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 ^{238}U. Temperatureoptimizedmore »
 Authors:

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 Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
 Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
 Publication Date:
 Grant/Contract Number:
 AC0500OR22725
 Type:
 Accepted Manuscript
 Journal Name:
 Journal of Computational Physics
 Additional Journal Information:
 Journal Volume: 335; Journal Issue: C; Journal ID: ISSN 00219991
 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. Temperatureoptimized free Doppler kernel reconstruction significantly outperforms all previous interpolationbased 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}
}