TY - JOUR

T1 - An Analytic Benchmark for Neutron Boltzmann Transport with Downscattering—Part I

T2 - Flux and Eigenvalue Solutions

AU - Sobes, Vladimir

AU - Ducru, Pablo

AU - Alhajri, Abdulla

AU - Ganapol, Barry

AU - Forget, Benoit

N1 - Funding Information:
The authors are truly indebted to Andrew Holcomb of Oak Ridge National Laboratory for his assistance in validating the analytic benchmark problem with SCALE 6.2.3. The second author, P. Ducru, was supported by the Consortium for Advanced Simulation of Light Water Reactors, an Energy Innovation Hub for Modeling and Simulation of Nuclear Reactors under U.S. Department of Energy contract number DE-AC05-00OR22725.
Publisher Copyright:
© 2021 American Nuclear Society.

PY - 2021

Y1 - 2021

N2 - Computing in the energy dimension is one of the greatest challenges confronting present-day deterministic neutron transport solvers. Accurately resolving the neutron flux as neutrons downscatter across resonances in the nuclear cross sections currently requires considerable computing power and suffers from approximation errors. Flux uncertainty resulting from the uncertainty of the resonance structure is the single-largest cause of reactivity uncertainty. Any additional reference solution for the critical neutron downscattering problem with resonance phenomena would be a boon to verification and validation of neutronics codes. This paper establishes a benchmark to verify the accuracy of neutron transport criticality solvers along the energy dimension. For the first time, the analytic solution of the flux amplitude is derived in the particular case of an infinite homogeneous medium with isotropic scattering in the center of mass and an arbitrary number of no-threshold, neutral particle reaction resonances (e.g., radiative capture, fission, and resonance scattering). Original analytic expressions are established to quantify the discrepancy between the (Formula presented.) and (Formula presented.) flux amplitudes, respective solutions of the multiplication factor (Formula presented.), or the exponential time-evolution frequency (Formula presented.) eigenproblems. The physical study of these relations led to analysis of their first-order relative difference near the criticality condition (Formula presented.). Finally, numerical solutions are provided to a benchmark problem constituted of the first resonance of 239Pu, the 6.67-eV resonance of 238U, and a scattering isotope with a flat cross section, allowing for the computational verification of the energy resolution of current neutron transport criticality codes. Through these novel results, this analytic benchmark can serve as a reference to verify the energy resolution and sensitivity analysis of neutron transport criticality calculations.

AB - Computing in the energy dimension is one of the greatest challenges confronting present-day deterministic neutron transport solvers. Accurately resolving the neutron flux as neutrons downscatter across resonances in the nuclear cross sections currently requires considerable computing power and suffers from approximation errors. Flux uncertainty resulting from the uncertainty of the resonance structure is the single-largest cause of reactivity uncertainty. Any additional reference solution for the critical neutron downscattering problem with resonance phenomena would be a boon to verification and validation of neutronics codes. This paper establishes a benchmark to verify the accuracy of neutron transport criticality solvers along the energy dimension. For the first time, the analytic solution of the flux amplitude is derived in the particular case of an infinite homogeneous medium with isotropic scattering in the center of mass and an arbitrary number of no-threshold, neutral particle reaction resonances (e.g., radiative capture, fission, and resonance scattering). Original analytic expressions are established to quantify the discrepancy between the (Formula presented.) and (Formula presented.) flux amplitudes, respective solutions of the multiplication factor (Formula presented.), or the exponential time-evolution frequency (Formula presented.) eigenproblems. The physical study of these relations led to analysis of their first-order relative difference near the criticality condition (Formula presented.). Finally, numerical solutions are provided to a benchmark problem constituted of the first resonance of 239Pu, the 6.67-eV resonance of 238U, and a scattering isotope with a flat cross section, allowing for the computational verification of the energy resolution of current neutron transport criticality codes. Through these novel results, this analytic benchmark can serve as a reference to verify the energy resolution and sensitivity analysis of neutron transport criticality calculations.

KW - Neutron transport

KW - analytic benchmark

KW - neutron slowing down

KW - nuclear cross-section resonances

KW - resonance self-shielding

UR - http://www.scopus.com/inward/record.url?scp=85102941675&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85102941675&partnerID=8YFLogxK

U2 - 10.1080/00295639.2021.1874777

DO - 10.1080/00295639.2021.1874777

M3 - Article

AN - SCOPUS:85102941675

VL - 195

SP - 795

EP - 812

JO - Nuclear Science and Engineering

JF - Nuclear Science and Engineering

SN - 0029-5639

IS - 8

ER -