Deep-Penetration Calculationpeace99.web.fc2.com/KEKreport2002-12.pdf · for the ISIS Target Station Shielding Using the MARS Monte Carlo Code ... A calculation of neutron penetration

Deep-Penetration Calculationfor the ISIS Target Station ShieldingUsing the MARS Monte Carlo Code

Tomoya Nunomiya, Noriaki Nakao, Hiroshi Iwase, Takashi Nakamura

High Energy Accelerator Research Organization

Deep-Penetration Calculationfor the ISIS Target Station Shielding

Using the MARS Monte Carlo Code

Tomoya Nunomiya1 , Noriaki Nakao2† , Hiroshi Iwase1 , Takashi Nakamura1

1, Department of Quantum Science and Energy Engineering, Tohoku University,Aoba, Aramaki, Aoba-ku, Sendai, 980-8579, Japan

2, High Energy Accelerator Research Organization (KEK),Oho 1-1, Tsukuba, Ibaraki, 305-0801, Japan

Abstract

A calculation of neutron penetration through a thick shield was performed with

a three-dimensional multi-layer technique using the MARS14(02) Monte Carlo code to

compare with the experimental shielding data in 1998 at the ISIS spallation neutron source

facility. In this calculation, secondary particles from a tantalum target bombarded by 800-

MeV protons were transmitted through a bulk shield of approximately 3-m-thick iron and

1-m-thick concrete. To accomplish this deep-penetration calculation with good statistics,

the following three techniques were used in this study. First, the geometry of the bulk

shield was three-dimensionally divided into several layers of about 50-cm thickness, and

a step-by-step calculation was carried out to multiply the number of penetrated particles

at the boundaries between the layers. Second, the source particles in the layers were

divided into two parts to maintain the statistical balance on the spatial-flux distribution.

Third, only high-energy particles above 20 MeV were transported up to approximately

1 m before the region for benchmark calculation.

Finally, the energy spectra of neutrons behind the very thick shield were calculated

down to the thermal energy with good statistics, and typically agree well within a factor

of two with the experimental data over a broad energy range. The 12C(n,2n)11C reaction

rates behind the bulk shield were also calculated, which agree with the experimental data

typically within 60%. These results are quite impressive in calculation accuracy for deep-

penetration problem.

In this report, the calculation conditions, geometry and the variance reduction

techniques used in the deep-penetration calculation with the MARS14 code are clarified,

and several subroutines of MARS14 which were used in our calculation are also given

in the appendix. The numerical data of the calculated neutron energy spectra, reaction

rates, dose rates and their C/E (Calculation/Experiment) values are also summarized.

The numerical data in this report are available at the following web site:

http://idsun1.kek.jp/isis98

† Corresponding author, Tel : +81-298-79-6004, E-mail : [email protected]

1

MARSモンテカルロコードを用いたISIS中性子ターゲットステーション遮蔽の深層透過計算

布宮智也1 , 中尾徳晶 2† , 岩瀬広1 , 中村尚司1

1, 東北大学大学院工学研究科量子エネルギー工学専攻, 980-8579 仙台市青葉区荒巻字青葉2, 高エネルギー加速器研究機構 (KEK), 放射線科学センター, 305-0801 茨城県つくば市大穂 1-1

概要

MARS14(02)モンテカルロ計算コードを用いて、1998年の ISIS遮蔽実験を模擬した深層透過計算を行った。非常に厚い遮蔽の透過計算は、モンテカルロ法による一回の計算では統計精度良く結果を得ることは困難であり、過小評価する危険性がある。本研究では、精度の良い深層透過計算を行うために、ISISターゲットステーションの遮蔽体系を 50cm

厚程度の三次元的な“層”に分割し、順次独立に計算を行う手法を用いた。初めにタンタルターゲットに 800MeV陽子を入射させ、核破砕中性子が約 3m厚の鉄及び約 1m厚のコンクリートから成るバルク遮蔽を透過する際、“層”から外側に漏れ出た粒子の座標、方向ベクトル、エネルギー、ウェイトを記録し、次の“層”での線源として用いた。統計精度をあげるために、次の“層”ではその線源粒子数を 5∼10倍にした (e.g. splitting 法)。この手法を用いることで、比較的短時間で遮蔽体外側まで粒子を到達させることが可能となり、統計精度の良い中性子エネルギースペクトルを得ることができた。また、粒子束の低い位置でも統計精度の良い結果を得るために、粒子束の分布に応じて統計的バランスを考慮した分割計算を行った。さらに、バルク遮蔽を透過する間に中性子エネルギースペクトルは平衡に達し、その減衰は 100MeV以上の高エネルギー中性子に支配されるため、ベンチマーク計算を行う領域の約 1m手前までは、全粒子のエネルギーカットオフを20MeVとして計算時間を短縮した。本計算の結果、約 3mの鉄と約 1mのコンクリートという非常に厚い遮蔽の後ろでエネ

ルギースペクトルが 10−4eVから 400MeVにわたる広いエネルギー範囲で概ね約 2倍以内で実験値と一致し、また 12C(n, 2n)反応率は概ね 60%以内で実験値と一致した。この結果は、深層透過問題の計算精度として画期的なものである。本報告書では、MARS14(02)コードによる深層透過計算で用いた計算条件、体系、分散

低減法を明らかにし、さらにこの計算で用いたMARSコードのサブルーチンをAppendix

に載せた。また、本シミュレーションの結果得られた中性子エネルギースペクトル、反応率、線量率及びそれらのC/E値を全て数値データでまとめた。

この報告書にまとめた数値データは、以下のwebサイトから入手可能である。http://idsun1.kek.jp/isis98

† 連絡先, Tel : 0298-79-6004, E-mail : [email protected]

2

Contents

1 Introduction 6

2 Experimental data and geometry 7

3 Calculation geometry 73.1 Geometry of target system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73.2 Geometry of bulk shield . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83.3 Material compositions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

4 Calculation methods 84.1 Secondary particles from the target system . . . . . . . . . . . . . . . . . . . . . 84.2 Three-dimensional multi-layer calculation for variance reduction . . . . . . . . . . 84.3 Statistical balance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94.4 Energy cut-off . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

5 Data analysis 105.1 Neutron energy spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105.2 Reaction rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105.3 Neutron dose rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

6 Results and discussions 116.1 Calculated results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

6.1.1 Secondary particles from the target system . . . . . . . . . . . . . . . . . 116.1.2 Neutron energy spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116.1.3 Attenuation of the reaction rates and dose rates . . . . . . . . . . . . . . 126.1.4 Duct streaming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

6.2 Comparison between the calculation and the experiment . . . . . . . . . . . . . . 126.2.1 Neutron energy spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126.2.2 Spatial distribution of the reaction rates . . . . . . . . . . . . . . . . . . . 136.2.3 Attenuation of the reaction rate . . . . . . . . . . . . . . . . . . . . . . . 136.2.4 Neutron attenuation length . . . . . . . . . . . . . . . . . . . . . . . . . . 14

7 Conclusion 14

A User subroutines 65A.1 Source particle generation (BEG1) . . . . . . . . . . . . . . . . . . . . . . . . . . 65A.2 Leak particle storing (LEAK) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67A.3 Geometry and materials (REG1) . . . . . . . . . . . . . . . . . . . . . . . . . . . 68A.4 Geometry boundary definition (XYOUT) . . . . . . . . . . . . . . . . . . . . . . 74A.5 Estimator (MFILL) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75A.6 Output the neutron energy spectra (SPCOUT) . . . . . . . . . . . . . . . . . . . 76A.7 Data base file (SPC−DB) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77A.8 Parameters (SPC.INC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

3

List of Tables

1 Atomic compositions and averaged densities of the target system and the surroundingmaterials used in this calculation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2 Atomic compositions of the bulk shield and the additional shields used in this calculation.The composition of the iron-igloo is equivalent to that of the additional shield. . . . . . . 16

3 Cross-section data of 27Al(n, α)24Na, 12C(n, 2n)11C and 209Bi(n, xn)210−xBi used in thisstudy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

4 Neutron flux-to-dose conversion factor of 1-cm depth dose equivalent cited from ICRPpub. 74 [15]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

5 Comparison of the measured and calculated neutron energy spectra on the shield top floorand behind the additional concrete and iron shields. (Experimental data given in Table 13of Ref. [5] were misprinted, and those are corrected here.) . . . . . . . . . . . . . . . . . . 19

6 Comparison of the measured and calculated 12C(n, 2n)11C reaction rates at various positions. 207 Comparison of the measured and calculated 209Bi(n, xn)210−xBi (x=4∼10) reaction rates

at ”center” position. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218 Comparison of the measured and calculated 27Al(n, α)24Na reaction rates at “center”

position. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229 Comparison of the measured and calculated neutron dose rates at various positions. . . . 2210 Comparison of the measured and calculated attenuation lengths estimated from the 12C(n, 2n)11C

reaction rate at “center” position. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

List of Figures

1 Cross-sectional view of the target station of neutron spallation source with an 800-MeVproton beam at ISIS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2 Cross-sectional view of the shielding plug above the target vessel. . . . . . . . . . . . . . . 243 Horizontal and vertical cross-sectional views of the iron igloo and an additional shield. The

five detector positions of “center”, “up50”, “down50”, “left50” and “right50” are shownas white circles in the upper figure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

4 Geometry of target system consisting of a target, a container and a reflector. All cylindershave a common center at (0, 0, 0). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

5 Cross-sectional view of the Y-Z plane of the simplified geometry of target station used inthe calculation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

6 Cross-sectional view of the X-Z plane of the simplified geometry of target station used inthe calculation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

7 Cross-sectional view of the simplified geometry of target station on the horizontal plane atA∼N cross sections in Fig. 6. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

8 Schematic view of the target system calculation (layer (a) in Fig. 9). . . . . . . . . . . . . 369 Schematic view of the three-dimensional multi-layer calculation. Protons, neutrons and

pions crossing outwards the layer boundaries are stored in a file with their energy, coordi-nates, directions and weight to be used as a source in the next layer calculation. . . . . . 36

10 Track length estimator locations. (a)∼(c) show the cross-sectional view of X-Y, X-Z andY-Z plane, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

11 Neutron track plots projected on the X-Z plane at layer (j) (Z>500cm). . . . . . . . . . . 3812 Graphical plots of recorded neutrons leaked at layer (b) calculation. Calculation of layer (c)

is carried out separately by using two different sources of “forward-duct”(1:green-region)and “side-back”(2:red-region). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

13 Flow chart of a step-by-step calculation. Right-lane indicates “side-back” calculation andleft-lane indicates “forward-duct” calculation. Three calculations were carried out usingsame source particles leaked from layer (i) at “side-back” and those from layer (h’) at“forward-duct”, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

14 Cross-sectional view of layers in the multi-layer calculation (X-Z plane), which are used in“side-back” calculation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

15 Cross-sectional view of layers in the multi-layer calculation (X-Z plane), which are used in“forward-duct” calculation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

4

16 Cross-section data of the measured 12C(n, 2n)11C reaction [12, 13] and eye guide along thedata. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

17 Cross-section data of the 27Al(n, α)24Na reaction calculated by Fukahori using the ALICEcode [11]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

18 Cross-section data of the 209Bi(n, xn)210−xBi (x=4∼10) reaction cited from ENDF/B-VIhigh-energy file [14] compared with the measured data [12]. . . . . . . . . . . . . . . . . . 44

19 Neutron flux-to-dose conversion factor of the 1-cm depth dose equivalent cited from ICRPpub.74 [15]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

20 Angular and energy distributions of (a) neutron, (b) proton and (c) pion leakage from thetarget assembly surface calculated with MARS14 Monte Carlo code. . . . . . . . . . . . . 46

21 Calculated neutron energy spectra in the bulk shield and above the shield top at variouspositions; (a) center, (b) left50, (c) right50, (d) up50, (e) down50, (f) left130, (g) right130,(h) up130, (i) down130. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

22 Attenuation profiles of the 12C(n, 2n)11C reaction rate estimated from the calculated neu-tron energy spectra through the bulk shield at various positions shown in Fig. 10. . . . . . 51

23 Attenuation profiles of the neutron dose rate estimated from the calculated neutron energyspectra through the bulk shield at various positions shown in Fig 10. . . . . . . . . . . . . 52

24 Attenuation profiles of the 12C(n, 2n)11C reaction rate (upper figure) and dose rate (lowerfigure) through the He-duct estimated from the calculated neutron energy spectra, whichis relatively compared with the attenuation curve of Nakamura and Uwamino’s formura. . 53

25 Comparison between the calculated and measured neutron energy spectra on the shieldtop floor, behind the additional concrete and iron shields at “center” position. . . . . . . 54

26 Comparison between the calculated and measured 12C(n, 2n)11C reaction rates above theshield top without an additional shield (air) along the left-right axis (Y-axis). . . . . . . 55

27 Comparison between the calculated and measured 12C(n, 2n)11C reaction rates above theshield top without an additional shield (air) along the up-down axis (X-axis). . . . . . . 56

28 Comparison between the calculated and measured 12C(n, 2n)11C reaction rates above theshield top behind the additional concrete shield along the left-right axis (Y-axis). . . . . 57

29 Comparison between the calculated and measured 12C(n, 2n)11C reaction rates above theshield top behind the additional concrete shield along the up-down axis (X-axis). . . . . 58

30 Comparison between the calculated and measured 12C(n, 2n)11C reaction rates above theshield top behind the additional iron shield along the left-right axis (Y-axis). . . . . . . . 59

31 Comparison between the calculated and measured 12C(n, 2n)11C reaction rates above theshield top behind the additional iron shield along the up-down axis (X-axis). . . . . . . . 60

32 Comparison between the calculated and measured attenuations of 12C(n, 2n)11C reactionrate above the shield top (air) and behind the additional concrete and iron shields at the“center” position. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

33 Comparison between the calculated and measured attenuations of 209Bi(n, xn)210−xBi(x=4∼10) reaction rate behind the additional concrete shield at the “center” position. . 62

34 Comparison between the calculated and measured attenuations of 209Bi(n, xn)210−xBi(x=4∼10) reaction rate behind the additional iron shield at the “center” position. . . . . 63

35 Comparison between the calculated and measured attenuations of neutron dose rate behindadditional concrete and iron shields at the “center” position. . . . . . . . . . . . . . . . . 64

5

1 Introduction

Although steady progress in computer technologies has made calculations ever

faster, reliable calculations of neutron transmission through a very thick shield still remain

quite difficult. This is because a long computing time and sophisticated variance reduction

techniques are needed to obtain particle fluxes and energy spectra with good statistics.

At the same time, the corresponding experimental data for benchmark calculation are

rather scarce.

Since 1992, at the intense spallation neutron source facility, ISIS (800MeV proton),

of the Rutherford Appleton Laboratory (RAL), measurements of deeply penetrating neu-

trons through a thick bulk shielding were performed to obtain benchmark experimental

data [1, 2]. In a 1998 experiment, concrete and iron shields were additionally installed on

the top floor of the target station to measure the neutron energy spectra and the reaction

rates behind shields of various thickness using activation detectors [3, 4, 5]. All of the

experimental conditions, geometry and results are clearly described and are numerically

given in Ref [5].

Since a calculation with three-dimensional geometry based on the actual shield struc-

ture could hardly be accomplished, a Monte Carlo calculation under the one-dimensional

geometry [6] and a two-dimensional discrete ordinate calculation [7] were performed ear-

lier to analyze this ISIS shielding experiment; they are, however, inadequate to estimate

the particle flux distributions. In this work, a deep-penetration calculation was per-

formed with a three-dimensional multi-layer technique using the MARS14(02) Monte

Carlo code [8] to analyze the ISIS shielding experiment, and the spatial distribution of

the neutron flux and the energy spectra were obtained.

In this report, the calculation conditions, geometry and variance reduction tech-

niques are described in detail, and numerical data of the calculation conditions, results

and C/E-values are summarized.

6

2 Experimental data and geometry

All experimental data which are compared with the calculations in this work are

cited from the shielding experiment performed at ISIS in 1998 [3, 4, 5]. Neutrons were

produced by 800 MeV protons impinging on thick tantalum target at the center of target

station. The beam intensity was about 170µA at the target with a 50-Hz repetition rate.

A cross-sectional view of the target station at ISIS is shown in Fig. 1. A 130-cm

void, which represents the inside of the target vessel, is covered on the top by a shielding

plug consisting of 284-cm-thick steel (density of 7.35 g/cm3) and 97-cm-thick concrete

(density of 2.3 g/cm3), a 6-cm-thick steel vacuum plate and a steel support plate, as

shown in Fig. 2. The surface of the support plate was located 528 cm above the beam

line as shown in Fig. 3.

Neutrons behind various thicknesses of the additional concrete or iron shield were

measured using activation detectors of graphite, bismuth and aluminum. Neutron reaction

rates of 12C(n, 2n)11C, 27Al(n,α)24Na and 209Bi(n,xn)210−xBi(x=4∼10) were obtained, and

their attenuation profiles through concrete and iron were clarified. Attenuation lengths

of high-energy neutrons for concrete and iron were also estimated in this experiment. A

multi-moderator spectrometer (Bonner ball) using indium-oxide activation detector was

also used for the measurement, and the neutron energy spectra in the energy range from

thermal to 400 MeV were obtained by an unfolding technique using the above reaction

rates(C, Al and Bi) and 115In(n,γ)116mIn.

3 Calculation geometry

3.1 Geometry of target system

Fig. 4 shows the calculation model of the target system, which consists of

1 : target (Ta + D2O cooling water),2 : container (Fe + D2O),3 : reflector (Be + D2O).

All of these are of cylindrical shape and have a common center at (0, 0, 0). Two small

cylinders are parallel to the X-axis, and the largest cylinder is perpendicular to it. The

axes are defined as follows:

X : proton beam axis,Y : horizontal axis perpendicular to proton beam,Z : vertical axis.

7

3.2 Geometry of bulk shield

For calculations, the actual shield geometries shown in Figs. 1 ∼ 3 were simplified,

and the calculation geometries used in this study in vertical cross section are shown in

Figs. 5 and 6 for the Y-Z plane and the X-Z plane, respectively. The horizontal cross

sections in the X-Y plane are also given in Fig. 7 for all Z-regions.

3.3 Material compositions

The densities and atomic compositions of the target system and the shields are

given in Tables 1 and 2, respectively, and the heterogeneous structure was changed homo-

geneously. Where deuteron is not included in the MARS code, hydrogen was used instead

of deuteron, and the atomic densities of hydrogen were set to be equivalent to that of the

deuteron. The composition of the iron-igloo was considered to be the same as that of the

additional iron shield.

4 Calculation methods

4.1 Secondary particles from the target system

An 800-MeV proton beam was injected from the bottom center of the smallest

cylinder (target) along the X-axis, as shown in Fig. 4. The energies, coordinates, directions

and weights of the neutrons, protons and pions leaked from the target system were first

calculated with the MARS14(02) Monte Carlo code and stored as source particles for a

bulk shield calculation. Since the geometry of the target system was symmetrical with

respect to the Z=0 plane and bulk shield of Z<0 was not taken into account in this work,

particles leaked in the region of Z<0 were stored as those having an absolute value of the

Z-coordinate and the reversed Z vector, and the weights of all particles were multiplied

by 0.5, as shown in Fig. 8.

4.2 Three-dimensional multi-layer calculation for variance re-

duction

To accomplish a deep-penetration calculation in good statistics with a reasonable

computing time, a three-dimensional multi-layer technique was developed in this work.

The shielding geometry was three-dimensionally divided into several layers, as shown in

Fig. 9, where layer (a) is the target system, layer (b) to (h) are the target vessel and the

bulk shield, layer (i) is the uppermost bulk shield and the upper space, layer (j) is the

area surrounded with the iron igloo. If a particle crossed outwards from a layer boundary,

the particle tracking was terminated and the particle informations were recorded in a

file. They were used for a next-layer calculation as source particles having the numbers

multiplied by a factor of 5 to 10, like a splitting method. The initial weight of the particle

8

in the new layer, W2, is given as

W2 =N1−leak

N1

W1, (1)

where W1 is the weight of the particle leaked from the previous layer, N1 is the number

of source particle in the previous layer and N1−leak is the number of particle leaked in

the previous layer. Track-length estimators (e.g. 20-cm diameter and 2-cm thick) were

located at various positions throughout the bulk shield and above the shield top, as shown

in Fig. 10 to obtain the neutron energy spectra, where Fig. 10 (a) is a top view of X-Y

plane, (b) and (c) are side view of X-Z plane and Y-Z plane, respectively.

In the final layer (j) of Fig. 9, three calculations were carried out by changing

the additional shield (air, concrete and iron) using the same source particles leaked from

layer (i). Fig. 11 exemplifies the neutron track plots in the final layer (j) (Z>500cm),

in the case when the additional iron shield was arranged in the iron-igloo. The source

particles were emitted from the shield top floor (Z = 511 cm) and from the outer surface

of the iron-igloo shown in Fig. 9.

4.3 Statistical balance

Since the forwardness of the particle production at the target and the streaming

through the large He-duct are dominant as seen in Fig. 1, the particle intensity at down-

stream is much higher than in the other area. To keep a good statistical balance in the

whole region of a layer, particles leaked around the He-duct were recorded separately in

the case of layer (b) (see Fig. 9), as shown in Fig. 12. Using these two source particles

of “forward-duct” and “side-back”, the calculations from layer (c) to layer (i) (see Fig. 9)

were performed in two ways, and the two results were summed in every estimator. A

simple flow chart of this step-by-step calculation is shown in Fig. 13. Figs. 14 and 15

show the layers used in the calculation of “side-back” and “forward-duct”, respectively.

Note that each layer includes the previous layers (e.g. layer (c) includes layer (a) and

layer (b)); the thicknesses of the layers were from 100 cm to 200 cm to take the reflected

particles into consideration.

4.4 Energy cut-off

Since the experimental data are given above the shield top floor, in order to save

computing time, the cut-off energies of all particles were set to 20 MeV, up to about 1 m

below the shield top floor (Z = 394 cm); above that region, those of neutrons and charged

hadrons were set to be thermal and 0.2 MeV, respectively. The neutron attenuation

in the lower energy region is much faster than that in the high-energy region, and the

contribution of the lower energy neutron penetrated through 1-m-thick shield behind is

negligible compared with the lower energy neutrons newly generated due to the high-

energy hadron cascade.

9

For a calculation below 14.5 MeV, the MARS default option of the 28-group-BNAB

low-energy neutron transport [9] was used in this study.

5 Data analysis

5.1 Neutron energy spectrum

Monte Carlo particle tracking was performed in several batches. The neutron energy

spectra were estimated by a track-length estimation method, as follows:

φik =1

N

∑(� × W )

V, (2)

φi =1

M

M∑k=1

φik, (3)

where φi is the neutron fluence, i is the energy bin, φik is the neutron fluence at energy

bin i of the kth batch, � is the track length of neutron, W is the weight of neutron, M is

the number of the batch (= 10 in this study), V is the volume of the estimator and N is

the number of source particles in the batch. The standard deviation [10] of the neutron

fluence, ∆φi, in each bin was estimated for statistic error, as

∆φi =

√√√√ 1

M − 1

M∑k=1

( φik − φi )2. (4)

5.2 Reaction rate

The reaction rates of 12C(n, 2n)11C, 27Al(n, α)24Na and 209Bi(n, xn)210−xBi (x=4∼10)

are estimated using the calculated neutron energy spectra and cross section data as

R =1

M

M∑k=1

Rk =1

M

M∑k=1

(∑i

σi · φik

), (5)

∆R =

√√√√ 1

M − 1

M∑k=1

(Rk − R )2, (6)

where R is the reaction rate, Rk is the reaction rate at the kth batch and σi is the reaction

cross section at energy bin i. The cross sections of 12C(n, 2n)11C evaluated by eye guide

along the experimental data [12, 13], those of 27Al(n, α)24Na calculated by Fukahori using

the ALICE code [11], and those of 209Bi(n, xn)210−xBi cited from ENDF/B-VI high-energy

library [14], were used as shown in Figs. 16, 17 and 18, respectively. Their numerical data

are tabulated in Table 3.

10

5.3 Neutron dose rate

The neutron dose rate, H , is estimated using the calculated neutron energy spectra

H =1

M

M∑k=1

Hk =1

M

M∑k=1

(∑i

H∗(10)i · φik

), (7)

∆H =

√√√√ 1

M − 1

M∑k=1

(Hk − H )2, (8)

where H is the neutron dose rate and H∗(10)i is the neutron flux-to-dose conversion factor

of 1-cm depth dose equivalent at energy bin i cited from ICRP pub.74 [15]; it is assumed

to be constant at E > 200MeV, as shown in Fig. 19. The numerical data are tabulated

in Table 4.

6 Results and discussions

6.1 Calculated results

6.1.1 Secondary particles from the target system

Fig. 20 shows the angular- and energy-distributions of the neutrons, protons and

pions leaked from the target system in unit of [sr−1 proton−1 lethargy−1], estimated above

20 MeV. It can be seen that the neutrons generated in the forward direction reach 800

MeV, which is the energy of the primary proton beam. The leakage ratios of protons and

pions to that of neutrons are about 10% and 0.1% from the figures.

6.1.2 Neutron energy spectra

Figs. 21 (a) ∼ (i) show the calculated neutron energy spectra through the bulk

shield, on the shield top floor at center, left-, right-, up- and down-position as shown in

Fig. 10. All neutron energy spectra have a hadron cascade peak of around 100 MeV.

The neutron energy spectra in a concrete region at Z=422.5 cm (see Fig. 10) of “cen-

ter”, “left50”, “right50”, “up50” and “down50” (Figs. 21 (a)∼(e)) have a typical 1/E

slowing-down spectrum (flat in lethargy spectrum). For “left130”, “right130”, “up130”

and “down130” (Fig 21 (f)∼(i)), on the other hand, the points of Z=422.5 cm are in iron

region and neutron energy spectra have a broad peak over the region from 10−4 to 10 MeV.

These spectra are similar to the neutron energy spectra on the shield top, respectively,

that is the neutron energy spectrum in the concrete floor region outside the igloo have a

typical 1/E spectrum shown in Z=512.5 cm of Figs. 21 (f)∼(i), and inside the iron igloo

shown in Z=528.6 cm of Figs. 21 (a)∼(e) have a broad peak component due to inelastic

scattering in iron plates.

The neutron energy spectra at the left- and right-position look very similar because

the calculation geometry is symmetrical to the X-axis, while on the contrary in a com-

parison between the up- and down-position, the neutron energy spectra of “down” are

11

generally several-times larger than those of “up” because of the duct streaming and the

forwardness of secondary particle production from the target.

6.1.3 Attenuation of the reaction rates and dose rates

Figs. 22 and 23 show the attenuation profiles of the estimated 12C(n, 2n)11C reaction

rates and the neutron dose rates, respectively, through the bulk shield and above the shield

top floor with no additional shield at various positions. Both the reaction rates and the

dose rates estimated from the calculated energy spectra were obtained in good statistics,

and their attenuations could be clarified. Since the 12C(n, 2n)11C reaction has a threshold

energy of 20 MeV and the reaction cross section above 20 MeV have almost a constant

value of 20 mb, the 12C(n, 2n)11 reaction rate corresponds to the high-energy neutron flux

above 20 MeV. Fig. 22 gives high-energy neutron attenuations through iron and concrete.

It can be seen that neutron dose rates increase temporary at around 394 cm and 520 cm

from the target in all attenuation profiles shown in Fig. 23. Many low-energy neutrons

(∼ several hundreds keV) are generated around these two boundary regions because the

neutron energy cut-off is changed from 20-MeV to thermal energy at 394 cm, and there

is an approximately 10-cm-thick iron plate on the shield top floor at 520 cm.

6.1.4 Duct streaming

Fig. 24 shows the attenuation profiles of the 12C(n, 2n)11C reaction rate and the

neutron dose equivalent along the estimators located through the He-duct shown in

Fig. 10 (b). It can be found that the reaction rates increase at the entrance of each

leg, because the backscattered neutrons increase on the wall of the next leg. The esti-

mated neutron dose rates agree relatively well with the attenuation curve of Nakamura

and Uwamino’s (N & U’s) formula [16]. Although low-energy neutrons below 20 MeV are

not taken into account in the neutron dose rate down to the middle of the 3rd leg, these

two attenuation profiles of the dose rates are in comparatively good agreement.

6.2 Comparison between the calculation and the experiment

6.2.1 Neutron energy spectra

Fig. 25 shows the calculated neutron energy spectra on the shield top floor, behind

the 60-cm-thick additional concrete and behind the 30-cm-thick additional iron at the

“center” position compared with the experimental data [5]; the numerical data of these

spectra and C/E values are given in Table 5. High energy neutrons above 250 MeV

are not counted in the calculations. Note that the calculated energy spectrum on the

additional concrete shield is in a good agreement with the experiment within about 40%

in the energy region above 1 MeV. Generally, the calculated energy spectra agree with

the measured ones within a factor of 2 over a broad energy range with the maximum

differences reaching a factor of 3∼6. These results are quite impressive in the transport

12

calculation through very thick shield. The previous calculation with the ANISN and

HETC code [6] underestimated about one order of magnitude.

It is said that calculations using the MCNP option instead of the 28-group-BNAB

of MARS for low-energy neutron transport are expected to improve the agreement with

the experiment below 14.5 MeV.

6.2.2 Spatial distribution of the reaction rates

Figs. 26∼31 show the spatial distributions of the estimated 12C(n, 2n)11C reaction

rates in the inner area of the igloo on the shield top, compared with the experimental

results; their numerical data and C/E values are given in Table 6. Figs. 26 and 27 show

the distributions in the case of air instead of an additional shield, Figs. 28 and 29 show

those behind the additional concrete shield, and Figs. 30 and 31 show those behind the

additional iron shield. The spatial distributions along the left-right distribution (Y-axis)

are shown in Figs. 26, 28 and 30; on the other hand, those along the up-down direction (X-

axis) are shown in Figs. 27, 29 and 31. The experimental and calculated values agree well

within about a factor of 2, except at the “down130”, where there are many complicated

equipments near this points on the shield top floor.

6.2.3 Attenuation of the reaction rate

12C(n, 2n)11C reaction rate

Fig. 32 shows the attenuation profiles of the 12C(n, 2n)11C reaction rates above the

shield top floor without an additional shield (e.g. air), behind the additional concrete

and iron shields at “center” position; these numerical data are given in Table 6. The

attenuation profiles of the measured and calculated reaction rates show a slight difference

especially in the case of air, and the discrepancy of the reaction rate is typically within

60% and within a factor of 2 in the maximum case. It can be clarified that this calculation

gave much more accurate values than the earlier simple calculations (Ref. [6]), which gave

big underestimations of about one order.

209Bi(n, xn)210−xBi reaction rate

Figs. 33 and 34 show the 209Bi(n, xn)210−xBi (x=4∼10) reaction rates behind the

additional concrete and iron shields at the “center” position, respectively; these numerical

data are given in Table 7. The reaction rates estimated from the calculated neutron energy

spectra agree well with the experimental results within a factor of 3 for all case.

27Al(n, α)24Na reaction rate

The 27Al(n, α)24Na reaction rates (threshold energy of the reaction of 3.25 MeV)

on the shield top floor and behind the 60-cm-thick concrete and 30-cm-thick iron at the

“center” position are tabulated in Table 8. The experimental and calculated results agree

very well behind the concrete shield, and agree by about a factor of 2 on the shield top

13

floor and behind the iron shield.

Neutron dose rate

The calculated neutron dose rates are compared with those measured by a neutron

dose meter at various positions of shield top floor and at the “center” position behind

various thicknesses of the additional concrete and iron. All of the numerical data and C/E

values are given in Table 9. Fig. 35 shows the attenuation profiles through the additional

concrete and iron shields at the “center” position and compared with the experimental

results. For the concrete shield, the experimental and calculated results agree well within

70% except for the case of 120 cm. The iron shield calculations are, however, generally

overestimated by about a factor of 2 due to the overestimation of low-energy neutrons, as

shown in Fig. 25.

6.2.4 Neutron attenuation length

The neutron attenuation lengths were estimated from the attenuation profiles of

the 12C(n, 2n)11C reaction rates using the least-mean square method, which corresponds

to the neutron flux attenuation above 20 MeV, these values are tabulated in Table 10.

Attenuation curves based on the attenuation lengths are drawn in Fig. 32. The attenuation

lengths for both concrete and iron, estimated from the calculated 12C(n, 2n)11C reaction

rate, are about 7% shorter than those estimated from the experiment.

7 Conclusion

A deep-penetration calculation was performed with a three-dimensional multi-layer

technique using the MARS14(02) Monte Carlo code. The neutron energy spectra behind

a very thick shield of approximately 3-m-thick iron and 1-m-thick concrete were calcu-

lated with good statistics in the energy range from thermal to 400 MeV. The calculation

results were compared with the ISIS shielding experiment of 1998, and the neutron energy

spectra typically agreed within a factor of 2 over a broad energy range with the maximum

differences reaching a factor of 6. The 12C(n, 2n)11C reaction rates were also estimated

from the calculated neutron energy spectra, and typically agreed with the experiment

within 60%, in the maximum case within a factor of 2 behind the additional concrete and

iron shields at the “center”. These good results are quite impressive in the calculation for

deep-penetration problems.

Acknowledments

We would like to thank Dr. Nikolai Mokhov of Fermi National Accelerator Labo-

ratory for his great help with the MARS code system and useful comments.

14

References

[1] Y. Uwamino, T. Shibata, T. Ohkubo, S. Sato and D. Perry, ”Study on Bulk Shielding of an 800-MeV Proton Accelerator”, OECD/NEA/NSC The Specialists’ Meeting on Shielding Aspects ofAccelerators, Targets, and Irradiation Facilities (SATIF-1), Arlington, Texas, (April, 1994) 185.

[2] N. Nakao, T. Shibata, T. Ohkubo, S. Sato, Y. Uwamino, Y. Sakamoto and D. R. Perry, ”Shieldingexperiment at 800 MeV proton accelerator facility”, Proc. 1998 ANS Radiation Protection andShielding Division Topical Conference, Nashville, Tennessee, Vol. 2, pp. 192-199, (1998).

[3] T. Nunomiya, N. Nakao, P. Wright, T. Nakamura, E. Kim, T. Kurosawa, S. Taniguchi, M. Sasaki,H. Iwase, T. Shibata, Y. Uwamino, S. Ito, and D. R. Perry, ”Measurement of deep penetration ofneutron produces by 800-MeV proton beam through concrete and iron”, Nuclear Instrument andMethods B, 179, 89-102, (2001).

[4] N. Nakao, T. Shibata, T.Nunomiya, T. Nakamura, E. Kim, T. Kurosawa, S. Taniguchi, M. Sasaki,H. Iwase, Y. Uwamino, S. Ito, P. Wright and D. R. Perry ”Deep penetration experiment at ISIS”,OECD/Nuclear Energy Agency, The Specialists’ Meeting on Shielding Aspects of Accelerators, Tar-gets and Irradiation Facilities (SATIF-5), Paris, France, (July 2000) 18.

[5] T. Nunomiya, N. Nakao, P. Wright, T. Nakamura, E. Kim, T. Kurosawa, S. Taniguchi, M. Sasaki,H. Iwase, T. Shibata, Y. Uwamino, S. Ito, and D. R. Perry, ”Experimental Data of Deep-PenetrationNeutrons through a Concrete and Iron Shield at the ISIS Spallation Neutron Source Facility usingan 800-MeV Proton Beam”, KEK Report 2001-24, February 2002.

[6] N. Nakao and Y. Uwamino, ”Deep Penetration Calculation Compared with the Shielding Experi-ments at ISIS” , Proceedings of Ninth International Conference on Radiation Shielding, J. Nucl. Sci.Technol., Supplement 1 (March 2000) 162.

[7] H. Handa, M. Saitoh, K. Hayashi, K. Yamada, T. Abe and Y. Uwamino, ”Analysis on high energyneutron shielding experiments in ISIS”, SARE-3, KEK proceedings 97-5, Vol. 97-5, 300, (1997).

[8] N.V. Mokhov, ”The Mars Code System User’s Guide”, Fermilab-FN-628 (1995);N.V. Mokhov and O. E. Krivosheev, ”MARS Code Status”, Fermilab-Conf-00/181 (2000);http://www-ap.fnal.gov/MARS.

[9] L. P. Abagyan, N. O. Bazazyants, M. N. Nikolaev and A. M. Tsybulya, “Group Cross-Sections forReactor and Shielding Calculations”, Moscaw, Energoizdat (1981).

[10] Glenn. F. Knoll, ”Radiation Detection and Measurement, 3rd Edition”, John Wiley & Sons, Inc.,New York (2000)

[11] M. Blann, Code ALICE/89, (1989).

[12] E. Kim, T. Nakamura and A. Konno, ”Measurements of Neutron Spallation Cross Sections of 12Cand 209Bi in the 20- to 150-MeV Energy Range”, Nucl. Sci. Eng. 129, 209-223, (1998).

[13] Y. Uno, Y. Uwamino, T. S. Soewarsono and T. Nakamura, ”Measurement of the neutron activationcross sections of 12C, 30Si, 47Ti, 48Ti, 52Cr, 59Co, and 58Ni between 15 and 40 MeV”, Nucl. Sci.Eng. 122, 247, (1996).

[14] “Evaluated Nuclear Data File”, ENDF/B-VI, National Neutron Cross Section Center, BrookhavenNational Laboratory (1990).

[15] International Commission on Radiological Protection, ICRP Publication 74, (1995).

[16] Y. Uwamino, T. Nakamura and T. Ohkubo, “Measurement and calculation of neutron leakage froma medical electron accelerator”, Medical Physics, 13, 374, (1986).

15

Table 1Atomic compositions and averaged densities of the target system and the surroundingmaterials used in this calculation.

Averaged target container reflectordensity 14.5 g/cm3 3.58 g/cm3 1.69 g/cm3

wt % atom/cm3 wt % atom/cm3 wt % atom/cm3

H† 0.19 8.29E+21* 3.9 4.22E+22 21.1 1.37E+22Be - - - - 68.3 9.83E+22O 0.75 4.14E+21 15.6 2.11E+22 10.6 6.84E+21Fe - - 80.5 3.10E+22 - -Ta 99.06 4.84E+22 - - - -

† Deuteron is replaced by hydrogen* Read as 8.29 x 1021

Table 2Atomic compositions of the bulk shield and the additional shields used in this calculation.The composition of the iron-igloo is equivalent to that of the additional shield.

Bulk shieldConcrete Iron

Density 2.3 g/cm3 7.35 g/cm3

Additional shieldConcrete Iron

Density 2.36 g/cm3 7.8 g/cm3

wt % atom/cm3 wt % atom/cm3

H 1.08 1.52E+22* - -C 6.01 7.11E+21 0.14 5.47E+20O 51.34 4.56E+22 - -Na 0.12 7.42E+19 - -Mg 0.28 1.64E+20 - -Al 0.76 4.00E+20 - -Si 12.56 6.35E+21 0.32 5.35E+20P - - 0.02 3.03E+19S 0.19 8.42E+19 0.008 1.34E+19K 0.28 1.02E+20 - -Ca 21.99 7.79E+21 - -Ti 0.03 8.90E+18 - -Mn - - 1.0 8.55E+20Fe 5.36 1.36E+21 98.51 8.28E+22

* Read as 1.52 x 1022

16

Table 3Cross-section data of 27Al(n, α)24Na, 12C(n, 2n)11C and 209Bi(n, xn)210−xBi used in thisstudy.

Upper Cross sectionneutron [ barn ]energy[MeV] 27Al(n, α) 12C(n, 2n) 209Bi(n,4n) (n,5n) (n,6n) (n,7n) (n,8n) (n,9n) (n,10n)

1.00E – 10*4.14E – 07 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+001.12E – 06 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+005.04E – 06 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+002.26E – 05 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+004.54E – 04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+003.35E – 03 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+001.50E – 02 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+008.65E – 02 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+002.24E – 01 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+004.98E – 01 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+009.07E – 01 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+001.35E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+002.02E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+003.01E+00 1.73E – 17 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+004.49E+00 6.38E – 06 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+006.70E+00 8.36E – 03 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+001.00E+01 6.78E – 02 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+001.35E+01 1.18E – 01 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+001.75E+01 8.43E – 02 1.02E – 05 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+002.25E+01 3.27E – 02 9.03E – 04 1.00E – 10 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+002.75E+01 8.39E – 03 7.54E – 03 2.66E – 01 8.33E – 11 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+003.50E+01 2.73E – 03 1.35E – 02 1.43E+00 2.61E – 05 1.00E – 10 0.00E+00 0.00E+00 0.00E+00 0.00E+004.50E+01 5.79E – 03 1.66E – 02 7.02E – 01 7.82E – 01 4.01E – 02 0.00E+00 0.00E+00 0.00E+00 0.00E+005.50E+01 8.35E – 03 1.75E – 02 2.72E – 01 8.01E – 01 4.29E – 01 2.64E – 02 0.00E+00 0.00E+00 0.00E+006.50E+01 1.04E – 02 1.79E – 02 1.55E – 01 3.82E – 01 4.43E – 01 2.75E – 01 9.79E – 03 1.00E – 10 0.00E+008.00E+01 1.46E – 02 1.85E – 02 1.01E – 01 1.88E – 01 2.23E – 01 3.41E – 01 1.71E – 01 2.91E – 02 3.51E – 051.00E+02 1.68E – 02 1.88E – 02 6.91E – 02 1.06E – 01 1.06E – 01 1.78E – 01 1.90E – 01 1.70E – 01 4.87E – 021.20E+02 1.51E – 02 1.90E – 02 5.15E – 02 8.05E – 02 6.79E – 02 9.72E – 02 1.10E – 01 1.41E – 01 9.40E – 021.60E+02 1.17E – 02 1.92E – 02 3.66E – 02 5.46E – 02 4.63E – 02 5.63E – 02 5.65E – 02 7.99E – 02 6.13E – 022.00E+02 9.68E – 03 1.93E – 02 2.63E – 02 4.05E – 02 3.43E – 02 3.88E – 02 3.58E – 02 4.59E – 02 3.41E – 022.50E+02 8.33E – 03 1.95E – 02 2.46E – 02 3.30E – 02 2.86E – 02 2.97E – 02 2.86E – 02 3.49E – 02 2.63E – 023.00E+02 7.69E – 03 1.95E – 02 2.28E – 02 2.89E – 02 2.49E – 02 2.72E – 02 2.44E – 02 2.93E – 02 2.23E – 023.50E+02 7.50E – 03 1.96E – 02 2.09E – 02 2.75E – 02 2.22E – 02 2.69E – 02 2.15E – 02 2.61E – 02 2.00E – 024.00E+02 7.01E – 03 1.96E – 02 1.78E – 02 2.55E – 02 2.02E – 02 2.51E – 02 1.95E – 02 2.37E – 02 1.80E – 02

* Read as 1.00 x 10−10

17

Table 4Neutron flux-to-dose conversion factor of 1-cm depth dose equivalent cited from ICRPpub. 74 [15].

Upper Neutron Upper Neutronenergy H*(10) energy H*(10)[MeV] [pSv cm2] [MeV] [pSv cm2]

1.00E– 10†4.14E– 07 1.00E+01 1.35E+01 4.74E+021.12E– 06 1.34E+01 1.75E+01 5.44E+025.04E– 06 1.26E+01 2.25E+01 5.91E+022.26E– 05 1.11E+01 2.75E+01 5.56E+024.54E– 04 8.98E+00 3.50E+01 5.11E+023.35E– 03 7.81E+00 4.50E+01 4.56E+021.50E– 02 9.61E+00 5.50E+01 4.00E+028.65E– 02 4.16E+01 6.50E+01 3.83E+022.24E– 01 1.33E+02 8.00E+01 3.30E+024.98E– 01 2.59E+02 1.00E+02 3.02E+029.07E– 01 3.68E+02 1.20E+02 2.76E+021.35E+00 4.20E+02 1.60E+02 2.52E+022.02E+00 4.22E+02 2.00E+02 2.53E+023.01E+00 4.16E+02 2.50E+02 2.60E+024.49E+00 4.09E+02 3.00E+02 2.60E+026.70E+00 4.03E+02 3.50E+02 2.60E+021.00E+01 4.16E+02 4.00E+02 2.60E+02

† read as 1.00 x 10−10

18

Table 5Comparison of the measured and calculated neutron energy spectra on the shield topfloor and behind the additional concrete and iron shields. (Experimental data given inTable 13 of Ref. [5] were misprinted, and those are corrected here.)

Upperneutron Floor Concrete 60cm Iron 30cmenergy Exp. Cal. C/E Exp. Cal. C/E Exp. Cal. C/E[MeV] [n cm−2 Coulomb−1] [n cm−2 Coulomb−1] [n cm−2 Coulomb−1]

1.00E – 10*4.14E – 07 3.84E+03 3.71E+02 0.10 2.13E+04 2.37E+03 0.11 1.40E+02 6.62E+02 4.731.12E – 06 1.71E+04 1.20E+04 0.70 6.52E+03 9.76E+03 1.50 5.97E+03 3.00E+04 5.025.04E – 06 3.63E+04 1.79E+04 0.49 9.90E+03 1.25E+04 1.27 1.97E+04 5.41E+04 2.742.26E – 05 7.83E+04 2.44E+04 0.31 2.01E+04 1.14E+04 0.57 4.65E+04 9.11E+04 1.964.54E – 04 1.54E+05 3.26E+04 0.21 2.94E+04 1.24E+04 0.42 1.27E+05 1.33E+05 1.043.35E – 03 1.95E+05 9.29E+04 0.48 3.11E+04 1.31E+04 0.42 1.82E+05 2.77E+05 1.531.50E – 02 2.34E+05 1.83E+05 0.78 3.18E+04 1.76E+04 0.55 2.15E+05 4.25E+05 1.988.65E – 02 4.86E+05 7.05E+05 1.45 3.87E+04 1.73E+04 0.45 4.21E+05 7.47E+05 1.772.24E – 01 6.54E+05 1.97E+06 3.02 4.72E+04 2.94E+04 0.62 3.23E+05 1.53E+06 4.724.98E – 01 9.37E+05 2.15E+06 2.30 4.68E+04 3.42E+04 0.73 6.00E+05 1.19E+06 1.989.07E – 01 7.85E+05 1.10E+06 1.40 6.40E+04 3.26E+04 0.51 2.10E+05 3.52E+05 1.671.35E+00 4.48E+05 7.45E+05 1.66 4.50E+04 3.24E+04 0.72 8.21E+04 2.13E+05 2.602.02E+00 2.37E+05 8.14E+05 3.44 5.37E+04 5.90E+04 1.10 3.55E+04 2.27E+05 6.403.01E+00 1.34E+05 4.47E+05 3.34 6.47E+04 3.96E+04 0.61 2.04E+04 9.71E+04 4.764.49E+00 1.29E+05 2.93E+05 2.28 3.62E+04 3.95E+04 1.09 3.97E+04 6.32E+04 1.596.70E+00 1.38E+05 1.56E+05 1.13 3.25E+04 3.01E+04 0.93 3.19E+04 3.70E+04 1.161.00E+01 1.01E+05 1.81E+05 1.80 2.16E+04 1.82E+04 0.85 2.19E+04 2.73E+04 1.251.35E+01 7.98E+04 1.55E+05 1.94 1.66E+04 1.72E+04 1.04 1.63E+04 2.92E+04 1.791.75E+01 8.00E+04 2.59E+05 3.24 1.50E+04 2.08E+04 1.39 1.59E+04 3.26E+04 2.052.25E+01 9.18E+04 2.34E+05 2.55 1.99E+04 3.09E+04 1.55 1.72E+04 4.05E+04 2.352.75E+01 1.00E+05 2.74E+05 2.73 2.83E+04 3.70E+04 1.31 1.43E+04 4.07E+04 2.843.50E+01 1.23E+05 3.39E+05 2.75 3.25E+04 4.75E+04 1.46 2.19E+04 5.46E+04 2.494.50E+01 1.38E+05 3.59E+05 2.59 3.85E+04 4.83E+04 1.25 3.13E+04 6.24E+04 1.995.50E+01 1.64E+05 4.16E+05 2.54 4.96E+04 6.36E+04 1.28 4.25E+04 7.54E+04 1.776.50E+01 2.60E+05 3.81E+05 1.47 6.80E+04 6.13E+04 0.90 5.84E+04 5.59E+04 0.968.00E+01 2.58E+05 4.31E+05 1.68 7.00E+04 7.54E+04 1.08 4.26E+04 4.28E+04 1.011.00E+02 1.90E+05 3.68E+05 1.94 6.78E+04 7.77E+04 1.15 2.82E+04 5.75E+04 2.041.20E+02 1.61E+05 4.49E+05 2.79 6.83E+04 6.51E+04 0.95 2.69E+04 4.64E+04 1.721.60E+02 1.51E+05 3.43E+05 2.27 6.06E+04 6.53E+04 1.08 2.63E+04 3.59E+04 1.372.00E+02 1.10E+05 1.57E+05 1.42 3.87E+04 2.53E+04 0.65 1.97E+04 1.84E+04 0.932.50E+02 4.69E+04 9.24E+04 1.97 1.54E+04 1.40E+04 0.91 8.51E+03 9.16E+03 1.083.00E+02 1.30E+04 0.00E+00 - 3.98E+03 0.00E+00 - 2.34E+03 0.00E+00 -3.50E+02 2.62E+03 0.00E+00 - 7.73E+02 0.00E+00 - 4.60E+02 0.00E+00 -4.00E+02 0.00E+00 0.00E+00 - 0.00E+00 0.00E+00 - 0.00E+00 0.00E+00 -

* read as 1.00x10−10

19

Table 6Comparison of the measured and calculated 12C(n, 2n)11C reaction rates at various posi-tions.

Additional Reaction rate [atom−1 Coulomb−1]shield Center Left50 Right50[cm] Exp. Cal. C/E Exp. Cal. C/E Exp. Cal. C/E

floor 0 6.75E – 21* 1.34E – 20 1.99 1.08E – 20 1.37E – 20 1.27 1.20E – 20 1.20E – 20 1.00air 20 8.52E – 21 8.42E – 21 0.99 1.03E – 20 7.03E – 21 0.68 1.06E – 20 7.13E – 21 0.67

40 8.27E – 21 7.36E – 21 0.89 8.91E – 21 5.33E – 21 0.60 7.78E – 21 5.54E – 21 0.7160 8.34E – 21 6.18E – 21 0.74 7.32E – 21 4.60E – 21 0.63 7.82E – 21 4.01E – 21 0.5180 7.08E – 21 4.28E – 21 0.60 6.31E – 21 3.76E – 21 0.60 6.53E – 21 3.23E – 21 0.49

100 6.14E – 21 3.55E – 21 0.58 5.00E – 21 2.96E – 21 0.59 4.95E – 21 2.53E – 21 0.51120 5.19E – 21 2.84E – 21 0.55 4.43E – 21 2.30E – 21 0.52 4.20E – 21 2.12E – 21 0.50

concrete 20 4.90E – 21 5.73E – 21 1.17 6.44E – 21 4.67E – 21 0.73 5.94E – 21 4.72E – 21 0.7940 3.38E – 21 3.38E – 21 1.00 3.12E – 21 2.61E – 21 0.84 3.44E – 21 2.54E – 21 0.7460 2.04E – 21 2.20E – 21 1.08 2.06E – 21 1.60E – 21 0.78 3.00E – 21 1.30E – 21 0.4380 1.37E – 21 1.24E – 21 0.91 1.40E – 21 8.51E – 22 0.61 1.53E – 21 8.16E – 22 0.53

100 9.07E – 22 7.32E – 22 0.81 7.35E – 22 5.18E – 22 0.70 7.23E – 22 4.98E – 22 0.69120 6.00E – 22 7.97E – 22 1.33 - 4.93E – 22 - - 4.66E – 22 -

iron 10 4.09E – 21 5.33E – 21 1.30 8.02E – 21 4.67E – 21 0.58 5.48E – 21 4.64E – 21 0.8520 2.37E – 21 3.13E – 21 1.32 5.46E – 21 2.61E – 21 0.48 3.50E – 21 2.69E – 21 0.7730 1.46E – 21 1.83E – 21 1.25 1.96E – 21 1.57E – 21 0.80 1.85E – 21 1.49E – 21 0.8140 8.55E – 22 1.02E – 21 1.19 1.48E – 21 9.29E – 22 0.63 9.73E – 22 8.97E – 22 0.9250 5.14E – 22 5.44E – 22 1.06 6.00E – 22 5.51E – 22 0.92 5.14E – 22 5.52E – 22 1.0760 3.19E – 22 5.31E – 22 1.66 4.04E – 22 5.05E – 22 1.25 4.65E – 22 4.78E – 22 1.03

Up50 Down50 Left130[cm] Exp. Cal. C/E Exp. Cal. C/E Exp. Cal. C/E

floor 0 7.90E – 21 6.24E – 21 0.79 2.04E– 20 2.85E – 20 1.40 floorair 20 7.39E – 21 4.30E – 21 0.58 1.56E– 20 1.07E – 20 0.69 7.98E – 21 9.00E – 21 1.13

40 6.41E – 21 4.63E – 21 0.72 1.39E– 20 6.73E – 21 0.4860 5.95E – 21 4.23E – 21 0.71 9.91E– 21 4.18E – 21 0.42 Right13080 5.86E – 21 3.47E – 21 0.59 7.38E– 21 2.94E – 21 0.40 Exp. Cal. C/E

100 5.02E – 21 2.67E – 21 0.53 6.24E– 21 2.20E – 21 0.35 floor120 5.09E – 21 2.49E – 21 0.49 4.98E– 21 1.96E – 21 0.39 1.03E – 20 9.21E – 21 0.89

concrete 20 4.67E – 21 2.54E – 21 0.54 1.08E– 20 8.90E – 21 0.8240 3.65E – 21 1.74E – 21 0.48 4.39E– 21 4.62E – 21 1.05 Up13060 1.76E – 21 1.02E – 21 0.58 3.00E– 21 2.51E – 21 0.84 Exp. Cal. C/E80 1.28E – 21 6.86E – 22 0.54 1.72E– 21 1.31E – 21 0.76 floor

100 1.06E – 21 4.01E – 22 0.38 1.16E– 21 7.30E – 22 0.63 3.47E – 21 3.88E – 21 1.12120 - 4.76E – 22 - - 8.31E – 22 -

iron 10 4.04E – 21 2.16E – 21 0.53 1.08E– 20 1.02E – 20 0.94 Down13020 2.29E – 21 1.42E – 21 0.62 6.43E– 21 6.40E – 21 1.00 Exp. Cal. C/E30 1.41E – 21 8.40E – 22 0.60 3.90E– 21 3.83E – 21 0.98 floor40 8.29E – 22 4.52E – 22 0.55 1.83E– 21 2.35E – 21 1.28 5.15E – 20 1.85E – 19 3.5950 6.89E – 22 2.42E – 22 0.35 1.29E– 21 1.49E – 21 1.1660 4.88E – 22 3.62E – 22 0.74 9.07E– 22 1.62E – 21 1.79

* read as 6.75 x 10−21

20

Table 7Comparison of the measured and calculated 209Bi(n, xn)210−xBi (x=4∼10) reaction ratesat ”center” position.

Additional Reaction rate [atom−1 Coulomb−1]shield 209Bi(n, 4n)206Bi 209Bi(n, 5n)205Bi 209Bi(n, 6n)204Bi[cm] Exp. Cal. C/E Exp. Cal. C/E Exp. Cal. C/E

floor 0 1.00E – 19* 2.51E – 19 2.51 9.18E – 20 2.01E – 19 2.19 5.31E – 20 1.08E – 19 2.03concrete 20 6.71E – 20 1.10E – 19 1.64 6.43E – 20 8.63E – 20 1.34 3.63E – 20 4.52E – 20 1.24


100 1.22E – 20 1.11E – 20 0.91 1.11E – 20 8.99E – 21 0.81 5.83E – 21 5.24E – 21 0.90120 - 1.23E – 20 - - 1.03E – 20 - - 5.62E – 21 -

iron 10 5.36E – 20 1.06E – 19 1.98 3.87E – 20 8.73E – 20 2.26 2.96E – 20 4.61E – 20 1.5620 3.42E – 20 5.77E – 20 1.69 3.23E – 20 4.94E – 20 1.53 1.77E – 20 2.70E – 20 1.5330 1.82E – 20 4.03E – 20 2.22 1.95E – 20 3.24E – 20 1.66 1.03E – 20 1.58E – 20 1.5440 1.55E – 20 2.13E – 20 1.37 1.47E – 20 1.74E – 20 1.18 5.78E – 21 8.07E – 21 1.4050 7.82E – 21 1.22E – 20 1.56 - 8.09E – 21 - 3.13E – 21 4.27E – 21 1.3760 6.45E – 21 9.08E – 21 1.41 - 7.60E – 21 - 1.90E – 21 4.44E – 21 2.34

209Bi(n, 7n)203Bi 209Bi(n, 8n)202Bi 209Bi(n, 9n)201Bi[cm] Exp. Cal. C/E Exp. Cal. C/E Exp. Cal. C/E

floor 0 4.40E – 20 8.04E – 20 1.83 2.74E – 20 4.80E – 20 1.75 1.69E – 20 3.83E – 20 2.27concrete 20 3.05E – 20 3.38E – 20 1.11 1.98E – 20 2.05E – 20 1.04 1.76E – 20 1.68E – 20 0.96


100 5.38E – 21 4.39E – 21 0.82 3.41E – 21 3.04E – 21 0.89 4.31E – 21 2.58E – 21 0.60120 - 4.44E – 21 - - 3.05E – 21 - - 2.75E – 21 -

iron 10 2.34E – 20 3.16E – 20 1.35 1.59E – 20 1.44E – 20 0.90 1.06E – 20 1.80E – 20 1.7020 1.57E – 20 1.84E – 20 1.17 1.06E – 20 8.63E – 21 0.81 6.86E – 21 1.08E – 20 1.5730 9.13E – 21 9.91E – 21 1.09 5.08E – 21 4.72E – 21 0.93 2.07E – 21 5.77E – 21 2.7940 9.07E – 21 5.84E – 21 0.64 4.69E – 21 2.65E – 21 0.57 - 3.38E – 21 -50 2.99E – 21 3.49E – 21 1.17 2.63E – 21 1.37E – 21 0.52 - 1.95E – 21 -60 4.53E – 21 3.60E – 21 0.79 1.74E – 21 1.48E – 21 0.85 - 2.13E – 21 -

209Bi(n, 10n)200Bi[cm] Exp. Cal. C/E

floor 0 8.48E – 21 1.95E – 20 2.30concrete 20 6.52E – 21 8.21E – 21 1.26

40 4.86E – 21 4.77E – 21 0.9860 3.56E – 21 3.39E – 21 0.9580 3.67E – 21 2.05E – 21 0.56

100 2.04E – 21 1.28E – 21 0.63120 - 1.41E – 21 -

iron 10 5.04E – 21 6.88E – 21 1.3720 2.71E – 21 4.28E – 21 1.5830 1.49E – 21 2.25E – 21 1.5140 - 1.33E – 21 -50 - 6.44E – 22 -60 - 6.67E – 22 -

* read as 1.00 x 10−19

21

Table 8Comparison of the measured and calculated 27Al(n, α)24Na reaction rates at “center”position.

Additional Reaction rate [atom−1 Coulomb−1]shield 27Al(n, α)24Na[cm] Exp. Cal. C/E

floor 0 1.25E – 20* 2.67E – 20 2.14concrete 60 3.09E– 21 3.29E – 21 1.06iron 30 2.48E– 21 4.01E – 21 1.62

* read as 1.25 x 10−20

Table 9Comparison of the measured and calculated neutron dose rates at various positions.

Additional Neutron dose rate [µSv Coulomb−1]shield Center Left 50 Left 130 Right 50 Right 130[cm] Exp. Cal. C/E Exp. Cal. C/E Exp. Cal. C/E Exp. Cal. C/E Exp. Cal. C/E

floor 0 766 1830 2.4 floor floor floor floorconcrete 20 258 320 1.2 917 1950 2.1 500 623 1.2 917 1840 2.0 450 675 1.5

40 123 173 1.460 65 108 1.7 Up 50 Up 130 Down 50 Down 13080 43 69 1.6 Exp. Cal. C/E Exp. Cal. C/E Exp. Cal. C/E Exp. Cal. C/E

100 24 38 1.6 floor floor floor floor120 20 76 3.9 567 1060 1.9 150 257 1.7 1333 3820 2.9 1500 8400 5.6

iron 10 627 1360 2.220 475 1020 2.130 374 758 2.040 260 537 2.150 197 355 1.860 153 499 3.3

Table 10Comparison of the measured and calculated attenuation lengths estimated from the12C(n, 2n)11C reaction rate at “center” position.

Shielding Attenuation length [g/cm2]material Exp. Cal. C/EConcrete

(2.36 g/cm3) 125.4±5.1 116.7±3.8 0.93Iron

(7.8 g/cm3) 161.1±2.1 150.3±5.8 0.93

22

6cm-thick Steel Plate

460520

220

81 147 97

123

98

190

130

284

Top Center of Shielding Plug

He duct

511

H+ 800MeV 170µA 50Hz

unit : cm

Target Vessel

Ta target

ConcreteSteel

Building floor level

124470

Shield top level

26585

439

130

42.5

Fig. 1Cross-sectional view of the target station of neutron spallation source with an 800-MeVproton beam at ISIS.

23

φ 123

φ 98

φ 147

9710

314

120

20

unit : cmFlange on Void Vessel

Vacuum Plate (6cm thick Steel)

φ 174

Concrete

Steel

Gap 1.5 Steel 2

Gap

1.5

φ 52

Gap 4

3.6Shield top level

steel support plate

φ 24

φ 30

φ 36

Gap 1.5

Gap 3

16.6

Fig. 2 Cross-sectional view of the shielding plug above the target vessel.

24

～～

Tantalum target

H+ 800MeV50Hz 170µΑ

90°

Concrete

Steel

196

528

Horizontal Cross Sectional View

Vertical Cross Sectional View

Steel support platefor fixing Igloo andadditional shield

Iron Igloo

120

60Proton beam direction

60

60

-60

-60

Center Up

Down

Left

Right

50

-50

120 0

Iron Igloo

Additional shield

Unit : cm

Additional shield

Steel disk plate for vacuum cap

Fig. 3Horizontal and vertical cross-sectional views of the iron igloo and an additional shield.The five detector positions of “center”, “up50”, “down50”, “left50” and “right50” areshown as white circles in the upper figure.

25

800MeV Proton

1: Ta + D2O

2 : Fe + D2O

3 : Be + D2O

φ 54.2

78.0

43.0

φ 18.2

33.8

φ 9.0

Unit : cmX

Z

Y

(0, 0, 0)

Fig. 4Geometry of target system consisting of a target, a container and a reflector. All cylindershave a common center at (0, 0, 0).

26

8197

124

10039.521.5

101.5

511

196

17

Unit : cm

Ta targ

et

4

Iron igloo

Y

Z

21.5

46

Con

crete

Steel

Z=0

Fig. 5Cross-sectional view of the Y-Z plane of the simplified geometry of target station used inthe calculation.

27

He du

ct

p-800MeV

X

Z

265

126

42.5

42.5

130439

42.5

80

Unit: cm

235

Z=0A B C

DE

FG

H I JK L M

N

Fig. 6Cross-sectional view of the X-Z plane of the simplified geometry of target station used inthe calculation.

28

φ 316

φ 1200

φ 1000

X

YConcrete

Steel

Target

Void

(A) Z=0∼85cm

φ 400φ 316-98

42.5

172.5

X

YConcrete

Steel

He duct

(B) Z=85∼130cm

Fig. 7Cross-sectional view of the simplified geometry of target station on the horizontal planeat A∼N cross sections in Fig. 6.

29

42.5

φ 98φ 400

Concrete

Steel

He duct

X

Y

Gap 1.5

(C) Z=130∼209cm

42.5

φ 98

Shielding plugGap 1.5

42.5

Concrete

Steel

X

Y

(D) Z=209∼230cm

Fig. 7 continued.

30

He duct

Gap 1.5

Concrete

Steel

42.5 x 42.5

He duct

Gap 1.5

Concrete

Steel

130

172.5

42.5

X

Y

X

Y

(E) Z=230∼265cm

He duct

Gap 1.5

Concrete

Steel

130

172.5

42.5

X

Y

(F) Z=265∼269.5cm

Fig. 7 continued.

31

X

YConcrete

Steel

Gap 1.5

He duct

φ 98

(G) Z=269.5∼291cm

X

YConcrete

Steel

Gap 1.5

He duct

φ123

(H) Z=291∼307.5cm

Fig. 7 continued.

32

He duct

Gap 1.5

Concrete

SteelX

Y

42.5 x 42.5

φ123

439

Shielding plug

(I) Z=307.5∼392.5cm

Concrete

SteelX

Y

φ 147

Gap 1.5

He duct

439

(J) Z=392.5∼414cm

Fig. 7 continued.

33

X

Y

He duct

Concrete

Steel

Shielding plug Concrete

φ 147

(K) Z=414∼430cm

X

YConcrete

He duct

φ 147

(L) Z=430∼511cm

Fig. 7 continued.

34

φ 174

X

Y

Steel plate

(M) Z=511∼528cm

X

Y

φ147

φ120

φ120

Iron igloo

(N) Z=528∼724cm

Fig. 7 continued.

35

X

Z

Z=0Weight x 0.5

n, p, π

80

60

40

Fig. 8 Schematic view of the target system calculation (layer (a) in Fig. 9).

015

020

051

125

0

600

600

200

250

300 p-800MeV

Shield top floor level

Estimator

(b)

(c)

(d)

centerUnit : cm

0

40

30

(a)

( j ) ( i )

～～

0120

724

Air Air

400

( i )( i )

( i )

Air

Bulkshield

Iron igloo andadditional shield area

X

Z

～～～～～～～～

Fig. 9Schematic view of the three-dimensional multi-layer calculation. Protons, neutrons andpions crossing outwards the layer boundaries are stored in a file with their energy, coor-dinates, directions and weight to be used as a source in the next layer calculation.

36

Up 300

Down 300

Down 400

Down 130

Up 130

Up 50

Down 50

Right 300Left 300 Left 130 Right 130

Right 50

Left 50

Center

Y

X

He duct

Up 75

(Beam direction)(Upstream)

(Downstream)

(a) Top view

Up 50

He duct

Z

X

Up 300

Down 300

Down 400

Down 130

Up 130

Down 50

Center

(Beam direction)

422.5

528.6

Y

Z

Right 300

Left 300

Left 130

Right 130

Right 50

Left 50

Center

422.5

528.6

(b) Side view (c)

Fig. 10Track length estimator locations. (a)∼(c) show the cross-sectional view of X-Y, X-Z andY-Z plane, respectively.

37

neutron trackIron Iglooair

estimator

concretebulk shield

additionaliron shield

steeldisk plates

X

Z

Fig. 11 Neutron track plots projected on the X-Z plane at layer (j) (Z>500cm).

1 : forward-duct2 : side-back

　2　　1　

X

Y

( Beam direction )

Fig. 12Graphical plots of recorded neutrons leaked at layer (b) calculation. Calculation oflayer (c) is carried out separately by using two different sources of “forward-duct”(1:green-region) and “side-back”(2:red-region).

38

layer (a)

layer (b)

layer (c)

layer (d)

layer (e)

layer (f )

layer (g )

layer ( h )

layer ( i )

layer (c' )

layer (d' )

layer (e' )

layer (f ' )

layer (g' )

layer ( j )iron

layer ( j )air

leak

side-backleak

forward-ductleak

leak

leak

leak

leak

leak

leak

leak

leak

leak

leak

leak

leak

layer (h' )

leak

"side-back""forward-duct"

layer ( j )air

layer ( j )concrete

layer ( j )concrete

layer ( j )iron

Fig. 13Flow chart of a step-by-step calculation. Right-lane indicates “side-back” calculation andleft-lane indicates “forward-duct” calculation. Three calculations were carried out usingsame source particles leaked from layer (i) at “side-back” and those from layer (h’) at“forward-duct”, respectively.

39

layer(a) layer(b)

layer(c) layer(d)

layer(e) layer(f)

Fig. 14Cross-sectional view of layers in the multi-layer calculation (X-Z plane), which are usedin “side-back” calculation.

40

layer(g) layer(h)

layer(i) layer(j)

Fig. 14 continued.

41

layer(c’) layer(d’)

layer(e’) layer(f’)

layer(g’) layer(h’)

Fig. 15Cross-sectional view of layers in the multi-layer calculation (X-Z plane), which are usedin “forward-duct” calculation.

42

100 101 102 10310-4

10-3

10-2

10-1

100

eye guide

12C(n, 2n)11C

Exp. (INS) Exp. (TIARA) Exp. (RIKEN)

Cross Section [barn]

Neutron Energy [MeV]Fig. 16Cross-section data of the measured 12C(n, 2n)11C reaction [12, 13] and eye guide alongthe data.

100 101 102 10310-4

10-3

10-2

10-1

100

27Al(n,α)24Na

Cross Section [barn]

Neutron Energy [MeV]Fig. 17Cross-section data of the 27Al(n, α)24Na reaction calculated by Fukahori using the ALICEcode [11].

43

101 102 10310-14

10-12

1x10-10

1x10-8

1x10-6

1x10-4

1x10-2

1x100

ENDF/B-VI

EXP(n,4n) (n,5n) x 10-1

(n,6n) x 10-2

(n,7n) x 10-3

(n,8n) x 10-4

(n,9n) x 10-5

(n,10n) x 10-6

Neutron Energy [MeV]

Cross Sectin

[barn]

Fig. 18Cross-section data of the 209Bi(n, xn)210−xBi (x=4∼10) reaction cited from ENDF/B-VIhigh-energy file [14] compared with the measured data [12].

44

10-10 10-9 10-8 10-7 10-6 1x10-51x10-4 10-3 10-2 10-1 100 101 102 103100

101

102

103

10-610-7 10-5

Flux-to-dose conversion factor [pSv cm 2

]

Neutron energy [MeV]

Fig. 19Neutron flux-to-dose conversion factor of the 1-cm depth dose equivalent cited from ICRPpub.74 [15].

45

101 102 10310-4

10-3

10-2

10-1

Neutron

Neutron leakage [sr-1 proton-1 lethargy-1]


MARS14(02) 0-30 deg 30-50 deg 50-70 deg 70-85 deg 85-95 deg 95-110 deg 110-140 deg 140-180 deg

(a)

101 102 10310-6

1x10-5

1x10-4

10-3

10-2

Proton

Proton leakage [sr-1 proton-1 lethargy-1]

Proton energy [MeV]

MARS14(02) 0-30 deg 85-95 deg 30-50 deg 95-110 deg 50-70 deg 110-140 deg 70-85 deg 140-180 deg

(b)

Fig. 20Angular and energy distributions of (a) neutron, (b) proton and (c) pion leakage from thetarget assembly surface calculated with MARS14 Monte Carlo code.

46

101 102 10310-8

10-7

10-6

1x10-5

1x10-4

π+, π−

Pion leakage [sr-1 proton-1 lethargy-1]

Pion energy [MeV]

MARS14(02) 0-30 deg 85-95 deg /50 30-50 deg /5 95-110 deg /100 50-70 deg /10 110-140 deg /200 70-85 deg /20 140-180 deg /1000

(c)

Fig. 20 Continued.

47

10-9 1x10-7 1x10-5 1x10-3 1x10-1 1x101 1x103102

103

104

105

106

107

108

109

1010

1011

1012

1013

Center

Neutron fluence [n cm-2 Coulomb-1 lethargy-1]


x = 0 cm y = 0 cm

z = 80.5 cm z = 182.5 cm z = 257.5 cm z = 322.5 cm z = 422.5 cm z = 528.6 cm

(a)

Fig. 21Calculated neutron energy spectra in the bulk shield and above the shield top at variouspositions; (a) center, (b) left50, (c) right50, (d) up50, (e) down50, (f) left130, (g) right130,(h) up130, (i) down130.

48

1x10-7 1x10-5 1x10-3 1x10-1 1x101 1x103102

103

104

105

106

107

108

109

1010

1011

1012

1013

10-9

left 50



x = 0 cm y = -50.0 cm


1x10-7 1x10-5 1x10-3 1x10-1 1x101 1x103102

103

104

105

106

107

108

109

1010

1011

1012

1013

10-9

right 50



x = 0 cm y = 50.0 cm


(b) (c)

10-9 1x10-7 1x10-5 1x10-3 1x10-1 1x101 1x103102

103

104

105

106

107

108

109

1010

1011

1012

1013

up 50



x = -50.0 cm y = 0 cm


1x10-7 1x10-5 1x10-3 1x10-1 1x101 1x103102

103

104

105

106

107

108

109

1010

1011

1012

1013

10-9


down 50


x = 50.0 cm y = 0 cm


(d) (e)

Fig. 21 continued.

49

1x10-7 1x10-5 1x10-3 1x10-1 1x101 1x103102

103

104

105

106

107

108

109

1010

1011

1012

1013

10-9

left 130



x = 0 cm y = -130.0 cm


1x10-7 1x10-5 1x10-3 1x10-1 1x101 1x103102

103

104

105

106

107

108

109

1010

1011

1012

1013

10-9

right 130



x = 0 cm y = 130.0 cm


(f) (g)

1x10-7 1x10-5 1x10-3 1x10-1 1x101 1x103102

103

104

105

106

107

108

109

1010

1011

1012

1013

10-9

up 130



x = -130.0 cm y = 0 cm


1x10-7 1x10-5 1x10-3 1x10-1 1x101 1x103102

103

104

105

106

107

108

109

1010

1011

1012

1013

10-9

down 130



x = 130.0 cm y = 0 cm


(h) (i)

Fig. 21 continued.

50

1x10-281x10-261x10-241x10-221x10-201x10-181x10-161x10-141x10-12

1x10-281x10-261x10-241x10-221x10-201x10-181x10-161x10-14

0 100 200 300 400 500 600 7001x10-30

1x10-28

1x10-26

1x10-24

1x10-22

1x10-20

1x10-18

1x10-16

Air

Air gap and steel plate

Concrete(2.3 g/cm3)

Steel(7.35 g/cm3)

Void

12C(n,2n)

center left50 (x10-2) right50 (x10-4) up50 (x10-6) down50 (x10-8)

AirConcrete(2.3 g/cm3)

Steel(7.35 g/cm3)

Void

left130 right130 (x10-2) up130 (x10-4) down130 (x10-8)


Steel(7.35 g/cm3)

Void

Reaction rate [atom-1 Coulomb-1]

Distance from the target [cm]

left300 right300 (x10-2) up300 (x10-4) down300 (x10-6) down400 (x10-8)

Fig. 22Attenuation profiles of the 12C(n, 2n)11C reaction rate estimated from the calculatedneutron energy spectra through the bulk shield at various positions shown in Fig. 10.

51

1x10-5

10-3

10-1

101

103

105

107

109

1x10-4

10-2

100

102

104

106

108

0 100 200 300 400 500 600 70010-6

1x10-4

10-2

100

102

104

106

Neutron dose rate

Air gap and steel plate

center left50 (x10-2) right50 (x10-4) up50 (x10-6) down50 (x10-8)

AirVoid

Steel(7.35 g/cm3)

Concrete(2.3 g/cm3)

left130 right130 (x10-2) up130 (x10-4) down130 (x10-8)

Dose rate [ µSv Coulomb-1]

Air

Concrete(2.3 g/cm3)

Steel(7.35 g/cm3)

Void


Steel(7.35 g/cm3)

Void

Distance from the target [cm]

left300 right300 (x10-2) up300 (x10-5) down300 (x10-6) down400 (x10-8)

Fig. 23Attenuation profiles of the neutron dose rate estimated from the calculated neutron energyspectra through the bulk shield at various positions shown in Fig 10.

52

0 100 200 300 400 500 600 700 800 900 1000

10-21

10-20

10-19

10-18

10-17

1x10-16

10-15

1x10-14

1x10-13

1x10-12

1x10-11

MARS calculation

Shield topfloor level

Distance from the target center [cm]

Target vessel

3rd leg

2nd leg

1st leg

Through the He-duct

12C(n,2n)11C


0 100 200 300 400 500 600 700 800 900 1000102

103

104

105

106

107

108

109

1010

1011

thermal20MeVCut-off

Shield topfloor level

Target vessel

3rd leg

2nd leg

1st leg

Inside the He-duct

MARS calculation Nakamura and Uwamino's formula

Neutron dose rate [ µSv Coulomb-1]

Distance from the target center [cm]

Fig. 24Attenuation profiles of the 12C(n, 2n)11C reaction rate (upper figure) and dose rate (lowerfigure) through the He-duct estimated from the calculated neutron energy spectra, whichis relatively compared with the attenuation curve of Nakamura and Uwamino’s formura.

53

1x10-7 1x10-5 1x10-3 1x10-1 1x101 1x10310-5

10-4

10-3

10-2

10-1

100

101

102

103

104

105

106

107

10-9

528cm above the target

(558cm above the target) x 10-6

(588cm above the target) x 10-3

floor + iron 30cm

floor + concrete 60cm

Shield top floor

Neutron flux [n cm-2 Coulomb-1 lethargy-1]


Cal. Exp.

Fig. 25Comparison between the calculated and measured neutron energy spectra on the shieldtop floor, behind the additional concrete and iron shields at “center” position.

54

-140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 120 14010-28

10-27

10-26

10-25

1x10-24

1x10-23

10-22

1x10-21

1x10-20

1x10-19Exp. Cal.□○△▽◇■●▲▼◆

air (no additional shield)

120cm(x10-6)

100cm(x10-5)

80cm(x10-4)

60cm(x10-3)

40cm(x10-2)

20cm(x10-1)

0cmfloor

rightcenterleftIron iglooIron igloo

Distance from shield top center [cm]


Fig. 26Comparison between the calculated and measured 12C(n, 2n)11C reaction rates above theshield top without an additional shield (air) along the left-right axis (Y-axis).

55

-140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 120 14010-28

10-27

10-26

10-25

1x10-24

1x10-23

10-22

1x10-21

1x10-20

1x10-19

Cal.Exp. □○△▽◇■●▲▼◆

80cm(x10-4)

120cm(x10-6)

100cm(x10-5)

60cm(x10-3)

40cm(x10-2)

20cm(x10-1)

0cmfloor


air (no additional shield)

Beam direction up downcenterIron igloo


Fig. 27Comparison between the calculated and measured 12C(n, 2n)11C reaction rates above theshield top without an additional shield (air) along the up-down axis (X-axis).

56

-140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 120 14010-28

10-27

10-26

10-25

1x10-24

1x10-23

10-22

1x10-21

1x10-20

1x10-19Cal.Exp. □○△▽◇■●▲▼◆

120cm(x10-6)

100cm(x10-5)

80cm(x10-4)

60cm(x10-3)

40cm(x10-2)

20cm(x10-1)

0cmfloor

Iron igloo Iron igloocenter rightleft

concrete



Fig. 28Comparison between the calculated and measured 12C(n, 2n)11C reaction rates above theshield top behind the additional concrete shield along the left-right axis (Y-axis).

57

-140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 120 14010-28

10-27

10-26

10-25

1x10-24

1x10-23

10-22

1x10-21

1x10-20

1x10-19

Cal.Exp. □○△▽◇■●▲▼◆

120cm(x10-6)

100cm(x10-5)

80cm(x10-4)

60cm(x10-3)

40cm(x10-2)

20cm(x10-1)

0cmfloor

center

Concrete

up down Iron iglooBeam direction



Fig. 29Comparison between the calculated and measured 12C(n, 2n)11C reaction rates above theshield top behind the additional concrete shield along the up-down axis (X-axis).

58

-140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 120 14010-28

10-27

10-26

10-25

1x10-24

1x10-23

10-22

1x10-21

1x10-20

1x10-19Cal.Exp. □○△▽◇■●▲▼◆

120cm(x10-6)

100cm(x10-5)

80cm(x10-4)

60cm(x10-3)

40cm(x10-2)

20cm(x10-1)

0cmfloor

Iron iglooIron igloo

Iron

left center right



Fig. 30Comparison between the calculated and measured 12C(n, 2n)11C reaction rates above theshield top behind the additional iron shield along the left-right axis (Y-axis).

59

-140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 120 14010-28

10-27

10-26

10-25

1x10-24

1x10-23

10-22

1x10-21

1x10-20

1x10-19

Cal.Exp. □○△▽◇■●▲▼◆

120cm(x10-6)

100cm(x10-5)

80cm(x10-4)

60cm(x10-3)

40cm(x10-2)

20cm(x10-1)

0cmfloor

downcenterupBeam directionIron igloo

Iron



Fig. 31Comparison between the calculated and measured 12C(n, 2n)11C reaction rates above theshield top behind the additional iron shield along the up-down axis (X-axis).

60

0 20 40 60 80 100 12010-22

1x10-21

1x10-2012C(n,2n)11C


Additional shield thickness [cm]

Cal. Exp. air concrete iron

Fig. 32Comparison between the calculated and measured attenuations of 12C(n, 2n)11C reactionrate above the shield top (air) and behind the additional concrete and iron shields at the“center” position.

61

0 20 40 60 80 100 12010-28

10-27

10-26

10-25

1x10-24

1x10-23

10-22

1x10-21

1x10-20

1x10-19

10-18Cal.□○△▽◇Exp.■●▲▼◆

Bi(n,10n)(x 10-6)

Bi(n,9n)(x 10-5)

Bi(n,8n)(x 10-4)

Bi(n,7n)(x 10-3)

Bi(n,6n)(x 10-2)

Bi(n,5n)(x 10-1)

Bi(n,4n)

Concrete

Reaction Rate [atom-1 Coulomb-1]

Shield Thickness [cm]

Fig. 33Comparison between the calculated and measured attenuations of 209Bi(n, xn)210−xBi(x=4∼10) reaction rate behind the additional concrete shield at the “center” position.

62

0 10 20 30 40 50 6010-28

10-27

10-26

10-25

1x10-24

1x10-23

10-22

1x10-21

1x10-20

1x10-19

10-18Cal.Exp. □○△▽◇■●▲▼◆

Bi(n,10n)(x 10-6)

Bi(n,9n)(x 10-5)

Bi(n,8n)(x 10-4)

Bi(n,7n)(x 10-3)

Bi(n,6n)(x 10-2)

Bi(n,5n)(x 10-1)

Bi(n,4n)

Iron

Reaction Rate [atom-1 Coulomb-1]

Shield Thickness [cm]

Fig. 34Comparison between the calculated and measured attenuations of 209Bi(n, xn)210−xBi(x=4∼10) reaction rate behind the additional iron shield at the “center” position.

63

0 20 40 60 80 100 120100

101

102

103

104

Exp. Cal. Concrete Iron (x 10-2)

Dose rate [

µSv Coulomb-1]

Additional shield thickness [cm]

Fig. 35Comparison between the calculated and measured attenuations of neutron dose rate be-hind additional concrete and iron shields at the “center” position.

64

Appendix

A User subroutines

The user subroutines of the MARS code modified in this work are listed here. The blockdata, which include files and subroutines which were newly created in this study, are alsolisted and open to the public.

A.1 Source particle generation (BEG1)

Subroutine BEG1 is a source particle generator which defines the type of particle, kineticenergy, initial weight, position and vector. In the following subroutine, information aboutleaked particles (LEAK1.INP) in the previous layer calculation is read, and the corre-sponding weights are estimated using Eq. (1). The calculation is separated into severalbatches in this case to estimate the standard deviation of the result.

C-----------------------------------------------------------------SUBROUTINE BEG1(JJ,W,E,X,Y,Z,DCX,DCY,DCZ,TOFF,INTA,NREG1)

C-----------------------------------------------------------------IMPLICIT DOUBLE PRECISION (A-H,O-Z), INTEGER (I-N)LOGICAL IND

INCLUDE ’azwmat.inc’INCLUDE ’biount.inc’INCLUDE ’blreg1.inc’INCLUDE ’cmasnsg.inc’

* INCLUDE ’tally2.inc’include ’spc.inc’

COMMON/MATINT/IM: /LOGIND/IND(20): /BLZTAG/ZORIG,PHIT,XHIT,YHIT,ZHIT,JHIT: /BG/E0,ELEAK(3),ELGA,ELEN,ELEAMU,ENEUNO,ALIO(3),BLEAK(3,2): /BLTOFF/TOFMIN,TOFMAX,TOFSHF: /SELEC2/CS,SS,CH,SH: /HIST/NI,NSTOP,NUPRI,NHIPR

data NENTER/0/save NENTER

data ncount/0/data mcount/0/

save wa,w_avedata ns/0/

if (NENTER.eq.0) thenNENTER=1

c*************************************************open(7,file="LEAK1.INP")open(61,file=’HISTRY’)

65

c*************************************************write(*,13)write(61,13)

13 format(/’Reading Souce Particles ....’)

wtot=0.0d0ns=0read(7,*) NSTOP_pre

12 READ(7,100,END=10)jj,x,y,zp,dcx,dcy,dcz,e,wwtot=wtot+wns=ns+1goto 12

10 rewind(7)read(7,*) NSTOP_prewa=DBLE(ns)/DBLE(NSTOP_pre)w_ave=wtot/DBLE(NSTOP_pre)write( *,11)NSTOP_pre,ns,wa,w_avewrite(61,11)NSTOP_pre,ns,wa,w_ave

11 format(’Previous calculation No. 1’,/& ’ source particle =’,i10/& ’ leakage particle =’,i10/& ’ weight correction =’,1pe10.3/& ’ average weight =’,1pe10.3//)

ENDIF

c****************************************************c Calculation startc Forward leak sourcec****************************************************

200 READ(7,100,END=201) jj,X,Y,Z,DCX,DCY,DCZ,e,w

w=w*wa ! weightncount=ncount + 1

if (ncount.ge.NSTOP/20) thenwrite(*,*) NI,NSTOPwrite(61,*) NI,NSTOPncount=0

endif

100 format(i1,0p3f6.1,0p3f6.3,1p2e9.2)

c**** count batch number *********************************if ((mcount.eq.0).or.(mcount.ge.NSTOP/nbat +1)) then

kbat=kbat+1 ! batch numbermcount=1 !

end ifmcount=mcount+1

c**********************************************************

RETURN201 rewind(7)

read(1,*)goto 200END

66

A.2 Leak particle storing (LEAK)

Subroutine LEAK handles particles which escape from the calculation system. In thisstudy, a boundary of the system is defined in subroutine XYOUT (A.4) for each shieldlayer. If the particles leak from the system, this subroutine is called and the information ofthe particle is written in the file of LEAK1.OUT, which is read in subroutine BEG1 (A.1)in the next new layer calculation. Following is an example used in the shield layer (c).

C------------------------------------------------------------SUBROUTINE LEAK(N,K,JJ,W,E,X,Y,Z,DCX,DCY,DCZ,TOFF)

C------------------------------------------------------------C PARTICLES LEAKAGE SPECIAL SCORINGC JJ= 1 2 3 4 5 6 7 8 9 10 11 12C P N PI+ PI- K+ K- MU+ MU- GAM E- E+ APCC REVISION: 01-JUN-2001CC---------------------------------------------------------

IMPLICIT DOUBLE PRECISION (A-H,O-Z), INTEGER (I-N)

INCLUDE ’blreg1.inc’INCLUDE ’cmasnsg.inc’

COMMON: /HIST/NI,NSTOP,NUPRI,NHIPR: /BLZTAG/ZORIG,PHIT,XHIT,YHIT,ZHIT,JHITcommon /isis7/xy_data(4)

data xy_data/ 280.0d0, 0.0d0, 200.0d0, 40.0d0 /

PARAMETER (CLIGHT=29979245800.D0)C---------------------------------------------------------


open(58,file="LEAK1.OUT")

if (jj.gt.4)return ! select only p,n,pi+,pi-

if (NENTER.eq.0)thenwrite(58,*) NSTOPNENTER=1

end if

rr = sqrt(x**2 + y**2)if ( z.le.xy_data(2)) returnif (rr.gt.6.0d2) returnif ( z.gt.8.0d2) return

write(58,100) jj,x,y,z,dcx,dcy,dcz,e,w

100 format(i1,0p3f6.1,0p3f6.3,1p2e9.2)150 format(0p3f7.1)999 RETURN

END

67

A.3 Geometry and materials (REG1)

Subroutine REG1 defines the calculation geometry and materials. Although whole com-plete geometry of the ISIS target station is described in this subroutine, a boundary ofcorresponding shield layer is defined in XYOUT (A.4) which is called in the middle of thissubroutine. All regions are uniquely numbered as NON−STANDARD REGIONs whichare independent of the shield layer defined by subroutine XYOUT.

c---------------------------------------------------------------SUBROUTINE REG1(X,Y,Z,N,NIM)

c---------------------------------------------------------------IMPLICIT DOUBLE PRECISION (A-H,O-Z), INTEGER (I-N)

INCLUDE ’blreg1.inc’INCLUDE ’tally1.inc’include ’spc.inc’

C+++ Don’t touch !!! +++++++++++++++++PARAMETER (M_MAX1=M_MAX+1)CHARACTER*8 VNAME,VNAMEBUFDIMENSION IMUN(1:M_MAX1) ! buffer material indeciesDATA IMUN(M_MAX1)/0/,INCREM/1/DATA VNAMEBUF/’ ’/

C+++++++++++++++++++++++++++++++++++++


c 1: ’FE’ bulk steel (20MeV < En)c 2: ’CONC’ bulk concrete (20MeV < En)c 3: ’MIX1’ Tantalum + D2Oc 4: ’MIX2’ Container+ D2Oc 5: ’MIX3’ Be + D2Oc 6: ’MIX4’ Additional concrete (No cut-off)c 7 ’MIX5’ Additional iron (No cut-off)c 8: ’FE’ bulk steel (No cut-off)c 9: ’CONC’ bulk concrete (No cut-off)c 10: ’FE’ vacuum plate (No cut-off)c 11: ’FE’ iron igloo (No cut off)c 12: ’AIR’ (No cut-off)

DATA (IMUN(I),I=1,M_MAX)/# 1,1,8,9,2,12, !6 bulk shield# 0,5,4,3, !4 target vessel : void,Be,SUS,Ta# 2, !1 concrete above target vessel# 0,1,0, 0,1,0, 0,1,0,# 0,1,0, 0,1,0, 0,1,0,# 0,8,0, 0,9,0, 1,# !25 shielding plug# 10,12,10,10,12,10, !6 shield top steel plate# 11,12,6,7, !4 iron igloo, air, add-conc, add-iron# 0,0,0,0, !4 He duct (Bulk total 50)## 0,1,1,1,1,1,1,1,1,1,1,1,1,8,8,9,9,9,9,9,9,9,9,9,12,10,12,# 12,12,12,12,12,12,12,12,12,12,12,12,12,# ! 40 center

68

# 0,1,1,1,1,1,1,1,1,1,1,1,1,8,8,9,9,9,9,9,9,9,9,9,12,10,12,# 12,12,12,12,12,12,12,12,12,12,12,12,12,# ! 40 up50# 0,1,1,1,1,1,1,1,1,1,1,1,1,8,8,9,9,9,9,9,9,9,9,9,12,10,12,# 12,12,12,12,12,12,12,12,12,12,12,12,12,# ! 40 down50# 0,1,1,1,1,1,1,1,1,1,1,1,1,8,8,9,9,9,9,9,9,9,9,9,12,10,12,# 12,12,12,12,12,12,12,12,12,12,12,12,12,# ! 40 left50# 0,1,1,1,1,1,1,1,1,1,1,1,1,8,8,9,9,9,9,9,9,9,9,9,12,10,12,# 12,12,12,12,12,12,12,12,12,12,12,12,12,# ! 40 right50# 0,2,2,2,1,1,1,1,1,1,1,1,1,8,8,8,9,9,9,9,9,9,9,9,12,12,12,# 12,12,12,12,12,12,12,12,12,12,12,12,12,# ! 40 down120# 0,2,2,2,1,1,1,1,1,1,1,1,1,8,8,8,9,9,9,9,9,9,9,9,12,12,12,# 12,12,12,12,12,12,12,12,12,12,12,12,12,# ! 40 up120# 0,2,2,2,1,1,1,1,1,1,1,1,1,8,8,8,9,9,9,9,9,9,9,9,12,12,12,# 12,12,12,12,12,12,12,12,12,12,12,12,12,# ! 40 left120# 0,2,2,2,1,1,1,1,1,1,1,1,1,8,8,8,9,9,9,9,9,9,9,9,12,12,12,# 12,12,12,12,12,12,12,12,12,12,12,12,12,# ! 40 right120# 1,1,1,1,1,1,1,0,0,1,1,1,1,8,8,8,9,9,9,9,9,9,9,9,12,12,12,# 12,12,12,12,12,12,12,12,12,12,12,12,12,# ! 40 down300# 1,1,1,1,1,1,1,1,1,1,1,1,1,8,8,8,9,9,9,9,9,9,9,9,12,12,12,# 12,12,12,12,12,12,12,12,12,12,12,12,12,# ! 40 up300# 1,1,1,1,1,1,1,1,1,1,1,1,1,8,8,8,9,9,9,9,9,9,9,9,12,12,12,# 12,12,12,12,12,12,12,12,12,12,12,12,12,# ! 40 right300# 1,1,1,1,1,1,1,1,1,1,1,1,1,8,8,8,9,9,9,9,9,9,9,9,12,12,12,# 12,12,12,12,12,12,12,12,12,12,12,12,12,# ! 40 left300# 1,1,1,1,1,1,1,0,0,1,1,1,1,8,8,8,9,9,9,9,9,9,9,9,12,12,12,# 12,12,12,12,12,12,12,12,12,12,12,12,12,# ! 40 down400# 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,12,12,12# ! He duct# /

C- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -M=0VNAME=VNAMEBUF

IF(NENTER.EQ.0) THENCALL REG3NCELMX = NFZPEX+M_MAXNENTER=1IF(M_MAX.EQ.0) INCREM=-1IF(M_MAX.GT.0) THEN

INUG=1WRITE(*,*)’There are non-standard zones M_MAX= ’,M_MAXDO L=1,M_MAX,INCREM

MATIND(NFZPEX+L)=IMUN(L)VOLNM (NFZPEX+L)=VNAMEBUF

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END DO

NVTEST=1CALL VFAN(NVTEST,V)

ELSEINUG=0WRITE(*,*)’There are no non-standard zones in this run !’RETURN

END IFEND IF

C===================================================================C+++ INSERT YOUR NON-STANDARD ZONE NUMBER FINDING ALGORITHM HERE +++

M=0ioutflug=0call xyout(x,y,z,ioutflug)if (ioutflug.eq.1) return

x2y2=sqrt(x**2+y**2)z2y2=sqrt(z**2+y**2)

c ISIS bulk shield =======================================if (x2y2.lt.600.) then

if (z.lt.800.) M=6 ! voidif (z.lt.511.) M=5 ! bulk concrete

end if

if (x2y2.lt.500.) thenif (z.lt.511.) M=4 ! bulk concretif (z.lt.430.) M=3 ! bulk steelif (z.lt.394.) M=2 ! bulk steelif (z.lt. 80.) M=1 ! bulk steel

end if

nz=6

c target =========================================** target vessel

if (z.lt.130.) thenif (x2y2.lt.158) M=nz+1 ! void

endif** Be Reflector

if ((z.ge.-39.0).and.(z.lt.39.0))thenif (x2y2.lt.27.1) M=nz+2 ! Be + D2O

end if** target containor : SUS

if ((x.ge.-21.5).and.(x.le.21.5))thenif (z2y2.le.9.1) M=nz+3 ! SUS + D2O

end if** Ta target

if ((x.ge.-16.9).and.(x.le.16.9))thenif (z2y2.le.4.5) M=nz+4 ! Ta + D2O

end ifnz=nz+4

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c concrete above target vessel ==============================

if ((z.lt.204.).and.(z.gt.80.)) thenRR=(152.5-z)/0.4587

if (x2y2.ge.RR) thenif ((x2y2.lt.235.).and.(x2y2.gt.49)) M=nz+1 ! concrete

end ifend if

nz=nz+1

c shielding plug ==========================================

if ((z.lt.230.).and.(z.ge.130.))thenif (x2y2.lt.50.5) M=nz+1 ! voidif (x2y2.lt.49. ) M=nz+2 ! pulg steelif ((x2y2.lt.12.5).and.(x2y2.gt.12.)) M=nz+3 ! void

end ifif ((z.lt.269.5).and.(z.ge.230.))then

if (x2y2.lt.50.5) M=nz+4 ! voidif (x2y2.lt.49. ) M=nz+5 ! plug steelif ((x2y2.lt.15.5).and.(x2y2.gt.15.)) M=nz+6 ! void

end if

if ((z.lt.271.).and.(z.ge.269.5))thenif (x2y2.lt.50.5) M=nz+7 ! voidif (x2y2.lt.49. ) M=nz+8 ! plug steelif ((x2y2.lt.15.5).and.(x2y2.gt.15.)) M=nz+9 ! void

end ifif ((z.lt.291.).and.(z.ge.271.))then

if (x2y2.lt.63 ) M=nz+10 ! voidif (x2y2.lt.61.5) M=nz+11 ! plug steelif ((x2y2.lt.15.5).and.(x2y2.gt.15.)) M=nz+12 ! void

end ifif ((z.lt.392.5).and.(z.ge.291.))then

if (x2y2.lt.63 ) M=nz+13 ! voidif (x2y2.lt.61.5) M=nz+14 ! pulg steelif ((x2y2.lt.18.5).and.(x2y2.gt.18.)) M=nz+15 ! void

end if

if ((z.lt.394.).and.(z.ge.392.5))thenif (x2y2.lt.75. ) M=nz+16 ! voidif (x2y2.lt.61.5) M=nz+17 ! pulg steelif ((x2y2.lt.18.5).and.(x2y2.gt.18.)) M=nz+18 ! void


if (x2y2.lt.75. ) M=nz+19 ! voidif (x2y2.lt.73.5) M=nz+20 ! plug steelif ((x2y2.lt.18.5).and.(x2y2.gt.18.)) M=nz+21 ! void


if (x2y2.lt.75. ) M=nz+22 ! voidif (x2y2.lt.73.5) M=nz+23 ! plug concreteif ((x2y2.lt.26.5).and.(x2y2.gt.26.)) M=nz+24 ! void

end if

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c flange on void vessel ===================================

if ((z.lt.130.).and.(z.ge.126.))thenif (x2y2.lt.50.5 ) M=nz+25 ! steel

end ifnz=nz+25

c shield top steel plate ==================================

if ((z.lt.514.).and.(z.ge.511.)) thenif (x2y2.lt.87.) M=nz+1 ! steelif (x2y2.lt.75.) M=nz+2 ! void

end if

if ((z.lt.520.).and.(z.ge.514.)) thenif (x2y2.lt.87.) M=nz+3 ! steel

end if

if ((z.lt.524.).and.(z.ge.520.)) thenif (x2y2.lt.87.) M=nz+4 ! steelif (x2y2.lt.60.) M=nz+5 ! void

end if

if ((z.lt.527.6).and.(z.ge.524.)) thenif (x2y2.lt.87.) M=nz+6 ! steel

endif

nz=nz+6

c iron igloo ==============================================if ((z.lt.724.).and.(z.gt.527.6))then

if ((x2y2.lt.120.).and.(x2y2.gt.60)) M=nz+1 ! steelif ((x.lt.-44).and.(x.gt.-120))then

if(abs(y).lt.40) M=nz+2 ! voidend if

end if

** additional shield (concrete)

c if ((z.lt.648.).and.(z.gt.527.6))thenc if (x2y2.le.60) M=nz+3 ! concretec end if

** additional shield (iron)cc if ((z.lt.588.).and.(z.gt.527.6))thenc if (x2y2.le.60) M=nz+4 ! ironc end ifc

nz=nz+4

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c-------------------------------------------c He ductc-------------------------------------------

if ((z.lt.511.).and.(z.gt.307.5)) thenif ((x.lt.481.5).and.(x.gt.439.)) then

if (abs(y).lt.21.25) M=nz+1end if

end if

if ((z.lt.307.5).and.(z.gt.265.)) thenif ((x.lt.481.5).and.(x.gt.130.)) then


end if

if ((z.lt.265.).and.(z.gt.127.5)) thenif ((x.lt.172.5).and.(x.gt.130.)) then


end if

if ((z.lt.127.5).and.(z.gt.85.)) thenif ((x.lt.172.5).and.(x.gt.53.)) then


end if

nz=nz+4

c============================================c detector (estimator)c============================================

do i=1,ndat1iii=i*5-4Rxy=sqrt((x - det_data(iii+1))**2+(y - det_data(iii+2))**2)if ((z.ge.det_data(iii+3)).and.(z.le.det_data(iii+4)))then

if (Rxy.le.det_data(iii)) thenM=nz+i ! detector

end ifend if

end do

1000 continueC===================================================================

IF(M.GT.0) THENN = NFZPEX+MVOLNM (N)=VNAME

ELSE IF(M.LT.0) THEN ! Non-standard blackholeN = M

END IF

RETURNEND

73

A.4 Geometry boundary definition (XYOUT)

Subroutine XYOUT was originally created in this work to define the layer boundary. Thissubroutine is called in the middle of REG1 (A.3). Following is an example used in theshield layer (e).

C-----------------------------------------------------------subroutine xyout(x,y,z,ioutflug)

C-----------------------------------------------------------IMPLICIT DOUBLE PRECISION (A-H,O-Z), INTEGER (I-N)

x2y2=sqrt((x - 60.0d0)**2 + y**2)

if (x2y2.gt.380.0d0) thenioutflug=1return

end if

if (z.lt.200.0d0) thenioutflug=1return

end if

if (z.gt.300.0d0) thenioutflug=1return

end if

returnend

74

A.5 Estimator (MFILL)

Subroutine MFILL stores track lengths of particles in the required regions in this case.A variable STEP is track length in each calculation step. STEP×W, which indicatesEq. (2), is stored in SPC array of corresponding bins of energy, region and batch number.

C-----------------------------------------------------------------------SUBROUTINE MFILL(IHTYP,NREG,IM,JJ,E1,E2,DELE,W,X1,Y1,Z1,X2,Y2,Z2,

& DCX,DCY,DCZ,STEP,TOF,NI)C-----------------------------------------------------------------------

IMPLICIT DOUBLE PRECISION (A-H,O-Z), INTEGER (I-N)

c***********************include ’spc.inc’data mcount/0/data kbat/1/

c***********************

c********************************************************do j=1,ndat1

if (nreg.eq.NR(j)) thenJNR=jgoto 990

end ifend doreturn

990 continuec********************************************************

if (IHTYP.ne.2) return ! Track-lengthif (JJ.ne.2) return ! only neutron

do i=1,nEBif ((E1.ge.EBIN(i-1)).and.(E1.le.EBIN(i))) then

SPC(i,JNR,kbat) = SPC(i,JNR,kbat) + STEP * Wgoto 222

end ifend do

c********************************************************333 format(i2,1p7E11.3,2I4,1p3E11.3)222 continue

RETURNEND

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A.6 Output the neutron energy spectra (SPCOUT)

Subroutine SPCOUT was originally created in this work for writing the estimator volumeand the energy spectra of each batch in the completion of the Monte Carlo calculation.This subroutine is called in the last line of marsmain.f.

c-------------------------------------------------subroutine spcout

c-------------------------------------------------IMPLICIT DOUBLE PRECISION (A-H,O-Z), INTEGER (I-N)COMMON /HIST/NI,NSTOP,NUPRI,NHIPRcommon /BLSEED/IJKLIN,NTOTIN,NTOT2N ! for seed

include ’spc.inc’open(97,file=’NFLUX_bat’) ! batch file

c***** output ****************************c For check the final seed number

call RM48UT(IJKLIN,NTOTIN,NTOT2N)c*****************************************

c***** batch *****************************************write(97,*)IJKLIN,NTOTIN,NTOT2N,’ --seed’write(97,422)NSTOP,NDAT1,nbat

do j=2,ndat1N=NR(j) ! Non-standard + standardcall VFAN(N,V)write(97,420)N,V

do i=1,nEBwrite(97,421)(SPC(i,j,k),k=1,nbat)

end doend do

c*****************************************************

420 format(i3,0pf10.1)421 format(1p10e10.3)422 format(i8,3x,i5,3x,i3,3x,"--NSTOP,NDET1,NBAT")

returnend

76

A.7 Data base file (SPC−DB)

Block data SPC−DB defines neutron energy boundaries for energy spectra.

C-------------------------------------------------------block data spc_db

C-------------------------------------------------------IMPLICIT DOUBLE PRECISION (A-H,O-Z), INTEGER (I-N)

include ’spc.inc’

data SPC/nEBDAT*0./data TOTSPC/ndat1*0/data AVEbin/mEBDAT*0/data ERR/mEBDAT*0/

data EBIN/ ! [GeV]& 1.00d-13, 4.14d-10, 1.12d-09, 5.04d-09, 2.26d-08,& 4.54d-07, 3.35d-06, 1.50d-05, 8.65d-05, 2.24d-04,& 4.98d-04, 9.07d-04, 1.35d-03, 2.02d-03, 3.01d-03,& 4.49d-03, 6.70d-03, 1.00d-02, 1.35d-02, 1.75d-02,& 2.25d-02, 2.75d-02, 3.50d-02, 4.50d-02, 5.50d-02,& 6.50d-02, 8.00d-02, 1.00d-01, 1.20d-01, 1.60d-01,& 2.00d-01, 2.50d-01, 3.00d-01, 3.50d-01, 4.00d-01& /

end

77

A.8 Parameters (SPC.INC)

This include file SPC.INC is called in the subroutines of BEG1, MFILL, REG1, SPCOUTand SPC−DB.

c*******************************c**** spc.inc ****************c*******************************

parameter (nGarea=50) ! number of Geometry areaparameter (ndat1=580) ! number of detecterparameter (nEB =34) ! number of energy binparameter (nbat =10) ! times of bat (default=10)parameter (nEBDAT=nEB*ndat1*(nbat+1))parameter (mEBDAT=nEB*ndat1)parameter (NDET5=ndat1*5)! number of detecter coardinatePARAMETER (M_MAX=nGarea+ndat1)PARAMETER (PI=3.141592653589793227D+00)

common /isis1/SPC(nEB,ndat1,0:nbat)common /isis2/NR(ndat1),det_data(NDET5)common /isis3/EBIN(0:nEB)common /isis4/

& AVEbin(nEB,ndat1),TOTSPC(ndat1),VV(ndat1),NSTOPS(ndat1),& det_vol(ndat1),iNR(ndat1),ERR(nEB,ndat1)common /isis5/

& XsecIn1(nEB),XsecIn2(nEB),XsecIn3(nEB),XsecIn4(nEB),& XsecIn5(nEB),XsecC(nEB) ,XsecAl(nEB) ,XsecIn(nEB) ,& Xsec4Bi(nEB),Xsec5Bi(nEB),Xsec6Bi(nEB),Xsec7Bi(nEB),& Xsec8Bi(nEB),Xsec9Bi(nEB),Xsec10Bi(nEB)common /isis6/kbat

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Deep-Penetration Calculationpeace99.web.fc2.com/KEKreport2002-12.pdf · for the ISIS Target Station Shielding Using the MARS Monte Carlo Code ... A calculation of neutron penetration

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