# Is the Standard Monte Carlo Power Iteration Approach the Wrong Approach?

## Abstract

The power iteration method is the standard Monte Carlo approach for obtaining the eigenfunctions of a nuclear system, but the power method sometimes converges very slowly. Most discussions give a mathematical reason for the slow convergence of the Monte Carlo power method using the same concepts and terminology as when the power method is applied to a deterministic problem. This note first looks at why the convergence is slow from an intuitive Monte Carlo neutron perspective. Second, this note proposes building an eigenfunction intuitively in a cumulative (and noniterative) neutron by neutron manner that tends to better direct neutrons to where the neutrons need to be. Third, a very similar method for building the second eigenfunction is speculatively proposed.

- 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:
- 1043017

- Report Number(s):
- LA-UR-12-21928

TRN: US1203078

- DOE Contract Number:
- AC52-06NA25396

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 97 MATHEMATICAL METHODS AND COMPUTING; CONVERGENCE; EIGENFUNCTIONS; NEUTRONS

### Citation Formats

```
Booth, Thomas E.
```*Is the Standard Monte Carlo Power Iteration Approach the Wrong Approach?*. United States: N. p., 2012.
Web. doi:10.2172/1043017.

```
Booth, Thomas E.
```*Is the Standard Monte Carlo Power Iteration Approach the Wrong Approach?*. United States. doi:10.2172/1043017.

```
Booth, Thomas E. Tue .
"Is the Standard Monte Carlo Power Iteration Approach the Wrong Approach?". United States. doi:10.2172/1043017. https://www.osti.gov/servlets/purl/1043017.
```

```
@article{osti_1043017,
```

title = {Is the Standard Monte Carlo Power Iteration Approach the Wrong Approach?},

author = {Booth, Thomas E},

abstractNote = {The power iteration method is the standard Monte Carlo approach for obtaining the eigenfunctions of a nuclear system, but the power method sometimes converges very slowly. Most discussions give a mathematical reason for the slow convergence of the Monte Carlo power method using the same concepts and terminology as when the power method is applied to a deterministic problem. This note first looks at why the convergence is slow from an intuitive Monte Carlo neutron perspective. Second, this note proposes building an eigenfunction intuitively in a cumulative (and noniterative) neutron by neutron manner that tends to better direct neutrons to where the neutrons need to be. Third, a very similar method for building the second eigenfunction is speculatively proposed.},

doi = {10.2172/1043017},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2012},

month = {6}

}