Calculating Alpha Eigenvalues and Eigenfunctions with a Markov Transition Rate Matrix Monte Carlo Method
Abstract
For a nuclear system in which the entire αeigenvalue spectrum is known, eigenfunction expansion yields the timedependent flux response to any arbitrary source. Applications in which this response is of interest include pulsedneutron experiments, acceleratordriven subcritical systems, and fast burst reactors, where a steadystate assumption used in neutron transport is invalid for characterizing the timedependent flux. To obtain the αeigenvalue spectrum, the transition rate matrix method (TRMM) tallies transition rates describing neutron behavior in a discretized positiondirectionenergy phase space using Monte Carlo. Interpretation of the resulting Markov process transition rate matrix as the operator in the adjoint αeigenvalue problem provides an avenue for determining a large finite set of α eigenvalues and eigenfunctions of a nuclear system. Results from the TRMM are verified using analytic solutions, timedependent Monte Carlo simulations, and modal expansion from diffusion theory. For simplified infinitemedium and onedimensional geometries, the TRMM accurately calculates eigenvalues, eigenfunctions, and eigenfunction expansion solutions. Applications and comparisons to measurements are made for the small fast burst reactor CALIBAN and the Fort St. Vrain hightemperature gascooled reactor. For large threedimensional geometries, discretization of the large positionenergydirection phase space limits the accuracy of eigenfunction expansion solutions using the TRMM, but it can still generatemore »
 Authors:

 Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
 Univ. of Michigan, Ann Arbor, MI (United States)
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Publication Date:
 Research Org.:
 Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 1492187
 DOE Contract Number:
 AC0500OR22725
 Resource Type:
 Journal Article
 Journal Name:
 Nuclear Science and Engineering
 Additional Journal Information:
 Journal Volume: 192; Journal Issue: 2; Journal ID: ISSN 00295639
 Publisher:
 American Nuclear Society  Taylor & Francis
 Country of Publication:
 United States
 Language:
 English
 Subject:
 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; Alpha eigenvalue; timedependent transport; transition rate matrix; Markov process
Citation Formats
Betzler, Benjamin R., Kiedrowski, Brian C., Martin, William R., and Brown, Forrest B. Calculating Alpha Eigenvalues and Eigenfunctions with a Markov Transition Rate Matrix Monte Carlo Method. United States: N. p., 2018.
Web. doi:10.1080/00295639.2018.1497397.
Betzler, Benjamin R., Kiedrowski, Brian C., Martin, William R., & Brown, Forrest B. Calculating Alpha Eigenvalues and Eigenfunctions with a Markov Transition Rate Matrix Monte Carlo Method. United States. doi:10.1080/00295639.2018.1497397.
Betzler, Benjamin R., Kiedrowski, Brian C., Martin, William R., and Brown, Forrest B. Fri .
"Calculating Alpha Eigenvalues and Eigenfunctions with a Markov Transition Rate Matrix Monte Carlo Method". United States. doi:10.1080/00295639.2018.1497397.
@article{osti_1492187,
title = {Calculating Alpha Eigenvalues and Eigenfunctions with a Markov Transition Rate Matrix Monte Carlo Method},
author = {Betzler, Benjamin R. and Kiedrowski, Brian C. and Martin, William R. and Brown, Forrest B.},
abstractNote = {For a nuclear system in which the entire αeigenvalue spectrum is known, eigenfunction expansion yields the timedependent flux response to any arbitrary source. Applications in which this response is of interest include pulsedneutron experiments, acceleratordriven subcritical systems, and fast burst reactors, where a steadystate assumption used in neutron transport is invalid for characterizing the timedependent flux. To obtain the αeigenvalue spectrum, the transition rate matrix method (TRMM) tallies transition rates describing neutron behavior in a discretized positiondirectionenergy phase space using Monte Carlo. Interpretation of the resulting Markov process transition rate matrix as the operator in the adjoint αeigenvalue problem provides an avenue for determining a large finite set of α eigenvalues and eigenfunctions of a nuclear system. Results from the TRMM are verified using analytic solutions, timedependent Monte Carlo simulations, and modal expansion from diffusion theory. For simplified infinitemedium and onedimensional geometries, the TRMM accurately calculates eigenvalues, eigenfunctions, and eigenfunction expansion solutions. Applications and comparisons to measurements are made for the small fast burst reactor CALIBAN and the Fort St. Vrain hightemperature gascooled reactor. For large threedimensional geometries, discretization of the large positionenergydirection phase space limits the accuracy of eigenfunction expansion solutions using the TRMM, but it can still generate a fair estimate of the fundamental eigenvalue and eigenfunction. These results show that the TRMM generates an accurate estimate of a large number of α eigenvalues. This is not possible with existing Monte Carlo–based methods.},
doi = {10.1080/00295639.2018.1497397},
journal = {Nuclear Science and Engineering},
issn = {00295639},
number = 2,
volume = 192,
place = {United States},
year = {2018},
month = {9}
}
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