. https://www.osti.gov/servlets/purl/1377778.
@article{osti_1377778,
title = {Time Evolving Fission Chain Theory and Fast Neutron and Gamma-Ray Counting Distributions},
author = {Kim, K. S. and Nakae, L. F. and Prasad, M. K. and Snyderman, N. J. and Verbeke, J. M.},
abstractNote = {Here, we solve a simple theoretical model of time evolving fission chains due to Feynman that generalizes and asymptotically approaches the point model theory. The point model theory has been used to analyze thermal neutron counting data. This extension of the theory underlies fast counting data for both neutrons and gamma rays from metal systems. Fast neutron and gamma-ray counting is now possible using liquid scintillator arrays with nanosecond time resolution. For individual fission chains, the differential equations describing three correlated probability distributions are solved: the time-dependent internal neutron population, accumulation of fissions in time, and accumulation of leaked neutrons in time. Explicit analytic formulas are given for correlated moments of the time evolving chain populations. The equations for random time gate fast neutron and gamma-ray counting distributions, due to randomly initiated chains, are presented. Correlated moment equations are given for both random time gate and triggered time gate counting. There are explicit formulas for all correlated moments are given up to triple order, for all combinations of correlated fast neutrons and gamma rays. The nonlinear differential equations for probabilities for time dependent fission chain populations have a remarkably simple Monte Carlo realization. A Monte Carlo code was developed for this theory and is shown to statistically realize the solutions to the fission chain theory probability distributions. Combined with random initiation of chains and detection of external quanta, the Monte Carlo code generates time tagged data for neutron and gamma-ray counting and from these data the counting distributions.},
doi = {10.13182/NSE14-120},
journal = {Nuclear Science and Engineering},
number = 3,
volume = 181,
place = {United States},
year = {Sun Nov 01 00:00:00 EDT 2015},
month = {Sun Nov 01 00:00:00 EDT 2015}
}
Free Publicly Available Full Text
Publisher's Version of Record
Other availability
Search WorldCat to find libraries that may hold this journal
Cited by: 5 works
Citation information provided by
Web of Science
Web of Science
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.
Works referenced in this record:
Prompt -ray production in neutron-induced fission of Pu
journal, April 2013
- Ullmann, J. L.; Bond, E. M.; Bredeweg, T. A.
- Physical Review C, Vol. 87, Issue 4
Neutron Signal Multiplet Analysis for the Mass Determination of Spontaneous Fission Isotopes
journal, December 1983
- Dierckx, R.; Hage, W.
- Nuclear Science and Engineering, Vol. 85, Issue 4
Third Moment of the Number of Neutrons Detected in Short Time Intervals
journal, February 1968
- Furuhashi, Akira; Izumi, Akira
- Journal of Nuclear Science and Technology, Vol. 5, Issue 2
The number distribution of neutrons and gamma photons generated in a multiplying sample
journal, October 2006
- Enqvist, Andreas; Pázsit, Imre; Pozzi, Sara
- Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, Vol. 566, Issue 2
Probability distribution of neutrons and precursors in a multiplying assembly
journal, February 1963
- Bell, George I.
- Annals of Physics, Vol. 21, Issue 2
Models for a three-parameter analysis of neutron signal correlation measurements for fissile material assay
journal, November 1986
- Cifarelli, D. M.; Hage, W.
- Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, Vol. 251, Issue 3
The detection statistics of neutrons and photons emitted from a fissile sample
journal, August 2009
- Enqvist, Andreas; Pozzi, Sara A.; Pázsit, Imre
- Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, Vol. 607, Issue 2
The Effect of Multiplication on the Quantitative Determination of Spontaneously Fissioning Isotopes by Neutron Correlation Analysis
journal, May 1985
- Böhnel, K.
- Nuclear Science and Engineering, Vol. 90, Issue 1
Time Interval Distributions and the Rossi Correlation Function
journal, May 2013
- Prasad, M.; Snyderman, N.; Verbeke, J.
- Nuclear Science and Engineering, Vol. 174, Issue 1
Correlation Analysis with Neutron Count Distributions in Randomly or Signal Triggered Time Intervals for Assay of Special Fissile Materials
journal, February 1985
- Hage, W.; Cifarelli, D. M.
- Nuclear Science and Engineering, Vol. 89, Issue 2, p. 159-176
Statistical Theory of Fission Chains and Generalized Poisson Neutron Counting Distributions
journal, November 2012
- Prasad, Manoj K.; Snyderman, Neal J.
- Nuclear Science and Engineering, Vol. 172, Issue 3
Works referencing / citing this record:
Results of Three Neutron Diagnosed Subcritical Experiments
journal, December 2018
- Gomez, J. A.; Koehler, P. E.; Cutler, T. E.
- Nuclear Science and Engineering, Vol. 193, Issue 5
Correlated prompt fission data in transport simulations
journal, January 2018
- Talou, P.; Vogt, R.; Randrup, J.
- The European Physical Journal A, Vol. 54, Issue 1
Correlated Prompt Fission Data in Transport Simulations
text, January 2017
- Talou, P.; Vogt, R.; Randrup, J.
- arXiv