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Excitation of Neutron Waves by Modulated And Pulsed Sources; Excitation d'Ondes Neutroniques au Moyen de Sources Modulees et Pulsees; Vozbuzhdenie nejtronnykh voln s pomoshch'yu modulirovannykh i impul'snykh istochnikov; Excitacion de Ondas Neutronicas Mediante Fuentes Moduladas y Pulsadas

Conference:

Abstract

Placement of either a sinusoidally modulated or pulsed source of thermal neutrons at one of the boundaries of a nuclear assembly creates a disturbance which can be analysed in terms of wave components, propagating away from the localized source with frequency-dependent attenuation factors and wave velocities. The dispersive properties of the assembly are expressed through the dispersion relation, connecting the inverse complex relaxation length (or complex wave number). {rho}({omega}), to the frequency of the excitation and the nuclear parameters of the system. It will be shown that the dispersion relation is of the form {rho}{sup 2}({omega}) = {Sigma}{sub n(even)} B{sup (n)}{omega}{sup n} + i {Sigma}{sub n(odd}) B{sup (n)} {omega}{sup n} (1) where the coefficients B{sup (n)} are related to matrix elements of the various operators in moderating and multiplicative media. In a neutron wave experiment one measures the attenuation factor {alpha}({omega}) and the phase shift per unit length {delta}({omega}), which satisfy the relationships {alpha}{sup 2}({omega}) - {delta}{sup 2}({omega}) = {Sigma}{sub n(even)} B{sup (n)}{omega}{sup n}. (2) 2{alpha}({omega}){delta}({omega}) = {Sigma}{sub n(odd)} B{sup (n)}{omega}{sup n}. (3) One has then the advantage over the conventional pulsing with fast neutrons of measuring two independent magnitudes (real and imaginary part of the wave number) from which  More>>
Authors:
Perez, R. B.; Booth, R. S. [1] 
  1. University of Florida, Gainesville, FL (United States)
Publication Date:
Oct 15, 1965
Product Type:
Conference
Report Number:
IAEA-SM-62/77
Resource Relation:
Conference: Symposium on Pulsed Neutron Research, Karlsruhe (Germany), 10-14 May 1965; Other Information: 24 refs., 4 tabs., 10 figs.; Related Information: In: Pulsed Neutron Research. Vol. II. Proceedings of the Symposium on Pulsed Neutron Research| 934 p.
Subject:
73 NUCLEAR PHYSICS AND RADIATION PHYSICS; BUCKLING; COCKCROFT-WALTON ACCELERATORS; DIFFUSION; DISPERSION RELATIONS; DISTURBANCES; EXCITATION; EXPERIMENTAL DATA; FAST NEUTRONS; FOURIER ANALYSIS; FREQUENCY DEPENDENCE; GRAPHITE; IRON; LEAD; LEAST SQUARE FIT; MEV RANGE; NUCLEAR PROPERTIES; PARAFFIN; PHASE SHIFT; PULSED NEUTRON TECHNIQUES; RELAXATION; THERMAL NEUTRONS; THERMALIZATION; VAN DE GRAAFF ACCELERATORS; WATER
OSTI ID:
22127305
Research Organizations:
International Atomic Energy Agency, Vienna (Austria)
Country of Origin:
IAEA
Language:
English
Other Identifying Numbers:
Other: ISSN 0074-1884; TRN: XA13M2642082384
Submitting Site:
INIS
Size:
page(s) 701-725
Announcement Date:
Sep 12, 2013

Conference:

Citation Formats

Perez, R. B., and Booth, R. S. Excitation of Neutron Waves by Modulated And Pulsed Sources; Excitation d'Ondes Neutroniques au Moyen de Sources Modulees et Pulsees; Vozbuzhdenie nejtronnykh voln s pomoshch'yu modulirovannykh i impul'snykh istochnikov; Excitacion de Ondas Neutronicas Mediante Fuentes Moduladas y Pulsadas. IAEA: N. p., 1965. Web.
Perez, R. B., & Booth, R. S. Excitation of Neutron Waves by Modulated And Pulsed Sources; Excitation d'Ondes Neutroniques au Moyen de Sources Modulees et Pulsees; Vozbuzhdenie nejtronnykh voln s pomoshch'yu modulirovannykh i impul'snykh istochnikov; Excitacion de Ondas Neutronicas Mediante Fuentes Moduladas y Pulsadas. IAEA.
Perez, R. B., and Booth, R. S. 1965. "Excitation of Neutron Waves by Modulated And Pulsed Sources; Excitation d'Ondes Neutroniques au Moyen de Sources Modulees et Pulsees; Vozbuzhdenie nejtronnykh voln s pomoshch'yu modulirovannykh i impul'snykh istochnikov; Excitacion de Ondas Neutronicas Mediante Fuentes Moduladas y Pulsadas." IAEA.
@misc{etde_22127305,
title = {Excitation of Neutron Waves by Modulated And Pulsed Sources; Excitation d'Ondes Neutroniques au Moyen de Sources Modulees et Pulsees; Vozbuzhdenie nejtronnykh voln s pomoshch'yu modulirovannykh i impul'snykh istochnikov; Excitacion de Ondas Neutronicas Mediante Fuentes Moduladas y Pulsadas}
author = {Perez, R. B., and Booth, R. S.}
abstractNote = {Placement of either a sinusoidally modulated or pulsed source of thermal neutrons at one of the boundaries of a nuclear assembly creates a disturbance which can be analysed in terms of wave components, propagating away from the localized source with frequency-dependent attenuation factors and wave velocities. The dispersive properties of the assembly are expressed through the dispersion relation, connecting the inverse complex relaxation length (or complex wave number). {rho}({omega}), to the frequency of the excitation and the nuclear parameters of the system. It will be shown that the dispersion relation is of the form {rho}{sup 2}({omega}) = {Sigma}{sub n(even)} B{sup (n)}{omega}{sup n} + i {Sigma}{sub n(odd}) B{sup (n)} {omega}{sup n} (1) where the coefficients B{sup (n)} are related to matrix elements of the various operators in moderating and multiplicative media. In a neutron wave experiment one measures the attenuation factor {alpha}({omega}) and the phase shift per unit length {delta}({omega}), which satisfy the relationships {alpha}{sup 2}({omega}) - {delta}{sup 2}({omega}) = {Sigma}{sub n(even)} B{sup (n)}{omega}{sup n}. (2) 2{alpha}({omega}){delta}({omega}) = {Sigma}{sub n(odd)} B{sup (n)}{omega}{sup n}. (3) One has then the advantage over the conventional pulsing with fast neutrons of measuring two independent magnitudes (real and imaginary part of the wave number) from which more information can be extracted about the nuclear properties of interest. Experiments were performed using graphite as the moderating material. Two different sources of thermal neutrons were used. In one case 14-MeV neutrons generated by a Cockcroft-Walton machine were thermalized in a tank containing several layers of iron, lead and graphite immersed in water. Lately the University of Florida 4-MeV Van de Graaff accelerator produced 29-keV neutrons from the (Li-p) reaction which were thermalized in a few inches of paraffin. In both instances the ion beams could be modulated sinusoidally or pulsed. Fourier analysis of the slow pulses showed very good agreement with the results obtained from the sinusoidal excitation of the waves. The range of frequencies studied was between zero and 1200 c/s Least-squares fits of the experimental data with equations (4) and (5) yielded the results B{sup (0)} = B{sup 2}{sub Up-Tack} + a{sub 1}/L{sub 0} = (6.6 {+-} 0.1) 10{sup -3} (cm{sup -2}) (4) B{sup (1)} = a{sub 2}/D{sub 0} = (4.38 {+-} 0.2) 10{sup -6} (cm{sup -2}) (5) B{sup (2)} = {Sigma}{sub {gamma}} H{sub 0{gamma}}/ Empty-Set {sub {gamma}{gamma}} = (2.5 {+-} 0.2) 10{sup -10} ({gamma} = 0, 1, 2, .....10) B{sup 2}{sub Up-Tack} = Transverse buckling (cm{sup -2}) = 5.96 x 10{sup -3} cm{sup -2} (6) where a{sub 1}, a{sub 2}, H{sub 0{gamma}} and Empty-Set {sub {gamma}{gamma}} are related to matrix elements of the diffusion and thermalization operators. From Eq. (5) a value of D{sub 0} = (2.2 {+-} 0.1) x 10{sup 5} cm{sup 2}/s was found in agreement with conventional pulsed neutron measurements. Theoretical calculations using various kernels also agree with the experimental results. (author) [French] En placant une source de neutrons thermiques puisee sinusoldalement a l'une des frontieres d'un assemblage nucleaire, on provoque une perturbation que l'on peut analyser sous forme de composantes d'onde, se propageant a partir de la source avec des facteurs d'attenuation et des vitesses variables selon la frequence. Les caracteristiques de dispersion de l'ensemble sont exprimees par la relation de dispersion qui relie l'inverse de la longueur de relaxation complexe (ou nombre d'onde complexe), {rho}({omega}), a la frequence de l'excitation et aux parametres nucleaires du systeme. Les auteurs montrent que la relation de dispersion se presente sous la forme {rho}{sup 2}({omega}) = {Sigma}{sub n(pair}) B{sup (n)}{omega}{sup n} + i {Sigma}{sub n(impair}) B{sup (n)} {omega}{sup n} (1) dans laquelle les coefficients B{sup (n)} dependent des elements de matrice des differents operateurs dans les milieux ralentisseurs et multiplicateurs. Dans les experiences sur les ondes neutroniques, on mesure le facteur d'attenuation {alpha}({omega}) et le dephasage par unite de longueur Greek-Small-Letter-Delta ({omega}), qui satisfont aux relations {alpha}{sup 2}({omega}) - Greek-Small-Letter-Delta {sup 2}({omega}) = {Sigma}{sub n(pair}) B{sup (n)}{omega}{sup n}. (2) 2{alpha}({omega}) Greek-Small-Letter-Delta ({omega}) = {Sigma}{sub n(impair}) B{sup (n)}{omega}{sup n}. (3) Par rapport a la methode classique des bouffees de neutrons rapides, cette facon de proceder donne alors l'avantage de mesurer deux grandeurs independantes (la partie reelle et la partie imaginaire du nombre d'otfde) dont on peut extraire davantage de renseignements sur les proprietes nucleaires qui presentent un interet. Les experiences ont ete effectuees en utilisant le graphite comme ralentisseur et deux sources differentes de neutrons thermiques. Dans l'un des cas, des neutrons de 14 MeV produits par une machine Cockcroft-Walton ont ete thermalises dans un reservoir contenant plusieurs couches de fer, de plomb et de graphite immerges dans l'eau. Recemment, l'accelerateur Van de Graaff (4 MeV) de l'Universite de Floride a produit a partir de la reaction (Li-p) des neutrons de 29 keV, qui ont ete thermalises dans quelques centimetres de paraffine. Dans les deux cas, on pouvait moduler sinusoldaleme; it ou puiser les faisceaux d'ions. Les auteurs ont trouve que les resultats de l'analyse de Fourier des bouffees de neutrons lents etaient en tres bon accord avec les resultats obtenus par excitation sinusoiedale des ondes. La gamme de frequence etudiee allait de zero a 1200 Hz. L'application de la methode des moindres carres aux donnees experimentales dans les equations (4) et (5) donne les resultats suivants: B{sup (0)} = B{sup 2}{sub Up-Tack} + a{sub 1}/L{sub 0} = (6.6 {+-} 0.1) 10{sup -3} (cm{sup -2}) (4) B{sup (1)} = a{sub 2}/D{sub 0} = (4.38 {+-} 0.2) 10{sup -6} (cm{sup -2}) (5) B{sup (2)} = {Sigma}{sub {gamma}} H{sub 0{gamma}}/ Empty-Set {sub {gamma}{gamma}} = (2.5 {+-} 0.2) 10{sup -10} ({gamma} = 0, 1, 2, .....10) B{sup 2}{sub Up-Tack} = Laplacien transversal (cm{sup -2}) = 5.96 x 10{sup -3} cm{sup -2} (6) dans lesquels a{sub 1}, a{sub 2}, H{sub 0{gamma}} and Empty-Set {sub {gamma}{gamma}} dependent des elements de matrice des operateurs de diffusion et de thermalisation. A partir de l'equation (5), on a trouve une valeur D{sub 0} = (2.2 {+-} 0.1) x 10{sup 5} cm{sup 2}/s qui concorde avec les mesures classiques au moyen des neutrons puises. Les calculs theoriques au moyen de divers noyaux concordent egalement avec les resultats experimentaux. (author) [Spanish] La colocacion de una fuente de neutrones termicos modulada o pulsada sinusoidalmente en uno de los limites de un conjunto nuclear crea una perturbacion que puede analizarse como si se operase con componentes de una onda que, al propagarse, se aleja de la fuente localizada, con factores de atenuacion y velocidades de onda dependientes de la frecuencia. Las propiedades de dispersion del conjunto se expresan mediante la relacion de dispersion, que vincula la inversa de la longitud de relajamiento compleja (o niimero de onda complejo), {rho}({omega}), con la frecuencia de la excitacion y con los parametros nucleares del sistema. Los autores senalan que la relacion de dispersion presenta la forma {rho}{sup 2}({omega}) = {Sigma}{sub n(par}) B{sup (n)}{omega}{sup n} + i {Sigma}{sub n(impair}) B{sup (n)} {omega}{sup n} (1) expresion en la que los coeficientes B{sup (n)} estan relacionados con elementos matriciales de diversos operadores en medios moderadores y multiplicadores. En un experimento sobre ondas neutronicas se miden el factor de atenuacion, {alpha}({omega}), y el desplazamiento de fase por unidad de longitud, Greek-Small-Letter-Delta ({omega}), que satisfacen las relaciones {alpha}{sup 2}({omega}) - Greek-Small-Letter-Delta {sup 2}({omega}) = {Sigma}{sub n(par}) B{sup (n)}{omega}{sup n}. (2) 2{alpha}({omega}) Greek-Small-Letter-Delta ({omega}) = {Sigma}{sub n(impair}) B{sup (n)}{omega}{sup n}. (3) De esta forma se tiene la ventaja, sobre el empleo del metodo tradicional de los neutrones rapidos pulsados, de poder medir dos magnitudes independientes (partes real e imaginaria del numero de onda) de las cuales puede obtenerse mas informacion sobre las propiedades nucleares de interes. Los autores realizaron experimentos empleando grafito como moderador, y neutrones termicos procedentes de dos fuentes distintas. En uno de los casos termalizaron en un tanque que contenia varias capas de hierro, plomo y grafito emergiendo parcialmente del agua, neutrones de 14 MeV generados por un aparato Cockcroft- Walton. Con el acelerador Van de Graaff de 4 MeV de la Universidad de Florida se obtuvieron, en virtud de la reaccion Li-p, neutrones de 29 keV que se termalizaron en una capa de parafina de algunas pulgadas de espesor. En ambos casos, fue posible pulsar o modular sinusoidalmente los haces ionicos. El analisis por el metodo de Fourier de los impulsos de neutrones lentos dio resultados que concordaron con los obtenidos partiendo de la excitacion sinusoidal de las ondas. El intervalo de frecuencias estudiado estuvo comprendido entre 0 y 1200 Hz. El ajuste de los datos experimentales a las ecuaciones (4) y (5) por el metodo de los cuadrados minimos dio los siguientes resultados: B{sup (0)} = B{sup 2}{sub Up-Tack} + a{sub 1}/L{sub 0} = (6.6 {+-} 0.1) 10{sup -3} (cm{sup -2}) (4) B{sup (1)} = a{sub 2}/D{sub 0} = (4.38 {+-} 0.2) 10{sup -6} (cm{sup -2}) (5) B{sup (2)} = {Sigma}{sub {gamma}} H{sub 0{gamma}}/ Empty-Set {sub {gamma}{gamma}} = (2.5 {+-} 0.2) 10{sup -10} ({gamma} = 0, 1, 2, .....10) B{sup 2}{sub Up-Tack} = Laplaciano transversal (cm{sup -2}) = 5.96 x 10{sup -3} cm{sup -2} (6) en donde a{sub 1}, a{sub 2}, H{sub 0{gamma}} y Empty-Set {sub {gamma}{gamma}} estan relacionados con elementos matriciales de los operadores de difusion y terma- lizacion. Partiendo de la ecuacion (5), se hallo un valor de D{sub 0} = (2.2 {+-} 0.1) x 10{sup 5} cm{sup 2}/s crri/s que concuerda con los resultados de las mediciones realizadas por el metodo tradicional de los neutrones pulsados. Los resultados de calculos teoricos realizados empleando diversos nucleos concuerdan tambien con los datos experimentales. (author) [Russian] Esli postavit' sinusoidal'no modulirovannyj ili impul'snyj istochnik teplovyh nejtronov na odnu iz granic jadernoj sborki, to jeto sozdaet narushenie, kotoroe mozhno proanalizirovat' s tochki zrenija volnovyh komponentov, rasprostranjajushhihsja iz lokalizovannogo istochnika s kojefficientami oslablenija, zavisjashhego ot chastoty, i s volnovymi skorostjami. Dispersionnye svojstva sborki vyrazhajutsja s pomoshh'ju dispersionnogo sootnoshenija, svjazyvajushhego obratnuju volnu kompleksnogo zatuhanija (ili kompleksnoe volnovoe chislo), {rho}({omega}), s chastotoj vozbuzhdenija i jadernymi parametrami sborki. Dispersionnoe sootnoshenie imeet sledujushhij vid: {rho}{sup 2}({omega}) = {Sigma}{sub n(chetnye}) B{sup (n)}{omega}{sup n} + i {Sigma}{sub n(nechetnye}) B{sup (n)} {omega}{sup n} (1) gde kojefficienty B{sup (n)} svjazany s matrichnymi jelementami razlichnyh operatorov v zamedljajushhih i razmnozhajushhih sredah. Pri jeksperimente s nejtronnoj volnoj izmerjaetsja kojefficient oslablenija {alpha}({omega}) i sdvig fazy na edinicu dliny Greek-Small-Letter-Delta ({omega}), kotorye udovletvorjajut sootnoshenijam: {alpha}{sup 2}({omega}) - Greek-Small-Letter-Delta {sup 2}({omega}) = {Sigma}{sub n(chetnye}) B{sup (n)}{omega}{sup n}. (2) 2{alpha}({omega}) Greek-Small-Letter-Delta ({omega}) = {Sigma}{sub n(nechetnye}) B{sup (n)}{omega}{sup n}. (3) Takim obrazom poluchajut preimushhestvo po sravneniju s obychnym metodom s ispol'zovaniem pul'sacii s bystrymi nejtronami, kotoroe zakljuchaetsja v izmerenii dvuh nezavisimyh velichin (dejstvitel'noj i mnimoj chast'ju volnovogo chisla), blagodarja kotorym mozhno poluchit' bol'she informacii o jadernyh svojstvah, predstavljajushhih interes. Pri provedenii jeksperimentov v kachestve zamedlitelja ispol'zovali grafit. Ispol'zovali dva razlichnyh istochnika teplovyh nejtronov. V odnom sluchae nejtrony s jenergiej 14 Mjev, poluchennye s pomoshh'ju uskoritelja Kokrofta-Uoltona, byli termalizovany v bake, soderzhashhem neskol'ko sloev zheleza, svinca i grafita, pogruzhennyh v vodu. Pozdnee s po* moshh'ju imejushhegosja vo Floridskom universitete uskoritelja Van de Graafa moshhnost'ju 4 Mjev byli polucheny nejtrony s jenergiej 29 kjev iz reakcii ( Li -r) , kotorye byli termalizovany v neskol'kih djujmah parafina. V oboih sluchajah ionnye puchki mogli byt' sinusoidal'no modulirovannymi ili pul'sirujushhimi. Rezul'taty analiza Fur'e, provedennogo s medlennymi impul'sami, prekrasno soglasujutsja s rezul'tatami, poluchennymi pri sinusoidal'nom vozbuzhdenii voln. Issleduemye chastoty byli v diapazone ot nulja do 1200 gc. V rezul'tate aproksimacii jeksperimental'nyh dannyh sposobom naimen'shih kvadratov s primeneniem uravnenij (4) i (5) byli polucheny sledujushhie rezul'taty: B{sup (0)} = B{sup 2}{sub Up-Tack} + a{sub 1}/L{sub 0} = (6.6 {+-} 0.1) 10{sup -3} (cm{sup -2}) (4) B{sup (1)} = a{sub 2}/D{sub 0} = (4.38 {+-} 0.2) 10{sup -6} (cm{sup -2}) (5) B{sup (2)} = {Sigma}{sub {gamma}} H{sub 0{gamma}}/ Empty-Set {sub {gamma}{gamma}} = (2.5 {+-} 0.2) 10{sup -10} ({gamma} = 0, 1, 2, .....10) (6) B{sup 2}{sub Up-Tack} = poperechnyj laplasian (cm{sup -2}) = 5.96 x 10{sup -3} cm{sup -2} otnosjatsja k matrichnym jelementam diffuzionnyh i termalizacionnyh operatorov. S pomoshh'ju uravnenija (5) opredeleno, chto znachenie D{sub 0} = (2.2 {+-} 0.1) x 10{sup 5} cm{sup 2}/sek-l soglasuetsja s obychnymi izmerenijami impul'snyh nejtronov (5). Teoreticheskie raschety s ispol'zovaniem razlichnyh modelej jadra takzhe soglasujutsja s jeksperimental'nymi rezul'tatami. (author)}
place = {IAEA}
year = {1965}
month = {Oct}
}