Kernel reconstruction methods for Doppler broadening — Temperature interpolation by linear combination of reference cross sections at optimally chosen temperatures
Abstract
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:
 Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
 Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
 Publication Date:
 Research Org.:
 Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
 Sponsoring Org.:
 USDOE National Nuclear Security Administration (NNSA)
 OSTI Identifier:
 1344987
 Alternate Identifier(s):
 OSTI ID: 1397789
 Grant/Contract Number:
 AC0500OR22725
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 Journal of Computational Physics
 Additional Journal Information:
 Journal Volume: 335; Journal Issue: C; Journal ID: ISSN 00219991
 Publisher:
 Elsevier
 Country of Publication:
 United States
 Language:
 English
 Subject:
 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; Doppler broadening; nuclear cross sections; temperature interpolation; kernel reconstruction
Citation Formats
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., 2017.
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. Wed .
"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 = {Wed Jan 25 00:00:00 EST 2017},
month = {Wed Jan 25 00:00:00 EST 2017}
}
Web of Science

Exact Doppler broadening of tabulated cross sections. [SIGMA 1 kernel broadening method]
The SIGMA1 kernel broadening method is presented to Doppler broaden to any required accuracy a cross section that is described by a table of values and linearlinear interpolation in energycross section between tabulated values. The method is demonstrated to have no temperature or energy limitations and to be equally applicable to neutron or chargedparticle cross sections. The method is qualitatively and quantitatively compared to contemporary approximate methods of Doppler broadening with particular emphasis on the effect of each approximation introduced. 
TREND code for reconstruction of neutron reaction cross sections and calculation of the Doppler broadening in the region of resolved resonances
The TREND code is developed for reconstruction of neutron cross sections in the region of resolved resonances from the data of the international evaluated nuclear data libraries using the ReichMoore, AdlerAdler, and BreitWigner formalisms and for calculation of the Doppler broadening of the resulting cross sections within the classical approximation. The TREND code is incorporated into the MCU code package for Monte Carlo reactor calculations. The TREND and MCU codes have been used to evaluate the data of the ROSFOND data bank on uranium and plutonium isotopes in comparison with the data of the ICSBEP data bank. 
Onthefly Doppler broadening of unresolved resonance region cross sections
In this paper, two methods for computing temperaturedependent unresolved resonance region cross sections onthefly within continuousenergy Monte Carlo neutron transport simulations are presented. The first method calculates Doppler broadened cross sections directly from zerotemperature average resonance parameters. In a simulation, at each event that requires cross section values, a realization of unresolved resonance parameters is generated about the desired energy and temperaturedependent singlelevel BreitWigner resonance cross sections are computed directly via the analytical Ψx Doppler integrals. The second method relies on the generation of equiprobable cross section magnitude bands on an energytemperature mesh. Within a simulation, the bands are sampledmore »