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

JOURNAL OF COMPUTATIONAL PHYSICS

卷:335

Article

Ducru, Pablo¹  Josey, Colin¹  Dibert, Karia¹  Sobes, Vladimir²  Forget, Benoit¹  Smith, Kord¹ 

[1] MIT, Nucl Sci & Engn Dept, 77 Massachusetts Ave, Cambridge, MA 02139 USA

[2] Oak Ridge Natl Lab, 1 Bethel Valley Rd, Oak Ridge, TN USA

关键词: Doppler broadening;    Nuclear cross sections;    Temperature interpolation;    Kernel reconstruction;   

DOI  :  10.1016/j.jcp.2017.01.039

来源: Elsevier

【 摘 要 】

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 (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 To 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 infinity 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 U-238. Temperature-optimized free Doppler kernel reconstruction significantly outperforms all previous interpolation-based methods, achieving 0.1% relative error on temperature interpolation of U-238 total cross section over the temperature range [300 K, 3000 K] with only 9 reference temperatures. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free