# General Improvements to the MCNP Alpha-Eigenvalue Solver

## Abstract

In this document, a new algorithm for computing the α-eigenvalue is implemented and tested in MCNP. The algorithm follows the traditional k-α method in which neutrons are followed from birth until fission in batches. During this simulation, a number of tallies are performed which are derived from integrating the transport equation over all phase space. These new tallies along with the collapsed transport equation are used to compute a physically valid α with or without delayed neutrons. The performance and accuracy of the method is then tested, in which it is found that the new algorithm typically out- performs the current implementation while also representing a more complete physical picture. Through a convergence analysis, it was found that many simple test problems had unexpectedly large biases for reasonable quantities of neutrons per batch. This occurred with both the old and the new algorithm. However, the tally method had lower biases for all problems tested. Special implementation considerations are also discussed.

- Authors:

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

- Publication Date:

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

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

- OSTI Identifier:
- 1431059

- Report Number(s):
- LA-UR-18-22738

- DOE Contract Number:
- AC52-06NA25396

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICS AND COMPUTING; transport theory; criticality

### Citation Formats

```
Josey, Colin James.
```*General Improvements to the MCNP Alpha-Eigenvalue Solver*. United States: N. p., 2018.
Web. doi:10.2172/1431059.

```
Josey, Colin James.
```*General Improvements to the MCNP Alpha-Eigenvalue Solver*. United States. doi:10.2172/1431059.

```
Josey, Colin James. Thu .
"General Improvements to the MCNP Alpha-Eigenvalue Solver". United States. doi:10.2172/1431059. https://www.osti.gov/servlets/purl/1431059.
```

```
@article{osti_1431059,
```

title = {General Improvements to the MCNP Alpha-Eigenvalue Solver},

author = {Josey, Colin James},

abstractNote = {In this document, a new algorithm for computing the α-eigenvalue is implemented and tested in MCNP. The algorithm follows the traditional k-α method in which neutrons are followed from birth until fission in batches. During this simulation, a number of tallies are performed which are derived from integrating the transport equation over all phase space. These new tallies along with the collapsed transport equation are used to compute a physically valid α with or without delayed neutrons. The performance and accuracy of the method is then tested, in which it is found that the new algorithm typically out- performs the current implementation while also representing a more complete physical picture. Through a convergence analysis, it was found that many simple test problems had unexpectedly large biases for reasonable quantities of neutrons per batch. This occurred with both the old and the new algorithm. However, the tally method had lower biases for all problems tested. Special implementation considerations are also discussed.},

doi = {10.2172/1431059},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2018},

month = {3}

}