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A new calculation of dose rates from high energy electrons and photons incident on 30 cm water slabs
NUCLEAR
INSTRUMENTS
AND
METHODS
78 0970)
333-334;
©
NORTH-HOLLAND
PUBLISHING
CO.
A N E W CALCULATION OF D O S E RATES F R O M HIGH ENERGY ELECTRONS A N D P H O T O N S INCIDENT ON 30 em WATER SLABS H. L. BECK Health and Safety Laboratory, U.S. Atomic Energy Commission, New York, N. Y. 10014~ U.S.A.
Received 20 October 1969 Dose rates are calculated, accounting for the density effect correction to the electron stopping power. Lower values are obtained than heretofore reported.
A l s m i l l e r a n d M o r a n 1) h a v e p u b l i s h e d M o n t e C a r l o electron-photon shower calculations of energy deposited ( d o s e rate in r a d / h ) in 30 c m w a t e r slabs. M o r e r e c e n t w o r k 2'3) has i n d i c a t e d t h a t t h e i r c a l c u l a t i o n s are high, u p to 3 5 % for 1 G e V e l e c t r o n i n i t i a t e d s h o w e r s at s m a l l d e p t h s . T h i s w a s a t t r i b u t e d to t h e i r o m i s s i o n o f a d e n s i t y effect c o r r e c t i o n in t h e f o r m u l a e f o r t h e electron stopping power. I h a v e r e c a l c u l a t e d t h e d o s e rates in 30 c m w a t e r slabs d u e to i n c i d e n t h i g h e n e r g y p h o t o n s a n d e l e c t r o n s f r o m 100 M e V to 20 G e V using a r e c e n t l y d e v e l o p e d M o n t e C a r l o c o d e 4) w h i c h i n c l u d e s t h e d e n s i t y effect
c o r r e c t i o n . T h e results o f t h e s e c a l c u l a t i o n s are g i v e n in t a b l e 1. T h i s c o d e neglects c h a n g e s in d i r e c t i o n d u e to e l e c t r o n s c a t t e r i n g but in a l m o s t all o t h e r respects is q u i t e s i m i l a r to a n d utilizes m a n y o f t h e f e a t u r e s o f t h e c o d e used by A l s m i l l e r a n d M o r a n . W h e n t h e s a m e p h y s i c a l effects are c o n s i d e r e d in b o t h codes, s i m i l a r results are o b t a i n e d . T h i s is s h o w n in t a b l e 2 w h e r e m y c a l c u l a t i o n s o f t h e t o t a l e n e r g y d e p o s i t e d in the entire 30 c m slab (i.e. in a c o l u m n 1 c m × 30 c m for a n o r m a l l y i n c i d e n t b r o a d b e a m o f 1 p a r t i c l e p e r cm 2 incident) are c o m p a r e d w i t h A l s m i l l e r a n d M o r a n ' s v a l u e s a n d e x a m p l e s are g i v e n o f c a l c u l a t i o n s o f e n e r g y
TABLE 1
Total energy deposited in 30 cm slabs of water by incident electrons and photons, comparison with Alsmiller and Moran.
TABLE 2 Dose rate in water from incident electrons and photons.
Incident electron energy (GeV)
0.1 0.2 0.5 1.0 5.2 10.0 20.0 Incident photon energy (GeV) 0.1 0.2 0.5 1.0 5.2 10.0 20.0
Deposited energy (MeV)
Dose rate averaged over depth interval 10-4 (rad/h)/(electron/cm2-sec) 0-5
5-10
10-15 15-20
1.29 1.33 1.38 1.41 1.50 1.54 1.57
1.32 1.38 1.46 1.53 1.65 1.70 1.76
1.31 1.44 1.60 1.73 1.95 2.00 2.08
0.10 0.13 0.13 0.12 0.16 0.18 0.14
0.25 0.32 0.32 0.35 0.43 0.44 0.42
0.36 0.46 0.53 0.60 0.68 0.71 0.73
1.27 1.50 1.73 1.98 2.32 2.36 2.52
0.47 0.59 0.75 0.82 0.96 1.02 1.06
Electron energy (GeV)
This work
This work omitting density effect
Alsmiller and Moran
0.100 0.200 0.500 1.00 5.20 10.0 20.0
65.2 74.9 87.7 98.0 115.0 119.8 127.6
-91.8 -125.7 158.7 169.8 --
72.8 92.4 111.0 124.9 160.0 174.2 195.1
Photon energy (GeV) 0.100 0.200 0.500 1.00 5.20 10.0 20.0
19.8 25,5 32.4 36.3 42.2 46,4 48,9
-25.7 -48.4 65.2 65.8 --
22.6 31.2 41.0 47.6 60.7 67.3 70.2
20-25 25-30cm 1.18 1.51 1.90 2.21 2.70 2.82 3.08
0.53 0.68 0.94 1.04 1.27 1.32 1.43
1.03 1.49 2.05 2.44 3.15 3.40 3.70
0.57 0.76 1.06 1.25 1.60 1.68 1.85
333
334
~. L. BaCK
deposition omitting the density effect. The differences in the last two columns o f table 2 are p r o b a b l y due to statistical fluctuations, since each calculation was carried out for only 1000 incident particles. The dose rates in table 1 are in some cases considerably lower than those originally published by Alsmiller and Moran2). It should also be noted that the calculated dose rates for incident 5.2 GeV electrons are considerably lower than the experimental values of Tesch4). This latter comparison, however, may be inappropriate due to the difficulty in interpreting Tesch's results which were with a bremsstrahlung contaminated electron beam and tissue equivalent material rather than with a clean monoenergetic 5.2 GeV electron beam and water.
The close agreement with recent experimental data of my calculations of energy deposition in water and aluminum slabs by incident 1 GeV electrons 3) suggests that the values given in table 1 are probably accurate to better than ___10%.
References 1) R. G. Alsmiller, Jr. and H. S. Moran, Nucl. Instr. and Meth. 58 (1968) 343. 2) R. G. Alsmiller, Jr. and H. S. Moran, ORNL-TM-2559 (1969); also Nucl. Sci. Eng., in press. 3) H. L. Beck, Nucl. Sci. Eng., in press. 4) H. L. Beck, USAEC Report HASL-213 (1969). 5) K. Tesch, Nukleonik 8 (1966) 264 (ORNL-TR-1250).
INSTRUMENTS
AND
METHODS
78 0970)
333-334;
©
NORTH-HOLLAND
PUBLISHING
CO.
A N E W CALCULATION OF D O S E RATES F R O M HIGH ENERGY ELECTRONS A N D P H O T O N S INCIDENT ON 30 em WATER SLABS H. L. BECK Health and Safety Laboratory, U.S. Atomic Energy Commission, New York, N. Y. 10014~ U.S.A.
Received 20 October 1969 Dose rates are calculated, accounting for the density effect correction to the electron stopping power. Lower values are obtained than heretofore reported.
A l s m i l l e r a n d M o r a n 1) h a v e p u b l i s h e d M o n t e C a r l o electron-photon shower calculations of energy deposited ( d o s e rate in r a d / h ) in 30 c m w a t e r slabs. M o r e r e c e n t w o r k 2'3) has i n d i c a t e d t h a t t h e i r c a l c u l a t i o n s are high, u p to 3 5 % for 1 G e V e l e c t r o n i n i t i a t e d s h o w e r s at s m a l l d e p t h s . T h i s w a s a t t r i b u t e d to t h e i r o m i s s i o n o f a d e n s i t y effect c o r r e c t i o n in t h e f o r m u l a e f o r t h e electron stopping power. I h a v e r e c a l c u l a t e d t h e d o s e rates in 30 c m w a t e r slabs d u e to i n c i d e n t h i g h e n e r g y p h o t o n s a n d e l e c t r o n s f r o m 100 M e V to 20 G e V using a r e c e n t l y d e v e l o p e d M o n t e C a r l o c o d e 4) w h i c h i n c l u d e s t h e d e n s i t y effect
c o r r e c t i o n . T h e results o f t h e s e c a l c u l a t i o n s are g i v e n in t a b l e 1. T h i s c o d e neglects c h a n g e s in d i r e c t i o n d u e to e l e c t r o n s c a t t e r i n g but in a l m o s t all o t h e r respects is q u i t e s i m i l a r to a n d utilizes m a n y o f t h e f e a t u r e s o f t h e c o d e used by A l s m i l l e r a n d M o r a n . W h e n t h e s a m e p h y s i c a l effects are c o n s i d e r e d in b o t h codes, s i m i l a r results are o b t a i n e d . T h i s is s h o w n in t a b l e 2 w h e r e m y c a l c u l a t i o n s o f t h e t o t a l e n e r g y d e p o s i t e d in the entire 30 c m slab (i.e. in a c o l u m n 1 c m × 30 c m for a n o r m a l l y i n c i d e n t b r o a d b e a m o f 1 p a r t i c l e p e r cm 2 incident) are c o m p a r e d w i t h A l s m i l l e r a n d M o r a n ' s v a l u e s a n d e x a m p l e s are g i v e n o f c a l c u l a t i o n s o f e n e r g y
TABLE 1
Total energy deposited in 30 cm slabs of water by incident electrons and photons, comparison with Alsmiller and Moran.
TABLE 2 Dose rate in water from incident electrons and photons.
Incident electron energy (GeV)
0.1 0.2 0.5 1.0 5.2 10.0 20.0 Incident photon energy (GeV) 0.1 0.2 0.5 1.0 5.2 10.0 20.0
Deposited energy (MeV)
Dose rate averaged over depth interval 10-4 (rad/h)/(electron/cm2-sec) 0-5
5-10
10-15 15-20
1.29 1.33 1.38 1.41 1.50 1.54 1.57
1.32 1.38 1.46 1.53 1.65 1.70 1.76
1.31 1.44 1.60 1.73 1.95 2.00 2.08
0.10 0.13 0.13 0.12 0.16 0.18 0.14
0.25 0.32 0.32 0.35 0.43 0.44 0.42
0.36 0.46 0.53 0.60 0.68 0.71 0.73
1.27 1.50 1.73 1.98 2.32 2.36 2.52
0.47 0.59 0.75 0.82 0.96 1.02 1.06
Electron energy (GeV)
This work
This work omitting density effect
Alsmiller and Moran
0.100 0.200 0.500 1.00 5.20 10.0 20.0
65.2 74.9 87.7 98.0 115.0 119.8 127.6
-91.8 -125.7 158.7 169.8 --
72.8 92.4 111.0 124.9 160.0 174.2 195.1
Photon energy (GeV) 0.100 0.200 0.500 1.00 5.20 10.0 20.0
19.8 25,5 32.4 36.3 42.2 46,4 48,9
-25.7 -48.4 65.2 65.8 --
22.6 31.2 41.0 47.6 60.7 67.3 70.2
20-25 25-30cm 1.18 1.51 1.90 2.21 2.70 2.82 3.08
0.53 0.68 0.94 1.04 1.27 1.32 1.43
1.03 1.49 2.05 2.44 3.15 3.40 3.70
0.57 0.76 1.06 1.25 1.60 1.68 1.85
333
334
~. L. BaCK
deposition omitting the density effect. The differences in the last two columns o f table 2 are p r o b a b l y due to statistical fluctuations, since each calculation was carried out for only 1000 incident particles. The dose rates in table 1 are in some cases considerably lower than those originally published by Alsmiller and Moran2). It should also be noted that the calculated dose rates for incident 5.2 GeV electrons are considerably lower than the experimental values of Tesch4). This latter comparison, however, may be inappropriate due to the difficulty in interpreting Tesch's results which were with a bremsstrahlung contaminated electron beam and tissue equivalent material rather than with a clean monoenergetic 5.2 GeV electron beam and water.
The close agreement with recent experimental data of my calculations of energy deposition in water and aluminum slabs by incident 1 GeV electrons 3) suggests that the values given in table 1 are probably accurate to better than ___10%.
References 1) R. G. Alsmiller, Jr. and H. S. Moran, Nucl. Instr. and Meth. 58 (1968) 343. 2) R. G. Alsmiller, Jr. and H. S. Moran, ORNL-TM-2559 (1969); also Nucl. Sci. Eng., in press. 3) H. L. Beck, Nucl. Sci. Eng., in press. 4) H. L. Beck, USAEC Report HASL-213 (1969). 5) K. Tesch, Nukleonik 8 (1966) 264 (ORNL-TR-1250).