Calculating infinite-medium α-eigenvalue spectra with Monte Carlo using a transition rate matrix method

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

doi:10.1016/j.nucengdes.2015.07.052

Title: Calculating infinite-medium α-eigenvalue spectra with Monte Carlo using a transition rate matrix method

Abstract

The time-dependent behavior of the energy spectrum in neutron transport was investigated with a formulation, based on continuous-time Markov processes, for computing α eigenvalues and eigenvectors in an infinite medium. In this study, a research Monte Carlo code called “TORTE” (To Obtain Real Time Eigenvalues) was created and used to estimate elements of a transition rate matrix. TORTE is capable of using both multigroup and continuous-energy nuclear data, and verification was performed. Eigenvalue spectra for infinite homogeneous mixtures were obtained, and an eigenfunction expansion was used to investigate transient behavior of the neutron energy spectrum.

Authors:

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

Univ. of Michigan, Ann Arbor, MI (United States)
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Publication Date:: Fri Aug 28 00:00:00 EDT 2015

Research Org.:: Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

Sponsoring Org.:: USDOE National Nuclear Security Administration (NNSA)

OSTI Identifier:: 1223665

Alternate Identifier(s):: OSTI ID: 1247414

Grant/Contract Number:: AC05-00OR22725

Resource Type:: Accepted Manuscript

Journal Name:: Nuclear Engineering and Design

Additional Journal Information:: Journal Name: Nuclear Engineering and Design; Journal ID: ISSN 0029-5493

Publisher:: Elsevier

Country of Publication:: United States

Language:: English

Subject:: 73 NUCLEAR PHYSICS AND RADIATION PHYSICS

Citation Formats


                    Betzler, Benjamin R., Kiedrowski, Brian C., Brown, Forrest B., and Martin, William R. Calculating infinite-medium α-eigenvalue spectra with Monte Carlo using a transition rate matrix method.  United States: N. p., 2015. 
Web.  doi:10.1016/j.nucengdes.2015.07.052.

Copy to clipboard


                    Betzler, Benjamin R., Kiedrowski, Brian C., Brown, Forrest B., & Martin, William R. Calculating infinite-medium α-eigenvalue spectra with Monte Carlo using a transition rate matrix method.  United States.  https://doi.org/10.1016/j.nucengdes.2015.07.052

Copy to clipboard


                    Betzler, Benjamin R., Kiedrowski, Brian C., Brown, Forrest B., and Martin, William R. Fri .  
"Calculating infinite-medium α-eigenvalue spectra with Monte Carlo using a transition rate matrix method".  United States.  https://doi.org/10.1016/j.nucengdes.2015.07.052.  https://www.osti.gov/servlets/purl/1223665.

Copy to clipboard


                    
@article{osti_1223665,

  title        = {Calculating infinite-medium α-eigenvalue spectra with Monte Carlo using a transition rate matrix method},

  author       = {Betzler, Benjamin R. and Kiedrowski, Brian C. and Brown, Forrest B. and Martin, William R.},

  abstractNote = {The time-dependent behavior of the energy spectrum in neutron transport was investigated with a formulation, based on continuous-time Markov processes, for computing α eigenvalues and eigenvectors in an infinite medium. In this study, a research Monte Carlo code called “TORTE” (To Obtain Real Time Eigenvalues) was created and used to estimate elements of a transition rate matrix. TORTE is capable of using both multigroup and continuous-energy nuclear data, and verification was performed. Eigenvalue spectra for infinite homogeneous mixtures were obtained, and an eigenfunction expansion was used to investigate transient behavior of the neutron energy spectrum.},

  doi          = {10.1016/j.nucengdes.2015.07.052},

  journal      = {Nuclear Engineering and Design},

  number       = ,

  volume       = ,

  place        = {United States},

  year         = {Fri Aug 28 00:00:00 EDT 2015},

  month        = {Fri Aug 28 00:00:00 EDT 2015}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Accepted Manuscript (Publisher)

Accepted Manuscript (DOE)

Publisher's Version of Record

https://doi.org/10.1016/j.nucengdes.2015.07.052

Other availability

Search WorldCat to find libraries that may hold this journal

Citation Metrics:

Cited by: 7 works

Citation information provided by
Web of Science

Save / Share:

Export Metadata

Save to My Library

Works referenced in this record:

On the spectrum of the linear transport operator
journal, November 1974

Larsen, Edward W.; Zweifel, Paul F.
Journal of Mathematical Physics, Vol. 15, Issue 11
DOI: 10.1063/1.1666570

ENDF/B-VII.1 Nuclear Data for Science and Technology: Cross Sections, Covariances, Fission Product Yields and Decay Data
journal, December 2011

Chadwick, M. B.; Herman, M.; Obložinský, P.
Nuclear Data Sheets, Vol. 112, Issue 12
DOI: 10.1016/j.nds.2011.11.002

ENDF/B-VII.0: Next Generation Evaluated Nuclear Data Library for Nuclear Science and Technology
journal, December 2006

Chadwick, M. B.; Obložinský, P.; Herman, M.
Nuclear Data Sheets, Vol. 107, Issue 12
DOI: 10.1016/j.nds.2006.11.001

Higher Order αMode Eigenvalue Calculation by Monte Carlo Power Iteration
journal, January 2011

Yamamoto, Toshihiro
Progress in Nuclear Science and Technology, Vol. 2, Issue 0
DOI: 10.15669/pnst.2.826

Works referencing / citing this record:

A Diffusion Monte Carlo–Based Algorithm for Estimation of Higher Modes of a Reactor
journal, May 2019

Srivastava, Argala; Singh, K. P.; Mallick, Amod Kishore
Nuclear Science and Engineering, Vol. 193, Issue 9
DOI: 10.1080/00295639.2019.1596721

Similar Records in DOE PAGES and OSTI.GOV collections:

Calculating infinite-medium {alpha}-eigenvalue spectra with a transition rate matrix method

Conference Betzler, B. R. ; Kiedrowski, B. C. ; Brown, F. B. ; ...

The time-dependent behavior of the energy spectrum in neutron transport was investigated with a formulation, based on continuous-time Markov processes, for computing {alpha}-eigenvalues and eigenvectors in an infinite medium. For this, a research Monte Carlo code called TORTE was created and used to estimate elements of a transition rate matrix. TORTE is capable of using both multigroup and continuous-energy nuclear data, and verification was performed. Eigenvalue spectra for infinite homogeneous mixtures were obtained and an eigenfunction expansion was used to investigate transient behavior of the neutron energy spectrum. (authors)
Calculating Alpha Eigenvalues and Eigenfunctions with a Markov Transition Rate Matrix Monte Carlo Method

Journal Article Betzler, Benjamin R. ; Kiedrowski, Brian C. ; Martin, William R. ; ... - Nuclear Science and Engineering

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 providesmore »« less
Cited by 6
https://doi.org/10.1080/00295639.2018.1497397

Full Text Available
Calculating alpha Eigenvalues in a Continuous-Energy Infinite Medium with Monte Carlo

Technical Report Betzler, Benjamin R. ; Kiedrowski, Brian C. ; Brown, Forrest B. ; ...

The {alpha} eigenvalue has implications for time-dependent problems where the system is sub- or supercritical. We present methods and results from calculating the {alpha}-eigenvalue spectrum for a continuous-energy infinite medium with a simplified Monte Carlo transport code. We formulate the {alpha}-eigenvalue problem, detail the Monte Carlo code physics, and provide verification and results. We have a method for calculating the {alpha}-eigenvalue spectrum in a continuous-energy infinite-medium. The continuous-time Markov process described by the transition rate matrix provides a way of obtaining the {alpha}-eigenvalue spectrum and kinetic modes. These are useful for the approximation of the time dependence of the system.
https://doi.org/10.2172/1050477

Full Text Available
Multigroup Constant Calculation with Static α-Eigenvalue Monte Carlo for Time-Dependent Neutron Transport Simulations

Journal Article Variansyah, Ilham ; Betzler, Benjamin R. ; Martin, William R. - Nuclear Science and Engineering

Herein, multigroup constants for deterministic methods that preserve the time-dependent physics of the neutron transport equations are derived. Alternative multigroup constant weighting spectra are discussed: (1) the fundamental k-eigenfunction, (2) the fundamental α-eigenfunction, and (3) a composite of several α-modes. To generate the fundamental α-eigenfunction for calculating the multigroup constants, a static fundamental α-eigenvalue method is implemented into the open source Monte Carlo code OpenMC. Several static and kinetic problems are devised to verify the implementations and to investigate the relative performance of the alternative multigroup constant weighting spectra. Results emphasize that as a multigroup constant weighting spectrum, the fundamentalmore »« less
https://doi.org/10.1080/00295639.2020.1743578

Full Text Available
Fission Matrix Capability for MCNP Monte Carlo

Technical Report Carney, Sean E. ; Brown, Forrest B. ; Kiedrowski, Brian C. ; ...

In a Monte Carlo criticality calculation, before the tallying of quantities can begin, a converged fission source (the fundamental eigenvector of the fission kernel) is required. Tallies of interest may include powers, absorption rates, leakage rates, or the multiplication factor (the fundamental eigenvalue of the fission kernel, k{sub eff}). Just as in the power iteration method of linear algebra, if the dominance ratio (the ratio of the first and zeroth eigenvalues) is high, many iterations of neutron history simulations are required to isolate the fundamental mode of the problem. Optically large systems have large dominance ratios, and systems containing poormore »« less
https://doi.org/10.2172/1050495

Full Text Available

Similar Records

Title: Calculating infinite-medium α-eigenvalue spectra with Monte Carlo using a transition rate matrix method

Abstract

Citation Formats

On the spectrum of the linear transport operator journal, November 1974

ENDF/B-VII.1 Nuclear Data for Science and Technology: Cross Sections, Covariances, Fission Product Yields and Decay Data journal, December 2011

ENDF/B-VII.0: Next Generation Evaluated Nuclear Data Library for Nuclear Science and Technology journal, December 2006

Higher Order αMode Eigenvalue Calculation by Monte Carlo Power Iteration journal, January 2011

A Diffusion Monte Carlo–Based Algorithm for Estimation of Higher Modes of a Reactor journal, May 2019

On the spectrum of the linear transport operator
journal, November 1974

ENDF/B-VII.1 Nuclear Data for Science and Technology: Cross Sections, Covariances, Fission Product Yields and Decay Data
journal, December 2011

ENDF/B-VII.0: Next Generation Evaluated Nuclear Data Library for Nuclear Science and Technology
journal, December 2006

Higher Order αMode Eigenvalue Calculation by Monte Carlo Power Iteration
journal, January 2011

A Diffusion Monte Carlo–Based Algorithm for Estimation of Higher Modes of a Reactor
journal, May 2019