# Kernel reconstruction methods for Doppler broadening — Temperature interpolation by linear combination of reference cross sections at optimally chosen temperatures

## Abstract

This paper establishes a new family of methods to perform temperature interpolation of nuclear interactions cross sections, reaction rates, or cross sections times the energy. One of these quantities at temperature *T* is approximated as a linear combination of quantities at reference temperatures (T _{j}). The problem is formalized in a cross section independent fashion by considering the kernels of the different operators that convert cross section related quantities from a temperature T _{0} to a higher temperature *T* — namely the Doppler broadening operation. Doppler broadening interpolation of nuclear cross sections is thus here performed by reconstructing the kernel of the operation at a given temperature *T* by means of linear combination of kernels at reference temperatures (T _{j}). The choice of the L _{2} metric yields optimal linear interpolation coefficients in the form of the solutions of a linear algebraic system inversion. The optimization of the choice of reference temperatures (T _{j}) is then undertaken so as to best reconstruct, in the L∞ sense, the kernels over a given temperature range [T _{min},T _{max}]. The performance of these kernel reconstruction methods is then assessed in light of previous temperature interpolation methods by testing them upon isotope ^{238}U. Temperature-optimizedmore »

- Authors:

- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

- Publication Date:

- Research Org.:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

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

- OSTI Identifier:
- 1344987

- Alternate Identifier(s):
- OSTI ID: 1397789

- Grant/Contract Number:
- AC05-00OR22725

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Journal of Computational Physics

- Additional Journal Information:
- Journal Volume: 335; Journal Issue: C; Journal ID: ISSN 0021-9991

- Publisher:
- Elsevier

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; Doppler broadening; nuclear cross sections; temperature interpolation; kernel reconstruction

### Citation Formats

```
Ducru, Pablo, Josey, Colin, Dibert, Karia, Sobes, Vladimir, Forget, Benoit, and Smith, Kord.
```*Kernel reconstruction methods for Doppler broadening — Temperature interpolation by linear combination of reference cross sections at optimally chosen temperatures*. United States: N. p., 2017.
Web. doi:10.1016/j.jcp.2017.01.039.

```
Ducru, Pablo, Josey, Colin, Dibert, Karia, Sobes, Vladimir, Forget, Benoit, & Smith, Kord.
```*Kernel reconstruction methods for Doppler broadening — Temperature interpolation by linear combination of reference cross sections at optimally chosen temperatures*. United States. doi:10.1016/j.jcp.2017.01.039.

```
Ducru, Pablo, Josey, Colin, Dibert, Karia, Sobes, Vladimir, Forget, Benoit, and Smith, Kord. Wed .
"Kernel reconstruction methods for Doppler broadening — Temperature interpolation by linear combination of reference cross sections at optimally chosen temperatures". United States.
doi:10.1016/j.jcp.2017.01.039. https://www.osti.gov/servlets/purl/1344987.
```

```
@article{osti_1344987,
```

title = {Kernel reconstruction methods for Doppler broadening — Temperature interpolation by linear combination of reference cross sections at optimally chosen temperatures},

author = {Ducru, Pablo and Josey, Colin and Dibert, Karia and Sobes, Vladimir and Forget, Benoit and Smith, Kord},

abstractNote = {This paper establishes a new family of methods to perform temperature interpolation of nuclear interactions cross sections, reaction rates, or cross sections times the energy. One of these quantities at temperature T is approximated as a linear combination of quantities at reference temperatures (Tj). The problem is formalized in a cross section independent fashion by considering the kernels of the different operators that convert cross section related quantities from a temperature T0 to a higher temperature T — namely the Doppler broadening operation. Doppler broadening interpolation of nuclear cross sections is thus here performed by reconstructing the kernel of the operation at a given temperature T by means of linear combination of kernels at reference temperatures (Tj). The choice of the L2 metric yields optimal linear interpolation coefficients in the form of the solutions of a linear algebraic system inversion. The optimization of the choice of reference temperatures (Tj) is then undertaken so as to best reconstruct, in the L∞ sense, the kernels over a given temperature range [Tmin,Tmax]. The performance of these kernel reconstruction methods is then assessed in light of previous temperature interpolation methods by testing them upon isotope 238U. Temperature-optimized free Doppler kernel reconstruction significantly outperforms all previous interpolation-based methods, achieving 0.1% relative error on temperature interpolation of 238U total cross section over the temperature range [300 K,3000 K] with only 9 reference temperatures.},

doi = {10.1016/j.jcp.2017.01.039},

journal = {Journal of Computational Physics},

number = C,

volume = 335,

place = {United States},

year = {Wed Jan 25 00:00:00 EST 2017},

month = {Wed Jan 25 00:00:00 EST 2017}

}

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