# A Comparison of Monte Carlo and Deterministic Solvers for keff and Sensitivity Calculations

## Abstract

Verification and validation of our solutions for calculating the neutron reactivity for nuclear materials is a key issue to address for many applications, including criticality safety, research reactors, power reactors, and nuclear security. Neutronics codes solve variations of the Boltzmann transport equation. The two main variants are Monte Carlo versus deterministic solutions, e.g. the MCNP [1] versus PARTISN [2] codes, respectively. There have been many studies over the decades that examined the accuracy of such solvers and the general conclusion is that when the problems are well-posed, either solver can produce accurate results. However, the devil is always in the details. The current study examines the issue of self-shielding and the stress it puts on deterministic solvers. Most Monte Carlo neutronics codes use continuous-energy descriptions of the neutron interaction data that are not subject to this effect. The issue of self-shielding occurs because of the discretisation of data used by the deterministic solutions. Multigroup data used in these solvers are the average cross section and scattering parameters over an energy range. Resonances in cross sections can occur that change the likelihood of interaction by one to three orders of magnitude over a small energy range. Self-shielding is the numerical effectmore »

- 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), Office of Defense Programs (DP) (NA-10)

- OSTI Identifier:
- 1412920

- Report Number(s):
- LA-UR-17-31177

TRN: US1801163

- DOE Contract Number:
- AC52-06NA25396

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; NEUTRONS; MONTE CARLO METHOD; BOLTZMANN EQUATION; Deterministic; Monte Carlo; comparison

### Citation Formats

```
Haeck, Wim, Parsons, Donald Kent, White, Morgan Curtis, Saller, Thomas, and Favorite, Jeffrey A.
```*A Comparison of Monte Carlo and Deterministic Solvers for keff and Sensitivity Calculations*. United States: N. p., 2017.
Web. doi:10.2172/1412920.

```
Haeck, Wim, Parsons, Donald Kent, White, Morgan Curtis, Saller, Thomas, & Favorite, Jeffrey A.
```*A Comparison of Monte Carlo and Deterministic Solvers for keff and Sensitivity Calculations*. United States. doi:10.2172/1412920.

```
Haeck, Wim, Parsons, Donald Kent, White, Morgan Curtis, Saller, Thomas, and Favorite, Jeffrey A. Tue .
"A Comparison of Monte Carlo and Deterministic Solvers for keff and Sensitivity Calculations". United States.
doi:10.2172/1412920. https://www.osti.gov/servlets/purl/1412920.
```

```
@article{osti_1412920,
```

title = {A Comparison of Monte Carlo and Deterministic Solvers for keff and Sensitivity Calculations},

author = {Haeck, Wim and Parsons, Donald Kent and White, Morgan Curtis and Saller, Thomas and Favorite, Jeffrey A.},

abstractNote = {Verification and validation of our solutions for calculating the neutron reactivity for nuclear materials is a key issue to address for many applications, including criticality safety, research reactors, power reactors, and nuclear security. Neutronics codes solve variations of the Boltzmann transport equation. The two main variants are Monte Carlo versus deterministic solutions, e.g. the MCNP [1] versus PARTISN [2] codes, respectively. There have been many studies over the decades that examined the accuracy of such solvers and the general conclusion is that when the problems are well-posed, either solver can produce accurate results. However, the devil is always in the details. The current study examines the issue of self-shielding and the stress it puts on deterministic solvers. Most Monte Carlo neutronics codes use continuous-energy descriptions of the neutron interaction data that are not subject to this effect. The issue of self-shielding occurs because of the discretisation of data used by the deterministic solutions. Multigroup data used in these solvers are the average cross section and scattering parameters over an energy range. Resonances in cross sections can occur that change the likelihood of interaction by one to three orders of magnitude over a small energy range. Self-shielding is the numerical effect that the average cross section in groups with strong resonances can be strongly affected as neutrons within that material are preferentially absorbed or scattered out of the resonance energies. This affects both the average cross section and the scattering matrix.},

doi = {10.2172/1412920},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Tue Dec 12 00:00:00 EST 2017},

month = {Tue Dec 12 00:00:00 EST 2017}

}