Encyclopedia of Physical Science and Technology - Atomic and Molecular Physics 2001
2001-015 - International Atomic Energy Agency
Transcript of 2001-015 - International Atomic Energy Agency
JAERI-Tech2001-015
7 ? > h AftCD 2
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B * m =¥• u w % p/fJapan Atomic Energy Research Institute
319-1195
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This report is issued irregularly.
Inquiries about availability of the reports should be addressed to Research Information
Division, Department of Intellectual Resources, Japan Atomic Energy Research Institute,
Tokai-mura, Naka-gun, Ibaraki-ken, 319-1195, Japan.
© J a p a n Atomic Energy Research Institute, 2001
JAERI-Tech 2001-015
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JAERl-Tech 2001-015
Measurement of Two-dimensional Thermal Neutron Flux in a Water
Phantom and Evaluation of Dose Distribution Characteristics
Kazuyoshi YAMAMOTO, Hiroaki KUMADA, Toshiaki KISHI, Yoshiya TORII
and Yoji HORIGUCHI
Department of Research Reactor
Tokai Research Establishment
Japan Atomic Energy Research Institute
Tokai-mura, Naka-gun, Ibaraki-ken
(Received February 2, 2001)
To evaluate nitrogen dose, boron dose and gamma-ray dose occurred by neutron capture
reaction of the hydrogen at the medical irradiation, two-dimensional distribution of the thermal
neutron flux is very important because these doses are proportional to the thermal neutron
distribution.
This report describes the measurement of the two-dimensional thermal neutron
distribution in a head water phantom by neutron beams of the JRR-4 and evaluation of the dose
distribution characteristic. Thermal neutron flux in the phantom was measured by gold wire
placed in the spokewise of every 30 degrees in order to avoid the interaction. Distribution of the
thermal neutron flux was also calculated using two-dimensional Lagrange's interpolation
program (radius, angle direction) developed this time.
As a result of the analysis, it was confirmed to become distorted distribution which has
annular peak at outside of the void, though improved dose profile of the deep direction was
confirmed in the case which the radiation field in the phantom contains void.
Keywords: Two-dimensional Distribution, Boron Neutron Capture Therapy, JRR-4, Thermal
Neutron Flux Distribution, Water Phantom, Epithermal Neutron Beam, Void
Effectiveness, 2D Interpolation, Lagrange's Interpolation, Dosimetry
JAERI-Tech 2001-015
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JAERI-Tech 2001-015
Contents
1 Introduction 1
2 Out line of JRR-4 Neutron Beam Facility 1
3 Experiment Material and Method.- 2
4 Measurement and Analysis 3
4.1 /3 - y Coincidence Counting Method 3
4.2 Calculation of Thermal Neutron Flux from Au Detector 4
4.3 Development of Interpolation Method 7
4.3.1 Lagrange's Interpolation Polynomial for One-dimension 7
4.3.2 Lagrange's Interpolation Polynomial for Two-dimensions 8
5 Results 9
5.1 Depth Distribution 9
5.1.1 Case without the Void 9
5.1.2 Case within the Void 11
5.2 Two-dimensional Distribution 12
5.2.1 Case without the Void 13
5.2.2 Case within the Void 14
6 Consideration of Theramal-epithermal Mixed Ratio 14
7 Conclusion 15
Acknowledgment 17
References 18
IV
JAERI-Tech 2001-015
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JAERI-Tech 2001-015
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- 11 -
JAERI-Tech 2001-015
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JAERl-Tech 2001-015
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JAERI-Tcch 2001-015
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JAERI-Tcch 2001-015
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JAERI-Tcch 2001-015
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JAERI-Tech 2001-015
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JAERI-Tech 2001-015
1) H.Hatanaka and Y.Urano : Eighteen Autopsy Cases of Malignant Brain Tumors Treated by
Boron-Neutron Capture Therapy between 1968 and 1985,Boron-Neutron Capture Therapy for
Tumors, ed. H.Hatanaka, 1986, p381-416
m^^t^^-^mmmom^m ^ m®*?m±WiX, 1994,3) H.Kumada, Y.Torii, K.Saito, Y.Yamagushi, A.Matsumura, Y.Nakagawa, F. Sakurai : A
Development of Computation Dosimetry System for BNCT at JRR-4, abst. of Eight
International Symposium on Neutron Capture Therapy for Cancer. La Jolla, California, USA,
September 13 -18 abstract, 1998, p58
4) K.Yokoo, T.Yamado, F.Sakurai, T. Nakajima, N. Ohhashi and H. Izumo, A New Medical
Irradiation Facility at JRR-4, Advance in Neutron Capture Therapy Volume I, Medicine and
Physics, ed. B. Larsson, J. Crawford and R. Weinreich, 1997, p326-330
5) Y.Torii, T.Kishi, H.Kumada, K.Yamamoto, K.Yokoo, N.Ohhashi, F.Sakurai : BNCT
Irradiation Facility at JRR-4, JAERI-Conf 99-006, 1999, p228-231
6) mmmm, n^n-t^ nmm, w m *?$t#*, m m n ^ mmmx, rmsmwkim%ft:&0ffi%te#VZ&rp^mto&&ffi, JAERI-M 94-058, 1994
7) &*ffiH : Mi^E^fflMllC+tt^tf-AtSfK U*m?tl¥£t& Vol.38,No.8,1996,673-682
8) w\m:wmm&fctttzm\-^ttmvzffiffim7vY3-)), mm) ^ 19989) Y. Nakagawa and H. Hatanaka : Boron Neutron Capture Therapy, j . Neuro Oncol. 33, 1997,
105-115
10)L.E.Gaper,B.J.Fisher,D.R.Macdonald, D.V.Leber, E.C.Halperin, C.Jr.Shhold, J.G.Carincross :
Supratentorial Malignant Glioma : Patterns of Recurrence and Implications for External Beam
Local Treatment, Int. J. Radiat. Oncol. Biol. Phys. 17, 1989, pl347-1350
- 18 -
JAERI-Tech 2001-015
Table 1 Condition of neutron beam facility for the beam modes
12cm 33cm 8cm
TPS18cm 18cm 18cm
M (7cm (7cm 4} (7cmglOcnu 12cm, 15cm, 20cm
Table 2 Performance of the beams under free air condition
collimatorThermal Neutron
Beam Mode IThermal Neutron
Beam Mode IIepithermal
Neutron BeamMode
Thermal Neutron flux(n/cm2/sec)
10cm
1.7X109
5.3 X 10s
—
15cm
2.0 X109
6.5 X108
3.6 X108
gamma dose rate(Gy/h)
10cm
2.64
—
—
15cm
2.79
0.54
1.86
Cadmium Ratio
10cm
2.3
10.6
—
15cm
2.5
13.5
1.15
Table 3 Performance of neutron beams with 15cm coUimator
energyunit
Thermal NeutronBeam Mode I
Thermal NeutronBeam Mode II
epithermalNeutron Beam
Mode
Thermal flux~0.5eV
(n/cm2/sec)
2.0xl09
6.5X108
3.6X108
Epithermal flux0.5eV~ lOkeV
(n/cm2/sec)
9.0X108
3.2xl07
2.2xlO9
fast flux10keV~
(n/cm2/sec)
2.7xl07
6.2X105
9.5xl07
- 19 -
JAERI-Tech 2001-015
Table 4 The measurement condition for the thermal neutron flux
distribution in the
mode
themallthemallthemallthemallthemallthemallthemal2
epithermalepithermalepithermalepithermalepithermalepithermal
collimatorsize
10cm10cm12cm12cm15cm15cm15cm10cm10cm12cm12cm15cm15cm
phantom
Void
+-+-+--+-+-+-
date
1999.9.101999.8.202000.5.192000.4.271999.5.211999.3.261999.5.71999.9.171999.8.27
2000.10.302000.10.17
1999.7.91999.4.7
irradiation timeAu
60min60min60min60min60min60minGOmin60min60min60min60min60min60min
Au + Cd120min60min90min120min120min60min180min90min120min90min90min120min90min
thermall: Thermal Neutron Beam Mode I, thermal2: Thermal Neutron
Beam Mode II, epithermal: Epithermal Neutron Beam Mode
Table5 the maximum thermal neutron flux in the phantom
Beam Mode
Thermal Neutron Beam Mode I
Thermal Neutron Beam Mode II
Epithermal Neutron Beam Mode
collimatorsize
10cm
12cm
15cm
15cm
10cm
12cm
15cm
Void
+-+-+--+-+-+-
Peak Fluxn/cm2/sec4.27xlO9
5.17 xlO9
4.56xlO9
5.18xlO9
5.96 xlO9
5.89 xlO9
1.40 xlO9
2.44 xlO9
3.00 xlO9
2.78xlO9
3.44xlO9
3.77 xlO9
4.04 xlO9
surface fluxn/cm2/sec3.35 xlO9
3.97 xlO9
3.44 xlO9
3.89 xlO9
4.32 xlO9
4.28 xlO9
1.19 xlO9
6.36 xlO8
1.14 xlO9
1.19xlO9
1.21xlO9
1.52 xlO9
1.41 xlO9
peak/surface
1.271.301.331.331.381.381.183.842.632.342.842.482.86
The peak flux is calculated from 2D distribution with Lagrange's interpolation polynomial.
- 20 -
JAERI-Tcch 2001-015
Table6 Thermal neutron flux distributions on the phantom axis line
ModeCollimatorDepth(mm)0.0OE+003.00E+005.50E+001.05E+011.55E+012.05E+012.55E+013.05E+013.80E+014.80E+015.80E+016.80E+017.80E+018.80E+019.80E+01
th215cm
Void(-)1.19E+091.39E+091.29E+091.12E+099.45E+087.96E+086.57E+085.40E+083.92E+082.68E+081.73E+081.15E+087.68E+074.84E+073.41E+07
thl10cm
Void(-)3.97E+095.14E+094.94E+094.58E+094.01E+093.45E+092.92E+092.44E+091.85E+091.26E+098.35E+085.43E+083.55E+082.27E+081.49E+08
thl12cm
Void(-)3.89E+095.13E+095.08E+094.89E+094.46E+093.92E+093.39E+092.89E+092.26E+091.57E+091.05E+097.05E+084.66E+083.06E+081.98E+08
thl15cm
Void(-)4.28E+095.77E+095.66E+095.35E+094.87E+094.26E+093.74E+093.22E+092.47E+091.74E+091.19E+098.13E+085.82E+083.61E+082.39E+08
epi10cm
VoidQ1.14E+092.2E+09
2.44E+092.86E+092.96E+092.82E+092.60E+092.33E+091.89E+091.37E+099.46E+086.5E+08
4.33E+082.88E+081.89E+08
epi12cm
Void(-)1.21E+092.3E+09
2.69E+093.28E+093.44E+093.31E+093.04E+092.78E+092.26E+091.65E+091.17E+098.11E+085.45E+083.69E+082.4E+08
epi15cm
VoidQ1.41E+092.8E+09
3.25E+093.73E+094.03E+093.95E+093.75E+093.35E+092.87E+092.18E+091.59E+091.09E+097.56E+085.10E+083.40E+08
thl: Thermal Neutron Beam Mode I, th2: Thermal Neutron Beam Mode II,
epi: Epithermal Neutron Beam Mode
Table 7 Thermal Neutron Flux Distributions on The Phantom Axis Line
ModeCollimatorDepth(mm)0.00E+003.00E+008.00E+001.80E+012.55E+013.05E+013.55E+014.05E+014.55E+015.O5E+O15.55E+016.05E+016.80E+017.80E+018.80E+019.80E+01
thl10cm
Void(+)3.35E+093.99E+093.88E+093.70E+093.55E+093.50E+093.40E+092.97E+092.43E+091.96E+091.57E+091.26E+099.06E+085.78E+083.67E+082.32E+08
thl12cm
Void(+)3.44E+094.27E+094.19E+094.07E+093.96E+093.89E+093.83E+093.25E+092.65E+092.15E+091.75E+091.39E+091.01E+096.39E+084.08E+082.64E+08
thl15cm
Void(+)4.32E+095.33E+095.30E+095.17E+094.99E+094.90E+094.72E+094.08E+093.38E+092.75E+092.26E+091.80E+091.32E+098.65E+085.65E+083.69E+08
epi10cm
Void(+)6.36E+081.61E+091.87E+092.00E+092.05E+092.10E+092.16E+092.13E+091.99E+091.77E+091.53E+091.29E+099.87E+086.68E+084.41E+082.92E+08
epi12cm
Void(+)1.11E+092.19E+092.31E+092.51E+092.56E+092.59E+092.66E+092.66E+092.41 E+092.17E+091.82E+091.54E+091.15E+097.96E+085.23E+083.49E+08
epi15cm
Void(+)1.52E+092.81E+093.00E+093.19E+093.29E+093.25E+093.28E+093.22E+092.97E+092.65E+092.29E+091.94E+091.49E+091.02E+096.93E+084.44E+08
thl: Thermal Neutron Beam Mode I, th2: Thermal Neutron Beam Mode II,
epi: Epithermal Neutron Beam Mode
- 21 -
JAERI-Tech 2001-015
Table8 Maximum thermal neutron flux measured in the phantom
Beam Mode
Thermal Neutron Beam Mode I
Thermal Neutron Beam Mode II
Epithermal Neutron Beam Mode
collimatorsize
10cm
12cm
15cm
15cm
10cm
12cm
15cm
Void
+-+-+--+-+-+-
Peak Fluxn/cm2/sec4.27xlO9
5.17 xlO9
4.56x109
5.18xlO9
5.96 xlO9
5.89 xlO9
1.40 xlO9
2.44 xlO9
3.00 xlO9
2.78xlO9
3.44xlO9
3.77 xlO9
4.04 xlO9
Irradiationtime
78min64min73min64min56min57min
238min137minl l lmin120min97min88min83min
advantagedepth(mm)
57.539.658.445.158.144.333.772.756.373.658.372.362.2
The peak fluxes were calculated from 2D distribution with Lagrange's interpolation
polynomial.
- 2 2 -
JAERI-Tcch 2001-015
Fig. 1 JRR-4 neutron beam facility
- 23 -
CH3
c=oo
CH3
PMMA molecyle
• a
eE
1
F
E
i
= ]
I
]
]
1
1
i
i
t' 1!
1
240
Y////////////////////A7,
\ HIT
m
PMMA
Fig.2 The water Cylindrical phantom made of PMMA modeling the human head.
JAERI-Tech 2001-015
Fig.3 Gold wire as neutron detctor were arranged spokewise at the pitch of 30 degrees
in the phantom.
- 25 -
JAERI-Tech 2001-015
HighVoltageORTEC 478
output
HV
inputy
sig
pre AmpORTEC 113
outputV input
Spect.AmplifierORTEC 570
Uniplar output A.M/PC input
Timing SingleChan. Analyz.ORTEC 551
POS out
SealerORTEC 994Bch
/3 Ray AbsorberAl 3mmt
Plastic2inxt0.118in
Nal(Tl)3inx3in
V\
Source(0,7)
Photomultiplier
'oncidence UnitDRTEC 418A
output
SealerORTEC 996
HV
sig
HighVoltageORTEC 478
output
input \|/
pre AmpORTEC 113
outputyinput
Spect.AmplifierORTEC 570
A.1Uniplar output
VDC inputTiming SingleChan. Analyz.ORTEC 551
POS out
VSealerORTEC 994Ach
Fig. 4 /3 - 7 Coincidence System at JRR-4
1.3725198Au 2.696d
/».
02
Tt
r3
0.285
0.961
1.373
0.41180
0.67589
1.08769
\
98.6 " " ' '
0.025 ^
95.5%
1.06
0.23
4.27
1.0877
Fig. 5 Decay Scheme of Au-198
- 26 -
JAERI-Tech 2001-015
iht)2
Fig.6 The reactor power transition at JRR-4
ri+1
ri-1
Fig.7 The current region of calculation with the Lagrange's interpolation polynomial for two
dimensions as angular and radius. This interpolation technique were used to determine
the thermal neutron flux 2D distributions
- 27 -
JAERI-Tech 2001-015
0.6 0.8 1Current-Flux Ratio J / <t> (-)
1.2
Fig.8 Peak/Surface Flux Ratio in a Phantom (020cm) with
10cm collimator for pure thermal neutron beam
6.E+09
jj> 5.E+09
4.E+09
3.E+09|
1 2.E+09
v1.E+09
0.E+00
I 1
IB,
\
" • - t h i 10cm Void(-]—*—th1 12cm VoidC-]- • - t h i 15cm VoidH- Q - t h 1 10cm Void(+:—&~th1 12cm Void(+^-- O " th i 15cm Void(+:
k
20 40 60Depth from Phantom Surface (mm)
80 100
Fig.9 Distributions of thermal neutron flux on beam Axis in the phantom within/without a void
(0 40mm x L30mm) for thermal neutron beam mode I
- 28 -
JAERI-Tech 2001-015
2.0E+09
o<n
1.5E+09EocX3
§1.0E+09
4) 5.0E+08
0.0E+00
k- O t h 2 15cm Void(-)
o K > O n
20 40 60Depth from Pharitom Surface (mm)
80 100
Fig. 10 Distribution of thermal neutron flux on beam Axis in the phantom without a void for
thermal neutron beam mode II
5.0E+09
epi 10cm Void(-)epi 12cm Void(-)epi 15cm Void(-)
• epi 10cm Void(+)—A— epi 12cm Void(+)
0.0E+0020 40 60 80
Depth from The Phantom Surface(mm)100
Fig. 11 Distributions of thermal neutron flux on beam Axis in the phantom within/without a void
(040mm X L30mm) for epithermal neutron beam mode
- 29 -
JAERI-Tech 2001-015
1.0E+10
th1 10cm Void(-)th1 12cm Void(-)th1 15cm Void(-)th1 10cmVoid(+)
12cm Void(+)-thi 15cm Void(+)
1.0E+080 20 40 60
Depth from Phantom Surface(mm)80 100
Fig. 12 Distribution of thermal neutron flux on beam Axis in the phantom within/without a void
(0 40 X L30mm) for thermal neutron beam mode I (logarithmic scale)
1.0E+10
o4)
§
IEi.OE+08(0
<0
1.0E+07
-O-th2 15cm Void(-)
20 40 60Depth from Phantom Surface(mm)
80 100
Fig. 13 Distribution of thermal neutron flux on beam Axis in the phantom without a void for
thermal neutron beam mode II (logarithmic scale)
- 30 -
JAERI-Tech 2001-015
1.0E+10
o4>(0
N
u
EZ§ 1.0E+09
ID
z15
1.0E+08
V?/[/
~~*~epi 10cm Void(-)^ epi 12cm Void(-)
" • " " epi 15cm Void(-)- O - e p i 10cm Void(+)—A— epi 12cm Void(+)—O -epi 15cm Void(+)
20 40 60 80Depth from Phantom Surface(mm)
100
Fig. 14 Distribution of thermal neutron flux on beam Axis in the phantom within/without a void
(04OxL3Omm) for epithermal neutron beam mode (logarithmic scale)
- 31 -
JAERI-Tech 2001-015
epi 10cm Void(-)—A-epi 12cm Void(-)
epi 15cm Void(-)
40 60Depth from phantom surface (mm)
Fig. 15 Normalized distribution of thermalized neutron from epithermal neutron with the
epithermal neutron beam mode
1.2
q=
2
C
T3_NTo
th1 10cm Void(-)
th1 12cm Void(-)
•th1 15cm Void(-)
20 40 60Depth from phantom surface (mm)
80 100
Fig. 16 Normalized distribution of thermalized neutron from epithermal neutron with the thermal
neutron beam mode I
- 32 -
JAERI-Tech 2001-015
c15
4>N
0.1
0.01
9^ '
/
• epi 10cmVoid(-)—^~epi 12cm Void(-)—°— epi 15cm Void(-)
• • ^
'•.V V
20 40 60 80
Depth from phantom surface (mm)100
Fig. 17 Normalized distribution of thermalized neutron from epithermal neutron with the
epithermal neutron beam mode (logarithmic scale)
X
I
-a0)N
o
0.1
0.01
¥•-O- th1
—A-th1
- C ^ t h !
"•
10cm Void(-)
12cm Void(-)
15cm Void(-)
'"D
20 40 60Depth from phantom surface (mm)
80 100
Fig. 18 Normalized distribution of thermalized neutron from epithermal neutron with the thermal
neutron beam mode I (logarithmic scale)
- 33 -
JAERI-Tech 2001-015
50
45
40
?35
s 3 0
8 25QS20>
10
5
rr
W——
LA
v"n \ .
• a - th1 10cm Void(-)—A-th1 12cmVoid(-)- O - t h 1 15cmVoid(-0
- —
10 20 30 40 50 60 70Depth from phantom surface(mm)
80 90 100
Fig. 19 Nakagawa's physical dose profile using the thermal neutron beam mode I with the
assumption of boron concentration (28ppm)
50
45
40
?35
s 3 05S25QS200)
a. 15
10
0
f >\ \
\
rL
"" O^ > O O
10 20 80 90 10030 40 50 60 70Depth from phantom surface(mm)
Fig.20 Nakagawa's physical dose profile using the thermal neutron beam mode II with the
assumption of boron concentration (28ppm)
- 34 -
JAERI-Tech 2001-015
30 40 50 60 70Depth from phantom surface(mm)
Fig.21 Nakagawa's physical dose profile using the epithermal neutron beam mode with the
assumption of boron concentration (28ppm)
- 35 -
JAERI-Tech 2001-015
50
45
40
?35
s 3 0
S25Q
S20
a. 15
10
5
E h - * *
V
• a - t h 1 10cm Void(+)— 1—th1 12cm Void(+]- O - t h 1 15cmVoid(+
^ Q
10 20 30 40 50 60 70Depth from phantom surface(mm)
80 90 100
Fig.22 Nakagawa's physical dose profile of the void-in phantom using the thermal neutron beam
mode I with the assumption of boron concentration (28ppm)
50
45
- * - - > * - * - - \• • Or • epi 10cm Void(+!—&- epi 12cm Void(+!
epi 15cm Void(+!
10 30 40 50 60 70Depth from phantom surface(mm)
80 90 100
Fig.23 Nakagawa's physical dose profile of the void-in phantom using the epithermal neutron
beam mode with the assumption of boron concentration (28ppm)
- 36 -
7.0E+09
E£ 1.OE+09
0.0E+00
7.0E+09
'o 6.0E+09(A\
£ 5.0E+09
* 4.0E+09
3.0E+09-
ro
2.0E+09
1.OE+09
0.0E+00
i
;
\•
t v ^k% m
\\
Wc* tL , 0°
U I Z ^ U +3(
«SICj=tL, +6C
(f-AH±)
)°
20 40 60 80 100
Radius(mm)
0.0 20.0 40.0 60.0 80.0 100.0 120.0
Depth (mm)
25
Fig.24 the distribution of thermal neutron fluxes as function of radius and depth in the phantom with
a void using the thermal neutron beam mode I (with collimator size of 015cm)
JAERI-Tcch 2001-015
, - I -.. /[j Y -
Fig.25 Two-dimensional distribution of thermal neutron flux in the phantom with a void using
the thermal neutron beam mode I with collimator of $ 15cm, which were calculated with
the Lagrange's interpolation polynomial for two dimensions as angular and radius
4• ; ; ; : ; : : • • : ; : ,
: • ; : : : ; ; : ;
ifittrate
————
• • • : : : : : : ' :
Eglon+?• • • : • • • : • • ; ;
fesSi!!!!!!!!
torn)
• ^
-80 -60 -40 -20 O 20 40 60 80
Fig.26 Tumor or Void (cavity) region and infiltrate region of assumption
- 38
-80 -60 -40 -20 0 20 40 60 80
(a-1) 15cm collimator, Void(-)
-80 - 6 0 - 4 0 - 2 0 0 20 40 60 80
(a-2) 12cm collimator, Void(-)
-60 -40 -20 0 20 40 60 80
(b-1) 15cm collimator, Void(+)
-80 -60 -40 -20 0
(b-2) 12cm collimator, Void(+)
Fig.27(a) Two dimensional thermal flux distribution normalized by the peak flux for thermal neutron beam mode I, which were
calculated with the Lagrange's interpolation polynomial for two dimensions as angular and radius
>
2H
o
i /
o©
• ©00
ov©
-80 -60 -40 -20 0 20 40
(a-3) 10cm collimator, Void(-)
60 80 - 8 0 _60 -40 -20 0 20 40
(b-3) 10cm collimator, Void(+)
Fig.27(b) Two dimensional thermal flux distribution normalized by the peak flux for thermal neutron beam mode I, which
calculated with the Lagrange's interpolation polynomial for two dimensions as angular and radius
80
were
-80 -60 60-4O -20 0 20 40
(c-1) 15cm collimator, Void(-)
Fig.28 Two dimensional thermal flux distribution normalized by the peak flux for thermal neutron beam mode II with 15cm
collimator and Void(-), which were calculated with the Lagrange's interpolation polynomial for two dimensions as angular and
>m
2i
-80 -60 -40 -20 0 20 40 60 80(d-1) 15cm collimator, Void(-)
1°00
i
!
1
-80 -60~*""^40 "36 6 ^"^ 40 60 "^0
(d-2) 12cm collimator, Void(-)
-80 -60 -40 -20 0 20 40 60 80(e-1) 15cm collimator, Void(+)
' ( ' • , .
1°' |O
ER
I-
orr
too
23 ~40"" ™60-80 -60 -40 -20
(e-2) 12cm collimator, Void(+)
Fig.29(a) Two dimensional thermal flux distribution normalized by the peak flux for thermal neutron beam mode I, which were
calculated with the Lagrange's interpolation polynomial for two dimensions as angular and radius
-60 -40 -20 0 20 40 60
(d-3) 10cm collimator, Void(-)
80 -80 -60 -40 -20 0 20 40 60
(e-3) 10cm colhmator, Void(+)
80>m70
Fig.29(b) Two dimensional thermal flux distribution normalized by the peak flux for thermal neutron beam mode I, which were
calculated with the Lagrange's interpolation polynomial for two dimensions as angular and radius
I
t, f
: /
••'
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• ' . • • • " . ' , . . - - ' . " ' - • » " " • • • • • • . . ^
' '" '• ' -<" ' - " • : { : ' > - ^ C ; •• N \ N-.
' • ' - ' ' ' - . s " % s \ \ '• '
//%— -•• - -JSvC\\\\YV I
-80 -60 -40 -20 0 20 40 60 80 -80 -60 -40 -20 0 20 '10 60 SO -80 -60 -40 -20 0 20 40 60
-SO -60 -40 -20 0 20 40 60 80 -80 -60 -40 -20 O 20 <10 60 80 -80 -60 -40 -20 O 20 40 60 80
-80 -«) --1C'/JJ
60 80 -80 -60 -40 -20 O 20 40 60 80 -80 -60 -JO -20 0 20 40 60 80
Fig.3O Two-dimensional dose distributions as the function of thermal and epithermal irradiation mixed condition using the thermal
neutron beam mode (collimator 10cm) and the epithermal neutron beam mode (collirnator 10cm)
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