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
40 4.86E – 20 5.89E – 20 1.21 4.18E – 20 5.05E – 20 1.21 2.53E – 20 2.80E – 20 1.1160 2.86E – 20 3.62E – 20 1.27 2.60E – 20 3.07E – 20 1.18 1.63E – 20 1.78E – 20 1.0980 2.01E – 20 2.06E – 20 1.03 2.59E – 20 1.61E – 20 0.62 1.08E – 20 8.89E – 21 0.83
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
40 2.30E – 20 2.21E – 20 0.96 1.42E – 20 1.33E – 20 0.94 9.49E – 21 1.04E – 20 1.1060 1.40E – 20 1.41E – 20 1.01 9.33E – 21 8.73E – 21 0.94 5.75E – 21 6.94E – 21 1.2180 9.98E – 21 7.80E – 21 0.78 8.73E – 21 5.14E – 21 0.59 5.51E – 21 4.14E – 21 0.75
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]
Neutron energy [MeV]
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]
Neutron energy [MeV]
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
Neutron energy [MeV]
Neutron fluence [n cm-2 Coulomb-1 lethargy-1]
x = 0 cm y = -50.0 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
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
Neutron energy [MeV]
Neutron fluence [n cm-2 Coulomb-1 lethargy-1]
x = 0 cm y = 50.0 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
(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
Neutron energy [MeV]
Neutron fluence [n cm-2 Coulomb-1 lethargy-1]
x = -50.0 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
1x10-7 1x10-5 1x10-3 1x10-1 1x101 1x103102
103
104
105
106
107
108
109
1010
1011
1012
1013
10-9
Neutron fluence [n cm-2 Coulomb-1 lethargy-1]
down 50
Neutron energy [MeV]
x = 50.0 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
(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
Neutron energy [MeV]
Neutron fluence [n cm-2 Coulomb-1 lethargy-1]
x = 0 cm y = -130.0 cm
z = 80.5 cm z = 182.5 cm z = 257.5 cm z = 322.5 cm z = 422.5 cm z = 512.5 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
Neutron energy [MeV]
Neutron fluence [n cm-2 Coulomb-1 lethargy-1]
x = 0 cm y = 130.0 cm
z = 80.5 cm z = 182.5 cm z = 257.5 cm z = 322.5 cm z = 422.5 cm z = 512.5 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
Neutron energy [MeV]
Neutron fluence [n cm-2 Coulomb-1 lethargy-1]
x = -130.0 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 = 512.5 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
Neutron energy [MeV]
Neutron fluence [n cm-2 Coulomb-1 lethargy-1]
x = 130.0 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 = 512.5 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)
AirConcrete(2.3 g/cm3)
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
AirConcrete(2.3 g/cm3)
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
Reaction rate [atom-1 Coulomb-1]
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]
Neutron energy [MeV]
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]
Reaction rate [atom-1 Coulomb-1]
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
Distance from shield top center [cm]
air (no additional shield)
Beam direction up downcenterIron igloo
Reaction rate [atom-1 Coulomb-1]
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
Distance from shield top center [cm]
Reaction rate [atom-1 Coulomb-1]
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
Reaction rate [atom-1 Coulomb-1]
Distance from shield top center [cm]
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
Distance from shield top center [cm]
Reaction rate [atom-1 Coulomb-1]
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
Distance from shield top center [cm]
Reaction rate [atom-1 Coulomb-1]
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
Reaction rate [atom-1 Coulomb-1]
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---------------------------------------------------------
data NENTER/0/save NENTER
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+++++++++++++++++++++++++++++++++++++
data NENTER/0/save NENTER
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
69
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
70
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
end ifif ((z.lt.414.).and.(z.ge.394.))then
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
end ifif ((z.lt.511.).and.(z.ge.414.))then
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
71
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
72
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
if (abs(y).lt.21.25) M=nz+2end if
end if
if ((z.lt.265.).and.(z.gt.127.5)) thenif ((x.lt.172.5).and.(x.gt.130.)) then
if (abs(y).lt.21.25) M=nz+3end if
end if
if ((z.lt.127.5).and.(z.gt.85.)) thenif ((x.lt.172.5).and.(x.gt.53.)) then
if (abs(y).lt.21.25) M=nz+4end if
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
75
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
78
Top Related