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Anisotropic Migration in Slab Lattices; Migration Anisotrope dans les Reseaux a Plaques; Anizotropicheskaya migratsiya v reshetkakh iz plastin; Migracion Anisotropica en Reticulados de Placas

Conference:

Abstract

One of the newest applications of pulsed neutron experiments is the measurement of the thermal neutron diffusion coefficient in different directions in a heterogeneous medium. This paper describes a theoretical method developed to predict these diffusion coefficients and presents some results for experiments in progress at Brookhaven National Laboratory. The interpretation of these experiments is considerably simplified if the experimental assembly is large. Diffusion cooling can then be ignored, the spectra taken to be Maxwellian, and a single energy group considered. With this simplification, it is possible to solve the transport equation numerically for the case of slab geometry. We insert a solution of the form Empty-Set (x, y, z, {Omega}, t) = exp (iB{sub 1}X + iB{sub 2}y - {lambda}t) Empty-Set (x, {Omega}) into the transport equation and solve for Empty-Set (x, {Omega}) by a combination of DSN and integral transport theory methods. The principal advantages of this method over existing methods is that absorption and anisotropic scattering are easily included, and the cell may be composed of many sub-regions. While we might attempt to find the eigenvalue {lambda}, given B{sub 1} and B{sub 2}, it is more convenient to replace iB{sub 1} by K{sub 1}, iB{sub 2} by  More>>
Authors:
Honeck, H. C.; Quiquemelle, B. C. [1] 
  1. Brookhaven National Laboratory, Upton, NY (United States)
Publication Date:
Aug 15, 1965
Product Type:
Conference
Report Number:
IAEA-SM-62/70
Resource Relation:
Conference: Symposium on Pulsed Neutron Research, Karlsruhe (Germany), 10-14 May 1965; Other Information: 22 refs., 3 figs., 1 tab.; Related Information: In: Pulsed Neutron Research. Vol. I. Proceedings of the Symposium on Pulsed Neutron Research| 713 p.
Subject:
73 NUCLEAR PHYSICS AND RADIATION PHYSICS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ABSORPTION; ALUMINIUM; ANISOTROPY; BOLTZMANN STATISTICS; CROSS SECTIONS; DIFFUSION; EIGENVALUES; MATHEMATICAL SOLUTIONS; NEUTRON SPECTRA; NEUTRON TRANSPORT THEORY; POLYETHYLENES; POWER SERIES; PULSED NEUTRON TECHNIQUES; SCATTERING; SLABS; THERMAL NEUTRONS
OSTI ID:
22122980
Research Organizations:
International Atomic Energy Agency, Vienna (Austria)
Country of Origin:
IAEA
Language:
English
Other Identifying Numbers:
Other: ISSN 0074-1884; TRN: XA13M2581078782
Submitting Site:
INIS
Size:
page(s) 309-320
Announcement Date:
Aug 30, 2013

Conference:

Citation Formats

Honeck, H. C., and Quiquemelle, B. C. Anisotropic Migration in Slab Lattices; Migration Anisotrope dans les Reseaux a Plaques; Anizotropicheskaya migratsiya v reshetkakh iz plastin; Migracion Anisotropica en Reticulados de Placas. IAEA: N. p., 1965. Web.
Honeck, H. C., & Quiquemelle, B. C. Anisotropic Migration in Slab Lattices; Migration Anisotrope dans les Reseaux a Plaques; Anizotropicheskaya migratsiya v reshetkakh iz plastin; Migracion Anisotropica en Reticulados de Placas. IAEA.
Honeck, H. C., and Quiquemelle, B. C. 1965. "Anisotropic Migration in Slab Lattices; Migration Anisotrope dans les Reseaux a Plaques; Anizotropicheskaya migratsiya v reshetkakh iz plastin; Migracion Anisotropica en Reticulados de Placas." IAEA.
@misc{etde_22122980,
title = {Anisotropic Migration in Slab Lattices; Migration Anisotrope dans les Reseaux a Plaques; Anizotropicheskaya migratsiya v reshetkakh iz plastin; Migracion Anisotropica en Reticulados de Placas}
author = {Honeck, H. C., and Quiquemelle, B. C.}
abstractNote = {One of the newest applications of pulsed neutron experiments is the measurement of the thermal neutron diffusion coefficient in different directions in a heterogeneous medium. This paper describes a theoretical method developed to predict these diffusion coefficients and presents some results for experiments in progress at Brookhaven National Laboratory. The interpretation of these experiments is considerably simplified if the experimental assembly is large. Diffusion cooling can then be ignored, the spectra taken to be Maxwellian, and a single energy group considered. With this simplification, it is possible to solve the transport equation numerically for the case of slab geometry. We insert a solution of the form Empty-Set (x, y, z, {Omega}, t) = exp (iB{sub 1}X + iB{sub 2}y - {lambda}t) Empty-Set (x, {Omega}) into the transport equation and solve for Empty-Set (x, {Omega}) by a combination of DSN and integral transport theory methods. The principal advantages of this method over existing methods is that absorption and anisotropic scattering are easily included, and the cell may be composed of many sub-regions. While we might attempt to find the eigenvalue {lambda}, given B{sub 1} and B{sub 2}, it is more convenient to replace iB{sub 1} by K{sub 1}, iB{sub 2} by K{sub 2}, and determine K{sub 1}, given K{sub 2} and {lambda}. The {lambda} can then be expressed as a power series in K{sup 2}{sub 1} and K{sup 2}{sub 2} (or equivalently B{sup 2}{sub 1} and B{sup 2}{sub 2}). The diffusion coefficients are then given by D{sub n} = -d{lambda}/K{sup 2}{sub n} Experiments are in progress at Brookhaven National Laboratory on alternating slabs of aluminium and polyethylene. We have selected the following one-group cross-sections: aluminium, {Sigma}{sub a} = 0.01228 cm{sup -1}, {Sigma}{sub S} = 0.08428 cm{sup -1}, {mu} = 0; polyethylene, {Sigma}{sub a} = 0.01947 cm{sup -1}, {Sigma}{sub S} = 2.593 cm{sup -1}, {mu} = 0.25. (author) [French] Une des dernieres applications des experiences au moyen des neutrons puises est la mesure des coefficients de diffusion anisotrope des neutrons thermiques dans un milieu heterogene. Les auteurs exposent une methode theorique elaboree pour prevoir ces coefficients de diffusion et ils indiquent quelques resultats obtenus au cours des experiences qui sont actuellement faites au Laboratoire national de Brookhaven. L'interpretation de ces experiences se trouve grandement simplifiee si l'assemblage experimental est de grande dimension. On peut alors negliger le refroidissement par diffusion, admettre que les spectres sont maxwelliens et ne considerer qu'un seul groupe d'energies. Grace a cette simplification, il est possible de resoudre numeriquement l'equation de transport pour le cas d'une geometrie a plaques. Dans l'equation de transport, les auteurs introduisent une solution ayant la forme Empty-Set (x, y, z, {Omega}, t) = exp (iB{sub 1}X + iB{sub 2}y - {lambda}t) Empty-Set (x, {Omega}) et ils la resolvent par rapport a Empty-Set (x, {Omega}) a) en combinant la methode DSN et des methodes fondees sur la theorie du transport. Les principaux avantages de ce procede par rapport aux methodes existantes sont les suivants: il permet d'inclure facilement l'absorption et la diffusion anisotrope et la cellule peut etre composee de nombreuses subdivisions. Les auteurs auraient pu essayer de determiner la valeur propre{lambda}pour Bx et B2 donnes, mais il est plus commode de remplacer iB{sub 1} par et iB{sub 2} par K{sub 2}, puis de determiner pour et {lambda} donnes. La valeur de {lambda} peut alors etre exprimee sous la forme d'une serie de puissances en K{sup 2}{sub 1} et K{sup 2}{sub 2} (ou de maniere equivalente en B{sup 2}{sub 1} et B{sup 2}{sub 2}). Dans ce cas les coefficients de diffusion sont donnes par la formule D{sub n} = -d{lambda}/K{sup 2}{sub n}. Au Laboratoire national de Brookhaven des experiences sont actuellement en cours sut des plaques alternees d'aluminium et de polyethylene. Les auteurs ont choisi les sections efficaces 3 un groupe ci-apres: aluminium, {Sigma}{sub a} = 0.01228 cm{sup -1}, {Sigma}{sub S} = 0.08428 cm{sup -1}, {mu} = 0; polyethylene, {Sigma}{sub a} = 0.01947 cm{sup -1}, {Sigma}{sub S} = 2.593 cm{sup -1}, {mu} = 0.25. (author) [Spanish] Una de las aplicaciones mas modernas de los experimentos con neutrones pulsados es la medicion en diferentes direcciones de los coeficientes de difusion anisotropica de neutrones termicos en un medio heterogeneo. La memoria describe un metodo teorico que se ha establecido para predecir estos coeficientes de difusion, y presenta algunos de los resultados obtenidos en los experimentos que se realizan en el Brookhaven National Laboratory. La interpretacion de los resultados se simplifica considerablemente si el conjunto experimental es de grandes dimensiones. En este caso cabe prescindir del enfriamiento por difusion, suponeT que los espectros son maxwellianos y considerar un solo grupo energetico. Gracias a esta simplficacion se consigue resolver numericamente la ecuacion de transporte cuando se trata de una geometria de placas. Los autores introducen en esta ecuacion una solucion de la forma Empty-Set (x, y, z, {Omega}, t) = exp (iB{sub 1}X + iB{sub 2}y - {lambda}t) Empty-Set (x, {Omega}) y despejan Empty-Set (x, {Omega}) por una combinacion de metodos DSN y de teorfa integral del transporte. Las principales ventajas de este procedimiento son que permite facilmente incluir la absorcion y la dispersion anisotropica, y que la celda se puede componer de muchas subregiones. Es posible tratar de encontrar el valor propio {lambda} cuando se conocen B{sub 1} y B{sub 2}, pero conviene mas sustituir iB{sub 1} por K{sub 1}, iB{sub 2} por K{sub 2}, y determinar K{sub 1}, una vez conocidos K{sub 2} y {lambda}. En este caso, {lambda} se puede expresar como serie exponencial de K{sup 2}{sub 1} y K{sup 2}{sub 2} (o lo que es equivalente, de B{sup 2}{sub 1} y de B{sup 2}{sub 2}). Entonces, la ecuacion D{sub n} = -d{lambda}/K{sup 2}{sub n} dara los coeficientes de difusion. En el Brookhaven National Laboratory se estan haciendo experimentos con placas alternadas de aluminio y polietileno. Los autores han seleccionado las siguientes secciones eficaces en un solo grupo: aluminio, {Sigma}a = 0, 01228 cm{sup -1}, {Sigma}s = 0, 08428 cm{sup -1}, {mu} = 0; polietileno, {Sigma}a - 0, 01947 cm-1, {Sigma}s = 2,593 cm{sup -1}, {mu} = 0,25. (author) [Russian] Odnoj iz samyh novyh oblastej primenenija jeksperimentov s impul'snymi nejtronami javljaetsja izmerenie kojefficienta diffuzii teplovyh nejtronov v razlichnyh napravlenijah v geterogennoj srede. Opisyvaetsja teoreticheskij metod, razrabotannyj s celyo predskazanija takih kojefficientov diffuzii, i predstavljajutsja nekotorye rezul'taty jeksperimentov, provodimyh v nastojashhee vremja v Brukhejvene. Interpretacija jetih jeksperimentov v znachitel'noj stepeni uproshhaetsja, esli jeksperimental'naja sborka javljaetsja bol'shoj. V jetom sluchae mozhno prenebregat' diffuzionnym ohlazhdeniem, spektry schitat' maksvellovskimi i rassmatrivat' edinstvennuju gruppu energii. Pri takom uproshhenii mozhno chislenno reshit' uravnenie perekosa dlja sluchaja plastinchatoj geometrii. My podstavljaem reshenie modeli Empty-Set (x, y, z, {Omega}, t) = exp (iB{sub 1}X + iB{sub 2}y - {lambda}t) Empty-Set (x, {Omega}) v uravnenie perenosa i reshaem Empty-Set (x, {Omega}) putem sochetanija metodov fil'trov dlja vyravnivanija dannyh i integral'noj teorii perenosa. Osnovnye preimushhestva jetogo metoda po sravneniju s sushhestvujushhimi sostojat v tom, chto legko vkljuchajutsja pogloshhenie i anijeotropiches- koe rassejanie i jachejka mozhet sostojat' iz mnogih podoblastej. Hotja sdelana popytka najti B{sub 1} i B{sub 2} s dannym sobstvennym znacheniem {lambda}, udobnee vmesto iB{sub l} postavit' kj i vmesto i V{sub 2} - k{sub 2} i opredelit' k{sub 2} s dannym k{sub 1} i {lambda} takom sluchae {lambda} mozhno vyrazit' v vide stelennogo rjada K{sup 2}{sub 1} i K{sup 2}{sub 2} (ili sootvetstvenno a B{sup 2}{sub 1} i B{sup 2}{sub 2}). Kojefficienty diffuzii zatem vyvodjatsja iz uravnenija D{sub n} = -d{lambda}/K{sup 2}{sub n}. V nastojashhee vremja v BNL provodjatsja jeksperimenty s peremennymi plastinami iz aljuminija i polijetilena. Otobrany sledujushhie poperechnye sechenija odnoj gruppy: aljuminij {Sigma}a - 0,01228sm{sup -1}, {Sigma}s = 0,08428 sm{sup -1}, {mu} = 0; polijetilen {Sigma}a = 0,01947 sm{sup -1}, {Sigma}s = 2,593 sm{sup -1} , {mu} = 0,25. (author)}
place = {IAEA}
year = {1965}
month = {Aug}
}