Kernel reconstruction methods for Doppler broadening — Temperature interpolation by linear combination of reference cross sections at optimally chosen temperatures
Name
Forget_Kernel reconstruction methods for Doppler broadening.pdf
Description
Accepted version
Size
732.33 KB
Format
Adobe PDF
Checksum (MD5)
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Author(s)
Ducru, Pablo
Josey, Colin
Dibert, Karia
Sobes, Vladimir
Forget, Benoit
Smith, Kord
Date Issued
2017
Journal
Journal of Computational Physics
Publisher
Elsevier BV
Citation
Ducru, Pablo, et al. "Kernel Reconstruction Methods for Doppler Broadening - Temperature Interpolation by Linear Combination of Reference Cross Sections at Optimally Chosen Temperatures." Journal of Computational Physics 335 (2017): 535-57.
Version
Author's final manuscript
Abstract
© 2017 Elsevier Inc. This article 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.
MIT Department
Massachusetts Institute of Technology. Department of Nuclear Science and Engineering
Terms of Use
Creative Commons Attribution-NonCommercial-NoDerivs License
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1016/J.JCP.2017.01.039
