Shielding study of bremsstrahlung in bulk media with electrons part II: Spatial bremsstrahlung distribution in water, aluminum, iron and lead bombarded by 22 MeV electrons

NUCLEAR INSTRUMENTS

AND METHODS

151 ( 1 9 7 8 )

2 7 7 - 2 8 4 ; (~) N O R T H - H O L L A N D

P U B L I S H I N G CO.

SHIELDING STUDY OF BREMSSTRAHLUNG IN BULK MEDIA WITH ELECTRONS PART II: SPATIAL BREMSSTRAHLUNG DISTRIBUTION IN WATER, ALUMINUM, IRON AND LEAD BOMBARDED BY 22 MeV ELECTRONS TAKASHI NAKAMURA

Institute for Nuclear Study, University of Tokyo, Midori-cho, Tanashi, Tokyo, Japan and HIDEO HIRAYAMA

National Laboratory for High Energy Physics, Oho-machi, Tsukuba, lbaraki, Japan and KAZUO SHIN

Department of Nuclear Engineering, Kyoto University, Yoshida, Sakyo-ku, Kyoto, Japan Received 20 September 1977 The electron-photon cascade Monte Carlo code, TAURUS, was applied to calculate the spatial bremsstrahlung distribution in bulk medium exposed to 22 MeV electron beams. The calculated results are generally in good agreement with our experimental results for water, aluminum and iron systems measured with activation detectors. Based upon this calculation, the photon flux integrated above 1 MeV was represented in a simple analytical form as a function of space parameters. The coefficients of the analytical function were determined for water, aluminum, iron and lead, and their dependence on the atomic number of the medium was discussed about.

1. Introduction Various kinds of high energy electron accelerators have recently been used in practice for medical, industrial and scientific research applications. It is very important problem to protect mankind and instruments from a large amount of bremsstrahlung generating from a target bombarded by electrons. The space--energy distribution of bremsstrahlung in and through a bulk medium like a beam stop of the electron accelerator is especially important for the study of radiation shielding, residual activity and radiation damage of accelerator and target materials. Many works have been per-

formed on the depth--dose and the energy--deposition distributions due to thick-target bremsstrahlung, which are summarized in s o m e b o o k s l - 3 ) , but there were no papers on the space--energy distribution of photons produced due to direct electron incidence. We have recently published several papers on the spatial distributions of bremsstrahlung in water and water-iron4), aluminum and iron 5) bombarded by 22 MeV electrons measured with our new method of determining bremsstrahlung spectrum from the activities induced in detectors by various photo-nuclear reactions6-8). In this paper,

TABLE 1 Various experimental and calculated conditions

System Water Aluminum Iron Lead

Thickness (cm) 100 J0 18.5 15

Cross-section (cm) 80×60 100x60 80x60 30×30

a See text. b Re is the electron range in the system.

fmax a (cm) 30 30 30 15

Electron spectrum fig. fig. fig. fig.

2a 2b 2b 2b

Segment size 1/40 Re b 1/40 Re 1/30 Re 1/40 Re

History number 10 000 20 000 20 000 10 000 -30000

278

T. N A K A M U R A

those experimental results are compared with the Monte Carlo calculation by the TAURUS code and the dependence of spatial bremsstrahlung distribution to atomic number of the material has been pursued from this calculation.

2. Comparison between calculation and experiment 2.1 .DESCRIPTIONOF EXPERIMENT The spatial distributions of bremsstrahlung in water, aluminum and iron bombarded by 22 MeV electron beams were measured with photonuclear reactions of various activation detectors. The experimental arrangement is shown in fig. 1. The dimensions of water, aluminum and iron systems are shown in table 1. The activation detectors were set at several (r, z)-positions in each system, where r is the lateral distance from the electron beam axis and z the longitudinal distance from the front face of the medium. To reduce the contribution of the spurious bremsstrahlung radiation from the accelerating tube, the target end of the

et al.

tube was surrounded with the lead blocks as shown in fig. 1 only for the experiment of the water system. The incident electron beam has a broad energy spectrum having a peak at about 22MeV as shown in fig. 2. The electron energy spectrum is much broader for aluminum and iron experiments than for water experiment. The ),-ray activities of the detectors induced by brernsstrahlung were converted to the bremsstrahlung energy spectrum, $(E) by the LYRA unfolding code6). The experimental bremsstrahlung spectra were obtained in the energy ranges above 8 MeV for water and above 5.5 MeV for aluminum and iron, de-

(12

o 0.16

~ 0.12

.o

~

L

.=.,

•

D. -

?,;0: ,oi,

,,--rI ~0

, i

[

i

I

•

•e

no

•

• •e

•

i el i

6i u!, % . ' II • II=,', I atii,.~ , ~-20-d

I I

I •

I

UJ

i , :

, :

""-~Z

(a)

Aluminum

i.-,

•

j

•

r

•

• ".•j,~

L

-i

:

r

1/.

18 20 22 24 26 28 E l e c t r o n E n e r g y , MeV

16

r-13~I"','" ",

l=e ~ i

"15"

e~

a

30

( a ) Water I

*~8

I

1

1

I

I

I

24 MeV

26

28

10

--...~ Z

(b)

Iron 8 .<

25~-

25~=- 25-~25-~ r-

eU .5-------I

Lead shield (C)

0

Water L : Linear Accelerator,

D : Detector

Fig. 1. Experimental a r r a n g e m e n t s for water, a l u m i n u m a n d iron slabs.

16

18 20 22 Electron E n e r g y , (b)

Aluminum

and

Iron

Fig. 2. Incident electron energy spectra for water, a l u m i n u m and iron experiments.

279

S H I E L D I N G STUDY OF B R E M S S T R A H L U N G IN BULK M E D I A , PART II

pending on the different kinds of activation detectors used in these three experiments. 2.2. ENERGY SPECTRUM

The bremsstrahlung energy spectrum was calculated from eq. (7) in part I, taking account of the energy spectrum of the incident electron beam (see fig. 2). Figs. 3-5 show the calculated bremsstrahlung spectra at representative (r, z)-positions in water, aluminum and iron, respectively. In the figures, is shown each one example of the experimental spectrum which is in good agreement with the absolute value of the calculated result. One can clearly see good agreement of the spectrum shapes between experiment and calculation for all three systems. The energy spectra become soft through penetrating these systems due to the photon energy degradation by Compton scattering. The larger the atomic number of the medium Z is, the more rapidly the photon attenuates in it, since the photon absorption by photoelectric effect is proportional to = Z 5 . Let us take up a point in the

system on the electron beam axis and not so far from the beam incident point, i.e. z = 10 cm for water and z = 1 cm for AI and Fe in figs. 3--5. The photon spectra at these points are considered to be almost equal to the thick-target bremsstrahlung spectra without scattering, and the spectrum shapes become softer and their absolute values larger from water to iron. 2.3. LATERAL FLUX DISTRIBUTION

The photon fluxes ~(r,z) at each (r,z)-position were obtained by integrating the bremsstrahlung spectra ~(E) above 8 MeV for water system and above 5.5 MeV for aluminum and iron systems. The lateral distributions of experimental and calculated photon fluxes ¢(r, z) are shown in figs. 6-8 as a function of lateral distance, r, at several axial depth, z in water, aluminum and iron. Fig. 6 clearly reveals that the agreement between experiment and calculation is very good in absolute values for water system. For aluminum, on the other hand, I

i+..,~ e"

x

Water -

162

Calculated

Calculated

-

I II Expem ri ena tl

I II Experimental (r.z)= (0,I0)

163

I

Au lmn ium

~> 6 ~

cwi

L" L

(r,z)= (0,1)

u

W

. ~ 104 E (r,z) __

l

= (5.29.30) cm

I~3 ,.

(r,z) = (1,762.10) cm

(

~

>,,, Ow C l.IJ

Th,

(r,z)=(1.5,50) • cm

,m %

165_

t-

-.0 1($+

q

0 ,,i:

IX, 166

10 t

0

I

5

10 15 20 Photon E n e r g y , MeV

25

Fig. 3. Comparison of calculated bremsstrahlung spectra at several (r, z)-positions in water with our experimental spectrum.

i+,0

,

5

C,10ul,+"-'1

U 20

25

Photon Energy, MeV Fig. 4. Comparison of calculated bmmsstrahlung spectra at several (r, z)-pesitions in aluminum with our experimental spectrum.

280

T. N A K A M U R A et al.

the experimental photon fluxes are about a factor 10 larger than the calculated ones at small (r, z)positions (z = 4, 10 cm and r = 4, 10 cm), but the agreement between experiment and calculation is rather good (a factor of 2-3) at (r, z)-positions away from the electron incident point (z = 20, 30 cm and r = 4 , 10, 18cm), as shown in fig. 7. This large discrepancy may be explained from the following reasons: 1) the target end of the accelerating tube was not shielded differently from the experiment of water system, then the spurious bremsstrahlung radiation from the tube injected into aluminum system can not be neglected; 2) the aluminum system was placed 35 cm away from the target end of the tube and the electron beam through the target end became spread when incident on the system, on the contrary to the calculational model which assumed a narrow electron beam; 3) with penetrating the aluminum system, the contribution of the spurious bremsstrahlung radiation and the electron beam spread beI

I

I

I

I

I

comes less important, because of the bremsstrahlung production and its multiple scattering in the system. The experimental photon fluxes are in good agreement with the calculated ones at small (r, z)-positions (z=l.9, 4.6cm and r=2, 6 cm) in the iron system but the former is about a factor 10 smaller than the latter at large (r,z)-positions (z=9.6, 15.4 cm and r=2, 6, 14cm) as shown in fig. 8, on the contrary to the aluminum experiment. The good agreement of experiment and calculation in the vicinity of the beam incident point may be attributed to the following facts: 1) the electron beam spread is relatively small, since the iron system was placed close to the target end of the accelerating tube (5 cm away from the end); 2) the attenuation coefficient of iron is much larger than that of aluminum, then the contribution of the spurious bremsstrahlung radiation incident to iron is small compared with the aluminum experiment. I

I

I

I

Iron

Catculated

Water

niL_

I

I

--- Experimental

-- Calcutate<1

16' C

161 -

~

2

(r,z)= (0ol)

u

@

16t

g E

(1.09,3)

II~5

=¢ Q-

(r,z) = (2,1.9) II

ehi~ ¢'-

L~

ii I

d-

&

I I~ I

Q.

16 ~

l1

( r , z ) = (3.26,185: cm

16 7

I 30 0

5

10 Photon

15 20 E n e r g y , MeV

25

3O

Fig. 5. Comparison of calculated bremsstrahlung spectra at several (r, z)-positions in iron with our experimental spectrum.

I 20

I 10

II

0

I 10

I 20

I 30

Lateral D i s t a n c e , r , cm Fig. 6. Comparison of calculated lateral distribution of photon fluxes integrated above 8 MeV in water with our experimental results.

S H I E L D I N G STUDY OF B R E M S S T R A H L U N G

I

I

1(~1~_

I

I

I

I

[cZm) Exp. Col.

Iron

il.9

--J~- --e-

4.6 C

--~-

--,=-

9.6 -,~--

o u

281

IN BULK M E D I A , PART 1I

15.4 --t~-- -o-

u

O u

u

J tl.I

UJ

,t II A Nq i..

I!

~k- /

-0-

30

20

10

0

10

20

30

Lateral Distance, r , cm Fig. 7. Comparison of calculated lateral distribution of photon fluxes integrated above 5.5 MeV in aluminum with our experimental results.

Unfortunately, it has not been explained until now that the experimental photon fluxes at distant positions from the beam incident point in iron give quite smaller values than the calculated ones. At large lateral distances r = 20, 30 cm in both aluminum and iron systems, the experimental data have large statistical errors due to small counting rates and include back-ground photons coming from room scattering to some extent. Generally speaking, the estimation of the spatial distribution of bremsstrahlung radiation in bulk media by the TAURUS calculation gives the good agreement with our experimental results except for some poor experimental data. 3. Dependence of spatial bremsstrahlung distribution to atomic number of material The spatial bremsstrahlung distributions in bulk media of water, aluminum, iron and lead were calculated in the photon energy range above 1 MeV by the TAURUS code which was confirmed to give its good estimation. In this calculation, it is assumed that an electron beam is narrow and has the energy spectrum shown in fig. 2a for water

30

20

10

0

10

20

30

Lateral Distance, r , cm Fig. 8. Comparison of calculated lateral distribution of photon fluxes integrated above 5.5 MeV in iron with our experimental results.

and in fig. 2b for aluminum, iron and lead, as listed in table 1. The history number and the segment siZe of the electron path settled in this calculation are also shown in table 1. These four materials commonly used as beam stopper and shield cover a wide range of atomic number from Z = 7 . 2 3 of water to Z = 8 2 of lead. The dimensions of water, aluminum and iron systems in this calculation were set to be equal to those in section 2 and the lead system was selected as 15cm in thickness and 3 0 × 3 0 c m 2 in area, as shown in table 1.

,4 ,'1

A r _

,4 ,4

,4 •

;

,4

Z

,4 ,4 ,4 A ,4 ,,4

Fig. 9. Schematic diagram of a relation between space parameters.

282

T. N A K A M U R A et al.

3.1. ANGULAR FLUX DISTRIBUTION To get more detailed information on the spatial bremsstrahlung distribution in a bulk medium, the photon flux O ( R , 0 ) w a s calculated and integrated above 1 MeV in the 0 direction at the transmission length R instead of ¢(r,z) integrated above 5.5 MeV and 8 MeV. The relation among R, 0, r and z is shown in fig. 9. Fig. 10 shows the calculated flux distribution multiplied by the square of the length R2,R 2 O(R, 0) as a function of R for water, aluminum, iron and lead. As shown in fig. 10, the quantity R 2 O(R, 0) obeys an exponential attenuation law having the same slope for every value of parameter 0 for these four meR ,cm

,p,,

,0

c

4, (R, 0) = C e - ~oR 2e-~'R

=,

I = " ~

,'_

J.

R ;~ Ro,

(l)

The values of ,a. and/z are shown in fig. 12 as a function of the atomic number Z. It is interesting that the value of p in cm2/g keeps almost constant from water to iron. Table 2 and fig. 12 also include the calculated values of ¢(Re, 0°) for these

o"

10 t

£

for

,

where R o = ~ 15 cm for water, = ~, 4 em for A1, = ~, 1 em for Fe and Pb.

O"

a "¢'----...~

dja except in the vicinity of the beam incident point. The slope increases with the atomic number of the system as shown in table 2, due to the increase of the photon absorption cross-section. Fig. 11 shows the variation of R 2 ~(R, 0) at a certain position P with the angle 0. The value of Rp was fixed to 60 cm for water, 15 cm for AI and 6 cm for Fe and Pb, respectively, at which position R 2 ~ (R, 0) is subject to an exponential attenuation in fig. ]0. The figure clearly indicates also the exponential decrease of R 2 ~(R, 0) with 0, but the slope of the curve deoreases with increasing the atomic number of the system, Z as shown in table 2. From figs. 10 and l l , the angular photon flux distribution ~(R, 0) can be expressed as:

I

I

i

I

I

i

b-..

, 0:

'° 1,o.

--2

-e- Water

,°1-

,\\~ o~

I /

,,um,no

_

-~- Iron

~_.k'°"

1(~4

6O-

0

10

20 30 z,O R, cm Fig. 10. Calculated spatial distribution of photon fluxes integrated above ] MeV, ¢(R, 0), in water, aluminum, iron and lead as a function of R, where R is the distance from a beam incident point to a point in a medium: The R 2 ¢(R, 0) distribution is drawn for several values of parameter 0 in the figure.

1~ 0

i

i

i

i

i

i

10

20

30

40

50

60

e , degree Fig. 11. Calculated spatial photon distribution R 2 ¢(R, 0) at R = Rp in water, aluminum, iron and lead as a function of 0, where 0 is the polar angle from the beam axis: The value of Rp was adopted as 60 cm for water, 15 cm for aluminum, and 6 cm for iron and lead, as described in the text.

SHIELDING STUDY OF BREMSSTRAHLUNG IN BULK MEDIA, PART 11

283

TABLE 2 Coefficients of analytical representation fitted to spatial bremsstrahlung distribution System

Atomic number Z

~a (cm 2/g)

2a (rad)- I

ad (cm2/g)

Initial electron range Re (cm)

7.23 13 26 82

0.0256 0.0254 0.0281 0.0377

8.66 6.10 4.16 2.81

0.0268 0.0275 0.0312 0.0410

10 4.2 1.4 0.84

Water Aluminum Iron Lead

¢(Re, 0°)b (cmz electron)-

i

z

4.46 x 102.3 x 10- l 1.5 3.51

a The values of/~, ~ and = were obtained by least square fittin~t of the values of R z ¢(R, 0) in fig. 10. See text.

four materials, where Re is the range of 22 MeV electron as seen in table 2. The quantity ¢(Re, 0 °) is considered approximately to be the forward thick-target bremsstrahlung yield which increases with the atomic number Z. 3.2. LONGITUDINALFLUX DISTRIBUTION T h e longitudinal flux distribution 10

'1",

,,|

i

I

i

!

,

.

@(z) can

be

obtained by: ~(z) =

~Or a l l x

d~(R,O) 2nr dr,

(2)

w h i c h c o r r e s p o n d s to t h e p h o t o n n u m b e r a b o v e 1 M e V c r o s s i n g a circle o f r a d i u s rm, x n o r m a l to t h e e l e c t r o n b e a m axis. T h e @(z) d i s t r i b u t i o n s a l o n g t h e axial d e p t h z i n t e g r a t e d f r o m t h e ~ ( R , 0) 1~"

•

I

I

I

I

I

I

I

I

"~

Water

.

=

__

? E

v

U

1 O

¢

L.

¢,¢

20 4o 6o 8o ~

C,I SM

q

I

C

E

I

~0 20 3o Lead

I

u v

=[ ,6'

II

E

1q

-

--

I

,O4 ,Q

d

la:

* ,i|

I

I

I

l

I

AtomicNumber,

I I

ii~'

1o

Z

Fig. 12. Variation of ,a.,/~ in eq. (1), a~ in eq. (5) and ~ (Re, 0°) approximating the forward thick-target bremsstrahlung yield with the atomic number of the material.

o

t

,g

o

5

Axial Depth,z , cm

10

15

Fig. 13. Longitudinal distribution of photon fluxes, @(z) integrated from eq. (2) and eq. (4) for various rmsx values.

284

T. NAKAMURA et al.

values in fig. 10 are shown in fig. 13 for several rm.x values. In fig. 13, the 4,(z) distribution approaches to an exponential attenuation with increasing the rmax value, excluding at the point of z = 18.5 cm in iron owing to the poor statistics in the Monte Carlo calculation and at the points near the beam incident point. The distribution ¢,(z) is also possible to be obtained from eq. (1) as follows: ~(z) =

~

rl~ax

dp(R,O) 2~r d r , rmax e - A 0

---21rC

I

e-uR

R2

rdr,

for

R>Ro.

(3)

do

By using the relation R cos O=z from fig. 9"

where Zo~-Ro for water and aluminum and z0~3 cm for iron and lead. The value of at is shown in table 2 and increases with ~, 1.1/z,

(6)

from water to lead. 4. S u m m a r y

The spatial aistributions of bremsstrahlung in water, aluminum, iron and lead bombarded by 22 MeV electron beam were calculated by the electron-photon cascade Monte Carlo method. The photon flux ¢(R, 0) integrated above 1 MeV in the 0 direction to the beam axis and at the distance R from the beam incident point to the point concerned can be represented by the following analytical form:

Omx

• (z) = 2nC

I

e -~° e - ' / c ' ° tan 0 dO,

(4)

~(R,O) = C e'-~ e-"~

Rz

do

where r2ax q- Z 2

•

io o ~ ( R , O) 2nr dr oc e - = ,

R > Ro.

Then the longitudinal flux distribution ¢~(z), which is the total photon number crossing a plane normal to the beam axis, is obtained as

In fig. 13, the ¢~(z) values calculated from eq. (4) are shown for three rmax values for these four systems. The first rm~x value is fixed to the largest value among them used in the q,(z) calculation by eq. (2) in order to compare both ¢,(z) results and the second rmax is fixed to the dimension of the system used in this research ?r,ax which is listed in table 1, and the third one is infinitive. The ¢~(z) values for rmax=fma~ and rm,x = oo are almost equal together in fig. 13, except for water system, which means that the system sizes of aluminum, iron and lead used in this research are considered to be infinitive. The good agreement between two ¢,(z) values from eq. (2) and eq. (4) can be seen for R > R o in fig. 13, except for z = 18.5 cm in iron. When rmx is infinitive, ¢,(z) is the total photon number above 1 MeV crossing a plane normal to the beam axis and is found from fig. 13 as: • (z) =

,

z > Zo,

(5)

[*~/2

• (z) = 2 1 r C l 30 oC e - ~ ,

e -~° e -~/°°'° tan0 dO, z > zo .

References F. H. Attix, W. C. Roesch and E. Tochillin, Radiation dosimetry, 2nd ed., vol. 3 (Academic Press, New York, 1969). 2) H. W. Patterson and R. H. Thomas, Accelerator health physics (Academic Press, New York, 1973). 3) W. P. Swanson, Radiological safety aspects of the operation of electron linear accelerators, IAEA, Vienna (1975). 4) T. Nakamura, T. Nishimoto and H. Hirayama, J. Nucl. Sci. Technol. 14 (1977) 31. 5) H. Hirayama and T. Nakamura, Nucl. Instr. and Meth. 133 (1976) 355. 6) H. Hirayama and T. Nakamura, Nucl. Sci. Eng. 50 (1973) 248. 7) T. Nakamura and H. Hirayama, Nucl. Sci. Eng. 59 (1976) 237. s) H. Hirayama and T. Nakamura, Nucl. Instr. and Meth. 147 (1977) 563. 1)