ORIG. RUSSIAN: DESCRIPTION OF NEUTRON ATTENUATION BY BIOLOGICAL SHIELD WITH THE AID OF MULTIGROUP MODEL TO DIFFUSION APPRO.

• Document Type: CREST
• Collection: General CIA Records
• Document Number (FOIA) /ESDN (CREST): CIA-RDP88-00904R000100110043-2
• Release Decision: RIPPUB
• Original Classification: U
• Document Page Count: 20
• Document Creation Date: December 22, 2016
• Document Release Date: August 26, 2009
• Sequence Number: 43
• Publication Date: May 1, 1964
• Content Type: STUDY

 Approved For Release 2009/08/26: CIA-RDP88-00904R000100110043-2
Third United Nations
International Conference
on the Peaceful Uses
of Atomic Energy
Confidential until official release during Conference
A/CON?. 28/1'/721
BYELORUSSIAN sSR
Mae' 1964
Originali RUSSIAN
DESCRIPTION OF NEUTRON ATTENUATION BY BIOLOGICAL SHIELD WITH
TI AID OP M ULTIGROU1' MODEL TO DIFFUSION APPROXIMATION
by V.A.Naumov,
IIeat and Mass Transfer Institute ,the B.S.S.R.Aoademy of
Sciences, Minek,B.S.3R.,U.S.S.R.
INTRODUCTION
itecently,in some countries a large number of works is carried
out in which nuclear reactors are used as power source in both great
stationary power plants and transport units.Reaotors of ouch plants
are powerful radiation sources because of high thermal stress in
their cores, To attenuate the radiation to the level which is
safe for the human health,the thickness of a biological shield
may be of several meters and its weight may reach some hundreds
of tons.The main demand of the reactor radiation shield,for examp-
le,of a transport plant,is threferore that for its minimum weight
and size ,and the design of some plants with atomic engines depends
completely on the solution of that problem.The experience in des-
igning of great stationary atomic power plants has revealed the im-
portance of shielding since co-csts of a plant depend essentially
on the shield weight.Designing of a nuclear reactor radiation
shield of moderate weights and sizes is extremely difficult,and
it may be successfully fulfilled only when a designer has suffici-
ently reliable and simple calculation methods for reactor-radiat-
ion attenuation.
In the present work,the author attempts to extend. multigroup
methods of the diffusion theory,used for calculation of physical
effects in the reactor core,to calculation of neutron-flux atten-
uation by a multilayer biological shield and to prove their ap-
plicability to metal-water shields.The applicability of the pre-
sent method to calculation of thermal and biological shield is
shown by way of the analysis of predicted and experimental data
on the neutron-flux distribution in biological shields of operat-
ing reactors of the research type-IRT (U.S.S.R.) and the power
type -APPR (USA).
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METHOD
Main assumptions and eguations.The oimpliect form of neutron-
flux equations may be found by using the diffusion approximation
of the kinetic equation which is widely adopted in nuclear-plant
designing. Several workers have applied the diffusion approximati-
on to the development of calculation method of neutron flux also
[lJ, but the analysis involving assumptions of the diffusion theo-
ry was,as a rule,restrioted to slowing-down and thermal neutrons
solely.Moreover,fast neutron attenuation was prescribed by a cer-
tain semi-theoretical method.
In the present work the possibility is shown to describe the
behaviour of both thermal and slowing-down as well as fast neutron
in the framework of the diffusion theory.The solution is based on
a number of peculiarities of the neutron-flux attenuation mechan-
ism in a water-metal shield.These are:
(a) Fast neutron are essentially attenuated by inelastic
collision with heavy nuclei (Fe,Pb).Inelastic scattering may be
considered isotropic to the first approximation.
(b) Fast neutrons of high energy of the order of 4-6 Mev are
very probable to excite the first levels of the medium nuclei (Fe,
Ni,Cr etc.) with a relatively small energy loss.This mechanism
of neutron interaction is similar to elastic scattering.
(o) Though extremely anisotropic on all nuclei at high neut-
ron energies elastic scattering is inessential for the attenua-
tion mechanism and reactions of fast neutron 'ibsorbtion seem hard-
ly possible.
(d) In the range of energies below inelastic scattering thre-
shold for the nuclei of Fe,Pb, elastic scattering, isotropic or
slightly anisotropic on all nuclei (except hydrogen) is the main
attenuation mechanism.
The above factors provide promises for application of the
spherical harmonic method to low approximations to calculation
of attenuation of fast (and especially slowing-down) neutrons
when angular neutron distribution is characterized by a small
number of series terms with respect to spherical functions,in par-
ticular in the diffusion approximation, by two terms.In addition
because of rough representation of angular neutron distribution
passing long distances inside hydrogen-containing shield,it should
be expected that this method will cause worsening of the accuracy
-2-
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with the cfictanoo from the source.
A biological shield may be considered to a first appro-
ximation to consist of a number of successive uniform media,Let
us consider such a medium,assuming that:
1.The medium absorbs and scatters neutrons.
2.Inelestio scattering is isotropic.
3.According to Weiskopf's statistical theory,neutron spect-
rum inelestioally scattered on heavy nuclei (Pb,U-235,U-238)
has the form of Maxwellian distribution.The inelastic scattering
law for medium nuclei (Al,Pe,Ni,Cr) is obtained by excitation
functions of nuclear levels predicted by means of assumptions of
the optical nuclear, model r21 .
4.Elastio scattering in non-isotropic In the coordinate sys-
tem where the centre of the neutron mass and scattering nucleus
is fixed. Scattering anisotropy is estimated by linear and angu-
lar scattering law.
Then, in accordance with the method,the scalar neutron flux
should satisfy (as the function of space and energy),the fol-
lowing equation for the steady-state case:
-J(El ti 1 (? E)+ Z (El (c E)=1 ~(c' E, E ('f9Wso~E, EJdE'ff ~~z,Elzus (E)w1, , (E, E)c' ' (1)
with boundary condition corresponding to the real geometry.In
equation (1) Wsa , Wino are coefficients of indicatrices expan-
sion of elastic Ws and inelastic Win scattering which are equal
to
Wso (E'EJ. (A. )2 ~4 4 A' 2
' 4AE { 2 A1-0,6 OW' E '(92+
~/%~, (E ~E - 4>i' Wtn = E? exp E
? -
P(_
T~FyIx
and the indicatrix of elastic scattering
WS ? E E~= ~xAE2~~+2 y 06 - ~A= ~
_ E~'
for ?CE