Radiation shielding of the sterilization installation based on gamma-radiating europium isitopes
The method of calculation of a radiation protection from a source of a gamma radiation including isotopes of europium-152 and europium-154 by activity 1.5 MCi everyone is presented. As a material of protection the iron, concrete and homogeneous mixture of iron ore and concrete was used. The way of...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
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Razsukovanyj, B.N. Mazilov, A.A. Mazilov, A.V. 2015-04-18T17:47:50Z 2015-04-18T17:47:50Z 2004 НазваниеRadiation shielding of the sterilization installation based on gamma-radiating europium isitopes / B.N. Razsukovanyj, A.A. Mazilov, A.V. Mazilov // Вопросы атомной науки и техники. — 2004. — № 5. — С. 72-77. — Бібліогр.: 7 назв. — англ. 1562-6016 PACS: 06.60.Wa, 87.50.N,P https://nasplib.isofts.kiev.ua/handle/123456789/80522 The method of calculation of a radiation protection from a source of a gamma radiation including isotopes of europium-152 and europium-154 by activity 1.5 MCi everyone is presented. As a material of protection the iron, concrete and homogeneous mixture of iron ore and concrete was used. The way of computation of radiation parameters necessary for performance of calculation of protection from nontraditional materials is shown. Представлено спосіб розрахунку радіаційного захисту від джерела гамма-випромінювання, що включає в себе ізотопи європій-152 і європій-154 активністю 1.5 МКи кожний. Як матеріал захисту використано залізо, бетон і гомогенна суміш залізної руди і бетону. Показано спосіб обчислення радіаційних параметрів, необхідних для виконання розрахунку захисту з нетрадиційних матеріалів. Представлен способ расчёта радиационной защиты от источника гамма-излучения, включающего в себя изотопы европий-152 и европий-154 активностью 1.5 МКи каждый. В качестве материала защиты использованы железо, бетон и гомогенная смесь железной руды и бетона. Показан способ вычисления радиационных параметров, необходимых для выполнения расчёта защиты из нетрадиционных материалов. The work is fulfilled under the support of STCU Project №1801. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Экспериментальные методы и обработка данных Radiation shielding of the sterilization installation based on gamma-radiating europium isitopes Радіаційний захист установки стерилізації на базі гамма-випромінюючих ізотопів європію Радиационная защита установки стерилизации на базе гамма-излучающих изотопов европия Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| title |
Radiation shielding of the sterilization installation based on gamma-radiating europium isitopes |
| spellingShingle |
Radiation shielding of the sterilization installation based on gamma-radiating europium isitopes Razsukovanyj, B.N. Mazilov, A.A. Mazilov, A.V. Экспериментальные методы и обработка данных |
| title_short |
Radiation shielding of the sterilization installation based on gamma-radiating europium isitopes |
| title_full |
Radiation shielding of the sterilization installation based on gamma-radiating europium isitopes |
| title_fullStr |
Radiation shielding of the sterilization installation based on gamma-radiating europium isitopes |
| title_full_unstemmed |
Radiation shielding of the sterilization installation based on gamma-radiating europium isitopes |
| title_sort |
radiation shielding of the sterilization installation based on gamma-radiating europium isitopes |
| author |
Razsukovanyj, B.N. Mazilov, A.A. Mazilov, A.V. |
| author_facet |
Razsukovanyj, B.N. Mazilov, A.A. Mazilov, A.V. |
| topic |
Экспериментальные методы и обработка данных |
| topic_facet |
Экспериментальные методы и обработка данных |
| publishDate |
2004 |
| language |
English |
| container_title |
Вопросы атомной науки и техники |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| format |
Article |
| title_alt |
Радіаційний захист установки стерилізації на базі гамма-випромінюючих ізотопів європію Радиационная защита установки стерилизации на базе гамма-излучающих изотопов европия |
| description |
The method of calculation of a radiation protection from a source of a gamma radiation including isotopes of
europium-152 and europium-154 by activity 1.5 MCi everyone is presented. As a material of protection the iron,
concrete and homogeneous mixture of iron ore and concrete was used. The way of computation of radiation
parameters necessary for performance of calculation of protection from nontraditional materials is shown.
Представлено спосіб розрахунку радіаційного захисту від джерела гамма-випромінювання, що включає в
себе ізотопи європій-152 і європій-154 активністю 1.5 МКи кожний. Як матеріал захисту використано залізо,
бетон і гомогенна суміш залізної руди і бетону. Показано спосіб обчислення радіаційних параметрів,
необхідних для виконання розрахунку захисту з нетрадиційних матеріалів.
Представлен способ расчёта радиационной защиты от источника гамма-излучения, включающего в себя
изотопы европий-152 и европий-154 активностью 1.5 МКи каждый. В качестве материала защиты
использованы железо, бетон и гомогенная смесь железной руды и бетона. Показан способ вычисления
радиационных параметров, необходимых для выполнения расчёта защиты из нетрадиционных материалов.
|
| issn |
1562-6016 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/80522 |
| citation_txt |
НазваниеRadiation shielding of the sterilization installation based on gamma-radiating europium isitopes / B.N. Razsukovanyj, A.A. Mazilov, A.V. Mazilov // Вопросы атомной науки и техники. — 2004. — № 5. — С. 72-77. — Бібліогр.: 7 назв. — англ. |
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2025-11-24T05:52:12Z |
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| fulltext |
RADIATION SHIELDING OF THE STERILIZATION INSTALLATION
BASED ON GAMMA-RADIATING EUROPIUM ISITOPES
B.N. Razsukovanyj, A.A. Mazilov, A.V. Mazilov
National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine
e-mail: Mazilov@kipt.kharkov.ua
The method of calculation of a radiation protection from a source of a gamma radiation including isotopes of
europium-152 and europium-154 by activity 1.5 MCi everyone is presented. As a material of protection the iron,
concrete and homogeneous mixture of iron ore and concrete was used. The way of computation of radiation
parameters necessary for performance of calculation of protection from nontraditional materials is shown.
PACS: 06.60.Wa, 87.50.N,P
INTRODUCTION
Among the methods used for radiation treatment
(sterilization) of diverse products there is application of
a radionuclide gamma-source with ultra-high activity as
a radiating means. In the process of realization of
similar projects one of the most important stages is the
selection of material and performing of calculations on
radiation shield providing the radiological protection of
personnel and population. The specialists of the NSC
KIPT are developing, under STCU support, physical
fundamentals of radiation technologies with the use of
gamma-sources on the base of europium isotopes. As a
radiation-protective material it is suggested to use in one
case iron, and in another case – homogeneous mixture
of iron ore and concrete (further: reinforced concrete) of
a density ρ = 4.0 g/cm3. In the world practice a similar
material for protection from photon irradiation is used
rather often due to the increased value of an effective
atomic number, as compared with conventional
concrete. However, up to the present, there are not any
universal data on radiation parameters constituting the
algorithm of calculation of a radiation shield made from
a similar material. It is explained by the variety of the
weight content of iron in the protective material.
The present work is continuation and supplement of
work [1] and gives the calculation of the radiation shield
and equivalent dose rate around the shield of a gamma-
source with defined geometrical dimensions composed
of isotopes europium-152 and europium-154, every
having an activity of 1.5 MCi. We consider two variants
of the upper shield: one from iron, and another from the
mixture of iron ore and concrete.
Besides, the side face and the side frontal shields
from the reinforced concrete-iron ore mixture are
considered. For calculations we have used the
interpolation of known literature data on radiation
parameters of iron and concrete as applied to the offered
project of the radiation shield geometry and design.
1. RADIATION SOURCE AND SHIELD
GEOMETRY
A gamma-radiation source represents two
rectangular plates of a height H=200 cm and a length
L=400 cm with the activity uniformly distributed over
the plane of every plate. It is conditioned by the isotopes
Eu-152 and Eu-154 each of which has the activity
Q=1.5.106 Ci. Thus, every plate acts as a radiation
source with the total energy spectrum of isotopes Eu-
152 and Eu-154 and corresponding partial gamma-
constants Kji. The total gamma-constant is equal to the
sum of total gamma-constants of Eu-152 and Eu-154
and the surface density of the activity is
./109,1
2
24 cmmCi
LH
Q ⋅==σ
In Table 1 given are the main energy gamma-lines of
the source Ei (MeV), partial gamma-constants Kji
(mrem∙cm2)/(g∙mCi) and the contribution of the partial
gamma-constant into the full gamma-constant
ni(%)=(Kji/∑Kji)∙100.
Generally speaking Kji has the dimensionality
(R∙cm2)/(h∙mCi). We have assumed that the exposition
dose of gamma-radiation equal to 1 R corresponds to
the equivalent dose equal to 1 rem, though in the
different literature data this coefficient is varying from
0.64 to 1.0.
Table 1. The energy spectrum and gamma-constants of the source [2]
Ei 1.405 1.277 1.210 1.110 1.085 1.007 0.998 0.963 0.875 0.866 0.725 0.720
Kji 1772 2772 127 709 754 926 757 736 630 288 857 41
ni 15.75 24.64 1.13 6.30 6.70 8.23 6.73 6.54 5.60 2.56 7.62 0.36
Ei 0.593 0.550 0.442 0.248 0.244 0.123 0.122
Kji 136 16 127 80 118 78 327 ∑ = 11251
ni 1.21 0.14 1.13 0.71 1.05 0.69 2.91 ∑ = 100
72 PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2004, № 5.
Series: Nuclear Physics Investigations (44), p. 72-77.
The geometry of the shield has the following form.
The sources, arranged in-series in the one plane at a
distance L1=300 cm from each other, are closed at the
top, in one case, by the iron plate of a thickness
Δ=45 cm (Fig. 1), and, in another case, by the
reinforced concrete plate of a thickness Δ=150 cm
(Fig. 2) in the arc form.
The lateral wall on the face side of plates (Fig. 3)
and on the frontal side (Fig. 4) is made from reinforced
concrete of a thickness Δ=150 cm.
All linear dimensions necessary for calculations are
indicated on the below-given figures.
Fig. 1. Upper shield from iron
Fig. 2. Upper arc-like shield from reinforced concrete
Fig. 3. Lateral face shield from reinforced concrete
Fig. 4. Lateral frontal shield from reinforced concrete
2. RADIATION PARAMETERS
In the general case of an extended source the dose
rate P at point A on the outside of the shield (Fig. 5) is
proportional to the integral (without taking into account
the self-absorption in the source):
( )( ) ,
|| 2
)(
rdrbB
r
eCP
rb
−
∫= (1)
where С is the proportionality coefficient; b=μx is the
dimensionless value equal to the length x (cm) of
radiation passage from the source element to the
observation point A in the shielding material and
expressed in lengths of a free path in this material; μ
(cm-1) is the linear factor of gamma-radiation
attenuation in the shielding material depending on the
atomic number of the shielding material Z and on the
radiation energy E; B(E,b,Z) is the dose factor of
accumulation taking into account the diffuse radiation in
the shielding material depending on the shield thickness
b, as well as, on the radiation energy and shielding
material Z; r is the radius-vector from the point A into
the source element (elementary volume, surface
element, length). Integration in Eq. (1) is performed
over the whole source.
Fig. 5. Geometry of the extended source and of the shield
The dose factor ( )( )rbВ
is a slowly changing
function as compared to the function 2)( ||/ re rb − and
therefore for practical calculations it is removed from
the sign of integration, however, we take into account
only its dependence on Е, b, Z.
For conventional shielding materials, e.g. iron and
concrete used in the project, in the literature one widely
presents the table data on the radiation parameters of the
linear attenuation coefficient of γ-radiation μ(Е,Z) and
on the dose factor of accumulation В(Е,b,Z). The values
of these data, in general, slightly differ from each other.
We have used for the parameter μ(Е,Z) the data of [2] ,
and for the parameter В(Е,b,Z) the data of [3].
Table 2 gives the values of gamma-lines of the
source energy-spectrum and the values of the parameter
μ (cm-1) interpolated by the energy for iron and
concrete.
Table 2. Values of the linear coefficient of attenuation for the source energy spectrum
Ei 1.405 1.277 1.210 1.110 1.085 1.007 0.998 0.963 0.875 0.866 0.725 0.720
μ(ir) 0.398 0.419 0.431 0.448 0.452 0.466 0.468 0.477 0.500 0.503 0.549 0.551
μ(concr.) 0.126 0.131 0.135 0.142 0.143 0.149 0.149 0.152 0.160 0.160 0.174 0.175
Ei 0.593 0.550 0.442 0.248 0.244 0.123 0.122
μ(ir.) 0.600 0.622 0.689 0.952 0.962 2.061 2.085
μ(concr.) 0.190 0.196 0.215 0.269 0.272 0.362 0.364
73
73
Comparison of the radiation parameters given in
Tables 1 and 2 shows that the major contribution into
the dose rate on the outside of the shield is made by two
gamma-lines of the spectrum: Е1=1.405 МeV and
Е2=1.277 МeV. Indeed, the linear coefficient of
attenuation µ increases considerably with energy
decreasing, and it means significant decrease of the
function ( )Ebе − at characteristic thicknesses of the shield
designed. Besides, gamma-lines of lower energies make
a lesser contribution into the dose rate at the expense of
low values of partial gamma-constants. At the same
time, the value of the dose factor of accumulation B in
the range of the energy spectrum of source gamma-
radiation increases much slowly than the decrease of the
first two factors (μ and ( )Ebе − ) [3].
So, in calculations of the dose rate on the outside of
the shield we will take into account only the first two
lines of the spectrum with energies Е1=1.405 MeV and
Е2=1.277 МeV and the radiation values and parameters
with indexes 1 and 2, used for calculations, will,
respectively, refer to these energies.
To determine the radiation parameters of reinforced
concrete it is necessary to know its effective atomic
number Zef. Let us consider reinforced concrete with a
density ρ=3.5 g/cm3 as a homogeneous mixture of two
components, namely, of iron (ρI=7.89 g/cm3) and
concrete (ρC=2.35 g/cm3), which, in turn, is a
homogeneous mixture of some elements with proper
effective atomic number ZC. The weight composition of
concrete (%) is taken [4] so: 0.56Н; 40.83О; 1.71Na;
0.24Mg; 4.56Al; 31.58Si; 0.12S; 1.93K; 8.26Ca; 1.22Fe.
The weight composition of reinforced concrete is
determined from the relation: (1–x)ρI+xρC=ρ, from
where we determine that the reinforced concrete
contains 79.2% of concrete and 20.8% of iron.
At our energies (Е1 and Е2) the main processes of
gamma-quantum interaction with material will be
photo-effect and Compton-scattering at which the
effective atomic number Z is determined by the formula
of [3]:
( ) 3
14
ii
4
ii ZaZaZ ∑∑ ⋅⋅= (2)
where ai is the weight fraction of the element (material)
with the effective atomic number Zi. Applying this
formula to concrete and reinforced concrete, we obtain
ZC=15; ZIC=20 respectively.
Using the data for μ1and μ2 from table 2 and
interpolating by the atomic number in the range ZC=15
and ZI=26 we obtain for concrete: μ1=0.182 cm-1 and
μ2=0.191 cm-1. We have interpolated not the linear
coefficients of attenuation, but the values independent
on the material density, i.e. the mass coefficient of
attenuation µ =μ/ρ.
To obtain the values of accumulation factors В1(b)
and В2(b) for reinforced concrete, the data of [3] for iron
and concrete were, at first, interpolated by the energy,
thus В1I(b) and В2C(b) were obtained. Then these values
were interpolated by the atomic number and the values
В1(b) and В2(b) were obtained. The results are given in
Table 3 where besides values В1I(b), В2I(b), В1C(b),
В2C(b), В1(b) and В2(b) shown are the values of
accumulation factors for the design thicknesses of the
shield: В1I and В2I at b1=μ1IΔ1=17.9; b2=μ2IΔ1=18.9, as
well as, В1 and В2 at b1=μ1Δ2=27.3 and b2=μ2Δ2=28.65.
Table 3. Dose factors B for iron, concrete and reinforced concrete for energies Е1=1.405 МeV and Е2=1.277 МeV
В Material b=10 b=15 b=17.9 b=18.9 b=20 b=25 b=27.l3 b=28.65 b=30
В1
Iron 13.2 22.0 27.8 - 32.0 43.2 - - 55.2
reinforced
concrete 14.6 24.0 - - 36.0 48.8 55.2 - 62.7
concrete 15.8 25.6 - - 39.4 53.5 - - 68.9
В2
Iron 14.0 23.7 - 32.5 34.9 47.4 - - 61.4
reinforced
concrete 15.8 27.1 - - 40.4 55.2 - 67.2 71.7
concrete 17.3 30.0 - - 44.9 61.7 - - 80.3
3. DOSE RATE ON THE OUTSIDE OF THE
SHIELD DESIGNED
It is absolutely clear, that the maximum dose rate on
the outside of the shield designed (see Fig. 1-4) is
expected at points A located on the shield surface above
the middle of the length of every plate (Fig. 1, 2), at a
level of the half-height of plates (Fig. 3) and against the
center of each of plates (Fig. 4).
It is important to note that the contribution of the
plates distant from the point A into the dose rate is
negligibly small as compared to the dose rate created by
the nearest plate. It is connected with that the radiation
from the distant plate must pass in the shield an
effective distance being larger approximately by a factor
of 1.4 than the distance passed by the radiation from the
nearest-to- point A plate. From Eq (1) it follows that at
characteristic values of shield thicknesses of the order of
b=20, the contribution of the distant plate will, at least,
less by a factor of е0.4b=3·103 than that of the nearest
one. This affirmation is valid for the cases of the upper
shield (Fig. 1, 2) and the lateral frontal shield (Fig. 4).
In the case of lateral face shield (Fig. 3), of course, the
contribution of both plates should be taken into account.
Besides below-given calculations of dose rates on
the outside of the shield designed, we have calculated
the shield thickness d providing the dose rate decreasing
up to the value not exceeding the limit established by
the normative documents of Ukraine in the field of
radiation protection [5,6]. In accordance with normative
documents, when designing the shield from the external
irradiation for places of probable personnel situation
74
(independently on the time of stay) it is necessary to
take into account the safety factor equal to 2. Thus, the
permissible dose rate behind the shield should be not
higher than the value Рd=0.6 mrem/h for the personnel
of category A.
Calculation of the shield thickness d for all four
cases was performed by the method of “competitive”
lines [7] that consists in the following. For every line of
the energy spectrum, the shield thickness providing a
required multiplicity of dose rate attenuation is
calculated. Among defined thicknesses the maximum
thickness dm (corresponding to the “main” energy line)
and the next one dk (corresponding to the “competitive”
energy line) are selected. For each of these thicknesses
the layer of half-attenuation Δ1/2=d/log2K=dln2/lnK is
determined, where K is the multiplicity of dose rate
attenuation equal to the relation of the dose rate, created
by the corresponding energy line in the absence of the
protection Рo, to the permissible dose rate Рd: K=P0/Pd.
From two obtained values of layers of half-attenuation,
Δ1/2m and Δ1/2k, the higher value is selected. Then with a
good approximation the final thickness should be found
from the relationships:
if dm - dk = 0, then d = dm + Δ1/2; (3а)
if dm - dk < Δ1/2, then d = dk + Δ1/2; (3b)
if dm - dk > Δ1/2, then d = dm. (3c)
In the energy spectrum of the source (Table 1)
without any calculations one can see that the
“competitive” lines are the lines E1=1.405 МeV and
E2=1.277 MeV. It still remains to calculate only the
corresponding values d1 and d2 and to determine which
of them is “main” and which is “competitive” in every
particular case of shielding.
3.1. UPPER SHIELD MADE FROM IRON (FIG. 1)
Integration over the plane of the plate (by one of
coordinates) in (1) leads to the expression for the dose
rate on the outside of the shield at point A:
( ) ( )[ ] ,,2 dx
x
bxFKbBP
Ha
a
∫
+
⋅= ασγ (4)
where ( )[ ]
( )
αα
α
α debxF
x
o
b
∫= cos, is the integral cosine,
α(x)=arctg(α(x))=arctg(L/2x). Substituting in this
expression the numerical values of constants
b1=Δ1μ1I=17.9 (see Table 2); В1=27.8 (see Table 3);
mCih
cmmremK
⋅
⋅=
2
1 1772γ (see Table 1); b2=18.9; B2=32.5;
mCih
cmmremK
⋅
⋅=
2
2 2772γ ; σ=1.9·10
4
mCi/cm
2
;
a=200 сm;
Н=200 cm and L=400 cm, we obtain after numerical
integration: Р1(Δ1)=5.84 mrem/h, Р2(Δ1)=3.80 mrem/h
and in the sum of two energy lines Е1 and Е2
Р(Δ1)=9.64 mrem/h=16.1 Pd.
So, the shield from iron of a thickness Δ1=45 cm is
insufficient for decrease of the dose rate to the
permissible one. Applying the above-described method
of “competitive” lines and changing in Eq. (4) Р by Pd,
we obtain the equations for determination of dk and dm:
( )[ ] dx
x
bxFbB
=⋅ ∫−
400
200
1
9 ,109,8 α
and
( ) ( )[ ]dx
x
bxFbB ∫=⋅ −
400
200
2
9107,5 α
, (5)
the solutions of which are b1=20.4 or d1=51.3 cm
(B1(20.4)=32.9); b2=21.0 or d2=50.0 cm (at
B2(21.0)=37.5). The “main” line is E1 and dг=51,3 cm,
the “competitive” line is E2 and dk=50.0 cm. Thus, in the
absence of a shield the dose rate at point A is:
dx
x
Larctg
x
KP
Ha
a 2
120 ∫
+
= δγ , (6)
or P01=2.63·107 mrem/h, from where К1=Р01/Р=4.38·107;
Δ1/2(1)=d1ln2/lnK1=2.0 сm;
P02=4.12·107 mrem/h, from where К2=Р02/Р=6.87·107;
Δ1/2(2)=d2ln2/lnK2=1.9 cm. It means that Δ1/2=2.0 cm.
As dm–dk=1.3 cm < Δ1/2=2.0 cm, then, according to
Eq. (3b), d=dk+Δ1/2, i.e. d=52.1 cm.
At d=52.1; b1=20.7; B1=33.6; b2=21.8; B2=39.5, by
Eq. (4) we find: P1(d)=0,41 mrem/h; P2(d)=0,24 mrem/h;
P(d)=0.65 mrem/h.
3.2. UPPER SHIELD FROM REINFORCED
CONCRETE (FIG. 2)
In this case in Eq (4) we should change the
constants: b1=Δμ1=27.3; B1=55.2; b2=Δμ2=28.65;
B2=67.2; a=450. After numerical integration we obtain:
P1(Δ)=4.0·104 mrem/h; P2(Δ)=2.0·104 mrem/h, and the
summary dose rate from two lines E1 and E2: P=6.0·10-
4 mrem/h=103 Рd.
To determine a required thickness d we solve two
equations Eq. (5) (with a=450 cm and a+Н=650 cm)
relatively to b, from which we obtain: b1=19.5;
d1=107 cm (at B1(19.5) =34.8) and b2=20.4; d2=107 cm
(at B2(20.4)=41.6), i.e. dm=dk=107 cm. In this case in the
absence of the shield the dose rate at point A is
determined by Eq. (6):
P01=8.1·106 mrem/h, from where К1=1.35·107 and
Δ1/2(1)=4,5 cm;
P02=1.27·107 mrem/h, from where К2=2.11·107 and
Δ1/2(2)=4.4 cm, i.e. Δ1/2=4.5 cm.
Then according to Eq. (3а): d=dm+Δ1/2 or d=111.5 cm.
At d=111.5 cm; b1=20.3; B1(20.3)=36.8; b2=21.3;
B2(21,3)=44.2, by Eq. (4) we find: P1(d)=0,37 mrem/h;
P2(d)=0.25 mrem/h, i.e. P(d)=0.62 mrem/h.
3.3. LATERAL FACE SHIELD FROM
REINFORCED CONCRETE (FIG. 3)
The dose rate on the outsideside of the shield at
point A is determined by the equation:
( ) ( )[ ] ( )[ ]
+⋅= ∫ ∫
+ ++
++
La
a
LLa
LLa
dx
x
bxFdx
x
bxFKbBР
1
1
2 ,,2 αασγ ,
(7)
where α(x)=arctg(H/2x), and the radial parameters are
the same as in section 3.2. After numerical integration
we obtain P1(Δ)=5.8·10-4 mrem/h and P2(Δ)=2.9·104 mrem/h,
and the total dose rate created by the energy gamma-
lines E1 and E2 is:
75
75
( ) дPhmremP 34 105,1107,8 −− ⋅=⋅=∆ .
To determine the required thickness d we have two
equations relatively to b:
( ) ( )[ ] ( )[ ]
+⋅=⋅ ∫ ∫−
850
450
1550
1150
1
9 ,,109,8 dx
x
bxFdx
x
bxFbB αα
,
( ) ( )[ ] ( )[ ]
+⋅=⋅ ∫ ∫−
850
450
1550
1150
2
9 ,,107,5 dx
x
bxFdx
x
bxFbB αα
, (8)
from which we obtain: b1=20.0 or d1=110 cm
(B1(20.0)=36.0) and b2=20.6 or d2=108 cm
(B2(20.6)=42.1), i.e. the “main” line is Е1 with
dm=110 cm, and the “competitive” one is Е2 with
dk=108 cm. In the absence of the shield the rate dose at
point A is:
+⋅= ∫ ∫
+ ++
+
L LL
L
dx
x
Harctg
x
dx
x
Harctg
x
KР
α
α
α
α
γ σ
12
0 2
1
2
12 , (9)
or Р01=7.4·106 mrem/h, from where К1=1,23·107 and
Δ1/2(1)=4.7 cm; Р02=1,16·107 mrem/h, from where
К2=1,93·107 and Δ1/2(2)=4.5 cm, i.e. Δ1/2=4.7 cm.
According to (3b), d=dk+Δ1/2 or d=112.7 cm. In this
case at d=112.7 cm; b1=20.5; B1(20.5)=37.3; b2=21.5;
B2(21.5)=44.8 by Eq. (7) we find: P1(d)=0.32 mrem/h
and P2(d)=0.22 mrem/h, i.e. P(d)=0.54 mrem/h.
3.4. LATERAL FRONTAL SHIELD MADE FROM
REINFORCED CONCRETE (FIG. 4)
The dose rate behind the shield at point A is
determined by the equation:
( ) ( )
−
+−⋅= ∫
LHarctg
o
d
a
LbEbEKbBP α
α
πσγ 22
2
11 cos4
1
2
4
+− ∫
2
22
2
1 sin4
1
π
α
α
L
Harctg
d
a
HbE , (10)
where a=325 cm; ( ) dtt
LbE
b
t
∫
∞
−
=1 is the exponential
integral function, and the radiation parameters are the
same as in sections 3.2 and 3.3. After numerical
integration we obtain: P1(Δ)=5.1·10-4 mrem/h;
P2(Δ)=2.5·10-4 mrem/h, and the total dose rate from the
energy lines Е1 and Е2: P(Δ)=7.6·104 mrem/h= 1.3·10-
3Pd. For the numerical integration we used the
approximations: ( ) bLbF −= αα , at small α;
( )
b
LbFbF
b−
=
≈ 2,1,
2
, πα at large α; ( ) ( )
+
+
+
=
−
21 1
11
1 bb
LbE
b
at
b>10. These approximations overvalued the calculated
dose rates not more than by 15% and practically had no
effect on the calculated thicknesses of the shield. To
determine a required thickness α of the shield we have
two equations relatively to b:
( ) ( )
−
+−⋅=⋅ ∫−
46,0
0
2111
9
cos
38,01
2
104,4 α
α
π dbEbEbB
+− ∫
2
46,0
21 sin
095,01
π
α
α
dbE and
( ) ( )
−
+−⋅=⋅ ∫−
46,0
0
2111
9
cos
38,01
2
108,2 α
α
π dbEbEbB
+− ∫
2
46,0
21 sin
095,01
π
α
α
dbE , (11)
from which we obtain: b1=20.2 or d1=111.0 cm (at
B1(20.2)=36.5); b2=20.7 or d2=108.4 cm (at
B2(20.7)=42.5).
It means, that the “main” line is Е1 with dm=111.0 cm
and the “competitive” one is Е1 with dk=108.4 cm. In the
absence of the shield the dose rate at point A is:
( )
( )∫
+
+
=
L
H
d
L
a
L
a
arctg
KP
0
22
22
0
2
2
1
4 α
α
α
σγ
, (12)
or Р01=2,0·107 mrem/h, from where K1=3.3·107 and
Δ1/2(1)=4.4 cm;
Р02=3,1·107 mrem/h, from where K2=5,2·107 and
Δ1/2(2)=4.2 cm, ie. Δ1/2=4.4 cm.
According to Eq. (3b) d=dk+Δ1/2 or d=112.8 cm.
At d=112.8 cm; b1=20.5; B1(20.5)=37.3; b2=21.5;
B2(21,5)=44.8 by Eq. (10) we find: P1(d)=0.40 mrem/h;
P2(d)=0.26 mrem/h, i.e. P(d)=0.66 mrem/h.
It is easy to see that with the required thicknesses d,
calculated by the above method, the total dose rate on
the outside of the shield P is defined by two energy
lines E1 and E2 differs from the permissible dose rate Pd:
P=η∙Pd, where just η determines the error of the method
of “competitive” lines related with the approximations
Eq. (3a, b, c).
It is possible to avoid this error, changing the
required thickness d by some correcting value δ that
leads to the equality P(d+δ)=Pd. It is easy to show that
δ is related with the layer of half-attenuation Δ1/2 by the
relationship δ=Δ1/2∙lnη/ln2.
In our calculations for four variants of the shield
(values of η equal to 1.083; 1.033; 0.9; 1.1) the
corresponding values of the correcting thickness: δ
=+0.2; +0.2; -0.7; +0.6 cm are determined.
Below in Table 4 presented are the main results of
the above-described calculations: required thickness of
the radiation shield d, dose rate on the outside of the
shield Р1 and Р2, defined by the energy gamma-lines Е1
and Е2, their sum in the units of Рd, layer of half-
attenuation Δ1/2 and correcting thickness δ.
Table 4. Main results of calculations
Type and material of a shield d, cm
h
mremР ,1 h
mremР ,2 P/Pd Δ1/2, cm δ, cm
Upper, iron 52.1 0.41 0.24 1.083 2.0 +0.2
Upper, reinforced concrete 111.5 0.37 0.25 1.033 4.4 +0.2
Lateral face, reinforced concrete 112.7 0.32 0.22 0.9 4.7 -0.7
Frontal, concrete 112.8 0.40 0.26 1.1 4.4 +0.6
76
CONCLUSIONS
The paper presented the method offered for
calculation of radiation parameters necessary for
designing a shield from unconventional materials. For
solution of this problem one can have very restricted
quantity of initial data - only the density and weight
composition of radiation shielding material. Operating
with these and known literature data, using the
interpolation method it is possible to obtain all the
parameters necessary for carrying out of the calculation.
It should be noted, that during execution of the work
we used the normative documents: Radiation Safety
Standards of Ukraine (НРБУ-97) and Main Sanitary
Rules of Radiation Protection of Ukraine (ОСПУ-
2000). The calculation results show that the use of iron
ore and concrete, as a photon radiation shielding
material, is of great practical significance due to the
availability of material components, possibility to vary
the percentage composition of these components, and
possibility to decrease the shield overall dimensions as
compared to conventional concrete.
The work is fulfilled under the support of STCU
Project №1801.
REFERENCES
1. A.V. Mazilov, B.N. Razsukovanyj, V.V. Kolo-
senko et al. Radiation shield design for the
gamma-irradiation source of europium with the
activity of 6.106 Ki: Preprint KIPT 2003-1,
Kharkov, 2003, p. 11 (in Russian).
2. L.R. Kimel’, V.P. Mashkovich. Ionizing
Radiation Protection Guide. M., Atomizdat,
1972 (in Russian).
3. V.P. Mashkovich, A.V. Kudryavtseva. Ionizing
Radiation Protection Guide. 4-d issue, M.:
“Energoatomizdat”, 1995 (in Russian).
4. V.F. Kozlov. Radiation Protection Guide. M.:
“Atomizdat”, 1977 (in Russian).
5. Main Sanitary Rules of Radiation Protection of
Ukraine. Kiev, 2001
6. Radiation Safety Standards of Ukraine. Kiev,
1997.
7. Ionizing Radiation Protection. Ed. N.G. Gusev.
M.: “Atomizdat”, 1969, v. 1; 1973, v. 2 (in
Russian).
РАДИАЦИОННАЯ ЗАЩИТА УСТАНОВКИ СТЕРИЛИЗАЦИИ
НА БАЗЕ ГАММА-ИЗЛУЧАЮЩИХ ИЗОТОПОВ ЕВРОПИЯ
Б.Н. Разсукованный, А.А. Мазилов, А.В. Мазилов
Представлен способ расчёта радиационной защиты от источника гамма-излучения, включающего в себя
изотопы европий-152 и европий-154 активностью 1.5 МКи каждый. В качестве материала защиты
использованы железо, бетон и гомогенная смесь железной руды и бетона. Показан способ вычисления
радиационных параметров, необходимых для выполнения расчёта защиты из нетрадиционных материалов.
РАДІАЦІЙНИЙ ЗАХИСТ УСТАНОВКИ СТЕРИЛІЗАЦІЇ
НА БАЗІ ГАММА-ВИПРОМІНЮЮЧИХ ІЗОТОПІВ ЄВРОПІЮ
Б.М. Разсукованний, О.О. Мазілов, О.В. Мазілов
Представлено спосіб розрахунку радіаційного захисту від джерела гамма-випромінювання, що включає в
себе ізотопи європій-152 і європій-154 активністю 1.5 МКи кожний. Як матеріал захисту використано залізо,
бетон і гомогенна суміш залізної руди і бетону. Показано спосіб обчислення радіаційних параметрів,
необхідних для виконання розрахунку захисту з нетрадиційних матеріалів.
77
77
RADIATION SHIELDING OF THE STERILIZATION INSTALLATION BASED ON GAMMA-RADIATING EUROPIUM ISITOPES
INTRODUCTION
1. RADIATION SOURCE AND SHIELD GEOMETRY
2. RADIATION PARAMETERS
3. DOSE RATE ON THE OUTSIDE OF THE SHIELD DESIGNED
3.1. UPPER SHIELD MADE FROM IRON (FIG. 1)
3.2. UPPER SHIELD FROM REINFORCED CONCRETE (FIG. 2)
3.3. LATERAL FACE SHIELD FROM REINFORCED CONCRETE (FIG. 3)
3.4. LATERAL FRONTAL SHIELD MADE FROM REINFORCED CONCRETE (FIG. 4)
CONCLUSIONS
REFERENCES
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