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

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 238U. Temperature-optimizedmore » 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.« less
Authors:
ORCiD logo [1] ;  [1] ;  [1] ;  [2] ;  [1] ;  [1]
  1. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
  2. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Publication Date:
Grant/Contract Number:
AC05-00OR22725
Type:
Accepted Manuscript
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 335; Journal Issue: C; Journal ID: ISSN 0021-9991
Publisher:
Elsevier
Research Org:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org:
USDOE National Nuclear Security Administration (NNSA)
Country of Publication:
United States
Language:
English
Subject:
73 NUCLEAR PHYSICS AND RADIATION PHYSICS; Doppler broadening; nuclear cross sections; temperature interpolation; kernel reconstruction
OSTI Identifier:
1344987
Alternate Identifier(s):
OSTI ID: 1397789

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., 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. 2017. "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 = {2017},
month = {1}
}