Time-dependent integral transport in one-dimensional infinite media using dimensionless variables and the reduced collision formulation

Moll, Eli; Aplin, C.S.; Henderson, D.

doi:10.1016/j.anucene.2019.106990

Cited by 4 publications

(7 citation statements)

References 14 publications

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“…Predominantly, the correlation between neutron self-shield factors and the set of parameters involved in the calculation of its value had been studied by several scientists [17][18][19][20][21][22][23][24][25][26][27], who gave dimensionless variables to identify and encompass the physical and geometric varieties of the sample geometries in order to attain a universal formula for self-shielding. The Montè-Carlo approach effectively calculates self-shielding, but it takes time and an experienced user to achieve acceptable accuracy and efficiency [28], see A. Empirical expressions, such as those given by researchers in [19][20][21][22][23] based on [17] have been derived for a few specific geometries and a limited number of elements.…”

Section: Introductionmentioning

confidence: 99%

Mathematical formulae for neutron self-shielding properties of media in an isotropic neutron field

Elmaghraby,

Mahmoud,

Salama

et al. 2024

Phys. Scr.

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In the current study, an ab initio derivation of the neutron self-shielding factor to solve the complex neutron transport problem of the decrease of the neutron ﬂux as it penetrates into a material placed in an isotropic neutron ﬁeld. The theory of steady-state neutron transport was employed, starting from Stuart’s formula, to derive simple analytical formulae based on the integral cross-section parameters. The formulae could be adopted by the user according to various variables, such as the neutron ﬂux distribution and geometry of the simulation at hand. The concluded formulae of the self-shielding factors comprise an inverted sigmoid function normalized with a weight representing the ratio between the macroscopic total and scattering cross-sections of the medium. The general convex volume geometries are reduced to a set of chord lengths, while the neutron interaction probabilities within the volume are parameterized to the epithermal and thermal neutron energies. The arguments of the inverted-sigmoid function were derived from a simpliﬁed version of neutron transport formulation. The derived analytic formulae agreed greatly with the experimental observations for diﬀerent elements and geometries.

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Section: Introductionmentioning

confidence: 99%

Mathematical formulae for neutron self-shielding properties of media in an isotropic neutron field

Elmaghraby,

Mahmoud,

Salama

et al. 2024

Phys. Scr.

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“…There is an interplay between neutron absorption in the sample and the overall neutron flux [14]. Predominantly, the correlation between neutrons self-shield factors and the set of parameters involved in the calculation of its value had been studied by several scientists [15][16][17][18][19][20][21][22][23][24][25], who gave dimensionless variables to identify and encompass the physical and geometric varieties of the samples geometries in order to attain a universal formula for self-shielding. The Montè-Carlo approach effectively calculates self-shielding, but it takes time and an experienced user to achieve acceptable accuracy and efficiency [26], see Appendix E. Empirical expressions such as those given by researchers in Refs.…”

Section: Introductionmentioning

confidence: 99%

“…Here, n and λ are unit vectors in the direction of the normal to the surface and the neutron wavevector, respectively. The point symmetry neutron collision kernel has the form of Green's function [25,[69][70][71]:…”

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confidence: 99%

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Mathematical formulae for neutron self-shielding properties of media in an isotropic neutron field

W.¹,

Elmaghraby²,

Salama³

et al. 2022

Preprint

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The complexity of the neutron transport phenomenon throws its shadows on every physical system wherever neutron is produced or used. In the current study, an ab initio derivation of the neutron self-shielding factor, the problem of the decrease of the neutron flux as it penetrates into a material placed in an isotropic neutron field, has been attempted employing the theory of steady-state neutron transport, starting from Stuart's formula. Simple formulae were derived based on the integral cross-section parameters, which can be adopted by the user according to various variables, such as the neutron flux distribution and geometry of the simulation at hand. The concluded formulae of the self-shielding factors comprise an inverted sigmoid function normalized a weight representing the ratio between the total and scattering macroscopic cross-sections of the medium. The general convex volume geometries are reduced to a set of chord lengths, while the neutron interactions probabilities within the volume are parameterized to the epithermal and thermal neutron energies. The arguments of the inverted-sigmoid function were derived from a simplified version of neutron transport formulation. Accordingly, the obtained general formulae were successful in giving the experimental values of the neutron self-shielding factor for different elements and different geometries. The results were validated by comparing them to the experimental data as well as a variety of data extracted from the literature.

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“…There is an interplay between neutron absorption in the sample and the overall neutron flux [13]. Predominantly, the correlation between neutron self-shield factors and the set of parameters involved in the calculation of its value had been studied by several scientists [14][15][16][17][18][19][20][21][22][23][24][25], who gave dimensionless variables to identify and encompass the physical and geometric varieties of the sample's geometries to attain a universal formula for self-shielding. In this study, neutron self-shielding factors for Indium and gold samples were determined experimentally.…”

Section: Introductionmentioning

confidence: 99%

Experimental Measurement of Infinite Dilution Thermal Neutron Self-shielding Factor

Elmaghraby

Salama

et al. 2022

Braz J Phys

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The absorption of neutrons in media together with its transport properties cause the neutron flux to decrease as it penetrates the material because the absorption of neutrons in the sample itself attenuates the neutrons flux as it goes deeper into the sample. In the present work, the thermal neutron self-shielding factors of indium, gold, zinc, and mercury were determined experimentally. The current results together with those found in the literature were used to validate a mathematical ab initio formulae based on integral cross-section parameters used to compare our results. The complete agreement among these species of data suggests the validity of correlating the neutron migration length in the convex-shaped material with the average chord length described in the mathematical model.

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Time-dependent integral transport in one-dimensional infinite media using dimensionless variables and the reduced collision formulation

Cited by 4 publications

References 14 publications

Mathematical formulae for neutron self-shielding properties of media in an isotropic neutron field

Mathematical formulae for neutron self-shielding properties of media in an isotropic neutron field

Mathematical formulae for neutron self-shielding properties of media in an isotropic neutron field

Experimental Measurement of Infinite Dilution Thermal Neutron Self-shielding Factor

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