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7 ? > h AftCD 2

mM m&•# mm-ma

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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- 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

: /

••'

.Ut f

\ \ \

* s/ /

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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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