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The Impulse Response of an Exponential Assembly; Reponse d'un Assemblage Exponentiel aux Impulsions; Impul'snaya kharakteristika ehksponentsial'noj sborki; Respuesta de un Conjunto Exponencial a los Impulsos

## Abstract

A spatial-dependent transfer function of an exponential assembly with rectangular geometry and the neutron source located at the origin in the middle of one side has been derived using diffusion theory and the usual approximations. If the end correction factor is neglected, the result G (x, y, z, s) = ({Delta}#Greek Phi Symbol#(x, y, z, s))/{Delta}S (o, o, o, o, s) = 2/abD {sup {infinity}}{Sigma}{sub m} {sub =} {sub 1} {sup {infinity}}{Sigma}{sub n} {sub =} {sub 1} 1/({rho}{sub mn}(s) cos (m{pi}x)/a cos (n{pi}y)/b e{sup -{rho}}mn{sup (s)Z} (1) where {rho}{sub mn}{sup (s)} = [s/(VD) + B{sup 2}{sub Up-Tack mn} - B{sup 2}{sub m}]{sup 1/2} = [s/VD - {gamma}{sup 2}{sub mn}]{sup 1/2} (2) The inverse Laplace transform of Eq. (1) gives the spatial dependent impulse response function (Green's function) to be g (x, y, z, t) = 2/ab {radical}v/{pi}D 1/{radical}t e{sup -z{sup 2/4}} {sup VDt} {sup {infinity}}{Sigma}{sub m} {sub =} {sub 1} {sup {infinity}}{Sigma}{sub n} {sub =} {sub 1} cos m{pi}x/a cos n{pi}y/b e{sup -VD{gamma}{sup 2mn{sup t}}} (3) If only the terms of Eq. (3) outside the double summation are considered (i.e. multiplicative and leakage effects are neglected) the result is 2/ab {radical}V/{pi}D 1/{radical}t e{sup -z{sup 2/4}} {sup VDt} = 4V/ab P(z),  More>>
Authors:
Uhrig, R. E. [1]
1. University of Florida, Gainesville, FL (United States)
Publication Date:
Apr 15, 1964
Product Type:
Conference
Report Number:
IAEA-SM-42/43
Resource Relation:
Conference: Symposium on Exponential and Critical Experiments, Amsterdam (Netherlands), 2-6 Sep 1963; Other Information: 45 refs., 18 figs.; Related Information: In: Exponential and Critical Experiments. Vol. III. Proceedings of the Symposium on Exponential and Critical Experiments| 494 p.
Subject:
21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS; APPROXIMATIONS; GAUSS FUNCTION; GREEN FUNCTION; HARMONICS; HEAVY WATER; HEAVY WATER MODERATED REACTORS; LAPLACE TRANSFORMATION; MODERATORS; NATURAL URANIUM; NEUTRON DENSITY; NEUTRON SOURCES; NUCLEAR FUELS; PULSES; REACTOR PHYSICS; RESPONSE FUNCTIONS; THERMAL NEUTRONS; TRANSFER FUNCTIONS
OSTI ID:
22123056
Research Organizations:
International Atomic Energy Agency, Vienna (Austria)
Country of Origin:
IAEA
Language:
English
Other Identifying Numbers:
Other: ISSN 0074-1884; TRN: XA13M2712078858
Submitting Site:
INIS
Size:
page(s) 205-239
Announcement Date:
Aug 30, 2013

## Citation Formats

Uhrig, R. E. The Impulse Response of an Exponential Assembly; Reponse d'un Assemblage Exponentiel aux Impulsions; Impul'snaya kharakteristika ehksponentsial'noj sborki; Respuesta de un Conjunto Exponencial a los Impulsos. IAEA: N. p., 1964. Web.
Uhrig, R. E. The Impulse Response of an Exponential Assembly; Reponse d'un Assemblage Exponentiel aux Impulsions; Impul'snaya kharakteristika ehksponentsial'noj sborki; Respuesta de un Conjunto Exponencial a los Impulsos. IAEA.
Uhrig, R. E. 1964. "The Impulse Response of an Exponential Assembly; Reponse d'un Assemblage Exponentiel aux Impulsions; Impul'snaya kharakteristika ehksponentsial'noj sborki; Respuesta de un Conjunto Exponencial a los Impulsos." IAEA.
@misc{etde_22123056,
title = {The Impulse Response of an Exponential Assembly; Reponse d'un Assemblage Exponentiel aux Impulsions; Impul'snaya kharakteristika ehksponentsial'noj sborki; Respuesta de un Conjunto Exponencial a los Impulsos}
author = {Uhrig, R. E.}