# Calculating infinite-medium {alpha}-eigenvalue spectra with 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 {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)

- Authors:

- Department of Nuclear Engineering and Radiological Sciences, University of Michigan, 2355 Bonisteel Boulevard, Ann Arbor, MI 48109 (United States)
- X-Computational Physics Division, Monte Carlo Codes Group, Los Alamos National Laboratory, P.O. Box 1663, Los Alamos, NM 87545 (United States)

- Publication Date:

- Research Org.:
- American Nuclear Society, 555 North Kensington Avenue, La Grange Park, IL 60526 (United States)

- OSTI Identifier:
- 22212917

- Resource Type:
- Conference

- Resource Relation:
- Conference: M and C 2013: 2013 International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, Sun Valley, ID (United States), 5-9 May 2013; Other Information: Country of input: France; 7 refs.; Related Information: In: Proceedings of the 2013 International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering - M and C 2013| 3016 p.

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; CRITICALITY; EIGENFUNCTIONS; EIGENVALUES; ENERGY SPECTRA; HOMOGENEOUS MIXTURES; MARKOV PROCESS; MATRICES; MONTE CARLO METHOD; NEUTRON TRANSPORT; NEUTRONS; TIME DEPENDENCE

### Citation Formats

```
Betzler, B. R., Kiedrowski, B. C., Brown, F. B., and Martin, W. R.
```*Calculating infinite-medium {alpha}-eigenvalue spectra with a transition rate matrix method*. United States: N. p., 2013.
Web.

```
Betzler, B. R., Kiedrowski, B. C., Brown, F. B., & Martin, W. R.
```*Calculating infinite-medium {alpha}-eigenvalue spectra with a transition rate matrix method*. United States.

```
Betzler, B. R., Kiedrowski, B. C., Brown, F. B., and Martin, W. R. Mon .
"Calculating infinite-medium {alpha}-eigenvalue spectra with a transition rate matrix method". United States.
doi:.
```

```
@article{osti_22212917,
```

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

author = {Betzler, B. R. and Kiedrowski, B. C. and Brown, F. B. and Martin, W. 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 {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)},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Mon Jul 01 00:00:00 EDT 2013},

month = {Mon Jul 01 00:00:00 EDT 2013}

}

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