Verification of analytic energy moments for the one-dimensional energy dependent neutron diffusion equation with MCNP5 and Attila-7.1.0

Douglas S. Crawford; Terry A. Ring

doi:10.1016/j.anucene.2012.06.022

Verification of analytic energy moments for the one-dimensional energy dependent neutron diffusion equation with MCNP5 and Attila-7.1.0

Douglas S. Crawford, Terry A. Ring

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3 Scopus citations

Abstract

The energy dependent neutron diffusion equation (EDNDE) is converted into a moment equation which is solved analytically for the 1-D problem of a bare sphere of pure ²³⁵U. The normalized moments 0-5 generated analytically are compared to normalized energy moments, from Monte Carlo N Particle 5 version 1.40 (MCNP5) and Attila-7.1.0-beta version (Attila). The analytic normalized neutron energy moments, fall between the results from MCNP5 (lower bound) and Attila (upper bound) and are accurate compared to MCNP5 neutron energy moments when error in this Monte Carlo simulation are considered. The error range is from 0% to 14%. The Attila moments are less accurate when compared to MCNP5 than the analytical moments derived in this work. The method of moments is shown to be a fast reliable method, compared to either Monte Carlo methods (MCNP5) or 30 multi-energy group methods (Attila).

Original language	English
Pages (from-to)	18-32
Number of pages	15
Journal	Annals of Nuclear Energy
Volume	50
DOIs	https://doi.org/10.1016/j.anucene.2012.06.022
State	Published - Dec 2012
Externally published	Yes

Keywords

Attila
Energy moments
MCNP5
Neutron diffusion
Statistics moments

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10.1016/j.anucene.2012.06.022

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@article{b707f7a915f3442e8c7ad6ed0a0fe5e0,

title = "Verification of analytic energy moments for the one-dimensional energy dependent neutron diffusion equation with MCNP5 and Attila-7.1.0",

abstract = "The energy dependent neutron diffusion equation (EDNDE) is converted into a moment equation which is solved analytically for the 1-D problem of a bare sphere of pure 235U. The normalized moments 0-5 generated analytically are compared to normalized energy moments, from Monte Carlo N Particle 5 version 1.40 (MCNP5) and Attila-7.1.0-beta version (Attila). The analytic normalized neutron energy moments, fall between the results from MCNP5 (lower bound) and Attila (upper bound) and are accurate compared to MCNP5 neutron energy moments when error in this Monte Carlo simulation are considered. The error range is from 0% to 14%. The Attila moments are less accurate when compared to MCNP5 than the analytical moments derived in this work. The method of moments is shown to be a fast reliable method, compared to either Monte Carlo methods (MCNP5) or 30 multi-energy group methods (Attila).",

keywords = "Attila, Energy moments, MCNP5, Neutron diffusion, Statistics moments",

author = "Crawford, {Douglas S.} and Ring, {Terry A.}",

year = "2012",

month = dec,

doi = "10.1016/j.anucene.2012.06.022",

language = "English",

volume = "50",

pages = "18--32",

journal = "Annals of Nuclear Energy",

issn = "0306-4549",

publisher = "Elsevier",

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TY - JOUR

T1 - Verification of analytic energy moments for the one-dimensional energy dependent neutron diffusion equation with MCNP5 and Attila-7.1.0

AU - Crawford, Douglas S.

AU - Ring, Terry A.

PY - 2012/12

Y1 - 2012/12

N2 - The energy dependent neutron diffusion equation (EDNDE) is converted into a moment equation which is solved analytically for the 1-D problem of a bare sphere of pure 235U. The normalized moments 0-5 generated analytically are compared to normalized energy moments, from Monte Carlo N Particle 5 version 1.40 (MCNP5) and Attila-7.1.0-beta version (Attila). The analytic normalized neutron energy moments, fall between the results from MCNP5 (lower bound) and Attila (upper bound) and are accurate compared to MCNP5 neutron energy moments when error in this Monte Carlo simulation are considered. The error range is from 0% to 14%. The Attila moments are less accurate when compared to MCNP5 than the analytical moments derived in this work. The method of moments is shown to be a fast reliable method, compared to either Monte Carlo methods (MCNP5) or 30 multi-energy group methods (Attila).

AB - The energy dependent neutron diffusion equation (EDNDE) is converted into a moment equation which is solved analytically for the 1-D problem of a bare sphere of pure 235U. The normalized moments 0-5 generated analytically are compared to normalized energy moments, from Monte Carlo N Particle 5 version 1.40 (MCNP5) and Attila-7.1.0-beta version (Attila). The analytic normalized neutron energy moments, fall between the results from MCNP5 (lower bound) and Attila (upper bound) and are accurate compared to MCNP5 neutron energy moments when error in this Monte Carlo simulation are considered. The error range is from 0% to 14%. The Attila moments are less accurate when compared to MCNP5 than the analytical moments derived in this work. The method of moments is shown to be a fast reliable method, compared to either Monte Carlo methods (MCNP5) or 30 multi-energy group methods (Attila).

KW - Attila

KW - Energy moments

KW - MCNP5

KW - Neutron diffusion

KW - Statistics moments

UR - http://www.scopus.com/inward/record.url?scp=84866106861&partnerID=8YFLogxK

U2 - 10.1016/j.anucene.2012.06.022

DO - 10.1016/j.anucene.2012.06.022

M3 - Article

AN - SCOPUS:84866106861

SN - 0306-4549

VL - 50

SP - 18

EP - 32

JO - Annals of Nuclear Energy

JF - Annals of Nuclear Energy

ER -

Verification of analytic energy moments for the one-dimensional energy dependent neutron diffusion equation with MCNP5 and Attila-7.1.0

Abstract

Keywords

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