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Reactivity coefficients by perturbation theory; Calcul des coefficients de re activite par la theorie des perturbations; Koehffitsienty reaktivnosti, opredelennye pri pomoshchi teorii vozmushchenij; Determinacion, de coeficientes de reactividad con ayuda de la teoria de las perturbaciones

Conference:

Abstract

The development of the formulae of perturbation theory provides a good opportunity to use one of the principal devices of mathematical heuristics, i.e. proceeding by analogy from something that is simple to something that is more complicated. This paper: (a) Reviews the formulation of perturbation theory as a method of calculating reactivity coefficients; this consists mainly of developing the differential equation for the adjoint flux, as a continuous function of position and lethargy, by proceeding by analogy from the one-group differential equation for adjoint flux. (b) Presents an application of the two-group form of perturbation theory to a boiling-mercury-cooled fast-breeder reactor (MCBR). It is seen that the net Hg density coefficient of reactivity for the first-design-try for the MCBR is negative for some regions and positive for others. However, it is negative for regions of highest statistical weight and where the density change for a power change would be the greatest. The overall Hg density coefficient is thus negative, i.e. the void coefficient is positive-an unsafe condition. It can be easily seen from the two-group formulation what design changes had to be made to obtain a design which would have a negative void coefficient. It developed in subsequent investigations that  More>>
Authors:
Webster, J W [1] 
  1. International Atomic Energy Agency, Vienna (Austria)
Publication Date:
Mar 15, 1962
Product Type:
Conference
Resource Relation:
Conference: Seminar on Physics of Fast and Intermediate Reactors, Vienna (Austria), 3-11 Aug 1961; Other Information: 3 refs, 3 figs, 2 tabs; Related Information: In: Physics of Fast and Intermediate Reactors. Vol. II. Proceedings of the Seminar on the Physics of Fast and Intermediate Reactors. Vol. II| 418 p.
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; 21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS; ADJOINT FLUX; DENSITY; DIFFERENTIAL EQUATIONS; FBR TYPE REACTORS; LIQUID METAL COOLED REACTORS; MERCURY; PERTURBATION THEORY; VOID COEFFICIENT
OSTI ID:
22075975
Research Organizations:
International Atomic Energy Agency, Vienna (Austria)
Country of Origin:
IAEA
Language:
English
Other Identifying Numbers:
Other: ISSN 0074-1884; TRN: XA13S0009035060
Submitting Site:
INIS
Size:
page(s) 149-164
Announcement Date:
Mar 21, 2013

Conference:

Citation Formats

Webster, J W. Reactivity coefficients by perturbation theory; Calcul des coefficients de re activite par la theorie des perturbations; Koehffitsienty reaktivnosti, opredelennye pri pomoshchi teorii vozmushchenij; Determinacion, de coeficientes de reactividad con ayuda de la teoria de las perturbaciones. IAEA: N. p., 1962. Web.
Webster, J W. Reactivity coefficients by perturbation theory; Calcul des coefficients de re activite par la theorie des perturbations; Koehffitsienty reaktivnosti, opredelennye pri pomoshchi teorii vozmushchenij; Determinacion, de coeficientes de reactividad con ayuda de la teoria de las perturbaciones. IAEA.
Webster, J W. 1962. "Reactivity coefficients by perturbation theory; Calcul des coefficients de re activite par la theorie des perturbations; Koehffitsienty reaktivnosti, opredelennye pri pomoshchi teorii vozmushchenij; Determinacion, de coeficientes de reactividad con ayuda de la teoria de las perturbaciones." IAEA.
@misc{etde_22075975,
title = {Reactivity coefficients by perturbation theory; Calcul des coefficients de re activite par la theorie des perturbations; Koehffitsienty reaktivnosti, opredelennye pri pomoshchi teorii vozmushchenij; Determinacion, de coeficientes de reactividad con ayuda de la teoria de las perturbaciones}
author = {Webster, J W}
abstractNote = {The development of the formulae of perturbation theory provides a good opportunity to use one of the principal devices of mathematical heuristics, i.e. proceeding by analogy from something that is simple to something that is more complicated. This paper: (a) Reviews the formulation of perturbation theory as a method of calculating reactivity coefficients; this consists mainly of developing the differential equation for the adjoint flux, as a continuous function of position and lethargy, by proceeding by analogy from the one-group differential equation for adjoint flux. (b) Presents an application of the two-group form of perturbation theory to a boiling-mercury-cooled fast-breeder reactor (MCBR). It is seen that the net Hg density coefficient of reactivity for the first-design-try for the MCBR is negative for some regions and positive for others. However, it is negative for regions of highest statistical weight and where the density change for a power change would be the greatest. The overall Hg density coefficient is thus negative, i.e. the void coefficient is positive-an unsafe condition. It can be easily seen from the two-group formulation what design changes had to be made to obtain a design which would have a negative void coefficient. It developed in subsequent investigations that there were such design changes that could be made and a design of the MCBR with a negative void coefficient was eventually achieved. (author) [French] La mise au points des formules de la theorie des perturbations fournit une bonne occasion d'employer en mathematiques une des principales regles de la methode heuristique, celle qui consiste a proceder par analogie du simple au complexe. L'auteur du memoire: a) Expose une methode permettant de calculer les coefficients de reactivite en utilisant les formules de la theorie des perturbations; en substance, cette methode consiste a developper l'equation differentielle relative au flux adjoint en fonction continue de la position et de la lethargie, en procedant par analogie a partir de l'equation differentielle a un groupe relative au flux adjoint. b) Montre comment appliquer la forme a deux groupes de la theorie des perturbations au cas d'un reacteur surgenerateur a neutrons rapides, refroidi au mercure. Lors de l'essai preliminaire du reacteur, on a constate que la variation de reactivite accompagnant une variation de densite du mercure est telle que le coefficient net de la reactivite est negatif pour certaines regions et positif pour d'autres. Il est negatif pour les regions de poids statistique le plus eleve et ou une variation de puissance entrainerait le changement de densite le plus important. Le coefficient global de densite du mercure est donc negatif, et par consequent le coefficient cavitaire est positif, ce qui est dangereux. On peut facilement voir, en employant la forme a deux groupes, quelles modifications doivent etre apportees aux plans du reacteur etudie pour obtenir un coefficient cavitaire negatif. Au cours de recherches ulterieures, il s'est revele possible d'apporter certaines de ces modifications, et l'on est finalement parvenu a etablir des plans tels que le coefficient cavitaire du reacteur soit negatif. (author) [Spanish] Las formulas de la teoria de las perturbaciones pueden establecerse empleando uno de los procedimientos mas importantes de la heuristica matematica, que consiste en partir de una expresion sencilla para llegar por analogia a una expresion mas compleja. La presente memoria: (a) Formula la teoria de las perturbaciones como metodo para calcular los coeficientes de reactividad. Consiste principalmente en desarrollar la ecuacion diferencial del flujo adjunto como funcion continua de la posicion y del letargo, procediendo por analogia a partir de la ecuacion diferencial de un solo grupo para el flujo adjunto. (b) Presenta una aplicacion de la forma de dos grupos de la teoria de las perturba ciones a un reactor reproductor rapido, refrigerado por mercurio hirviente (MCBR). Al calcular la reactividad, se comprueba que el coeficiente correspondiente a la densidad neta del mercurio en el primer proyecto del MCBR es negativo en algunas regiones, y positivo en otras. Es negativo en las regiones de peso estadistico maximo y en las que los cambios de densidad serian mayores al variar la potencia. Por lo tanto, el coeficiente global de densidad del mercurio es negativo, esto es, el coeficiente de vacios es positivo, lo que constituye una condicion que implica peligro. En la formulacion de dos grupos, se aprecia facilmente que modificaciones es preciso introducir en el diseno para que el coeficiente de cavidad sea negativo. Nuevas investigaciones demostraron que era posible introducir dichas modificaciones, lograndose establecer para el MCBR un diseno cuyo coeficiente de vacios es negativo. (author) [Russian] Razvitie formuly teorii vozmushchenij daet khoroshuyu vozmozhnost' ispol'zovat' odin iz glavnykh metodov matematicheskogo issledovaniya, t.e. proizvesti dejstvie po analogii ot prostogo k bolee slozhnomu. V ehtom doklade: a) Rassmatrivaets ya formulirovka teorii vozmushchenij v kachestve metoda rascheta koehffitsientov reaktivnosti. On sostoit, glavnym obrazom, iz razvitiya differentsial'nog o uravneniya dlya sopryazhennogo potoka kak postoyannoj funktsii polozheniya i letargii, vyvodimoe po analogii ot odnoj gruppy differentsial'nog o uravneniya dlya sopryazhennogo potoka. b) Daetsya primenenie dvukhgruppovoj formy teorii vozmushchenij dlya kipyashchego reaktorarazmnozhitelya na bystrykh nejtronakh s rtutnym teplonositelem (MCBR). Vidno, chto koehffitsient reaktivnosti rtuti nizshej plotnosti v khode pervogo ispytaniya proekta MCBR yavlyaetsya otritsatel'nym dlya nekotorykh oblastej i polozhitel'nym dlya drugikh. Odnako on yavlyaetsya otritsatel'nym dlya oblastej naivysshego statisticheskogo vesa i tam, gde izmenenie plotnosti s izmeneniem ehnergii okazyvaetsya naibol'shim. Obshchij koehffitsient plotnosti rtuti yavlyaetsya, takim obrazom, otritsatel'nym , t.e. koehffitsient poroznosti yavlyaetsya polozhitel'nym , chto predstavlyaet soboj opasnoe uslovie. Mozhno legko videt' iz dvukhgruppovoj formy, kakie izmeneniya v proekte dolzhny byt' sdelany, chtoby poluchit' proekt s otritsatel'nym koehffitsientom poroznosti. Proekt poluchil dal'nejshee razvitie v posleduyushchikh issledovaniyakh, v khode kotorykh opredeleny osushchestvimye izmeneniya dlya proekta, i proekt MCBR s otritsatel'nym koehffitsientom poroznosti byl, v konechnom schete, dostignut. (author)}
place = {IAEA}
year = {1962}
month = {Mar}
}