Calculating Alpha Eigenvalues and Eigenfunctions with a Markov Transition Rate Matrix Monte Carlo Method

Betzler, Benjamin R.; Kiedrowski, Brian C.; Martin, William R.; Brown, Forrest B.

doi:10.1080/00295639.2018.1497397

Calculating Alpha Eigenvalues and Eigenfunctions with a Markov Transition Rate Matrix Monte Carlo Method

Journal Article · Fri Sep 21 00:00:00 EDT 2018 · Nuclear Science and Engineering

DOI:https://doi.org/10.1080/00295639.2018.1497397· OSTI ID:1492187

^[1]; Kiedrowski, Brian C. ^[2]; Martin, William R. ^[2]; Brown, Forrest B. ^[3]

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)

For a nuclear system in which the entire α-eigenvalue spectrum is known, eigenfunction expansion yields the time-dependent flux response to any arbitrary source. Applications in which this response is of interest include pulsed-neutron experiments, accelerator-driven subcritical systems, and fast burst reactors, where a steady-state assumption used in neutron transport is invalid for characterizing the time-dependent flux. To obtain the α-eigenvalue spectrum, the transition rate matrix method (TRMM) tallies transition rates describing neutron behavior in a discretized position-direction-energy phase space using Monte Carlo. Interpretation of the resulting Markov process transition rate matrix as the operator in the adjoint α-eigenvalue 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, time-dependent Monte Carlo simulations, and modal expansion from diffusion theory. For simplified infinite-medium and one-dimensional 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 high-temperature gas-cooled reactor. For large three-dimensional geometries, discretization of the large position-energy-direction 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.

View Accepted Manuscript (DOE)

Research Organization:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC05-00OR22725

OSTI ID:: 1492187

Journal Information:: Nuclear Science and Engineering, Journal Name: Nuclear Science and Engineering Journal Issue: 2 Vol. 192; ISSN 0029-5639

Publisher:: American Nuclear Society - Taylor & FrancisCopyright Statement

Country of Publication:: United States

Language:: English

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Cited By (3)

Calculating Time Eigenvalues of the Neutron Transport Equation with Dynamic Mode Decomposition McClarren, Ryan G. Nuclear Science and Engineering, Vol. 193, Issue 8 https://doi.org/10.1080/00295639.2018.1565014	journal	February 2019
A Diffusion Monte Carlo–Based Algorithm for Estimation of Higher Modes of a Reactor Srivastava, Argala; Singh, K. P.; Mallick, Amod Kishore Nuclear Science and Engineering, Vol. 193, Issue 9 https://doi.org/10.1080/00295639.2019.1596721	journal	May 2019
Calculating Time Eigenvalues of the Neutron Transport Equation with Dynamic Mode Decomposition McClarren, Ryan G. arXiv https://doi.org/10.48550/arxiv.1810.10678	text	January 2018

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73 NUCLEAR PHYSICS AND RADIATION PHYSICS
Alpha eigenvalue
Markov process
time-dependent transport
transition rate matrix

Calculating Alpha Eigenvalues and Eigenfunctions with a Markov Transition Rate Matrix Monte Carlo Method

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