An improved target velocity sampling algorithm for free gas elastic scattering

Romano, Paul K.; Walsh, Jonathan A.

doi:10.1016/j.anucene.2017.12.044

Cited by 14 publications

(9 citation statements)

References 15 publications

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“…However, storing all these precomputed cross sections at reference temperatures {T i } represents a considerable memory burden, which is why methods to minimize the memory footprint and perform Doppler broadening (136) on the fly have been actively sought after [96]. The most stateof-the-art approaches are either optimal temperature Doppler kernel reconstruction quadratures [98] (which only require ten reference temperatures {T i } for standard nuclear reactor codes), new Fourier-transform methods [97], or Monte Carlo target motion sampling rejection schemes [101][102][103].…”

Section: A Doppler Broadening Of Nuclear Cross Sections: Solbrig's Ke...mentioning

confidence: 99%

Windowed multipole representation of R -matrix cross sections

et al. 2021

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Nuclear cross sections are basic inputs to any nuclear computation. Campaigns of experiments are fitted with the parametric R-matrix model of quantum nuclear interactions, and the resulting cross sections are documented-both pointwise and as resonance parameters (with uncertainties)-in standard evaluated nuclear data libraries (ENDF, JEFF, BROND, JENDL, CENDL, TENDL): these constitute our common knowledge of fundamental low-energy nuclear cross sections. In the past decade, a collaborative effort has been deployed to establish a new nuclear cross-section library format-the Windowed Multipole Library-with the goal of considerably reducing the computational cost of cross-section calculations in nuclear transport simulations. This paper lays the theoretical foundations underpinning these efforts. From general R-matrix scattering theory, we derive the windowed multipole representation of nuclear cross sections. Though physically and mathematically equivalent to R-matrix cross sections, the windowed multipole representation is particularly well suited for subsequent temperature treatment of angle-integrated cross sections, in particular Doppler broadening, which is the averaging of cross sections over the thermal motion of the target atoms. Doppler broadening is of critical importance in neutron transport applications, as it ensures the stability of many nuclear reactors (negative thermal reactivity). Yet, Doppler broadening of nuclear cross sections has been a considerable bottleneck for nuclear transport computations, often requiring memory-costly pretabulations. We show that the windowed multipole representation can perform accurate Doppler broadening analytically (up to the first reaction threshold), from which we derive cross-section temperature derivatives to any order-all computable on the fly (without precalculations stored in memory). Furthermore, we here establish a way of converting the R-matrix resonance parameters uncertainty (covariance matrices) into windowed multipole parameters uncertainty. We show that generating stochastic nuclear cross sections by sampling from the resulting windowed multipole covariance matrix can reproduce the cross-section uncertainty in the original nuclear data file. The windowed multipole representation is therefore a novel nuclear physics formalism able to generate Doppler broadened stochastic nuclear cross sections on the fly, unlocking breakthrough computational gains for nuclear computations. Through this foundational paper, we hope to make the windowed multipole representation accessible, reproducible, and usable for the nuclear physics community, as well as provide the theoretical basis for future research on expanding its capabilities.

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Section: A Doppler Broadening Of Nuclear Cross Sections: Solbrig's Ke...mentioning

confidence: 99%

Windowed multipole representation of R -matrix cross sections

et al. 2021

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“…( 2) of [25]. This scripture is the conjugate continuation real part of N L + c poles, as identified in [63]: the N L radioactive poles (102), poles of the Kapur-Peierls operator (49), plus the roots ω n of the outgoing wavefunction O(ρ). However, we have proved the latter cancel out of the transmission matrix, and thus of the cross section (theorem 3 of [38]).…”

Section: Exact Multipole Representationsmentioning

confidence: 99%

“…However, storing all these pre-computed cross sections at reference temperatures T i represents a considerable memory burden, which is why methods to minimize the memory footprint and perform Doppler broadening (136) on-the-fly have been actively sought after [94]. The most state-of-the-art approaches are either optimal temperature Doppler kernel reconstruction quadratures [96] (which only require 10 reference temperatures T i for standard nuclear reactor codes), new Fourier transform methods [95], or Monte Carlo target motion sampling rejection schemes [100][101][102].…”

Section: Doppler Broadening Of Windowed Multipole Cross Sectionsmentioning

confidence: 99%

Windowed multipole representation of R-matrix cross sections

Ducru,

Sobes,

Alhajri

et al. 2020

Preprint

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“…The method has since been implemented in numerous continuous energy Monte Carlo neutron transport programs [4,39,35,18], and has shown to successfully model the resonance upscatter effect. However, DBRC suffers from rejection probabilities as high as 99.995% [31] for neutron energies in the vicinity of a resonance.…”

Section: Introductionmentioning

confidence: 99%

“…The relative velocity sampling (RVS) method [38,31] was created to ameliorate the high rejection rates characteristic to the rejection algorithms used to model resonance upscatter. These schemes, in essence, sample probability distributions proportional to f (x)g(x), where f (x) is a distribution and g(x) ∈ [0, 1].…”

Section: Introductionmentioning

confidence: 99%

Resonance Scattering Treatment with the Windowed Multipole Formalism

Ridley¹,

Forget²,

Burke³

2023

Preprint

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A new method for directly sampling the resonance upscattering effect is presented. Alternatives have relied on inefficient rejection sampling techniques or large tabular storage of relative velocities. None of these approaches, which require pointwise energy data, are particularly well suited to the windowed multipole cross section representation. The new method called multipole analytic resonance scattering (MARS) overcomes these limitations by inverse transform sampling from the target relative velocity distribution where the cross section is expressed in the multipole formalism. The closed form relative speed distribution contains a novel special function we deem the incomplete Faddeeva function, and we present the first results on its efficient numerical evaluation.

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An improved target velocity sampling algorithm for free gas elastic scattering

Cited by 14 publications

References 15 publications

Windowed multipole representation of R -matrix cross sections

Windowed multipole representation of R -matrix cross sections

Windowed multipole representation of R-matrix cross sections

Resonance Scattering Treatment with the Windowed Multipole Formalism

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