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

Journal Article · Wed Jan 25 00:00:00 EST 2017 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2017.01.039· OSTI ID:1344987

Ducru, Pablo  ^[1]; Josey, Colin ^[1]; Dibert, Karia ^[1]; Sobes, Vladimir ^[2]; Forget, Benoit ^[1]; Smith, Kord ^[1]

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

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 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 (T_j). 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 (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-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.

• Research Organization: Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA)
• Grant/Contract Number: AC05-00OR22725
• OSTI ID: 1344987
• Alternate ID(s): OSTI ID: 1397789
• Journal Information: Journal of Computational Physics, Vol. 335, Issue C; ISSN 0021-9991
• Publisher: Elsevier
• Country of Publication: United States
• Language: English

Related Subjects

73 NUCLEAR PHYSICS AND RADIATION PHYSICS
Doppler broadening
nuclear cross sections
temperature interpolation
kernel reconstruction