# Calculating alpha Eigenvalues in a Continuous-Energy Infinite Medium with Monte Carlo

## Abstract

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.

- Authors:

- Los Alamos National Laboratory

- Publication Date:

- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Sponsoring Org.:
- DOE/LANL

- OSTI Identifier:
- 1050477

- Report Number(s):
- LA-UR-12-24472

TRN: US1204699

- DOE Contract Number:
- AC52-06NA25396

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; 97 MATHEMATICAL METHODS AND COMPUTING; APPROXIMATIONS; EIGENVALUES; KINETICS; MARKOV PROCESS; PHYSICS; TIME DEPENDENCE; TRANSPORT; VERIFICATION

### Citation Formats

```
Betzler, Benjamin R., Kiedrowski, Brian C., Brown, Forrest B., and Martin, William R.
```*Calculating alpha Eigenvalues in a Continuous-Energy Infinite Medium with Monte Carlo*. United States: N. p., 2012.
Web. doi:10.2172/1050477.

```
Betzler, Benjamin R., Kiedrowski, Brian C., Brown, Forrest B., & Martin, William R.
```*Calculating alpha Eigenvalues in a Continuous-Energy Infinite Medium with Monte Carlo*. United States. doi:10.2172/1050477.

```
Betzler, Benjamin R., Kiedrowski, Brian C., Brown, Forrest B., and Martin, William R. Tue .
"Calculating alpha Eigenvalues in a Continuous-Energy Infinite Medium with Monte Carlo". United States. doi:10.2172/1050477. https://www.osti.gov/servlets/purl/1050477.
```

```
@article{osti_1050477,
```

title = {Calculating alpha Eigenvalues in a Continuous-Energy Infinite Medium with Monte Carlo},

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

abstractNote = {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.},

doi = {10.2172/1050477},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2012},

month = {9}

}

Save to My Library

You must Sign In or Create an Account in order to save documents to your library.