Analyses of the TIARA 43MeV Proton Benchmark Shielding ...downloads.hindawi.com/journals/stni/2017/9152580.pdf · The accuracy of ARES calculations with FENDL/MG-3.0 libraries was

Research ArticleAnalyses of the TIARA 43MeV Proton Benchmark ShieldingExperiments Using the ARES Transport Code

Bin Zhang Liang Zhang and Yixue Chen

North China Electric Power University No 2 Beinong Road Changping District Beijing 102206 China

Correspondence should be addressed to Bin Zhang zhangbinncepueducn

Received 29 April 2017 Revised 16 June 2017 Accepted 27 June 2017 Published 24 July 2017

Academic Editor Rafael Miro

Copyright copy 2017 Bin Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

ARES is a multidimensional parallel discrete ordinates particle transport code with arbitrary order anisotropic scattering It can beapplied to a wide variety of radiation shielding calculations and reactor physics analysis To validate the applicability of the codeto accelerator shielding problems ARES is adopted to simulate a series of accelerator shielding experiments for 43MeV proton-7Li quasi-monoenergetic neutrons which is performed at Takasaki Ion Accelerator for Advanced Radiation Application Theseexperiments on iron and concrete were analyzed using the ARES code with FENDLMG-30 multigroup libraries and compared todirect measurements from the BC501A detector The simulations show good agreement with the experimental data The ratios ofcalculated values to experimental data for integrated neutron flux at peak and continuum energy regions are within 64 and 25discrepancy for the concrete and iron experiments respectively The results demonstrate the accuracy and efficiency of ARES codefor accelerator shielding calculation

1 Introduction

Validation is an essential part of software quality assuranceto ensure that the solutions obtained from the code matchreality sufficiently well Therefore validation requires com-parison of computed results with experimentally measureddata For reliable accelerator shielding calculations it isnecessary to validate the transport code through analy-ses of shielding experiments This paper reports on thevalidation exercise based on the Takasaki Ion Accelera-tor for Advanced Radiation Application (TIARA) [1] atJapan Atomic Energy Research Institute (JAERI) one of aset of international benchmark experiments for acceleratorshielding

Shielding analyses for the TIARA pose significant com-putational challenges including highly anisotropic highenergy sources and a combination of deep penetrationshielding and unshielded beamline The experiments oniron and concrete were analyzed using the ARES code withFENDLMG-30 [2] multigroup libraries to validate ARESperformance

The ARES methodologies are described and summa-rized in Section 2 and the shielding experiment details arepresented in Section 3 Results and analysis are summarizedin Section 4 and our concluding remarks are presented inSection 5

2 ARES Methodology

ARES [3 4] is a multidimensional parallel discrete ordi-nates neutral particle transport code that uses state-of-the-art methods to obtain accurate solutions to the Boltz-mann transport equation The ARES transport code systemconsists of seven main modules DONTRAN1D DON-TRAN2D DONTRAN3D RAY2D RAY3D ARES PRE andARES POST DONTRAN1D DONTRAN2D and DON-TRAN3D are the DONTRAN series to solve one- two-and three-dimensional transport problems respectively RAYadopts the first collision source method to mitigate rayeffects in two or three dimensions (RAY2D and RAY3Dresp) ARES PRE incorporates the geometry and materialinformation of the calculated model and deals with the

HindawiScience and Technology of Nuclear InstallationsVolume 2017 Article ID 9152580 5 pageshttpsdoiorg10115520179152580

2 Science and Technology of Nuclear Installations

quadrature sets and cross sectionmessage Preliminary verifi-cation and validation for theARES transport code systemhadbeen performed by experiment benchmarking and referencecode

ARES employs discrete ordinates method in discretizingangular variables and adopts spherical harmonic to expandscattering source The angular variable is usually discretizedby replacing angular integrals with quadrature sums Rayeffects are nonphysical anomalies that often appear in opti-cally thin multidimensional discrete ordinates calculationsbecause the solution propagates along a finite set of directionsdefined by the angular quadrature set The first collisionsource method was used to eliminate or mitigate ray effects

A variety of spatial differencing scheme options are avail-able including diamond difference (DD) with or withoutlinear-zero flux fixup theta weighted (TW) directional thetaweighted (DTW) exponential directional weighted (EDW)and linear discontinuous finite element The most generalsolution technique is source iteration which is a simple andeffective method for many classes of transport problemsHowever for optically thick problems dominated by scatter-ing the source iterationmethod converges very slowly Diffu-sion synthetic acceleration (DSA) has been shown to signif-icantly decrease the iterations ARES uses the Koch-Baker-Alcouffe parallel sweep algorithm to obtain high parallelefficiency

The neutron transport calculation in the energy regionbetween 20 and 100MeV is the most crucial problem foraccelerator shielding designs because high energy neutronshave strong penetrability The spatial differencing schemesare very important to accurately simulate neutron transportThe diamond difference method assumes a linear relation-ship between the directional flux at the cell center andcell boundaries and is simple and accurate for small meshintervals However when the mesh interval is too largemeasured along the discrete direction through the cell thedifference equations may yield negative fluxes which causeoscillations in the iterative process and frequently causenegative scalar flux The TW DTW and EDW variationson the DD method were developed to eliminate negativefluxes without significantly sacrificing computational cost oraccuracy

The balance equation can be obtained by integrating theangular discretized form of the transport equation over themesh cell (Δ119909 Δ119910 Δ119911)

120583119898Δ119909

(120595119894out minus 120595119894in) +120578119898Δ119910

(120595119895out minus 120595119895in)

+ 120585119898Δ119911

(120595119896out minus 120595119896in) + Σ119905119894119895119896120595119860 = 119902119860(1)

where Ω119898 = (120583119898 120578119898 120585119898) is the discretized direction-of-flight variables 120595119860 is the cell average flux and the enteringand exiting angular fluxes are referred to using ldquoinrdquo andldquooutrdquo subscripts Σ119905119894119895119896 is the total cross section 119902119860 is knownfromprevious source iteration and the entering angular fluxesare known from the boundary values When using diamond

difference scheme the cell averaged angular flux can becalculated by

120595119860

=119902119860119881 + 2 1003816100381610038161003816120583119898

1003816100381610038161003816 119860120595119894in + 21003816100381610038161003816120578119898

1003816100381610038161003816 119861120595119895in + 21003816100381610038161003816120585119898

1003816100381610038161003816 119862120595119896in2 1003816100381610038161003816120583119898

1003816100381610038161003816 119860 + 2 10038161003816100381610038161205781198981003816100381610038161003816 119861 + 2

10038161003816100381610038161205851198981003816100381610038161003816 119862 + Σ119905119881

(2)

where 119860 = Δ119910Δ119911 119861 = Δ119909Δ119911 119862 = Δ119909Δ119910Ray effects are nonphysical oscillations in the scalar flux

They are caused by the inability of a quadrature set in discreteordinates approximation to accurately integrate the angularflux Ray effects may represent themost significant deficiencyof the 119878119873 method The first collision source method [5] wasemployed to mitigate ray effects The method analyticallycalculates the uncollided flux to obtain the first collisionsource term which is then applied to calculate the collidedflux using the standard 119878119873methodThe total flux is composedof the uncollided and collided flux

Thus the first collision source method decomposes theflux 120595119892( 119903 Ω) into uncollided components 120595119892

(119906)( 119903 Ω) and

collided components 120595119892(119888)( 119903 Ω)

120595119892 ( 119903 Ω) = 120595119892(119906)( 119903 Ω) + 120595119892

(119888)( 119903 Ω) (3)

and the transport equation is decomposed into

Ω sdot nabla120595119892(119906)( 119903 Ω) + Σ119892119905 ( 119903) 120595

119892

(119906)( 119903 Ω) = 119902119892119890 ( 119903 Ω)

Ω sdot nabla120595119892(119888)( 119903 Ω) + Σ119892119905 ( 119903) 120595

119892

(119888)( 119903 Ω) =

119866

sum1198921015840=1

119873

sum119899=0

2119899 + 14120587

sdot Σ1198921198921015840

119904119899 ( 119903)119899

sum119896=minus119899

119884119899119896 (Ω) 1206011198921015840(119888)

119899119896 ( 119903) + 119902(119906)119904 ( 119903 Ω)

(4)

where 119902119892119890 ( 119903 Ω) is fixed source and 119902(119906)119904 ( 119903 Ω) is the firstcollision source which is calculated from uncollided fluxmoments Σ119892119892

1015840

119904119899 is the Legendre moment of scattering crosssection from group 1198921015840 to group 119892 and 119884119899119896 is sphericalharmonics

RAY employs ray tracing method to accelerate opticaldistance calculations and the point source correction factoris introduced to improve the accuracy of calculation resultsThe RAY module within ARES has been verified elsewhereby a series of international benchmarks such as Kobayashibenchmarks [6] and can effectively eliminate ray effects andobtain reasonable results

3 Overview of Shielding Experiments

Figure 1 shows a cross sectional view of the TIARAfacility with the experimental arrangement [7] Quasi-monoenergetic source neutrons were generated by 43MeVprotons bombarding 7Li targets Neutrons produced in theforward angle reached the experiment room through a109 cm diameter 225 cm long iron collimator embedded inthe concrete wall A test shield of iron or concrete 10ndash150 cm

Science and Technology of Nuclear Installations 3

Shielding wall (concrete)

Iron collimator(iron ball and iron sand llers)

Acceleratorroom

176 22030 30

3010

5019

Beamdump(iron)

FC(U-238)

FC(-232)

Faraday cup

Clearingmagnet

p

3rdlight-ionroom

Test shield

DetectorRotary shutter

(iron) Polyethylene

109 cm diam

Movable stand

Units in cm

1207Ｃ target

Figure 1 Experimental arrangement of shielding experiments

thick was located at the end of the collimator with an addi-tional iron shield To measure the neutron energy spectraa 127 cm diameter 127 cm long BC501A liquid scintillationdetector was placed behind the test shields The density andthe atomic composition of the concrete and iron shields aredescribed in [8]

Source neutron spectra were obtained by TOF measure-ments The peak energies of quasi-monoenergetic neutronsources were 40MeV for 43MeV protons and the minimumneutron energy that could bemeasuredwith the TOFmethodwas 7MeV

The experimental geometry was reproduced within theARES discrete ordinates transport code with 69212 mesh Anisotropic neutron point source was set at the target positionwith energy spectrum as shown in Figure 2 [9]

Fixed source calculations were performed in the 1198755-11987816approximation where 1198755 corresponds to the order of theexpansion in Legendre polynomials of the scattering crosssection matrix and 11987816 represents the order of the fluxangular discretization Level symmetric quadrature sets wereapplied to calculate the neutron flux Diamond differencingwith linear-zero flux fixup approximation was selected forthe flux extrapolation model In all the calculations thesame numerical value (10119864 minus 03) for the point-wise fluxconvergence criterion was employed Since the geometryincluded the narrow collimator prior to the discrete ordinatescalculation the first collision source was generated by theRAY3D code to remove the ray effects

FENDLMG-30 [10] multigroup libraries were usedto simulate the TIARA benchmark shielding experimentsFENDLMG-30 is a multigroup formatted library intendedfor deterministic transport codesThe library contains multi-group cross section data in the 211n42g Vitamin J+ energystructures (matching the 175n Vitamin J energy structurebelow 1964MeV) for multigroup transport codes

4 Results and Discussion

We selected the BC501A detector measured neutron spectraat the beam axis behind 10 20 and 40 cm thick iron and25 50 100 and 150 cm thick concrete to validate AREStransport code This paper compared ARES calculations and

0

1

2

3

4

5

Neu

tron

ux

(ns

rle

thar

gym

icro

C)

353025 5040 452015105Neutron energy (MeV)

times1010

Figure 2 Source neutron spectra


ExptARES

25 cm thick

50 cm thick

100 cm thick

150 cm thick

10minus3

10minus2

10minus1

100

101

102

103

104

105

Neu

tron

ux

(n＝Ｇ

2le

thar

gym

icro

C)

Figure 3 Measured and calculated neutron spectra of the concreteexperiment

measurements for neutron spectra above 7MeV Calculatedvalues of the transmitted spectra were normalized by protonbeam charge Figures 3 and 4 show the measured andcalculated neutron spectra on the beam axis for the concreteand iron experiment respectively Tables 1 and 2 summarizethe ratios of the calculated to experimental values for the inte-grated neutron flux at peak and continuum energy regions Inaddition theMORSEMonte Carlo calculated results [1 9] forconcrete shielding and iron shielding are listed in Tables 1 and2 respectively

Figure 3 shows the measured and calculated neutronspectra of the concrete experiment for 43MeV p-7Li neutronsources The ARES results show good agreement with theexperimental data but the agreement falls away with increas-ing assembly thickness This underestimation is due to threefactors


Table 1 The ratio of calculation to measurement in peak and continuum regions for concrete shielding experiments

Shield thickness (cm)Peak region (35ndash45MeV) Continuum region (10ndash35MeV)

Experimental(ncm2s)

Calculated(ncm2s) CE CE

(MORSE)Experimental(ncm2s)


(MORSE)25 269380 330374 123 107 186503 202065 108 11150 30045 42304 141 109 15629 16603 106 142100 503 827 164 119 334 183 055 170150 012 017 142 126 011 004 037 211

Table 2 The ratio of calculation to measurement in peak and continuum regions for iron shielding experiments


Experimental(ncm2s)




(MORSE)10 420553 500787 119 098 353932 398047 112 10420 102281 113441 111 105 82222 78202 095 10540 5053 4827 096 115 3582 2682 075 133


20 cm thick

40 cm thick

10 cm thick

ExptARES

10minus1

100

101

102

103

104

105

Neu

tron

ux

(n＝Ｇ

2le

thar

gym

icro

C)

Figure 4 Measured and calculated neutron spectra of the ironexperiment

(1) Angular dependence of the differential scatteringcross section is typically represented as a truncatedLegendre series expansion The accuracy of AREScalculations with 1198755 Legendre expansion for thisproblem worsens with increasing thickness becausethe 1198755 Legendre expansion cannot present forwardpeaked angular distribution of secondary neutronsprecisely for high energy neutrons

(2) If the scattering cross section is highly anisotropicthe expansion may produce negative regions Suchanisotropy exists with light nuclei and nuclei at highenergy These negative regions may cause negativevalues in the discrete ordinates scattering sourcewhich could greatly affect transport results [11]

(3) Discrete ordinates calculations are presumed to trans-port particles from cell to cell in the directions

specified in the quadrature sets However diamonddifference approximations introduce undamped lat-eral oscillations resulting in severely nonphysicalflux representations Nonlinear fixups can preventnegativity but do not correct the underlying failure toproperly propagate rays [12]

Table 1 compares the measured and calculated fluxesintegrated into the continuum and the peak regions for43MeV p-7Li neutron sources The calculated spectra inthe peak region agreed well with the measured spectrawith 23ndash64 discrepancy In the continuum region thecalculation provided smaller values than measured fluxeswith increasing concrete thickness but even in the worst casethe ratio was 037

Figure 5 depicts the 50 cm thick concrete shielding exper-iment model with neutron flux contours The three largestenergy group neutron fluxes have similar distributions

Figure 4 shows the measured and calculated neutronspectra of the iron experiment for 43MeV p-7Li neutronsourcesTheARES calculated results show good agreement toexperimental data except for neutron spectra below 17MeVwith 40 cm thickness iron shielding ARES slightly under-estimate spectra within 31sim38MeV when the iron thicknessexceeds 20 cm The main reason for this underestimation isthe insufficiency of the Legendre expansion order for thescattering matrix in the multigroup libraries The Legendreexpansion order is usually 5 because of calculation constraintsof the FENDL libraries From 10 to 40MeV intervals thescattering cross section data of 56Fe is highly anisotropicand truncation of a highly anisotropic scattering cross sectionmay produce undesirable oscillations producing regionswhere the cross section expansion becomes negative withconsequential effects on accuracy

The calculations are in good agreement with measure-ments on the neutron beam axis for the 43-MeV p-7Lineutron source with up to 25 discrepancy as shown inTable 2 The calculated spectra in the peak region agreed


41-42 MeV 40-41 MeV 39-40 MeV

100E + 10

100E + 09

100E + 08

100E + 07

100E + 06

100E + 05

100E + 04

100E + 03

100E + 02

100E + 01

100E + 00

100E minus 01

100E minus 02

100E minus 03

Figure 5 Neutron flux distribution of 50 cm thick concrete shield-ing experiment

well with the measured spectra within 4ndash19 discrep-ancy In the continuum region the calculation providessmaller values than the measured fluxes with increasing ironthickness but even in the 40 cm thick case the ratio is075

5 Conclusions

The accuracy of ARES calculations with FENDLMG-30libraries was investigated through analysis of iron andconcrete shielding experiments for 43MeV p-7Li neutronsources at JAERITIARA The ARES results show goodagreement to experimental concrete shielding within 50 cmthickness and iron shielding within 20 cm thickness Asthe shielding thickness increased ARES underestimate theresults The calculated spectra in the peak region agreedwell with the measured spectra with up to 20 and 64discrepancy for the iron and concrete experiments respec-tively In the continuum region the ARES calculation pro-vided smaller values than the measured fluxes with increas-ing shielding thickness with calculatedexperiment rations037ndash112

In some energy regions the underestimation can beimproved by calculating with higher Legendre series expan-sion multigroup libraries and finer angular quadrature setsNegative scattering source removal is an important researcharea in the process of ARES development ARES is undergo-ing continuous developmentwithmany new features plannedfor implementation

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This work was supported by National Natural Science Foun-dation of China (11505059 11575061) and the FundamentalResearch Funds for the Central Universities (2016MS59)

References

[1] H Nakashima N Nakao S-I Tanaka et al ldquoTransmissionthrough shields of quasi-monoenergetic neutrons generatedby 43- and 68-MeV protons - II Iron shielding experimentand analysis for investigating calculational method and cross-section datardquo Nuclear Science and Engineering vol 124 no 2pp 243ndash257 1996

[2] C Konno K Ochiai S Sato and M Ohta ldquoAnalyses ofiron and concrete shielding experiments at JAEATIARA withJENDLHE-2007 ENDFB-VII1 and FENDL-30rdquo Fusion Engi-neering and Design vol 98-99 pp 2178ndash2181 2015

[3] Y Chen B Zhang L Zhang J Zheng Y Zheng and C LiuldquoARES A Parallel Discrete Ordinates Transport Code for Radi-ation Shielding Applications and Reactor Physics AnalysisrdquoScience and Technology of Nuclear Installations vol 2017 pp 1ndash11 2017

[4] L Zhang B Zhang P Zhang et al ldquoVerification of AREStransport code system with TAKEDA benchmarksrdquo NuclearInstruments and Methods in Physics Research Section A Accel-erators Spectrometers Detectors and Associated Equipment vol797 Article ID 57880 pp 297ndash303 2015

[5] T A Wareing J E Morel and D K Parsons A First CollisionMethod for ATTILA an Unstructured Tetrahedral Mesh DiscreteOrdinates Code Los Alamos National Laboratory USA 1996

[6] M Chen B Zhang and Y Chen ldquoVerification for ray effectselimination module of radiation shielding code ARES bykobayashi benchmarksrdquo in Proceedings of the 22nd InternationalConference on Nuclear Engineering (ICONE rsquo14) Prague CzechRepublic July 2014

[7] C Konno FMaekawaMWadaHNakashima andKKosakoldquoDORT analysis of iron and concrete shielding experimentsat JAERITIARArdquo in Proceedings of JAERI Conference JAERI-Conf-99-002 pp 164ndash169 1999

[8] Y Nakane K Hayashi Y Sakamoto et alNeutron transmissionbenchmark problems for iron and concrete shields in low interme-diate and high energy proton accelerator facilities Japan AtomicEnergy Research Institute 1996

[9] N Nakao H Nakashima T Nakamura et al ldquoTransmissionthrough shields of quasi-monoenergetic neutrons generated by43- and 68-MeV protons - I Concrete shielding experimentand calculation for practical applicationrdquo Nuclear Science andEngineering vol 124 no 2 pp 228ndash242 1996

[10] R A Forresr R Capote N Otsuka et al ldquoFENDL-3 librarysummary documentationrdquo INDC(NDS)-0628 IAEA NuclearData Section 2012

[11] J A Dahl Positive anisotropic scattering sources for discreteordinate methods [PhD thesis] University of Arizona 1989

[12] K A Mathews ldquoOn the propagation of rays in discrete ordi-natesrdquo Nuclear Science and Engineering vol 132 no 2 pp 155ndash180 1999

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Journal of


Renewable Energy

Submit your manuscripts athttpswwwhindawicom


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EnergyJournal of


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Volume 201Hindawi Publishing Corporation httpwwwhindawicom Volume 201

International Journal ofInternational Journal of


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High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


quadrature sets and cross sectionmessage Preliminary verifi-cation and validation for theARES transport code systemhadbeen performed by experiment benchmarking and referencecode

ARES employs discrete ordinates method in discretizingangular variables and adopts spherical harmonic to expandscattering source The angular variable is usually discretizedby replacing angular integrals with quadrature sums Rayeffects are nonphysical anomalies that often appear in opti-cally thin multidimensional discrete ordinates calculationsbecause the solution propagates along a finite set of directionsdefined by the angular quadrature set The first collisionsource method was used to eliminate or mitigate ray effects

A variety of spatial differencing scheme options are avail-able including diamond difference (DD) with or withoutlinear-zero flux fixup theta weighted (TW) directional thetaweighted (DTW) exponential directional weighted (EDW)and linear discontinuous finite element The most generalsolution technique is source iteration which is a simple andeffective method for many classes of transport problemsHowever for optically thick problems dominated by scatter-ing the source iterationmethod converges very slowly Diffu-sion synthetic acceleration (DSA) has been shown to signif-icantly decrease the iterations ARES uses the Koch-Baker-Alcouffe parallel sweep algorithm to obtain high parallelefficiency

The neutron transport calculation in the energy regionbetween 20 and 100MeV is the most crucial problem foraccelerator shielding designs because high energy neutronshave strong penetrability The spatial differencing schemesare very important to accurately simulate neutron transportThe diamond difference method assumes a linear relation-ship between the directional flux at the cell center andcell boundaries and is simple and accurate for small meshintervals However when the mesh interval is too largemeasured along the discrete direction through the cell thedifference equations may yield negative fluxes which causeoscillations in the iterative process and frequently causenegative scalar flux The TW DTW and EDW variationson the DD method were developed to eliminate negativefluxes without significantly sacrificing computational cost oraccuracy

The balance equation can be obtained by integrating theangular discretized form of the transport equation over themesh cell (Δ119909 Δ119910 Δ119911)

120583119898Δ119909

(120595119894out minus 120595119894in) +120578119898Δ119910

(120595119895out minus 120595119895in)

+ 120585119898Δ119911

(120595119896out minus 120595119896in) + Σ119905119894119895119896120595119860 = 119902119860(1)

where Ω119898 = (120583119898 120578119898 120585119898) is the discretized direction-of-flight variables 120595119860 is the cell average flux and the enteringand exiting angular fluxes are referred to using ldquoinrdquo andldquooutrdquo subscripts Σ119905119894119895119896 is the total cross section 119902119860 is knownfromprevious source iteration and the entering angular fluxesare known from the boundary values When using diamond

difference scheme the cell averaged angular flux can becalculated by

120595119860

=119902119860119881 + 2 1003816100381610038161003816120583119898

1003816100381610038161003816 119860120595119894in + 21003816100381610038161003816120578119898

1003816100381610038161003816 119861120595119895in + 21003816100381610038161003816120585119898

1003816100381610038161003816 119862120595119896in2 1003816100381610038161003816120583119898

1003816100381610038161003816 119860 + 2 10038161003816100381610038161205781198981003816100381610038161003816 119861 + 2

10038161003816100381610038161205851198981003816100381610038161003816 119862 + Σ119905119881

(2)

where 119860 = Δ119910Δ119911 119861 = Δ119909Δ119911 119862 = Δ119909Δ119910Ray effects are nonphysical oscillations in the scalar flux

They are caused by the inability of a quadrature set in discreteordinates approximation to accurately integrate the angularflux Ray effects may represent themost significant deficiencyof the 119878119873 method The first collision source method [5] wasemployed to mitigate ray effects The method analyticallycalculates the uncollided flux to obtain the first collisionsource term which is then applied to calculate the collidedflux using the standard 119878119873methodThe total flux is composedof the uncollided and collided flux

Thus the first collision source method decomposes theflux 120595119892( 119903 Ω) into uncollided components 120595119892

(119906)( 119903 Ω) and

collided components 120595119892(119888)( 119903 Ω)

120595119892 ( 119903 Ω) = 120595119892(119906)( 119903 Ω) + 120595119892

(119888)( 119903 Ω) (3)

and the transport equation is decomposed into

Ω sdot nabla120595119892(119906)( 119903 Ω) + Σ119892119905 ( 119903) 120595

119892

(119906)( 119903 Ω) = 119902119892119890 ( 119903 Ω)

Ω sdot nabla120595119892(119888)( 119903 Ω) + Σ119892119905 ( 119903) 120595

119892

(119888)( 119903 Ω) =

119866

sum1198921015840=1

119873

sum119899=0

2119899 + 14120587

sdot Σ1198921198921015840

119904119899 ( 119903)119899

sum119896=minus119899

119884119899119896 (Ω) 1206011198921015840(119888)

119899119896 ( 119903) + 119902(119906)119904 ( 119903 Ω)

(4)

where 119902119892119890 ( 119903 Ω) is fixed source and 119902(119906)119904 ( 119903 Ω) is the firstcollision source which is calculated from uncollided fluxmoments Σ119892119892

1015840

119904119899 is the Legendre moment of scattering crosssection from group 1198921015840 to group 119892 and 119884119899119896 is sphericalharmonics

RAY employs ray tracing method to accelerate opticaldistance calculations and the point source correction factoris introduced to improve the accuracy of calculation resultsThe RAY module within ARES has been verified elsewhereby a series of international benchmarks such as Kobayashibenchmarks [6] and can effectively eliminate ray effects andobtain reasonable results

3 Overview of Shielding Experiments

Figure 1 shows a cross sectional view of the TIARAfacility with the experimental arrangement [7] Quasi-monoenergetic source neutrons were generated by 43MeVprotons bombarding 7Li targets Neutrons produced in theforward angle reached the experiment room through a109 cm diameter 225 cm long iron collimator embedded inthe concrete wall A test shield of iron or concrete 10ndash150 cm




Acceleratorroom

176 22030 30

3010

5019

Beamdump(iron)

FC(U-238)

FC(-232)

Faraday cup

Clearingmagnet

p

3rdlight-ionroom

Test shield


(iron) Polyethylene

109 cm diam

Movable stand

Units in cm

1207Ｃ target









0

1

2

3

4

5

Neu

tron

ux

(ns

rle

thar

gym

icro

C)


times1010



ExptARES

25 cm thick

50 cm thick

100 cm thick

150 cm thick

10minus3

10minus2

10minus1

100

101

102

103

104

105

Neu

tron

ux

(n＝Ｇ

2le

thar

gym

icro

C)







Experimental(ncm2s)




(MORSE)25 269380 330374 123 107 186503 202065 108 11150 30045 42304 141 109 15629 16603 106 142100 503 827 164 119 334 183 055 170150 012 017 142 126 011 004 037 211



Experimental(ncm2s)




(MORSE)10 420553 500787 119 098 353932 398047 112 10420 102281 113441 111 105 82222 78202 095 10540 5053 4827 096 115 3582 2682 075 133


20 cm thick

40 cm thick

10 cm thick

ExptARES

10minus1

100

101

102

103

104

105

Neu

tron

ux

(n＝Ｇ

2le

thar

gym

icro

C)











41-42 MeV 40-41 MeV 39-40 MeV

100E + 10

100E + 09

100E + 08

100E + 07

100E + 06

100E + 05

100E + 04

100E + 03

100E + 02

100E + 01

100E + 00

100E minus 01

100E minus 02

100E minus 03



5 Conclusions





Acknowledgments


References















FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of



Journal of

















Acceleratorroom

176 22030 30

3010

5019

Beamdump(iron)

FC(U-238)

FC(-232)

Faraday cup

Clearingmagnet

p

3rdlight-ionroom

Test shield


(iron) Polyethylene

109 cm diam

Movable stand

Units in cm

1207Ｃ target









0

1

2

3

4

5

Neu

tron

ux

(ns

rle

thar

gym

icro

C)


times1010



ExptARES

25 cm thick

50 cm thick

100 cm thick

150 cm thick

10minus3

10minus2

10minus1

100

101

102

103

104

105

Neu

tron

ux

(n＝Ｇ

2le

thar

gym

icro

C)







Experimental(ncm2s)




(MORSE)25 269380 330374 123 107 186503 202065 108 11150 30045 42304 141 109 15629 16603 106 142100 503 827 164 119 334 183 055 170150 012 017 142 126 011 004 037 211



Experimental(ncm2s)




(MORSE)10 420553 500787 119 098 353932 398047 112 10420 102281 113441 111 105 82222 78202 095 10540 5053 4827 096 115 3582 2682 075 133


20 cm thick

40 cm thick

10 cm thick

ExptARES

10minus1

100

101

102

103

104

105

Neu

tron

ux

(n＝Ｇ

2le

thar

gym

icro

C)











41-42 MeV 40-41 MeV 39-40 MeV

100E + 10

100E + 09

100E + 08

100E + 07

100E + 06

100E + 05

100E + 04

100E + 03

100E + 02

100E + 01

100E + 00

100E minus 01

100E minus 02

100E minus 03



5 Conclusions





Acknowledgments


References















FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of



Journal of

















Experimental(ncm2s)




(MORSE)25 269380 330374 123 107 186503 202065 108 11150 30045 42304 141 109 15629 16603 106 142100 503 827 164 119 334 183 055 170150 012 017 142 126 011 004 037 211



Experimental(ncm2s)




(MORSE)10 420553 500787 119 098 353932 398047 112 10420 102281 113441 111 105 82222 78202 095 10540 5053 4827 096 115 3582 2682 075 133


20 cm thick

40 cm thick

10 cm thick

ExptARES

10minus1

100

101

102

103

104

105

Neu

tron

ux

(n＝Ｇ

2le

thar

gym

icro

C)











41-42 MeV 40-41 MeV 39-40 MeV

100E + 10

100E + 09

100E + 08

100E + 07

100E + 06

100E + 05

100E + 04

100E + 03

100E + 02

100E + 01

100E + 00

100E minus 01

100E minus 02

100E minus 03



5 Conclusions





Acknowledgments


References















FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of



Journal of















41-42 MeV 40-41 MeV 39-40 MeV

100E + 10

100E + 09

100E + 08

100E + 07

100E + 06

100E + 05

100E + 04

100E + 03

100E + 02

100E + 01

100E + 00

100E minus 01

100E minus 02

100E minus 03



5 Conclusions





Acknowledgments


References















FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of



Journal of
















FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of



Journal of














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